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nmod_vec.h
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788 lines (686 loc) · 35.1 KB
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/*
Copyright (C) 2010 William Hart
Copyright (C) 2021 Fredrik Johansson
Copyright (C) 2024 Vincent Neiger
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#ifndef NMOD_VEC_H
#define NMOD_VEC_H
#ifdef NMOD_VEC_INLINES_C
#define NMOD_VEC_INLINE
#else
#define NMOD_VEC_INLINE static inline
#endif
#include "flint.h"
#include "nmod.h" // nmod_mul, nmod_fmma
#ifdef __cplusplus
extern "C" {
#endif
#define NMOD_VEC_NORM(vec, i) \
do { \
while ((i) && vec[(i) - 1] == UWORD(0)) \
(i)--; \
} while (0)
NMOD_VEC_INLINE
nn_ptr _nmod_vec_init(slong len)
{
return (nn_ptr) flint_malloc(len * sizeof(ulong));
}
NMOD_VEC_INLINE
void _nmod_vec_clear(nn_ptr vec)
{
flint_free(vec);
}
void _nmod_vec_randtest(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod);
void _nmod_vec_rand(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod);
NMOD_VEC_INLINE
void _nmod_vec_zero(nn_ptr vec, slong len)
{
slong i;
for (i = 0; i < len; i++)
vec[i] = 0;
}
flint_bitcnt_t _nmod_vec_max_bits(nn_srcptr vec, slong len);
NMOD_VEC_INLINE
void _nmod_vec_set(nn_ptr res, nn_srcptr vec, slong len)
{
slong i;
for (i = 0; i < len; i++)
res[i] = vec[i];
}
NMOD_VEC_INLINE
void _nmod_vec_swap(nn_ptr a, nn_ptr b, slong length)
{
slong i;
for (i = 0; i < length; i++)
{
ulong t = a[i];
a[i] = b[i];
b[i] = t;
}
}
NMOD_VEC_INLINE
int _nmod_vec_equal(nn_srcptr vec, nn_srcptr vec2, slong len)
{
slong i;
for (i = 0; i < len; i++)
if (vec[i] != vec2[i]) return 0;
return 1;
}
NMOD_VEC_INLINE
int _nmod_vec_is_zero(nn_srcptr vec, slong len)
{
slong i;
for (i = 0; i < len; i++)
if (vec[i] != 0) return 0;
return 1;
}
/* some IO functions */
#ifdef FLINT_HAVE_FILE
int _nmod_vec_fprint_pretty(FILE * file, nn_srcptr vec, slong len, nmod_t mod);
int _nmod_vec_fprint(FILE * f, nn_srcptr vec, slong len, nmod_t mod);
#endif
void _nmod_vec_print_pretty(nn_srcptr vec, slong len, nmod_t mod);
int _nmod_vec_print(nn_srcptr vec, slong len, nmod_t mod);
/* reduce, add, scalar mul */
void _nmod_vec_reduce(nn_ptr res, nn_srcptr vec, slong len, nmod_t mod);
void _nmod_vec_add(nn_ptr res, nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
void _nmod_vec_sub(nn_ptr res, nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
void _nmod_vec_neg(nn_ptr res, nn_srcptr vec, slong len, nmod_t mod);
void _nmod_vec_scalar_mul_nmod(nn_ptr res, nn_srcptr vec, slong len, ulong c, nmod_t mod);
void _nmod_vec_scalar_mul_nmod_generic(nn_ptr res, nn_srcptr vec, slong len, ulong c, nmod_t mod);
void _nmod_vec_scalar_mul_nmod_shoup(nn_ptr res, nn_srcptr vec, slong len, ulong c, nmod_t mod);
void _nmod_vec_scalar_addmul_nmod(nn_ptr res, nn_srcptr vec, slong len, ulong c, nmod_t mod);
void _nmod_vec_scalar_addmul_nmod_generic(nn_ptr res, nn_srcptr vec, slong len, ulong c, nmod_t mod);
