258 lines
9.1 KiB
Plaintext
258 lines
9.1 KiB
Plaintext
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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) 2010 William Hart
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******************************************************************************/
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*******************************************************************************
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Memory management
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*******************************************************************************
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mp_ptr _nmod_vec_init(slong len)
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Returns a vector of the given length. The entries are not necessarily
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zero.
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void _nmod_vec_clear(mp_ptr vec)
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Frees the memory used by the given vector.
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*******************************************************************************
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Modular reduction and arithmetic
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*******************************************************************************
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void nmod_init(nmod_t * mod, mp_limb_t n)
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Initialises the given \code{nmod_t} structure for reduction modulo $n$
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with a precomputed inverse.
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NMOD_RED2(r, a_hi, a_lo, mod)
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Macro to set $r$ to $a$ reduced modulo \code{mod.n}, where $a$
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consists of two limbs \code{(a_hi, a_lo)}. The \code{mod} parameter
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must be a valid \code{nmod_t} structure. It is assumed that \code{a_hi}
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is already reduced modulo \code{mod.n}.
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NMOD_RED(r, a, mod)
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Macro to set $r$ to $a$ reduced modulo \code{mod.n}. The \code{mod}
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parameter must be a valid \code{nmod_t} structure.
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NMOD2_RED2(r, a_hi, a_lo, mod)
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Macro to set $r$ to $a$ reduced modulo \code{mod.n}, where $a$
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consists of two limbs \code{(a_hi, a_lo)}. The \code{mod} parameter
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must be a valid \code{nmod_t} structure. No assumptions are made
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about \code{a_hi}.
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NMOD_RED3(r, a_hi, a_me, a_lo, mod)
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Macro to set $r$ to $a$ reduced modulo \code{mod.n}, where $a$
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consists of three limbs \code{(a_hi, a_me, a_lo)}. The \code{mod}
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parameter must be a valid \code{nmod_t} structure. It is assumed
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that \code{a_hi} is already reduced modulo \code{mod.n}.
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NMOD_ADDMUL(r, a, b, mod)
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Macro to set $r$ to $r + ab$ reduced modulo \code{mod.n}. The
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\code{mod} parameter must be a valid \code{nmod_t} structure. It is
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assumed that $r$, $a$, $b$ are already reduced modulo \code{mod.n}.
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mp_limb_t _nmod_add(mp_limb_t a, mp_limb_t b, nmod_t mod)
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Returns $a + b$ modulo \code{mod.n}. It is assumed that \code{mod} is
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no more than \code{FLINT_BITS - 1} bits. It is assumed that $a$ and $b$
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are already reduced modulo \code{mod.n}.
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mp_limb_t nmod_add(mp_limb_t a, mp_limb_t b, nmod_t mod)
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Returns $a + b$ modulo \code{mod.n}. No assumptions are made about
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\code{mod.n}. It is assumed that $a$ and $b$ are already reduced
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modulo \code{mod.n}.
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mp_limb_t _nmod_sub(mp_limb_t a, mp_limb_t b, nmod_t mod)
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Returns $a - b$ modulo \code{mod.n}. It is assumed that \code{mod}
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is no more than \code{FLINT_BITS - 1} bits. It is assumed that
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$a$ and $b$ are already reduced modulo \code{mod.n}.
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mp_limb_t nmod_sub(mp_limb_t a, mp_limb_t b, nmod_t mod)
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Returns $a - b$ modulo \code{mod.n}. No assumptions are made about
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\code{mod.n}. It is assumed that $a$ and $b$ are already reduced
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modulo \code{mod.n}.
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mp_limb_t nmod_neg(mp_limb_t a, nmod_t mod)
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Returns $-a$ modulo \code{mod.n}. It is assumed that $a$ is already
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reduced modulo \code{mod.n}, but no assumptions are made about the
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latter.
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mp_limb_t nmod_mul(mp_limb_t a, mp_limb_t b, nmod_t mod)
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Returns $ab$ modulo \code{mod.n}. No assumptions are made about
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\code{mod.n}. It is assumed that $a$ and $b$ are already reduced
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modulo \code{mod.n}.
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mp_limb_t nmod_inv(mp_limb_t a, nmod_t mod)
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Returns $a^{-1}$ modulo \code{mod.n}. The inverse is assumed to exist.
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mp_limb_t nmod_div(mp_limb_t a, mp_limb_t b, nmod_t mod)
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Returns $a^{-1}$ modulo \code{mod.n}. The inverse of $b$ is assumed to
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exist. It is assumed that $a$ is already reduced modulo \code{mod.n}.
