Remove bundled FLINT
This commit is contained in:
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FLINT has been developed since 2007 by a large number of people. Initially
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the library was started by David Harvey and William Hart. Later maintenance
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of the library was taken over solely by William Hart.
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The authors of FLINT to date:
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$\bullet$ William Hart -- integer and polynomial arithmetic, factorisation and
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primality testing, general infrastructure (supported by EPSRC Grant
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EP/G004870/1 and DFG Priority programme SPP1489)
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$\bullet$ Sebastian Pancratz -- polynomial arithmetic over $\Z$, $\Z/n\Z$ and
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$\Q$, $p$-adic and $q$-adic arithmetic, including polynomials and matrices
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(supported by ERC Grant 204083)
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$\bullet$ Andy Novocin -- LLL, polynomial factorisation over $Z$, polynomial
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composition
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$\bullet$ Fredrik Johansson -- matrices, polynomial and power series
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arithmetic, special functions (supported by Austrian Science Fund FWF Grant
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Y464-N18)
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$\bullet$ Tom Bachmann -- \code{C++} expressions template wrapper,
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documentation parser (Google Summer of Code 2013)
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$\bullet$ Mike Hansen -- Finite fields (small and large $\F_q$),
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polynomials/matrices over $\F_q$, Finite fields with Zech logarithm
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representation, Fast factorisation of polynomials over $\F_q$ (supported by
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Macaulay2 developers NSF Grant 1002171)
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$\bullet$ Martin Lee -- Fast factorisation of polynomials over $\Z/n\Z$,
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faster Brent-Kung modular composition
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$\bullet$ David Harvey -- Fast Fourier Transform code, \code{zn_poly} for
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polynomial arithmetic over $\Z/n\Z$, \code{mpz_poly}, profiling and
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graphing code and many other parts of the FLINT library
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$\bullet$ Jan Tuitman -- helped with the $p$-adic interface
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$\bullet$ Jason Papadopoulos -- Block Lanczos code for quadratic sieve and
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multiprecision complex root finding code for polynomials.
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$\bullet$ Gonzalo Tornaria -- Theta function module, Montgomery multiplication
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and significant contributions to the $\Z[x]$ modular multiplication code.
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$\bullet$ Burcin Erocal -- wrote the primary FLINT wrapper in the SAGE system
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(Robert Bradshaw also wrote a preliminary version of this and Martin Albrecht
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and others have also contributed to it.) Burcin also contributed by writing
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grant applications via his Lmonade organisation to Google. (Supported by DFG
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Priority programme SPP1489.)
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$\bullet$ Tom Boothby -- Improved factoring of unsigned longs, detection of
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perfect powers
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$\bullet$ Andres Goens -- $\F_q$ module and polynomials over $\F_q$ (supported
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by DFG Priority program SPP1489)
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$\bullet$ Lina Kulakova -- factorisation for polynomials over $\F_p$ for large
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$p$ (Google Summer of Code 2012)
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$\bullet$ Thomas DuBuisson -- logical ops for fmpz module, patches to the build
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system
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$\bullet$ Jean-Pierre Flori -- many build system patches and Sage integration
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$\bullet$ Frithjof Schulze -- some fmpz functions and various patches
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$\bullet$ Curtis Bright -- numerous patches including 32 bit support
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$\bullet$ Daniel Woodhouse -- Contributed an implementation of multivariate
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multiplication over $\Z/n\Z$ and used this to implement a fast ``saturation''
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algorithm for Laurent polynomials. (Funded by Alessio Corti and Tom Coates
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at Imperial College)
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$\bullet$ Tomasz Lechowski -- Contributed some NTL and Pari polynomial
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profiling code and researched algorithms for polynomials over finite fields.
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(Funded by the Nuffield Foundation)
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$\bullet$ Daniel Scott -- Researched lazy and relaxed algorithms of Joris van
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der Hoeven. (Funded by Warwick University's Undergraduate Research Scholars
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Scheme)
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$\bullet$ David Howden -- Wrote code for computing Bernoulli numbers mod many
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primes, including fast polynomial multiplication over $\Z/p\Z$ specifically for
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the task. (Funded by Warwick University's Undergraduate Research Scholars
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Scheme)
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$\bullet$ Daniel Ellam -- Helped design a module for $p$-adic arithmetic for
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FLINT. (Funded by Warwick University's Undergraduate Research Scholars Scheme)
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$\bullet$ Richard Howell-Peak -- Wrote polynomial factorisation and
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irreducibility testing code for polynomials over $\Z/p\Z$. (Funded by Warwick
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University's Undergraduate Research Scholars Scheme)
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$\bullet$ Peter Shrimpton -- Wrote code for a basic prime sieve,
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Pocklington-Lehmer, Lucas, Fibonacci, BSPW and $n-1$ primality tests and a
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Weiferich prime search. (Funded by the Nuffield Foundation)
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$\bullet$ Patches and bug reports have been made by Michael Abshoff,
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Didier Deshommes, Craig Citro, Timothy Abbot, Carl Witty, Gonzalo Tornaria,
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Jaap Spies, Kiran Kedlaya, William Stein, Kate Minola, Didier Deshommes, Robert
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Bradshaw, Serge Torres, Dan Grayson, Martin Lee, Bob Smith, Antony Vennard,
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Fr\'{e}d\'{e}ric Chyzak, Julien Puydt, Dana Jacobsen, Michael Jacobson Jr.,
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Mike Stillman, Jan Englehardt, Jean-Pierre Flori, Jeroen Demeyer, Shi Bai,
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Qingwen Guan, Frithjof Schulze, Robert Baillie, Oleksandr Motsak, Hans
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Schoenemann, Janko Boehm, Ahmed Soliman, Francois Bissey and others.
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$\bullet$ In addition Michael Abshoff, William Stein and Robert Bradshaw have
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contributed to the build system of FLINT.
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$\bullet$ Michael Abshoff deserves special recognition for his help in
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resolving a number of difficult build issues which came to light as FLINT was
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incorporated into SAGE and for bringing numerous bugs to the attention of the
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FLINT maintainers. Michael regularly checked FLINT for memory leaks and
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corruption, which directly led to numerous issues being identified early!
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He also helped with setting up various pieces of infrastructure for the FLINT
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project.
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$\bullet$ Numerous people have contributed to wrapping FLINT in Sage and
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debugging, including Mike Hansen, Jean-Pierre Flori, Burcin Erocal, Robert
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Bradshaw, Martin Albrecht, Sebastian Pancratz, Fredrik Johansson, Jeroen
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Demeyer and Leif Lionhardy, amongst others.
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Some code (notably \code{longlong.h} and \code{clz_tab.c}) has been used from
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the GMP library, whose main author is Torbjorn Granlund.
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FLINT 2 was a complete rewrite from scratch which began in about 2010.
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@ -1,26 +0,0 @@
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Instructions on intalling flint 2
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---------------------------------
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FLINT 2 follows a standard format for installation:
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./configure
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make
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make check
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make install
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However, this assumes that MPIR and MPFR are already installed on your system in
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/usr/local. If the libraries are not in this location you must specify where
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they are by passing their location to configure. It also assumes you wish to
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install FLINT 2 at the prefix /usr/local. If not you must pass the prefix (the
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directory containing lib and include subdirectories into which FLINT will be
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installed) to configure:
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./configure --with-mpir=/home/user1/mpir-2.1.1/ --with-mpfr=/usr --prefix=/usr
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Note that the FLINT configure system can handle MPIR/MPFR as installed (in lib
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and include dirs) at some location, or as source builds (built from source and
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not installed).
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For further configure and make options, please refer to the FLINT 2
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documentation.
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@ -1,254 +0,0 @@
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# This file is autogenerated by ./configure -- do not edit!
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SHELL=/bin/sh
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FLINT_STATIC=1
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FLINT_SHARED=0
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FLINT_LIB=libflint.so
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EXEEXT=
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PREFIX=/usr
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WANT_NTL=0
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FLINT_CPIMPORT_DIR=/usr/share/flint
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FLINT_CPIMPORT=/usr/share/flint/CPimport.txt
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INCS=-I$(CURDIR) -I/usr/include -I/usr/include
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LIBS=-L$(CURDIR) -L/usr/lib -L/usr/lib -lflint -lpthread -lmpfr -lgmp -lm
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LIBS2=-L$(CURDIR) -L/usr/lib -L/usr/lib -lpthread -lmpfr -lgmp -lm
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CC=gcc
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CXX=g++
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AR=ar
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CFLAGS=-ansi -pedantic -Wall -O2 -funroll-loops -g -mpopcnt -DFLINT_CPIMPORT=\"/usr/share/flint/CPimport.txt\"
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ABI_FLAG=
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PIC_FLAG=-fPIC
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EXTRA_SHARED_FLAGS=
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DLPATH=LD_LIBRARY_PATH
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DLPATH_ADD=$(CURDIR):/usr/lib:/usr/lib
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EXTENSIONS=
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EXTRA_BUILD_DIRS=
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ifdef $(DLPATH)
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$(DLPATH):=$($(DLPATH)):$(DLPATH_ADD)
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else
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$(DLPATH):=$(DLPATH_ADD)
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endif
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QUIET_CC = @echo ' ' CC ' ' $@;
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QUIET_CXX = @echo ' ' CXX ' ' $@;
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QUIET_AR = @echo ' ' AR ' ' $@;
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AT=@
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BUILD_DIRS = ulong_extras long_extras perm fmpz fmpz_vec fmpz_poly \
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fmpq_poly fmpz_mat mpfr_vec mpfr_mat nmod_vec nmod_poly \
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nmod_poly_factor arith mpn_extras nmod_mat fmpq fmpq_mat padic \
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fmpz_poly_q fmpz_poly_mat nmod_poly_mat fmpz_mod_poly \
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fmpz_mod_poly_factor fmpz_factor fmpz_poly_factor fft qsieve \
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double_extras padic_poly padic_mat qadic \
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fq fq_vec fq_mat fq_poly fq_poly_factor\
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fq_nmod fq_nmod_vec fq_nmod_mat fq_nmod_poly fq_nmod_poly_factor \
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fq_zech fq_zech_vec fq_zech_mat fq_zech_poly fq_zech_poly_factor \
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$(EXTRA_BUILD_DIRS)
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TEMPLATE_DIRS = fq_vec_templates fq_mat_templates fq_poly_templates \
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fq_poly_factor_templates
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export
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SOURCES = printf.c fprintf.c sprintf.c scanf.c fscanf.c sscanf.c clz_tab.c memory_manager.c version.c profiler.c thread_support.c
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LIB_SOURCES = $(wildcard $(patsubst %, %/*.c, $(BUILD_DIRS))) $(patsubst %, %/*.c, $(TEMPLATE_DIRS))
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HEADERS = $(patsubst %, %.h, $(BUILD_DIRS)) NTL-interface.h flint.h longlong.h config.h gmpcompat.h fft_tuning.h fmpz-conversions.h profiler.h templates.h $(patsubst %, %.h, $(TEMPLATE_DIRS))
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OBJS = $(patsubst %.c, build/%.o, $(SOURCES))
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LIB_OBJS = $(patsubst %, build/%/*.o, $(BUILD_DIRS))
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LOBJS = $(patsubst %.c, build/%.lo, $(SOURCES))
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LIB_LOBJS = $(patsubst %, build/%/*.lo, $(BUILD_DIRS))
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MOD_LOBJS = $(patsubst %, build/%.lo, $(BUILD_DIRS))
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EXMP_SOURCES = $(wildcard examples/*.c)
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EXMPS = $(patsubst %.c, %, $(EXMP_SOURCES))
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TEST_SOURCES = $(wildcard test/*.c)
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TESTS = $(patsubst %.c, build/%$(EXEEXT), $(TEST_SOURCES))
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PROF_SOURCES = $(wildcard profile/*.c)
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PROFS = $(patsubst %.c, %$(EXEEXT), $(PROF_SOURCES))
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TUNE_SOURCES = $(wildcard tune/*.c)
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TUNE = $(patsubst %.c, %$(EXEEXT), $(TUNE_SOURCES))
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EXT_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/*.c)))
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EXT_TEST_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/test/t-*.c)))
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EXT_TUNE_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/tune/*.c)))
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EXT_PROF_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/profile/p-*.c)))
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EXT_OBJS = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), build/$(dir).lo))
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EXT_HEADERS = $(foreach ext, $(EXTENSIONS), $(wildcard $(ext)/*.h))
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all: library
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quiet: library
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verbose:
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$(MAKE) AT= QUIET_CC= QUIET_CXX= QUIET_AR=
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clean:
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$(AT)$(foreach dir, $(BUILD_DIRS), BUILD_DIR=../build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) clean || exit $$?;)
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$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) clean || exit $$?;))
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rm -rf test_helpers.o profiler.o
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rm -f $(OBJS) $(LOBJS) $(TESTS) $(PROFS) $(EXMPS) $(FLINT_LIB) libflint.a
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rm -rf build
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distclean: clean
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rm -f config.h fft_tuning.h fmpz-conversions.h Makefile fmpz/fmpz.c
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dist:
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git archive --format tar --prefix flint-2.4.2/ flint-2.4 > ../flint-2.4.2.tar; gzip ../flint-2.4.2.tar
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profile: library $(PROF_SOURCES) $(EXT_PROF_SOURCES) build/profiler.o
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mkdir -p build/profile
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ifndef MOD
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$(AT)$(foreach prog, $(PROFS), $(CC) $(ABI_FLAG) -std=c99 -O2 -g $(INCS) $(prog).c build/profiler.o -o build/$(prog) $(LIBS) || exit $$?;)
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$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/profile; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) profile || exit $$?;)
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$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/profile; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) profile || exit $$?;))
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else
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$(AT)$(foreach dir, $(MOD), mkdir -p build/$(dir)/profile; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) profile || exit $$?;)
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endif
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tune: library $(TUNE_SOURCES) $(EXT_TUNE_SOURCES)
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mkdir -p build/tune
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$(AT)$(foreach prog, $(TUNE), $(CC) $(CFLAGS) $(INCS) $(prog).c -o build/$(prog) $(LIBS) || exit $$?;)
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$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/tune; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) tune || exit $$?;)
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$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/tune; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) tune || exit $$?;))
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examples: library $(EXMP_SOURCES)
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mkdir -p build/examples
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$(AT)$(foreach prog, $(EXMPS), $(CC) $(CFLAGS) $(INCS) $(prog).c -o build/$(prog) $(LIBS) || exit $$?;)
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$(FLINT_LIB): $(LOBJS) $(LIB_SOURCES) $(EXT_SOURCES) $(HEADERS) $(EXT_HEADERS) | build build/interfaces
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$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir); BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) shared || exit $$?;))
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$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir); BUILD_DIR=../build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) shared || exit $$?;)
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$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
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$(MAKE) build/interfaces/NTL-interface.lo; \
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$(CXX) $(ABI_FLAG) -shared $(EXTRA_SHARED_FLAGS) build/interfaces/NTL-interface.lo $(LOBJS) $(MOD_LOBJS) $(EXT_OBJS) $(LIBS2) -o $(FLINT_LIB); \
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fi
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$(AT)if [ "$(WANT_NTL)" -ne "1" ]; then \
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$(CC) $(ABI_FLAG) -shared $(EXTRA_SHARED_FLAGS) $(LOBJS) $(MOD_LOBJS) $(EXT_OBJS) $(LIBS2) -o $(FLINT_LIB); \
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fi
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libflint.a: $(OBJS) $(LIB_SOURCES) $(EXT_SOURCES) $(HEADERS) $(EXT_HEADERS) | build build/interfaces
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$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir); BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) static || exit $$?;))
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$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir); BUILD_DIR=../build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) static || exit $$?;)
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$(AT)if [ "$(FLINT_SHARED)" -eq "0" ]; then \
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touch test/t-*.c; \
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$(foreach dir, $(BUILD_DIRS), touch $(dir)/test/t-*.c;) \
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$(foreach ext, $(EXTENSIONS), $(foreach mod, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), touch $(ext)/$(mod)/test/t-*.c;)) \
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fi
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$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
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$(MAKE) build/interfaces/NTL-interface.o; \
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$(AR) rcs libflint.a build/interfaces/NTL-interface.o; \
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fi
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$(QUIET_AR) $(AR) rcs libflint.a $(OBJS);
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$(AT)$(foreach mod, $(BUILD_DIRS), $(AR) rcs libflint.a build/$(mod)/*.o || exit $$?;)
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$(AT)$(foreach ext, $(EXTENSIONS), $(foreach mod, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(AR) rcs libflint.a build/$(mod)/*.o || exit $$?;))
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library:
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$(AT)if [ "$(FLINT_SHARED)" -eq "1" ]; then \
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$(MAKE) shared; \
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fi
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$(AT)if [ "$(FLINT_STATIC)" -eq "1" ]; then \
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$(MAKE) static; \
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fi
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shared: $(FLINT_LIB)
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static: libflint.a
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tests: library test_helpers.o $(TESTS)
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$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) tests || exit $$?;)
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$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) tests || exit $$?;))
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mkdir -p build/interfaces/test
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$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
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$(MAKE) build/interfaces/test/t-NTL-interface; \
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fi
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check: library test_helpers.o
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ifndef MOD
|
||||
$(AT)$(MAKE) $(TESTS)
|
||||
$(AT)$(foreach prog, $(TESTS), $(prog) || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) check || exit $$?;))
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) check || exit $$?;)
|
||||
mkdir -p build/interfaces/test
|
||||
$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
|
||||
$(MAKE) build/interfaces/test/t-NTL-interface; \
|
||||
build/interfaces/test/t-NTL-interface; \
|
||||
fi
|
||||
else
|
||||
$(AT)$(foreach dir, $(MOD), test ! -d $(dir) || mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; test ! -d $(dir) || $(MAKE) -f ../Makefile.subdirs -C $(dir) check || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(AT)$(foreach dir, $(MOD), MOD_DIR=$(dir); export MOD_DIR; test ! -d $(ext)/$(dir) || mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; test ! -d $(ext)/$(dir) || $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) check || exit $$?;))
|
||||
endif
|
||||
|
||||
valgrind: library
|
||||
ifndef MOD
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) valgrind || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) valgrind || exit $$?;))
|
||||
else
|
||||
$(AT)$(foreach dir, $(MOD), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) valgrind || exit $$?;)
|
||||
endif
|
||||
|
||||
install: library
|
||||
mkdir -p $(DESTDIR)$(PREFIX)/lib
|
||||
mkdir -p $(DESTDIR)$(PREFIX)/include/flint
|
||||
$(AT)if [ "$(FLINT_SHARED)" -eq "1" ]; then \
|
||||
cp $(FLINT_LIB) $(DESTDIR)$(PREFIX)/lib; \
|
||||
fi
|
||||
$(AT)if [ "$(FLINT_STATIC)" -eq "1" ]; then \
|
||||
cp libflint.a $(DESTDIR)$(PREFIX)/lib; \
|
||||
fi
|
||||
cp $(HEADERS) $(DESTDIR)$(PREFIX)/include/flint
|
||||
$(AT)if [ ! -z $(EXT_HEADERS) ]; then \
|
||||
cp $(EXT_HEADERS) $(DESTDIR)$(PREFIX)/include/flint; \
|
||||
fi
|
||||
mkdir -p $(DESTDIR)$(FLINT_CPIMPORT_DIR)
|
||||
cp qadic/CPimport.txt $(DESTDIR)$(FLINT_CPIMPORT_DIR)
|
||||
mkdir -p $(DESTDIR)$(PREFIX)/include/flint/flintxx
|
||||
cp flintxx/*.h $(DESTDIR)$(PREFIX)/include/flint/flintxx
|
||||
cp *xx.h $(DESTDIR)$(PREFIX)/include/flint
|
||||
|
||||
build:
|
||||
mkdir -p build
|
||||
|
||||
build/%.lo: %.c $(HEADERS) | build
|
||||
$(QUIET_CC) $(CC) $(PIC_FLAG) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/%.o: %.c $(HEADERS) | build
|
||||
$(QUIET_CC) $(CC) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/test/%$(EXEEXT): test/%.c $(HEADERS) | build/test
|
||||
$(QUIET_CC) $(CC) $(CFLAGS) $(INCS) $< -o $@ $(LIBS)
|
||||
|
||||
build/test:
|
||||
mkdir -p build/test
|
||||
|
||||
build/interfaces:
|
||||
mkdir -p build/interfaces
|
||||
|
||||
build/interfaces/NTL-interface.lo: interfaces/NTL-interface.cpp NTL-interface.h
|
||||
$(QUIET_CXX) $(CXX) $(PIC_FLAG) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/interfaces/NTL-interface.o: interfaces/NTL-interface.cpp NTL-interface.h
|
||||
$(QUIET_CXX) $(CXX) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/interfaces/test/t-NTL-interface$(EXEEXT): interfaces/test/t-NTL-interface.cpp
|
||||
$(QUIET_CXX) $(CXX) $(CFLAGS) $(INCS) $< build/interfaces/NTL-interface.o -o $@ $(LIBS);
|
||||
|
||||
print-%:
|
||||
@echo '$*=$($*)'
|
||||
|
||||
.PHONY: profile library shared static clean examples tune check tests distclean dist install all valgrind
|
||||
|
||||
|
|
@ -1,221 +0,0 @@
|
|||
ifdef $(DLPATH)
|
||||
$(DLPATH):=$($(DLPATH)):$(DLPATH_ADD)
|
||||
else
|
||||
$(DLPATH):=$(DLPATH_ADD)
|
||||
endif
|
||||
|
||||
QUIET_CC = @echo ' ' CC ' ' $@;
|
||||
QUIET_CXX = @echo ' ' CXX ' ' $@;
|
||||
QUIET_AR = @echo ' ' AR ' ' $@;
|
||||
|
||||
AT=@
|
||||
|
||||
BUILD_DIRS = ulong_extras long_extras perm fmpz fmpz_vec fmpz_poly \
|
||||
fmpq_poly fmpz_mat mpfr_vec mpfr_mat nmod_vec nmod_poly \
|
||||
nmod_poly_factor arith mpn_extras nmod_mat fmpq fmpq_mat padic \
|
||||
fmpz_poly_q fmpz_poly_mat nmod_poly_mat fmpz_mod_poly \
|
||||
fmpz_mod_poly_factor fmpz_factor fmpz_poly_factor fft qsieve \
|
||||
double_extras padic_poly padic_mat qadic \
|
||||
fq fq_vec fq_mat fq_poly fq_poly_factor\
|
||||
fq_nmod fq_nmod_vec fq_nmod_mat fq_nmod_poly fq_nmod_poly_factor \
|
||||
fq_zech fq_zech_vec fq_zech_mat fq_zech_poly fq_zech_poly_factor \
|
||||
$(EXTRA_BUILD_DIRS)
|
||||
|
||||
TEMPLATE_DIRS = fq_vec_templates fq_mat_templates fq_poly_templates \
|
||||
fq_poly_factor_templates
|
||||
|
||||
export
|
||||
|
||||
SOURCES = printf.c fprintf.c sprintf.c scanf.c fscanf.c sscanf.c clz_tab.c memory_manager.c version.c profiler.c thread_support.c
|
||||
LIB_SOURCES = $(wildcard $(patsubst %, %/*.c, $(BUILD_DIRS))) $(patsubst %, %/*.c, $(TEMPLATE_DIRS))
|
||||
|
||||
HEADERS = $(patsubst %, %.h, $(BUILD_DIRS)) NTL-interface.h flint.h longlong.h config.h gmpcompat.h fft_tuning.h fmpz-conversions.h profiler.h templates.h $(patsubst %, %.h, $(TEMPLATE_DIRS))
|
||||
|
||||
OBJS = $(patsubst %.c, build/%.o, $(SOURCES))
|
||||
LIB_OBJS = $(patsubst %, build/%/*.o, $(BUILD_DIRS))
|
||||
|
||||
LOBJS = $(patsubst %.c, build/%.lo, $(SOURCES))
|
||||
LIB_LOBJS = $(patsubst %, build/%/*.lo, $(BUILD_DIRS))
|
||||
MOD_LOBJS = $(patsubst %, build/%.lo, $(BUILD_DIRS))
|
||||
|
||||
EXMP_SOURCES = $(wildcard examples/*.c)
|
||||
EXMPS = $(patsubst %.c, %, $(EXMP_SOURCES))
|
||||
|
||||
TEST_SOURCES = $(wildcard test/*.c)
|
||||
TESTS = $(patsubst %.c, build/%$(EXEEXT), $(TEST_SOURCES))
|
||||
|
||||
PROF_SOURCES = $(wildcard profile/*.c)
|
||||
PROFS = $(patsubst %.c, %$(EXEEXT), $(PROF_SOURCES))
|
||||
|
||||
TUNE_SOURCES = $(wildcard tune/*.c)
|
||||
TUNE = $(patsubst %.c, %$(EXEEXT), $(TUNE_SOURCES))
|
||||
|
||||
EXT_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/*.c)))
|
||||
EXT_TEST_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/test/t-*.c)))
|
||||
EXT_TUNE_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/tune/*.c)))
|
||||
EXT_PROF_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/profile/p-*.c)))
|
||||
EXT_OBJS = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), build/$(dir).lo))
|
||||
EXT_HEADERS = $(foreach ext, $(EXTENSIONS), $(wildcard $(ext)/*.h))
|
||||
|
||||
all: library
|
||||
|
||||
quiet: library
|
||||
|
||||
verbose:
|
||||
$(MAKE) AT= QUIET_CC= QUIET_CXX= QUIET_AR=
|
||||
|
||||
clean:
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), BUILD_DIR=../build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) clean || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) clean || exit $$?;))
|
||||
rm -rf test_helpers.o profiler.o
|
||||
rm -f $(OBJS) $(LOBJS) $(TESTS) $(PROFS) $(EXMPS) $(FLINT_LIB) libflint.a
|
||||
rm -rf build
|
||||
|
||||
distclean: clean
|
||||
rm -f config.h fft_tuning.h fmpz-conversions.h Makefile fmpz/fmpz.c
|
||||
|
||||
dist:
|
||||
git archive --format tar --prefix flint-2.4.2/ flint-2.4 > ../flint-2.4.2.tar; gzip ../flint-2.4.2.tar
|
||||
|
||||
profile: library $(PROF_SOURCES) $(EXT_PROF_SOURCES) build/profiler.o
|
||||
mkdir -p build/profile
|
||||
ifndef MOD
|
||||
$(AT)$(foreach prog, $(PROFS), $(CC) $(ABI_FLAG) -std=c99 -O2 -g $(INCS) $(prog).c build/profiler.o -o build/$(prog) $(LIBS) || exit $$?;)
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/profile; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) profile || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/profile; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) profile || exit $$?;))
|
||||
else
|
||||
$(AT)$(foreach dir, $(MOD), mkdir -p build/$(dir)/profile; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) profile || exit $$?;)
|
||||
endif
|
||||
|
||||
tune: library $(TUNE_SOURCES) $(EXT_TUNE_SOURCES)
|
||||
mkdir -p build/tune
|
||||
$(AT)$(foreach prog, $(TUNE), $(CC) $(CFLAGS) $(INCS) $(prog).c -o build/$(prog) $(LIBS) || exit $$?;)
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/tune; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) tune || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/tune; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) tune || exit $$?;))
|
||||
|
||||
examples: library $(EXMP_SOURCES)
|
||||
mkdir -p build/examples
|
||||
$(AT)$(foreach prog, $(EXMPS), $(CC) $(CFLAGS) $(INCS) $(prog).c -o build/$(prog) $(LIBS) || exit $$?;)
|
||||
|
||||
$(FLINT_LIB): $(LOBJS) $(LIB_SOURCES) $(EXT_SOURCES) $(HEADERS) $(EXT_HEADERS) | build build/interfaces
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir); BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) shared || exit $$?;))
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir); BUILD_DIR=../build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) shared || exit $$?;)
|
||||
$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
|
||||
$(MAKE) build/interfaces/NTL-interface.lo; \
|
||||
$(CXX) $(ABI_FLAG) -shared $(EXTRA_SHARED_FLAGS) build/interfaces/NTL-interface.lo $(LOBJS) $(MOD_LOBJS) $(EXT_OBJS) $(LIBS2) -o $(FLINT_LIB); \
|
||||
fi
|
||||
$(AT)if [ "$(WANT_NTL)" -ne "1" ]; then \
|
||||
$(CC) $(ABI_FLAG) -shared $(EXTRA_SHARED_FLAGS) $(LOBJS) $(MOD_LOBJS) $(EXT_OBJS) $(LIBS2) -o $(FLINT_LIB); \
|
||||
fi
|
||||
|
||||
libflint.a: $(OBJS) $(LIB_SOURCES) $(EXT_SOURCES) $(HEADERS) $(EXT_HEADERS) | build build/interfaces
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir); BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) static || exit $$?;))
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir); BUILD_DIR=../build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) static || exit $$?;)
|
||||
$(AT)if [ "$(FLINT_SHARED)" -eq "0" ]; then \
|
||||
touch test/t-*.c; \
|
||||
$(foreach dir, $(BUILD_DIRS), touch $(dir)/test/t-*.c;) \
|
||||
$(foreach ext, $(EXTENSIONS), $(foreach mod, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), touch $(ext)/$(mod)/test/t-*.c;)) \
|
||||
fi
|
||||
$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
|
||||
$(MAKE) build/interfaces/NTL-interface.o; \
|
||||
$(AR) rcs libflint.a build/interfaces/NTL-interface.o; \
|
||||
fi
|
||||
$(QUIET_AR) $(AR) rcs libflint.a $(OBJS);
|
||||
$(AT)$(foreach mod, $(BUILD_DIRS), $(AR) rcs libflint.a build/$(mod)/*.o || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach mod, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(AR) rcs libflint.a build/$(mod)/*.o || exit $$?;))
|
||||
|
||||
library:
|
||||
$(AT)if [ "$(FLINT_SHARED)" -eq "1" ]; then \
|
||||
$(MAKE) shared; \
|
||||
fi
|
||||
$(AT)if [ "$(FLINT_STATIC)" -eq "1" ]; then \
|
||||
$(MAKE) static; \
|
||||
fi
|
||||
|
||||
shared: $(FLINT_LIB)
|
||||
|
||||
static: libflint.a
|
||||
|
||||
tests: library test_helpers.o $(TESTS)
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) tests || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) tests || exit $$?;))
|
||||
mkdir -p build/interfaces/test
|
||||
$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
|
||||
$(MAKE) build/interfaces/test/t-NTL-interface; \
|
||||
fi
|
||||
|
||||
check: library test_helpers.o
|
||||
ifndef MOD
|
||||
$(AT)$(MAKE) $(TESTS)
|
||||
$(AT)$(foreach prog, $(TESTS), $(prog) || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) check || exit $$?;))
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) check || exit $$?;)
|
||||
mkdir -p build/interfaces/test
|
||||
$(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \
|
||||
$(MAKE) build/interfaces/test/t-NTL-interface; \
|
||||
build/interfaces/test/t-NTL-interface; \
|
||||
fi
|
||||
else
|
||||
$(AT)$(foreach dir, $(MOD), test ! -d $(dir) || mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; test ! -d $(dir) || $(MAKE) -f ../Makefile.subdirs -C $(dir) check || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(AT)$(foreach dir, $(MOD), MOD_DIR=$(dir); export MOD_DIR; test ! -d $(ext)/$(dir) || mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; test ! -d $(ext)/$(dir) || $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) check || exit $$?;))
|
||||
endif
|
||||
|
||||
valgrind: library
|
||||
ifndef MOD
|
||||
$(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) valgrind || exit $$?;)
|
||||
$(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) valgrind || exit $$?;))
|
||||
else
|
||||
$(AT)$(foreach dir, $(MOD), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) valgrind || exit $$?;)
|
||||
endif
|
||||
|
||||
install: library
|
||||
mkdir -p $(DESTDIR)$(PREFIX)/lib
|
||||
mkdir -p $(DESTDIR)$(PREFIX)/include/flint
|
||||
$(AT)if [ "$(FLINT_SHARED)" -eq "1" ]; then \
|
||||
cp $(FLINT_LIB) $(DESTDIR)$(PREFIX)/lib; \
|
||||
fi
|
||||
$(AT)if [ "$(FLINT_STATIC)" -eq "1" ]; then \
|
||||
cp libflint.a $(DESTDIR)$(PREFIX)/lib; \
|
||||
fi
|
||||
cp $(HEADERS) $(DESTDIR)$(PREFIX)/include/flint
|
||||
$(AT)if [ ! -z $(EXT_HEADERS) ]; then \
|
||||
cp $(EXT_HEADERS) $(DESTDIR)$(PREFIX)/include/flint; \
|
||||
fi
|
||||
mkdir -p $(DESTDIR)$(FLINT_CPIMPORT_DIR)
|
||||
cp qadic/CPimport.txt $(DESTDIR)$(FLINT_CPIMPORT_DIR)
|
||||
mkdir -p $(DESTDIR)$(PREFIX)/include/flint/flintxx
|
||||
cp flintxx/*.h $(DESTDIR)$(PREFIX)/include/flint/flintxx
|
||||
cp *xx.h $(DESTDIR)$(PREFIX)/include/flint
|
||||
|
||||
build:
|
||||
mkdir -p build
|
||||
|
||||
build/%.lo: %.c $(HEADERS) | build
|
||||
$(QUIET_CC) $(CC) $(PIC_FLAG) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/%.o: %.c $(HEADERS) | build
|
||||
$(QUIET_CC) $(CC) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/test/%$(EXEEXT): test/%.c $(HEADERS) | build/test
|
||||
$(QUIET_CC) $(CC) $(CFLAGS) $(INCS) $< -o $@ $(LIBS)
|
||||
|
||||
build/test:
|
||||
mkdir -p build/test
|
||||
|
||||
build/interfaces:
|
||||
mkdir -p build/interfaces
|
||||
|
||||
build/interfaces/NTL-interface.lo: interfaces/NTL-interface.cpp NTL-interface.h
|
||||
$(QUIET_CXX) $(CXX) $(PIC_FLAG) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/interfaces/NTL-interface.o: interfaces/NTL-interface.cpp NTL-interface.h
|
||||
$(QUIET_CXX) $(CXX) $(CFLAGS) $(INCS) -c $< -o $@;
|
||||
|
||||
build/interfaces/test/t-NTL-interface$(EXEEXT): interfaces/test/t-NTL-interface.cpp
|
||||
$(QUIET_CXX) $(CXX) $(CFLAGS) $(INCS) $< build/interfaces/NTL-interface.o -o $@ $(LIBS);
|
||||
|
||||
print-%:
|
||||
@echo '$*=$($*)'
|
||||
|
||||
.PHONY: profile library shared static clean examples tune check tests distclean dist install all valgrind
|
||||
|
||||
|
|
@ -1,89 +0,0 @@
|
|||
QUIET_CC = @echo ' ' CC ' ' $@;
|
||||
|
||||
AT=@
|
||||
|
||||
SOURCES = $(wildcard *.c)
|
||||
|
||||
HEADERS = $(wildcard ../*.h)
|
||||
TEST_HEADERS = $(wildcard *.h)
|
||||
|
||||
OBJS = $(patsubst %.c, $(BUILD_DIR)/$(MOD_DIR)_%.o, $(SOURCES))
|
||||
|
||||
LOBJS = $(patsubst %.c, $(BUILD_DIR)/%.lo, $(SOURCES))
|
||||
MOD_LOBJ = $(BUILD_DIR)/../$(MOD_DIR).lo
|
||||
|
||||
TEST_SOURCES = $(wildcard test/*.c)
|
||||
TESTXX_SOURCES = $(wildcard test/*.cpp)
|
||||
|
||||
PROF_SOURCES = $(wildcard profile/*.c)
|
||||
|
||||
TUNE_SOURCES = $(wildcard tune/*.c)
|
||||
|
||||
TESTS = $(patsubst %.c, $(BUILD_DIR)/%$(EXEEXT), $(TEST_SOURCES)) \
|
||||
$(patsubst %.cpp, $(BUILD_DIR)/%$(EXEEXT), $(TESTXX_SOURCES))
|
||||
|
||||
TESTS_RUN = $(patsubst %, %_RUN, $(TESTS))
|
||||
|
||||
VALGRIND_RUN = $(patsubst %, %_VALGRIND_RUN, $(TESTS))
|
||||
|
||||
PROFS = $(patsubst %.c, $(BUILD_DIR)/%$(EXEEXT), $(PROF_SOURCES))
|
||||
|
||||
TUNE = $(patsubst %.c, %$(EXEEXT), $(TUNE_SOURCES))
|
||||
|
||||
all: shared static
|
||||
|
||||
shared: $(MOD_LOBJ)
|
||||
|
||||
static: $(OBJS)
|
||||
|
||||
profile: $(PROFS)
|
||||
|
||||
-include $(patsubst %, %.d, $(PROFS))
|
||||
|
||||
$(BUILD_DIR)/profile/%$(EXEEXT): profile/%.c $(BUILD_DIR)/../profiler.o
|
||||
$(QUIET_CC) $(CC) $(ABI_FLAG) -O2 -std=c99 -g $(INCS) $< ../build/profiler.o -o $@ $(LIBS) -MMD -MP -MF $@.d -MT "$@" -MT "$@.d"
|
||||
|
||||
tune: $(TUNE_SOURCES) $(HEADERS)
|
||||
$(AT)$(foreach prog, $(TUNE), $(CC) $(CFLAGS) $(INCS) $(prog).c -o $(BUILD_DIR)/$(prog) $(LIBS) || exit $$?;)
|
||||
|
||||
-include $(OBJS:.o=.d)
|
||||
|
||||
$(BUILD_DIR)/$(MOD_DIR)_%.o: %.c
|
||||
$(QUIET_CC) $(CC) $(CFLAGS) $(INCS) -c $< -o $@ -MMD -MP -MF "$(BUILD_DIR)/$(MOD_DIR)_$*.d" -MT "$(BUILD_DIR)/$(MOD_DIR)_$*.d" -MT "$@"
|
||||
|
||||
$(MOD_LOBJ): $(LOBJS)
|
||||
$(QUIET_CC) $(CC) $(ABI_FLAG) -Wl,-r $^ -o $@ -nostdlib
|
||||
|
||||
-include $(LOBJS:.lo=.d)
|
||||
|
||||
$(BUILD_DIR)/%.lo: %.c
|
||||
$(QUIET_CC) $(CC) $(PIC_FLAG) $(CFLAGS) $(INCS) -c $< -o $@ -MMD -MP -MF "$(BUILD_DIR)/$*.d" -MT "$(BUILD_DIR)/$*.d" -MT "$@"
|
||||
|
||||
clean:
|
||||
rm -rf $(BUILD_DIR) $(MOD_LOBJ)
|
||||
|
||||
tests: $(TESTS)
|
||||
|
||||
check: tests $(TESTS_RUN)
|
||||
|
||||
valgrind: tests $(VALGRIND_RUN)
|
||||
|
||||
-include $(patsubst %, %.d, $(TESTS))
|
||||
|
||||
ifeq ($(FLINT_SHARED), 0)
|
||||
$(BUILD_DIR)/test/%$(EXEEXT): $(BUILD_DIR)/../../libflint.a
|
||||
endif
|
||||
|
||||
$(BUILD_DIR)/test/%$(EXEEXT): test/%.c $(BUILD_DIR)/../../test_helpers.o
|
||||
$(QUIET_CC) $(CC) $(CFLAGS) $(INCS) $< $(BUILD_DIR)/../../test_helpers.o -o $@ $(LIBS) -MMD -MP -MF $@.d -MT "$@" -MT "$@.d"
|
||||
|
||||
$(BUILD_DIR)/test/%$(EXEEXT): test/%.cpp $(BUILD_DIR)/../../test_helpers.o
|
||||
$(QUIET_CC) $(CXX) $(CFLAGS) $(INCS) $< $(BUILD_DIR)/../../test_helpers.o -o $@ $(LIBS) -MMD -MP -MF $@.d -MT "$@" -MT "$@.d"
|
||||
|
||||
%_RUN: %
|
||||
@$<
|
||||
|
||||
%_VALGRIND_RUN: %
|
||||
valgrind --track-origins=yes --leak-check=full --show-reachable=yes --log-file="$*.valgrind" $<
|
||||
|
||||
.PHONY: profile tune clean check tests all shared static valgrind %_RUN %_VALGRIND_RUN
|
||||
File diff suppressed because it is too large
Load Diff
|
|
@ -1,172 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
NTL-interface.h: Header file for NTL-interface.cpp
|
||||
|
||||
Copyright (C) 2007 William Hart
|
||||
Copyright (C) 2011 Sebastian Pancratz
|
||||
Copyright (C) 2013 Mike Hansen
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#ifndef FLINT_NTL_INT_H
|
||||
#define FLINT_NTL_INT_H
|
||||
|
||||
#include <NTL/ZZ.h>
|
||||
#include <NTL/ZZX.h>
|
||||
#include <NTL/ZZ_p.h>
|
||||
#include <NTL/ZZ_pX.h>
|
||||
#include <NTL/ZZ_pXFactoring.h>
|
||||
#include <NTL/ZZ_pE.h>
|
||||
#include <NTL/ZZ_pEX.h>
|
||||
#include <NTL/lzz_p.h>
|
||||
#include <NTL/lzz_pX.h>
|
||||
#include <NTL/lzz_pXFactoring.h>
|
||||
#include <NTL/lzz_pE.h>
|
||||
#include <NTL/lzz_pEX.h>
|
||||
#include <NTL/vec_ZZ.h>
|
||||
|
||||
#include "flint.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_poly.h"
|
||||
#include "fmpz_mod_poly.h"
|
||||
#include "fq.h"
|
||||
#include "fq_poly.h"
|
||||
|
||||
NTL_CLIENT
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
/*
|
||||
Converts an NTL ZZ to an fmpz_t.
|
||||
|
||||
Assumes the fmpz_t has already been allocated to have sufficient space.
|
||||
*/
|
||||
void fmpz_set_ZZ(fmpz_t rop, const ZZ& op);
|
||||
|
||||
/*
|
||||
Converts an fmpz_t to an NTL ZZ. Allocation is automatically handled.
|
||||
*/
|
||||
void fmpz_get_ZZ(ZZ& rop, const fmpz_t op);
|
||||
|
||||
|
||||
/*
|
||||
Converts an NTL ZZ_p to an fmpz_t.
|
||||
|
||||
Assumes the fmpz_t has already been allocated to have sufficient space.
|
||||
*/
|
||||
void fmpz_set_ZZ_p(fmpz_t rop, const ZZ_p& op);
|
||||
|
||||
/*
|
||||
Converts an fmpz_t to an NTL ZZ_p. Allocation is automatically handled.
|
||||
*/
|
||||
void fmpz_get_ZZ_p(ZZ_p& rop, const fmpz_t op);
|
||||
|
||||
/*
|
||||
Converts an NTL zz_p to an fmpz_t.
|
||||
*/
|
||||
void fmpz_set_zz_p(fmpz_t rop, const zz_p& op);
|
||||
|
||||
/*
|
||||
Converts an fmpz_t to an NTL zz_p.
|
||||
*/
|
||||
void fmpz_get_zz_p(zz_p& rop, const fmpz_t op);
|
||||
|
||||
/*
|
||||
Converts an fmpz_poly_t to an NTL ZZX.
|
||||
*/
|
||||
void fmpz_poly_get_ZZX(ZZX& rop, const fmpz_poly_t op);
|
||||
|
||||
/*
|
||||
Converts an NTL ZZX to an fmpz_poly_t.
|
||||
*/
|
||||
void fmpz_poly_set_ZZX(fmpz_poly_t rop, const ZZX& op);
|
||||
|
||||
/*
|
||||
Converts an fmpz_mod_poly_t to an NTL ZZ_pX.
|
||||
*/
|
||||
void fmpz_mod_poly_get_ZZ_pX(ZZ_pX& rop, const fmpz_mod_poly_t op);
|
||||
|
||||
/*
|
||||
Converts an NTL ZZ_pX to an fmpz_poly_t.
|
||||
*/
|
||||
void fmpz_mod_poly_set_ZZ_pX(fmpz_mod_poly_t rop, const ZZ_pX& op);
|
||||
|
||||
/*
|
||||
Converts an fq_t to an NTL ZZ_pE.
|
||||
*/
|
||||
void fq_get_ZZ_pE(ZZ_pE& rop, const fq_t op, const fq_ctx_t ctx);
|
||||
|
||||
/*
|
||||
Converts an NTL ZZ_pE to an fq_t.
|
||||
*/
|
||||
void fq_set_ZZ_pE(fq_t rop, const ZZ_pE& op, const fq_ctx_t ctx);
|
||||
|
||||
|
||||
/*
|
||||
Converts an fq_poly_t to an NTL ZZ_pEX.
|
||||
*/
|
||||
void fq_poly_get_ZZ_pEX(ZZ_pEX& rop, const fq_poly_t op, const fq_ctx_t ctx);
|
||||
|
||||
/*
|
||||
Converts an NTL ZZ_pEX to an fq_poly_t.
|
||||
*/
|
||||
void fq_poly_set_ZZ_pEX(fq_poly_t rop, const ZZ_pEX& op, const fq_ctx_t ctx);
|
||||
|
||||
/*
|
||||
Converts an fmpz_mod_poly_t to an NTL zz_pX.
|
||||
*/
|
||||
void fmpz_mod_poly_get_zz_pX(zz_pX& rop, const fmpz_mod_poly_t op);
|
||||
|
||||
/*
|
||||
Converts an NTL zz_pX to an fmpz_poly_t.
|
||||
*/
|
||||
void fmpz_mod_poly_set_zz_pX(fmpz_mod_poly_t rop, const zz_pX& op);
|
||||
|
||||
/*
|
||||
Converts an fq_t to an NTL zz_pE.
|
||||
*/
|
||||
void fq_get_zz_pE(zz_pE& rop, const fq_t op, const fq_ctx_t ctx);
|
||||
|
||||
/*
|
||||
Converts an NTL zz_pE to an fq_t.
|
||||
*/
|
||||
void fq_set_zz_pE(fq_t rop, const zz_pE& op, const fq_ctx_t ctx);
|
||||
|
||||
|
||||
/*
|
||||
Converts an fq_poly_t to an NTL zz_pEX.
|
||||
*/
|
||||
void fq_poly_get_zz_pEX(zz_pEX& rop, const fq_poly_t op, const fq_ctx_t ctx);
|
||||
|
||||
/*
|
||||
Converts an NTL zz_pEX to an fq_poly_t.
|
||||
*/
|
||||
void fq_poly_set_zz_pEX(fq_poly_t rop, const zz_pEX& op, const fq_ctx_t ctx);
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
#endif
|
||||
|
||||
|
|
@ -1,15 +0,0 @@
|
|||
FLINT 2
|
||||
=======
|
||||
|
||||
FLINT (Fast Library for Number Theory) is a C library in support of computations
|
||||
in number theory. It's also a research project into algorithms in number theory.
