340 lines
13 KiB
C
340 lines
13 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2013 Tom Bachmann
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******************************************************************************/
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#ifndef ARITHXX_H
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#define ARITHXX_H
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#include "arith.h"
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#include "fmpq_polyxx.h"
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#include "fmpqxx.h"
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#include "fmpz_matxx.h"
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#include "fmpz_vecxx.h"
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#include "fmpzxx.h"
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#include "nmod_vecxx.h"
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// TODO namespace arith?
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// TODO arith_hrr_expsum_factored
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// TODO codegen / vector improvements
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namespace flint {
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namespace detail {
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template<class T>
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inline typename T::wrapped_traits::data_srcref_t extract_data(const T& t,
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typename mp::enable_if<flint_classes::is_flint_class<T> >::type* = 0)
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{
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return t._data().inner;
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}
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template<class T>
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inline typename T::wrapped_traits::data_ref_t extract_data(T& t,
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typename mp::enable_if<flint_classes::is_flint_class<T> >::type* = 0)
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{
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return t._data().inner;
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}
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template<class T>
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const T& extract_data(const T& t,
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typename mp::disable_if<flint_classes::is_flint_class<T> >::type* = 0)
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{
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return t;
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}
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template<class T>
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typename T::arrayref_t extract_data(T& t,
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typename mp::disable_if<flint_classes::is_flint_class<T> >::type* = 0,
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typename mp::enable_if<mp::or_<rules::FMPZ_VECXX_COND_S<T>,
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rules::FMPQ_VECXX_COND_S<T> > >::type* = 0)
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{
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return t._array();
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}
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}
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#define ARITHXX_DEFINE_UNOP(name, Return, Cond) \
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FLINT_DEFINE_UNOP(name) \
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namespace rules { \
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FLINT_DEFINE_UNARY_EXPR_COND(name##_op, Return, Cond, \
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arith_##name(detail::extract_data(to), detail::extract_data(from))) \
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}
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#define ARITHXX_DEFINE_BINOP(name, Return, Cond1, Cond2) \
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FLINT_DEFINE_BINOP(name) \
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namespace rules { \
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FLINT_DEFINE_BINARY_EXPR_COND2(name##_op, Return, Cond1, Cond2, \
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arith_##name(detail::extract_data(to), detail::extract_data(e1), \
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detail::extract_data(e2))) \
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}
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namespace at {
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template<class T> struct slong : traits::fits_into_slong<T> { };
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template<class T> struct ulong : traits::is_unsigned_integer<T> { };
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} // at
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ARITHXX_DEFINE_UNOP(primorial, fmpzxx, at::slong)
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ARITHXX_DEFINE_UNOP(harmonic_number, fmpqxx, at::slong)
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ARITHXX_DEFINE_BINOP(stirling_number_1u, fmpzxx, at::slong, at::slong)
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ARITHXX_DEFINE_BINOP(stirling_number_1, fmpzxx, at::slong, at::slong)
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ARITHXX_DEFINE_BINOP(stirling_number_2, fmpzxx, at::slong, at::slong)
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ARITHXX_DEFINE_BINOP(stirling_number_1u_vec, fmpz_vecxx, at::slong, at::slong)
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ARITHXX_DEFINE_BINOP(stirling_number_1_vec, fmpz_vecxx, at::slong, at::slong)
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ARITHXX_DEFINE_BINOP(stirling_number_2_vec, fmpz_vecxx, at::slong, at::slong)
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FLINT_DEFINE_BINOP(stirling_number_1u_vec_next)
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FLINT_DEFINE_BINOP(stirling_number_1_vec_next)
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FLINT_DEFINE_BINOP(stirling_number_2_vec_next)
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FLINT_DEFINE_BINOP(stirling_matrix_1u)
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FLINT_DEFINE_BINOP(stirling_matrix_1)