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mp_limb_t nmod_pow_ui(mp_limb_t a, ulong e, nmod_t mod)
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Returns $a^e$ modulo \code{mod.n}. No assumptions are made about
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\code{mod.n}. It is assumed that $a$ is already reduced
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modulo \code{mod.n}.
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*******************************************************************************
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Random functions
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*******************************************************************************
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void _nmod_vec_randtest(mp_ptr vec, flint_rand_t state, slong len, nmod_t mod)
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Sets \code{vec} to a random vector of the given length with entries
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reduced modulo \code{mod.n}.
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*******************************************************************************
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Basic manipulation and comparison
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*******************************************************************************
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void _nmod_vec_set(mp_ptr res, mp_srcptr vec, slong len)
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Copies \code{len} entries from the vector \code{vec} to \code{res}.
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void _nmod_vec_zero(mp_ptr vec, slong len)
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Zeros the given vector of the given length.
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void _nmod_vec_swap(mp_ptr a, mp_ptr b, slong length)
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Swaps the vectors \code{a} and \code{b} of length $n$ by actually
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swapping the entries.
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void _nmod_vec_reduce(mp_ptr res, mp_srcptr vec, slong len, nmod_t mod)
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Reduces the entries of \code{(vec, len)} modulo \code{mod.n} and set
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\code{res} to the result.
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mp_bitcnt_t _nmod_vec_max_bits(mp_srcptr vec, slong len)
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Returns the maximum number of bits of any entry in the vector.
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int _nmod_vec_equal(mp_srcptr vec, mp_srcptr vec2, slong len)
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Returns~$1$ if \code{(vec, len)} is equal to \code{(vec2, len)},
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otherwise returns~$0$.
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*******************************************************************************
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Arithmetic operations
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*******************************************************************************
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void _nmod_vec_add(mp_ptr res, mp_srcptr vec1,
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mp_srcptr vec2, slong len, nmod_t mod)
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Sets \code{(res, len)} to the sum of \code{(vec1, len)}
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and \code{(vec2, len)}.
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void _nmod_vec_sub(mp_ptr res, mp_srcptr vec1,
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mp_srcptr vec2, slong len, nmod_t mod)
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Sets \code{(res, len)} to the difference of \code{(vec1, len)}
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and \code{(vec2, len)}.
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void _nmod_vec_neg(mp_ptr res, mp_srcptr vec, slong len, nmod_t mod)
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Sets \code{(res, len)} to the negation of \code{(vec, len)}.
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void _nmod_vec_scalar_mul_nmod(mp_ptr res, mp_srcptr vec,
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slong len, mp_limb_t c, nmod_t mod)
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Sets \code{(res, len)} to \code{(vec, len)} multiplied by $c$.
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void _nmod_vec_scalar_addmul_nmod(mp_ptr res, mp_srcptr vec,
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slong len, mp_limb_t c, nmod_t mod)
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Adds \code{(vec, len)} times $c$ to the vector \code{(res, len)}.
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*******************************************************************************
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Dot products
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*******************************************************************************
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int _nmod_vec_dot_bound_limbs(slong len, nmod_t mod)
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Returns the number of limbs (0, 1, 2 or 3) needed to represent the
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unreduced dot product of two vectors of length \code{len} having entries
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modulo \code{mod.n}, assuming that \code{len} is nonnegative and that
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\code{mod.n} is nonzero. The computed bound is tight. In other words,
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this function returns the precise limb size of \code{len} times
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\code{(mod.n - 1) ^ 2}.
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macro NMOD_VEC_DOT(res, i, len, expr1, expr2, mod, nlimbs)
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Effectively performs the computation
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\begin{verbatim}
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res = 0;
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for (i = 0; i < len; i++)
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res += (expr1) * (expr2);
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\end{verbatim}
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but with the arithmetic performed modulo \code{mod}.
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The \code{nlimbs} parameter should be 0, 1, 2 or 3, specifying the
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number of limbs needed to represent the unreduced result.
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mp_limb_t _nmod_vec_dot(mp_srcptr vec1, mp_srcptr vec2,
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slong len, nmod_t mod, int nlimbs)
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Returns the dot product of (\code{vec1}, \code{len}) and
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(\code{vec2}, \code{len}). The \code{nlimbs} parameter should be
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0, 1, 2 or 3, specifying the number of limbs needed to represent the
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unreduced result.
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mp_limb_t
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_nmod_vec_dot_ptr(mp_srcptr vec1, const mp_ptr * vec2, slong offset, slong len,
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nmod_t mod, int nlimbs)
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Returns the dot product of (\code{vec1}, \code{len}) and the values at
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\code{vec2[i][offset]}. The \code{nlimbs} parameter should be
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0, 1, 2 or 3, specifying the number of limbs needed to represent the
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unreduced result.
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