|
||||
|
||||
FLINT 2 is a complete rewrite of the FLINT library from scratch. It includes
|
||||
much cleaner code and in many cases much faster algorithms and implementations.
|
||||
|
||||
At this stage FLINT consists mainly of fast integer and polynomial
|
||||
arithmetic and linear algebra. In the future it is planned that FLINT will
|
||||
contain algorithms for algebraic number theory and other number theoretic
|
||||
functionality.
|
||||
|
||||
William Hart -- 16 Jan 2011.
|
||||
|
|
@ -1,242 +0,0 @@
|
|||
/*============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
===============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010-2012 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#ifndef ARITH_H
|
||||
#define ARITH_H
|
||||
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpz_poly.h"
|
||||
#include "fmpq_poly.h"
|
||||
#include "fmpq.h"
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C" {
|
||||
#endif
|
||||
|
||||
/* MPFR extras ***************************************************************/
|
||||
|
||||
void mpfr_zeta_inv_euler_product(mpfr_t res, ulong s, int char_4);
|
||||
void mpfr_pi_chudnovsky(mpfr_t res, mpfr_rnd_t rnd);
|
||||
|
||||
/* Various arithmetic functions **********************************************/
|
||||
|
||||
void arith_primorial(fmpz_t res, slong n);
|
||||
|
||||
void _arith_harmonic_number(fmpz_t num, fmpz_t den, slong n);
|
||||
void arith_harmonic_number(fmpq_t x, slong n);
|
||||
|
||||
void arith_ramanujan_tau(fmpz_t res, const fmpz_t n);
|
||||
void arith_ramanujan_tau_series(fmpz_poly_t res, slong n);
|
||||
|
||||
void arith_divisors(fmpz_poly_t res, const fmpz_t n);
|
||||
void arith_divisor_sigma(fmpz_t res, const fmpz_t n, ulong k);
|
||||
|
||||
int arith_moebius_mu(const fmpz_t n);
|
||||
|
||||
void arith_euler_phi(fmpz_t res, const fmpz_t n);
|
||||
|
||||
/* Stirling numbers **********************************************************/
|
||||
|
||||
void arith_stirling_number_1u(fmpz_t s, slong n, slong k);
|
||||
void arith_stirling_number_1(fmpz_t s, slong n, slong k);
|
||||
void arith_stirling_number_2(fmpz_t s, slong n, slong k);
|
||||
|
||||
void arith_stirling_number_1u_vec(fmpz * row, slong n, slong klen);
|
||||
void arith_stirling_number_1_vec(fmpz * row, slong n, slong klen);
|
||||
void arith_stirling_number_2_vec(fmpz * row, slong n, slong klen);
|
||||
|
||||
void arith_stirling_number_1u_vec_next(fmpz * row,
|
||||
const fmpz * prev, slong n, slong klen);
|
||||
void arith_stirling_number_1_vec_next(fmpz * row,
|
||||
const fmpz * prev, slong n, slong klen);
|
||||
void arith_stirling_number_2_vec_next(fmpz * row,
|
||||
const fmpz * prev, slong n, slong klen);
|
||||
|
||||
void arith_stirling_matrix_1u(fmpz_mat_t mat);
|
||||
void arith_stirling_matrix_1(fmpz_mat_t mat);
|
||||
void arith_stirling_matrix_2(fmpz_mat_t mat);
|
||||
|
||||
/* Bell numbers **************************************************************/
|
||||
|
||||
#if FLINT64
|
||||
#define BELL_NUMBER_TAB_SIZE 26
|
||||
#else
|
||||
#define BELL_NUMBER_TAB_SIZE 16
|
||||
#endif
|
||||
|
||||
extern const mp_limb_t bell_number_tab[];
|
||||
|
||||
double arith_bell_number_size(ulong n);
|
||||
|
||||
void arith_bell_number(fmpz_t b, ulong n);
|
||||
void arith_bell_number_bsplit(fmpz_t res, ulong n);
|
||||
void arith_bell_number_multi_mod(fmpz_t res, ulong n);
|
||||
|
||||
void arith_bell_number_vec(fmpz * b, slong n);
|
||||
void arith_bell_number_vec_recursive(fmpz * b, slong n);
|
||||
void arith_bell_number_vec_multi_mod(fmpz * b, slong n);
|
||||
|
||||
mp_limb_t arith_bell_number_nmod(ulong n, nmod_t mod);
|
||||
|
||||
void arith_bell_number_nmod_vec(mp_ptr b, slong n, nmod_t mod);
|
||||
void arith_bell_number_nmod_vec_recursive(mp_ptr b, slong n, nmod_t mod);
|
||||
void arith_bell_number_nmod_vec_series(mp_ptr b, slong n, nmod_t mod);
|
||||
|
||||
|
||||
/* Euler numbers *************************************************************/
|
||||
|
||||
#if FLINT64
|
||||
#define SMALL_EULER_LIMIT 25
|
||||
#else
|
||||
#define SMALL_EULER_LIMIT 15
|
||||
#endif
|
||||
|
||||
static const mp_limb_t euler_number_small[] = {
|
||||
UWORD(1), UWORD(1), UWORD(5), UWORD(61), UWORD(1385), UWORD(50521), UWORD(2702765),
|
||||
UWORD(199360981),
|
||||
#if FLINT64
|
||||
UWORD(19391512145), UWORD(2404879675441), UWORD(370371188237525),
|
||||
UWORD(69348874393137901), UWORD(15514534163557086905)
|
||||
#endif
|
||||
};
|
||||
|
||||
double arith_euler_number_size(ulong n);
|
||||
|
||||
void arith_euler_number_vec(fmpz * res, slong n);
|
||||
|
||||
void _arith_euler_number_zeta(fmpz_t res, ulong n);
|
||||
void arith_euler_number(fmpz_t res, ulong n);
|
||||
|
||||
void arith_euler_polynomial(fmpq_poly_t poly, ulong n);
|
||||
|
||||
/* Bernoulli numbers *********************************************************/
|
||||
|
||||
#if FLINT64
|
||||
#define BERNOULLI_SMALL_NUMER_LIMIT 35
|
||||
#else
|
||||
#define BERNOULLI_SMALL_NUMER_LIMIT 27
|
||||
#endif
|
||||
|
||||
static const slong _bernoulli_numer_small[] = {
|
||||
WORD(1), WORD(1), WORD(-1), WORD(1), WORD(-1), WORD(5), WORD(-691), WORD(7), WORD(-3617), WORD(43867), WORD(-174611), WORD(854513),
|
||||
WORD(-236364091), WORD(8553103),
|
||||
#if FLINT64
|
||||
WORD(-23749461029), WORD(8615841276005), WORD(-7709321041217), WORD(2577687858367)
|
||||
#endif
|
||||
};
|
||||
|
||||
void _arith_bernoulli_number(fmpz_t num, fmpz_t den, ulong n);
|
||||
void arith_bernoulli_number(fmpq_t x, ulong n);
|
||||
|
||||
void _arith_bernoulli_number_vec(fmpz * num, fmpz * den, slong n);
|
||||
void arith_bernoulli_number_vec(fmpq * num, slong n);
|
||||
|
||||
void arith_bernoulli_number_denom(fmpz_t den, ulong n);
|
||||
double arith_bernoulli_number_size(ulong n);
|
||||
|
||||
void arith_bernoulli_polynomial(fmpq_poly_t poly, ulong n);
|
||||
|
||||
void _arith_bernoulli_number_zeta(fmpz_t num, fmpz_t den, ulong n);
|
||||
void _arith_bernoulli_number_vec_multi_mod(fmpz * num, fmpz * den, slong n);
|
||||
void _arith_bernoulli_number_vec_recursive(fmpz * num, fmpz * den, slong n);
|
||||
void _arith_bernoulli_number_vec_zeta(fmpz * num, fmpz * den, slong n);
|
||||
|
||||
/* Cyclotomic polynomials ****************************************************/
|
||||
|
||||
void _arith_cyclotomic_polynomial(fmpz * a, ulong n, mp_ptr factors,
|
||||
slong num_factors, ulong phi);
|
||||
void arith_cyclotomic_polynomial(fmpz_poly_t poly, ulong n);
|
||||
|
||||
void _arith_cos_minpoly(fmpz * coeffs, slong d, ulong n);
|
||||
void arith_cos_minpoly(fmpz_poly_t poly, ulong n);
|
||||
|
||||
/* Hypergeometric polynomials ************************************************/
|
||||
|
||||
void arith_legendre_polynomial(fmpq_poly_t poly, ulong n);
|
||||
void arith_chebyshev_t_polynomial(fmpz_poly_t poly, ulong n);
|
||||
void arith_chebyshev_u_polynomial(fmpz_poly_t poly, ulong n);
|
||||
|
||||
/* Swinnerton-Dyer polynomials ***********************************************/
|
||||
|
||||
void arith_swinnerton_dyer_polynomial(fmpz_poly_t poly, ulong n);
|
||||
|
||||
/* Landau function ***********************************************************/
|
||||
|
||||
void arith_landau_function_vec(fmpz * res, slong len);
|
||||
|
||||
/* Dedekind sums *************************************************************/
|
||||
|
||||
void arith_dedekind_sum_naive(fmpq_t s, const fmpz_t h, const fmpz_t k);
|
||||
double arith_dedekind_sum_coprime_d(double h, double k);
|
||||
void arith_dedekind_sum_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k);
|
||||
void arith_dedekind_sum_coprime(fmpq_t s, const fmpz_t h, const fmpz_t k);
|
||||
void arith_dedekind_sum(fmpq_t s, const fmpz_t h, const fmpz_t k);
|
||||
|
||||
/* Exponential sums **********************************************************/
|
||||
|
||||
typedef struct
|
||||
{
|
||||
int n;
|
||||
int prefactor;
|
||||
mp_limb_t sqrt_p;
|
||||
mp_limb_t sqrt_q;
|
||||
mp_limb_signed_t cos_p[FLINT_BITS];
|
||||
mp_limb_t cos_q[FLINT_BITS];
|
||||
} trig_prod_struct;
|
||||
|
||||
typedef trig_prod_struct trig_prod_t[1];
|
||||
|
||||
static __inline__
|
||||
void trig_prod_init(trig_prod_t sum)
|
||||
{
|
||||
sum->n = 0;
|
||||
sum->prefactor = 1;
|
||||
sum->sqrt_p = 1;
|
||||
sum->sqrt_q = 1;
|
||||
}
|
||||
|
||||
void arith_hrr_expsum_factored(trig_prod_t prod, mp_limb_t k, mp_limb_t n);
|
||||
|
||||
/* Number of partitions ******************************************************/
|
||||
|
||||
void arith_number_of_partitions_nmod_vec(mp_ptr res, slong len, nmod_t mod);
|
||||
void arith_number_of_partitions_vec(fmpz * res, slong len);
|
||||
void arith_number_of_partitions_mpfr(mpfr_t x, ulong n);
|
||||
void arith_number_of_partitions(fmpz_t x, ulong n);
|
||||
|
||||
/* Number of sums of squares representations *********************************/
|
||||
|
||||
void arith_sum_of_squares(fmpz_t r, ulong k, const fmpz_t n);
|
||||
void arith_sum_of_squares_vec(fmpz * r, ulong k, slong n);
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
#endif
|
||||
|
|
@ -1,37 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_bell_number(fmpz_t b, ulong n)
|
||||
{
|
||||
if (n < BELL_NUMBER_TAB_SIZE)
|
||||
fmpz_set_ui(b, bell_number_tab[n]);
|
||||
else if (n < 5000)
|
||||
arith_bell_number_bsplit(b, n);
|
||||
else
|
||||
arith_bell_number_multi_mod(b, n);
|
||||
}
|
||||
|
|
@ -1,124 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
|
||||
static slong
|
||||
_bell_series_cutoff(slong n)
|
||||
{
|
||||
double N, log_N, log_pow, log_fac;
|
||||
|
||||
N = n;
|
||||
log_N = (N==0 ? 0 : log(N));
|
||||
log_pow = n * log_N;
|
||||
log_fac = N*log_N - N;
|
||||
while (log_pow - log_fac >= -2)
|
||||
{
|
||||
N++;
|
||||
log_N = log(N);
|
||||
log_pow = n * log_N;
|
||||
log_fac += log_N;
|
||||
}
|
||||
return N;
|
||||
}
|
||||
|
||||
static void
|
||||
_mpz_bell_bsplit(mpz_t P, mpz_t Q, slong a, slong b, slong n, slong bmax)
|
||||
{
|
||||
if (b - a < 20)
|
||||
{
|
||||
mpz_t u;
|
||||
slong k;
|
||||
mpz_init(u);
|
||||
flint_mpz_set_ui(P, UWORD(0));
|
||||
flint_mpz_set_ui(Q, UWORD(0));
|
||||
flint_mpz_set_ui(Q, (b - 1 == bmax) ? UWORD(1) : b);
|
||||
for (k = b - 1; k >= a; k--)
|
||||
{
|
||||
flint_mpz_set_ui(u, k);
|
||||
flint_mpz_pow_ui(u, u, n);
|
||||
mpz_addmul(P, Q, u);
|
||||
if (k != a)
|
||||
flint_mpz_mul_ui(Q, Q, k);
|
||||
}
|
||||
mpz_clear(u);
|
||||
}
|
||||
else
|
||||
{
|
||||
slong m;
|
||||
mpz_t P1, Q2;
|
||||
m = (a + b) / 2;
|
||||
mpz_init(P1);
|
||||
mpz_init(Q2);
|
||||
_mpz_bell_bsplit(P1, Q, a, m, n, bmax);
|
||||
_mpz_bell_bsplit(P, Q2, m, b, n, bmax);
|
||||
mpz_mul(Q, Q, Q2);
|
||||
mpz_addmul(P, P1, Q2);
|
||||
mpz_clear(P1);
|
||||
mpz_clear(Q2);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
arith_bell_number_bsplit(fmpz_t b, ulong n)
|
||||
{
|
||||
slong N;
|
||||
mp_bitcnt_t prec;
|
||||
mpz_t P, Q;
|
||||
mpfr_t Pf, Qf, E, one;
|
||||
|
||||
N = _bell_series_cutoff(n);
|
||||
|
||||
mpz_init(P);
|
||||
mpz_init(Q);
|
||||
|
||||
_mpz_bell_bsplit(P, Q, 1, N + 1, n, N);
|
||||
|
||||
prec = mpz_sizeinbase(P, 2) - mpz_sizeinbase(Q, 2) + 10;
|
||||
|
||||
mpfr_init2(Pf, prec);
|
||||
mpfr_init2(Qf, prec);
|
||||
mpfr_init2(E, prec);
|
||||
mpfr_init2(one, 2);
|
||||
|
||||
mpfr_set_z(Pf, P, GMP_RNDN);
|
||||
mpfr_set_z(Qf, Q, GMP_RNDN);
|
||||
mpfr_set_ui(one, 1, GMP_RNDN);
|
||||
mpfr_exp(E, one, GMP_RNDN);
|
||||
mpfr_mul(Qf, Qf, E, GMP_RNDN);
|
||||
mpfr_div(Pf, Pf, Qf, GMP_RNDN);
|
||||
mpfr_get_z(P, Pf, GMP_RNDN);
|
||||
|
||||
fmpz_set_mpz(b, P);
|
||||
|
||||
mpfr_clear(one);
|
||||
mpfr_clear(Pf);
|
||||
mpfr_clear(Qf);
|
||||
mpfr_clear(E);
|
||||
mpz_clear(P);
|
||||
mpz_clear(Q);
|
||||
}
|
||||
|
|
@ -1,65 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_bell_number_multi_mod(fmpz_t res, ulong n)
|
||||
{
|
||||
fmpz_comb_temp_t temp;
|
||||
fmpz_comb_t comb;
|
||||
nmod_t mod;
|
||||
mp_ptr primes, residues;
|
||||
slong k, num_primes;
|
||||
mp_bitcnt_t size, prime_bits;
|
||||
|
||||
size = arith_bell_number_size(n);
|
||||
prime_bits = FLINT_BITS - 1;
|
||||
num_primes = (size + prime_bits - 1) / prime_bits;
|
||||
|
||||
primes = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
residues = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
|
||||
primes[0] = n_nextprime(UWORD(1) << prime_bits, 0);
|
||||
for (k = 1; k < num_primes; k++)
|
||||
primes[k] = n_nextprime(primes[k-1], 0);
|
||||
|
||||
for (k = 0; k < num_primes; k++)
|
||||
{
|
||||
nmod_init(&mod, primes[k]);
|
||||
residues[k] = arith_bell_number_nmod(n, mod);
|
||||
}
|
||||
|
||||
fmpz_comb_init(comb, primes, num_primes);
|
||||
fmpz_comb_temp_init(temp, comb);
|
||||
|
||||
fmpz_multi_CRT_ui(res, residues, comb, temp, 0);
|
||||
|
||||
fmpz_comb_clear(comb);
|
||||
fmpz_comb_temp_clear(temp);
|
||||
|
||||
flint_free(primes);
|
||||
flint_free(residues);
|
||||
}
|
||||
|
|
@ -1,110 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
const mp_limb_t bell_number_tab[] =
|
||||
{
|
||||
UWORD(1), UWORD(1), UWORD(2), UWORD(5), UWORD(15), UWORD(52), UWORD(203), UWORD(877), UWORD(4140), UWORD(21147), UWORD(115975),
|
||||
UWORD(678570), UWORD(4213597), UWORD(27644437), UWORD(190899322), UWORD(1382958545),
|
||||
#if FLINT64
|
||||
UWORD(10480142147), UWORD(82864869804), UWORD(682076806159), UWORD(5832742205057),
|
||||
UWORD(51724158235372), UWORD(474869816156751), UWORD(4506715738447323),
|
||||
UWORD(44152005855084346), UWORD(445958869294805289),
|
||||
UWORD(4638590332229999353),
|
||||
#endif
|
||||
};
|
||||
|
||||
static const char bell_mod_2[3] = {1, 1, 0};
|
||||
static const char bell_mod_3[13] = {1, 1, 2, 2, 0, 1, 2, 1, 0, 0, 1, 0, 1};
|
||||
|
||||
mp_limb_t
|
||||
arith_bell_number_nmod(ulong n, nmod_t mod)
|
||||
{
|
||||
mp_limb_t s, t, u;
|
||||
mp_ptr facs, pows;
|
||||
slong i, j;
|
||||
|
||||
if (n < BELL_NUMBER_TAB_SIZE)
|
||||
return n_mod2_preinv(bell_number_tab[n], mod.n, mod.ninv);
|
||||
|
||||
if (mod.n == 2) return bell_mod_2[n % 3];
|
||||
if (mod.n == 3) return bell_mod_3[n % 13];
|
||||
|
||||
if (mod.n <= n)
|
||||
{
|
||||
mp_ptr bvec = flint_malloc(sizeof(mp_limb_t) * (n + 1));
|
||||
arith_bell_number_nmod_vec_recursive(bvec, n + 1, mod);
|
||||
s = bvec[n];
|
||||
flint_free(bvec);
|
||||
return s;
|
||||
}
|
||||
|
||||
/* Compute inverse factorials */
|
||||
/* We actually compute (n! / i!) and divide out (n!)^2 at the end */
|
||||
facs = flint_malloc(sizeof(mp_limb_t) * (n + 1));
|
||||
facs[n] = 1;
|
||||
for (i = n - 1; i >= 0; i--)
|
||||
facs[i] = n_mulmod2_preinv(facs[i + 1], i + 1, mod.n, mod.ninv);
|
||||
|
||||
/* Compute powers */
|
||||
pows = flint_calloc(n + 1, sizeof(mp_limb_t));
|
||||
pows[0] = n_powmod2_ui_preinv(0, n, mod.n, mod.ninv);
|
||||
pows[1] = n_powmod2_ui_preinv(1, n, mod.n, mod.ninv);
|
||||
|
||||
for (i = 2; i <= n; i++)
|
||||
{
|
||||
if (pows[i] == 0)
|
||||
pows[i] = n_powmod2_ui_preinv(i, n, mod.n, mod.ninv);
|
||||
|
||||
for (j = 2; j <= i && i * j <= n; j++)
|
||||
if (pows[i * j] == 0)
|
||||
pows[i * j] = n_mulmod2_preinv(pows[i],
|
||||
pows[j], mod.n, mod.ninv);
|
||||
}
|
||||
|
||||
for (s = t = i = 0; i <= n; i++)
|
||||
{
|
||||
if (i % 2 == 0)
|
||||
t = n_addmod(t, facs[i], mod.n);
|
||||
else
|
||||
t = n_submod(t, facs[i], mod.n);
|
||||
|
||||
u = pows[n - i];
|
||||
u = n_mulmod2_preinv(u, facs[n - i], mod.n, mod.ninv);
|
||||
u = n_mulmod2_preinv(u, t, mod.n, mod.ninv);
|
||||
s = n_addmod(s, u, mod.n);
|
||||
}
|
||||
|
||||
/* Remove (n!)^2 */
|
||||
u = n_invmod(facs[0], mod.n);
|
||||
u = n_mulmod2_preinv(u, u, mod.n, mod.ninv);
|
||||
s = n_mulmod2_preinv(s, u, mod.n, mod.ninv);
|
||||
|
||||
flint_free(facs);
|
||||
flint_free(pows);
|
||||
|
||||
return s;
|
||||
}
|
||||
|
|
@ -1,35 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_bell_number_nmod_vec(mp_ptr b, slong n, nmod_t mod)
|
||||
{
|
||||
if (n < 2000 || mod.n <= n)
|
||||
arith_bell_number_nmod_vec_recursive(b, n, mod);
|
||||
else
|
||||
arith_bell_number_nmod_vec_series(b, n, mod);
|
||||
}
|
||||
|
|
@ -1,56 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_bell_number_nmod_vec_recursive(mp_ptr b, slong n, nmod_t mod)
|
||||
{
|
||||
slong i, k;
|
||||
mp_ptr t;
|
||||
|
||||
if (n < BELL_NUMBER_TAB_SIZE)
|
||||
{
|
||||
for (i = 0; i < n; i++)
|
||||
b[i] = n_mod2_preinv(bell_number_tab[i], mod.n, mod.ninv);
|
||||
return;
|
||||
}
|
||||
|
||||
n -= 1;
|
||||
t = _nmod_vec_init(n);
|
||||
|
||||
t[0] = b[0] = b[1] = 1;
|
||||
|
||||
for (i = 1; i < n; i++)
|
||||
{
|
||||
t[i] = t[0];
|
||||
for (k = i; k > 0; k--)
|
||||
t[k - 1] = n_addmod(t[k - 1], t[k], mod.n);
|
||||
|
||||
b[i + 1] = t[0];
|
||||
}
|
||||
|
||||
_nmod_vec_clear(t);
|
||||
}
|
||||
|
|
@ -1,62 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_bell_number_nmod_vec_series(mp_ptr res, slong n, nmod_t mod)
|
||||
{
|
||||
mp_limb_t fac, c;
|
||||
mp_ptr tmp;
|
||||
slong k;
|
||||
|
||||
if (n < 1)
|
||||
return;
|
||||
|
||||
tmp = flint_malloc(sizeof(mp_limb_t) * n);
|
||||
|
||||
/* Divide by factorials */
|
||||
fac = n_factorial_mod2_preinv(n-1, mod.n, mod.ninv);
|
||||
c = n_invmod(fac, mod.n);
|
||||
|
||||
for (k = n - 1; k > 0; k--)
|
||||
{
|
||||
tmp[k] = c;
|
||||
c = n_mulmod2_preinv(c, k, mod.n, mod.ninv);
|
||||
}
|
||||
tmp[0] = UWORD(0);
|
||||
|
||||
_nmod_poly_exp_series(res, tmp, n, mod);
|
||||
|
||||
/* Multiply by factorials */
|
||||
c = UWORD(1);
|
||||
for (k = 1; k < n; k++)
|
||||
{
|
||||
c = n_mulmod2_preinv(c, k, mod.n, mod.ninv);
|
||||
res[k] = n_mulmod2_preinv(res[k], c, mod.n, mod.ninv);
|
||||
}
|
||||
|
||||
flint_free(tmp);
|
||||
}
|
||||
|
|
@ -1,36 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "flint.h"
|
||||
|
||||
double
|
||||
arith_bell_number_size(ulong n)
|
||||
{
|
||||
if (n == 0)
|
||||
return 2;
|
||||
|
||||
return n * log(0.792 * n/log(n+1)) * 1.44269504088896 + 2;
|
||||
}
|
||||
|
|
@ -1,35 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_bell_number_vec(fmpz * res, slong n)
|
||||
{
|
||||
if (n < 5000)
|
||||
arith_bell_number_vec_recursive(res, n);
|
||||
else
|
||||
arith_bell_number_vec_multi_mod(res, n);
|
||||
}
|
||||
|
|
@ -1,105 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "nmod_poly.h"
|
||||
#include "arith.h"
|
||||
|
||||
#define CRT_MAX_RESOLUTION 16
|
||||
|
||||
void
|
||||
arith_bell_number_vec_multi_mod(fmpz * res, slong n)
|
||||
{
|
||||
fmpz_comb_t comb[CRT_MAX_RESOLUTION];
|
||||
fmpz_comb_temp_t temp[CRT_MAX_RESOLUTION];
|
||||
mp_ptr primes, residues;
|
||||
mp_ptr * polys;
|
||||
nmod_t mod;
|
||||
slong i, j, k, num_primes, num_primes_k, resolution;
|
||||
mp_bitcnt_t size, prime_bits;
|
||||
|
||||
if (n < 1)
|
||||
return;
|
||||
|
||||
resolution = FLINT_MAX(1, FLINT_MIN(CRT_MAX_RESOLUTION, n / 16));
|
||||
|
||||
size = arith_bell_number_size(n);
|
||||
prime_bits = FLINT_BITS - 1;
|
||||
num_primes = (size + prime_bits - 1) / prime_bits;
|
||||
|
||||
primes = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
residues = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
polys = flint_malloc(num_primes * sizeof(mp_ptr));
|
||||
|
||||
/* Compute Bell numbers mod p */
|
||||
primes[0] = n_nextprime(UWORD(1)<<prime_bits, 0);
|
||||
for (k = 1; k < num_primes; k++)
|
||||
primes[k] = n_nextprime(primes[k-1], 0);
|
||||
|
||||
for (k = 0; k < num_primes; k++)
|
||||
{
|
||||
/* flint_printf("prime %wd of %wd\n", k, num_primes); */
|
||||
polys[k] = _nmod_vec_init(n);
|
||||
nmod_init(&mod, primes[k]);
|
||||
arith_bell_number_nmod_vec(polys[k], n, mod);
|
||||
}
|
||||
|
||||
/* Init CRT comb */
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
fmpz_comb_init(comb[i], primes, num_primes * (i + 1) / resolution);
|
||||
fmpz_comb_temp_init(temp[i], comb[i]);
|
||||
}
|
||||
|
||||
/* Reconstruction */
|
||||
for (k = 0; k < n; k++)
|
||||
{
|
||||
size = arith_bell_number_size(k);
|
||||
/* Use only as large a comb as needed */
|
||||
num_primes_k = (size + prime_bits - 1) / prime_bits;
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
if (comb[i]->num_primes >= num_primes_k)
|
||||
break;
|
||||
}
|
||||
num_primes_k = comb[i]->num_primes;
|
||||
for (j = 0; j < num_primes_k; j++)
|
||||
residues[j] = polys[j][k];
|
||||
fmpz_multi_CRT_ui(res + k, residues, comb[i], temp[i], 0);
|
||||
}
|
||||
|
||||
/* Cleanup */
|
||||
for (k = 0; k < num_primes; k++)
|
||||
_nmod_vec_clear(polys[k]);
|
||||
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
fmpz_comb_temp_clear(temp[i]);
|
||||
fmpz_comb_clear(comb[i]);
|
||||
}
|
||||
|
||||
flint_free(primes);
|
||||
flint_free(residues);
|
||||
flint_free(polys);
|
||||
}
|
||||
|
|
@ -1,57 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_bell_number_vec_recursive(fmpz * b, slong n)
|
||||
{
|
||||
slong i, k;
|
||||
fmpz * t;
|
||||
|
||||
if (n < BELL_NUMBER_TAB_SIZE)
|
||||
{
|
||||
for (i = 0; i < n; i++)
|
||||
fmpz_set_ui(b + i, bell_number_tab[i]);
|
||||
return;
|
||||
}
|
||||
|
||||
n -= 1;
|
||||
t = _fmpz_vec_init(n);
|
||||
|
||||
fmpz_one(t);
|
||||
fmpz_one(b);
|
||||
fmpz_one(b + 1);
|
||||
|
||||
for (i = 1; i < n; i++)
|
||||
{
|
||||
fmpz_set(t + i, t);
|
||||
for (k = i; k > 0; k--)
|
||||
fmpz_add(t + k - 1, t + k - 1, t + k);
|
||||
fmpz_set(b + i + 1, t);
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(t, n);
|
||||
}
|
||||
|
|
@ -1,36 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void _arith_bernoulli_number(fmpz_t num, fmpz_t den, ulong n)
|
||||
{
|
||||
_arith_bernoulli_number_zeta(num, den, n);
|
||||
}
|
||||
|
||||
void arith_bernoulli_number(fmpq_t x, ulong n)
|
||||
{
|
||||
_arith_bernoulli_number(fmpq_numref(x), fmpq_denref(x), n);
|
||||
}
|
||||
|
|
@ -1,80 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
#define BERNOULLI_DENOM_MAX_SMALL 178
|
||||
|
||||
#if FLINT64
|
||||
#define __u32 unsigned int
|
||||
#else
|
||||
#define __u32 mp_limb_t
|
||||
#endif
|
||||
|
||||
static const __u32 __bernoulli_denom_small[] =
|
||||
{
|
||||
UWORD(1), UWORD(6), UWORD(30), UWORD(42), UWORD(30), UWORD(66), UWORD(2730), UWORD(6), UWORD(510), UWORD(798), UWORD(330),
|
||||
UWORD(138), UWORD(2730), UWORD(6), UWORD(870), UWORD(14322), UWORD(510), UWORD(6), UWORD(1919190), UWORD(6), UWORD(13530),
|
||||
UWORD(1806), UWORD(690), UWORD(282), UWORD(46410), UWORD(66), UWORD(1590), UWORD(798), UWORD(870), UWORD(354),
|
||||
UWORD(56786730), UWORD(6), UWORD(510), UWORD(64722), UWORD(30), UWORD(4686), UWORD(140100870), UWORD(6), UWORD(30),
|
||||
UWORD(3318), UWORD(230010), UWORD(498), UWORD(3404310), UWORD(6), UWORD(61410), UWORD(272118), UWORD(1410), UWORD(6),
|
||||
UWORD(4501770), UWORD(6), UWORD(33330), UWORD(4326), UWORD(1590), UWORD(642), UWORD(209191710), UWORD(1518),
|
||||
UWORD(1671270), UWORD(42), UWORD(1770), UWORD(6), UWORD(2328255930), UWORD(6), UWORD(30), UWORD(4357878), UWORD(510),
|
||||
UWORD(8646), UWORD(4206930), UWORD(6), UWORD(4110), UWORD(274386), UWORD(679470), UWORD(6), UWORD(2381714790),
|
||||
UWORD(6), UWORD(4470), UWORD(2162622), UWORD(30), UWORD(138), UWORD(1794590070), UWORD(6), UWORD(230010),
|
||||
UWORD(130074), UWORD(2490), UWORD(1002), UWORD(3404310), UWORD(66), UWORD(5190), UWORD(2478), UWORD(1043970),
|
||||
UWORD(1074),
|
||||
};
|
||||
|
||||
void arith_bernoulli_number_denom(fmpz_t den, ulong n)
|
||||
{
|
||||
slong i;
|
||||
mp_limb_t p;
|
||||
const mp_limb_t * primes;
|
||||
|
||||
if (n % 2 == 1)
|
||||
{
|
||||
fmpz_set_ui(den, 1 + (n == 1));
|
||||
}
|
||||
else if (n <= BERNOULLI_DENOM_MAX_SMALL)
|
||||
{
|
||||
fmpz_set_ui(den, __bernoulli_denom_small[n / 2]);
|
||||
}
|
||||
else
|
||||
{
|
||||
n_prime_pi_bounds(&p, &p, n);
|
||||
primes = n_primes_arr_readonly(p + 1);
|
||||
|
||||
fmpz_set_ui(den, UWORD(6));
|
||||
for (i = 2; i < n; i++)
|
||||
{
|
||||
p = primes[i];
|
||||
if (p - 1 > n)
|
||||
break;
|
||||
if (n % (p - 1) == 0)
|
||||
fmpz_mul_ui(den, den, p);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -1,41 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
double arith_bernoulli_number_size(ulong n)
|
||||
{
|
||||
double x;
|
||||
|
||||
/* |B_n| < 2 */
|
||||
if (n <= 14)
|
||||
return 1.0;
|
||||
|
||||
x = 2 + (n + 1) * log(n + 1) * 1.44269504088897; /* 1/log(2) */
|
||||
x -= n * 4.0941911703612822; /* log2(2*pi*e) */
|
||||
|
||||
return x + 2;
|
||||
}
|
||||
|
|
@ -1,59 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void _arith_bernoulli_number_vec(fmpz * num, fmpz * den, slong n)
|
||||
{
|
||||
if (n < 700)
|
||||
_arith_bernoulli_number_vec_recursive(num, den, n);
|
||||
else if (n < 3900)
|
||||
_arith_bernoulli_number_vec_zeta(num, den, n);
|
||||
else
|
||||
_arith_bernoulli_number_vec_multi_mod(num, den, n);
|
||||
}
|
||||
|
||||
void arith_bernoulli_number_vec(fmpq * x, slong n)
|
||||
{
|
||||
fmpz * num, * den;
|
||||
slong i;
|
||||
|
||||
if (n <= 0)
|
||||
return;
|
||||
|
||||
num = _fmpz_vec_init(n * 2);
|
||||
den = num + n;
|
||||
|
||||
_arith_bernoulli_number_vec(num, den, n);
|
||||
|
||||
for (i = 0; i < n; i++)
|
||||
{
|
||||
fmpz_swap(num + i, fmpq_numref(x + i));
|
||||
fmpz_swap(den + i, fmpq_denref(x + i));
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(num, n * 2);
|
||||
}
|
||||
|
||||
|
|
@ -1,150 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
static void
|
||||
__bernoulli_number_vec_mod_p(mp_ptr res, mp_ptr tmp, const fmpz * den,
|
||||
slong m, nmod_t mod)
|
||||
{
|
||||
mp_limb_t fac, c, t;
|
||||
slong k;
|
||||
|
||||
/* x^2/(cosh(x)-1) = \sum_{k=0}^{\infty} 2(1-2k)/(2k)! B_2k x^(2k) */
|
||||
|
||||
/* Divide by factorials */
|
||||
fac = n_factorial_mod2_preinv(2*m, mod.n, mod.ninv);
|
||||
c = n_invmod(fac, mod.n);
|
||||
for (k = m - 1; k >= 0; k--)
|
||||
{
|
||||
tmp[k] = c;
|
||||
c = n_mulmod2_preinv(c, (2*k+1)*(2*k+2), mod.n, mod.ninv);
|
||||
}
|
||||
|
||||
_nmod_poly_inv_series(res, tmp, m, mod);
|
||||
res[0] = UWORD(1);
|
||||
|
||||
/* N_(2k) = -1 * D_(2k) * (2k)! / (2k-1) */
|
||||
c = n_negmod(UWORD(1), mod.n);
|
||||
for (k = 1; k < m; k++)
|
||||
{
|
||||
t = fmpz_fdiv_ui(den + 2*k, mod.n);
|
||||
t = n_mulmod2_preinv(c, t, mod.n, mod.ninv);
|
||||
res[k] = n_mulmod2_preinv(res[k], t, mod.n, mod.ninv);
|
||||
c = n_mulmod2_preinv(c, 2*(k+1)*(2*k-1), mod.n, mod.ninv);
|
||||
}
|
||||
}
|
||||
|
||||
#define CRT_MAX_RESOLUTION 16
|
||||
|
||||
void _arith_bernoulli_number_vec_multi_mod(fmpz * num, fmpz * den, slong n)
|
||||
{
|
||||
fmpz_comb_t comb[CRT_MAX_RESOLUTION];
|
||||
fmpz_comb_temp_t temp[CRT_MAX_RESOLUTION];
|
||||
mp_limb_t * primes;
|
||||
mp_limb_t * residues;
|
||||
mp_ptr * polys;
|
||||
mp_ptr temppoly;
|
||||
nmod_t mod;
|
||||
slong i, j, k, m, num_primes, num_primes_k, resolution;
|
||||
mp_bitcnt_t size, prime_bits;
|
||||
|
||||
if (n < 1)
|
||||
return;
|
||||
|
||||
for (i = 0; i < n; i++)
|
||||
arith_bernoulli_number_denom(den + i, i);
|
||||
|
||||
/* Number of nonzero entries (apart from B_1) */
|
||||
m = (n + 1) / 2;
|
||||
resolution = FLINT_MAX(1, FLINT_MIN(CRT_MAX_RESOLUTION, m / 16));
|
||||
|
||||
/* Note that the denominators must be accounted for */
|
||||
size = arith_bernoulli_number_size(n) + _fmpz_vec_max_bits(den, n) + 2;
|
||||
|
||||
prime_bits = FLINT_BITS - 1;
|
||||
num_primes = (size + prime_bits - 1) / prime_bits;
|
||||
|
||||
primes = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
residues = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
polys = flint_malloc(num_primes * sizeof(mp_ptr));
|
||||
|
||||
/* Compute Bernoulli numbers mod p */
|
||||
primes[0] = n_nextprime(UWORD(1)<<prime_bits, 0);
|
||||
for (k = 1; k < num_primes; k++)
|
||||
primes[k] = n_nextprime(primes[k-1], 0);
|
||||
temppoly = _nmod_vec_init(m);
|
||||
for (k = 0; k < num_primes; k++)
|
||||
{
|
||||
polys[k] = _nmod_vec_init(m);
|
||||
nmod_init(&mod, primes[k]);
|
||||
__bernoulli_number_vec_mod_p(polys[k], temppoly, den, m, mod);
|
||||
}
|
||||
|
||||
/* Init CRT comb */
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
fmpz_comb_init(comb[i], primes, num_primes * (i + 1) / resolution);
|
||||
fmpz_comb_temp_init(temp[i], comb[i]);
|
||||
}
|
||||
|
||||
/* Trivial entries */
|
||||
if (n > 1)
|
||||
fmpz_set_si(num + 1, WORD(-1));
|
||||
for (k = 3; k < n; k += 2)
|
||||
fmpz_zero(num + k);
|
||||
|
||||
/* Reconstruction */
|
||||
for (k = 0; k < n; k += 2)
|
||||
{
|
||||
size = arith_bernoulli_number_size(k) + fmpz_bits(den + k) + 2;
|
||||
/* Use only as large a comb as needed */
|
||||
num_primes_k = (size + prime_bits - 1) / prime_bits;
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
if (comb[i]->num_primes >= num_primes_k)
|
||||
break;
|
||||
}
|
||||
num_primes_k = comb[i]->num_primes;
|
||||
for (j = 0; j < num_primes_k; j++)
|
||||
residues[j] = polys[j][k / 2];
|
||||
fmpz_multi_CRT_ui(num + k, residues, comb[i], temp[i], 1);
|
||||
}
|
||||
|
||||
/* Cleanup */
|
||||
for (k = 0; k < num_primes; k++)
|
||||
_nmod_vec_clear(polys[k]);
|
||||
_nmod_vec_clear(temppoly);
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
fmpz_comb_temp_clear(temp[i]);
|
||||
fmpz_comb_clear(comb[i]);
|
||||
}
|
||||
|
||||
flint_free(primes);
|
||||
flint_free(residues);
|
||||
flint_free(polys);
|
||||
}
|
||||
|
|
@ -1,165 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
static void
|
||||
__ramanujan_even_common_denom(fmpz * num, fmpz * den, slong start, slong n)
|
||||
{
|
||||
fmpz_t t, c, d, cden;
|
||||
slong j, k, m, mcase;
|
||||
int prodsize;
|
||||
|
||||
if (start >= n)
|
||||
return;
|
||||
|
||||
fmpz_init(t);
|
||||
fmpz_init(c);
|
||||
fmpz_init(d);
|
||||
fmpz_init(cden);
|
||||
|
||||
/* Common denominator */
|
||||
arith_primorial(cden, n + 1);
|
||||
|
||||
start += start % 2;
|
||||
|
||||
/* Convert initial values to common denominator */
|
||||
for (k = 0; k < start; k += 2)
|
||||
{
|
||||
fmpz_divexact(t, cden, den + k);
|
||||
fmpz_mul(num + k, num + k, t);
|
||||
}
|
||||
|
||||
/* Ramanujan's recursive formula */
|
||||
for (m = start; m < n; m += 2)
|
||||
{
|
||||
mcase = m % 6;
|
||||
|
||||
fmpz_mul_ui(num + m, cden, m + UWORD(3));
|
||||
fmpz_divexact_ui(num + m, num + m, UWORD(3));
|
||||
|
||||
if (mcase == 4)
|
||||
{
|
||||
fmpz_neg(num + m, num + m);
|
||||
fmpz_divexact_ui(num + m, num + m, UWORD(2));
|
||||
}
|
||||
|
||||
/* All factors are strictly smaller than m + 4; choose prodsize such
|
||||
that (m + 4)^prodsize fits in an slong. */
|
||||
{
|
||||
#if FLINT64
|
||||
if (m < WORD(1444)) prodsize = 6;
|
||||
else if (m < WORD(2097148)) prodsize = 3;
|
||||
else if (m < WORD(3037000495)) prodsize = 2; /* not very likely... */
|
||||
else abort();
|
||||
#else
|
||||
if (m < WORD(32)) prodsize = 6;
|
||||
else if (m < WORD(1286)) prodsize = 3;
|
||||
else if (m < WORD(46336)) prodsize = 2;
|
||||
else abort();
|
||||
#endif
|
||||
}
|
||||
|
||||
/* c = t = binomial(m+3, m) */
|
||||
fmpz_set_ui(t, m + UWORD(1));
|
||||
fmpz_mul_ui(t, t, m + UWORD(2));
|
||||
fmpz_mul_ui(t, t, m + UWORD(3));
|
||||
fmpz_divexact_ui(t, t, UWORD(6));
|
||||
fmpz_set(c, t);
|
||||
|
||||
for (j = 6; j <= m; j += 6)
|
||||
{
|
||||
slong r = m - j;
|
||||
|
||||
/* c = binomial(m+3, m-j); */
|
||||
switch (prodsize)
|
||||
{
|
||||
case 2:
|
||||
fmpz_mul_ui(c, c, (r+6)*(r+5));
|
||||
fmpz_mul_ui(c, c, (r+4)*(r+3));
|
||||
fmpz_mul_ui(c, c, (r+2)*(r+1));
|
||||
fmpz_set_ui(d, (j+0)*(j+3));
|
||||
fmpz_mul_ui(d, d, (j-2)*(j+2));
|
||||
fmpz_mul_ui(d, d, (j-1)*(j+1));
|
||||
fmpz_divexact(c, c, d);
|
||||
break;
|
||||
|
||||
case 3:
|
||||
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4));
|
||||
fmpz_mul_ui(c, c, (r+3)*(r+2)*(r+1));
|
||||
fmpz_set_ui(d, (j+0)*(j+3)*(j-2));
|
||||
fmpz_mul_ui(d, d, (j+2)*(j-1)*(j+1));
|
||||
fmpz_divexact(c, c, d);
|
||||
break;
|
||||
|
||||
case 6:
|
||||
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4)*(r+3)*(r+2)*(r+1));
|
||||
fmpz_divexact_ui(c, c, (j+0)*(j+3)*(j-2)*(j+2)*(j-1)*(j+1));
|
||||
break;
|
||||
}
|
||||
|
||||
fmpz_submul(num + m, c, num + (m - j));
|
||||
}
|
||||
fmpz_divexact(num + m, num + m, t);
|
||||
}
|
||||
|
||||
/* Convert to separate denominators */
|
||||
for (k = 0; k < n; k += 2)
|
||||
{
|
||||
arith_bernoulli_number_denom(den + k, k);
|
||||
fmpz_divexact(t, cden, den + k);
|
||||
fmpz_divexact(num + k, num + k, t);
|
||||
}
|
||||
|
||||
fmpz_clear(t);
|
||||
fmpz_clear(c);
|
||||
fmpz_clear(d);
|
||||
fmpz_clear(cden);
|
||||
}
|
||||
|
||||
void _arith_bernoulli_number_vec_recursive(fmpz * num, fmpz * den, slong n)
|
||||
{
|
||||
slong i, start;
|
||||
fmpz_t t;
|
||||
fmpz_t d;
|
||||
|
||||
fmpz_init(t);
|
||||
fmpz_init(d);
|
||||
|
||||
start = FLINT_MIN(BERNOULLI_SMALL_NUMER_LIMIT, n);
|
||||
|
||||
/* Initial values */
|
||||
for (i = 0; i < start; i += 2)
|
||||
_arith_bernoulli_number(num + i, den + i, i);
|
||||
|
||||
__ramanujan_even_common_denom(num, den, start, n);
|
||||
|
||||
/* Odd values */
|
||||
for (i = 1; i < n; i += 2)
|
||||
_arith_bernoulli_number(num + i, den + i, i);
|
||||
|
||||
fmpz_clear(d);
|
||||
fmpz_clear(t);
|
||||
}
|
||||
|
|
@ -1,35 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void _arith_bernoulli_number_vec_zeta(fmpz * num, fmpz * den, slong n)
|
||||
{
|
||||
slong i;
|
||||
|
||||
/* Go backwards to exploit MPFR cache for pi */
|
||||
for (i = n - 1; i >= 0; i--)
|
||||
_arith_bernoulli_number_zeta(num + i, den + i, i);
|
||||
}
|
||||
|
|
@ -1,87 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void _arith_bernoulli_number_zeta(fmpz_t num, fmpz_t den, ulong n)
|
||||
{
|
||||
mpz_t r;
|
||||
mpfr_t t, u, z, pi;
|
||||
mp_bitcnt_t prec, pi_prec;
|
||||
|
||||
arith_bernoulli_number_denom(den, n);
|
||||
|
||||
if (n % 2)
|
||||
{
|
||||
fmpz_set_si(num, -(n == 1));
|
||||
return;
|
||||
}
|
||||
|
||||
if (n < BERNOULLI_SMALL_NUMER_LIMIT)
|
||||
{
|
||||
fmpz_set_si(num, _bernoulli_numer_small[n / 2]);
|
||||
return;
|
||||
}
|
||||
|
||||
prec = arith_bernoulli_number_size(n) + fmpz_bits(den);
|
||||
prec += 10 + 2*FLINT_BIT_COUNT(n);
|
||||
pi_prec = prec;
|
||||
|
||||
mpz_init(r);
|
||||
mpfr_init2(t, prec);
|
||||
mpfr_init2(u, prec);
|
||||
mpfr_init2(z, prec);
|
||||
mpfr_init2(pi, pi_prec);
|
||||
|
||||
/* t = 2 * n! / (2*pi)^n */
|
||||
flint_mpz_fac_ui(r, n);
|
||||
mpfr_set_z(t, r, GMP_RNDN);
|
||||
mpfr_mul_2exp(t, t, 1, GMP_RNDN);
|
||||
mpfr_const_pi(pi, GMP_RNDN);
|
||||
mpfr_mul_2exp(pi, pi, 1, GMP_RNDN);
|
||||
mpfr_pow_ui(pi, pi, n, GMP_RNDN);
|
||||
mpfr_div(t, t, pi, GMP_RNDN);
|
||||
|
||||
/* t = t / zeta(n) */
|
||||
mpfr_zeta_inv_euler_product(z, n, 0);
|
||||
mpfr_div(t, t, z, GMP_RNDN);
|
||||
|
||||
/* round numerator */
|
||||
fmpz_get_mpz(r, den);
|
||||
mpfr_mul_z(t, t, r, GMP_RNDN);
|
||||
mpfr_round(t, t);
|
||||
mpfr_get_z(r, t, GMP_RNDN);
|
||||
fmpz_set_mpz(num, r);
|
||||
|
||||
if (n % 4 == 0)
|
||||
fmpz_neg(num, num);
|
||||
|
||||