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FLINT_DEFINE_BINOP(stirling_matrix_2)
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namespace vectors {
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template<>
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struct outsize<operations::stirling_number_1u_vec_op>
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{
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template<class Expr>
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static unsigned get(const Expr& e) {return e._data().second();}
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};
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template<> struct outsize<operations::stirling_number_1_vec_op>
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: outsize<operations::stirling_number_1u_vec_op> { };
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template<> struct outsize<operations::stirling_number_2_vec_op>
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: outsize<operations::stirling_number_1u_vec_op> { };
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template<>
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struct outsize<operations::stirling_number_1u_vec_next_op>
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{
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template<class Expr>
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static unsigned get(const Expr& e)
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{
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slong r = e._data().first().size();
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if(r == e._data().second())
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return r + 1;
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return r;
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}
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};
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template<> struct outsize<operations::stirling_number_1_vec_next_op>
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: outsize<operations::stirling_number_1u_vec_next_op> { };
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template<> struct outsize<operations::stirling_number_2_vec_next_op>
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: outsize<operations::stirling_number_1u_vec_next_op> { };
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} // vectors
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namespace matrices {
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template<>
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struct outsize<operations::stirling_matrix_1u_op>
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{
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template<class Expr>
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static slong rows(const Expr& e) {return e._data().first();}
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template<class Expr>
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static slong cols(const Expr& e) {return e._data().second();}
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};
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template<> struct outsize<operations::stirling_matrix_1_op>
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: outsize<operations::stirling_matrix_1u_op> { };
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template<> struct outsize<operations::stirling_matrix_2_op>
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: outsize<operations::stirling_matrix_1u_op> { };
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} // matrices
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namespace rules {
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FLINT_DEFINE_BINARY_EXPR_COND2(stirling_number_1u_vec_next_op, fmpz_vecxx,
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FMPZ_VECXX_COND_S, at::slong,
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arith_stirling_number_1u_vec_next(to._array(), e1._array(), e2,
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e1.size() + (e1.size() == e2)))
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FLINT_DEFINE_BINARY_EXPR_COND2(stirling_number_1_vec_next_op, fmpz_vecxx,
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FMPZ_VECXX_COND_S, at::slong,
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arith_stirling_number_1_vec_next(to._array(), e1._array(), e2,
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e1.size() + (e1.size() == e2)))
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FLINT_DEFINE_BINARY_EXPR_COND2(stirling_number_2_vec_next_op, fmpz_vecxx,
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FMPZ_VECXX_COND_S, at::slong,
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arith_stirling_number_2_vec_next(to._array(), e1._array(), e2,
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e1.size() + (e1.size() == e2)))
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FLINT_DEFINE_BINARY_EXPR_COND2(stirling_matrix_1u_op, fmpz_matxx,
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at::slong, at::slong, arith_stirling_matrix_1u(to._mat()))
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FLINT_DEFINE_BINARY_EXPR_COND2(stirling_matrix_1_op, fmpz_matxx,
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at::slong, at::slong, arith_stirling_matrix_1(to._mat()))
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FLINT_DEFINE_BINARY_EXPR_COND2(stirling_matrix_2_op, fmpz_matxx,
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at::slong, at::slong, arith_stirling_matrix_2(to._mat()))
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} // rules
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ARITHXX_DEFINE_UNOP(bell_number, fmpzxx, at::ulong)
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ARITHXX_DEFINE_UNOP(bell_number_bsplit, fmpzxx, at::ulong)
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ARITHXX_DEFINE_UNOP(bell_number_multi_mod, fmpzxx, at::ulong)
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ARITHXX_DEFINE_UNOP(bell_number_vec, fmpz_vecxx, at::slong)
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ARITHXX_DEFINE_UNOP(bell_number_vec_recursive, fmpz_vecxx, at::slong)
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ARITHXX_DEFINE_UNOP(bell_number_vec_multi_mod, fmpz_vecxx, at::slong)
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FLINT_DEFINE_BINOP(bell_number_nmod)