void _nmod_vec_scalar_addmul_nmod_shoup(nn_ptr res, nn_srcptr vec, slong len, ulong c, nmod_t mod);
/* ---- compute dot parameters ---- */
typedef enum
{
_DOT0 = 0, /* len == 0 || mod.n == 1 */
_DOT1 = 1, /* 1 limb */
#if (FLINT_BITS == 64)
_DOT2_SPLIT = 2, /* 2 limbs, modulus < ~2**30.5 (FLINT_BITS == 64 only) */
#endif // FLINT_BITS == 64
_DOT2_HALF = 3, /* 2 limbs, modulus < 2**(FLINT_BITS/2) */
_DOT2 = 4, /* 2 limbs */
_DOT3_ACC = 5, /* 3 limbs, modulus allowing some accumulation in 2 limbs */
_DOT3 = 6, /* 3 limbs */
_DOT_POW2 = 7, /* mod.n is a power of 2 */
} dot_method_t;
// if mod.n is a power of 2, we use _DOT_POW2 in all cases
// otherwise, number of limbs of unreduced dot product can be deduced:
// 1 limb <=> method <= _DOT1
// 2 limbs <=> _DOT1 < method <= _DOT2
// 3 limbs <=> _DOT2 < method
typedef struct
{
dot_method_t method;
ulong pow2_precomp; /* for splitting: (1L << 56) % mod.n */
} dot_params_t;
// for _DOT2_SPLIT
#if (FLINT_BITS == 64)
# define DOT_SPLIT_BITS 56
# define DOT_SPLIT_MASK UWORD(72057594037927935) // (1L << DOT_SPLIT_BITS) - 1
#endif // FLINT_BITS == 64
#define _FIXED_LEN_MOD_BOUNDS(fixedlen, onelimb_bnd, twolimb_bnd) \
if (len == fixedlen) \
{ \
if (mod.n <= UWORD(onelimb_bnd)) \
{ \
dot_params_t params = {_DOT1, UWORD(0)}; \
return params; \
} \
if (mod.n <= UWORD(twolimb_bnd)) \
{ \
dot_params_t params = {_DOT2, UWORD(0)}; \
return params; \
} \
dot_params_t params = {_DOT3, UWORD(0)}; \
return params; \
}
FLINT_FORCE_INLINE dot_params_t _nmod_vec_dot_params(ulong len, nmod_t mod)
{
if (len == 0 || mod.n == 1)
{
dot_params_t params = {_DOT0, UWORD(0)};
return params;
}
if ((mod.n & (mod.n - 1)) == 0)
{
dot_params_t params = {_DOT_POW2, UWORD(0)};
return params;
}
// from here on len >= 1, n > 1 not power of 2
// short dot products: we use only _DOT1, _DOT2, _DOT3 in that case
if (len <= 11)
{
#if FLINT_BITS == 64
// 64 bits: k limbs <=> n <= ceil(2**(32*k) / sqrt(len))
_FIXED_LEN_MOD_BOUNDS(11, 1294981365, 5561902608746059656);
_FIXED_LEN_MOD_BOUNDS(10, 1358187914, 5833372668713515885);
_FIXED_LEN_MOD_BOUNDS( 9, 1431655766, 6148914691236517206);
_FIXED_LEN_MOD_BOUNDS( 8, 1518500250, 6521908912666391107);
_FIXED_LEN_MOD_BOUNDS( 7, 1623345051, 6972213902555716131);
_FIXED_LEN_MOD_BOUNDS( 6, 1753413057, 7530851732716320753);
_FIXED_LEN_MOD_BOUNDS( 5, 1920767767, 8249634742471189718);
_FIXED_LEN_MOD_BOUNDS( 4, 2147483648, 9223372036854775808);
_FIXED_LEN_MOD_BOUNDS( 3, 2479700525, 10650232656628343402);
_FIXED_LEN_MOD_BOUNDS( 2, 3037000500, 13043817825332782213);
#else // FLINT_BITS == 64
// 32 bits: k limbs <=> n <= ceil(2**(16*k) / sqrt(len))
_FIXED_LEN_MOD_BOUNDS(11, 19760, 1294981365);
_FIXED_LEN_MOD_BOUNDS(10, 20725, 1358187914);
_FIXED_LEN_MOD_BOUNDS( 9, 21846, 1431655766);
_FIXED_LEN_MOD_BOUNDS( 8, 23171, 1518500250);
_FIXED_LEN_MOD_BOUNDS( 7, 24771, 1623345051);
_FIXED_LEN_MOD_BOUNDS( 6, 26755, 1753413057);
_FIXED_LEN_MOD_BOUNDS( 5, 29309, 1920767767);
_FIXED_LEN_MOD_BOUNDS( 4, 32768, 2147483648);