mpz_clear(r);
|
||||
mpfr_clear(t);
|
||||
mpfr_clear(u);
|
||||
mpfr_clear(z);
|
||||
mpfr_clear(pi);
|
||||
}
|
||||
|
||||
|
|
@ -1,73 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void arith_bernoulli_polynomial(fmpq_poly_t poly, ulong n)
|
||||
{
|
||||
fmpz_t t;
|
||||
fmpz * den;
|
||||
slong k;
|
||||
|
||||
if (n == 0)
|
||||
{
|
||||
fmpq_poly_set_ui(poly, UWORD(1));
|
||||
return;
|
||||
}
|
||||
|
||||
fmpq_poly_fit_length(poly, n + 1);
|
||||
|
||||
fmpz_init(t);
|
||||
den = _fmpz_vec_init(n + 1);
|
||||
|
||||
_arith_bernoulli_number_vec(poly->coeffs, den, n + 1);
|
||||
|
||||
/* Multiply the odd term by binomial(n,1) = n */
|
||||
fmpz_mul_ui(poly->coeffs + 1, poly->coeffs + 1, n);
|
||||
|
||||
/* Multiply even terms by binomial coefficients */
|
||||
fmpz_one(t);
|
||||
for (k = 2; k <= n; k += 2)
|
||||
{
|
||||
fmpz_mul2_uiui(t, t, n-k+1, n-k+2);
|
||||
fmpz_divexact2_uiui(t, t, k, k-1);
|
||||
fmpz_mul(poly->coeffs + k, poly->coeffs + k, t);
|
||||
}
|
||||
|
||||
/* Convert to common denominator */
|
||||
arith_primorial(poly->den, n + 2);
|
||||
for (k = 0; k <= n; k++)
|
||||
{
|
||||
fmpz_mul(poly->coeffs + k, poly->coeffs+k, poly->den);
|
||||
fmpz_divexact(poly->coeffs + k, poly->coeffs + k, den + k);
|
||||
}
|
||||
|
||||
_fmpz_poly_reverse(poly->coeffs, poly->coeffs, n + 1, n + 1);
|
||||
_fmpq_poly_set_length(poly, n + 1);
|
||||
fmpq_poly_canonicalise(poly);
|
||||
|
||||
_fmpz_vec_clear(den, n + 1);
|
||||
fmpz_clear(t);
|
||||
}
|
||||
|
|
@ -1,72 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
_arith_chebyshev_t_polynomial(fmpz * coeffs, ulong n)
|
||||
{
|
||||
slong k, i, d, m;
|
||||
|
||||
d = n % 2;
|
||||
|
||||
fmpz_zero(coeffs);
|
||||
fmpz_set_ui(coeffs + d, d ? n : 1);
|
||||
if (n % 4 >= 2)
|
||||
fmpz_neg(coeffs + d, coeffs + d);
|
||||
|
||||
m = n / 2;
|
||||
|
||||
for (k = 1; k <= m; k++)
|
||||
{
|
||||
i = 2 * k + d;
|
||||
fmpz_mul2_uiui(coeffs + i, coeffs + i - 2, 4*(m-k+1), n+k-m-1);
|
||||
fmpz_divexact2_uiui(coeffs + i, coeffs + i, n+2*k-2*m-1, n+2*k-2*m);
|
||||
fmpz_neg(coeffs + i, coeffs + i);
|
||||
fmpz_zero(coeffs + i - 1);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
arith_chebyshev_t_polynomial(fmpz_poly_t poly, ulong n)
|
||||
{
|
||||
if (n == 0)
|
||||
{
|
||||
fmpz_poly_set_ui(poly, UWORD(1));
|
||||
return;
|
||||
}
|
||||
|
||||
fmpz_poly_fit_length(poly, n + 1);
|
||||
|
||||
if (n == 1)
|
||||
{
|
||||
fmpz_zero(poly->coeffs);
|
||||
fmpz_one(poly->coeffs + 1);
|
||||
}
|
||||
else
|
||||
_arith_chebyshev_t_polynomial(poly->coeffs, n);
|
||||
|
||||
_fmpz_poly_set_length(poly, n + 1);
|
||||
}
|
||||
|
|
@ -1,72 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
_arith_chebyshev_u_polynomial(fmpz * coeffs, ulong n)
|
||||
{
|
||||
slong k, i, d, m;
|
||||
|
||||
d = n % 2;
|
||||
|
||||
fmpz_zero(coeffs);
|
||||
fmpz_set_ui(coeffs + d, d ? n + 1 : 1);
|
||||
if (n % 4 >= 2)
|
||||
fmpz_neg(coeffs + d, coeffs + d);
|
||||
|
||||
m = n / 2;
|
||||
|
||||
for (k = 1; k <= m; k++)
|
||||
{
|
||||
i = 2 * k + d;
|
||||
fmpz_mul2_uiui(coeffs + i, coeffs + i - 2, 4*(m-k+1), n+k-m);
|
||||
fmpz_divexact2_uiui(coeffs + i, coeffs + i, n+2*k-2*m-1, n+2*k-2*m);
|
||||
fmpz_neg(coeffs + i, coeffs + i);
|
||||
fmpz_zero(coeffs + i - 1);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
arith_chebyshev_u_polynomial(fmpz_poly_t poly, ulong n)
|
||||
{
|
||||
if (n == 0)
|
||||
{
|
||||
fmpz_poly_set_ui(poly, UWORD(1));
|
||||
return;
|
||||
}
|
||||
|
||||
fmpz_poly_fit_length(poly, n + 1);
|
||||
|
||||
if (n == 1)
|
||||
{
|
||||
fmpz_zero(poly->coeffs);
|
||||
fmpz_set_ui(poly->coeffs + 1, UWORD(2));
|
||||
}
|
||||
else
|
||||
_arith_chebyshev_u_polynomial(poly->coeffs, n);
|
||||
|
||||
_fmpz_poly_set_length(poly, n + 1);
|
||||
}
|
||||
|
|
@ -1,268 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
#define MAX_32BIT 58
|
||||
|
||||
static const int lookup_table[MAX_32BIT][28] =
|
||||
{
|
||||
{-1, 1}, {1, 1}, {1, 2}, {0, 1}, {-1, 2, 4}, {-1, 2},
|
||||
{-1, -4, 4, 8}, {-1, 0, 2}, {1, -6, 0, 8}, {-1, -2, 4},
|
||||
{1, 6, -12, -32, 16, 32}, {-3, 0, 4}, {-1, 6, 24, -32, -80, 32, 64},
|
||||
{1, -4, -4, 8}, {1, 8, -16, -8, 16}, {1, 0, -8, 0, 8},
|
||||
{1, -8, -40, 80, 240, -192, -448, 128, 256}, {-1, -6, 0, 8},
|
||||
{1, 10, -40, -160, 240, 672, -448, -1024, 256, 512}, {5, 0, -20, 0, 16},
|
||||
{1, -16, 32, 48, -96, -32, 64}, {-1, 6, 12, -32, -16, 32},
|
||||
{-1, -12, 60, 280, -560, -1792, 1792, 4608, -2304, -5120, 1024, 2048},
|
||||
{1, 0, -16, 0, 16}, {-1, 10, 100, -40, -800, 32, 2240, 0, -2560, 0,
|
||||
1024}, {-1, -6, 24, 32, -80, -32, 64},
|
||||
{1, 18, 0, -240, 0, 864, 0, -1152, 0, 512}, {-7, 0, 56, 0, -112, 0, 64},
|
||||
{-1, 14, 112, -448, -2016, 4032, 13440, -15360, -42240, 28160, 67584,
|
||||
-24576, -53248, 8192, 16384}, {1, -8, -16, 8, 16},
|
||||
{-1, -16, 112, 672, -2016, -8064, 13440, 42240, -42240, -112640, 67584,
|
||||
159744, -53248, -114688, 16384, 32768},
|
||||
{1, 0, -32, 0, 160, 0, -256, 0, 128},
|
||||
{1, -24, 48, 344, -688, -1088, 2176, 1280, -2560, -512, 1024},
|
||||
{1, 8, -40, -80, 240, 192, -448, -128, 256},
|
||||
{1, 16, -160, -368, 1760, 2272, -7232, -5504, 13824, 5632, -12288,
|
||||
-2048, 4096}, {-3, 0, 36, 0, -96, 0, 64},
|
||||
{-1, 18, 180, -960, -5280, 14784, 59136, -101376, -329472, 366080,
|
||||
1025024, -745472, -1863680, 860160, 1966080, -524288, -1114112, 131072,
|
||||
262144}, {-1, 10, 40, -160, -240, 672, 448, -1024, -256, 512},
|
||||
{1, 24, -48, -632, 1264, 3296, -6592, -6784, 13568, 6144, -12288, -2048,
|
||||
4096}, {1, 0, -48, 0, 304, 0, -512, 0, 256},
|
||||
{1, -20, -220, 1320, 7920, -25344, -109824, 219648, 768768, -1025024,
|
||||
-3075072, 2795520, 7454720, -4587520, -11141120, 4456448, 10027008,
|
||||
-2359296, -4980736, 524288, 1048576}, {1, 16, 32, -48, -96, 32, 64},
|
||||
{1, 22, -220, -1760, 7920, 41184, -109824, -439296, 768768, 2562560,
|
||||
-3075072, -8945664, 7454720, 19496960, -11141120, -26738688, 10027008,
|
||||
22413312, -4980736, -10485760, 1048576, 2097152},
|
||||
{-11, 0, 220, 0, -1232, 0, 2816, 0, -2816, 0, 1024},
|
||||
{1, -24, -144, 248, 1680, -864, -7168, 1152, 13824, -512, -12288, 0,
|
||||
4096}, {1, -12, -60, 280, 560, -1792, -1792, 4608, 2304, -5120, -1024,
|
||||
2048}, {-1, -24, 264, 2288, -11440, -64064, 192192, 823680, -1647360,
|
||||
-5857280, 8200192, 25346048, -25346048, -70189056, 50135040, 127008768,
|
||||
-63504384, -149422080, 49807360, 110100480, -22020096, -46137344,
|
||||
4194304, 8388608}, {1, 0, -64, 0, 320, 0, -512, 0, 256},
|
||||
{-1, 28, 196, -2968, -3136, 66304, 18816, -658816, -53760, 3587584,
|
||||
78848, -11741184, -57344, 24084480, 16384, -31195136, 0, 24772608, 0,
|
||||
-11010048, 0, 2097152}, {-1, -10, 100, 40, -800, -32, 2240, 0, -2560,
|
||||
0, 1024}, {1, 32, -64, -1504, 3008, 16832, -33664, -76288, 152576,
|
||||
173568, -347136, -210944, 421888, 131072, -262144, -32768, 65536},
|
||||
{13, 0, -364, 0, 2912, 0, -9984, 0, 16640, 0, -13312, 0, 4096},
|
||||
{-1, 26, 364, -2912, -21840, 96096, 512512, -1464320, -6223360,
|
||||
12446720, 44808192, -65175552, -206389248, 222265344, 635043840,
|
||||
-508035072, -1333592064, 784465920, 1917583360, -807403520,
|
||||
-1857028096, 530579456, 1157627904, -201326592, -419430400, 33554432,
|
||||
67108864}, {-1, 18, 0, -240, 0, 864, 0, -1152, 0, 512},
|
||||
{1, 24, -432, -1208, 15216, 28064, -185024, -263424, 1149184, 1250304,
|
||||
-4177920, -3356672, 9375744, 5324800, -13123584, -4947968, 11141120,
|
||||
2490368, -5242880, -524288, 1048576},
|
||||
{1, 0, -96, 0, 1376, 0, -6656, 0, 13568, 0, -12288, 0, 4096},
|
||||
{1, -40, 80, 2120, -4240, -31648, 63296, 194432, -388864, -613376,
|
||||
1226752, 1087488, -2174976, -1097728, 2195456, 589824, -1179648,
|
||||
-131072, 262144}, {-1, -14, 112, 448, -2016, -4032, 13440, 15360,
|
||||
-42240, -28160, 67584, 24576, -53248, -8192, 16384}
|
||||
};
|
||||
|
||||
/* The coefficients in 2^d * \prod_{i=1}^d (x - cos(a_i)) are
|
||||
easily bounded using the binomial theorem. */
|
||||
static slong
|
||||
magnitude_bound(slong d)
|
||||
{
|
||||
slong res;
|
||||
fmpz_t t;
|
||||
fmpz_init(t);
|
||||
fmpz_bin_uiui(t, d, d / 2);
|
||||
res = fmpz_bits(t);
|
||||
fmpz_clear(t);
|
||||
return FLINT_ABS(res) + d;
|
||||
}
|
||||
|
||||
static void
|
||||
fmpz_mul_or_div_2exp(fmpz_t x, fmpz_t y, slong s)
|
||||
{
|
||||
if (s >= 0)
|
||||
fmpz_mul_2exp(x, y, s);
|
||||
else
|
||||
fmpz_fdiv_q_2exp(x, y, -s);
|
||||
}
|
||||
|
||||
|
||||
/* Balanced product of linear factors (x+alpha_i) using
|
||||
fixed-point arithmetic with prec bits */
|
||||
static void
|
||||
balanced_product(fmpz * c, fmpz * alpha, slong len, slong prec)
|
||||
{
|
||||
if (len == 1)
|
||||
{
|
||||
fmpz_one(c + 1);
|
||||
fmpz_mul_2exp(c + 1, c + 1, prec);
|
||||
fmpz_set(c, alpha);
|
||||
}
|
||||
else if (len == 2)
|
||||
{
|
||||
fmpz_mul(c, alpha, alpha + 1);
|
||||
fmpz_fdiv_q_2exp(c, c, prec);
|
||||
fmpz_add(c + 1, alpha, alpha + 1);
|
||||
fmpz_one(c + 2);
|
||||
fmpz_mul_2exp(c + 2, c + 2, prec);
|
||||
}
|
||||
else
|
||||
{
|
||||
fmpz *L, *R;
|
||||
slong i, m;
|
||||
|
||||
m = len / 2;
|
||||
L = _fmpz_vec_init(len + 2);
|
||||
R = L + m + 1;
|
||||
|
||||
balanced_product(L, alpha, m, prec);
|
||||
balanced_product(R, alpha + m, len - m, prec);
|
||||
_fmpz_poly_mul(c, R, len - m + 1, L, m + 1);
|
||||
|
||||
for (i = 0; i < len + 1; i++)
|
||||
fmpz_fdiv_q_2exp(c + i, c + i, prec);
|
||||
|
||||
_fmpz_vec_clear(L, len + 2);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
_arith_cos_minpoly(fmpz * coeffs, slong d, ulong n)
|
||||
{
|
||||
slong i, j;
|
||||
fmpz * alpha;
|
||||
fmpz_t half;
|
||||
mpfr_t t, u;
|
||||
mp_bitcnt_t prec;
|
||||
slong exp;
|
||||
|
||||
if (n <= MAX_32BIT)
|
||||
{
|
||||
for (i = 0; i <= d; i++)
|
||||
fmpz_set_si(coeffs + i, lookup_table[n - 1][i]);
|
||||
return;
|
||||
}
|
||||
|
||||
/* Direct formula for odd primes > 3 */
|
||||
if (n_is_prime(n))
|
||||
{
|
||||
slong s = (n - 1) / 2;
|
||||
|
||||
switch (s % 4)
|
||||
{
|
||||
case 0:
|
||||
fmpz_set_si(coeffs, WORD(1));
|
||||
fmpz_set_si(coeffs + 1, -s);
|
||||
break;
|
||||
case 1:
|
||||
fmpz_set_si(coeffs, WORD(1));
|
||||
fmpz_set_si(coeffs + 1, s + 1);
|
||||
break;
|
||||
case 2:
|
||||
fmpz_set_si(coeffs, WORD(-1));
|
||||
fmpz_set_si(coeffs + 1, s);
|
||||
break;
|
||||
case 3:
|
||||
fmpz_set_si(coeffs, WORD(-1));
|
||||
fmpz_set_si(coeffs + 1, -s - 1);
|
||||
break;
|
||||
}
|
||||
|
||||
for (i = 2; i <= s; i++)
|
||||
{
|
||||
slong b = (s - i) % 2;
|
||||
fmpz_mul2_uiui(coeffs + i, coeffs + i - 2, s+i-b, s+2-b-i);
|
||||
fmpz_divexact2_uiui(coeffs + i, coeffs + i, i, i-1);
|
||||
fmpz_neg(coeffs + i, coeffs + i);
|
||||
}
|
||||
|
||||
return;
|
||||
}
|
||||
|
||||
prec = magnitude_bound(d) + 5 + FLINT_BIT_COUNT(d);
|
||||
|
||||
alpha = _fmpz_vec_init(d);
|
||||
fmpz_init(half);
|
||||
mpfr_init2(t, prec);
|
||||
mpfr_init2(u, prec);
|
||||
|
||||
fmpz_one(half);
|
||||
fmpz_mul_2exp(half, half, prec - 1);
|
||||
mpfr_const_pi(t, prec);
|
||||
mpfr_div_ui(t, t, n, MPFR_RNDN);
|
||||
|
||||
for (i = j = 0; j < d; i++)
|
||||
{
|
||||
if (n_gcd(n, i) == 1)
|
||||
{
|
||||
mpfr_mul_ui(u, t, 2 * i, MPFR_RNDN);
|
||||
mpfr_cos(u, u, MPFR_RNDN);
|
||||
mpfr_neg(u, u, MPFR_RNDN);
|
||||
exp = mpfr_get_z_2exp(_fmpz_promote(alpha + j), u);
|
||||
_fmpz_demote_val(alpha + j);
|
||||
fmpz_mul_or_div_2exp(alpha + j, alpha + j, exp + prec);
|
||||
j++;
|
||||
}
|
||||
}
|
||||
|
||||
balanced_product(coeffs, alpha, d, prec);
|
||||
|
||||
/* Scale and round */
|
||||
for (i = 0; i < d + 1; i++)
|
||||
{
|
||||
slong r = d;
|
||||
if ((n & (n - 1)) == 0)
|
||||
r--;
|
||||
fmpz_mul_2exp(coeffs + i, coeffs + i, r);
|
||||
fmpz_add(coeffs + i, coeffs + i, half);
|
||||
fmpz_fdiv_q_2exp(coeffs + i, coeffs + i, prec);
|
||||
}
|
||||
|
||||
fmpz_clear(half);
|
||||
mpfr_clear(t);
|
||||
mpfr_clear(u);
|
||||
_fmpz_vec_clear(alpha, d);
|
||||
}
|
||||
|
||||
void
|
||||
arith_cos_minpoly(fmpz_poly_t poly, ulong n)
|
||||
{
|
||||
if (n == 0)
|
||||
{
|
||||
fmpz_poly_set_ui(poly, UWORD(1));
|
||||
}
|
||||
else
|
||||
{
|
||||
slong d = (n <= 2) ? 1 : n_euler_phi(n) / 2;
|
||||
|
||||
fmpz_poly_fit_length(poly, d + 1);
|
||||
_arith_cos_minpoly(poly->coeffs, d, n);
|
||||
_fmpz_poly_set_length(poly, d + 1);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,160 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
_arith_cyclotomic_polynomial(fmpz * a, ulong n, mp_ptr factors,
|
||||
slong num_factors, ulong phi)
|
||||
{
|
||||
slong i, k;
|
||||
int small;
|
||||
ulong D;
|
||||
|
||||
D = phi / 2;
|
||||
|
||||
/* Phi_p(x) = 1 + x + x^2 + ... + x^{p-1} */
|
||||
if (num_factors == 1)
|
||||
{
|
||||
for (i = 0; i <= D; i++)
|
||||
fmpz_one(a + i);
|
||||
return;
|
||||
}
|
||||
|
||||
/* Phi_{2n}(x) = Phi_n(-x)*/
|
||||
if (factors[0] == UWORD(2))
|
||||
{
|
||||
_arith_cyclotomic_polynomial(a, n / 2, factors + 1,
|
||||
num_factors - 1, phi);
|
||||
for (i = 1; i <= D; i += 2)
|
||||
fmpz_neg(a + i, a + i);
|
||||
return;
|
||||
}
|
||||
|
||||
fmpz_one(a);
|
||||
for (i = 1; i <= D; i++)
|
||||
fmpz_zero(a + i);
|
||||
|
||||
/* Coefficients are guaranteed not to overflow an fmpz */
|
||||
small = (num_factors == 2) || /* Always +1/0/-1*/
|
||||
(n < WORD(10163195)) || /* At most 27 bits */
|
||||
(FLINT_BITS == 64 && n < WORD(169828113)); /* At most 60 bits */
|
||||
|
||||
/* Iterate over all divisors of n */
|
||||
for (k = 0; k < (WORD(1) << num_factors); k++)
|
||||
{
|
||||
int mu;
|
||||
ulong d;
|
||||
|
||||
mu = (num_factors & 1) ? -1 : 1;
|
||||
d = WORD(1);
|
||||
for (i = 0; i < num_factors; i++)
|
||||
{
|
||||
if ((k >> i) & 1)
|
||||
{
|
||||
d *= factors[i];
|
||||
mu = -mu;
|
||||
}
|
||||
}
|
||||
|
||||
/* Multiply by (x^d - 1)^{\mu(n/d)} */
|
||||
if (small)
|
||||
{
|
||||
if (mu == 1)
|
||||
for (i = D; i >= d; i--) a[i] -= a[i - d];
|
||||
else
|
||||
for (i = d; i <= D; i++) a[i] += a[i - d];
|
||||
}
|
||||
else
|
||||
{
|
||||
if (mu == 1)
|
||||
for (i = D; i >= d; i--) fmpz_sub(a + i, a + i, a + i - d);
|
||||
else
|
||||
for (i = d; i <= D; i++) fmpz_add(a + i, a + i, a + i - d);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
arith_cyclotomic_polynomial(fmpz_poly_t poly, ulong n)
|
||||
{
|
||||
n_factor_t factors;
|
||||
slong i, j;
|
||||
ulong s, phi;
|
||||
|
||||
if (n <= 2)
|
||||
{
|
||||
if (n == 0)
|
||||
{
|
||||
fmpz_poly_set_ui(poly, UWORD(1));
|
||||
}
|
||||
else
|
||||
{
|
||||
fmpz_poly_fit_length(poly, 2);
|
||||
fmpz_set_si(poly->coeffs, (n == 1) ? WORD(-1) : WORD(1));
|
||||
fmpz_set_si(poly->coeffs + 1, WORD(1));
|
||||
_fmpz_poly_set_length(poly, 2);
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* Write n = q * s where q is squarefree, compute the factors of q,
|
||||
and compute phi(s) which determines the degree of the polynomial. */
|
||||
n_factor_init(&factors);
|
||||
n_factor(&factors, n, 1);
|
||||
s = phi = UWORD(1);
|
||||
for (i = 0; i < factors.num; i++)
|
||||
{
|
||||
phi *= factors.p[i] - 1;
|
||||
while (factors.exp[i] > 1)
|
||||
{
|
||||
s *= factors.p[i];
|
||||
factors.exp[i]--;
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_poly_fit_length(poly, phi * s + 1);
|
||||
|
||||
/* Evaluate lower half of Phi_s(x) */
|
||||
_arith_cyclotomic_polynomial(poly->coeffs, n / s,
|
||||
factors.p, factors.num, phi);
|
||||
|
||||
/* Palindromic extension */
|
||||
for (i = 0; i < (phi + 1) / 2; i++)
|
||||
fmpz_set(poly->coeffs + phi - i, poly->coeffs + i);
|
||||
|
||||
/* Stretch */
|
||||
if (s != 1)
|
||||
{
|
||||
for (i = phi; i > 0; i--)
|
||||
{
|
||||
fmpz_set(poly->coeffs + i*s, poly->coeffs + i);
|
||||
for (j = 1; j < s; j++)
|
||||
fmpz_zero(poly->coeffs + i*s - j);
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_poly_set_length(poly, phi * s + 1);
|
||||
}
|
||||
|
|
@ -1,307 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
static const int mod4_tab[8] = { 2, 1, 3, 0, 0, 3, 1, 2 };
|
||||
|
||||
static const int gcd24_tab[24] = {
|
||||
24, 1, 2, 3, 4, 1, 6, 1, 8, 3, 2, 1,
|
||||
12, 1, 2, 3, 8, 1, 6, 1, 4, 3, 2, 1
|
||||
};
|
||||
|
||||
static mp_limb_t
|
||||
n_sqrtmod_2exp(mp_limb_t a, int k)
|
||||
{
|
||||
mp_limb_t x;
|
||||
int i;
|
||||
|
||||
if (a == 0 || k == 0)
|
||||
return 0;
|
||||
|
||||
if (k == 1)
|
||||
return 1;
|
||||
|
||||
if (k == 2)
|
||||
{
|
||||
if (a == 1)
|
||||
return 1;
|
||||
return 0;
|
||||
}
|
||||
|
||||
x = 1;
|
||||
for (i = 3; i < k; i++)
|
||||
x += (a - x * x) / 2;
|
||||
|
||||
if (k < FLINT_BITS)
|
||||
x &= ((UWORD(1) << k) - 1);
|
||||
|
||||
return x;
|
||||
}
|
||||
|
||||
static mp_limb_t
|
||||
n_sqrtmod_ppow(mp_limb_t a, mp_limb_t p, int k, mp_limb_t pk, mp_limb_t pkinv)
|
||||
{
|
||||
mp_limb_t r, t;
|
||||
int i;
|
||||
|
||||
r = n_sqrtmod(a, p);
|
||||
if (r == 0)
|
||||
return r;
|
||||
|
||||
i = 1;
|
||||
while (i < k)
|
||||
{
|
||||
t = n_mulmod2_preinv(r, r, pk, pkinv);
|
||||
t = n_submod(t, a, pk);
|
||||
t = n_mulmod2_preinv(t, n_invmod(n_addmod(r, r, pk), pk), pk, pkinv);
|
||||
r = n_submod(r, t, pk);
|
||||
i *= 2;
|
||||
}
|
||||
|
||||
return r;
|
||||
}
|
||||
|
||||
void
|
||||
trigprod_mul_prime_power(trig_prod_t prod, mp_limb_t k, mp_limb_t n,
|
||||
mp_limb_t p, int exp)
|
||||
{
|
||||
mp_limb_t m, mod, inv;
|
||||
|
||||
if (k <= 3)
|
||||
{
|
||||
if (k == 0)
|
||||
{
|
||||
prod->prefactor = 0;
|
||||
}
|
||||
else if (k == 2 && (n % 2 == 1))
|
||||
{
|
||||
prod->prefactor *= -1;
|
||||
}
|
||||
else if (k == 3)
|
||||
{
|
||||
switch (n % 3)
|
||||
{
|
||||
case 0:
|
||||
prod->prefactor *= 2;
|
||||
prod->cos_p[prod->n] = 1;
|
||||
prod->cos_q[prod->n] = 18;
|
||||
break;
|
||||
case 1:
|
||||
prod->prefactor *= -2;
|
||||
prod->cos_p[prod->n] = 7;
|
||||
prod->cos_q[prod->n] = 18;
|
||||
break;
|
||||
case 2:
|
||||
prod->prefactor *= -2;
|
||||
prod->cos_p[prod->n] = 5;
|
||||
prod->cos_q[prod->n] = 18;
|
||||
break;
|
||||
}
|
||||
prod->n++;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* Power of 2 */
|
||||
if (p == 2)
|
||||
{
|
||||
mod = 8 * k;
|
||||
inv = n_preinvert_limb(mod);
|
||||
|
||||
m = n_submod(1, n_mod2_preinv(24 * n, mod, inv), mod);
|
||||
m = n_sqrtmod_2exp(m, exp + 3);
|
||||
m = n_mulmod2_preinv(m, n_invmod(3, mod), mod, inv);
|
||||
|
||||
prod->prefactor *= n_jacobi(-1, m);
|
||||
if (exp % 2 == 1)
|
||||
prod->prefactor *= -1;
|
||||
prod->sqrt_p *= k;
|
||||
prod->cos_p[prod->n] = (mp_limb_signed_t)(k - m);
|
||||
prod->cos_q[prod->n] = 2 * k;
|
||||
prod->n++;
|
||||
return;
|
||||
}
|
||||
|
||||
/* Power of 3 */
|
||||
if (p == 3)
|
||||
{
|
||||
mod = 3 * k;
|
||||
inv = n_preinvert_limb(mod);
|
||||
|
||||
m = n_submod(1, n_mod2_preinv(24 * n, mod, inv), mod);
|
||||
m = n_sqrtmod_ppow(m, p, exp + 1, mod, inv);
|
||||
m = n_mulmod2_preinv(m, n_invmod(8, mod), mod, inv);
|
||||
|
||||
prod->prefactor *= (2 * n_jacobi_unsigned(m, 3));
|
||||
if (exp % 2 == 0)
|
||||
prod->prefactor *= -1;
|
||||
prod->sqrt_p *= k;
|
||||
prod->sqrt_q *= 3;
|
||||
prod->cos_p[prod->n] = (mp_limb_signed_t)(3 * k - 8 * m);
|
||||
prod->cos_q[prod->n] = 6 * k;
|
||||
prod->n++;
|
||||
return;
|
||||
}
|
||||
|
||||
/* Power of prime greater than 3 */
|
||||
inv = n_preinvert_limb(k);
|
||||
m = n_submod(1, n_mod2_preinv(24 * n, k, inv), k);
|
||||
|
||||
if (m % p == 0)
|
||||
{
|
||||
if (exp == 1)
|
||||
{
|
||||
prod->prefactor *= n_jacobi(3, k);
|
||||
prod->sqrt_p *= k;
|
||||
}
|
||||
else
|
||||
prod->prefactor = 0;
|
||||
return;
|
||||
}
|
||||
|
||||
m = n_sqrtmod_ppow(m, p, exp, k, inv);
|
||||
|
||||
if (m == 0)
|
||||
{
|
||||
prod->prefactor = 0;
|
||||
return;
|
||||
}
|
||||
|
||||
prod->prefactor *= 2;
|
||||
prod->prefactor *= n_jacobi(3, k);
|
||||
prod->sqrt_p *= k;
|
||||
prod->cos_p[prod->n] = 4 * n_mulmod2_preinv(m, n_invmod(24, k), k, inv);
|
||||
prod->cos_q[prod->n] = k;
|
||||
prod->n++;
|
||||
}
|
||||
|
||||
/*
|
||||
Solve (k2^2 * d2 * e) * n1 = (d2 * e * n + (k2^2 - 1) / d1) mod k2
|
||||
|
||||
TODO: test this on 32 bit
|
||||
*/
|
||||
static mp_limb_t
|
||||
solve_n1(mp_limb_t n, mp_limb_t k1, mp_limb_t k2,
|
||||
mp_limb_t d1, mp_limb_t d2, mp_limb_t e)
|
||||
{
|
||||
mp_limb_t inv, n1, u, t[2];
|
||||
|
||||
inv = n_preinvert_limb(k1);
|
||||
|
||||
umul_ppmm(t[1], t[0], k2, k2);
|
||||
sub_ddmmss(t[1], t[0], t[1], t[0], UWORD(0), UWORD(1));
|
||||
mpn_divrem_1(t, 0, t, 2, d1);
|
||||
|
||||
n1 = n_ll_mod_preinv(t[1], t[0], k1, inv);
|
||||
n1 = n_mod2_preinv(n1 + d2*e*n, k1, inv);
|
||||
|
||||
u = n_mulmod2_preinv(k2, k2, k1, inv);
|
||||
u = n_invmod(u * d2 * e, k1);
|
||||
n1 = n_mulmod2_preinv(n1, u, k1, inv);
|
||||
|
||||
return n1;
|
||||
}
|
||||
|
||||
|
||||
void
|
||||
arith_hrr_expsum_factored(trig_prod_t prod, mp_limb_t k, mp_limb_t n)
|
||||
{
|
||||
n_factor_t fac;
|
||||
int i;
|
||||
|
||||
if (k <= 1)
|
||||
{
|
||||
prod->prefactor = k;
|
||||
return;
|
||||
}
|
||||
|
||||
n_factor_init(&fac);
|
||||
n_factor(&fac, k, 0);
|
||||
|
||||
/* Repeatedly factor A_k(n) into A_k1(n1)*A_k2(n2) with k1, k2 coprime */
|
||||
for (i = 0; i + 1 < fac.num && prod->prefactor != 0; i++)
|
||||
{
|
||||
mp_limb_t p, k1, k2, inv, n1, n2;
|
||||
|
||||
p = fac.p[i];
|
||||
|
||||
/* k = 2 * k1 with k1 odd */
|
||||
if (p == UWORD(2) && fac.exp[i] == 1)
|
||||
{
|
||||
k2 = k / 2;
|
||||
inv = n_preinvert_limb(k2);
|
||||
|
||||
n2 = n_invmod(32, k2);
|
||||
n2 = n_mulmod2_preinv(n2,
|
||||
n_mod2_preinv(8*n + 1, k2, inv), k2, inv);
|
||||
n1 = ((k2 % 8 == 3) || (k2 % 8 == 5)) ^ (n & 1);
|
||||
|
||||
trigprod_mul_prime_power(prod, 2, n1, 2, 1);
|
||||
k = k2;
|
||||
n = n2;
|
||||
}
|
||||
/* k = 4 * k1 with k1 odd */
|
||||
else if (p == UWORD(2) && fac.exp[i] == 2)
|
||||
{
|
||||
k2 = k / 4;
|
||||
inv = n_preinvert_limb(k2);
|
||||
|
||||
n2 = n_invmod(128, k2);
|
||||
n2 = n_mulmod2_preinv(n2,
|
||||
n_mod2_preinv(8*n + 5, k2, inv), k2, inv);
|
||||
n1 = (n + mod4_tab[(k2 / 2) % 8]) % 4;
|
||||
|
||||
trigprod_mul_prime_power(prod, 4, n1, 2, 2);
|
||||
prod->prefactor *= -1;
|
||||
k = k2;
|
||||
n = n2;
|
||||
}
|
||||
/* k = k1 * k2 with k1 odd or divisible by 8 */
|
||||
else
|
||||
{
|
||||
mp_limb_t d1, d2, e;
|
||||
|
||||
k1 = n_pow(fac.p[i], fac.exp[i]);
|
||||
k2 = k / k1;
|
||||
|
||||
d1 = gcd24_tab[k1 % 24];
|
||||
d2 = gcd24_tab[k2 % 24];
|
||||
e = 24 / (d1 * d2);
|
||||
|
||||
n1 = solve_n1(n, k1, k2, d1, d2, e);
|
||||
n2 = solve_n1(n, k2, k1, d2, d1, e);
|
||||
|
||||
trigprod_mul_prime_power(prod, k1, n1, fac.p[i], fac.exp[i]);
|
||||
k = k2;
|
||||
n = n2;
|
||||
}
|
||||
}
|
||||
|
||||
if (fac.num != 0 && prod->prefactor != 0)
|
||||
trigprod_mul_prime_power(prod, k, n,
|
||||
fac.p[fac.num - 1], fac.exp[fac.num - 1]);
|
||||
|
||||
}
|
||||
|
|
@ -1,84 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_dedekind_sum(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
{
|
||||
if (fmpz_cmp_ui(k, UWORD(2)) <= 0 || fmpz_is_zero(h) || fmpz_equal(h, k))
|
||||
{
|
||||
fmpq_zero(s);
|
||||
}
|
||||
else if (fmpz_sgn(h) < 0)
|
||||
{
|
||||
fmpz_t t;
|
||||
fmpz_init(t);
|
||||
fmpz_neg(t, h);
|
||||
arith_dedekind_sum(s, t, k);
|
||||
fmpq_neg(s, s);
|
||||
fmpz_clear(t);
|
||||
}
|
||||
else
|
||||
{
|
||||
fmpz_t t, u, q;
|
||||
|
||||
fmpz_init(t);
|
||||
fmpz_init(u);
|
||||
fmpz_init(q);
|
||||
|
||||
fmpz_gcd(q, h, k);
|
||||
fmpz_divexact(t, h, q);
|
||||
fmpz_divexact(u, k, q);
|
||||
|
||||
if (fmpz_cmp(t, u) > 0)
|
||||
{
|
||||
fmpq_t r;
|
||||
fmpq_init(r);
|
||||
|
||||
/* r = (1 + h(h-3k) + k^2) / (12hk) */
|
||||
fmpz_mul_ui(fmpq_numref(r), u, UWORD(3));
|
||||
fmpz_sub(fmpq_numref(r), t, fmpq_numref(r));
|
||||
fmpz_mul(fmpq_numref(r), fmpq_numref(r), t);
|
||||
fmpz_addmul(fmpq_numref(r), u, u);
|
||||
fmpz_add_ui(fmpq_numref(r), fmpq_numref(r), UWORD(1));
|
||||
fmpz_mul(fmpq_denref(r), t, u);
|
||||
fmpz_mul_ui(fmpq_denref(r), fmpq_denref(r), UWORD(12));
|
||||
fmpq_canonicalise(r);
|
||||
arith_dedekind_sum_coprime(s, u, t);
|
||||
fmpq_sub(s, r, s);
|
||||
|
||||
fmpq_clear(r);
|
||||
}
|
||||
else
|
||||
{
|
||||
arith_dedekind_sum_coprime(s, t, u);
|
||||
}
|
||||
|
||||
fmpz_clear(t);
|
||||
fmpz_clear(u);
|
||||
fmpz_clear(q);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,54 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
/* Small enough that a numerical computation is safe */
|
||||
#define DOUBLE_CUTOFF (UWORD(1) << 21)
|
||||
|
||||
void
|
||||
arith_dedekind_sum_coprime(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
{
|
||||
if (fmpz_cmp_ui(k, DOUBLE_CUTOFF) < 0)
|
||||
{
|
||||
double t;
|
||||
|
||||
t = arith_dedekind_sum_coprime_d(*h, *k) * (6 * (*k));
|
||||
|
||||
/* Round to nearest after truncation */
|
||||
if (t > 0)
|
||||
t += 0.5;
|
||||
else
|
||||
t -= 0.5;
|
||||
|
||||
fmpz_set_d(fmpq_numref(s), t);
|
||||
fmpz_set_ui(fmpq_denref(s), UWORD(6) * (*k));
|
||||
fmpq_canonicalise(s);
|
||||
}
|
||||
else
|
||||
{
|
||||
arith_dedekind_sum_coprime_large(s, h, k);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,57 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
double
|
||||
arith_dedekind_sum_coprime_d(double h, double k)
|
||||
{
|
||||
double a, b, t, s, sign;
|
||||
|
||||
if (k <= 2)
|
||||
return 0.0;
|
||||
|
||||
a = k;
|
||||
b = h;
|
||||
s = 0.0;
|
||||
sign = 1.0;
|
||||
|
||||
while (b > 0)
|
||||
{
|
||||
s += sign * (1.0 + a*a + b*b) / (a * b);
|
||||
t = fmod(a, b);
|
||||
a = b;
|
||||
b = t;
|
||||
sign = -sign;
|
||||
}
|
||||
|
||||
s *= (1./12);
|
||||
|
||||
if (sign < 0)
|
||||
s -= 0.25;
|
||||
|
||||
return s;
|
||||
}
|
||||
|
|
@ -1,96 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_dedekind_sum_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
{
|
||||
fmpz_t sigma, p, pp, hh, kk, a, t;
|
||||
|
||||
int sign;
|
||||
|
||||
if (fmpz_cmp_ui(k, UWORD(2)) <= 0)
|
||||
{
|
||||
fmpq_zero(s);
|
||||
return;
|
||||
}
|
||||
|
||||
sign = 1;
|
||||
|
||||
fmpz_init(sigma);
|
||||
fmpz_init(hh);
|
||||
fmpz_init(kk);
|
||||
fmpz_init(p);
|
||||
fmpz_init(pp);
|
||||
fmpz_init(a);
|
||||
fmpz_init(t);
|
||||
|
||||
fmpz_set_ui(p, UWORD(1));
|
||||
fmpz_set(hh, h);
|
||||
fmpz_set(kk, k);
|
||||
|
||||
while (!fmpz_is_zero(hh))
|
||||
{
|
||||
fmpz_fdiv_qr(a, t, kk, hh);
|
||||
|
||||
if (sign == 1)
|
||||
fmpz_add(sigma, sigma, a);
|
||||
else
|
||||
fmpz_sub(sigma, sigma, a);
|
||||
|
||||
sign = -sign;
|
||||
|
||||
/* kk, hh = hh, kk mod hh */
|
||||
fmpz_swap(kk, hh);
|
||||
fmpz_swap(hh, t);
|
||||
|
||||
/* p, pp = a*p + pp, p */
|
||||
fmpz_addmul(pp, a, p);
|
||||
fmpz_swap(p, pp);
|
||||
}
|
||||
|
||||
if (sign < 0)
|
||||
fmpz_sub_ui(sigma, sigma, UWORD(3));
|
||||
|
||||
/* s = (sigma + (h - p*s) / p) / 12 */
|
||||
if (sign < 0)
|
||||
fmpz_add(fmpq_numref(s), h, pp);
|
||||
else
|
||||
fmpz_sub(fmpq_numref(s), h, pp);
|
||||
|
||||
fmpz_addmul(fmpq_numref(s), sigma, p);
|
||||
fmpz_mul_ui(fmpq_denref(s), p, UWORD(12));
|
||||
|
||||
_fmpq_canonicalise(fmpq_numref(s), fmpq_denref(s));
|
||||
|
||||
fmpz_clear(sigma);
|
||||
fmpz_clear(hh);
|
||||
fmpz_clear(kk);
|
||||
fmpz_clear(p);
|
||||
fmpz_clear(pp);
|
||||
fmpz_clear(a);
|
||||
fmpz_clear(t);
|
||||
}
|
||||
|
|
@ -1,82 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_dedekind_sum_naive(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
{
|
||||
fmpz_t i, j, q1, r1, q2, r2;
|
||||
|
||||
if (fmpz_is_zero(k))
|
||||
{
|
||||
fmpq_zero(s);
|
||||
return;
|
||||
}
|
||||
|
||||
fmpz_init(i);
|
||||
fmpz_init(j);
|
||||
fmpz_init(q1);
|
||||
fmpz_init(r1);
|
||||
fmpz_init(q2);
|
||||
fmpz_init(r2);
|
||||
|
||||
fmpz_zero(fmpq_numref(s));
|
||||
|
||||
for (fmpz_one(i); fmpz_cmp(i, k) < 0; fmpz_add_ui(i, i, 1))
|
||||
{
|
||||
fmpz_fdiv_qr(q1, r1, i, k);
|
||||
if (fmpz_is_zero(r1))
|
||||
continue;
|
||||
|
||||
fmpz_mul(j, h, i);
|
||||
fmpz_fdiv_qr(q2, r2, j, k);
|
||||
if (fmpz_is_zero(r2))
|
||||
continue;
|
||||
|
||||
fmpz_mul(q1, q1, k);
|
||||
fmpz_sub(q1, i, q1);
|
||||
fmpz_mul_ui(q1, q1, 2);
|
||||
fmpz_sub(q1, q1, k);
|
||||
|
||||
fmpz_mul(q2, q2, k);
|
||||
fmpz_sub(q2, j, q2);
|
||||
fmpz_mul_ui(q2, q2, 2);
|
||||
fmpz_sub(q2, q2, k);
|
||||
|
||||
fmpz_addmul(fmpq_numref(s), q1, q2);
|
||||
}
|
||||
|
||||
fmpz_mul(fmpq_denref(s), k, k);
|
||||
fmpz_mul_ui(fmpq_denref(s), fmpq_denref(s), 4);
|
||||
fmpq_canonicalise(s);
|
||||
|
||||
fmpz_clear(i);
|
||||
fmpz_clear(j);
|
||||
fmpz_clear(q1);
|
||||
fmpz_clear(r1);
|
||||
fmpz_clear(q2);
|
||||
fmpz_clear(r2);
|
||||
}
|
||||
|
|
@ -1,87 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
|
||||
/* note: destroys factors! */
|
||||
void
|
||||
_arith_divisor_sigma(fmpz_t res, const fmpz_factor_t factors, ulong k)
|
||||
{
|
||||
slong i;
|
||||
fmpz * p;
|
||||
fmpz_t r;
|
||||
|
||||
fmpz_one(res);
|
||||
|
||||
if (factors->num == 0)
|
||||
return;
|
||||
|
||||
fmpz_init(r);
|
||||
|
||||
if (k == 0)
|
||||
{
|
||||
for (i = 0; i < factors->num; i++)
|
||||
{
|
||||
fmpz_set_ui(r, factors->exp[i] + UWORD(1));
|
||||
fmpz_mul(res, res, r);
|
||||
}
|
||||
return;
|
||||
}
|
||||
else
|
||||
{
|
||||
for (i = 0; i < factors->num; i++)
|
||||
{
|
||||
p = factors->p + i;
|
||||
fmpz_set(p, factors->p + i);
|
||||
fmpz_pow_ui(p, p, k);
|
||||
fmpz_pow_ui(r, p, factors->exp[i] + UWORD(1));
|
||||
fmpz_sub_ui(r, r, UWORD(1));
|
||||
fmpz_sub_ui(p, p, UWORD(1));
|
||||
fmpz_divexact(p, r, p);
|
||||
}
|
||||
|
||||
_fmpz_vec_prod(res, factors->p, factors->num);
|
||||
}
|
||||
|
||||
fmpz_clear(r);
|
||||
}
|
||||
|
||||
void
|
||||
arith_divisor_sigma(fmpz_t res, const fmpz_t n, ulong k)
|
||||
{
|
||||
fmpz_factor_t factors;
|
||||
|
||||
if (fmpz_is_zero(n))
|
||||
{
|
||||
fmpz_zero(res);
|
||||
return;
|
||||
}
|
||||
|
||||
fmpz_factor_init(factors);
|
||||
fmpz_factor(factors, n);
|
||||
_arith_divisor_sigma(res, factors, k);
|
||||
fmpz_factor_clear(factors);
|
||||
}
|
||||
|
|
@ -1,165 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
|
||||
#define FLINT_NUM_TINY_DIVISORS FLINT_BITS
|
||||
|
||||
const int FLINT_TINY_DIVISORS_SIZE[FLINT_NUM_TINY_DIVISORS] = {
|
||||
0,1,2,2,3,2,4,2,4,3,4,2,6,2,4,4,5,2,6,2,6,4,4,2,8,3,4,4,6,2,8,2,
|
||||
#if FLINT64
|
||||
6,4,4,4,9,2,4,4,8,2,8,2,6,6,4,2,10,3,6,4,6,2,8,4,8,4,4,2,12,2,4,6
|
||||
#endif
|
||||
};
|
||||
|
||||
const ulong FLINT_TINY_DIVISORS_LOOKUP[FLINT_NUM_TINY_DIVISORS] = {
|
||||
UWORD(0x0),UWORD(0x2),UWORD(0x6),0xaUL,UWORD(0x16),UWORD(0x22),0x4eUL,UWORD(0x82),UWORD(0x116),0x20aUL,
|
||||
UWORD(0x426),UWORD(0x802),0x105eUL,UWORD(0x2002),UWORD(0x4086),0x802aUL,UWORD(0x10116),UWORD(0x20002),
|
||||
0x4024eUL,UWORD(0x80002),UWORD(0x100436),0x20008aUL,UWORD(0x400806),UWORD(0x800002),
|
||||
0x100115eUL,UWORD(0x2000022),UWORD(0x4002006),0x800020aUL,UWORD(0x10004096),UWORD(0x20000002),
|
||||
0x4000846eUL,UWORD(0x80000002),
|
||||
#if FLINT64
|
||||
UWORD(0x100010116),0x20000080aUL,UWORD(0x400020006),UWORD(0x8000000a2),0x100004125eUL,
|
||||
UWORD(0x2000000002),UWORD(0x4000080006),0x800000200aUL,UWORD(0x10000100536),
|
||||
UWORD(0x20000000002),0x400002040ceUL,UWORD(0x80000000002),UWORD(0x100000400816),
|
||||
0x20000000822aUL,UWORD(0x400000800006),UWORD(0x800000000002),0x100000101115eUL,
|
||||
UWORD(0x2000000000082),UWORD(0x4000002000426),0x800000002000aUL,UWORD(0x10000004002016),
|
||||
UWORD(0x20000000000002),0x4000000804024eUL,UWORD(0x80000000000822),
|
||||
UWORD(0x100000010004196),0x20000000008000aUL,UWORD(0x400000020000006),
|
||||
UWORD(0x800000000000002),0x100000004010947eUL,UWORD(0x2000000000000002),
|
||||
UWORD(0x4000000080000006),0x800000000020028aUL
|
||||
#endif
|
||||
};
|
||||
|
||||
|
||||
void
|
||||
_arith_divisors(fmpz *res, slong size, fmpz_factor_t factors)
|
||||
{
|
||||
slong i;
|
||||
slong *exp = flint_malloc(sizeof(slong) * factors->num);
|
||||
slong *exp_max = flint_malloc(sizeof(slong) * factors->num);
|
||||
fmpz *powers = _fmpz_vec_init(factors->num);
|
||||
fmpz_t d;
|
||||
|
||||
for (i = 0; i < factors->num; i++)
|
||||
{
|
||||
exp[i] = 0;
|
||||
fmpz_set(powers + i, factors->p + i);
|
||||
exp_max[i] = factors->exp[i];
|
||||
fmpz_pow_ui(powers + i, powers + i, exp_max[i]);
|
||||
}
|
||||
|
||||
fmpz_init(d);
|
||||
fmpz_one(res);
|
||||
fmpz_one(d);
|
||||
res++;
|
||||
|
||||
i = 0;
|
||||
while (1)
|
||||
{
|
||||
while (1)
|
||||
{
|
||||
if (i == factors->num)
|
||||
goto all_done;
|
||||
if (exp[i] < exp_max[i])
|
||||
{
|
||||
exp[i]++;
|
||||
fmpz_mul(d, d, factors->p + i);
|
||||
i = 0;
|
||||
break;
|
||||
}
|
||||
else
|
||||
{
|
||||
exp[i] = 0;
|
||||
fmpz_divexact(d, d, powers+i);
|
||||
i += 1;
|
||||
}
|
||||
}
|
||||
fmpz_set(res, d);
|
||||
res++;
|
||||
}
|
||||
|
||||
all_done:
|
||||
fmpz_clear(d);
|
||||
flint_free(exp);
|
||||
flint_free(exp_max);
|
||||
_fmpz_vec_clear(powers, factors->num);
|
||||
}
|
||||
|
||||
|
||||
void
|
||||
_arith_divisors_tiny(fmpz_poly_t res, slong n)
|
||||
{
|
||||
slong size;
|
||||
slong i, k;
|
||||
|
||||
size = FLINT_TINY_DIVISORS_SIZE[n];
|
||||
|
||||
fmpz_poly_fit_length(res, size);
|
||||
i = 0;
|
||||
for (k = 1; k <= n; k++)
|
||||
{
|
||||
if (FLINT_TINY_DIVISORS_LOOKUP[n] & (UWORD(1) << k))
|
||||
{
|
||||
fmpz_poly_set_coeff_si(res, i, k);
|
||||
i++;
|
||||
}
|
||||
}
|
||||
_fmpz_poly_set_length(res, size);
|
||||
return;
|
||||
}
|
||||
|
||||
void
|
||||
arith_divisors(fmpz_poly_t res, const fmpz_t n)
|
||||
{
|
||||
slong i, size, m;
|
||||
fmpz_factor_t factors;
|
||||
|
||||
if (!COEFF_IS_MPZ(*n))
|
||||
{
|
||||
m = fmpz_get_si(n);
|
||||
if (-FLINT_NUM_TINY_DIVISORS < m && m < FLINT_NUM_TINY_DIVISORS)
|
||||
{
|
||||
_arith_divisors_tiny(res, FLINT_ABS(m));
|
||||
return;
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_factor_init(factors);
|
||||
fmpz_factor(factors, n);
|
||||
|
||||
/* TODO: check for overflow for huge n */
|
||||
size = 1;
|
||||
for (i = 0; i < factors->num; i++)
|
||||
size *= factors->exp[i] + 1;
|
||||
|
||||
fmpz_poly_fit_length(res, size);
|
||||
_arith_divisors(res->coeffs, size, factors);
|
||||
_fmpz_poly_set_length(res, size);
|
||||
_fmpz_vec_sort(res->coeffs, size);
|
||||
|
||||
fmpz_factor_clear(factors);
|
||||
}
|
||||
|
|
@ -1,876 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010, 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Primorials
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_primorial(fmpz_t res, slong n)
|
||||
|
||||
Sets \code{res} to ``$n$ primorial'' or $n \#$, the product of all prime
|
||||
numbers less than or equal to $n$.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Harmonic numbers
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void _arith_harmonic_number(fmpz_t num, fmpz_t den, slong n)
|
||||
|
||||
Sets \code{(num, den)} to the reduced numerator and denominator of
|
||||
the $n$-th harmonic number $H_n = 1 + 1/2 + 1/3 + \dotsb + 1/n$. The
|
||||
result is zero if $n \leq 0$.