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FLINT_DEFINE_BINOP(bell_number_nmod_vec)
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FLINT_DEFINE_BINOP(bell_number_nmod_vec_recursive)
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FLINT_DEFINE_BINOP(bell_number_nmod_vec_series)
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namespace vectors {
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template<>
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struct outsize<operations::bell_number_vec_op>
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{
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template<class Expr> static unsigned get(const Expr& e)
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{return e._data().first();}
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};
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template<> struct outsize<operations::bell_number_vec_recursive_op>
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: outsize<operations::bell_number_vec_op> { };
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template<> struct outsize<operations::bell_number_vec_multi_mod_op>
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: outsize<operations::bell_number_vec_op> { };
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template<> struct outsize<operations::bell_number_nmod_vec_op>
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: outsize<operations::bell_number_vec_op> { };
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template<> struct outsize<operations::bell_number_nmod_vec_recursive_op>
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: outsize<operations::bell_number_vec_op> { };
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template<> struct outsize<operations::bell_number_nmod_vec_series_op>
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: outsize<operations::bell_number_vec_op> { };
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} // vectors
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namespace at {
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template<class T> struct nmod : mp::or_<mp::equal_types<T, nmodxx_ctx_srcref>,
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mp::equal_types<T, nmodxx_ctx> > { };
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} // at
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#define NMODXX_DEFINE_FIND_CTX_BY_OP(exprname, eval) \
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namespace traits { \
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template<class Data> \
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struct has_nmodxx_ctx< exprname, Data> > : mp::true_ { }; \
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} \
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namespace detail { \
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template<class Data> \
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struct get_nmodxx_ctx<exprname, Data> > \
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{ \
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template<class T> \
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static nmodxx_ctx_srcref get(const T& e) {return eval;} \
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}; \
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}
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#define FLINTXX_COMMA() ,
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NMODXX_DEFINE_FIND_CTX_BY_OP(nmodxx_expression<operations::bell_number_nmod_op,
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e._data().second())
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NMODXX_DEFINE_FIND_CTX_BY_OP(vector_expression<detail::nmod_vector_traits
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FLINTXX_COMMA() operations::bell_number_nmod_vec_op, e._data().second())
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NMODXX_DEFINE_FIND_CTX_BY_OP(vector_expression<detail::nmod_vector_traits
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FLINTXX_COMMA() operations::bell_number_nmod_vec_series_op,
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e._data().second())
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NMODXX_DEFINE_FIND_CTX_BY_OP(vector_expression<detail::nmod_vector_traits
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FLINTXX_COMMA() operations::bell_number_nmod_vec_recursive_op,
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e._data().second())
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namespace rules {
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FLINT_DEFINE_BINARY_EXPR_COND2(bell_number_nmod_op, nmodxx, at::ulong, at::nmod,
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to.set_nored(arith_bell_number_nmod(e1, e2._nmod())))
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FLINT_DEFINE_BINARY_EXPR_COND2(bell_number_nmod_vec_op, nmod_vecxx,
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at::ulong, at::nmod,
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arith_bell_number_nmod_vec(to._array(), e1, e2._nmod()))
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FLINT_DEFINE_BINARY_EXPR_COND2(bell_number_nmod_vec_recursive_op, nmod_vecxx,
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at::ulong, at::nmod,
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arith_bell_number_nmod_vec_recursive(to._array(), e1, e2._nmod()))
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FLINT_DEFINE_BINARY_EXPR_COND2(bell_number_nmod_vec_series_op, nmod_vecxx,
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at::ulong, at::nmod,
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arith_bell_number_nmod_vec_series(to._array(), e1, e2._nmod()))
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} // rules
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ARITHXX_DEFINE_UNOP(bernoulli_number, fmpqxx, at::ulong)
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ARITHXX_DEFINE_UNOP(bernoulli_polynomial, fmpq_polyxx, at::ulong)
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ARITHXX_DEFINE_UNOP(bernoulli_number_vec, fmpq_vecxx, at::ulong)
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ARITHXX_DEFINE_UNOP(bernoulli_number_denom, fmpzxx, at::ulong)
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namespace vectors {
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template<>
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struct outsize<operations::bernoulli_number_vec_op>