_FIXED_LEN_MOD_BOUNDS( 3, 37838, 2479700525);
_FIXED_LEN_MOD_BOUNDS( 2, 46341, 3037000500);
#endif // FLINT_BITS == 64
// remains len == 1
if (mod.n <= (UWORD(1) << FLINT_BITS / 2))
{
dot_params_t params = {_DOT1, UWORD(0)};
return params;
}
dot_params_t params = {_DOT2, UWORD(0)};
return params;
}
if (mod.n <= UWORD(1) << (FLINT_BITS / 2)) // implies <= 2 limbs
{
const ulong t0 = (mod.n - 1) * (mod.n - 1);
ulong u1, u0;
umul_ppmm(u1, u0, t0, len);
if (u1 == 0) // 1 limb
{
dot_params_t params = {_DOT1, UWORD(0)};
return params;
}
// u1 != 0 <=> 2 limbs
#if (FLINT_BITS == 64) // _SPLIT: see end of file for these constraints
if (mod.n <= UWORD(1515531528) && len <= WORD(380368697))
{
ulong pow2_precomp;
NMOD_RED(pow2_precomp, (UWORD(1) << DOT_SPLIT_BITS), mod);
dot_params_t params = {_DOT2_SPLIT, pow2_precomp};
return params;
}
#endif
dot_params_t params = {_DOT2_HALF, UWORD(0)};
return params;
}
// from here on, mod.n > 2**(FLINT_BITS / 2)
// --> unreduced dot cannot fit in 1 limb
ulong t2, t1, t0, u1, u0;
umul_ppmm(t1, t0, mod.n - 1, mod.n - 1);
umul_ppmm(t2, t1, t1, len);
umul_ppmm(u1, u0, t0, len);
add_ssaaaa(t2, t1, t2, t1, UWORD(0), u1);
if (t2 == 0) // 2 limbs
{
dot_params_t params = {_DOT2, UWORD(0)};
return params;
}
// 3 limbs:
#if (FLINT_BITS == 64)
if (mod.n <= UWORD(6521908912666391107)) // room for accumulating 8 terms
#else
if (mod.n <= UWORD(1518500250)) // room for accumulating 8 terms
#endif
{
dot_params_t params = {_DOT3_ACC, UWORD(0)};
return params;
}
dot_params_t params = {_DOT3, UWORD(0)};
return params;
}
#undef _FIXED_LEN_MOD_BOUNDS
int _nmod_vec_dot_bound_limbs(slong len, nmod_t mod);
int _nmod_vec_dot_bound_limbs_from_params(slong len, nmod_t mod, dot_params_t params);
/* ------ dot product, specific algorithms ------ */
/* vec1[i] * vec2[i] */
ulong _nmod_vec_dot_pow2(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot1(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot2_half(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot2(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot3_acc(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot3(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
#if FLINT_BITS == 64
ulong _nmod_vec_dot2_split(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod, ulong pow2_precomp);
#endif // FLINT_BITS == 64
/* vec1[i] * vec2[len-1-i] */
ulong _nmod_vec_dot_pow2_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot1_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot2_half_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot2_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot3_acc_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
ulong _nmod_vec_dot3_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod);
#if FLINT_BITS == 64
ulong _nmod_vec_dot2_split_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod, ulong pow2_precomp);
#endif // FLINT_BITS == 64
/* vec1[i] * vec2[i][offset] */