|
||||
|
||||
Table lookup is used for $H_n$ whose numerator and denominator
|
||||
fit in single limb. For larger $n$, the function
|
||||
\code{flint_mpn_harmonic_odd_balanced()} is used.
|
||||
|
||||
void arith_harmonic_number(fmpq_t x, slong n)
|
||||
|
||||
Sets \code{x} to the $n$-th harmonic number. This function is
|
||||
equivalent to \code{_arith_harmonic_number} apart from the output
|
||||
being a single \code{fmpq_t} variable.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Stirling numbers
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_stirling_number_1u(fmpz_t s, slong n, slong k)
|
||||
|
||||
void arith_stirling_number_1(fmpz_t s, slong n, slong k)
|
||||
|
||||
void arith_stirling_number_2(fmpz_t s, slong n, slong k)
|
||||
|
||||
Sets $s$ to $S(n,k)$ where $S(n,k)$ denotes an unsigned Stirling
|
||||
number of the first kind $|S_1(n, k)|$, a signed Stirling number
|
||||
of the first kind $S_1(n, k)$, or a Stirling number of the second
|
||||
kind $S_2(n, k)$. The Stirling numbers are defined using the
|
||||
generating functions
|
||||
\begin{align*}
|
||||
x_{(n)} & = \sum_{k=0}^n S_1(n,k) x^k \\
|
||||
x^{(n)} & = \sum_{k=0}^n |S_1(n,k)| x^k \\
|
||||
x^n & = \sum_{k=0}^n S_2(n,k) x_{(k)}
|
||||
\end{align*}
|
||||
where $x_{(n)} = x(x-1)(x-2) \dotsm (x-n+1)$ is a falling factorial
|
||||
and $x^{(n)} = x(x+1)(x+2) \dotsm (x+n-1)$ is a rising factorial.
|
||||
$S(n,k)$ is taken to be zero if $n < 0$ or $k < 0$.
|
||||
|
||||
These three functions are useful for computing isolated Stirling
|
||||
numbers efficiently. To compute a range of numbers, the vector or
|
||||
matrix versions should generally be used.
|
||||
|
||||
void arith_stirling_number_1u_vec(fmpz * row, slong n, slong klen)
|
||||
void arith_stirling_number_1_vec(fmpz * row, slong n, slong klen)
|
||||
void arith_stirling_number_2_vec(fmpz * row, slong n, slong klen)
|
||||
|
||||
Computes the row of Stirling numbers
|
||||
\code{S(n,0), S(n,1), S(n,2), ..., S(n,klen-1)}.
|
||||
|
||||
To compute a full row, this function can be called with
|
||||
\code{klen = n+1}. It is assumed that \code{klen} is at most $n + 1$.
|
||||
|
||||
void arith_stirling_number_1u_vec_next(fmpz * row, fmpz * prev, slong n,
|
||||
slong klen)
|
||||
|
||||
void arith_stirling_number_1_vec_next(fmpz * row, fmpz * prev, slong n,
|
||||
slong klen)
|
||||
|
||||
void arith_stirling_number_2_vec_next(fmpz * row, fmpz * prev, slong n,
|
||||
slong klen)
|
||||
|
||||
Given the vector \code{prev} containing a row of Stirling numbers
|
||||
\code{S(n-1,0), S(n-1,1), S(n-1,2), ..., S(n-1,klen-1)}, computes
|
||||
and stores in the row argument
|
||||
\code{S(n,0), S(n,1), S(n,2), ..., S(n,klen-1)}.
|
||||
|
||||
If \code{klen} is greater than \code{n}, the output ends with
|
||||
\code{S(n,n) = 1} followed by \code{S(n,n+1) = S(n,n+2) = ... = 0}.
|
||||
In this case, the input only needs to have length \code{n-1};
|
||||
only the input entries up to \code{S(n-1,n-2)} are read.
|
||||
|
||||
The \code{row} and \code{prev} arguments are permitted to be the
|
||||
same, meaning that the row will be updated in-place.
|
||||
|
||||
void arith_stirling_matrix_1u(fmpz_mat_t mat)
|
||||
void arith_stirling_matrix_1(fmpz_mat_t mat)
|
||||
void arith_stirling_matrix_2(fmpz_mat_t mat)
|
||||
|
||||
For an arbitrary $m$-by-$n$ matrix, writes the truncation of the
|
||||
infinite Stirling number matrix
|
||||
|
||||
\begin{lstlisting}
|
||||
row 0 : S(0,0)
|
||||
row 1 : S(1,0), S(1,1)
|
||||
row 2 : S(2,0), S(2,1), S(2,2)
|
||||
row 3 : S(3,0), S(3,1), S(3,2), S(3,3)
|
||||
\end{lstlisting}
|
||||
|
||||
up to row $m-1$ and column $n-1$ inclusive. The upper triangular
|
||||
part of the matrix is zeroed.
|
||||
|
||||
For any $n$, the $S_1$ and $S_2$ matrices thus obtained are
|
||||
inverses of each other.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Bell numbers
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_bell_number(fmpz_t b, ulong n)
|
||||
|
||||
Sets $b$ to the Bell number $B_n$, defined as the
|
||||
number of partitions of a set with $n$ members. Equivalently,
|
||||
$B_n = \sum_{k=0}^n S_2(n,k)$ where $S_2(n,k)$ denotes a Stirling number
|
||||
of the second kind.
|
||||
|
||||
This function automatically selects between table lookup, binary
|
||||
splitting, and the multimodular algorithm.
|
||||
|
||||
void arith_bell_number_bsplit(fmpz_t res, ulong n)
|
||||
|
||||
Computes the Bell number $B_n$ by evaluating a precise truncation of
|
||||
the series $B_n = e^{-1} \sum_{k=0}^{\infty} \frac{k^n}{k!}$ using
|
||||
binary splitting.
|
||||
|
||||
void arith_bell_number_multi_mod(fmpz_t res, ulong n)
|
||||
|
||||
Computes the Bell number $B_n$ using a multimodular algorithm.
|
||||
|
||||
This function evaluates the Bell number modulo several limb-size
|
||||
primes using\\ \code{arith_bell_number_nmod} and reconstructs the integer
|
||||
value using the fast Chinese remainder algorithm.
|
||||
A bound for the number of needed primes is computed using
|
||||
\code{arith_bell_number_size}.
|
||||
|
||||
void arith_bell_number_vec(fmpz * b, slong n)
|
||||
|
||||
Sets $b$ to the vector of Bell numbers $B_0, B_1, \ldots, B_{n-1}$
|
||||
inclusive. Automatically switches between the \code{recursive}
|
||||
and \code{multi_mod} algorithms depending on the size of $n$.
|
||||
|
||||
void arith_bell_number_vec_recursive(fmpz * b, slong n)
|
||||
|
||||
Sets $b$ to the vector of Bell numbers $B_0, B_1, \ldots, B_{n-1}$
|
||||
inclusive. This function uses table lookup if $B_{n-1}$ fits in a
|
||||
single word, and a standard triangular recurrence otherwise.
|
||||
|
||||
void arith_bell_number_vec_multi_mod(fmpz * b, slong n)
|
||||
|
||||
Sets $b$ to the vector of Bell numbers $B_0, B_1, \ldots, B_{n-1}$
|
||||
inclusive.
|
||||
|
||||
This function evaluates the Bell numbers modulo several limb-size
|
||||
primes using\\ \code{arith_bell_number_nmod_vec} and reconstructs the
|
||||
integer values using the fast Chinese remainder algorithm.
|
||||
A bound for the number of needed primes is computed using
|
||||
\code{arith_bell_number_size}.
|
||||
|
||||
mp_limb_t bell_number_nmod(ulong n, nmod_t mod)
|
||||
|
||||
Computes the Bell number $B_n$ modulo a prime $p$ given by \code{mod}
|
||||
|
||||
After handling special cases, we use the formula
|
||||
|
||||
$$B_n = \sum_{k=0}^n \frac{(n-k)^n}{(n-k)!}
|
||||
\sum_{j=0}^k \frac{(-1)^j}{j!}.$$
|
||||
|
||||
We arrange the operations in such a way that we only have to
|
||||
multiply (and not divide) in the main loop. As a further optimisation,
|
||||
we use sieving to reduce the number of powers that need to be
|
||||
evaluated. This results in $O(n)$ memory usage.
|
||||
|
||||
The divisions by factorials require $n > p$, so we fall back to
|
||||
calling\\ \code{bell_number_nmod_vec_recursive} and reading off the
|
||||
last entry when $p \le n$.
|
||||
|
||||
void arith_bell_number_nmod_vec(mp_ptr b, slong n, nmod_t mod)
|
||||
|
||||
Sets $b$ to the vector of Bell numbers $B_0, B_1, \ldots, B_{n-1}$
|
||||
inclusive modulo a prime $p$ given by \code{mod}. Automatically
|
||||
switches between the \code{recursive} and \code{series} algorithms
|
||||
depending on the size of $n$ and whether $p$ is large enough for the
|
||||
series algorithm to work.
|
||||
|
||||
void arith_bell_number_nmod_vec_recursive(mp_ptr b, slong n, nmod_t mod)
|
||||
|
||||
Sets $b$ to the vector of Bell numbers $B_0, B_1, \ldots, B_{n-1}$
|
||||
inclusive modulo a prime $p$ given by \code{mod}. This function uses
|
||||
table lookup if $B_{n-1}$ fits in a single word, and a standard
|
||||
triangular recurrence otherwise.
|
||||
|
||||
void arith_bell_number_nmod_vec_series(mp_ptr b, slong n, nmod_t mod)
|
||||
|
||||
Sets $b$ to the vector of Bell numbers $B_0, B_1, \ldots, B_{n-1}$
|
||||
inclusive modulo a prime $p$ given by \code{mod}. This function
|
||||
expands the exponential generating function
|
||||
$$\sum_{k=0}^{\infty} \frac{B_n}{n!} x^n = \exp(e^x-1).$$
|
||||
We require that $p \ge n$.
|
||||
|
||||
double arith_bell_number_size(ulong n)
|
||||
|
||||
Returns $b$ such that $B_n < 2^{\lfloor b \rfloor}$, using the inequality
|
||||
$$B_n < \left(\frac{0.792n}{\log(n+1)}\right)^n$$
|
||||
which is given in \cite{BerTas2010}.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Bernoulli numbers and polynomials
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void _arith_bernoulli_number(fmpz_t num, fmpz_t den, ulong n)
|
||||
|
||||
Sets \code{(num, den)} to the reduced numerator and denominator
|
||||
of the $n$-th Bernoulli number. As presently implemented,
|
||||
this function simply calls\\ \code{_arith_bernoulli_number_zeta}.
|
||||
|
||||
void arith_bernoulli_number(fmpq_t x, ulong n)
|
||||
|
||||
Sets \code{x} to the $n$-th Bernoulli number. This function is
|
||||
equivalent to\\ \code{_arith_bernoulli_number} apart from the output
|
||||
being a single \code{fmpq_t} variable.
|
||||
|
||||
void _arith_bernoulli_number_vec(fmpz * num, fmpz * den, slong n)
|
||||
|
||||
Sets the elements of \code{num} and \code{den} to the reduced
|
||||
numerators and denominators of the Bernoulli numbers
|
||||
$B_0, B_1, B_2, \ldots, B_{n-1}$ inclusive. This function automatically
|
||||
chooses between the \code{recursive}, \code{zeta} and \code{multi_mod}
|
||||
algorithms according to the size of $n$.
|
||||
|
||||
void arith_bernoulli_number_vec(fmpq * x, slong n)
|
||||
|
||||
Sets the \code{x} to the vector of Bernoulli numbers
|
||||
$B_0, B_1, B_2, \ldots, B_{n-1}$ inclusive. This function is
|
||||
equivalent to \code{_arith_bernoulli_number_vec} apart
|
||||
from the output being a single \code{fmpq} vector.
|
||||
|
||||
void arith_bernoulli_number_denom(fmpz_t den, ulong n)
|
||||
|
||||
Sets \code{den} to the reduced denominator of the $n$-th
|
||||
Bernoulli number $B_n$. For even $n$, the denominator is computed
|
||||
as the product of all primes $p$ for which $p - 1$ divides $n$;
|
||||
this property is a consequence of the von Staudt-Clausen theorem.
|
||||
For odd $n$, the denominator is trivial (\code{den} is set to 1 whenever
|
||||
$B_n = 0$). The initial sequence of values smaller than $2^{32}$ are
|
||||
looked up directly from a table.
|
||||
|
||||
double arith_bernoulli_number_size(ulong n)
|
||||
|
||||
Returns $b$ such that $|B_n| < 2^{\lfloor b \rfloor}$, using the inequality
|
||||
$$|B_n| < \frac{4 n!}{(2\pi)^n}$$ and $n! \le (n+1)^{n+1} e^{-n}$.
|
||||
No special treatment is given to odd $n$. Accuracy is not guaranteed
|
||||
if $n > 10^{14}$.
|
||||
|
||||
void arith_bernoulli_polynomial(fmpq_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the Bernoulli polynomial of degree $n$,
|
||||
$B_n(x) = \sum_{k=0}^n \binom{n}{k} B_k x^{n-k}$ where $B_k$
|
||||
is a Bernoulli number. This function basically calls
|
||||
\code{arith_bernoulli_number_vec} and then rescales the coefficients
|
||||
efficiently.
|
||||
|
||||
void _arith_bernoulli_number_zeta(fmpz_t num, fmpz_t den, ulong n)
|
||||
|
||||
Sets \code{(num, den)} to the reduced numerator and denominator
|
||||
of the $n$-th Bernoulli number.
|
||||
|
||||
This function first computes the exact denominator and a bound
|
||||
for the size of the numerator. It then computes an approximation
|
||||
of $|B_n| = 2n! \zeta(n) / (2 \pi)^n$ as a floating-point number
|
||||
and multiplies by the denominator to to obtain a real number
|
||||
that rounds to the exact numerator. For tiny $n$, the numerator
|
||||
is looked up from a table to avoid unnecessary overhead.
|
||||
|
||||
void _arith_bernoulli_number_vec_recursive(fmpz * num, fmpz * den, slong n)
|
||||
|
||||
Sets the elements of \code{num} and \code{den} to the reduced
|
||||
numerators and denominators of $B_0, B_1, B_2, \ldots, B_{n-1}$
|
||||
inclusive.
|
||||
|
||||
The first few entries are computed using \code{arith_bernoulli_number},
|
||||
and then Ramanujan's recursive formula expressing $B_m$ as a sum over
|
||||
$B_k$ for $k$ congruent to $m$ modulo 6 is applied repeatedly.
|
||||
|
||||
To avoid costly GCDs, the numerators are transformed internally
|
||||
to a common denominator and all operations are performed using
|
||||
integer arithmetic. This makes the algorithm fast for small $n$,
|
||||
say $n < 1000$. The common denominator is calculated directly
|
||||
as the primorial of $n + 1$.
|
||||
|
||||
%[1] http://en.wikipedia.org/w/index.php?
|
||||
% title=Bernoulli_number&oldid=405938876
|
||||
|
||||
void _arith_bernoulli_number_vec_zeta(fmpz * num, fmpz * den, slong n)
|
||||
|
||||
Sets the elements of \code{num} and \code{den} to the reduced
|
||||
numerators and denominators of $B_0, B_1, B_2, \ldots, B_{n-1}$
|
||||
inclusive. Uses repeated direct calls to\\
|
||||
\code{_arith_bernoulli_number_zeta}.
|
||||
|
||||
void _arith_bernoulli_number_vec_multi_mod(fmpz * num, fmpz * den, slong n)
|
||||
|
||||
Sets the elements of \code{num} and \code{den} to the reduced
|
||||
numerators and denominators of $B_0, B_1, B_2, \ldots, B_{n-1}$
|
||||
inclusive. Uses the generating function
|
||||
|
||||
$$\frac{x^2}{\cosh(x)-1} = \sum_{k=0}^{\infty}
|
||||
\frac{(2-4k) B_{2k}}{(2k)!} x^{2k}$$
|
||||
|
||||
which is evaluated modulo several limb-size primes using \code{nmod_poly}
|
||||
arithmetic to yield the numerators of the Bernoulli numbers after
|
||||
multiplication by the denominators and CRT reconstruction. This formula,
|
||||
given (incorrectly) in \citep{BuhlerCrandallSompolski1992}, saves about
|
||||
half of the time compared to the usual generating function $x/(e^x-1)$
|
||||
since the odd terms vanish.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Euler numbers and polynomials
|
||||
|
||||
Euler numbers are the integers $E_n$ defined by
|
||||
$$\frac{1}{\cosh(t)} = \sum_{n=0}^{\infty} \frac{E_n}{n!} t^n.$$
|
||||
With this convention, the odd-indexed numbers are zero and the even
|
||||
ones alternate signs, viz.
|
||||
$E_0, E_1, E_2, \ldots = 1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, \ldots$.
|
||||
The corresponding Euler polynomials are defined by
|
||||
$$\frac{2e^{xt}}{e^t+1} = \sum_{n=0}^{\infty} \frac{E_n(x)}{n!} t^n.$$
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_euler_number(fmpz_t res, ulong n)
|
||||
|
||||
Sets \code{res} to the Euler number $E_n$. Currently calls
|
||||
\code{_arith_euler_number_zeta}.
|
||||
|
||||
void arith_euler_number_vec(fmpz * res, slong n)
|
||||
|
||||
Computes the Euler numbers $E_0, E_1, \dotsc, E_{n-1}$ for $n \geq 0$
|
||||
and stores the result in \code{res}, which must be an initialised
|
||||
\code{fmpz} vector of sufficient size.
|
||||
|
||||
This function evaluates the even-index $E_k$ modulo several limb-size
|
||||
primes using the generating function and \code{nmod_poly} arithmetic.
|
||||
A tight bound for the number of needed primes is computed using
|
||||
\code{arith_euler_number_size}, and the final integer values are recovered
|
||||
using balanced CRT reconstruction.
|
||||
|
||||
double arith_euler_number_size(ulong n)
|
||||
|
||||
Returns $b$ such that $|E_n| < 2^{\lfloor b \rfloor}$, using the inequality
|
||||
$$|E_n| < \frac{2^{n+2} n!}{\pi^{n+1}}$$ and $n! \le (n+1)^{n+1} e^{-n}$.
|
||||
No special treatment is given to odd $n$.
|
||||
Accuracy is not guaranteed if $n > 10^{14}$.
|
||||
|
||||
void euler_polynomial(fmpq_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the Euler polynomial $E_n(x)$. Uses the formula
|
||||
$$E_n(x) = \frac{2}{n+1}\left(B_{n+1}(x) -
|
||||
2^{n+1}B_{n+1}\left(\frac{x}{2}\right)\right),$$
|
||||
with the Bernoulli polynomial $B_{n+1}(x)$ evaluated once
|
||||
using \code{bernoulli_polynomial} and then rescaled.
|
||||
|
||||
void _arith_euler_number_zeta(fmpz_t res, ulong n)
|
||||
|
||||
Sets \code{res} to the Euler number $E_n$. For even $n$, this function
|
||||
uses the relation $$|E_n| = \frac{2^{n+2} n!}{\pi^{n+1}} L(n+1)$$
|
||||
where $L(n+1)$ denotes the Dirichlet $L$-function with character
|
||||
$\chi = \{ 0, 1, 0, -1 \}$.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Legendre polynomials
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_legendre_polynomial(fmpq_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the $n$-th Legendre polynomial
|
||||
$$P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} \left[
|
||||
\left(x^2-1\right)^n \right].$$
|
||||
The coefficients are calculated using a hypergeometric recurrence.
|
||||
To improve performance, the common denominator is computed in one step
|
||||
and the coefficients are evaluated using integer arithmetic. The
|
||||
denominator is given by
|
||||
$\gcd(n!,2^n) = 2^{\lfloor n/2 \rfloor + \lfloor n/4 \rfloor + \ldots}.$
|
||||
|
||||
void arith_chebyshev_t_polynomial(fmpz_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the Chebyshev polynomial of the first kind $T_n(x)$,
|
||||
defined formally by $T_n(x) = \cos(n \cos^{-1}(x))$. The coefficients are
|
||||
calculated using a hypergeometric recurrence.
|
||||
|
||||
void arith_chebyshev_u_polynomial(fmpz_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the Chebyshev polynomial of the first kind $U_n(x)$,
|
||||
which satisfies $(n+1) U_n(x) = T'_{n+1}(x)$.
|
||||
The coefficients are calculated using a hypergeometric recurrence.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Multiplicative functions
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_euler_phi(fmpz_t res, const fmpz_t n)
|
||||
|
||||
Sets \code{res} to the Euler totient function $\phi(n)$, counting the
|
||||
number of positive integers less than or equal to $n$ that are coprime
|
||||
to $n$.
|
||||
|
||||
int arith_moebius_mu(const fmpz_t n)
|
||||
|
||||
Computes the Moebius function $\mu(n)$, which is defined as $\mu(n) = 0$
|
||||
if $n$ has a prime factor of multiplicity greater than $1$, $\mu(n) = -1$
|
||||
if $n$ has an odd number of distinct prime factors, and $\mu(n) = 1$ if
|
||||
$n$ has an even number of distinct prime factors. By convention,
|
||||
$\mu(0) = 0$.
|
||||
|
||||
void arith_divisor_sigma(fmpz_t res, const fmpz_t n, ulong k)
|
||||
|
||||
Sets \code{res} to $\sigma_k(n)$, the sum of $k$th powers of all
|
||||
divisors of $n$.
|
||||
|
||||
void arith_divisors(fmpz_poly_t res, const fmpz_t n)
|
||||
|
||||
Set the coefficients of the polynomial \code{res} to the divisors of $n$,
|
||||
including $1$ and $n$ itself, in ascending order.
|
||||
|
||||
void arith_ramanujan_tau(fmpz_t res, const fmpz_t n)
|
||||
|
||||
Sets \code{res} to the Ramanujan tau function $\tau(n)$ which is the
|
||||
coefficient of $q^n$ in the series expansion of
|
||||
$f(q) = q \prod_{k \geq 1} \bigl(1 - q^k\bigr)^{24}$.
|
||||
|
||||
We factor $n$ and use the identity $\tau(pq) = \tau(p) \tau(q)$
|
||||
along with the recursion
|
||||
$\tau(p^{r+1}) = \tau(p) \tau(p^r) - p^{11} \tau(p^{r-1})$
|
||||
for prime powers.
|
||||
|
||||
The base values $\tau(p)$ are obtained using the function
|
||||
\code{arith_ramanujan_tau_series()}. Thus the speed of
|
||||
\code{arith_ramanujan_tau()} depends on the largest prime factor of $n$.
|
||||
|
||||
Future improvement: optimise this function for small $n$, which
|
||||
could be accomplished using a lookup table or by calling
|
||||
\code{arith_ramanujan_tau_series()} directly.
|
||||
|
||||
void arith_ramanujan_tau_series(fmpz_poly_t res, slong n)
|
||||
|
||||
Sets \code{res} to the polynomial with coefficients
|
||||
$\tau(0),\tau(1), \dotsc, \tau(n-1)$, giving the initial $n$ terms
|
||||
in the series expansion of
|
||||
$f(q) = q \prod_{k \geq 1} \bigl(1-q^k\bigr)^{24}$.
|
||||
|
||||
We use the theta function identity
|
||||
|
||||
\begin{equation*}
|
||||
f(q) = q \Biggl( \sum_{k \geq 0} (-1)^k (2k+1) q^{k(k+1)/2} \Biggr)^8
|
||||
\end{equation*}
|
||||
|
||||
which is evaluated using three squarings. The first squaring is done
|
||||
directly since the polynomial is very sparse at this point.
|
||||
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Cyclotomic polynomials
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void _arith_cyclotomic_polynomial(fmpz * a, ulong n, mp_ptr factors,
|
||||
slong num_factors, ulong phi)
|
||||
|
||||
Sets \code{a} to the lower half of the cyclotomic polynomial $\Phi_n(x)$,
|
||||
given $n \ge 3$ which must be squarefree.
|
||||
|
||||
A precomputed array containing the prime factors of $n$ must be provided,
|
||||
as well as the value of the Euler totient function $\phi(n)$ as \code{phi}.
|
||||
If $n$ is even, 2 must be the first factor in the list.
|
||||
|
||||
The degree of $\Phi_n(x)$ is exactly $\phi(n)$. Only the low
|
||||
$(\phi(n) + 1) / 2$ coefficients are written; the high coefficients
|
||||
can be obtained afterwards by copying the low coefficients
|
||||
in reverse order, since $\Phi_n(x)$ is a palindrome for $n \ne 1$.
|
||||
|
||||
We use the sparse power series algorithm described as Algorithm 4
|
||||
\cite{ArnoldMonagan2011}. The algorithm is based on the identity
|
||||
|
||||
$$\Phi_n(x) = \prod_{d|n} (x^d - 1)^{\mu(n/d)}.$$
|
||||
|
||||
Treating the polynomial as a power series, the multiplications and
|
||||
divisions can be done very cheaply using repeated additions and
|
||||
subtractions. The complexity is $O(2^k \phi(n))$ where $k$ is the
|
||||
number of prime factors in $n$.
|
||||
|
||||
To improve efficiency for small $n$, we treat the \code{fmpz}
|
||||
coefficients as machine integers when there is no risk of overflow.
|
||||
The following bounds are given in Table 6 of \cite{ArnoldMonagan2011}:
|
||||
|
||||
For $n < 10163195$, the largest coefficient in any $\Phi_n(x)$
|
||||
has 27 bits, so machine arithmetic is safe on 32 bits.
|
||||
|
||||
For $n < 169828113$, the largest coefficient in any $\Phi_n(x)$
|
||||
has 60 bits, so machine arithmetic is safe on 64 bits.
|
||||
|
||||
Further, the coefficients are always $\pm 1$ or 0 if there are
|
||||
exactly two prime factors, so in this case machine arithmetic can be
|
||||
used as well.
|
||||
|
||||
Finally, we handle two special cases: if there is exactly one prime
|
||||
factor $n = p$, then $\Phi_n(x) = 1 + x + x^2 + \ldots + x^{n-1}$,
|
||||
and if $n = 2m$, we use $\Phi_n(x) = \Phi_m(-x)$ to fall back
|
||||
to the case when $n$ is odd.
|
||||
|
||||
void arith_cyclotomic_polynomial(fmpz_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the $n$th cyclotomic polynomial, defined as
|
||||
|
||||
$$\Phi_n(x) = \prod_{\omega} (x-\omega)$$
|
||||
|
||||
where $\omega$ runs over all the $n$th primitive roots of unity.
|
||||
|
||||
We factor $n$ into $n = qs$ where $q$ is squarefree,
|
||||
and compute $\Phi_q(x)$. Then $\Phi_n(x) = \Phi_q(x^s)$.
|
||||
|
||||
void _arith_cos_minpoly(fmpz * coeffs, slong d, ulong n)
|
||||
|
||||
For $n \ge 1$, sets \code{(coeffs, d+1)} to the minimal polynomial
|
||||
$\Psi_n(x)$ of $\cos(2 \pi / n)$, scaled to have integer coefficients
|
||||
by multiplying by $2^d$ ($2^{d-1}$ when $n$ is a power of two).
|
||||
|
||||
The polynomial $\Psi_n(x)$ is described in \cite{WaktinsZeitlin1993}.
|
||||
As proved in that paper, the roots of $\Psi_n(x)$ for $n \ge 3$ are
|
||||
$\cos(2 \pi k / n)$ where $0 \le k < d$ and where $\gcd(k, n) = 1$.
|
||||
|
||||
To calculate $\Psi_n(x)$, we compute the roots numerically with MPFR
|
||||
and use a balanced product tree to form a polynomial with fixed-point
|
||||
coefficients, i.e. an approximation of $2^p 2^d \Psi_n(x)$.
|
||||
|
||||
To determine the precision $p$, we note that the coefficients
|
||||
in $\prod_{i=1}^d (x - \alpha)$ can be bounded by the central
|
||||
coefficient in the binomial expansion of $(x+1)^d$.
|
||||
|
||||
When $n$ is an odd prime, we use a direct formula for the coefficients
|
||||
(\url{http://mathworld.wolfram.com/TrigonometryAngles.html}).
|
||||
|
||||
void arith_cos_minpoly(fmpz_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the minimal polynomial $\Psi_n(x)$ of
|
||||
$\cos(2 \pi / n)$, scaled to have integer coefficients. This
|
||||
polynomial has degree 1 if $n = 1$ or $n = 2$, and
|
||||
degree $\phi(n) / 2$ otherwise.
|
||||
|
||||
We allow $n = 0$ and define $\Psi_0 = 1$.
|
||||
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Swinnerton-Dyer polynomials
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_swinnerton_dyer_polynomial(fmpz_poly_t poly, ulong n)
|
||||
|
||||
Sets \code{poly} to the Swinnerton-Dyer polynomial $S_n$, defined as
|
||||
the integer polynomial
|
||||
$$S_n = \prod (x \pm \sqrt{2} \pm \sqrt{3}
|
||||
\pm \sqrt{5} \pm \ldots \pm \sqrt{p_n})$$
|
||||
where $p_n$ denotes the $n$-th prime number and all combinations
|
||||
of signs are taken. This polynomial has degree $2^n$ and is
|
||||
irreducible over the integers.
|
||||
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Landau's function
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_landau_function_vec(fmpz * res, slong len)
|
||||
|
||||
Computes the first \code{len} values of Landau's function $g(n)$
|
||||
starting with $g(0)$. Landau's function gives the largest order
|
||||
of an element of the symmetric group $S_n$.
|
||||
|
||||
Implements the ``basic algorithm'' given in
|
||||
\cite{DelegliseNicolasZimmermann2009}. The running time is
|
||||
$O(n^{3/2} / \sqrt{\log n})$.
|
||||
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Dedekind sums
|
||||
|
||||
Most of the definitions and relations used in the following section
|
||||
are given by Apostol \cite{Apostol1997}. The Dedekind sum $s(h,k)$ is
|
||||
defined for all integers $h$ and $k$ as
|
||||
|
||||
$$s(h,k) = \sum_{i=1}^{k-1} \left(\left(\frac{i}{k}\right)\right)
|
||||
\left(\left(\frac{hi}{k}\right)\right)$$
|
||||
|
||||
where
|
||||
|
||||
$$((x))=\begin{cases}
|
||||
x-\lfloor x\rfloor-1/2 &\mbox{if }
|
||||
x\in\mathbb{Q}\setminus\mathbb{Z}\\
|
||||
0 &\mbox{if }x\in\mathbb{Z}.
|
||||
\end{cases}$$
|
||||
|
||||
If $0 < h < k$ and $(h,k) = 1$, this reduces to
|
||||
|
||||
$$s(h,k) = \sum_{i=1}^{k-1} \frac{i}{k}
|
||||
\left(\frac{hi}{k}-\left\lfloor\frac{hi}{k}\right\rfloor
|
||||
-\frac{1}{2}\right).$$
|
||||
|
||||
The main formula for evaluating the series above is the following.
|
||||
Letting $r_0 = k$, $r_1 = h$, $r_2, r_3, \ldots, r_n, r_{n+1} = 1$
|
||||
be the remainder sequence in the Euclidean algorithm for
|
||||
computing GCD of $h$ and $k$,
|
||||
|
||||
$$s(h,k) = \frac{1-(-1)^n}{8} - \frac{1}{12} \sum_{i=1}^{n+1}
|
||||
(-1)^i \left(\frac{1+r_i^2+r_{i-1}^2}{r_i r_{i-1}}\right).$$
|
||||
|
||||
Writing $s(h,k) = p/q$, some useful properties employed are
|
||||
$|s| < k / 12$, $q | 6k$ and $2|p| < k^2$.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_dedekind_sum_naive(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
|
||||
Computes $s(h,k)$ for arbitrary $h$ and $k$ using a straightforward
|
||||
implementation of the defining sum using \code{fmpz} arithmetic.
|
||||
This function is slow except for very small $k$ and is mainly
|
||||
intended to be used for testing purposes.
|
||||
|
||||
double arith_dedekind_sum_coprime_d(double h, double k)
|
||||
|
||||
Returns an approximation of $s(h,k)$ computed by evaluating the
|
||||
remainder sequence sum using double-precision arithmetic.
|
||||
Assumes that $0 < h < k$ and $(h,k) = 1$, and that $h$, $k$ and
|
||||
their remainders can be represented exactly as doubles, e.g.
|
||||
$k < 2^{53}$.
|
||||
|
||||
We give a rough error analysis with IEEE double precision arithmetic,
|
||||
assuming $2 k^2 < 2^{53}$. By assumption, the terms in the sum evaluate
|
||||
exactly apart from the division. Thus each term is bounded in magnitude
|
||||
by $2k$ and its absolute error is bounded by $k 2^{-52}$.
|
||||
By worst-case analysis of the Euclidean algorithm, we also know that
|
||||
no more than 40 terms will be added.
|
||||
|
||||
It follows that the absolute error is at most $C k 2^{-53}$ for
|
||||
some constant $C$. If we multiply the output by $6 k$ in order
|
||||
to obtain an integer numerator, the order of magnitude of the error
|
||||
is around $6 C k^2 2^{-53}$, so rounding to the nearest integer gives
|
||||
a correct numerator whenever $k < 2^{26-d}$ for some small number of
|
||||
guard bits $d$. A computation has shown that $d = 5$ is sufficient,
|
||||
i.e. this function can be used for exact computation when
|
||||
$k < 2^{21} \approx 2 \times 10^6$. This bound can likely be improved.
|
||||
|
||||
void arith_dedekind_sum_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
|
||||
Computes $s(h,k)$ for $h$ and $k$ satisfying $0 \le h \le k$ and
|
||||
$(h,k) = 1$. This function effectively evaluates the remainder
|
||||
sequence sum using \code{fmpz} arithmetic, without optimising for
|
||||
any special cases. To avoid rational arithmetic, we use
|
||||
the integer algorithm of Knuth \cite{Knuth1977}.
|
||||
|
||||
void arith_dedekind_sum_coprime(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
|
||||
Computes $s(h,k)$ for $h$ and $k$ satisfying $0 \le h \le k$
|
||||
and $(h,k) = 1$.
|
||||
|
||||
This function calls \code{arith_dedekind_sum_coprime_d} if $k$ is small
|
||||
enough for a double-precision estimate of the sum to yield a correct
|
||||
numerator upon multiplication by $6k$ and rounding to the nearest integer.
|
||||
Otherwise, it calls \code{arith_dedekind_sum_coprime_large}.
|
||||
|
||||
void arith_dedekind_sum(fmpq_t s, const fmpz_t h, const fmpz_t k)
|
||||
|
||||
Computes $s(h,k)$ for arbitrary $h$ and $k$. If the caller
|
||||
can guarantee $0 < h < k$ and $(h,k) = 1$ ahead of time, it is always
|
||||
cheaper to call \code{arith_dedekind_sum_coprime}.
|
||||
|
||||
This function uses the following identities to reduce the general
|
||||
case to the situation where $0 < h < k$ and $(h,k) = 1$:
|
||||
If $k \le 2$ or $h = 0$, $s(h,k) = 0$.
|
||||
If $h < 0$, $s(h,k) = -s(-h,k)$.
|
||||
For any $q > 0$, $s(qh,qk) = s(h,k)$.
|
||||
If $0 < k < h$ and $(h,k) = 1$,
|
||||
$s(h,k) = (1+h(h-3k)+k^2) / (12hk) - t(k,h).$
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Number of partitions
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_number_of_partitions_vec(fmpz * res, slong len)
|
||||
|
||||
Computes first \code{len} values of the partition function $p(n)$
|
||||
starting with $p(0)$. Uses inversion of Euler's pentagonal series.
|
||||
|
||||
void arith_number_of_partitions_nmod_vec(mp_ptr res, slong len, nmod_t mod)
|
||||
|
||||
Computes first \code{len} values of the partition function $p(n)$
|
||||
starting with $p(0)$, modulo the modulus defined by \code{mod}.
|
||||
Uses inversion of Euler's pentagonal series.
|
||||
|
||||
void arith_hrr_expsum_factored(trig_prod_t prod, mp_limb_t k, mp_limb_t n)
|
||||
|
||||
Symbolically evaluates the exponential sum
|
||||
|
||||
$$A_k(n) = \sum_{h=0}^{k-1}
|
||||
\exp\left(\pi i \left[ s(h,k) - \frac{2hn}{k}\right]\right)$$
|
||||
|
||||
appearing in the Hardy-Ramanujan-Rademacher formula, where $s(h,k)$ is a
|
||||
Dedekind sum.
|
||||
|
||||
Rather than evaluating the sum naively, we factor $A_k(n)$ into a
|
||||
product of cosines based on the prime factorisation of $k$. This
|
||||
process is based on the identities given in \cite{Whiteman1956}.
|
||||
|
||||
The special \code{trig_prod_t} structure \code{prod} represents a
|
||||
product of cosines of rational arguments, multiplied by an algebraic
|
||||
prefactor. It must be pre-initialised with \code{trig_prod_init}.
|
||||
|
||||
This function assumes that $24k$ and $24n$ do not overflow a single limb.
|
||||
If $n$ is larger, it can be pre-reduced modulo $k$, since $A_k(n)$
|
||||
only depends on the value of $n \bmod k$.
|
||||
|
||||
void arith_number_of_partitions_mpfr(mpfr_t x, ulong n)
|
||||
|
||||
Sets the pre-initialised MPFR variable $x$ to the exact value of $p(n)$.
|
||||
The value is computed using the Hardy-Ramanujan-Rademacher formula.
|
||||
|
||||
The precision of $x$ will be changed to allow $p(n)$ to be represented
|
||||
exactly. The interface of this function may be updated in the future
|
||||
to allow computing an approximation of $p(n)$ to smaller precision.
|
||||
|
||||
The Hardy-Ramanujan-Rademacher formula is given with error bounds
|
||||
in \cite{Rademacher1937}. We evaluate it in the form
|
||||
|
||||
$$p(n) = \sum_{k=1}^N B_k(n) U(C/k) + R(n,N)$$
|
||||
|
||||
where
|
||||
|
||||
$$U(x) = \cosh(x) + \frac{\sinh(x)}{x},
|
||||
\quad C = \frac{\pi}{6} \sqrt{24n-1}$$
|
||||
|
||||
$$B_k(n) = \sqrt{\frac{3}{k}} \frac{4}{24n-1} A_k(n)$$
|
||||
|
||||
and where $A_k(n)$ is a certain exponential sum. The remainder satisfies
|
||||
|
||||
$$|R(n,N)| < \frac{44 \pi^2}{225 \sqrt{3}} N^{-1/2} +
|
||||
\frac{\pi \sqrt{2}}{75} \left(\frac{N}{n-1}\right)^{1/2}
|
||||
\sinh\left(\pi \sqrt{\frac{2}{3}} \frac{\sqrt{n}}{N} \right).$$
|
||||
|
||||
We choose $N$ such that $|R(n,N)| < 0.25$, and a working precision
|
||||
at term $k$ such that the absolute error of the term is expected to be
|
||||
less than $0.25 / N$. We also use a summation variable with increased
|
||||
precision, essentially making additions exact. Thus the sum of errors
|
||||
adds up to less than 0.5, giving the correct value of $p(n)$ when
|
||||
rounding to the nearest integer.
|
||||
|
||||
The remainder estimate at step $k$ provides an upper bound for the size
|
||||
of the $k$-th term. We add $\log_2 N$ bits to get low bits in the terms
|
||||
below $0.25 / N$ in magnitude.
|
||||
|
||||
Using \code{arith_hrr_expsum_factored}, each $B_k(n)$ evaluation
|
||||
is broken down to a product of cosines of exact rational multiples
|
||||
of $\pi$. We transform all angles to $(0, \pi/4)$ for optimal accuracy.
|
||||
|
||||
Since the evaluation of each term involves only $O(\log k)$ multiplications
|
||||
and evaluations of trigonometric functions of small angles, the
|
||||
relative rounding error is at most a few bits. We therefore just add
|
||||
an additional $\log_2 (C/k)$ bits for the $U(x)$ when $x$ is large.
|
||||
The cancellation of terms in $U(x)$ is of no concern, since Rademacher's
|
||||
bound allows us to terminate before $x$ becomes small.
|
||||
|
||||
This analysis should be performed in more detail to give a rigorous
|
||||
error bound, but the precision currently implemented is almost
|
||||
certainly sufficient, not least considering that Rademacher's
|
||||
remainder bound significantly overshoots the actual values.
|
||||
|
||||
To improve performance, we switch to doubles when the working precision
|
||||
becomes small enough. We also use a separate accumulator variable
|
||||
which gets added to the main sum periodically, in order to avoid
|
||||
costly updates of the full-precision result when $n$ is large.
|
||||
|
||||
void arith_number_of_partitions(fmpz_t x, ulong n)
|
||||
|
||||
Sets $x$ to $p(n)$, the number of ways that $n$ can be written
|
||||
as a sum of positive integers without regard to order.
|
||||
|
||||
This function uses a lookup table for $n < 128$ (where $p(n) < 2^{32}$),
|
||||
and otherwise calls \code{arith_number_of_partitions_mpfr}.