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{
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template<class Expr> static unsigned get(const Expr& e)
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{return e._data().first();}
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};
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} // vectors
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ARITHXX_DEFINE_UNOP(euler_number, fmpzxx, at::ulong)
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ARITHXX_DEFINE_UNOP(euler_number_vec, fmpz_vecxx, at::ulong)
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ARITHXX_DEFINE_UNOP(euler_polynomial, fmpq_polyxx, at::ulong)
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namespace vectors {
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template<> struct outsize<operations::euler_number_vec_op>
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: outsize<operations::bernoulli_number_vec_op> { };
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}
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ARITHXX_DEFINE_UNOP(legendre_polynomial, fmpq_polyxx, at::ulong)
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ARITHXX_DEFINE_UNOP(chebyshev_t_polynomial, fmpz_polyxx, at::ulong)
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ARITHXX_DEFINE_UNOP(chebyshev_u_polynomial, fmpz_polyxx, at::ulong)
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ARITHXX_DEFINE_UNOP(euler_phi, fmpzxx, FMPZXX_COND_S)
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ARITHXX_DEFINE_BINOP(divisor_sigma, fmpzxx, FMPZXX_COND_S, at::ulong)
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ARITHXX_DEFINE_UNOP(divisors, fmpz_polyxx, FMPZXX_COND_S)
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ARITHXX_DEFINE_UNOP(ramanujan_tau, fmpzxx, FMPZXX_COND_S)
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ARITHXX_DEFINE_UNOP(ramanujan_tau_series, fmpz_polyxx, at::slong)
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ARITHXX_DEFINE_UNOP(cyclotomic_polynomial, fmpz_polyxx, at::ulong)
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ARITHXX_DEFINE_UNOP(cos_minpoly, fmpz_polyxx, at::ulong)
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ARITHXX_DEFINE_UNOP(swinnerton_dyer_polynomial, fmpz_polyxx, at::ulong)
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ARITHXX_DEFINE_UNOP(landau_function_vec, fmpz_vecxx, at::slong)
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namespace vectors {
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template<> struct outsize<operations::landau_function_vec_op>
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: outsize<operations::bernoulli_number_vec_op> { };
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}
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ARITHXX_DEFINE_BINOP(dedekind_sum_naive, fmpqxx,
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FMPZXX_COND_S, FMPZXX_COND_S)
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ARITHXX_DEFINE_BINOP(dedekind_sum_coprime_large, fmpqxx,
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FMPZXX_COND_S, FMPZXX_COND_S)
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ARITHXX_DEFINE_BINOP(dedekind_sum_coprime, fmpqxx,
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FMPZXX_COND_S, FMPZXX_COND_S)
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ARITHXX_DEFINE_BINOP(dedekind_sum, fmpqxx,
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FMPZXX_COND_S, FMPZXX_COND_S)
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ARITHXX_DEFINE_UNOP(number_of_partitions_vec, fmpz_vecxx, at::slong)
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ARITHXX_DEFINE_UNOP(number_of_partitions, fmpzxx, at::ulong)
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FLINT_DEFINE_BINOP(number_of_partitions_nmod_vec)
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||
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namespace vectors {
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template<> struct outsize<operations::number_of_partitions_vec_op>
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: outsize<operations::bernoulli_number_vec_op> { };
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template<> struct outsize<operations::number_of_partitions_nmod_vec_op>
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: outsize<operations::bell_number_vec_op> { };
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}
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||
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NMODXX_DEFINE_FIND_CTX_BY_OP(vector_expression<detail::nmod_vector_traits
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||
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FLINTXX_COMMA() operations::number_of_partitions_nmod_vec_op,
|
||
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e._data().second())
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||
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namespace rules {
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||
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FLINT_DEFINE_BINARY_EXPR_COND2(number_of_partitions_nmod_vec_op, nmod_vecxx,
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||
|
|
at::ulong, at::nmod,
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||
|
|
arith_number_of_partitions_nmod_vec(to._array(), e1, e2._nmod()))
|
||
|
|
}
|
||
|
|
|
||
|
|
ARITHXX_DEFINE_BINOP(sum_of_squares, fmpzxx, at::ulong, FMPZXX_COND_S)
|
||
|
|
ARITHXX_DEFINE_BINOP(sum_of_squares_vec, fmpz_vecxx, at::ulong, at::slong)
|
||
|
|
|
||
|
|
namespace vectors {
|
||
|
|
template<> struct outsize<operations::sum_of_squares_vec_op>
|
||
|
|
: outsize<operations::stirling_number_1u_vec_op> { };
|
||
|
|
}
|
||
|
|
|
||
|
|
inline double bell_number_size(ulong n) {return arith_bell_number_size(n);}
|
||
|
|
inline double bernoulli_number_size(ulong n)
|
||
|
|
{return arith_bernoulli_number_size(n);}
|
||
|
|
inline double euler_number_size(ulong n) {return arith_euler_number_size(n);}
|
||
|
|
inline double dedekind_sum_coprime_d(double h, double k)
|
||
|
|
{return arith_dedekind_sum_coprime_d(h, k);}
|
||
|
|
|
||
|
|
template<class Fmpz>
|
||
|
|
inline typename mp::enable_if<traits::is_fmpzxx<Fmpz>, int>::type moebius_mu(
|
||
|
|
const Fmpz& n)
|
||
|
|
{
|
||
|
|
return arith_moebius_mu(n.evaluate()._fmpz());
|
||
|
|
}
|
||
|
|
} // flint
|
||
|
|
|
||
|
|
#endif
|