ulong _nmod_vec_dot_pow2_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod);
ulong _nmod_vec_dot1_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod);
ulong _nmod_vec_dot2_half_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod);
ulong _nmod_vec_dot2_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod);
ulong _nmod_vec_dot3_acc_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod);
ulong _nmod_vec_dot3_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod);
#if FLINT_BITS == 64
ulong _nmod_vec_dot2_split_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod, ulong pow2_precomp);
#endif // FLINT_BITS == 64
/* ------------- dot product, general --------------- */
// auxiliary for short dot products
// (fixedlen small constant: compiler unrolls the loops completely)
#define _NMOD_VEC_DOT_SHORT1(fixedlen,expr1,expr2) \
{ \
ulong res = (expr1) * (expr2); i++; \
for (slong j = 0; j < fixedlen-1; j++, i++) \
res += (expr1) * (expr2); \
NMOD_RED(res, res, mod); \
return res; \
} \
#define _NMOD_VEC_DOT_SHORT2(fixedlen,expr1,expr2) \
{ \
ulong s0, s1, u0, u1; \
umul_ppmm(u1, u0, (expr1), (expr2)); i++; \
for (slong j = 0; j < fixedlen-1; j++, i++) \
{ \
umul_ppmm(s1, s0, (expr1), (expr2)); \
add_ssaaaa(u1, u0, u1, u0, s1, s0); \
} \
NMOD2_RED2(s0, u1, u0, mod); \
return s0; \
} \
#define _NMOD_VEC_DOT_SHORT3(fixedlen,expr1,expr2) \
{ \
ulong t2 = UWORD(0); \
ulong t1, t0; \
umul_ppmm(t1, t0, (expr1), (expr2)); i++; \
for (slong j = 0; j < fixedlen - 1; j++, i++) \
{ \
ulong s0, s1; \
umul_ppmm(s1, s0, (expr1), (expr2)); \
add_sssaaaaaa(t2, t1, t0, \
t2, t1, t0, \
UWORD(0), s1, s0); \
} \
\
NMOD_RED(t2, t2, mod); \
ulong res; \
NMOD_RED3(res, t2, t1, t0, mod); \
return res; \
} \
// * supports 1 <= len <= 11, requires method==DOT1|DOT2|DOT3|DOT_POW2
// * i must be already initialized at the first wanted value
#define _NMOD_VEC_DOT_SHORT(i, expr1, expr2, len, mod, method) \
{ \
if (method == _DOT1 || method == _DOT_POW2) \
{ \
if (len == 1) _NMOD_VEC_DOT_SHORT1( 1, expr1, expr2) \
if (len == 2) _NMOD_VEC_DOT_SHORT1( 2, expr1, expr2) \
if (len == 3) _NMOD_VEC_DOT_SHORT1( 3, expr1, expr2) \
if (len == 4) _NMOD_VEC_DOT_SHORT1( 4, expr1, expr2) \
if (len == 5) _NMOD_VEC_DOT_SHORT1( 5, expr1, expr2) \
if (len == 6) _NMOD_VEC_DOT_SHORT1( 6, expr1, expr2) \
if (len == 7) _NMOD_VEC_DOT_SHORT1( 7, expr1, expr2) \
if (len == 8) _NMOD_VEC_DOT_SHORT1( 8, expr1, expr2) \
if (len == 9) _NMOD_VEC_DOT_SHORT1( 9, expr1, expr2) \
if (len == 10) _NMOD_VEC_DOT_SHORT1(10, expr1, expr2) \
_NMOD_VEC_DOT_SHORT1(11, expr1, expr2) \
} \
\
else if (method == _DOT2) \
{ \
if (len == 1) return nmod_mul((expr1), (expr2), mod); \
if (len == 2) _NMOD_VEC_DOT_SHORT2( 2, expr1, expr2) \
if (len == 3) _NMOD_VEC_DOT_SHORT2( 3, expr1, expr2) \
if (len == 4) _NMOD_VEC_DOT_SHORT2( 4, expr1, expr2) \
if (len == 5) _NMOD_VEC_DOT_SHORT2( 5, expr1, expr2) \
if (len == 6) _NMOD_VEC_DOT_SHORT2( 6, expr1, expr2) \
if (len == 7) _NMOD_VEC_DOT_SHORT2( 7, expr1, expr2) \