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
Sums of squares
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void arith_sum_of_squares(fmpz_t r, ulong k, const fmpz_t n)
|
||||
|
||||
Sets $r$ to the number of ways $r_k(n)$ in which $n$ can be represented
|
||||
as a sum of $k$ squares.
|
||||
|
||||
If $k = 2$ or $k = 4$, we write $r_k(n)$ as a divisor sum.
|
||||
|
||||
Otherwise, we either recurse on $k$ or compute the theta function
|
||||
expansion up to $O(x^{n+1})$ and read off the last coefficient.
|
||||
This is generally optimal.
|
||||
|
||||
void arith_sum_of_squares_vec(fmpz * r, ulong k, slong n)
|
||||
|
||||
For $i = 0, 1, \ldots, n-1$, sets $r_i$ to the number of
|
||||
representations of $i$ a sum of $k$ squares, $r_k(i)$.
|
||||
This effectively computes the $q$-expansion of $\vartheta_3(q)$
|
||||
raised to the $k$th power, i.e.
|
||||
|
||||
$$\vartheta_3^k(q) = \left( \sum_{i=-\infty}^{\infty} q^{i^2} \right)^k.$$
|
||||
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
MPFR extras
|
||||
|
||||
*******************************************************************************
|
||||
|
||||
void mpfr_pi_chudnovsky(mpfr_t x, mpfr_rnd_t rnd)
|
||||
|
||||
Sets \code{x} to $\pi$, rounded in the direction \code{rnd}.
|
||||
|
||||
Uses the Chudnovsky algorithm, which typically is about four times
|
||||
faster than the MPFR default function. As currently implemented, the
|
||||
value is not cached for repeated use.
|
||||
|
||||
|
|
@ -1,31 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void arith_euler_number(fmpz_t res, ulong n)
|
||||
{
|
||||
_arith_euler_number_zeta(res, n);
|
||||
}
|
||||
|
|
@ -1,38 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
double arith_euler_number_size(ulong n)
|
||||
{
|
||||
double x;
|
||||
|
||||
x = n + 2;
|
||||
x += ((n + 1) * log(n + 1) - n) * 1.44269504088897; /* 1/log(2) */
|
||||
x -= 1.6514961294723*(n+1); /* log2(pi) */
|
||||
|
||||
return x + 2;
|
||||
}
|
||||
|
|
@ -1,147 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
/* Computes length-m vector containing |E_{2k}| */
|
||||
static void
|
||||
__euler_number_vec_mod_p(mp_ptr res, mp_ptr tmp, slong m, nmod_t mod)
|
||||
{
|
||||
mp_limb_t fac, c;
|
||||
slong k;
|
||||
|
||||
/* Divide by factorials */
|
||||
fac = n_factorial_mod2_preinv(2*(m-1), mod.n, mod.ninv);
|
||||
c = n_invmod(fac, mod.n);
|
||||
for (k = m - 1; k >= 0; k--)
|
||||
{
|
||||
tmp[k] = c;
|
||||
c = n_mulmod2_preinv(c, (2*k)*(2*k-1), mod.n, mod.ninv);
|
||||
}
|
||||
|
||||
_nmod_poly_inv_series(res, tmp, m, mod);
|
||||
|
||||
/* Multiply by factorials */
|
||||
c = UWORD(1);
|
||||
for (k = 0; k < m; k++)
|
||||
{
|
||||
res[k] = n_mulmod2_preinv(res[k], c, mod.n, mod.ninv);
|
||||
c = n_mulmod2_preinv(c, (2*k+1)*(2*k+2), mod.n, mod.ninv);
|
||||
c = n_negmod(c, mod.n);
|
||||
}
|
||||
}
|
||||
|
||||
#define CRT_MAX_RESOLUTION 16
|
||||
|
||||
void __euler_number_vec_multi_mod(fmpz * res, slong n)
|
||||
{
|
||||
fmpz_comb_t comb[CRT_MAX_RESOLUTION];
|
||||
fmpz_comb_temp_t temp[CRT_MAX_RESOLUTION];
|
||||
mp_limb_t * primes;
|
||||
mp_limb_t * residues;
|
||||
mp_ptr * polys;
|
||||
mp_ptr temppoly;
|
||||
nmod_t mod;
|
||||
slong i, j, k, m, num_primes, num_primes_k, resolution;
|
||||
mp_bitcnt_t size, prime_bits;
|
||||
|
||||
if (n < 1)
|
||||
return;
|
||||
|
||||
/* Number of nonzero entries */
|
||||
m = (n + 1) / 2;
|
||||
|
||||
resolution = FLINT_MAX(1, FLINT_MIN(CRT_MAX_RESOLUTION, m / 16));
|
||||
|
||||
size = arith_euler_number_size(n);
|
||||
prime_bits = FLINT_BITS - 1;
|
||||
num_primes = (size + prime_bits - 1) / prime_bits;
|
||||
|
||||
primes = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
residues = flint_malloc(num_primes * sizeof(mp_limb_t));
|
||||
polys = flint_malloc(num_primes * sizeof(mp_ptr));
|
||||
|
||||
/* Compute Euler numbers mod p */
|
||||
primes[0] = n_nextprime(UWORD(1)<<prime_bits, 0);
|
||||
for (k = 1; k < num_primes; k++)
|
||||
primes[k] = n_nextprime(primes[k-1], 0);
|
||||
temppoly = _nmod_vec_init(m);
|
||||
for (k = 0; k < num_primes; k++)
|
||||
{
|
||||
polys[k] = _nmod_vec_init(m);
|
||||
nmod_init(&mod, primes[k]);
|
||||
__euler_number_vec_mod_p(polys[k], temppoly, m, mod);
|
||||
}
|
||||
|
||||
/* Init CRT comb */
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
fmpz_comb_init(comb[i], primes, num_primes * (i + 1) / resolution);
|
||||
fmpz_comb_temp_init(temp[i], comb[i]);
|
||||
}
|
||||
|
||||
/* Trivial entries */
|
||||
for (k = 1; k < n; k += 2)
|
||||
fmpz_zero(res + k);
|
||||
|
||||
/* Reconstruction */
|
||||
for (k = 0; k < n; k += 2)
|
||||
{
|
||||
size = arith_euler_number_size(k);
|
||||
/* Use only as large a comb as needed */
|
||||
num_primes_k = (size + prime_bits - 1) / prime_bits;
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
if (comb[i]->num_primes >= num_primes_k)
|
||||
break;
|
||||
}
|
||||
num_primes_k = comb[i]->num_primes;
|
||||
for (j = 0; j < num_primes_k; j++)
|
||||
residues[j] = polys[j][k / 2];
|
||||
fmpz_multi_CRT_ui(res + k, residues, comb[i], temp[i], 0);
|
||||
if (k % 4)
|
||||
fmpz_neg(res + k, res + k);
|
||||
}
|
||||
|
||||
/* Cleanup */
|
||||
for (k = 0; k < num_primes; k++)
|
||||
_nmod_vec_clear(polys[k]);
|
||||
_nmod_vec_clear(temppoly);
|
||||
for (i = 0; i < resolution; i++)
|
||||
{
|
||||
fmpz_comb_temp_clear(temp[i]);
|
||||
fmpz_comb_clear(comb[i]);
|
||||
}
|
||||
|
||||
flint_free(primes);
|
||||
flint_free(residues);
|
||||
flint_free(polys);
|
||||
}
|
||||
|
||||
void arith_euler_number_vec(fmpz * res, slong n)
|
||||
{
|
||||
__euler_number_vec_multi_mod(res, n);
|
||||
}
|
||||
|
|
@ -1,80 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void _arith_euler_number_zeta(fmpz_t res, ulong n)
|
||||
{
|
||||
mpz_t r;
|
||||
mpfr_t t, z, pi;
|
||||
mp_bitcnt_t prec, pi_prec;
|
||||
|
||||
if (n % 2)
|
||||
{
|
||||
fmpz_zero(res);
|
||||
return;
|
||||
}
|
||||
|
||||
if (n < SMALL_EULER_LIMIT)
|
||||
{
|
||||
fmpz_set_ui(res, euler_number_small[n / 2]);
|
||||
if (n % 4 == 2)
|
||||
fmpz_neg(res, res);
|
||||
return;
|
||||
}
|
||||
|
||||
prec = arith_euler_number_size(n) + 10;
|
||||
pi_prec = prec + FLINT_BIT_COUNT(n);
|
||||
|
||||
mpz_init(r);
|
||||
mpfr_init2(t, prec);
|
||||
mpfr_init2(z, prec);
|
||||
mpfr_init2(pi, pi_prec);
|
||||
|
||||
flint_mpz_fac_ui(r, n);
|
||||
mpfr_set_z(t, r, GMP_RNDN);
|
||||
mpfr_mul_2exp(t, t, n + 2, GMP_RNDN);
|
||||
|
||||
/* pi^(n + 1) * L(n+1) */
|
||||
mpfr_zeta_inv_euler_product(z, n + 1, 1);
|
||||
mpfr_const_pi(pi, GMP_RNDN);
|
||||
mpfr_pow_ui(pi, pi, n + 1, GMP_RNDN);
|
||||
mpfr_mul(z, z, pi, GMP_RNDN);
|
||||
|
||||
mpfr_div(t, t, z, GMP_RNDN);
|
||||
|
||||
/* round */
|
||||
mpfr_round(t, t);
|
||||
mpfr_get_z(r, t, GMP_RNDN);
|
||||
fmpz_set_mpz(res, r);
|
||||
|
||||
if (n % 4 == 2)
|
||||
fmpz_neg(res, res);
|
||||
|
||||
mpz_clear(r);
|
||||
mpfr_clear(t);
|
||||
mpfr_clear(z);
|
||||
mpfr_clear(pi);
|
||||
}
|
||||
|
|
@ -1,67 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmpz.h"
|
||||
#include "arith.h"
|
||||
|
||||
void arith_euler_phi(fmpz_t res, const fmpz_t n)
|
||||
{
|
||||
fmpz_factor_t factors;
|
||||
fmpz_t t;
|
||||
ulong exp;
|
||||
slong i;
|
||||
|
||||
if (fmpz_sgn(n) <= 0)
|
||||
{
|
||||
fmpz_zero(res);
|
||||
return;
|
||||
}
|
||||
|
||||
if (fmpz_abs_fits_ui(n))
|
||||
{
|
||||
fmpz_set_ui(res, n_euler_phi(fmpz_get_ui(n)));
|
||||
return;
|
||||
}
|
||||
|
||||
fmpz_factor_init(factors);
|
||||
fmpz_factor(factors, n);
|
||||
fmpz_one(res);
|
||||
|
||||
fmpz_init(t);
|
||||
for (i = 0; i < factors->num; i++)
|
||||
{
|
||||
fmpz_sub_ui(t, factors->p + i, UWORD(1));
|
||||
fmpz_mul(res, res, t);
|
||||
exp = factors->exp[i];
|
||||
if (exp != 1)
|
||||
{
|
||||
fmpz_pow_ui(t, factors->p + i, exp - UWORD(1));
|
||||
fmpz_mul(res, res, t);
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(t);
|
||||
fmpz_factor_clear(factors);
|
||||
}
|
||||
|
|
@ -1,53 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void arith_euler_polynomial(fmpq_poly_t poly, ulong n)
|
||||
{
|
||||
fmpz_t t;
|
||||
slong k;
|
||||
|
||||
if (n == 0)
|
||||
{
|
||||
fmpq_poly_set_ui(poly, UWORD(1));
|
||||
return;
|
||||
}
|
||||
|
||||
arith_bernoulli_polynomial(poly, n + 1);
|
||||
|
||||
fmpz_init(t);
|
||||
fmpz_set_si(t, WORD(-2));
|
||||
for (k = n; k >= 0; k--)
|
||||
{
|
||||
fmpz_mul(poly->coeffs + k, poly->coeffs + k, t);
|
||||
fmpz_mul_ui(t, t, UWORD(2));
|
||||
fmpz_sub_ui(t, t, UWORD(2));
|
||||
}
|
||||
fmpz_zero(poly->coeffs + n + 1);
|
||||
fmpz_mul_ui(poly->den, poly->den, n + 1);
|
||||
fmpq_poly_canonicalise(poly);
|
||||
fmpz_clear(t);
|
||||
}
|
||||
|
|
@ -1,124 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "mpn_extras.h"
|
||||
#include "arith.h"
|
||||
|
||||
#if FLINT64
|
||||
#define FLINT_HARMONIC_MAX_TINY 46
|
||||
#else
|
||||
#define FLINT_HARMONIC_MAX_TINY 24
|
||||
#endif
|
||||
|
||||
const mp_limb_t FLINT_HARMONIC_TINY_P[] =
|
||||
{
|
||||
UWORD(0), UWORD(1), UWORD(3), UWORD(11), UWORD(25), UWORD(137), UWORD(49), UWORD(363), UWORD(761), UWORD(7129), UWORD(7381),
|
||||
UWORD(83711), UWORD(86021), UWORD(1145993), UWORD(1171733), UWORD(1195757), UWORD(2436559), UWORD(42142223),
|
||||
UWORD(14274301), UWORD(275295799), UWORD(55835135), UWORD(18858053), UWORD(19093197), UWORD(444316699),
|
||||
UWORD(1347822955),
|
||||
#if FLINT64
|
||||
UWORD(34052522467), UWORD(34395742267), UWORD(312536252003), UWORD(315404588903),
|
||||
UWORD(9227046511387), UWORD(9304682830147), UWORD(290774257297357), UWORD(586061125622639),
|
||||
UWORD(53676090078349), UWORD(54062195834749), UWORD(54437269998109), UWORD(54801925434709),
|
||||
UWORD(2040798836801833), UWORD(2053580969474233), UWORD(2066035355155033),
|
||||
UWORD(2078178381193813), UWORD(85691034670497533), UWORD(12309312989335019),
|
||||
UWORD(532145396070491417), UWORD(5884182435213075787), UWORD(5914085889685464427),
|
||||
UWORD(5943339269060627227),
|
||||
#endif
|
||||
};
|
||||
|
||||
const mp_limb_t FLINT_HARMONIC_TINY_Q[] =
|
||||
{
|
||||
UWORD(1), UWORD(1), UWORD(2), UWORD(6), UWORD(12), UWORD(60), UWORD(20), UWORD(140), UWORD(280), UWORD(2520), UWORD(2520),
|
||||
UWORD(27720), UWORD(27720), UWORD(360360), UWORD(360360), UWORD(360360), UWORD(720720), UWORD(12252240),
|
||||
UWORD(4084080), UWORD(77597520), UWORD(15519504), UWORD(5173168), UWORD(5173168), UWORD(118982864),
|
||||
UWORD(356948592),
|
||||
#if FLINT64
|
||||
UWORD(8923714800), UWORD(8923714800), UWORD(80313433200), UWORD(80313433200), UWORD(2329089562800),
|
||||
UWORD(2329089562800), UWORD(72201776446800), UWORD(144403552893600), UWORD(13127595717600),
|
||||
UWORD(13127595717600), UWORD(13127595717600), UWORD(13127595717600), UWORD(485721041551200),
|
||||
UWORD(485721041551200), UWORD(485721041551200), UWORD(485721041551200),
|
||||
UWORD(19914562703599200), UWORD(2844937529085600), UWORD(122332313750680800),
|
||||
UWORD(1345655451257488800), UWORD(1345655451257488800), UWORD(1345655451257488800),
|
||||
#endif
|
||||
};
|
||||
|
||||
static void
|
||||
_mpq_harmonic_odd_balanced(fmpz_t num, fmpz_t den, slong n)
|
||||
{
|
||||
mpz_t p, q;
|
||||
|
||||
mp_ptr t, v;
|
||||
mp_size_t ts, vs;
|
||||
slong size;
|
||||
|
||||
if (n <= 0)
|
||||
{
|
||||
fmpz_zero(num);
|
||||
fmpz_one(den);
|
||||
return;
|
||||
}
|
||||
|
||||
/* TODO: we could avoid the copying/allocation overhead when there
|
||||
is guaranteed to be sufficient space in res already */
|
||||
|
||||
size = FLINT_BIT_COUNT(n) * (n+2) + 2*FLINT_BITS;
|
||||
mpz_init2(p, size);
|
||||
mpz_init2(q, size);
|
||||
t = p->_mp_d;
|
||||
v = q->_mp_d;
|
||||
|
||||
flint_mpn_harmonic_odd_balanced(t, &ts, v, &vs, 1, n+1, n, 1);
|
||||
p->_mp_size = ts;
|
||||
q->_mp_size = vs;
|
||||
|
||||
fmpz_set_mpz(num, p);
|
||||
fmpz_set_mpz(den, q);
|
||||
|
||||
mpz_clear(p);
|
||||
mpz_clear(q);
|
||||
|
||||
_fmpq_canonicalise(num, den);
|
||||
}
|
||||
|
||||
void _arith_harmonic_number(fmpz_t num, fmpz_t den, slong n)
|
||||
{
|
||||
n = FLINT_MAX(n, 0);
|
||||
|
||||
if (n <= FLINT_HARMONIC_MAX_TINY)
|
||||
{
|
||||
fmpz_set_ui(num, FLINT_HARMONIC_TINY_P[n]);
|
||||
fmpz_set_ui(den, FLINT_HARMONIC_TINY_Q[n]);
|
||||
}
|
||||
else
|
||||
{
|
||||
_mpq_harmonic_odd_balanced(num, den, n);
|
||||
}
|
||||
}
|
||||
|
||||
void arith_harmonic_number(fmpq_t x, slong n)
|
||||
{
|
||||
_arith_harmonic_number(fmpq_numref(x), fmpq_denref(x), n);
|
||||
}
|
||||
|
|
@ -1,68 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
void arith_landau_function_vec(fmpz * res, slong len)
|
||||
{
|
||||
mp_limb_t p, pmax;
|
||||
mp_limb_t pk, pkhi;
|
||||
fmpz_t a;
|
||||
ulong k, n;
|
||||
|
||||
if (len < 1)
|
||||
return;
|
||||
|
||||
for (k = 0; k < len; k++)
|
||||
fmpz_one(res + k);
|
||||
|
||||
pmax = 1.328 * sqrt(len*log(len) + 1);
|
||||
|
||||
fmpz_init(a);
|
||||
|
||||
for (p = UWORD(2); p <= pmax; p = n_nextprime(p, 0))
|
||||
{
|
||||
for (n = len - 1; n >= p; n--)
|
||||
{
|
||||
pk = p;
|
||||
pkhi = UWORD(0);
|
||||
|
||||
for (k = 1; k <= len; k++)
|
||||
{
|
||||
if (pk > n || pkhi)
|
||||
break;
|
||||
|
||||
fmpz_mul_ui(a, res + n - pk, pk);
|
||||
if (fmpz_cmp(res + n, a) < 0)
|
||||
fmpz_set(res + n, a);
|
||||
|
||||
umul_ppmm(pkhi, pk, pk, p);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(a);
|
||||
}
|
||||
|
|
@ -1,97 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
static __inline__ void __legendre_denom(fmpz_t den, ulong n)
|
||||
{
|
||||
ulong d, k;
|
||||
d = k = n >> 1;
|
||||
|
||||
while (k)
|
||||
{
|
||||
k >>= 1;
|
||||
d += k;
|
||||
}
|
||||
|
||||
fmpz_one(den);
|
||||
fmpz_mul_2exp(den, den, d);
|
||||
}
|
||||
|
||||
void _arith_legendre_polynomial(fmpz * coeffs, fmpz_t den, ulong n)
|
||||
{
|
||||
fmpz * r;
|
||||
int odd;
|
||||
slong k;
|
||||
ulong L;
|
||||
|
||||
L = n / 2;
|
||||
odd = n % 2;
|
||||
|
||||
r = coeffs + odd;
|
||||
|
||||
__legendre_denom(den, n);
|
||||
|
||||
fmpz_bin_uiui(r, n, L);
|
||||
fmpz_mul(r, r, den);
|
||||
if (odd)
|
||||
fmpz_mul_ui(r, r, L + 1);
|
||||
fmpz_fdiv_q_2exp(r, r, 2*L);
|
||||
if (L % 2)
|
||||
fmpz_neg(r, r);
|
||||
|
||||
for (k = 1; k <= L; k++)
|
||||
{
|
||||
fmpz_mul2_uiui(r + 2, r, L + 1 - k, 2*k + 2*L - 1 + 2*odd);
|
||||
fmpz_divexact2_uiui(r + 2, r + 2, k, 2*k - 1 + 2*odd);
|
||||
fmpz_neg(r + 2, r + 2);
|
||||
r += 2;
|
||||
}
|
||||
|
||||
for (k = 1 - odd; k < n; k += 2)
|
||||
fmpz_zero(coeffs + k);
|
||||
}
|
||||
|
||||
void arith_legendre_polynomial(fmpq_poly_t poly, ulong n)
|
||||
{
|
||||
if (n == 0)
|
||||
{
|
||||
fmpq_poly_set_ui(poly, UWORD(1));
|
||||
return;
|
||||
}
|
||||
|
||||
fmpq_poly_fit_length(poly, n + 1);
|
||||
|
||||
if (n == 1)
|
||||
{
|
||||
fmpz_zero(poly->coeffs);
|
||||
fmpz_one(poly->coeffs + 1);
|
||||
fmpz_one(poly->den);
|
||||
}
|
||||
else
|
||||
_arith_legendre_polynomial(poly->coeffs, poly->den, n);
|
||||
|
||||
_fmpq_poly_set_length(poly, n + 1);
|
||||
}
|
||||
|
|
@ -1,56 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmpz.h"
|
||||
#include "arith.h"
|
||||
|
||||
int arith_moebius_mu(const fmpz_t n)
|
||||
{
|
||||
fmpz_factor_t factors;
|
||||
slong i;
|
||||
int mu;
|
||||
|
||||
if (fmpz_abs_fits_ui(n))
|
||||
return n_moebius_mu(fmpz_get_ui(n));
|
||||
|
||||
fmpz_factor_init(factors);
|
||||
fmpz_factor(factors, n);
|
||||
|
||||
mu = 1;
|
||||
for (i = 0; i < factors->num; i++)
|
||||
{
|
||||
if (factors->exp[i] != UWORD(1))
|
||||
{
|
||||
mu = 0;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
if (factors->num % 2)
|
||||
mu = -mu;
|
||||
|
||||
fmpz_factor_clear(factors);
|
||||
return mu;
|
||||
}
|
||||
|
|
@ -1,70 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
/* This nice round number precisely fits on 32 bits */
|
||||
#define NUMBER_OF_SMALL_PARTITIONS 128
|
||||
|
||||
const unsigned int
|
||||
partitions_lookup[NUMBER_OF_SMALL_PARTITIONS] =
|
||||
{
|
||||
UWORD(1),UWORD(1),UWORD(2),UWORD(3),UWORD(5),UWORD(7),UWORD(11),UWORD(15),UWORD(22),UWORD(30),UWORD(42),UWORD(56),UWORD(77),UWORD(101),UWORD(135),
|
||||
UWORD(176),UWORD(231),UWORD(297),UWORD(385),UWORD(490),UWORD(627),UWORD(792),UWORD(1002),UWORD(1255),UWORD(1575),UWORD(1958),
|
||||
UWORD(2436),UWORD(3010),UWORD(3718),UWORD(4565),UWORD(5604),UWORD(6842),UWORD(8349),UWORD(10143),UWORD(12310),UWORD(14883),
|
||||
UWORD(17977),UWORD(21637),UWORD(26015),UWORD(31185),UWORD(37338),UWORD(44583),UWORD(53174),UWORD(63261),UWORD(75175),
|
||||
UWORD(89134),UWORD(105558),UWORD(124754),UWORD(147273),UWORD(173525),UWORD(204226),UWORD(239943),UWORD(281589),
|
||||
UWORD(329931),UWORD(386155),UWORD(451276),UWORD(526823),UWORD(614154),UWORD(715220),UWORD(831820),UWORD(966467),
|
||||
UWORD(1121505),UWORD(1300156),UWORD(1505499),UWORD(1741630),UWORD(2012558),UWORD(2323520),UWORD(2679689),
|
||||
UWORD(3087735),UWORD(3554345),UWORD(4087968),UWORD(4697205),UWORD(5392783),UWORD(6185689),UWORD(7089500),
|
||||
UWORD(8118264),UWORD(9289091),UWORD(10619863),UWORD(12132164),UWORD(13848650),UWORD(15796476),UWORD(18004327),
|
||||
UWORD(20506255),UWORD(23338469),UWORD(26543660),UWORD(30167357),UWORD(34262962),UWORD(38887673),
|
||||
UWORD(44108109),UWORD(49995925),UWORD(56634173),UWORD(64112359),UWORD(72533807),UWORD(82010177),
|
||||
UWORD(92669720),UWORD(104651419),UWORD(118114304),UWORD(133230930),UWORD(150198136),UWORD(169229875),
|
||||
UWORD(190569292),UWORD(214481126),UWORD(241265379),UWORD(271248950),UWORD(304801365),UWORD(342325709),
|
||||
UWORD(384276336),UWORD(431149389),UWORD(483502844),UWORD(541946240),UWORD(607163746),UWORD(679903203),
|
||||
UWORD(761002156),UWORD(851376628),UWORD(952050665),UWORD(1064144451),UWORD(1188908248),UWORD(1327710076),
|
||||
UWORD(1482074143),UWORD(1653668665),UWORD(1844349560),UWORD(2056148051),UWORD(2291320912),
|
||||
UWORD(2552338241),UWORD(2841940500),UWORD(3163127352),UWORD(3519222692),UWORD(3913864295)
|
||||
};
|
||||
|
||||
void
|
||||
arith_number_of_partitions(fmpz_t x, ulong n)
|
||||
{
|
||||
if (n < NUMBER_OF_SMALL_PARTITIONS)
|
||||
{
|
||||
fmpz_set_ui(x, partitions_lookup[n]);
|
||||
}
|
||||
else
|
||||
{
|
||||
mpfr_t t;
|
||||
mpfr_init(t);
|
||||
arith_number_of_partitions_mpfr(t, n);
|
||||
mpfr_get_z(_fmpz_promote(x), t, MPFR_RNDN);
|
||||
_fmpz_demote_val(x);
|
||||
mpfr_clear(t);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,539 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
Inspired by code written for Sage by Jonathan Bober.
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
#define DOUBLE_PREC 53
|
||||
#define PI 3.141592653589793238462643
|
||||
#define INV_LOG2 (1.44269504088896340735992468 + 1e-12)
|
||||
#define HRR_A (1.1143183348516376904 + 1e-12) /* 44*pi^2/(225*sqrt(3)) */
|
||||
#define HRR_B (0.0592384391754448833 + 1e-12) /* pi*sqrt(2)/75 */
|
||||
#define HRR_C (2.5650996603237281911 + 1e-12) /* pi*sqrt(2/3) */
|
||||
#define HRR_D (1.2424533248940001551 + 1e-12) /* log(2) + log(3)/2 */
|
||||
|
||||
|
||||
#define PI_USE_CHUDNOVSKY 1
|
||||
#define PI_CHUDNOVSKY_CUTOFF 1000000
|
||||
|
||||
#define VERBOSE 0
|
||||
|
||||
|
||||
static double
|
||||
partitions_remainder_bound(double n, double terms)
|
||||
{
|
||||
return HRR_A/sqrt(terms)
|
||||
+ HRR_B*sqrt(terms/(n-1)) * sinh(HRR_C * sqrt(n)/terms);
|
||||
}
|
||||
|
||||
/* Crude upper bound, sufficient to estimate the precision */
|
||||
static double
|
||||
log_sinh(double x)
|
||||
{
|
||||
if (x > 4)
|
||||
return x;
|
||||
else
|
||||
return log(x) + x*x*(1/6.);
|
||||
}
|
||||
|
||||
static double
|
||||
partitions_remainder_bound_log2(double n, double N)
|
||||
{
|
||||
double t1, t2;
|
||||
|
||||
t1 = log(HRR_A) - 0.5*log(N);
|
||||
t2 = log(HRR_B) + 0.5*(log(N) - log(n-1)) + log_sinh(HRR_C * sqrt(n)/N);
|
||||
|
||||
return (FLINT_MAX(t1, t2) + 1) * INV_LOG2;
|
||||
}
|
||||
|
||||
slong
|
||||
partitions_needed_terms(ulong n)
|
||||
{
|
||||
slong N;
|
||||
for (N = 1; partitions_remainder_bound_log2(n, N) > 10; N++);
|
||||
for ( ; partitions_remainder_bound(n, N) > (n > 1500 ? 0.25 : 1); N++);
|
||||
return N;
|
||||
}
|
||||
|
||||
static double
|
||||
partitions_term_bound(double n, double k)
|
||||
{
|
||||
return ((PI*sqrt(24*n-1) / (6.0*k)) + HRR_D - log(24.0*n-1) + 0.5*log(k)) * INV_LOG2;
|
||||
}
|
||||
|
||||
/* Bound number of prime factors in k */
|
||||
static mp_limb_t primorial_tab[] = {
|
||||
1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870,
|
||||
#if FLINT64
|
||||
UWORD(6469693230), UWORD(200560490130), UWORD(7420738134810), UWORD(304250263527210),
|
||||
UWORD(13082761331670030), UWORD(614889782588491410)
|
||||
#endif
|
||||
};
|
||||
|
||||
static __inline__ int
|
||||
bound_primes(ulong k)
|
||||
{
|
||||
int i;
|
||||
|
||||
for (i = 0; i < sizeof(primorial_tab) / sizeof(mp_limb_t); i++)
|
||||
if (k <= primorial_tab[i])
|
||||
return i;
|
||||
|
||||
return i;
|
||||
}
|
||||
|
||||
|
||||
static __inline__ slong
|
||||
log2_ceil(double x)
|
||||
{
|
||||
/* ceil(log2(n)) = bitcount(n-1);
|
||||
this is too large if x is a power of two */
|
||||
return FLINT_BIT_COUNT((slong) x);
|
||||
}
|
||||
|
||||
static slong
|
||||
partitions_prec_bound(ulong n, slong k, slong N)
|
||||
{
|
||||
slong prec;
|
||||
|
||||
prec = partitions_term_bound(n, k);
|
||||
prec += log2_ceil(8 * N * (26 * (sqrt(n) / k) + 7 * bound_primes(k) + 22));
|
||||
|
||||
return prec;
|
||||
}
|
||||
|
||||
double
|
||||
cos_pi_pq(mp_limb_signed_t p, mp_limb_signed_t q)
|
||||
{
|
||||
/* Force 0 <= p < q */
|
||||
p = FLINT_ABS(p);
|
||||
p %= (2 * q);
|
||||
if (p >= q)
|
||||
p = 2 * q - p;
|
||||
|
||||
if (4 * p <= q)
|
||||
return cos(p * PI / q);
|
||||
else if (4 * p < 3 * q)
|
||||
return sin((q - 2*p) * PI / (2 * q));
|
||||
else
|
||||
return -cos((q - p) * PI / q);
|
||||
}
|
||||
|
||||
void
|
||||
mpfr_sqrt_z(mpfr_t x, mpz_t z, mpfr_rnd_t rnd)
|
||||
{
|
||||
if (mpz_fits_ulong_p(z))
|
||||
mpfr_sqrt_ui(x, flint_mpz_get_ui(z), rnd);
|
||||
else
|
||||
{
|
||||
mpfr_set_z(x, z, rnd);
|
||||
mpfr_sqrt(x, x, rnd);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
mpfr_set_fmpz(mpfr_t c, const fmpz_t b)
|
||||
{
|
||||
if (COEFF_IS_MPZ(*b))
|
||||
mpfr_set_z(c, COEFF_TO_PTR(*b), MPFR_RNDN);
|
||||
else
|
||||
mpfr_set_si(c, *b, MPFR_RNDN);
|
||||
}
|
||||
|
||||
void
|
||||
mpfr_mul_fmpz(mpfr_t c, mpfr_srcptr a, const fmpz_t b)
|
||||
{
|
||||
if (COEFF_IS_MPZ(*b))
|
||||
mpfr_mul_z(c, a, COEFF_TO_PTR(*b), MPFR_RNDN);
|
||||
else
|
||||
mpfr_mul_si(c, a, *b, MPFR_RNDN);
|
||||
}
|
||||
|
||||
void
|
||||
mpfr_add_fmpz(mpfr_t c, mpfr_srcptr a, const fmpz_t b)
|
||||
{
|
||||
if (COEFF_IS_MPZ(*b))
|
||||
mpfr_add_z(c, a, COEFF_TO_PTR(*b), MPFR_RNDN);
|
||||
else
|
||||
mpfr_add_si(c, a, *b, MPFR_RNDN);
|
||||
}
|
||||
|
||||
|
||||
void
|
||||
_fmpz_poly_evaluate_mpfr(mpfr_t res, const fmpz * f, slong len,
|
||||
const mpfr_t a)
|
||||
{
|
||||
if (len == 0)
|
||||
mpfr_set_ui(res, 0, MPFR_RNDN);
|
||||
else if (len == 1)
|
||||
mpfr_set_fmpz(res, f);
|
||||
else
|
||||
{
|
||||
slong i = len - 1;
|
||||
mpfr_t t;
|
||||
mpfr_init2(t, mpfr_get_prec(res));
|
||||
mpfr_set_fmpz(res, f + i);
|
||||
for (i = len - 2; i >= 0; i--)
|
||||
{
|
||||
mpfr_mul(t, res, a, MPFR_RNDN);
|
||||
mpfr_add_fmpz(res, t, f + i);
|
||||
}
|
||||
mpfr_clear(t);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
fmpz_poly_evaluate_mpfr(mpfr_t res, const fmpz_poly_t f, const mpfr_t a)
|
||||
{
|
||||
if (res == a)
|
||||
{
|
||||
mpfr_t t;
|
||||
mpfr_init2(t, mpfr_get_prec(res));
|
||||
_fmpz_poly_evaluate_mpfr(t, f->coeffs, f->length, a);
|
||||
mpfr_swap(res, t);
|
||||
mpfr_clear(t);
|
||||
}
|
||||
else
|
||||
{
|
||||
_fmpz_poly_evaluate_mpfr(res, f->coeffs, f->length, a);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
findroot(mpfr_t x, fmpz_poly_t poly, double x0)
|
||||
{
|
||||
slong i;
|
||||
slong prec, initial_prec, target_prec, guard_bits;
|
||||
slong precs[FLINT_BITS];
|
||||
fmpz_poly_t poly2;
|
||||
mpfr_t t, u, xn;
|
||||
|
||||
initial_prec = 48;
|
||||
target_prec = mpfr_get_prec(x) + 32;
|
||||
|
||||
mpfr_init2(t, 53);
|
||||
mpfr_init2(u, 53);
|
||||
mpfr_init2(xn, 53);
|
||||
mpfr_set_d(xn, x0, MPFR_RNDN);
|
||||
|
||||
fmpz_poly_init(poly2);
|
||||
fmpz_poly_derivative(poly2, poly);
|
||||
guard_bits = fmpz_poly_max_bits(poly2);
|
||||
guard_bits = FLINT_ABS(guard_bits);
|
||||
|
||||
for (i = 0, prec = target_prec; prec >= initial_prec; i++)
|
||||
{
|
||||
precs[i] = prec;
|
||||
prec = prec / 2 + 8;
|
||||
}
|
||||
|
||||
for (i--; i >= 0; i--)
|
||||
{
|
||||
mpfr_set_prec(t, precs[i] + guard_bits);
|
||||
mpfr_set_prec(u, precs[i] + guard_bits);
|
||||
mpfr_prec_round(xn, precs[i], MPFR_RNDN);
|
||||
fmpz_poly_evaluate_mpfr(t, poly, xn);
|
||||
fmpz_poly_evaluate_mpfr(u, poly2, xn);
|
||||
mpfr_div(t, t, u, MPFR_RNDN);
|
||||
mpfr_sub(xn, xn, t, MPFR_RNDN);
|
||||
}
|
||||
|
||||
mpfr_set(x, xn, MPFR_RNDN);
|
||||
|
||||
fmpz_poly_clear(poly2);
|
||||
mpfr_clear(t);
|
||||
mpfr_clear(u);
|
||||
mpfr_clear(xn);
|
||||
}
|
||||
|
||||
void cos_minpoly(fmpz_poly_t poly, slong p, slong q)
|
||||
{
|
||||
if (p % 2 == 0)
|
||||
arith_cos_minpoly(poly, q);
|
||||
else
|
||||
arith_cos_minpoly(poly, 2 * q);
|
||||
}
|
||||
|
||||
int use_newton(slong prec, slong q)
|
||||
{
|
||||
if (q < 250 && prec > 400 + 4*q*q)
|
||||
return 1;
|
||||
return 0;
|
||||
}
|
||||
|
||||
void mpfr_cos_pi_pq(mpfr_t t, mp_limb_signed_t p, mp_limb_signed_t q)
|
||||
{
|
||||
/* Force 0 <= p < q */
|
||||
p = FLINT_ABS(p);
|
||||
p %= (2 * q);
|
||||
if (p >= q)
|
||||
p = 2 * q - p;
|
||||
|
||||
if (use_newton(mpfr_get_prec(t), q))
|
||||
{
|
||||
fmpz_poly_t poly;
|
||||
slong d;
|
||||
fmpz_poly_init(poly);
|
||||
d = n_gcd(q, p);
|
||||
q /= d;
|
||||
p /= d;
|
||||
cos_minpoly(poly, p, q);
|
||||
findroot(t, poly, cos(3.1415926535897932385 * p / q));
|
||||
fmpz_poly_clear(poly);
|
||||
}
|
||||
else
|
||||
{
|
||||
mpfr_const_pi(t, MPFR_RNDN);
|
||||
|
||||
if (4 * p <= q)
|
||||
{
|
||||
mpfr_mul_si(t, t, p, MPFR_RNDN);
|
||||
mpfr_div_ui(t, t, q, MPFR_RNDN);
|
||||
mpfr_cos(t, t, MPFR_RNDN);
|
||||
}
|
||||
else if (4 * p < 3 * q)
|
||||
{
|
||||
mpfr_mul_si(t, t, q - 2*p, MPFR_RNDN);
|
||||
mpfr_div_ui(t, t, 2 * q, MPFR_RNDN);
|
||||
mpfr_sin(t, t, MPFR_RNDN);
|
||||
}
|
||||
else
|
||||
{
|
||||
mpfr_mul_si(t, t, q - p, MPFR_RNDN);
|
||||
mpfr_div_ui(t, t, q, MPFR_RNDN);
|
||||
mpfr_cos(t, t, MPFR_RNDN);
|
||||
mpfr_neg(t, t, MPFR_RNDN);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
eval_trig_prod(mpfr_t sum, trig_prod_t prod)
|
||||
{
|
||||
int i;
|
||||
|
||||
if (prod->prefactor == 0)
|
||||
{
|
||||
mpfr_set_ui(sum, UWORD(0), MPFR_RNDN);
|
||||
return;
|
||||
}
|
||||
|
||||
if (mpfr_get_prec(sum) <= DOUBLE_PREC)
|
||||
{
|
||||
double s;
|
||||
s = prod->prefactor * sqrt((double)prod->sqrt_p/(double)prod->sqrt_q);
|
||||
for (i = 0; i < prod->n; i++)
|
||||
s *= cos_pi_pq(prod->cos_p[i], prod->cos_q[i]);
|
||||
mpfr_set_d(sum, s, MPFR_RNDN);
|
||||
}
|
||||
else
|
||||
{
|
||||
mp_limb_t v;
|
||||
mpfr_t t;
|
||||
|
||||
mpfr_init2(t, mpfr_get_prec(sum));
|
||||
mpfr_set_si(sum, prod->prefactor, MPFR_RNDN);
|
||||
v = n_gcd_full(prod->sqrt_p, prod->sqrt_q);
|
||||
prod->sqrt_p /= v;
|
||||
prod->sqrt_q /= v;
|
||||
|
||||
if (prod->sqrt_p != 1)
|
||||
{
|
||||
mpfr_sqrt_ui(t, prod->sqrt_p, MPFR_RNDN);
|
||||
mpfr_mul(sum, sum, t, MPFR_RNDN);
|
||||
}
|
||||
|
||||
if (prod->sqrt_q != 1)
|
||||
{
|
||||
mpfr_sqrt_ui(t, prod->sqrt_q, MPFR_RNDN);
|
||||
mpfr_div(sum, sum, t, MPFR_RNDN);
|
||||
}
|
||||
|
||||
for (i = 0; i < prod->n; i++)
|
||||
{
|
||||
mpfr_cos_pi_pq(t, prod->cos_p[i], prod->cos_q[i]);
|
||||
mpfr_mul(sum, sum, t, MPFR_RNDN);
|
||||
}
|
||||
|
||||
mpfr_clear(t);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
sinh_cosh_divk_precomp(mpfr_t sh, mpfr_t ch, mpfr_t ex, slong k)
|
||||
{
|
||||
mpfr_t t;
|
||||
mpfr_root(ch, ex, k, MPFR_RNDN);
|
||||
/* The second term doesn't need full precision,
|
||||
but this doesn't affect performance that much... */
|
||||
mpfr_init2(t, mpfr_get_prec(ch));
|
||||
mpfr_ui_div(t, 1, ch, MPFR_RNDN);
|
||||
mpfr_sub(sh, ch, t, MPFR_RNDN);
|
||||
mpfr_add(ch, ch, t, MPFR_RNDN);
|
||||
mpfr_div_2exp(ch, ch, 1, MPFR_RNDN);
|
||||
mpfr_div_2exp(sh, sh, 1, MPFR_RNDN);
|
||||
mpfr_clear(t);
|
||||
}
|
||||
|
||||
|
||||
void
|
||||
_arith_number_of_partitions_mpfr(mpfr_t x, ulong n, slong N0, slong N)
|
||||
{
|
||||
trig_prod_t prod;
|
||||
mpfr_t acc, C, t1, t2, t3, t4, exp1;
|
||||
mpz_t n24;
|
||||
double Cd;
|
||||
slong k;
|
||||
slong prec, guard_bits;
|
||||
#if VERBOSE
|
||||
timeit_t t0;
|
||||
#endif
|
||||
|
||||
if (n <= 2)
|
||||
{
|
||||
mpfr_set_ui(x, FLINT_MAX(1, n), MPFR_RNDN);
|
||||
return;
|
||||
}
|
||||
|
||||
/* Compute initial precision */
|
||||
guard_bits = 2 * FLINT_BIT_COUNT(N) + 32;
|
||||
prec = partitions_remainder_bound_log2(n, N0) + guard_bits;
|
||||
prec = FLINT_MAX(prec, DOUBLE_PREC);
|
||||
|
||||
mpfr_set_prec(x, prec);
|
||||
mpfr_init2(acc, prec);
|
||||
mpfr_init2(C, prec);
|
||||
mpfr_init2(t1, prec);
|
||||
mpfr_init2(t2, prec);
|
||||
mpfr_init2(t3, prec);
|
||||
mpfr_init2(t4, prec);
|
||||
|
||||
mpfr_set_ui(x, 0, MPFR_RNDN);
|
||||
mpfr_set_ui(acc, 0, MPFR_RNDN);
|
||||
|
||||
mpz_init(n24);
|
||||
flint_mpz_set_ui(n24, n);
|
||||
flint_mpz_mul_ui(n24, n24, 24);
|
||||
flint_mpz_sub_ui(n24, n24, 1);
|
||||
|
||||
#if VERBOSE
|
||||
timeit_start(t0);
|
||||
#endif
|
||||
|
||||
/* C = (pi/6)*sqrt(24*n-1) */
|
||||
|
||||
if (PI_USE_CHUDNOVSKY && prec > PI_CHUDNOVSKY_CUTOFF)
|
||||
mpfr_pi_chudnovsky(t1, MPFR_RNDN);
|
||||
else
|
||||
mpfr_const_pi(t1, MPFR_RNDN);
|
||||
|
||||
mpfr_sqrt_z(t2, n24, MPFR_RNDN);
|
||||
mpfr_mul(t1, t1, t2, MPFR_RNDN);
|
||||
mpfr_div_ui(C, t1, 6, MPFR_RNDN);
|
||||
Cd = mpfr_get_d(C, MPFR_RNDN);
|
||||
|
||||
mpfr_init2(exp1, prec);
|
||||
mpfr_exp(exp1, C, prec);
|
||||
|
||||
#if VERBOSE
|
||||
timeit_stop(t0);
|
||||
flint_printf("TERM 1: %wd ms\n", t0->cpu);
|
||||
#endif
|
||||
|
||||
for (k = N0; k <= N; k++)
|
||||
{
|
||||
trig_prod_init(prod);
|
||||
arith_hrr_expsum_factored(prod, k, n % k);
|
||||
|
||||
if (prod->prefactor != 0)
|
||||
{
|
||||
if (prec > DOUBLE_PREC)
|
||||
{
|
||||
prec = partitions_prec_bound(n, k, N);
|
||||
|
||||
mpfr_set_prec(t1, prec);
|
||||
mpfr_set_prec(t2, prec);
|
||||
mpfr_set_prec(t3, prec);
|
||||
mpfr_set_prec(t4, prec);
|
||||
}
|
||||
|
||||
/* Compute A_k(n) * sqrt(3/k) * 4 / (24*n-1) */
|
||||
prod->prefactor *= 4;
|
||||
prod->sqrt_p *= 3;
|
||||
prod->sqrt_q *= k;
|
||||
eval_trig_prod(t1, prod);
|
||||
mpfr_div_z(t1, t1, n24, MPFR_RNDN);
|
||||
|
||||
/* Multiply by (cosh(z) - sinh(z)/z) where z = C / k */
|
||||
if (prec <= DOUBLE_PREC)
|
||||
{
|
||||
double z = Cd / k;
|
||||
mpfr_mul_d(t1, t1, cosh(z) - sinh(z)/z, MPFR_RNDN);
|
||||
}
|
||||
else
|
||||
{
|
||||
mpfr_div_ui(t2, C, k, MPFR_RNDN);
|
||||
|
||||
if (k < 35)
|
||||
sinh_cosh_divk_precomp(t3, t4, exp1, k);
|
||||
else
|
||||
mpfr_sinh_cosh(t3, t4, t2, MPFR_RNDN);
|
||||
|
||||
mpfr_div(t3, t3, t2, MPFR_RNDN);
|
||||
mpfr_sub(t2, t4, t3, MPFR_RNDN);
|
||||
mpfr_mul(t1, t1, t2, MPFR_RNDN);
|
||||
}
|
||||
|
||||
/* Add to accumulator */
|
||||
mpfr_add(acc, acc, t1, MPFR_RNDN);
|
||||
if (mpfr_get_prec(acc) > 2 * prec + 32)
|
||||
{
|
||||
mpfr_add(x, x, acc, MPFR_RNDN);
|
||||
mpfr_set_prec(acc, prec + 32);
|
||||
mpfr_set_ui(acc, 0, MPFR_RNDN);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
mpfr_add(x, x, acc, MPFR_RNDN);
|
||||
|
||||
mpz_clear(n24);
|
||||
mpfr_clear(acc);
|
||||
mpfr_clear(exp1);
|
||||
mpfr_clear(C);
|
||||
mpfr_clear(t1);
|
||||
mpfr_clear(t2);
|
||||
mpfr_clear(t3);
|
||||
mpfr_clear(t4);
|
||||
}
|
||||
|
||||
void
|
||||
arith_number_of_partitions_mpfr(mpfr_t x, ulong n)
|
||||
{
|
||||
_arith_number_of_partitions_mpfr(x, n, 1, partitions_needed_terms(n));
|
||||
}
|
||||
|
|
@ -1,61 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_number_of_partitions_nmod_vec(mp_ptr res, slong len, nmod_t mod)
|
||||
{
|
||||
mp_ptr tmp;
|
||||
mp_limb_t r;
|
||||
slong k, n;
|
||||
|
||||
r = mod.n - UWORD(1);
|
||||
|
||||
if (len < 1)
|
||||
return;
|
||||
|
||||
tmp = _nmod_vec_init(len);
|
||||
_nmod_vec_zero(tmp, len);
|
||||
|
||||
tmp[0] = UWORD(1);
|
||||
|
||||
for (n = k = 1; n + 4*k + 2 < len; k += 2)
|
||||
{
|
||||
tmp[n] = r;
|
||||
tmp[n + k] = r;
|
||||
tmp[n + 3*k + 1] = UWORD(1);
|
||||
tmp[n + 4*k + 2] = UWORD(1);
|
||||
n += 6*k + 5;
|
||||
}
|
||||
|
||||
if (n < len) tmp[n] = r;
|
||||
if (n + k < len) tmp[n + k] = r;
|
||||
if (n + 3*k + 1 < len) tmp[n + 3*k + 1] = WORD(1);
|
||||
|
||||
_nmod_poly_inv_series(res, tmp, len, mod);
|
||||
|
||||
_nmod_vec_clear(tmp);
|
||||
}
|
||||
|
|
@ -1,57 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void
|
||||
arith_number_of_partitions_vec(fmpz * res, slong len)
|
||||
{
|
||||
fmpz * tmp;
|
||||
slong k, n;
|
||||
|
||||
if (len < 1)
|
||||
return;
|
||||
|
||||
tmp = _fmpz_vec_init(len);
|
||||
|
||||
tmp[0] = WORD(1);
|
||||
|
||||
for (n = k = 1; n + 4*k + 2 < len; k += 2)
|
||||
{
|
||||
tmp[n] = WORD(-1);
|
||||
tmp[n + k] = WORD(-1);
|
||||
tmp[n + 3*k + 1] = WORD(1);
|
||||
tmp[n + 4*k + 2] = WORD(1);
|
||||
n += 6*k + 5;
|
||||
}
|
||||
|
||||
if (n < len) tmp[n] = WORD(-1);
|
||||
if (n + k < len) tmp[n + k] = WORD(-1);
|
||||
if (n + 3*k + 1 < len) tmp[n + 3*k + 1] = WORD(1);
|
||||
|
||||
_fmpz_poly_inv_series(res, tmp, len);
|
||||
|
||||
_fmpz_vec_clear(tmp, len);
|
||||
}
|
||||
|
|
@ -1,653 +0,0 @@
|
|||
/* Pi computation using Chudnovsky's algortithm.
|
||||
|
||||
* Copyright 2002, 2005 Hanhong Xue (macroxue at yahoo dot com)
|
||||
|
||||
* Modified 2005 by Torbjorn Granlund (tege at swox dot com) to allow more than
|
||||
2G digits to be computed. Modified 2009 by Torbjorn Granlund for GMPbench.
|
||||
|
||||
* Modified 2011 by Fredrik Johansson to make reentrant and adapt for
|
||||
use in FLINT.
|
||||
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions are met:
|
||||
* 1. Redistributions of source code must retain the above copyright notice,
|
||||
* this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright notice,
|
||||
* this list of conditions and the following disclaimer in the documentation
|
||||
* and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND ANY EXPRESS OR
|
||||
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
||||
* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
|
||||
* EVENT SHALL THE AUTHORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
||||
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
|
||||
* OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
|
||||
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
|
||||
* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
|
||||
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <assert.h>
|
||||
#include <math.h>
|
||||
#include <stdlib.h>
|
||||
#include <string.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "arith.h"
|
||||
|
||||
#define A 13591409
|
||||
#define B 545140134
|
||||
#define C 640320
|
||||
#define D 12
|
||||
|
||||
#define BITS_PER_DIGIT 3.32192809488736234787
|
||||
#define DIGITS_PER_ITER 14.1816474627254776555
|
||||
#define DOUBLE_PREC 53
|
||||
|
||||
#define min(x,y) ((x)<(y)?(x):(y))
|
||||
#define max(x,y) ((x)>(y)?(x):(y))
|
||||
|
||||
typedef struct {
|
||||
ulong max_facs;
|
||||
ulong num_facs;
|
||||
ulong *fac;
|
||||
ulong *pow;
|
||||
} fac_t[1];
|
||||
|
||||
typedef struct {
|
||||
slong fac;
|
||||
slong pow;
|
||||
slong nxt;
|
||||
} sieve_t;
|
||||
|
||||
typedef struct
|
||||
{
|
||||
sieve_t *sieve;
|
||||
slong sieve_size;
|
||||
fac_t ftmp, fmul;
|
||||
mpz_t gcd;
|
||||
mpz_t *pstack, *qstack, *gstack;
|
||||
fac_t *fpstack, *fgstack;
|
||||
slong top;
|
||||
}
|
||||
pi_state_struct;
|
||||
|
||||
typedef pi_state_struct pi_state[1];
|
||||
|
||||
#define INIT_FACS 32
|
||||
|
||||
#define p1 (state->pstack[state->top])
|
||||
#define q1 (state->qstack[state->top])
|
||||
#define g1 (state->gstack[state->top])
|
||||
#define fp1 (state->fpstack[state->top])
|
||||
#define fg1 (state->fgstack[state->top])
|
||||
|
||||
#define p2 (state->pstack[state->top+1])
|
||||
#define q2 (state->qstack[state->top+1])
|
||||
#define g2 (state->gstack[state->top+1])
|
||||
#define fp2 (state->fpstack[state->top+1])
|
||||
#define fg2 (state->fgstack[state->top+1])
|
||||
|
||||
/* r = sqrt(x) */
|
||||
void
|
||||
my_sqrt_ui(pi_state state, mpf_t t1, mpf_t t2, mpf_t r, ulong x)
|
||||
{
|
||||
ulong prec, bits, prec0;
|
||||
|
||||
prec0 = mpf_get_prec(r);
|
||||
|
||||
if (prec0 <= DOUBLE_PREC)
|
||||
{
|
||||
mpf_set_d(r, sqrt(x));
|
||||
return;
|
||||
}
|
||||
|
||||
bits = 0;
|
||||
for (prec = prec0; prec > DOUBLE_PREC; )
|
||||
{
|
||||
int bit = prec&1;
|
||||
prec = (prec+bit)/2;
|
||||
bits = bits*2+bit;
|
||||
}
|
||||
|
||||
mpf_set_prec_raw(t1, DOUBLE_PREC);
|
||||
mpf_set_d(t1, 1/sqrt(x));
|
||||
|
||||
while (prec < prec0)
|
||||
{
|
||||
prec *=2;
|
||||
if (prec < prec0)
|
||||
{
|
||||
/* t1 = t1+t1*(1-x*t1*t1)/2; */
|
||||
mpf_set_prec_raw(t2, prec);
|
||||
mpf_mul(t2, t1, t1); /* half x half -> full */
|
||||
mpf_mul_ui(t2, t2, x);
|
||||
mpf_ui_sub(t2, 1, t2);
|
||||
mpf_set_prec_raw(t2, prec/2);
|
||||
mpf_div_2exp(t2, t2, 1);
|
||||
mpf_mul(t2, t2, t1); /* half x half -> half */
|
||||
mpf_set_prec_raw(t1, prec);
|
||||
mpf_add(t1, t1, t2);
|
||||
}
|
||||
else
|
||||
{
|
||||
break;
|
||||
}
|
||||
prec -= (bits&1);
|
||||
bits /=2;
|
||||
}
|
||||
|
||||
/* t2=x*t1, t1 = t2+t1*(x-t2*t2)/2; */
|
||||
mpf_set_prec_raw(t2, prec0/2);
|
||||
mpf_mul_ui(t2, t1, x);
|
||||
mpf_mul(r, t2, t2); /* half x half -> full */
|
||||
mpf_ui_sub(r, x, r);
|
||||
mpf_mul(t1, t1, r); /* half x half -> half */
|
||||
mpf_div_2exp(t1, t1, 1);
|
||||
mpf_add(r, t1, t2);
|
||||
}
|
||||
|
||||
/* r = y/x WARNING: r cannot be the same as y. */
|
||||
void
|
||||
my_div(pi_state state, mpf_t t1, mpf_t t2, mpf_t r, mpf_t y, mpf_t x)
|
||||
{
|
||||
ulong prec, bits, prec0;
|
||||
|
||||
prec0 = mpf_get_prec(r);
|
||||
|
||||
if (prec0 <= DOUBLE_PREC)
|
||||
{
|
||||
mpf_set_d(r, mpf_get_d(y) / mpf_get_d(x));
|
||||
return;
|
||||
}
|
||||
|
||||
bits = 0;
|
||||
for (prec = prec0; prec > DOUBLE_PREC; )
|
||||
{
|
||||
int bit = prec & 1;
|
||||
prec = (prec + bit) / 2;
|
||||
bits = bits*2 + bit;
|
||||
}
|
||||
|
||||
mpf_set_prec_raw(t1, DOUBLE_PREC);
|
||||
mpf_ui_div(t1, 1, x);
|
||||
|
||||
while (prec < prec0)
|
||||
{
|
||||
prec *= 2;
|
||||
if (prec < prec0)
|
||||
{
|
||||
/* t1 = t1+t1*(1-x*t1); */
|
||||
mpf_set_prec_raw(t2, prec);
|
||||
mpf_mul(t2, x, t1); /* full x half -> full */
|
||||
mpf_ui_sub(t2, 1, t2);
|
||||
mpf_set_prec_raw(t2, prec/2);
|
||||
mpf_mul(t2, t2, t1); /* half x half -> half */
|
||||
mpf_set_prec_raw(t1, prec);
|
||||
mpf_add(t1, t1, t2);
|
||||
}
|
||||
else
|
||||
{
|
||||
prec = prec0;
|
||||
/* t2=y*t1, t1 = t2+t1*(y-x*t2); */
|
||||
mpf_set_prec_raw(t2, prec / 2);
|
||||
mpf_mul(t2, t1, y); /* half x half -> half */
|
||||
mpf_mul(r, x, t2); /* full x half -> full */
|
||||
mpf_sub(r, y, r);
|
||||
mpf_mul(t1, t1, r); /* half x half -> half */
|
||||
mpf_add(r, t1, t2);
|
||||
break;
|
||||
}
|
||||
prec -= (bits & 1);
|
||||
bits /= 2;
|
||||
}
|
||||
}
|
||||
|
||||
/*///////////////////////////////////////////////////////////////////////////*/
|
||||
|
||||
|
||||
|
||||
static __inline__ void
|
||||
fac_reset(fac_t f)
|
||||
{
|
||||
f[0].num_facs = 0;
|
||||
}
|
||||
|
||||
static __inline__ void
|
||||
fac_init_size(fac_t f, slong s)
|
||||
{
|
||||
if (s < INIT_FACS)
|
||||
s = INIT_FACS;
|
||||
|
||||
f[0].fac = flint_malloc(s*sizeof(ulong)*2);
|
||||
f[0].pow = f[0].fac + s;
|
||||
f[0].max_facs = s;
|
||||
|
||||
fac_reset(f);
|
||||
}
|
||||
|
||||
static __inline__ void
|
||||
fac_init(fac_t f)
|
||||
{
|
||||
fac_init_size(f, INIT_FACS);
|
||||
}
|
||||
|
||||
static __inline__ void
|
||||
fac_clear(fac_t f)
|
||||
{
|
||||
flint_free(f[0].fac);
|
||||
}
|
||||
|
||||
static __inline__ void
|
||||
fac_resize(fac_t f, slong s)
|
||||
{
|
||||
if (f[0].max_facs < s)
|
||||
{
|
||||
fac_clear(f);
|
||||
fac_init_size(f, s);
|
||||
}
|
||||
}
|
||||
|
||||
/* f = base^pow */
|
||||
static __inline__ void
|
||||
fac_set_bp(pi_state state, fac_t f, ulong base, slong pow)
|
||||
{
|
||||
slong i;
|
||||
assert(base<state->sieve_size);
|
||||
for (i=0, base/=2; base>0; i++, base = state->sieve[base].nxt)
|
||||
{
|
||||
f[0].fac[i] = state->sieve[base].fac;
|
||||
f[0].pow[i] = state->sieve[base].pow*pow;
|
||||
}
|
||||
f[0].num_facs = i;
|
||||
assert(i<=f[0].max_facs);
|
||||
}
|
||||
|
||||
/* r = f*g */
|
||||
static __inline__ void
|
||||
fac_mul2(pi_state state, fac_t r, fac_t f, fac_t g)
|
||||
{
|
||||
slong i, j, k;
|
||||
|
||||
for (i=j=k=0; i<f[0].num_facs && j<g[0].num_facs; k++)
|
||||
{
|
||||
if (f[0].fac[i] == g[0].fac[j])
|
||||
{
|
||||
r[0].fac[k] = f[0].fac[i];
|
||||
r[0].pow[k] = f[0].pow[i] + g[0].pow[j];
|
||||
i++; j++;
|
||||
}
|
||||
else if (f[0].fac[i] < g[0].fac[j])
|
||||
{
|
||||
r[0].fac[k] = f[0].fac[i];
|
||||
r[0].pow[k] = f[0].pow[i];
|
||||
i++;
|
||||
}
|
||||
else
|
||||
{
|
||||
r[0].fac[k] = g[0].fac[j];
|
||||
r[0].pow[k] = g[0].pow[j];
|
||||
j++;
|
||||
}
|
||||
}
|
||||
|
||||
for (; i<f[0].num_facs; i++, k++)
|
||||
{
|
||||
r[0].fac[k] = f[0].fac[i];
|
||||
r[0].pow[k] = f[0].pow[i];
|
||||
}
|
||||
|
||||
for (; j<g[0].num_facs; j++, k++)
|
||||
{
|
||||
r[0].fac[k] = g[0].fac[j];
|
||||
r[0].pow[k] = g[0].pow[j];
|
||||
}
|
||||
|
||||
r[0].num_facs = k;
|
||||
assert(k<=r[0].max_facs);
|
||||
}
|
||||
|
||||
/* f *= g */
|
||||
static __inline__ void
|
||||
fac_mul(pi_state state, fac_t f, fac_t g)
|
||||
{
|
||||
fac_t tmp;
|
||||
fac_resize(state->fmul, f[0].num_facs + g[0].num_facs);
|
||||
fac_mul2(state, state->fmul, f, g);
|
||||
tmp[0] = f[0];
|
||||
f[0] = state->fmul[0];
|
||||
state->fmul[0] = tmp[0];
|
||||
}
|
||||
|
||||
/* f *= base^pow */
|
||||
static __inline__ void
|
||||
fac_mul_bp(pi_state state, fac_t f, ulong base, ulong pow)
|
||||
{
|
||||
fac_set_bp(state, state->ftmp, base, pow);
|
||||
fac_mul(state, f, state->ftmp);
|
||||
}
|
||||
|
||||
/* remove factors of power 0 */
|
||||
static __inline__ void
|
||||
fac_compact(fac_t f)
|
||||
{
|
||||
slong i, j;
|
||||
for (i=0, j=0; i<f[0].num_facs; i++)
|
||||
{
|
||||
if (f[0].pow[i]>0)
|
||||
{
|
||||
if (j < i)
|
||||
{
|
||||
f[0].fac[j] = f[0].fac[i];
|
||||
f[0].pow[j] = f[0].pow[i];
|
||||
}
|
||||
j++;
|
||||
}
|
||||
}
|
||||
f[0].num_facs = j;
|
||||
}
|
||||
|
||||
/* convert factorized form to number */
|
||||
void
|
||||
bs_mul(pi_state state, mpz_t r, slong a, slong b)
|
||||
{
|
||||
slong i, j;
|
||||
if (b-a<=32)
|
||||
{
|
||||
flint_mpz_set_ui(r, 1);
|
||||
for (i=a; i<b; i++)
|
||||
for (j=0; j<state->fmul[0].pow[i]; j++)
|
||||
flint_mpz_mul_ui(r, r, state->fmul[0].fac[i]);
|
||||
}
|
||||
else
|
||||
{
|
||||
mpz_t r2;
|
||||
mpz_init(r2);
|
||||
bs_mul(state, r2, a, (a+b)/2);
|
||||
bs_mul(state, r, (a+b)/2, b);
|
||||
mpz_mul(r, r, r2);
|
||||
mpz_clear(r2);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/* f /= gcd(f,g), g /= gcd(f,g) */
|
||||
void
|
||||
fac_remove_gcd(pi_state state, mpz_t p, fac_t fp, mpz_t g, fac_t fg)
|
||||
{
|
||||
slong i, j, k, c;
|
||||
|
||||
fac_resize(state->fmul, min(fp->num_facs, fg->num_facs));
|
||||
|
||||
for (i=j=k=0; i < fp->num_facs && j < fg->num_facs; )
|
||||
{
|
||||
if (fp->fac[i] == fg->fac[j])
|
||||
{
|
||||
c = min(fp->pow[i], fg->pow[j]);
|
||||
fp->pow[i] -= c;
|
||||
fg->pow[j] -= c;
|
||||
state->fmul->fac[k] = fp->fac[i];
|
||||
state->fmul->pow[k] = c;
|
||||
i++; j++; k++;
|
||||
}
|
||||
else if (fp->fac[i] < fg->fac[j])
|
||||
{
|
||||
i++;
|
||||
}
|
||||
else
|
||||
{
|
||||
j++;
|
||||
}
|
||||
}
|
||||
|
||||
state->fmul->num_facs = k;
|
||||
assert(k <= state->fmul->max_facs);
|
||||
|
||||
if (state->fmul->num_facs)
|
||||
{
|
||||
bs_mul(state, state->gcd, 0, state->fmul->num_facs);
|
||||
|
||||
mpz_divexact(p, p, state->gcd);
|
||||
mpz_divexact(g, g, state->gcd);
|
||||
|
||||
fac_compact(fp);
|
||||
fac_compact(fg);
|
||||
}
|
||||
}
|
||||
|
||||
/*///////////////////////////////////////////////////////////////////////////*/
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
/* binary splitting */
|
||||
void
|
||||
bs(pi_state state, ulong a, ulong b,
|
||||
unsigned gflag, slong level)
|
||||
{
|
||||
ulong i, mid;
|
||||
|
||||
if (b - a == 1)
|
||||
{
|
||||
/*
|
||||
g(b-1,b) = (6b-5)(2b-1)(6b-1)
|
||||
p(b-1,b) = b^3 * C^3 / 24
|
||||
q(b-1,b) = (-1)^b*g(b-1,b)*(A+Bb).
|
||||
*/
|
||||
flint_mpz_set_ui(p1, b);
|
||||
flint_mpz_mul_ui(p1, p1, b);
|
||||
flint_mpz_mul_ui(p1, p1, b);
|
||||
flint_mpz_mul_ui(p1, p1, (C/24)*(C/24));
|
||||
flint_mpz_mul_ui(p1, p1, C*24);
|
||||
|
||||
flint_mpz_set_ui(g1, 2*b-1);
|
||||
flint_mpz_mul_ui(g1, g1, 6*b-1);
|
||||
flint_mpz_mul_ui(g1, g1, 6*b-5);
|
||||
|
||||
flint_mpz_set_ui(q1, b);
|
||||
flint_mpz_mul_ui(q1, q1, B);
|
||||
flint_mpz_add_ui(q1, q1, A);
|
||||
mpz_mul (q1, q1, g1);
|
||||
|
||||
if (b%2)
|
||||
mpz_neg(q1, q1);
|
||||
|
||||
i=b;
|
||||
while ((i&1)==0) i>>=1;
|
||||
|
||||
fac_set_bp(state, fp1, i, 3); /* b^3 */
|
||||
fac_mul_bp(state, fp1, 3*5*23*29, 3);
|
||||
fp1[0].pow[0]--;
|
||||
|
||||
fac_set_bp(state, fg1, 2*b-1, 1); /* 2b-1 */
|
||||
fac_mul_bp(state, fg1, 6*b-1, 1); /* 6b-1 */
|
||||
fac_mul_bp(state, fg1, 6*b-5, 1); /* 6b-5 */
|
||||
}
|
||||
else
|
||||
{
|
||||
/*
|
||||
p(a,b) = p(a,m) * p(m,b)
|
||||
g(a,b) = g(a,m) * g(m,b)
|
||||
q(a,b) = q(a,m) * p(m,b) + q(m,b) * g(a,m)
|
||||
*/
|
||||
mid = a+(b-a)*0.5224; /* tuning parameter */
|
||||
bs(state, a, mid, 1, level+1);
|
||||
|
||||
state->top++;
|
||||
bs(state, mid, b, gflag, level+1);
|
||||
state->top--;
|
||||
|
||||
if (level>=4) { /* tuning parameter */
|
||||
fac_remove_gcd(state, p2, fp2, g1, fg1);
|
||||
}
|
||||
|
||||
mpz_mul(p1, p1, p2);
|
||||
mpz_mul(q1, q1, p2);
|
||||
mpz_mul(q2, q2, g1);
|
||||
mpz_add(q1, q1, q2);
|
||||
fac_mul(state, fp1, fp2);
|
||||
|
||||
if (gflag)
|
||||
{
|
||||
mpz_mul(g1, g1, g2);
|
||||
fac_mul(state, fg1, fg2);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
build_sieve(pi_state state, slong n, sieve_t *s)
|
||||
{
|
||||
slong m, i, j, k;
|
||||
|
||||
state->sieve_size = n;
|
||||
m = (slong)sqrt(n);
|
||||
memset(s, 0, sizeof(sieve_t)*n/2);
|
||||
|
||||
s[1/2].fac = 1;
|
||||
s[1/2].pow = 1;
|
||||
|
||||
for (i=3; i<=n; i+=2)
|
||||
{
|
||||
if (s[i/2].fac == 0)
|
||||
{
|
||||
s[i/2].fac = i;
|
||||
s[i/2].pow = 1;
|
||||
if (i <= m)
|
||||
{
|
||||
for (j=i*i, k=i/2; j<=n; j+=i+i, k++)
|
||||
{
|
||||
if (s[j/2].fac==0)
|
||||
{
|
||||
s[j/2].fac = i;
|
||||
if (s[k].fac == i)
|
||||
{
|
||||
s[j/2].pow = s[k].pow + 1;
|
||||
s[j/2].nxt = s[k].nxt;
|
||||
}
|
||||
else
|
||||
{
|
||||
s[j/2].pow = 1;
|
||||
s[j/2].nxt = k;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
mpfr_pi_chudnovsky(mpfr_t res, mpfr_rnd_t rnd)
|
||||
{
|
||||
mpf_t pi, qi, t1, t2;
|
||||
mpfr_prec_t prec;
|
||||
slong i, depth=1, terms;
|
||||
pi_state state;
|
||||
|
||||
prec = mpfr_get_prec(res) + 64;
|
||||
terms = prec / (BITS_PER_DIGIT * DIGITS_PER_ITER);
|
||||
while ((WORD(1)<<depth)<terms)
|
||||
depth++;
|
||||
depth++;
|
||||
|
||||
state->top = 0;
|
||||
state->sieve_size = max(3*5*23*29+1, terms*6);
|
||||
state->sieve = (sieve_t *)flint_malloc(sizeof(sieve_t)*(state->sieve_size)/2);
|
||||
build_sieve(state, state->sieve_size, state->sieve);
|
||||
|
||||
/* allocate stacks */
|
||||
state->pstack = flint_malloc(sizeof(mpz_t)*depth);
|
||||
state->qstack = flint_malloc(sizeof(mpz_t)*depth);
|
||||
state->gstack = flint_malloc(sizeof(mpz_t)*depth);
|
||||
state->fpstack = flint_malloc(sizeof(fac_t)*depth);
|
||||
state->fgstack = flint_malloc(sizeof(fac_t)*depth);
|
||||
for (i=0; i<depth; i++)
|
||||
{
|
||||
mpz_init(state->pstack[i]);
|
||||
mpz_init(state->qstack[i]);
|
||||
mpz_init(state->gstack[i]);
|
||||
fac_init(state->fpstack[i]);
|
||||
fac_init(state->fgstack[i]);
|
||||
}
|
||||
|
||||
mpz_init(state->gcd);
|
||||
fac_init(state->ftmp);
|
||||
fac_init(state->fmul);
|
||||
|
||||
/* begin binary splitting process */
|
||||
if (terms<=0)
|
||||
{
|
||||
flint_mpz_set_ui(p2,1);
|
||||
flint_mpz_set_ui(q2,0);
|
||||
flint_mpz_set_ui(g2,1);
|
||||
}
|
||||
else
|
||||
{
|
||||
bs(state, 0,terms,0,0);
|
||||
}
|
||||
|
||||
/* free some resources */
|
||||
flint_free(state->sieve);
|
||||
|
||||
mpz_clear(state->gcd);
|
||||
fac_clear(state->ftmp);
|
||||
fac_clear(state->fmul);
|
||||
|
||||
for (i=1; i<depth; i++)
|
||||
{
|
||||
mpz_clear(state->pstack[i]);
|
||||
mpz_clear(state->qstack[i]);
|
||||
mpz_clear(state->gstack[i]);
|
||||
fac_clear(state->fpstack[i]);
|
||||
fac_clear(state->fgstack[i]);
|
||||
}
|
||||
|
||||
mpz_clear(state->gstack[0]);
|
||||
fac_clear(state->fpstack[0]);
|
||||
fac_clear(state->fgstack[0]);
|
||||
|
||||
flint_free(state->gstack);
|
||||
flint_free(state->fpstack);
|
||||
flint_free(state->fgstack);
|
||||
|
||||
/*
|
||||
p*(C/D)*sqrt(C)
|
||||
pi = -----------------
|
||||
(q+A*p)
|
||||
*/
|
||||
|
||||
flint_mpz_addmul_ui(q1, p1, A);
|
||||
flint_mpz_mul_ui(p1, p1, C/D);
|
||||
|
||||
mpf_init2(pi, prec);
|
||||
mpf_set_z(pi, p1);
|
||||
mpz_clear(p1);
|
||||
|
||||
mpf_init2(qi, prec);
|
||||
mpf_set_z(qi, q1);
|
||||
mpz_clear(q1);
|
||||
|
||||
flint_free(state->pstack);
|
||||
flint_free(state->qstack);
|
||||
|
||||
/* initialize temp float variables for sqrt & div */
|
||||
mpf_init2(t1, prec);
|
||||
mpf_init2(t2, prec);
|
||||
|
||||
/* final step */
|
||||
my_div(state, t1, t2, qi, pi, qi);
|
||||
my_sqrt_ui(state, t1, t2, pi, C);
|
||||
mpf_mul(qi, qi, pi);
|
||||
|
||||
mpfr_set_f(res, qi, rnd);
|
||||
|
||||
/* free float resources */
|
||||
mpf_clear(pi);
|
||||
mpf_clear(qi);
|
||||
|
||||
mpf_clear(t1);
|
||||
mpf_clear(t2);
|
||||
}
|
||||
|
|
@ -1,151 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
Copyright (C) 2010 William Hart
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
#if FLINT64
|
||||
#define LARGEST_ULONG_PRIMORIAL 52
|
||||
#else
|
||||
#define LARGEST_ULONG_PRIMORIAL 28
|
||||
#endif
|
||||
|
||||
/* Only those with odd index */
|
||||
const ulong ULONG_PRIMORIALS[] =
|
||||
{
|
||||
UWORD(6),UWORD(30),UWORD(210),UWORD(210),UWORD(2310),UWORD(30030),UWORD(30030),UWORD(510510),UWORD(9699690),UWORD(9699690),
|
||||
UWORD(223092870),UWORD(223092870),UWORD(223092870)
|
||||
#if FLINT64
|
||||
,UWORD(6469693230),UWORD(200560490130),UWORD(200560490130),UWORD(200560490130),UWORD(7420738134810),
|
||||
UWORD(7420738134810),UWORD(304250263527210),UWORD(13082761331670030),UWORD(13082761331670030),
|
||||
UWORD(614889782588491410), UWORD(614889782588491410), UWORD(614889782588491410)
|
||||
#endif
|
||||
};
|
||||
|
||||
|
||||
#define PROD_LIMBS_DIRECT_CUTOFF 50
|
||||
|
||||
mp_size_t mpn_prod_limbs_direct(mp_limb_t * result, const mp_limb_t * factors,
|
||||
mp_size_t n)
|
||||
{
|
||||
mp_size_t k, len;
|
||||
mp_limb_t top;
|
||||
if (n < 1)
|
||||
{
|
||||
result[0] = UWORD(1);
|
||||
return 1;
|
||||
}
|
||||
result[0] = factors[0];
|
||||
len = 1;
|
||||
for (k=1; k<n; k++)
|
||||
{
|
||||
top = mpn_mul_1(result, result, len, factors[k]);
|
||||
if (top)
|
||||
{
|
||||
result[len] = top;
|
||||
len++;
|
||||
}
|
||||
}
|
||||
return len;
|
||||
}
|
||||
|
||||
mp_size_t mpn_prod_limbs_balanced(mp_limb_t * result, mp_limb_t * scratch,
|
||||
const mp_limb_t * factors, mp_size_t n, ulong bits)
|
||||
{
|
||||
mp_size_t an, bn, alen, blen, len;
|
||||
mp_limb_t top;
|
||||
|
||||
if (n < PROD_LIMBS_DIRECT_CUTOFF)
|
||||
return mpn_prod_limbs_direct(result, factors, n);
|
||||
|
||||
an = n/2;
|
||||
bn = n - an;
|
||||
|
||||
alen = mpn_prod_limbs_balanced(scratch, result, factors, an, bits);
|
||||
blen = mpn_prod_limbs_balanced(scratch + alen, result, factors + an, bn, bits);
|
||||
len = alen + blen;
|
||||
|
||||
if (alen <= blen)
|
||||
top = mpn_mul(result, scratch + alen, blen, scratch, alen);
|
||||
else
|
||||
top = mpn_mul(result, scratch, alen, scratch + alen, blen);
|
||||
|
||||
if (!top)
|
||||
len--;
|
||||
|
||||
return len;
|
||||
}
|
||||
|
||||
/*
|
||||
Set result to the product of the given factors, return the
|
||||
length of the result. It is assumed that no factors are zero.
|
||||
bits must be set to some bound on the bit size of the entries
|
||||
in factors. If no bound is known, simply use FLINT_BITS.