if (len == 8) _NMOD_VEC_DOT_SHORT2( 8, expr1, expr2) \
if (len == 9) _NMOD_VEC_DOT_SHORT2( 9, expr1, expr2) \
if (len == 10) _NMOD_VEC_DOT_SHORT2(10, expr1, expr2) \
_NMOD_VEC_DOT_SHORT2(11, expr1, expr2) \
} \
\
else if (method == _DOT3) \
{ \
if (len == 1) return nmod_mul((expr1), (expr2), mod); \
if (len == 2) _NMOD_VEC_DOT_SHORT3( 2, expr1, expr2) \
if (len == 3) _NMOD_VEC_DOT_SHORT3( 3, expr1, expr2) \
if (len == 4) _NMOD_VEC_DOT_SHORT3( 4, expr1, expr2) \
if (len == 5) _NMOD_VEC_DOT_SHORT3( 5, expr1, expr2) \
if (len == 6) _NMOD_VEC_DOT_SHORT3( 6, expr1, expr2) \
if (len == 7) _NMOD_VEC_DOT_SHORT3( 7, expr1, expr2) \
if (len == 8) _NMOD_VEC_DOT_SHORT3( 8, expr1, expr2) \
if (len == 9) _NMOD_VEC_DOT_SHORT3( 9, expr1, expr2) \
if (len == 10) _NMOD_VEC_DOT_SHORT3(10, expr1, expr2) \
_NMOD_VEC_DOT_SHORT3(11, expr1, expr2) \
} \
} while(0); \
FLINT_FORCE_INLINE ulong _nmod_vec_dot(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod, dot_params_t params)
{
if (len <= 11)
{
if (len == 0) return UWORD(0);
slong i = 0;
_NMOD_VEC_DOT_SHORT(i, vec1[i], vec2[i], len, mod, params.method);
}
if (params.method == _DOT1)
return _nmod_vec_dot1(vec1, vec2, len, mod);
#if FLINT_BITS == 64
if (params.method == _DOT2_SPLIT)
return _nmod_vec_dot2_split(vec1, vec2, len, mod, params.pow2_precomp);
#endif // FLINT_BITS == 64
if (params.method == _DOT2)
return _nmod_vec_dot2(vec1, vec2, len, mod);
if (params.method == _DOT3_ACC)
return _nmod_vec_dot3_acc(vec1, vec2, len, mod);
if (params.method == _DOT3)
return _nmod_vec_dot3(vec1, vec2, len, mod);
if (params.method == _DOT2_HALF)
return _nmod_vec_dot2_half(vec1, vec2, len, mod);
if (params.method == _DOT_POW2)
{
if (mod.n <= UWORD(1) << (FLINT_BITS / 2))
return _nmod_vec_dot1(vec1, vec2, len, mod);
else
return _nmod_vec_dot_pow2(vec1, vec2, len, mod);
}
// covers _DOT0 for len > 11 (i.e. mod.n == 1...)
return UWORD(0);
}
FLINT_FORCE_INLINE ulong _nmod_vec_dot_rev(nn_srcptr vec1, nn_srcptr vec2, slong len, nmod_t mod, dot_params_t params)
{
if (len <= 11)
{
if (len == 0) return UWORD(0);
slong i = 0;
_NMOD_VEC_DOT_SHORT(i, vec1[i], vec2[len-1-i], len, mod, params.method);
}
if (params.method == _DOT1)
return _nmod_vec_dot1_rev(vec1, vec2, len, mod);
#if FLINT_BITS == 64
if (params.method == _DOT2_SPLIT)
return _nmod_vec_dot2_split_rev(vec1, vec2, len, mod, params.pow2_precomp);
#endif // FLINT_BITS == 64
if (params.method == _DOT2)
return _nmod_vec_dot2_rev(vec1, vec2, len, mod);
if (params.method == _DOT3_ACC)
return _nmod_vec_dot3_acc_rev(vec1, vec2, len, mod);
if (params.method == _DOT3)
return _nmod_vec_dot3_rev(vec1, vec2, len, mod);
if (params.method == _DOT2_HALF)
return _nmod_vec_dot2_half_rev(vec1, vec2, len, mod);
if (params.method == _DOT_POW2)
{
if (mod.n <= UWORD(1) << (FLINT_BITS / 2))
return _nmod_vec_dot1_rev(vec1, vec2, len, mod);
else
return _nmod_vec_dot_pow2_rev(vec1, vec2, len, mod);
}
// covers _DOT0 for len > 11 (i.e. mod.n == 1...)
return UWORD(0);
}
FLINT_FORCE_INLINE ulong _nmod_vec_dot_ptr(nn_srcptr vec1, const nn_ptr * vec2, slong offset, slong len, nmod_t mod, dot_params_t params)
{
if (len <= 11)
{
if (len == 0) return UWORD(0);
slong i = 0;
_NMOD_VEC_DOT_SHORT(i, vec1[i], vec2[i][offset], len, mod, params.method);
}
if (params.method == _DOT1)
return _nmod_vec_dot1_ptr(vec1, vec2, offset, len, mod);
#if FLINT_BITS == 64
if (params.method == _DOT2_SPLIT)
return _nmod_vec_dot2_split_ptr(vec1, vec2, offset, len, mod, params.pow2_precomp);
#endif // FLINT_BITS == 64
if (params.method == _DOT2)
return _nmod_vec_dot2_ptr(vec1, vec2, offset, len, mod);
if (params.method == _DOT3_ACC)
return _nmod_vec_dot3_acc_ptr(vec1, vec2, offset, len, mod);
if (params.method == _DOT3)
return _nmod_vec_dot3_ptr(vec1, vec2, offset, len, mod);
if (params.method == _DOT2_HALF)
return _nmod_vec_dot2_half_ptr(vec1, vec2, offset, len, mod);
if (params.method == _DOT_POW2)
{
if (mod.n <= UWORD(1) << (FLINT_BITS / 2))
return _nmod_vec_dot1_ptr(vec1, vec2, offset, len, mod);
else
return _nmod_vec_dot_pow2_ptr(vec1, vec2, offset, len, mod);
}
// covers _DOT0 for len > 11 (i.e. mod.n == 1...)
return UWORD(0);
}
#undef _NMOD_VEC_DOT_SHORT1
#undef _NMOD_VEC_DOT_SHORT2
#undef _NMOD_VEC_DOT_SHORT3
/* ---- macros for dot product with expressions, specific algorithms ---- */
// _DOT1 (1 limb)
#define _NMOD_VEC_DOT1(res, i, len, expr1, expr2, mod) \
do \
{ \
res = UWORD(0); \
for (i = 0; i < (len); i++) \
res += (expr1) * (expr2); \
NMOD_RED(res, res, mod); \
} while(0);
// _DOT2_SPLIT (2 limbs, splitting at DOT_SPLIT_BITS bits, 8-unrolling)
#if (FLINT_BITS == 64)
#define _NMOD_VEC_DOT2_SPLIT(res, i, len, expr1, expr2, mod, pow2_precomp) \
do \
{ \
ulong dp_lo = 0; \
ulong dp_hi = 0; \
\
for (i = 0; i+7 < (len); ) \
{ \
dp_lo += (expr1) * (expr2); i++; \
dp_lo += (expr1) * (expr2); i++; \
dp_lo += (expr1) * (expr2); i++; \
dp_lo += (expr1) * (expr2); i++; \
dp_lo += (expr1) * (expr2); i++; \
dp_lo += (expr1) * (expr2); i++; \
dp_lo += (expr1) * (expr2); i++; \
dp_lo += (expr1) * (expr2); i++; \
\
dp_hi += dp_lo >> DOT_SPLIT_BITS; \
dp_lo &= DOT_SPLIT_MASK; \
} \
\
for ( ; i < (len); i++) \
dp_lo += (expr1) * (expr2); \
\
res = pow2_precomp * dp_hi + dp_lo; \
NMOD_RED(res, res, mod); \
} while(0);
#endif // FLINT_BITS == 64
// _DOT2_HALF (two limbs, modulus < 2**32)
// mod.n is too close to 2**32 to accumulate in some ulong
// still interesting: a bit faster than _NMOD_VEC_DOT2
#define _NMOD_VEC_DOT2_HALF(res, i, len, expr1, expr2, mod) \
do \
{ \
ulong s0zz = UWORD(0); \
ulong s1zz = UWORD(0); \
for (i = 0; i < (len); i++) \
{ \
const ulong prodzz = (expr1) * (expr2); \
add_ssaaaa(s1zz, s0zz, s1zz, s0zz, 0, prodzz); \
} \
NMOD2_RED2(res, s1zz, s0zz, mod); \
} while(0);
// _DOT2 (two limbs, general)
#define _NMOD_VEC_DOT2(res, i, len, expr1, expr2, mod) \
do \
{ \
ulong u0zz = UWORD(0); \
ulong u1zz = UWORD(0); \
\
for (i = 0; i+7 < (len); ) \
{ \
ulong s0zz, s1zz; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