|
||||
*/
|
||||
mp_size_t mpn_prod_limbs(mp_limb_t * result, const mp_limb_t * factors,
|
||||
mp_size_t n, ulong bits)
|
||||
{
|
||||
mp_size_t len, limbs;
|
||||
mp_limb_t * scratch;
|
||||
|
||||
if (n < PROD_LIMBS_DIRECT_CUTOFF)
|
||||
return mpn_prod_limbs_direct(result, factors, n);
|
||||
|
||||
limbs = (n * bits - 1)/FLINT_BITS + 2;
|
||||
|
||||
scratch = flint_malloc(sizeof(mp_limb_t) * limbs);
|
||||
len = mpn_prod_limbs_balanced(result, scratch, factors, n, bits);
|
||||
flint_free(scratch);
|
||||
|
||||
return len;
|
||||
}
|
||||
|
||||
void arith_primorial(fmpz_t res, slong n)
|
||||
{
|
||||
mp_size_t len, pi;
|
||||
ulong bits;
|
||||
__mpz_struct * mpz_ptr;
|
||||
const mp_limb_t * primes;
|
||||
|
||||
if (n <= LARGEST_ULONG_PRIMORIAL)
|
||||
{
|
||||
if (n <= 2)
|
||||
fmpz_set_ui(res, 1 + (n==2));
|
||||
else
|
||||
fmpz_set_ui(res, ULONG_PRIMORIALS[(n-1)/2-1]);
|
||||
return;
|
||||
}
|
||||
|
||||
pi = n_prime_pi(n);
|
||||
|
||||
primes = n_primes_arr_readonly(pi);
|
||||
bits = FLINT_BIT_COUNT(primes[pi - 1]);
|
||||
|
||||
mpz_ptr = _fmpz_promote(res);
|
||||
mpz_realloc2(mpz_ptr, pi*bits);
|
||||
|
||||
len = mpn_prod_limbs(mpz_ptr->_mp_d, primes, pi, bits);
|
||||
mpz_ptr->_mp_size = len;
|
||||
}
|
||||
|
|
@ -1,120 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright 2009 William Hart
|
||||
Copyright 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <mpfr.h>
|
||||
#include "profiler.h"
|
||||
#include "flint.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "arith.h"
|
||||
|
||||
typedef struct
|
||||
{
|
||||
ulong n;
|
||||
int algorithm;
|
||||
} bernoulli_vec_t;
|
||||
|
||||
|
||||
void sample(void * arg, ulong count)
|
||||
{
|
||||
fmpz * num;
|
||||
fmpz * den;
|
||||
bernoulli_vec_t * params = (bernoulli_vec_t *) arg;
|
||||
ulong n = params->n;
|
||||
slong i;
|
||||
int algorithm = params->algorithm;
|
||||
|
||||
num = _fmpz_vec_init(n);
|
||||
den = _fmpz_vec_init(n);
|
||||
|
||||
prof_start();
|
||||
|
||||
for (i = 0; i < count; i++)
|
||||
{
|
||||
if (algorithm == 0)
|
||||
{
|
||||
_arith_bernoulli_number_vec_recursive(num, den, n);
|
||||
}
|
||||
else if (algorithm == 1)
|
||||
{
|
||||
_arith_bernoulli_number_vec_multi_mod(num, den, n);
|
||||
}
|
||||
else if (algorithm == 2)
|
||||
{
|
||||
_arith_bernoulli_number_vec_zeta(num, den, n);
|
||||
mpfr_free_cache();
|
||||
}
|
||||
}
|
||||
|
||||
prof_stop();
|
||||
|
||||
_fmpz_vec_clear(num, n);
|
||||
_fmpz_vec_clear(den, n);
|
||||
}
|
||||
|
||||
int main(void)
|
||||
{
|
||||
double min_recursive, min_multi_mod, min_zeta, max;
|
||||
bernoulli_vec_t params;
|
||||
slong n;
|
||||
|
||||
flint_printf("n / recursive / multi_mod / zeta / best [times in us]\n");
|
||||
|
||||
for (n = 2; n <= 10000; n = (slong) ((double) n * 1.2) + 1)
|
||||
{
|
||||
params.n = n;
|
||||
|
||||
if (n < 1500)
|
||||
{
|
||||
params.algorithm = 0;
|
||||
prof_repeat(&min_recursive, &max, sample, ¶ms);
|
||||
}
|
||||
else
|
||||
min_recursive = 0.0;
|
||||
|
||||
params.algorithm = 1;
|
||||
prof_repeat(&min_multi_mod, &max, sample, ¶ms);
|
||||
|
||||
params.algorithm = 2;
|
||||
prof_repeat(&min_zeta, &max, sample, ¶ms);
|
||||
|
||||
flint_printf("%wd %.2f %.2f %.2f ",
|
||||
n, min_recursive, min_multi_mod, min_zeta);
|
||||
|
||||
if (min_recursive && min_recursive < min_multi_mod && \
|
||||
min_recursive < min_zeta)
|
||||
flint_printf("(recursive)\n");
|
||||
else if (min_multi_mod < min_zeta)
|
||||
flint_printf("(multi_mod)\n");
|
||||
else
|
||||
flint_printf("(zeta)\n");
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,120 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmpz.h"
|
||||
#include "arith.h"
|
||||
|
||||
void arith_ramanujan_tau_series(fmpz_poly_t res, slong n)
|
||||
{
|
||||
slong j, k, jv, kv;
|
||||
fmpz_t tmp;
|
||||
fmpz_poly_fit_length(res, n);
|
||||
_fmpz_vec_zero(res->coeffs, n);
|
||||
_fmpz_poly_set_length(res, n);
|
||||
fmpz_init(tmp);
|
||||
for (j = jv = 0; jv < n; jv += ++j)
|
||||
{
|
||||
fmpz_set_ui(tmp, 2*j+1);
|
||||
for (k = kv = 0; jv + kv < n; kv += ++k)
|
||||
{
|
||||
if ((j+k) & 1)
|
||||
fmpz_submul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
|
||||
else
|
||||
fmpz_addmul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
|
||||
}
|
||||
}
|
||||
fmpz_poly_sqrlow(res, res, n-1);
|
||||
fmpz_poly_sqrlow(res, res, n-1);
|
||||
fmpz_poly_shift_left(res, res, 1);
|
||||
fmpz_clear(tmp);
|
||||
}
|
||||
|
||||
void _arith_ramanujan_tau(fmpz_t res, fmpz_factor_t factors)
|
||||
{
|
||||
fmpz_poly_t poly;
|
||||
fmpz_t tau_p, p_11, next, this, prev;
|
||||
slong k, r;
|
||||
ulong max_prime;
|
||||
|
||||
max_prime = UWORD(1);
|
||||
for (k = 0; k < factors->num; k++)
|
||||
{
|
||||
/* TODO: handle overflow properly */
|
||||
max_prime = FLINT_MAX(max_prime, fmpz_get_ui(factors->p + k));
|
||||
}
|
||||
|
||||
fmpz_poly_init(poly);
|
||||
arith_ramanujan_tau_series(poly, max_prime + 1);
|
||||
|
||||
fmpz_one(res);
|
||||
fmpz_init(tau_p);
|
||||
fmpz_init(p_11);
|
||||
fmpz_init(next);
|
||||
fmpz_init(this);
|
||||
fmpz_init(prev);
|
||||
|
||||
for (k = 0; k < factors->num; k++)
|
||||
{
|
||||
ulong p = fmpz_get_ui(factors->p + k);
|
||||
|
||||
fmpz_set(tau_p, poly->coeffs + p);
|
||||
fmpz_set_ui(p_11, p);
|
||||
fmpz_pow_ui(p_11, p_11, 11);
|
||||
fmpz_one(prev);
|
||||
fmpz_set(this, tau_p);
|
||||
|
||||
for (r = 1; r < factors->exp[k]; r++)
|
||||
{
|
||||
fmpz_mul(next, tau_p, this);
|
||||
fmpz_submul(next, p_11, prev);
|
||||
fmpz_set(prev, this);
|
||||
fmpz_set(this, next);
|
||||
}
|
||||
fmpz_mul(res, res, this);
|
||||
}
|
||||
|
||||
fmpz_clear(tau_p);
|
||||
fmpz_clear(p_11);
|
||||
fmpz_clear(next);
|
||||
fmpz_clear(this);
|
||||
fmpz_clear(prev);
|
||||
fmpz_poly_clear(poly);
|
||||
}
|
||||
|
||||
void arith_ramanujan_tau(fmpz_t res, const fmpz_t n)
|
||||
{
|
||||
fmpz_factor_t factors;
|
||||
|
||||
if (fmpz_sgn(n) <= 0)
|
||||
{
|
||||
fmpz_zero(res);
|
||||
return;
|
||||
}
|
||||
|
||||
fmpz_factor_init(factors);
|
||||
fmpz_factor(factors, n);
|
||||
_arith_ramanujan_tau(res, factors);
|
||||
fmpz_factor_clear(factors);
|
||||
}
|
||||
|
|
@ -1,138 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
static void
|
||||
_rising_factorial(fmpz * res, slong a, slong b, slong trunc)
|
||||
{
|
||||
const slong span = b - a;
|
||||
|
||||
switch (span)
|
||||
{
|
||||
case 0:
|
||||
fmpz_one(res);
|
||||
break;
|
||||
case 1:
|
||||
fmpz_set_ui(res, a);
|
||||
if (trunc > 1) fmpz_one(res+1);
|
||||
break;
|
||||
case 2:
|
||||
fmpz_set_ui(res, a);
|
||||
fmpz_mul_ui(res, res, a + UWORD(1));
|
||||
if (trunc > 1)
|
||||
{
|
||||
fmpz_set_ui(res+1, 2*a + UWORD(1));
|
||||
if (trunc > 2) fmpz_one(res+2);
|
||||
}
|
||||
break;
|
||||
case 3:
|
||||
fmpz_set_ui(res, a);
|
||||
fmpz_mul_ui(res, res, a + UWORD(1));
|
||||
fmpz_mul_ui(res, res, a + UWORD(2));
|
||||
if (trunc > 1)
|
||||
{
|
||||
fmpz_set_ui(res+1, 3*a);
|
||||
fmpz_mul_ui(res+1, res+1, a + UWORD(2));
|
||||
fmpz_add_ui(res+1, res+1, 2);
|
||||
if (trunc > 2)
|
||||
{
|
||||
fmpz_set_ui(res+2, 3*(a+1));
|
||||
if (trunc > 3)
|
||||
fmpz_one(res+3);
|
||||
}
|
||||
}
|
||||
break;
|
||||
default:
|
||||
{
|
||||
const slong mid = (a + b) / 2;
|
||||
const int chk = (b - a + 1 < trunc); /* i.e. nprod < trunc */
|
||||
const slong nleft = chk ? mid - a + 1 : trunc;
|
||||
const slong nright = chk ? b - mid + 1 : trunc;
|
||||
|
||||
fmpz *left = _fmpz_vec_init(nleft);
|
||||
fmpz *right = _fmpz_vec_init(nright);
|
||||
|
||||
_rising_factorial(left, a, mid, trunc);
|
||||
_rising_factorial(right, mid, b, trunc);
|
||||
|
||||
if (chk)
|
||||
_fmpz_poly_mul(res, right, nright, left, nleft);
|
||||
else
|
||||
_fmpz_poly_mullow(res, left, nleft, right, nright, trunc);
|
||||
|
||||
_fmpz_vec_clear(left, nleft);
|
||||
_fmpz_vec_clear(right, nright);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_number_1u(fmpz_t s, slong n, slong k)
|
||||
{
|
||||
/* Various special cases
|
||||
TODO: factorials, binomial coefficients, harmonic numbers ... */
|
||||
if (k < 1)
|
||||
{
|
||||
fmpz_set_ui(s, (n == 0) & (k == 0));
|
||||
}
|
||||
if (k >= n)
|
||||
{
|
||||
fmpz_set_ui(s, n == k);
|
||||
}
|
||||
else
|
||||
{
|
||||
fmpz *tmp = _fmpz_vec_init(k+1);
|
||||
_rising_factorial(tmp, 0, n, k+1);
|
||||
fmpz_set(s, tmp+k);
|
||||
_fmpz_vec_clear(tmp, k+1);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_number_1(fmpz_t s, slong n, slong k)
|
||||
{
|
||||
arith_stirling_number_1u(s, n, k);
|
||||
if ((n + k) % 2)
|
||||
fmpz_neg(s, s);
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_number_1u_vec(fmpz * row, slong n, slong klen)
|
||||
{
|
||||
if (klen > 0)
|
||||
_rising_factorial(row, 0, n, klen);
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_number_1_vec(fmpz * row, slong n, slong klen)
|
||||
{
|
||||
slong k;
|
||||
|
||||
arith_stirling_number_1u_vec(row, n, klen);
|
||||
|
||||
for (k = (n + 1) % 2; k < klen; k += 2)
|
||||
fmpz_neg(row + k, row + k);
|
||||
}
|
||||
|
|
@ -1,134 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
static __inline__ void
|
||||
_fmpz_addmul_alt(fmpz_t s, fmpz_t t, fmpz_t u, int parity)
|
||||
{
|
||||
if (parity % 2)
|
||||
fmpz_submul(s, t, u);
|
||||
else
|
||||
fmpz_addmul(s, t, u);
|
||||
}
|
||||
|
||||
static void
|
||||
_fmpz_stirling2_powsum(fmpz_t s, slong n, slong k)
|
||||
{
|
||||
fmpz_t t, u;
|
||||
fmpz * bc;
|
||||
slong j, m, max_bc;
|
||||
|
||||
fmpz_init(t);
|
||||
fmpz_init(u);
|
||||
max_bc = (k+1) / 2;
|
||||
|
||||
bc = _fmpz_vec_init(max_bc + 1);
|
||||
fmpz_one(bc);
|
||||
for (j = 1; j <= max_bc; j++)
|
||||
{
|
||||
fmpz_set(bc+j, bc+j-1);
|
||||
fmpz_mul_ui(bc+j, bc+j, k+1-j);
|
||||
fmpz_divexact_ui(bc+j, bc+j, j);
|
||||
}
|
||||
|
||||
fmpz_zero(s);
|
||||
for (j = 1; j <= k; j += 2)
|
||||
{
|
||||
fmpz_set_ui(u, j);
|
||||
fmpz_pow_ui(u, u, n);
|
||||
m = j;
|
||||
/* Process each m = 2^p * j */
|
||||
while (1)
|
||||
{
|
||||
if (m > max_bc)
|
||||
_fmpz_addmul_alt(s, bc+k-m, u, k + m);
|
||||
else
|
||||
_fmpz_addmul_alt(s, bc+m, u, k + m);
|
||||
m *= 2;
|
||||
if (m > k)
|
||||
break;
|
||||
fmpz_mul_2exp(u, u, n);
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(bc, max_bc + 1);
|
||||
fmpz_fac_ui(t, k);
|
||||
fmpz_divexact(s, s, t);
|
||||
fmpz_clear(t);
|
||||
fmpz_clear(u);
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_number_2(fmpz_t s, slong n, slong k)
|
||||
{
|
||||
if (n < 0 || k < 0 || k > n)
|
||||
{
|
||||
fmpz_zero(s);
|
||||
return;
|
||||
}
|
||||
|
||||
/* Topmost diagonals */
|
||||
if (k >= n - 1)
|
||||
{
|
||||
if (k == n)
|
||||
fmpz_one(s);
|
||||
else /* k == n - 1 */
|
||||
{
|
||||
/* S(n,n-1) = binomial(n,2) */
|
||||
fmpz_set_ui(s, n);
|
||||
fmpz_mul_ui(s, s, n-1);
|
||||
fmpz_divexact_ui(s, s, UWORD(2));
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/* Leftmost columns */
|
||||
if (k <= 2)
|
||||
{
|
||||
if (k < 2)
|
||||
fmpz_set_ui(s, k);
|
||||
else
|
||||
{
|
||||
/* S(n,2) = 2^(n-1)-1 */
|
||||
fmpz_one(s);
|
||||
fmpz_mul_2exp(s, s, n-1);
|
||||
fmpz_sub_ui(s, s, UWORD(1));
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
_fmpz_stirling2_powsum(s, n, k);
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_number_2_vec(fmpz * row, slong n, slong klen)
|
||||
{
|
||||
slong m;
|
||||
|
||||
for (m = 0; m <= n; m++)
|
||||
arith_stirling_number_2_vec_next(row, row, m, klen);
|
||||
}
|
||||
|
||||
|
|
@ -1,119 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010, 2013 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
void arith_stirling_number_1u_vec_next(fmpz * row,
|
||||
const fmpz * prev, slong n, slong klen)
|
||||
{
|
||||
slong k;
|
||||
|
||||
if (klen > n) fmpz_one(row + n);
|
||||
if (n != 0 && klen != 0) fmpz_zero(row);
|
||||
|
||||
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
|
||||
{
|
||||
fmpz_mul_ui(row + k, prev + k, n - UWORD(1));
|
||||
fmpz_add(row + k, prev + k - 1, row + k);
|
||||
}
|
||||
|
||||
for (k = n + 1; k < klen; k++)
|
||||
fmpz_zero(row + k);
|
||||
}
|
||||
|
||||
void arith_stirling_number_1_vec_next(fmpz * row,
|
||||
const fmpz * prev, slong n, slong klen)
|
||||
{
|
||||
slong k;
|
||||
|
||||
if (klen > n) fmpz_one(row + n);
|
||||
if (n != 0 && klen != 0) fmpz_zero(row);
|
||||
|
||||
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
|
||||
{
|
||||
fmpz_mul_ui(row + k, prev + k, n - UWORD(1));
|
||||
fmpz_sub(row + k, prev + k - 1, row + k);
|
||||
}
|
||||
|
||||
for (k = n + 1; k < klen; k++)
|
||||
fmpz_zero(row + k);
|
||||
}
|
||||
|
||||
void arith_stirling_number_2_vec_next(fmpz * row,
|
||||
const fmpz * prev, slong n, slong klen)
|
||||
{
|
||||
slong k;
|
||||
|
||||
if (klen > n) fmpz_one(row + n);
|
||||
if (n != 0 && klen != 0) fmpz_zero(row);
|
||||
|
||||
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
|
||||
{
|
||||
fmpz_mul_ui(row + k, prev + k, k);
|
||||
fmpz_add(row + k, prev + k - 1, row + k);
|
||||
}
|
||||
|
||||
for (k = n + 1; k < klen; k++)
|
||||
fmpz_zero(row + k);
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_matrix_1u(fmpz_mat_t mat)
|
||||
{
|
||||
slong n;
|
||||
|
||||
if (fmpz_mat_is_empty(mat))
|
||||
return;
|
||||
|
||||
for (n = 0; n < mat->r; n++)
|
||||
arith_stirling_number_1u_vec_next(mat->rows[n],
|
||||
mat->rows[n - (n != 0)], n, mat->c);
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_matrix_1(fmpz_mat_t mat)
|
||||
{
|
||||
slong n;
|
||||
|
||||
if (fmpz_mat_is_empty(mat))
|
||||
return;
|
||||
|
||||
for (n = 0; n < mat->r; n++)
|
||||
arith_stirling_number_1_vec_next(mat->rows[n],
|
||||
mat->rows[n - (n != 0)], n, mat->c);
|
||||
}
|
||||
|
||||
void
|
||||
arith_stirling_matrix_2(fmpz_mat_t mat)
|
||||
{
|
||||
slong n;
|
||||
|
||||
if (fmpz_mat_is_empty(mat))
|
||||
return;
|
||||
|
||||
for (n = 0; n < mat->r; n++)
|
||||
arith_stirling_number_2_vec_next(mat->rows[n],
|
||||
mat->rows[n - (n != 0)], n, mat->c);
|
||||
}
|
||||
|
|
@ -1,137 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmpz.h"
|
||||
#include "arith.h"
|
||||
|
||||
static void
|
||||
sum_of_two_squares(fmpz_t r, const fmpz_t n)
|
||||
{
|
||||
fmpz_factor_t fac;
|
||||
slong i;
|
||||
|
||||
fmpz_factor_init(fac);
|
||||
fmpz_factor(fac, n);
|
||||
fmpz_one(r);
|
||||
|
||||
for (i = 0; i < fac->num; i++)
|
||||
{
|
||||
const int res = fmpz_fdiv_ui(fac->p + i, 4);
|
||||
|
||||
if (res == 1)
|
||||
{
|
||||
fac->exp[i]++;
|
||||
fmpz_mul_ui(r, r, fac->exp[i]);
|
||||
}
|
||||
else if (res == 3)
|
||||
{
|
||||
if (fac->exp[i] % 2)
|
||||
{
|
||||
fmpz_zero(r);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_mul_ui(r, r, 4);
|
||||
fmpz_factor_clear(fac);
|
||||
}
|
||||
|
||||
static void
|
||||
sum_of_four_squares(fmpz_t r, const fmpz_t n)
|
||||
{
|
||||
const mp_bitcnt_t v = fmpz_val2(n);
|
||||
|
||||
if (v == 0)
|
||||
{
|
||||
arith_divisor_sigma(r, n, 1);
|
||||
fmpz_mul_ui(r, r, 8);
|
||||
}
|
||||
else
|
||||
{
|
||||
fmpz_tdiv_q_2exp(r, n, v);
|
||||
arith_divisor_sigma(r, r, 1);
|
||||
fmpz_mul_ui(r, r, 24);
|
||||
}
|
||||
}
|
||||
|
||||
static void
|
||||
sum_of_squares_recursive(fmpz_t r, slong k, ulong n)
|
||||
{
|
||||
fmpz_t t, u;
|
||||
slong i, j;
|
||||
|
||||
fmpz_init(t);
|
||||
fmpz_init(u);
|
||||
fmpz_zero(r);
|
||||
|
||||
for (i = j = 0; j <= n; i++)
|
||||
{
|
||||
fmpz_set_ui(u, n - j);
|
||||
arith_sum_of_squares(t, k - 1, u);
|
||||
|
||||
if (j > 0)
|
||||
fmpz_mul_ui(t, t, 2);
|
||||
fmpz_add(r, r, t);
|
||||
|
||||
j += 2 * i + 1;
|
||||
}
|
||||
|
||||
fmpz_clear(t);
|
||||
fmpz_clear(u);
|
||||
}
|
||||
|
||||
static void
|
||||
sum_of_squares_series(fmpz_t r, ulong k, slong n)
|
||||
{
|
||||
fmpz * t;
|
||||
|
||||
t = _fmpz_vec_init(n + 1);
|
||||
arith_sum_of_squares_vec(t, k, n + 1);
|
||||
fmpz_set(r, t + n);
|
||||
_fmpz_vec_clear(t, n + 1);
|
||||
}
|
||||
|
||||
void
|
||||
arith_sum_of_squares(fmpz_t r, ulong k, const fmpz_t n)
|
||||
{
|
||||
if (fmpz_sgn(n) <= 0 || k == 0)
|
||||
fmpz_set_ui(r, fmpz_is_zero(n) != 0);
|
||||
else if (k == 1)
|
||||
fmpz_set_ui(r, 2 * (fmpz_is_square(n) != 0));
|
||||
else if (k == 2)
|
||||
sum_of_two_squares(r, n);
|
||||
else if (k == 4)
|
||||
sum_of_four_squares(r, n);
|
||||
else if (k == 3 || k == 5)
|
||||
sum_of_squares_recursive(r, k, fmpz_get_ui(n));
|
||||
else if (fmpz_fits_si(n))
|
||||
sum_of_squares_series(r, k, fmpz_get_ui(n));
|
||||
else
|
||||
{
|
||||
flint_printf("Exception (arith_sum_of_squares). n is too large.\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
|
@ -1,108 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "arith.h"
|
||||
|
||||
static void
|
||||
theta3_qexp(fmpz * r, slong n)
|
||||
{
|
||||
slong i, j;
|
||||
|
||||
_fmpz_vec_zero(r, n);
|
||||
|
||||
for (i = j = 0; j < n; i++)
|
||||
{
|
||||
fmpz_set_ui(r + j, i == 0 ? 1 : 2);
|
||||
j += 1 + 2*i;
|
||||
}
|
||||
}
|
||||
|
||||
static void
|
||||
theta3_qexp_squared(fmpz * r, slong n)
|
||||
{
|
||||
slong i, j, x, y;
|
||||
|
||||
_fmpz_vec_zero(r, n);
|
||||
|
||||
for (x = i = 0; x < n; i++)
|
||||
{
|
||||
for (y = j = 0; x + y < n; j++)
|
||||
{
|
||||
fmpz_add_ui(r + x + y, r + x + y, (x ? 2 : 1) * (y ? 2 : 1));
|
||||
y += 2 * j + 1;
|
||||
}
|
||||
x += 2 * i + 1;
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
arith_sum_of_squares_vec(fmpz * r, ulong k, slong n)
|
||||
{
|
||||
if (k == 0 || n <= 1)
|
||||
{
|
||||
_fmpz_vec_zero(r, n);
|
||||
if (n > 0)
|
||||
fmpz_set_ui(r, 1);
|
||||
}
|
||||
else if (k == 1)
|
||||
{
|
||||
theta3_qexp(r, n);
|
||||
}
|
||||
else if (k == 2)
|
||||
{
|
||||
theta3_qexp_squared(r, n);
|
||||
}
|
||||
else if (k % 2 == 0)
|
||||
{
|
||||
fmpz * t = _fmpz_vec_init(n);
|
||||
|
||||
theta3_qexp_squared(t, n);
|
||||
_fmpz_poly_pow_trunc(r, t, k / 2, n);
|
||||
_fmpz_vec_clear(t, n);
|
||||
}
|
||||
else
|
||||
{
|
||||
fmpz *t, *u;
|
||||
t = _fmpz_vec_init(n);
|
||||
u = _fmpz_vec_init(n);
|
||||
|
||||
theta3_qexp_squared(t, n);
|
||||
|
||||
if (k == 3)
|
||||
{
|
||||
theta3_qexp(u, n);
|
||||
_fmpz_poly_mullow(r, t, n, u, n, n);
|
||||
}
|
||||
else
|
||||
{
|
||||
_fmpz_poly_pow_trunc(u, t, (k - 1) / 2, n);
|
||||
theta3_qexp(t, n);
|
||||
_fmpz_poly_mullow(r, t, n, u, n, n);
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(t, n);
|
||||
_fmpz_vec_clear(u, n);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,138 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
Inspired by a Sage implementation written by William Stein.
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <math.h>
|
||||
#include "arith.h"
|
||||
|
||||
|
||||
/* Bound coefficients using (x + u)^(2^n) and the binomial
|
||||
coefficients. TODO: this is about 2x too large... */
|
||||
static slong __bound_prec(ulong n)
|
||||
{
|
||||
slong i;
|
||||
double u, N;
|
||||
|
||||
N = UWORD(1) << n;
|
||||
|
||||
/* u = (sum of square roots)^(2^n) */
|
||||
u = 0;
|
||||
for (i = 0; i < n; i++)
|
||||
u += sqrt(n_nth_prime(1 + i));
|
||||
u = N * log(u) * 1.44269504088897;
|
||||
|
||||
/* Central binomial coefficient C(N,N/2) < 2^N / sqrt(3*N/2) */
|
||||
u += N - 0.5*(n-1) - 0.792481250360578; /* log(sqrt(3)) */
|
||||
|
||||
return u;
|
||||
}
|
||||
|
||||
void arith_swinnerton_dyer_polynomial(fmpz_poly_t poly, ulong n)
|
||||
{
|
||||
fmpz *square_roots, *T, *tmp1, *tmp2, *tmp3;
|
||||
fmpz_t one;
|
||||
slong i, j, k, N;
|
||||
slong prec;
|
||||
|
||||
if (n == 0)
|
||||
{
|
||||
fmpz_poly_zero(poly);
|
||||
fmpz_poly_set_coeff_ui(poly, 1, UWORD(1));
|
||||
return;
|
||||
}
|
||||
|
||||
N = WORD(1) << n;
|
||||
|
||||
prec = __bound_prec(n);
|
||||
/* flint_printf("prec: %wd\n", prec); */
|
||||
|
||||
fmpz_poly_fit_length(poly, N + 1);
|
||||
T = poly->coeffs;
|
||||
|
||||
fmpz_init(one);
|
||||
fmpz_one(one);
|
||||
fmpz_mul_2exp(one, one, prec);
|
||||
|
||||
square_roots = _fmpz_vec_init(n);
|
||||
tmp1 = flint_malloc((N/2 + 1) * sizeof(fmpz));
|
||||
tmp2 = flint_malloc((N/2 + 1) * sizeof(fmpz));
|
||||
tmp3 = _fmpz_vec_init(N);
|
||||
|
||||
for (i = 0; i < n; i++)
|
||||
{
|
||||
fmpz_set_ui(square_roots + i, n_nth_prime(i + 1));
|
||||
fmpz_mul_2exp(square_roots + i, square_roots + i, 2 * prec);
|
||||
fmpz_sqrt(square_roots + i, square_roots + i);
|
||||
}
|
||||
|
||||
/* Build linear factors */
|
||||
for (i = 0; i < N; i++)
|
||||
{
|
||||
fmpz_zero(T + i);
|
||||
for (j = 0; j < n; j++)
|
||||
{
|
||||
if ((i >> j) & 1)
|
||||
fmpz_add(T + i, T + i, square_roots + j);
|
||||
else
|
||||
fmpz_sub(T + i, T + i, square_roots + j);
|
||||
}
|
||||
}
|
||||
|
||||
/* For each level... */
|
||||
for (i = 0; i < n; i++)
|
||||
{
|
||||
slong stride = UWORD(1) << i;
|
||||
|
||||
for (j = 0; j < N; j += 2*stride)
|
||||
{
|
||||
for (k = 0; k < stride; k++)
|
||||
{
|
||||
tmp1[k] = T[j + k];
|
||||
tmp2[k] = T[j + stride + k];
|
||||
}
|
||||
tmp1[stride] = *one;
|
||||
tmp2[stride] = *one;
|
||||
|
||||
_fmpz_poly_mullow(tmp3, tmp1, stride + 1, tmp2, stride + 1, 2*stride);
|
||||
_fmpz_vec_scalar_fdiv_q_2exp(T + j, tmp3, 2*stride, prec);
|
||||
}
|
||||
}
|
||||
|
||||
/* Round */
|
||||
fmpz_fdiv_q_2exp(one, one, 1);
|
||||
for (i = 0; i < N; i++)
|
||||
fmpz_add(T + i, T + i, one);
|
||||
|
||||
_fmpz_vec_scalar_fdiv_q_2exp(T, T, N, prec);
|
||||
fmpz_one(T + (UWORD(1) << n));
|
||||
_fmpz_poly_set_length(poly, N + 1);
|
||||
|
||||
_fmpz_vec_clear(square_roots, n);
|
||||
flint_free(tmp1);
|
||||
flint_free(tmp2);
|
||||
_fmpz_vec_clear(tmp3, UWORD(1) << n);
|
||||
fmpz_clear(one);
|
||||
}
|
||||
|
|
@ -1,120 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz * b1;
|
||||
fmpz * b2;
|
||||
slong n, k;
|
||||
|
||||
const slong maxn = 400;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bell_number....");
|
||||
fflush(stdout);
|
||||
|
||||
b1 = _fmpz_vec_init(maxn);
|
||||
|
||||
/* Consistency test */
|
||||
for (n = 0; n < maxn; n++)
|
||||
arith_bell_number(b1 + n, n);
|
||||
|
||||
for (n = 0; n < maxn; n++)
|
||||
{
|
||||
b2 = _fmpz_vec_init(n);
|
||||
arith_bell_number_vec(b2, n);
|
||||
|
||||
if (!_fmpz_vec_equal(b1, b2, n))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd\n", n);
|
||||
abort();
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(b2, n);
|
||||
}
|
||||
|
||||
/* Compare with B_n = sum of Stirling numbers of 2nd kind */
|
||||
for (n = 0; n < 1000; n += (n < 50) ? + 1 : n/4)
|
||||
{
|
||||
b2 = _fmpz_vec_init(n+1);
|
||||
|
||||
arith_stirling_number_2_vec(b2, n, n+1);
|
||||
|
||||
for (k = 1; k <= n; k++)
|
||||
fmpz_add(b2, b2, b2 + k);
|
||||
|
||||
arith_bell_number(b1, n);
|
||||
|
||||
if (!fmpz_equal(b1, b2))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd\n", n);
|
||||
fmpz_print(b1);
|
||||
flint_printf("\n");
|
||||
fmpz_print(b2);
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
/* Also check nmod value */
|
||||
{
|
||||
nmod_t mod;
|
||||
mp_limb_t bb;
|
||||
|
||||
nmod_init(&mod, n_randtest_prime(state, 0));
|
||||
bb = arith_bell_number_nmod(n, mod);
|
||||
|
||||
if (fmpz_fdiv_ui(b1, mod.n) != bb)
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd\n", n);
|
||||
fmpz_print(b1);
|
||||
flint_printf("\n");
|
||||
flint_printf("should be %wu mod %wu\n", bb, mod.n);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(b2, n+1);
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(b1, maxn);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,72 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
slong i;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bell_number_multi_mod....");
|
||||
fflush(stdout);
|
||||
|
||||
for (i = 0; i < 100; i++)
|
||||
{
|
||||
slong n;
|
||||
fmpz_t b1, b2;
|
||||
|
||||
fmpz_init(b1);
|
||||
fmpz_init(b2);
|
||||
|
||||
n = n_randint(state, 500);
|
||||
|
||||
arith_bell_number_bsplit(b1, n);
|
||||
arith_bell_number_multi_mod(b2, n);
|
||||
|
||||
if (!fmpz_equal(b1, b2))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd\n", n);
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_clear(b1);
|
||||
fmpz_clear(b2);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,77 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
slong i, j;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bell_number_nmod....");
|
||||
fflush(stdout);
|
||||
|
||||
for (i = 0; i < 10; i++)
|
||||
{
|
||||
mp_ptr b;
|
||||
slong n;
|
||||
nmod_t mod;
|
||||
mp_limb_t p;
|
||||
|
||||
n = n_randint(state, 1000);
|
||||
p = n_randtest_prime(state, 0);
|
||||
|
||||
nmod_init(&mod, p);
|
||||
|
||||
b = _nmod_vec_init(n + 1);
|
||||
arith_bell_number_nmod_vec(b, n + 1, mod);
|
||||
|
||||
for (j = 0; j <= n; j++)
|
||||
{
|
||||
mp_limb_t u = arith_bell_number_nmod(j, mod);
|
||||
|
||||
if (u != b[j])
|
||||
{
|
||||
flint_printf("FAIL: p = %wu, i = %wd\n", p, j);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
_nmod_vec_clear(b);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,78 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "nmod_vec.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
mp_ptr b1, b2;
|
||||
slong n;
|
||||
|
||||
const slong maxn = 3000;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bell_number_nmod_vec....");
|
||||
fflush(stdout);
|
||||
|
||||
b1 = _nmod_vec_init(maxn);
|
||||
b2 = _nmod_vec_init(maxn);
|
||||
|
||||
for (n = 0; n < maxn; n += (n < 50) ? + 1 : n/4)
|
||||
{
|
||||
nmod_t mod;
|
||||
mp_limb_t p;
|
||||
|
||||
do {
|
||||
p = n_randtest_prime(state, 0);
|
||||
} while (p < n);
|
||||
|
||||
nmod_init(&mod, p);
|
||||
|
||||
arith_bell_number_nmod_vec_recursive(b1, n, mod);
|
||||
arith_bell_number_nmod_vec_series(b2, n, mod);
|
||||
|
||||
if (!_nmod_vec_equal(b1, b2, n))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd\n", n);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
_nmod_vec_clear(b1);
|
||||
_nmod_vec_clear(b2);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,69 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz * b1;
|
||||
fmpz * b2;
|
||||
slong n;
|
||||
|
||||
const slong maxn = 1000;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bell_number_vec....");
|
||||
fflush(stdout);
|
||||
|
||||
b1 = _fmpz_vec_init(maxn);
|
||||
b2 = _fmpz_vec_init(maxn);
|
||||
|
||||
for (n = 0; n < maxn; n += (n < 50) ? + 1 : n/4)
|
||||
{
|
||||
arith_bell_number_vec_recursive(b1, n);
|
||||
arith_bell_number_vec_multi_mod(b2, n);
|
||||
|
||||
if (!_fmpz_vec_equal(b1, b2, n))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd\n", n);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(b1, maxn);
|
||||
_fmpz_vec_clear(b2, maxn);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,120 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpq_poly.h"
|
||||
#include "fmpq.h"
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz * num1;
|
||||
fmpz * den1;
|
||||
fmpz_t num2;
|
||||
fmpz_t den2;
|
||||
slong n, N;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bernoulli_number....");
|
||||
fflush(stdout);
|
||||
|
||||
N = 4000;
|
||||
|
||||
num1 = _fmpz_vec_init(N);
|
||||
den1 = _fmpz_vec_init(N);
|
||||
fmpz_init(num2);
|
||||
fmpz_init(den2);
|
||||
|
||||
_arith_bernoulli_number_vec_multi_mod(num1, den1, N);
|
||||
|
||||
for (n = 0; n < N; n++)
|
||||
{
|
||||
_arith_bernoulli_number(num2, den2, n);
|
||||
|
||||
if (!fmpz_equal(num1 + n, num2))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd, numerator\n", n);
|
||||
flint_printf("vec: "); fmpz_print(num1 + n); flint_printf("\n");
|
||||
flint_printf("single: "); fmpz_print(num2); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
if (!fmpz_equal(den1 + n, den2))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd, denominator\n", n);
|
||||
flint_printf("vec: "); fmpz_print(den1 + n); flint_printf("\n");
|
||||
flint_printf("single: "); fmpz_print(den2); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
/* Check non underscore versions */
|
||||
do
|
||||
{
|
||||
slong N = 100;
|
||||
fmpq * x;
|
||||
fmpq_t t;
|
||||
|
||||
fmpq_init(t);
|
||||
x = flint_malloc(sizeof(fmpq) * N);
|
||||
|
||||
for (n = 0; n < N; n++)
|
||||
fmpq_init(x + n);
|
||||
|
||||
arith_bernoulli_number_vec(x, N);
|
||||
for (n = 0; n < N; n++)
|
||||
{
|
||||
arith_bernoulli_number(t, n);
|
||||
if (!fmpq_equal(x + n, t))
|
||||
{
|
||||
flint_printf("FAIL!: n = %wd\n", n);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
for (n = 0; n < N; n++)
|
||||
fmpq_clear(x + n);
|
||||
flint_free(x);
|
||||
fmpq_clear(t);
|
||||
|
||||
} while (0);
|
||||
|
||||
_fmpz_vec_clear(num1, N);
|
||||
_fmpz_vec_clear(den1, N);
|
||||
fmpz_clear(num2);
|
||||
fmpz_clear(den2);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,67 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz_t s, t;
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bernoulli_number_denom....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(s);
|
||||
fmpz_init(t);
|
||||
|
||||
for (n = 0; n < 1000; n++)
|
||||
{
|
||||
arith_bernoulli_number_denom(t, n);
|
||||
fmpz_addmul_ui(s, t, n_nth_prime(n+1));
|
||||
}
|
||||
|
||||
fmpz_set_str(t, "34549631155954474103407159", 10);
|
||||
|
||||
if (!fmpz_equal(s, t))
|
||||
{
|
||||
flint_printf("FAIL: Hash disagrees with known value\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_clear(s);
|
||||
fmpz_clear(t);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,102 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpq_poly.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz * num1;
|
||||
fmpz * num2;
|
||||
fmpz * num3;
|
||||
fmpz * den1;
|
||||
fmpz * den2;
|
||||
fmpz * den3;
|
||||
slong i, n, N;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bernoulli_number_vec....");
|
||||
fflush(stdout);
|
||||
|
||||
N = 2000;
|
||||
|
||||
num1 = _fmpz_vec_init(N);
|
||||
num2 = _fmpz_vec_init(N);
|
||||
num3 = _fmpz_vec_init(N);
|
||||
den1 = _fmpz_vec_init(N);
|
||||
den2 = _fmpz_vec_init(N);
|
||||
den3 = _fmpz_vec_init(N);
|
||||
|
||||
for (n = 0; n < N; n += (n<100) ? 1 : n/3)
|
||||
{
|
||||
_arith_bernoulli_number_vec_recursive(num1, den1, n);
|
||||
_arith_bernoulli_number_vec_multi_mod(num2, den2, n);
|
||||
_arith_bernoulli_number_vec_zeta(num3, den3, n);
|
||||
|
||||
for (i = 0; i < n; i++)
|
||||
{
|
||||
if (!fmpz_equal(num1 + i, num2 + i) ||
|
||||
!fmpz_equal(num1 + i, num3 + i))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd, numerator of B_%wd\n", n, i);
|
||||
flint_printf("recursive: "); fmpz_print(num1 + i); flint_printf("\n");
|
||||
flint_printf("multi_mod: "); fmpz_print(num2 + i); flint_printf("\n");
|
||||
flint_printf("zeta: "); fmpz_print(num3 + i); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
if (!fmpz_equal(den1 + i, den2 + i) ||
|
||||
!fmpz_equal(den1 + i, den3 + i))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd, denominator of B_%wd\n", n, i);
|
||||
flint_printf("recursive: "); fmpz_print(den1 + i); flint_printf("\n");
|
||||
flint_printf("multi_mod: "); fmpz_print(den2 + i); flint_printf("\n");
|
||||
flint_printf("zeta: "); fmpz_print(den3 + i); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(num1, N);
|
||||
_fmpz_vec_clear(num2, N);
|
||||
_fmpz_vec_clear(num3, N);
|
||||
_fmpz_vec_clear(den1, N);
|
||||
_fmpz_vec_clear(den2, N);
|
||||
_fmpz_vec_clear(den3, N);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,89 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpq_poly.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpq_poly_t P, Q;
|
||||
mpz_t t;
|
||||
|
||||
slong k, n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("bernoulli_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
for (n = 0; n <= 100; n++)
|
||||
{
|
||||
fmpq_poly_init(P);
|
||||
fmpq_poly_init(Q);
|
||||
|
||||
mpz_init(t);
|
||||
|
||||
for (k = 0; k <= n; k++)
|
||||
{
|
||||
arith_bernoulli_polynomial(P, k);
|
||||
flint_mpz_bin_uiui(t, n+1, k);
|
||||
fmpq_poly_scalar_mul_mpz(P, P, t);
|
||||
fmpq_poly_add(Q, Q, P);
|
||||
}
|
||||
|
||||
fmpq_poly_scalar_div_ui(Q, Q, n+1);
|
||||
mpz_clear(t);
|
||||
|
||||
fmpq_poly_zero(P);
|
||||
fmpq_poly_set_coeff_ui(P, n, UWORD(1));
|
||||
|
||||
if (!fmpq_poly_equal(P, Q))
|
||||
{
|
||||
flint_printf("ERROR: sum up to n = %wd did not add to x^n\n", n);
|
||||
flint_printf("Sum: ");
|
||||
fmpq_poly_print_pretty(Q, "x");
|
||||
flint_printf("\nExpected: ");
|
||||
fmpq_poly_print_pretty(P, "x");
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpq_poly_clear(P);
|
||||
fmpq_poly_clear(Q);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,82 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_poly.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz_poly_t T0, T1, T2, t;
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("chebyshev_t_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_poly_init(T0);
|
||||
fmpz_poly_init(T1);
|
||||
fmpz_poly_init(T2);
|
||||
fmpz_poly_init(t);
|
||||
|
||||
arith_chebyshev_t_polynomial(T0, 0);
|
||||
arith_chebyshev_t_polynomial(T1, 1);
|
||||
|
||||
for (n = 2; n <= 500; n++)
|
||||
{
|
||||
arith_chebyshev_t_polynomial(T2, n);
|
||||
|
||||
/* Verify T_{n+1} = 2 x T_n - T_{n-1} */
|
||||
fmpz_poly_scalar_mul_ui(t, T1, UWORD(2));
|
||||
fmpz_poly_shift_left(t, t, 1);
|
||||
fmpz_poly_sub(t, t, T0);
|
||||
|
||||
if (!fmpz_poly_equal(t, T2))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd\n", n);
|
||||
flint_printf("t: "); fmpz_poly_print_pretty(t, "x"); flint_printf("\n");
|
||||
flint_printf("T2: "); fmpz_poly_print_pretty(T2, "x"); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_poly_swap(T0, T1);
|
||||
fmpz_poly_swap(T1, T2);
|
||||
}
|
||||
|
||||
fmpz_poly_clear(T0);
|
||||
fmpz_poly_clear(T1);
|
||||
fmpz_poly_clear(T2);
|
||||
fmpz_poly_clear(t);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,72 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_poly.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz_poly_t T, U;
|
||||
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("chebyshev_u_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_poly_init(T);
|
||||
fmpz_poly_init(U);
|
||||
|
||||
for (n = 0; n <= 500; n++)
|
||||
{
|
||||
arith_chebyshev_u_polynomial(U, n);
|
||||
arith_chebyshev_t_polynomial(T, n + 1);
|
||||
fmpz_poly_derivative(T, T);
|
||||
fmpz_poly_scalar_divexact_ui(T, T, n + 1);
|
||||
|
||||
if (!fmpz_poly_equal(T, U))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd\n", n);
|
||||
flint_printf("T: "); fmpz_poly_print_pretty(T, "x"); flint_printf("\n");
|
||||
flint_printf("U: "); fmpz_poly_print_pretty(U, "x"); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
fmpz_poly_clear(T);
|
||||
fmpz_poly_clear(U);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,129 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_poly.h"
|
||||
|
||||
|
||||
/*
|
||||
Generated with Mathematica:
|
||||
Table[Mod[MinimalPolynomial[Cos[2 Pi/n]][1337], 31337], {n,1,500}]
|
||||
*/
|
||||
|
||||
static const short testdata[] = {
|
||||
1,
|
||||
1336, 1338, 2675, 1337, 8113, 2673, 6283, 2719, 29508, 2765, 6949,
|
||||
5437, 2788, 26742, 25554, 26194, 29376, 29506, 30945, 15614, 8957,
|
||||
16643, 9263, 21050, 30556, 10533, 1570, 11562, 3988, 16546, 26642, 4041,
|
||||
3581, 109, 9839, 27175, 11691, 1460, 28287, 18369, 16503, 3184, 13336,
|
||||
23083, 12495, 3246, 14160, 8081, 5301, 8652, 28989, 24149, 17733, 1568,
|
||||
4800, 28863, 29280, 13741, 30919, 29819, 28584, 8913, 550, 6207, 13930,
|
||||
23373, 12644, 15265, 27975, 30386, 1603, 15894, 22276, 3138, 11610,
|
||||
2208, 515, 30817, 23050, 4333, 25031, 13615, 5116, 18609, 25490, 14555,
|
||||
22663, 8425, 21751, 19293, 3, 10688, 26829, 14467, 1426, 12413, 5305,
|
||||
25377, 27164, 3711,
|
||||
9613, 22340, 7457, 3704, 1795, 22877, 31060, 17472, 11317, 22274,
|
||||
11036, 7796, 27242, 22174, 3663, 10507, 16599, 18192, 15208, 7257, 7022,
|
||||
10810, 27891, 18495, 7032, 11383, 20768, 27351, 31089, 27723, 10486,
|
||||
2075, 25298, 20531, 28548, 25342, 6510, 20657, 15608, 5534, 22145,
|
||||
30150, 25222, 12128, 389, 21860, 9631, 4536, 4704, 3677, 27282, 26668,
|
||||
20784, 15684, 12847, 1307, 10586, 24355, 27553, 10952, 8886, 25029,
|
||||
29278, 29964, 17943, 1006, 5895, 11466, 16679, 17500, 5414, 3420, 17644,
|
||||
5165, 6255, 2807, 30577, 26277, 14032, 2425, 13945, 27988, 17437, 28204,
|
||||
11853, 12265, 8097, 24919, 10703, 18081, 19121, 23364, 14035, 2382,
|
||||
1722, 21617, 11863, 27682, 8538, 26401,
|
||||
1487, 14570, 14213, 18315, 30244, 14611, 25421, 13954, 29802,
|
||||
29118, 5788, 7547, 9710, 21645, 17858, 20672, 2295, 21286, 7217, 30405,
|
||||
5090, 22674, 5747, 5809, 13789, 16385, 23732, 12258, 10944, 14669, 2043,
|
||||
1453, 13510, 12422, 24073, 3025, 28094, 2770, 9198, 27411, 24736, 28958,
|
||||
23508, 27897, 17838, 10690, 5375, 29469, 22458, 9466, 28541, 16308,
|
||||
20491, 10320, 9836, 673, 26630, 20819, 25687, 19263, 16620, 28683,
|
||||
30268, 1113, 26632, 18450, 17555, 20121, 18083, 12796, 26659, 9788,
|
||||
10448, 2828, 29753, 26653, 13636, 6270, 10398, 16224, 1481, 1153, 26387,
|
||||
17835, 19289, 2683, 1937, 16760, 14372, 12632, 15716, 12423, 24202,
|
||||
14543, 10763, 27059, 437, 18647, 17133, 27774,
|
||||
2039, 3931, 7737, 20470, 11068, 26238, 28463, 22610, 28349, 23819,
|
||||
22780, 4101, 13218, 12878, 25048, 25163, 11032, 10129, 2571, 9319,
|
||||
11708, 6704, 19105, 11593, 24863, 26090, 15235, 18038, 22056, 19624,
|
||||
12066, 9798, 16508, 22376, 15776, 10595, 28391, 18898, 11645, 16655,
|
||||
19391, 11364, 28198, 4348, 6653, 11962, 22652, 18750, 22125, 21504,
|
||||
23718, 25662, 6768, 24234, 29605, 8280, 5246, 23064, 1360, 21538, 4374,
|
||||
8186, 7540, 24091, 3017, 23007, 12000, 11289, 8698, 22118, 5505, 18535,
|
||||
29647, 15878, 4416, 8598, 13062, 8878, 9674, 5066, 17770, 24888, 20643,
|
||||
1345, 22570, 1363, 3710, 18429, 11731, 14885, 12983, 18600, 26334,
|
||||
27101, 17858, 22221, 2471, 911, 12033, 2824,
|
||||
6354, 984, 28507, 3521, 17963, 6558, 11166, 24004, 24367, 8572,
|
||||
19198, 6937, 15220, 13122, 3540, 589, 17503, 14073, 14954, 26020, 12974,
|
||||
20684, 19844, 17852, 1097, 10831, 23848, 7013, 15683, 15954, 22290,
|
||||
30257, 15807, 22775, 13607, 9428, 30055, 11607, 30426, 2579, 340, 29747,
|
||||
25213, 28551, 5705, 15704, 10625, 16932, 3215, 16716, 6698, 21470,
|
||||
29839, 511, 23506, 4338, 30506, 18038, 20430, 20586, 18225, 7721, 15812,
|
||||
3140, 22149, 4949, 8125, 9897, 6323, 20612, 2012, 23744, 9414, 16497,
|
||||
5557, 5225, 8518, 30549, 21805, 5692, 25222, 16326, 22995, 27432, 16385,
|
||||
23506, 9911, 23131, 3880, 30647, 13222, 10416, 5619, 2078, 9411, 12398,
|
||||
22772, 7328, 17932, 19965,
|
||||
-1
|
||||
};
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz_poly_t p;
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("cyclotomic_cos_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_poly_init(p);
|
||||
|
||||
for (n = 0; testdata[n] != -1; n++)
|
||||
{
|
||||
mp_limb_t y;
|
||||
arith_cos_minpoly(p, n);
|
||||
y = fmpz_poly_evaluate_mod(p, 1337, 31337);
|
||||
|
||||
if (y != testdata[n])
|
||||
{
|
||||
flint_printf("FAIL: n = %wd\n", n);
|
||||
flint_printf("y = %wu\n", y);
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_poly_clear(p);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,145 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_poly.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
void cyclotomic_naive(fmpz_poly_t poly, ulong n)
|
||||
{
|
||||
fmpz_poly_t t;
|
||||
slong d;
|
||||
|
||||
fmpz_poly_init(t);
|
||||
|
||||
fmpz_poly_set_ui(poly, UWORD(1));
|
||||
for (d = 1; d <= n; d++)
|
||||
{
|
||||
if (n % d == 0)
|
||||
{
|
||||
if (n_moebius_mu(n / d) == 1)
|
||||
{
|
||||
fmpz_poly_zero(t);
|
||||
fmpz_poly_set_coeff_si(t, d, 1);
|
||||
fmpz_poly_set_coeff_si(t, 0, -1);
|
||||
fmpz_poly_mul(poly, poly, t);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
for (d = 1; d <= n; d++)
|
||||
{
|
||||
if (n % d == 0)
|
||||
{
|
||||
if (n_moebius_mu(n / d) == -1)
|
||||
{
|
||||
fmpz_poly_zero(t);
|
||||
fmpz_poly_set_coeff_si(t, d, 1);
|
||||
fmpz_poly_set_coeff_si(t, 0, -1);
|
||||
fmpz_poly_div(poly, poly, t);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_poly_clear(t);
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz_poly_t A, B;
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("cyclotomic_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
for (n = 0; n <= 1000; n++)
|
||||
{
|
||||
fmpz_poly_init(A);
|
||||
fmpz_poly_init(B);
|
||||
|
||||
arith_cyclotomic_polynomial(A, n);
|
||||
cyclotomic_naive(B, n);
|
||||
|
||||
if (!fmpz_poly_equal(A, B))
|
||||
{
|
||||
flint_printf("FAIL: wrong value of Phi_%wd(x)\n", n);
|
||||
flint_printf("Computed:\n");
|
||||
fmpz_poly_print_pretty(A, "x");
|
||||
flint_printf("\n\nExpected:\n");
|
||||
fmpz_poly_print_pretty(B, "x");
|
||||
flint_printf("\n\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_poly_clear(A);
|
||||
fmpz_poly_clear(B);
|
||||
}
|
||||
|
||||
/* We verify the first value that does not fit on 32 bits.
|
||||
This exercises the slow path at least on a 32 bit system.
|
||||
Testing the 64 bit value is a bit too much to do by default
|
||||
as it requires ~2 GB of memory and takes a few minutes. */
|
||||
{
|
||||
fmpz_t h, ref;
|
||||
|
||||
const ulong nn = UWORD(10163195);
|
||||
/* const ulong nn = UWORD(169828113); 64-bit case */
|
||||
|
||||
fmpz_init(h);
|
||||
fmpz_init(ref);
|
||||
fmpz_set_str(ref, "1376877780831", 10);
|
||||
/* fmpz_set_str(ref, "31484567640915734941", 10); 64-bit case */
|
||||
|
||||
fmpz_poly_init(A);
|
||||
arith_cyclotomic_polynomial(A, UWORD(10163195));
|
||||
fmpz_poly_height(h, A);
|
||||
|
||||
if (!fmpz_equal(h, ref))
|
||||
{
|
||||
flint_printf("Bad computation of Phi_%wd(x)\n", nn);
|
||||
flint_printf("Computed height:\n");
|
||||
fmpz_print(h);
|
||||
flint_printf("\nExpected height:\n");
|
||||
fmpz_print(ref);
|
||||
flint_printf("\n\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_poly_clear(A);
|
||||
fmpz_clear(h);
|
||||
fmpz_clear(ref);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,192 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpq.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "math.h"
|
||||
|
||||
/*
|
||||
The results in the following random test cases were computed with the
|
||||
naive implementation. Doing a live comparison with large values against
|
||||
the naive implementation would take too much time.
|
||||
*/
|
||||
static const slong testdata[][4] =
|
||||
{
|
||||
/* h, k, p/q */
|
||||
{WORD(20816815), WORD(29229), WORD(-10669), WORD(87687)},
|
||||
{WORD(-481962612), WORD(709105), WORD(-910639), WORD(141821)},
|
||||
{WORD(-70965), WORD(3384), WORD(1785), WORD(752)},
|
||||
{WORD(1899905), WORD(6657), WORD(-43795), WORD(5706)},
|
||||
{WORD(-1893), WORD(511167), WORD(-3411568), WORD(170389)},
|
||||
{WORD(1417295), WORD(10180), WORD(3543), WORD(4072)},
|
||||
{WORD(-1149), WORD(9350), WORD(6971), WORD(9350)},
|
||||
{WORD(-15520), WORD(22977640), WORD(-70331425), WORD(574441)},
|
||||
{WORD(3339), WORD(9873153), WORD(270746882), WORD(1097017)},
|
||||
{WORD(470645896), WORD(71754), WORD(-21713), WORD(107631)},
|
||||
{WORD(1153), WORD(1332403), WORD(258755243), WORD(2664806)},
|
||||
{WORD(-501576), WORD(292801), WORD(269095), WORD(292801)},
|
||||
{WORD(1861), WORD(34440), WORD(-723059), WORD(206640)},
|
||||
{WORD(-4278761), WORD(239321), WORD(791947), WORD(239321)},
|
||||
{WORD(9414763), WORD(30776409), WORD(-93285463), WORD(92329227)},
|
||||
{WORD(4872687), WORD(2199), WORD(146), WORD(733)},
|
||||
{WORD(-22349505), WORD(60581653), WORD(27694241), WORD(60581653)},
|
||||
{WORD(85739724), WORD(9289), WORD(961), WORD(2654)},
|
||||
{WORD(-5616), WORD(124023), WORD(-31447), WORD(41341)},
|
||||
{WORD(99382204), WORD(1378843), WORD(-2537405), WORD(2757686)},
|
||||
{WORD(1903), WORD(15842), WORD(102), WORD(89)},
|
||||
{WORD(-907226), WORD(5818), WORD(5608), WORD(2909)},
|
||||
{WORD(-948920), WORD(4768), WORD(-4815), WORD(1192)},
|
||||
{WORD(-352220914), WORD(15390287), WORD(-171358081), WORD(30780574)},
|
||||
{WORD(-159206), WORD(3028284), WORD(12921745), WORD(4542426)},
|
||||
{WORD(61951448), WORD(1624), WORD(-341), WORD(406)},
|
||||
{WORD(-49167), WORD(2092), WORD(-32915), WORD(4184)},
|
||||
{WORD(-20878222), WORD(586303210), WORD(-530581301), WORD(293151605)},
|
||||
{WORD(-1435637), WORD(3483), WORD(-4787), WORD(20898)},
|
||||
{WORD(-1129797), WORD(171620), WORD(238211), WORD(68648)},
|
||||
{WORD(-177095), WORD(2914), WORD(1132), WORD(1457)},
|
||||
{WORD(-343227551), WORD(1509), WORD(-3289), WORD(4527)},
|
||||
{WORD(57497376), WORD(1351), WORD(373), WORD(2702)},
|
||||
{WORD(3350543), WORD(5771893), WORD(-51196457), WORD(5771893)},
|
||||
{WORD(-44408), WORD(1670), WORD(367), WORD(1670)},
|
||||
{WORD(-4139), WORD(59959), WORD(-286689), WORD(119918)},
|
||||
{WORD(7397588), WORD(16695), WORD(-41627), WORD(20034)},
|
||||
{WORD(-78900791), WORD(10792), WORD(-30905), WORD(21584)},
|
||||
{WORD(-1204294), WORD(10134), WORD(-8945), WORD(30402)},
|
||||
{WORD(27649424), WORD(57014291), WORD(731583513), WORD(114028582)},
|
||||
{WORD(3275043), WORD(436410815), WORD(2018428417), WORD(174564326)},
|
||||
#if FLINT64 /* skip on 32 bit only because of the literals */
|
||||
{WORD(61247), WORD(81381215), WORD(3622491319), WORD(32552486)},
|
||||
{WORD(-52118), WORD(125095621), WORD(-24931204413), WORD(125095621)},
|
||||
{WORD(201446493), WORD(951783261), WORD(2467429915), WORD(634522174)},
|
||||
{WORD(176112), WORD(72187934), WORD(2692844825), WORD(72187934)},
|
||||
{WORD(1272), WORD(8722219), WORD(9972821075), WORD(17444438)},
|
||||
#endif
|
||||
{0, 0, 0, 0}
|
||||
};
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz_t hh, kk;
|
||||
fmpq_t s1, s2;
|
||||
slong i, h, k;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("dedekind_sum....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(hh);
|
||||
fmpz_init(kk);
|
||||
fmpq_init(s1);
|
||||
fmpq_init(s2);
|
||||
|
||||
for (k = -200; k < 200; k++)
|
||||
{
|
||||
for (h = -200; h < 200; h++)
|
||||
{
|
||||
fmpz_set_si(hh, h);
|
||||
fmpz_set_si(kk, k);
|
||||
|
||||
arith_dedekind_sum(s1, hh, kk);
|
||||
arith_dedekind_sum_naive(s2, hh, kk);
|
||||
|
||||
if (!fmpq_equal(s1, s2))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("s(%wd,%wd)\n", h, k);
|
||||
flint_printf("s1: "); fmpq_print(s1); flint_printf("\n");
|
||||
flint_printf("s2: "); fmpq_print(s2); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* Test large values, 10-30 bits */
|
||||
for (i = 0; testdata[i][0] != 0; i++)
|
||||
{
|
||||
h = testdata[i][0];
|
||||
k = testdata[i][1];
|
||||
|
||||
fmpz_set_si(hh, h);
|
||||
fmpz_set_si(kk, k);
|
||||
|
||||
arith_dedekind_sum(s1, hh, kk);
|
||||
|
||||
fmpz_set_si(fmpq_numref(s2), testdata[i][2]);
|
||||
fmpz_set_si(fmpq_denref(s2), testdata[i][3]);
|
||||
|
||||
if (!fmpq_equal(s1, s2))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("s(%wd,%wd)\n", h, k);
|
||||
flint_printf("s1: "); fmpq_print(s1); flint_printf("\n");
|
||||
flint_printf("s2: "); fmpq_print(s2); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
/* Check a large value computed with Pari */
|
||||
fmpz_set_ui(hh, 1);
|
||||
fmpz_mul_2exp(hh, hh, 1000);
|
||||
fmpz_add_ui(hh, hh, 1);
|
||||
fmpz_set_ui(kk, 1);
|
||||
fmpz_mul_2exp(kk, kk, 1001);
|
||||
fmpz_add_ui(kk, kk, 1);
|
||||
|
||||
arith_dedekind_sum(s1, hh, kk);
|
||||
if ((fmpz_fdiv_ui(fmpq_numref(s1), 1000000000) != 906445312) ||
|
||||
(fmpz_fdiv_ui(fmpq_denref(s1), 1000000000) != 8416259))
|
||||
{
|
||||
flint_printf("Wrong large value:\n");
|
||||
fmpq_print(s1);
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
|
||||
/* Just check that nothing crashes with bignums */
|
||||
for (i = 0; i < 1000; i++)
|
||||
{
|
||||
fmpz_randtest(hh, state, 300);
|
||||
fmpz_randtest(kk, state, 300);
|
||||
|
||||
arith_dedekind_sum(s1, hh, kk);
|
||||
}
|
||||
|
||||
fmpz_clear(hh);
|
||||
fmpz_clear(kk);
|
||||
fmpq_clear(s1);
|
||||
fmpq_clear(s2);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,86 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpq.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "math.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
double s1, s2f;
|
||||
fmpz_t hh, kk;
|
||||
fmpq_t s2;
|
||||
slong h, k;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("dedekind_sum_coprime_d....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(hh);
|
||||
fmpz_init(kk);
|
||||
fmpq_init(s2);
|
||||
|
||||
for (k = 0; k < 300; k++)
|
||||
{
|
||||
for (h = 0; h <= k; h++)
|
||||
{
|
||||
if (n_gcd(k, h) == 1)
|
||||
{
|
||||
fmpz_set_si(hh, h);
|
||||
fmpz_set_si(kk, k);
|
||||
|
||||
s1 = arith_dedekind_sum_coprime_d(h, k);
|
||||
arith_dedekind_sum_naive(s2, hh, kk);
|
||||
|
||||
s2f = ((double)fmpz_get_si(fmpq_numref(s2))) /
|
||||
fmpz_get_si(fmpq_denref(s2));
|
||||
|
||||
if (fabs(s1 - s2f) > 1e-10)
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("s(%wd,%wd)\n", h, k);
|
||||
flint_printf("s1: %.20f\n", s1);
|
||||
flint_printf("s2: %.20f\n", s2f);
|
||||
flint_printf("Exact: "); fmpq_print(s2); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(hh);
|
||||
fmpz_clear(kk);
|
||||
fmpq_clear(s2);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,83 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpq.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "math.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz_t hh, kk;
|
||||
fmpq_t s1, s2;
|
||||
slong h, k;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("dedekind_sum_coprime_large....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(hh);
|
||||
fmpz_init(kk);
|
||||
fmpq_init(s1);
|
||||
fmpq_init(s2);
|
||||
|
||||
for (k = 0; k < 300; k++)
|
||||
{
|
||||
for (h = 0; h <= k; h++)
|
||||
{
|
||||
if (n_gcd(k, h) == 1)
|
||||
{
|
||||
fmpz_set_si(hh, h);
|
||||
fmpz_set_si(kk, k);
|
||||
|
||||
arith_dedekind_sum_coprime_large(s1, hh, kk);
|
||||
arith_dedekind_sum_naive(s2, hh, kk);
|
||||
|
||||
if (!fmpq_equal(s1, s2))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("s(%wd,%wd)\n", h, k);
|
||||
flint_printf("s1: "); fmpq_print(s1); flint_printf("\n");
|
||||
flint_printf("s2: "); fmpq_print(s2); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(hh);
|
||||
fmpz_clear(kk);
|
||||
fmpq_clear(s1);
|
||||
fmpq_clear(s2);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,94 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "fmpz_poly.h"
|
||||
#include "fmpz.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
void fmpz_sigma_naive(fmpz_t x, ulong n, ulong k)
|
||||
{
|
||||
slong i = 0;
|
||||
|
||||
fmpz_t t;
|
||||
fmpz_poly_t p;
|
||||
fmpz_init(t);
|
||||
fmpz_poly_init(p);
|
||||
fmpz_set_ui(t, n);
|
||||
arith_divisors(p, t);
|
||||
|
||||
fmpz_zero(x);
|
||||
for (i = 0; i < p->length; i++)
|
||||
{
|
||||
fmpz_poly_get_coeff_fmpz(t, p, i);
|
||||
fmpz_pow_ui(t, t, k);
|
||||
fmpz_add(x, x, t);
|
||||
}
|
||||
|
||||
fmpz_clear(t);
|
||||
fmpz_poly_clear(p);
|
||||
}
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz_t m, a, b;
|
||||
slong n, k;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("divisor_sigma....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(a);
|
||||
fmpz_init(b);
|
||||
fmpz_init(m);
|
||||
|
||||
for (n = 0; n < 5000; n++)
|
||||
{
|
||||
for (k = 0; k < 10; k++)
|
||||
{
|
||||
fmpz_set_ui(m, n);
|
||||
arith_divisor_sigma(a, m, k);
|
||||
fmpz_sigma_naive(b, n, k);
|
||||
if (!fmpz_equal(a, b))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("wrong value for n=%wd, k=%wd\n", n, k);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(a);
|
||||
fmpz_clear(b);
|
||||
fmpz_clear(m);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,86 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "fmpz_poly.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
void arith_divisors_naive(fmpz_poly_t p, slong n)
|
||||
{
|
||||
slong k;
|
||||
slong i = 0;
|
||||
|
||||
n = FLINT_ABS(n);
|
||||
|
||||
fmpz_poly_zero(p);
|
||||
for (k = 1; k <= n; k++)
|
||||
{
|
||||
if (n % k == 0)
|
||||
{
|
||||
fmpz_poly_set_coeff_si(p, i, k);
|
||||
i++;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz_t t;
|
||||
fmpz_poly_t a, b;
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("divisors....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(t);
|
||||
fmpz_poly_init(a);
|
||||
fmpz_poly_init(b);
|
||||
|
||||
for (n = -1000; n < 1000; n++)
|
||||
{
|
||||
fmpz_set_si(t, n);
|
||||
arith_divisors(a, t);
|
||||
arith_divisors_naive(b, n);
|
||||
if (!fmpz_poly_equal(a, b))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("wrong value for n=%wd\n", n);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(t);
|
||||
fmpz_poly_clear(a);
|
||||
fmpz_poly_clear(b);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,81 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_vec.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz * r;
|
||||
fmpz_t s, t;
|
||||
slong k, n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("euler_number_vec....");
|
||||
fflush(stdout);
|
||||
|
||||
for (n = 2; n <= 3000; n += (n<100) ? 2 : n/3)
|
||||
{
|
||||
n += n % 2;
|
||||
r = _fmpz_vec_init(n + 1);
|
||||
fmpz_init(s);
|
||||
fmpz_init(t);
|
||||
|
||||
arith_euler_number_vec(r, n + 1);
|
||||
|
||||
/* sum binomial(n,k) E_k = 0 */
|
||||
fmpz_set_ui(t, UWORD(1));
|
||||
for (k = 0; k <= n; k++)
|
||||
{
|
||||
fmpz_addmul(s, r + k, t);
|
||||
fmpz_mul_ui(t, t, n - k);
|
||||
fmpz_divexact_ui(t, t, k + 1);
|
||||
}
|
||||
|
||||
if (!fmpz_is_zero(s))
|
||||
{
|
||||
flint_printf("ERROR: sum over 0,...,n = %wd\n", n);
|
||||
_fmpz_vec_print(r, n + 1);
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_clear(s);
|
||||
fmpz_clear(t);
|
||||
_fmpz_vec_clear(r, n + 1);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,74 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpq_poly.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz * ress;
|
||||
fmpz_t res;
|
||||
slong n, N;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("euler_number_zeta....");
|
||||
fflush(stdout);
|
||||
|
||||
N = 3000;
|
||||
|
||||
ress = _fmpz_vec_init(N);
|
||||
arith_euler_number_vec(ress, N);
|
||||
|
||||
for (n = 0; n < N; n++)
|
||||
{
|
||||
fmpz_init(res);
|
||||
|
||||
arith_euler_number(res, n);
|
||||
if (!fmpz_equal(res, ress + n))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd\n", n);
|
||||
flint_printf("Value: "); fmpz_print(res); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_clear(res);
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(ress, N);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,118 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <limits.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "profiler.h"
|
||||
|
||||
|
||||
int main(void)
|
||||
{
|
||||
slong i;
|
||||
ulong n;
|
||||
fmpz_t x, y, z;
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("euler_phi....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(x);
|
||||
fmpz_init(y);
|
||||
fmpz_init(z);
|
||||
|
||||
|
||||
for (i = 0; i < 100; i++)
|
||||
{
|
||||
fmpz_set_ui(x, i);
|
||||
arith_euler_phi(y, x);
|
||||
arith_euler_phi(x, x);
|
||||
fmpz_set_ui(z, n_euler_phi(i));
|
||||
if (!fmpz_equal(x, y) || !fmpz_equal(x, z))
|
||||
{
|
||||
flint_printf("FAIL: %wd\n", i);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
/* Aliasing test */
|
||||
for (i = 0; i < 1000; i++)
|
||||
{
|
||||
fmpz_randtest(x, state, FLINT_BITS);
|
||||
fmpz_randtest(y, state, 5);
|
||||
fmpz_pow_ui(y, y, n_randtest(state) % 100);
|
||||
fmpz_mul(x, x, y);
|
||||
fmpz_set(z, x);
|
||||
arith_euler_phi(y, x);
|
||||
arith_euler_phi(x, x);
|
||||
if (!fmpz_equal(x, y))
|
||||
{
|
||||
flint_printf("FAIL: ");
|
||||
fmpz_print(z);
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
/* Power of a single prime, phi(p^n) = (p-1) * p^(n-1) */
|
||||
for (i = 0; i < 100; i++)
|
||||
{
|
||||
n = (n_randtest(state) % 100) + 1;
|
||||
fmpz_set_ui(x, n_nth_prime(i+1));
|
||||
fmpz_pow_ui(x, x, n);
|
||||
arith_euler_phi(x, x);
|
||||
fmpz_set_ui(y, n_nth_prime(i+1));
|
||||
fmpz_pow_ui(y, y, n-1);
|
||||
fmpz_mul_ui(y, y, n_nth_prime(i+1)-1);
|
||||
if (!fmpz_equal(x, y))
|
||||
{
|
||||
flint_printf("FAIL: %wu ^ %wu\n", n_nth_prime(i+1), n);
|
||||
}
|
||||
}
|
||||
|
||||
/* Something nontrivial */
|
||||
fmpz_set_str(x, "10426024348053113487152988625265848110501553295256578345594388516660144", 10);
|
||||
fmpz_set_str(y, "2265085829098571747262267425315881590169106756213617459200000000000000", 10);
|
||||
arith_euler_phi(x, x);
|
||||
if (!fmpz_equal(x, y))
|
||||
{
|
||||
flint_printf("FAIL: special test value\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
|
||||
|
||||
fmpz_clear(x);
|
||||
fmpz_clear(y);
|
||||
fmpz_clear(z);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,93 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpq_poly.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpq_poly_t P, Q;
|
||||
mpz_t t;
|
||||
|
||||
slong k, n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("euler_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
for (n = 0; n <= 100; n++)
|
||||
{
|
||||
fmpq_poly_init(P);
|
||||
fmpq_poly_init(Q);
|
||||
|
||||
mpz_init(t);
|
||||
|
||||
for (k = 0; k < n; k++)
|
||||
{
|
||||
arith_euler_polynomial(P, k);
|
||||
flint_mpz_bin_uiui(t, n, k);
|
||||
fmpq_poly_scalar_mul_mpz(P, P, t);
|
||||
fmpq_poly_add(Q, Q, P);
|
||||
}
|
||||
|
||||
fmpq_poly_scalar_div_ui(Q, Q, 2);
|
||||
|
||||
arith_euler_polynomial(P, n);
|
||||
fmpq_poly_add(Q, Q, P);
|
||||
|
||||
mpz_clear(t);
|
||||
|
||||
fmpq_poly_zero(P);
|
||||
fmpq_poly_set_coeff_ui(P, n, UWORD(1));
|
||||
|
||||
if (!fmpq_poly_equal(P, Q))
|
||||
{
|
||||
flint_printf("ERROR: sum up to n = %wd did not add to x^n\n", n);
|
||||
flint_printf("Sum: ");
|
||||
fmpq_poly_print_pretty(Q, "x");
|
||||
flint_printf("\nExpected: ");
|
||||
fmpq_poly_print_pretty(P, "x");
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpq_poly_clear(P);
|
||||
fmpq_poly_clear(Q);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,154 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010,2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <limits.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpq.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "profiler.h"
|
||||
|
||||
|
||||
void numerical_test(fmpq_t res, slong n, double ans)
|
||||
{
|
||||
const double tol = 1e-13;
|
||||
double err;
|
||||
|
||||
mpq_t tmp;
|
||||
mpq_init(tmp);
|
||||
|
||||
arith_harmonic_number(res, n);
|
||||
fmpq_get_mpq(tmp, res);
|
||||
err = mpq_get_d(tmp) - ans;
|
||||
err = FLINT_ABS(err);
|
||||
|
||||
if (err > tol)
|
||||
{
|
||||
flint_printf("FAIL: %wd %.16f %.16f\n", n, mpq_get_d(tmp), ans);
|
||||
abort();
|
||||
}
|
||||
|
||||
mpq_clear(tmp);
|
||||
}
|
||||
|
||||
void
|
||||
mpq_harmonic_balanced(mpq_t res, slong a, slong b)
|
||||
{
|
||||
slong k;
|
||||
mpq_t t;
|
||||
|
||||
mpq_init(t);
|
||||
|
||||
if (b - a < 50)
|
||||
{
|
||||
flint_mpq_set_ui(res, 0, UWORD(1));
|
||||
for (k = a; k <= b; k++)
|
||||
{
|
||||
flint_mpq_set_ui(t, UWORD(1), k);
|
||||
mpq_add(res, res, t);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
mpq_harmonic_balanced(res, a, (a+b)/2);
|
||||
mpq_harmonic_balanced(t, (a+b)/2+1, b);
|
||||
mpq_add(res, res, t);
|
||||
}
|
||||
|
||||
mpq_clear(t);
|
||||
}
|
||||
|
||||
|
||||
int main(void)
|
||||
{
|
||||
slong i;
|
||||
mpq_t x, y;
|
||||
fmpq_t t;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("harmonic_number....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpq_init(t);
|
||||
mpq_init(x);
|
||||
mpq_init(y);
|
||||
|
||||
for (i = -2; i < 1000; i++)
|
||||
{
|
||||
mpq_harmonic_balanced(x, 1, i);
|
||||
arith_harmonic_number(t, i);
|
||||
fmpq_get_mpq(y, t);
|
||||
|
||||
if (!mpq_equal(x, y))
|
||||
{
|
||||
flint_printf("FAIL: %wd\n", i);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
numerical_test(t, 1000, 7.4854708605503449127);
|
||||
numerical_test(t, 1001, 7.4864698615493459117);
|
||||
numerical_test(t, 1002, 7.4874678655413618797);
|
||||
numerical_test(t, 1003, 7.4884648745144426375);
|
||||
|
||||
numerical_test(t, 10000, 9.7876060360443822642);
|
||||
numerical_test(t, 10001, 9.7877060260453821642);
|
||||
numerical_test(t, 10002, 9.7878060060493813643);
|
||||
numerical_test(t, 10003, 9.7879059760583786652);
|
||||
numerical_test(t, 10004, 9.7880059360743722677);
|
||||
|
||||
numerical_test(t, 20000, 10.480728217229327573);
|
||||
numerical_test(t, 30000, 10.886184992119899362);
|
||||
numerical_test(t, 40000, 11.173862897945522882);
|
||||
numerical_test(t, 50000, 11.397003949278482638);
|
||||
numerical_test(t, 60000, 11.579323839415955783);
|
||||
numerical_test(t, 70000, 11.733473328773164956);
|
||||
numerical_test(t, 80000, 11.867003828544530692);
|
||||
numerical_test(t, 90000, 11.984786169759202469);
|
||||
|
||||
numerical_test(t, 100000, 12.090146129863427947);
|
||||
numerical_test(t, 100001, 12.090156129763428947);
|
||||
numerical_test(t, 100002, 12.090166129563432947);
|
||||
numerical_test(t, 100003, 12.090176129263441947);
|
||||
numerical_test(t, 100004, 12.090186128863457946);
|
||||
|
||||
numerical_test(t, 300000, 13.188755085205611713);
|
||||
numerical_test(t, 500000, 13.699580042305528322);
|
||||
numerical_test(t, 700000, 14.036051993212618803);
|
||||
numerical_test(t, 900000, 14.287366262763433338);
|
||||
|
||||
mpq_clear(x);
|
||||
mpq_clear(y);
|
||||
fmpq_clear(t);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,70 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
|
||||
static const mp_limb_t known[] = {
|
||||
1, 1, 2, 3, 4, 6, 6, 12, 15, 20, 30, 30, 60, 60, 84, 105, 140, 210,
|
||||
210, 420, 420, 420, 420, 840, 840, 1260, 1260, 1540, 2310, 2520,
|
||||
4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380,
|
||||
27720, 30030, 32760, 60060, 60060, 60060, 60060, 120120
|
||||
};
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz * res;
|
||||
slong k, n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("landau_function_vec....");
|
||||
fflush(stdout);
|
||||
|
||||
n = 45;
|
||||
res = _fmpz_vec_init(n);
|
||||
arith_landau_function_vec(res, n);
|
||||
|
||||
for (k = 0; k < n; k++)
|
||||
{
|
||||
if (fmpz_cmp_ui(res + k, known[k]))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("k = %wd, res[k] = %wd, expected: %wd\n",
|
||||
k, fmpz_get_si(res + k), known[k]);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(res, n);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,86 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpq_poly.h"
|
||||
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpq_poly_t Pn, Pn1, Pn2, R;
|
||||
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("legendre_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpq_poly_init(Pn);
|
||||
fmpq_poly_init(Pn1);
|
||||
fmpq_poly_init(Pn2);
|
||||
fmpq_poly_init(R);
|
||||
|
||||
fmpq_poly_set_ui(Pn, UWORD(1));
|
||||
fmpq_poly_set_coeff_ui(Pn1, 1, UWORD(1));
|
||||
|
||||
for (n = 0; n <= 500; n++)
|
||||
{
|
||||
arith_legendre_polynomial(R, n);
|
||||
|
||||
if (!fmpq_poly_equal(Pn, R))
|
||||
{
|
||||
flint_printf("FAIL: n = %wd\n", n);
|
||||
flint_printf("Direct: "); fmpq_poly_print_pretty(R, "x"); flint_printf("\n");
|
||||
flint_printf("Recur.: "); fmpq_poly_print_pretty(Pn, "x"); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpq_poly_shift_left(Pn2, Pn1, 1);
|
||||
fmpq_poly_scalar_mul_ui(Pn2, Pn2, 2*n + 3);
|
||||
fmpq_poly_scalar_mul_si(Pn, Pn, -(n+1));
|
||||
fmpq_poly_add(Pn2, Pn2, Pn);
|
||||
fmpq_poly_scalar_div_ui(Pn2, Pn2, n+2);
|
||||
|
||||
fmpq_poly_swap(Pn, Pn1);
|
||||
fmpq_poly_swap(Pn1, Pn2);
|
||||
}
|
||||
|
||||
fmpq_poly_clear(Pn);
|
||||
fmpq_poly_clear(Pn1);
|
||||
fmpq_poly_clear(Pn2);
|
||||
fmpq_poly_clear(R);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,98 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <limits.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "profiler.h"
|
||||
|
||||
|
||||
void check(fmpz_t n, int expected)
|
||||
{
|
||||
int mu;
|
||||
|
||||
mu = arith_moebius_mu(n);
|
||||
if (mu != expected)
|
||||
{
|
||||
flint_printf("FAIL:");
|
||||
fmpz_print(n);
|
||||
flint_printf("\n");
|
||||
}
|
||||
}
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz_t x;
|
||||
ulong p;
|
||||
slong i, j, k, l;
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("moebius_mu....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(x);
|
||||
|
||||
for (i = -1000; i < 1000; i++)
|
||||
{
|
||||
fmpz_set_si(x, i);
|
||||
check(x, n_moebius_mu(FLINT_ABS(i)));
|
||||
}
|
||||
|
||||
for (i = 0; i < 1000; i++)
|
||||
{
|
||||
fmpz_set_ui(x, 1);
|
||||
/* Product of some primes */
|
||||
k = n_randtest(state) % 10;
|
||||
l = n_randtest(state) % 10;
|
||||
for (j = 0; j < k; j++)
|
||||
{
|
||||
l += (n_randtest(state) % 10) + 1;
|
||||
fmpz_mul_ui(x, x, n_nth_prime(l+1));
|
||||
}
|
||||
|
||||
check(x, (k % 2 ? -1 : 1));
|
||||
fmpz_neg(x, x);
|
||||
|
||||
check(x, (k % 2 ? -1 : 1));
|
||||
fmpz_abs(x, x);
|
||||
|
||||
/* No longer square-free */
|
||||
p = n_nth_prime(n_randtest(state) % 100 + 1);
|
||||
fmpz_mul_ui(x, x, p*p);
|
||||
check(x, 0);
|
||||
}
|
||||
|
||||
fmpz_clear(x);
|
||||
|
||||
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,160 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include <mpfr.h>
|
||||
#include "flint.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
/* Values mod 10^9 generated with Sage */
|
||||
static const ulong testdata[][2] =
|
||||
{
|
||||
{100000, 421098519},
|
||||
{100001, 33940350},
|
||||
{100002, 579731933},
|
||||
{100003, 625213730},
|
||||
{100004, 539454200},
|
||||
{100005, 69672418},
|
||||
{100006, 865684292},
|
||||
{100007, 641916724},
|
||||
{100008, 36737908},
|
||||
{100009, 293498270},
|
||||
{100010, 177812057},
|
||||
{100011, 756857293},
|
||||
{100012, 950821113},
|
||||
{100013, 824882014},
|
||||
{100014, 533894560},
|
||||
{100015, 660734788},
|
||||
{100016, 835912257},
|
||||
{100017, 302982816},
|
||||
{100018, 468609888},
|
||||
{100019, 221646940},
|
||||
{1000000, 104673818},
|
||||
{1000001, 980212296},
|
||||
{1000002, 709795681},
|
||||
{1000003, 530913758},
|
||||
{1000004, 955452980},
|
||||
{1000005, 384388683},
|
||||
{1000006, 138665072},
|
||||
{1000007, 144832602},
|
||||
{1000008, 182646067},
|
||||
{1000009, 659145045},
|
||||
{1000010, 17911162},
|
||||
{1000011, 606326324},
|
||||
{1000012, 99495156},
|
||||
{1000013, 314860251},
|
||||
{1000014, 497563335},
|
||||
{1000015, 726842109},
|
||||
{1000016, 301469541},
|
||||
{1000017, 227491620},
|
||||
{1000018, 704160927},
|
||||
{1000019, 995311980},
|
||||
{10000000, 677288980},
|
||||
{10000001, 433805210},
|
||||
{10000002, 365406948},
|
||||
{10000003, 120899894},
|
||||
{10000004, 272822040},
|
||||
{10000005, 71938624},
|
||||
{10000006, 637670808},
|
||||
{10000007, 766947591},
|
||||
{10000008, 980210244},
|
||||
{10000009, 965734705},
|
||||
{10000010, 187411691},
|
||||
{10000011, 485652153},
|
||||
{10000012, 825498761},
|
||||
{10000013, 895802660},
|
||||
{10000014, 152775845},
|
||||
{10000015, 791493402},
|
||||
{10000016, 299640598},
|
||||
{10000017, 383615481},
|
||||
{10000018, 378922331},
|
||||
{10000019, 37059200},
|
||||
{100000000, 836637702},
|
||||
{100000001, 66421565},
|
||||
{100000002, 747849093},
|
||||
{100000003, 465329748},
|
||||
{100000004, 166747980},
|
||||
{0, 0},
|
||||
};
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz_t p;
|
||||
fmpz * v;
|
||||
|
||||
slong i;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("number_of_partitions....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(p);
|
||||
v = _fmpz_vec_init(3000);
|
||||
|
||||
arith_number_of_partitions_vec(v, 3000);
|
||||
|
||||
for (i = 0; i < 3000; i++)
|
||||
{
|
||||
arith_number_of_partitions(p, i);
|
||||
if (!fmpz_equal(p, v + i))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("p(%wd) does not agree with power series\n", i);
|
||||
flint_printf("Computed p(%wd): ", i); fmpz_print(p); flint_printf("\n");
|
||||
flint_printf("Expected: "); fmpz_print(v + i); flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(v, 3000);
|
||||
|
||||
for (i = 0; testdata[i][0] != 0; i++)
|
||||
{
|
||||
arith_number_of_partitions(p, testdata[i][0]);
|
||||
|
||||
if (fmpz_fdiv_ui(p, 1000000000) != testdata[i][1])
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("p(%wd) does not agree with known value mod 10^9\n",
|
||||
testdata[i][0]);
|
||||
flint_printf("Computed: %wu\n", fmpz_fdiv_ui(p, 1000000000));
|
||||
flint_printf("Expected: %wu\n", testdata[i][1]);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(p);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,120 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <limits.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "profiler.h"
|
||||
#include "nmod_vec.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz * p;
|
||||
mp_ptr pmod;
|
||||
slong k, n;
|
||||
|
||||
const slong maxn = 1000;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("number_of_partitions_vec....");
|
||||
fflush(stdout);
|
||||
|
||||
p = _fmpz_vec_init(maxn);
|
||||
pmod = _nmod_vec_init(maxn);
|
||||
|
||||
for (n = 0; n < maxn; n += (n < 50) ? + 1 : n/4)
|
||||
{
|
||||
fmpz_t s, t;
|
||||
nmod_t mod;
|
||||
nmod_init(&mod, n_randtest_prime(state, 0));
|
||||
|
||||
arith_number_of_partitions_vec(p, n);
|
||||
arith_number_of_partitions_nmod_vec(pmod, n, mod);
|
||||
|
||||
for (k = 0; k < n; k++)
|
||||
{
|
||||
if (fmpz_fdiv_ui(p + k, mod.n) != pmod[k])
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd, k = %wd\n", n, k);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
if (n > 1)
|
||||
{
|
||||
fmpz_init(s);
|
||||
fmpz_init(t);
|
||||
|
||||
for (k = 1; k < n; k++)
|
||||
{
|
||||
slong j;
|
||||
|
||||
j = n - 1 - k*(3*k - 1)/2;
|
||||
if (j >= 0)
|
||||
fmpz_set(t, p + j);
|
||||
else
|
||||
fmpz_zero(t);
|
||||
|
||||
j = n - 1 - k*(3*k + 1)/2;
|
||||
if (j >= 0)
|
||||
fmpz_add(t, t, p + j);
|
||||
|
||||
if (k % 2)
|
||||
fmpz_add(s, s, t);
|
||||
else
|
||||
fmpz_sub(s, s, t);
|
||||
}
|
||||
|
||||
if (!fmpz_equal(s, p + n - 1))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("n = %wd\n", n);
|
||||
fmpz_print(s);
|
||||
flint_printf("\n");
|
||||
fmpz_print(p + n - 1);
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_clear(s);
|
||||
fmpz_clear(t);
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(p, maxn);
|
||||
_nmod_vec_clear(pmod);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,66 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
|
||||
int main(void)
|
||||
{
|
||||
slong k;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("pi_chudnovsky....");
|
||||
fflush(stdout);
|
||||
|
||||
for (k = 2; k < 20; k++)
|
||||
{
|
||||
mpfr_t x, y;
|
||||
|
||||
mpfr_init2(x, WORD(1) << k);
|
||||
mpfr_init2(y, WORD(1) << k);
|
||||
|
||||
mpfr_const_pi(x, MPFR_RNDN);
|
||||
mpfr_pi_chudnovsky(y, MPFR_RNDN);
|
||||
|
||||
if (!mpfr_equal_p(x, y))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("Wrong value at prec = %wd\n", WORD(1) << k);
|
||||
abort();
|
||||
}
|
||||
|
||||
mpfr_clear(x);
|
||||
mpfr_clear(y);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,69 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
|
||||
int main(void)
|
||||
{
|
||||
ulong k;
|
||||
fmpz_t x;
|
||||
fmpz_t y;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("primorial....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(x);
|
||||
fmpz_init(y);
|
||||
fmpz_set_ui(y, 1);
|
||||
|
||||
for (k = 0; k < 10000; k++)
|
||||
{
|
||||
arith_primorial(x, k);
|
||||
if (n_is_prime(k))
|
||||
fmpz_mul_ui(y, y, k);
|
||||
if (!fmpz_equal(x, y))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("primorial of %wu disagrees with direct product\n", k);
|
||||
fmpz_print(x);
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_clear(x);
|
||||
fmpz_clear(y);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,172 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "ulong_extras.h"
|
||||
|
||||
void check_value(slong n, char *ans)
|
||||
{
|
||||
fmpz_t x, y;
|
||||
fmpz_init(x);
|
||||
fmpz_init(y);
|
||||
fmpz_set_si(y, n);
|
||||
arith_ramanujan_tau(x, y);
|
||||
fmpz_set_str(y, ans, 10);
|
||||
if (!fmpz_equal(x,y))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("tau(%wd) gave ", n);
|
||||
fmpz_print(x);
|
||||
flint_printf(", expected %s\n", ans);
|
||||
abort();
|
||||
}
|
||||
fmpz_clear(x);
|
||||
fmpz_clear(y);
|
||||
}
|
||||
|
||||
void consistency_check(slong n)
|
||||
{
|
||||
fmpz_poly_t p;
|
||||
fmpz_t x, y;
|
||||
slong k;
|
||||
|
||||
fmpz_poly_init(p);
|
||||
fmpz_init(x);
|
||||
fmpz_init(y);
|
||||
|
||||
arith_ramanujan_tau_series(p, n);
|
||||
if (p->length != n && !(n == 1 && p->length == 0))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("wrong length of polynomial %wd\n", n);
|
||||
abort();
|
||||
}
|
||||
|
||||
for (k=0; k<n; k++)
|
||||
{
|
||||
fmpz_set_si(y, k);
|
||||
arith_ramanujan_tau(x, y);
|
||||
fmpz_poly_get_coeff_fmpz(y, p, k);
|
||||
if (!fmpz_equal(x,y))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("different tau n=%wd, k=%wd\n", n, k);
|
||||
fmpz_print(x);
|
||||
flint_printf("\n");
|
||||
fmpz_print(y);
|
||||
flint_printf("\n");
|
||||
abort();
|
||||
}
|
||||
}
|
||||
fmpz_clear(x);
|
||||
fmpz_clear(y);
|
||||
fmpz_poly_clear(p);
|
||||
}
|
||||
|
||||
int main(void)
|
||||
{
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("ramanujan_tau....");
|
||||
fflush(stdout);
|
||||
|
||||
check_value(0, "0");
|
||||
check_value(1, "1");
|
||||
check_value(2, "-24");
|
||||
check_value(3, "252");
|
||||
check_value(4, "-1472");
|
||||
check_value(5, "4830");
|
||||
check_value(6, "-6048");
|
||||
check_value(7, "-16744");
|
||||
check_value(8, "84480");
|
||||
check_value(9, "-113643");
|
||||
check_value(10, "-115920");
|
||||
check_value(11, "534612");
|
||||
check_value(12, "-370944");
|
||||
check_value(13, "-577738");
|
||||
check_value(14, "401856");
|
||||
check_value(15, "1217160");
|
||||
check_value(16, "987136");
|
||||
check_value(17, "-6905934");
|
||||
check_value(18, "2727432");
|
||||
check_value(19, "10661420");
|
||||
check_value(20, "-7109760");
|
||||
check_value(21, "-4219488");
|
||||
check_value(22, "-12830688");
|
||||
check_value(23, "18643272");
|
||||
check_value(24, "21288960");
|
||||
check_value(25, "-25499225");
|
||||
check_value(26, "13865712");
|
||||
check_value(27, "-73279080");
|
||||
check_value(28, "24647168");
|
||||
check_value(29, "128406630");
|
||||
check_value(30, "-29211840");
|
||||
check_value(31, "-52843168");
|
||||
check_value(32, "-196706304");
|
||||
check_value(33, "134722224");
|
||||
check_value(34, "165742416");
|
||||
check_value(35, "-80873520");
|
||||
check_value(36, "167282496");
|
||||
check_value(37, "-182213314");
|
||||
check_value(38, "-255874080");
|
||||
check_value(39, "-145589976");
|
||||
check_value(40, "408038400");
|
||||
check_value(41, "308120442");
|
||||
check_value(42, "101267712");
|
||||
check_value(43, "-17125708");
|
||||
check_value(44, "-786948864");
|
||||
check_value(45, "-548895690");
|
||||
check_value(46, "-447438528");
|
||||
check_value(47, "2687348496");
|
||||
check_value(48, "248758272");
|
||||
check_value(49, "-1696965207");
|
||||
|
||||
check_value(1000, "-30328412970240000");
|
||||
check_value(10000, "-482606811957501440000");
|
||||
check_value(100000, "-2983637890141033828147200000");
|
||||
check_value(5040, "9072480147209256960");
|
||||
check_value(25401600, "-982963272212951631424865761586105548800");
|
||||
check_value(100003, "1194906306375914517502892252");
|
||||
check_value(15251, "-67392761749743476612496");
|
||||
check_value(16777216, "5141538908507386166920374725609506471936");
|
||||
check_value(43046721, "447670851294004737003138291024309833342241");
|
||||
check_value(462594208,
|
||||
"-313042078739616847874899392539635327193629261824");
|
||||
|
||||
consistency_check(0);
|
||||
consistency_check(1);
|
||||
consistency_check(2);
|
||||
consistency_check(3);
|
||||
consistency_check(10);
|
||||
consistency_check(11);
|
||||
consistency_check(100);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,215 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2010 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <limits.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "ulong_extras.h"
|
||||
#include "profiler.h"
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz_mat_t mat, mat2, mat3;
|
||||
|
||||
fmpz * row;
|
||||
fmpz_t s;
|
||||
|
||||
slong n, k, mm, nn;
|
||||
|
||||
const slong maxn = 40;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("stirling....");
|
||||
fflush(stdout);
|
||||
|
||||
fmpz_init(s);
|
||||
|
||||
for (mm = 0; mm < maxn / 2; mm++)
|
||||
{
|
||||
/* Consistency test for stirling1u */
|
||||
|
||||
for (nn = 0; nn < maxn; nn++)
|
||||
{
|
||||
fmpz_mat_init(mat, mm, nn);
|
||||
arith_stirling_matrix_1u(mat);
|
||||
|
||||
for (n = 0; n < mm; n++)
|
||||
{
|
||||
for (k = 0; k < nn; k++)
|
||||
{
|
||||
row = _fmpz_vec_init(k);
|
||||
arith_stirling_number_1u_vec(row, n, k);
|
||||
if (!_fmpz_vec_equal(row, mat->rows[n], k))
|
||||
{
|
||||
flint_printf("stirling1u mat != vec ");
|
||||
flint_printf("nn,n,k=%wd,%wd,%wd\n", nn, n, k);
|
||||
flint_printf("mat: ");
|
||||
_fmpz_vec_print(mat->rows[n], k);
|
||||
flint_printf("\nvec: ");
|
||||
_fmpz_vec_print(row, k);
|
||||
abort();
|
||||
}
|
||||
_fmpz_vec_clear(row, k);
|
||||
|
||||
arith_stirling_number_1u(s, n, k);
|
||||
if (!fmpz_equal(mat->rows[n]+k, s))
|
||||
{
|
||||
flint_printf("stirling1u mat != single ");
|
||||
flint_printf("nn,n,k=%wd,%wd,%wd\n", nn, n, k);
|
||||
flint_printf("mat: ");
|
||||
fmpz_print(mat->rows[n]+k);
|
||||
flint_printf("\nsingle: ");
|
||||
fmpz_print(s);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_mat_clear(mat);
|
||||
}
|
||||
|
||||
/* Consistency test for stirling1 */
|
||||
for (nn = 0; nn < maxn; nn++)
|
||||
{
|
||||
fmpz_mat_init(mat, mm, nn);
|
||||
arith_stirling_matrix_1(mat);
|
||||
|
||||
for (n = 0; n < mm; n++)
|
||||
{
|
||||
for (k = 0; k < nn; k++)
|
||||
{
|
||||
row = _fmpz_vec_init(k);
|
||||
arith_stirling_number_1_vec(row, n, k);
|
||||
if (!_fmpz_vec_equal(row, mat->rows[n], k))
|
||||
{
|
||||
flint_printf("stirling1 mat != vec ");
|
||||
flint_printf("nn,n,k=%wd,%wd,%wd\n", nn, n, k);
|
||||
flint_printf("mat: ");
|
||||
_fmpz_vec_print(mat->rows[n], k);
|
||||
flint_printf("\nvec: ");
|
||||
_fmpz_vec_print(row, k);
|
||||
abort();
|
||||
}
|
||||
_fmpz_vec_clear(row, k);
|
||||
|
||||
arith_stirling_number_1(s, n, k);
|
||||
if (!fmpz_equal(mat->rows[n]+k, s))
|
||||
{
|
||||
flint_printf("stirling1 mat != single ");
|
||||
flint_printf("nn,n,k=%wd,%wd,%wd\n", nn, n, k);
|
||||
flint_printf("mat: ");
|
||||
fmpz_print(mat->rows[n]+k);
|
||||
flint_printf("\nsingle: ");
|
||||
fmpz_print(s);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_mat_clear(mat);
|
||||
}
|
||||
|
||||
/* Consistency test for stirling2 */
|
||||
for (nn = 0; nn < maxn; nn++)
|
||||
{
|
||||
fmpz_mat_init(mat, mm, nn);
|
||||
arith_stirling_matrix_2(mat);
|
||||
|
||||
for (n = 0; n < mm; n++)
|
||||
{
|
||||
for (k = 0; k < nn; k++)
|
||||
{
|
||||
row = _fmpz_vec_init(k);
|
||||
arith_stirling_number_2_vec(row, n, k);
|
||||
if (!_fmpz_vec_equal(row, mat->rows[n], k))
|
||||
{
|
||||
flint_printf("stirling2 mat != vec ");
|
||||
flint_printf("nn,n,k=%wd,%wd,%wd\n", nn, n, k);
|
||||
flint_printf("mat: ");
|
||||
_fmpz_vec_print(mat->rows[n], k);
|
||||
flint_printf("\nvec: ");
|
||||
_fmpz_vec_print(row, k);
|
||||
abort();
|
||||
}
|
||||
_fmpz_vec_clear(row, k);
|
||||
|
||||
arith_stirling_number_2(s, n, k);
|
||||
if (!fmpz_equal(mat->rows[n]+k, s))
|
||||
{
|
||||
flint_printf("stirling2 mat != single ");
|
||||
flint_printf("nn,n,k=%wd,%wd,%wd\n", nn, n, k);
|
||||
flint_printf("mat: ");
|
||||
fmpz_print(mat->rows[n]+k);
|
||||
flint_printf("\nsingle: ");
|
||||
fmpz_print(s);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fmpz_mat_clear(mat);
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
/* Matrix inverse test */
|
||||
for (nn = 1; nn < 50; nn++)
|
||||
{
|
||||
fmpz_mat_init(mat, nn, nn);
|
||||
fmpz_mat_init(mat2, nn, nn);
|
||||
fmpz_mat_init(mat3, nn, nn);
|
||||
|
||||
arith_stirling_matrix_1(mat);
|
||||
arith_stirling_matrix_2(mat2);
|
||||
fmpz_mat_mul(mat3, mat, mat2);
|
||||
|
||||
for (n = 0; n < nn; n++)
|
||||
{
|
||||
for (k = 0; k < nn; k++)
|
||||
{
|
||||
if (fmpz_get_ui(mat3->rows[n]+k) != (n == k))
|
||||
{
|
||||
flint_printf("not identity matrix: %wd, %wd, %wd\n", nn, n, k);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
fmpz_mat_clear(mat);
|
||||
fmpz_mat_clear(mat2);
|
||||
fmpz_mat_clear(mat3);
|
||||
}
|
||||
|
||||
fmpz_clear(s);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,88 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "fmpz_vec.h"
|
||||
|
||||
#define N 10
|
||||
|
||||
static const fmpz known[N][N] = {
|
||||
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
|
||||
{1, 2, 0, 0, 2, 0, 0, 0, 0, 2},
|
||||
{1, 4, 4, 0, 4, 8, 0, 0, 4, 4},
|
||||
{1, 6, 12, 8, 6, 24, 24, 0, 12, 30},
|
||||
{1, 8, 24, 32, 24, 48, 96, 64, 24, 104},
|
||||
{1, 10, 40, 80, 90, 112, 240, 320, 200, 250},
|
||||
{1, 12, 60, 160, 252, 312, 544, 960, 1020, 876},
|
||||
{1, 14, 84, 280, 574, 840, 1288, 2368, 3444, 3542},
|
||||
{1, 16, 112, 448, 1136, 2016, 3136, 5504, 9328, 12112},
|
||||
{1, 18, 144, 672, 2034, 4320, 7392, 12672, 22608, 34802}
|
||||
};
|
||||
|
||||
int main(void)
|
||||
{
|
||||
fmpz * r;
|
||||
fmpz_t t;
|
||||
slong i, j;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("sum_of_squares....");
|
||||
fflush(stdout);
|
||||
|
||||
r = _fmpz_vec_init(N);
|
||||
fmpz_init(t);
|
||||
|
||||
for (i = 0; i < N; i++)
|
||||
{
|
||||
arith_sum_of_squares_vec(r, i, N);
|
||||
|
||||
for (j = 0; j < N; j++)
|
||||
{
|
||||
fmpz_set_ui(t, j);
|
||||
arith_sum_of_squares(t, i, t);
|
||||
|
||||
if (!fmpz_equal(t, r + j) || !fmpz_equal(t, known[i] + j))
|
||||
{
|
||||
flint_printf("FAIL:\n");
|
||||
flint_printf("i, j = %wd, %wd, r[j] = %wd, r(j) = %wd, "
|
||||
"expected: %wd\n",
|
||||
i, j, fmpz_get_si(r + j), fmpz_get_si(t), known[i][j]);
|
||||
abort();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
_fmpz_vec_clear(r, N);
|
||||
fmpz_clear(t);
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,80 +0,0 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of FLINT.
|
||||
|
||||
FLINT is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
FLINT is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with FLINT; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2011 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <gmp.h>
|
||||
#include "flint.h"
|
||||
#include "arith.h"
|
||||
#include "profiler.h"
|
||||
#include "fmpz.h"
|
||||
#include "fmpz_mat.h"
|
||||
#include "fmpq_poly.h"
|
||||
|
||||
static const mp_limb_t known_values[] =
|
||||
{
|
||||
UWORD(2147483629),
|
||||
UWORD(1073742093),
|
||||
UWORD(1342248677),
|
||||
UWORD(3319936736),
|
||||
UWORD(2947821228),
|
||||
UWORD(1019513834),
|
||||
UWORD(3324951530),
|
||||
UWORD(1995039408),
|
||||
UWORD(3505683295),
|
||||
UWORD(3567639420),
|
||||
UWORD(394942914)
|
||||
};
|
||||
|
||||
int main()
|
||||
{
|
||||
fmpz_poly_t S;
|
||||
mp_limb_t r;
|
||||
slong n;
|
||||
|
||||
FLINT_TEST_INIT(state);
|
||||
|
||||
flint_printf("swinnerton_dyer_polynomial....");
|
||||
fflush(stdout);
|
||||
|
||||
for (n = 0; n <= 10; n++)
|
||||
{
|
||||
fmpz_poly_init(S);
|
||||
arith_swinnerton_dyer_polynomial(S, n);
|
||||
r = fmpz_poly_evaluate_mod(S, UWORD(2147483629), UWORD(4294967291));
|
||||
|
||||
if (r != known_values[n])
|
||||
{
|
||||
flint_printf("ERROR: wrong evaluation of S_%wd\n", n);
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpz_poly_clear(S);
|
||||
}
|
||||
|
||||
FLINT_TEST_CLEANUP(state);
|
||||
flint_printf("PASS\n");
|
||||
return 0;
|
||||
}
|
||||
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Reference in New Issue