} \
for ( ; i < (len); i++) \
{ \
ulong s0zz, s1zz; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
} \
\
NMOD2_RED2(res, u1zz, u0zz, mod); \
} while(0);
// _DOT3_ACC (three limbs, delayed accumulations)
// 8-unroll: requires 8 * (mod.n - 1)**2 < 2**128
#define _NMOD_VEC_DOT3_ACC(res, i, len, expr1, expr2, mod) \
do \
{ \
ulong t2zz = UWORD(0); \
ulong t1zz = UWORD(0); \
ulong t0zz = UWORD(0); \
\
for (i = 0; i+7 < (len); ) \
{ \
ulong s0zz, s1zz; \
ulong u0zz = UWORD(0); \
ulong u1zz = UWORD(0); \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
i++; \
add_sssaaaaaa(t2zz, t1zz, t0zz, \
t2zz, t1zz, t0zz, \
UWORD(0), u1zz, u0zz); \
} \
\
ulong s0zz, s1zz; \
ulong u0zz = UWORD(0); \
ulong u1zz = UWORD(0); \
for ( ; i < (len); i++) \
{ \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_ssaaaa(u1zz, u0zz, u1zz, u0zz, s1zz, s0zz); \
} \
\
add_sssaaaaaa(t2zz, t1zz, t0zz, \
t2zz, t1zz, t0zz, \
UWORD(0), u1zz, u0zz); \
\
NMOD_RED(t2zz, t2zz, mod); \
NMOD_RED3(res, t2zz, t1zz, t0zz, mod); \
} while(0);
// _DOT3 (three limbs, general)
// mod.n is too close to 2**64 to accumulate in two words
#define _NMOD_VEC_DOT3(res, i, len, expr1, expr2, mod) \
do \
{ \
ulong t2zz = UWORD(0); \
ulong t1zz = UWORD(0); \
ulong t0zz = UWORD(0); \
for (i = 0; i < (len); i++) \
{ \
ulong s0zz, s1zz; \
umul_ppmm(s1zz, s0zz, (expr1), (expr2)); \
add_sssaaaaaa(t2zz, t1zz, t0zz, \
t2zz, t1zz, t0zz, \
UWORD(0), s1zz, s0zz); \
} \
\
NMOD_RED(t2zz, t2zz, mod); \
NMOD_RED3(res, t2zz, t1zz, t0zz, mod); \
} while(0);
/* ---- macros for dot product with expressions, general ---- */
// currently no vectorization here
#if (FLINT_BITS == 64)
#define NMOD_VEC_DOT(res, i, len, expr1, expr2, mod, params) \
do \
{ \
res = UWORD(0); /* covers _DOT0 */ \
if (params.method == _DOT1 || params.method == _DOT_POW2) \
_NMOD_VEC_DOT1(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT2_SPLIT) \
_NMOD_VEC_DOT2_SPLIT(res, i, len, expr1, expr2, mod, \
params.pow2_precomp) \
else if (params.method == _DOT2_HALF) \
_NMOD_VEC_DOT2_HALF(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT2) \
_NMOD_VEC_DOT2(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT3_ACC) \
_NMOD_VEC_DOT3_ACC(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT3) \
_NMOD_VEC_DOT3(res, i, len, expr1, expr2, mod) \
} while(0);
#else // FLINT_BITS == 64
#define NMOD_VEC_DOT(res, i, len, expr1, expr2, mod, params) \
do \
{ \
res = UWORD(0); /* covers _DOT0 */ \
if (params.method == _DOT1 || params.method == _DOT_POW2) \
_NMOD_VEC_DOT1(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT2_HALF) \
_NMOD_VEC_DOT2_HALF(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT2) \
_NMOD_VEC_DOT2(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT3_ACC) \
_NMOD_VEC_DOT3_ACC(res, i, len, expr1, expr2, mod) \
else if (params.method == _DOT3) \
_NMOD_VEC_DOT3(res, i, len, expr1, expr2, mod) \
} while(0);
#endif // FLINT_BITS == 64
#ifdef __cplusplus
}
#endif
#endif