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mpn_extras.c
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mpn_extras.c
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/*============================================================================
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
===============================================================================*/
/******************************************************************************
mpn_extras.c
Extra functions for manipulating mpn's and limbs.
Copyright (C) 2006, William Hart
mp_limb_t mpn_divmod_1_preinv was adapted from GMP, (C) Free Software Foundation
******************************************************************************/
#include <gmp.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include "flint.h"
#include "longlong_wrapper.h"
#include "longlong.h"
#include "long_extras.h"
#include "memory-manager.h"
#include "mpn_extras.h"
#include "ZmodF_poly.h"
#include "ZmodF_mul.h"
#include "F_mpn_mul-tuning.h"
#define DEBUG2 1
/*=======================================================================================
Performs division by a limb d and places the quotient in qp and returns the
remainder. Requires a single limb approximation to 1/d as input. If the most
significant bit of d is not 1 it expects d to be shifted left (by norm bits)
until the most significant bit is 1 before the inverse is computed. However
the original d should be supplied to the function, not the shifted d.
This code has been adapted from code found in the GMP package version 4.2.1
(divrem_1.c) (C) Free Software Foundation
*/
mp_limb_t F_mpn_divrem_ui_precomp(mp_limb_t * qp, mp_limb_t * up,
unsigned long un, mp_limb_t d, mp_limb_t dinv)
{
mp_size_t n;
mp_size_t i;
mp_limb_t n1, n0;
mp_limb_t r = 0;
unsigned long norm;
n = un;
if (n == 0)
return 0;
count_lead_zeros(norm, d);
qp += (n - 1); /* Make qp point at most significant quotient limb */
if ((d & (1L<<(FLINT_BITS-1))) != 0)
{
if (un != 0)
{
/* High quotient limb is 0 or 1, skip a divide step. */
mp_limb_t q;
r = up[un - 1];
q = (r >= d);
*qp-- = q;
r -= (d & -q);
n--;
un--;
}
/* Multiply-by-inverse, divisor already normalized. */
for (i = un - 1; i >= 0; i--)
{
n0 = up[i];
udiv_qrnnd_preinv (*qp, r, r, n0, d, dinv);
qp--;
}
return r;
} else
{
/* Most significant bit of divisor == 0. */
/* Skip a division if high < divisor (high quotient 0). Testing here
before normalizing will still skip as often as possible. */
if (un != 0)
{
n1 = up[un - 1];
if (n1 < d)
{
r = n1;
*qp-- = 0;
n--;
if (n == 0) return r;
un--;
}
}
d <<= norm;
r <<= norm;
if (un != 0)
{
n1 = up[un - 1];
r |= (n1 >> (FLINT_BITS - norm));
for (i = un - 2; i >= 0; i--)
{
n0 = up[i];
udiv_qrnnd_preinv (*qp, r, r,
((n1 << norm) | (n0 >> (FLINT_BITS - norm))), d, dinv);
qp--;
n1 = n0;
}
udiv_qrnnd_preinv (*qp, r, r, n1 << norm, d, dinv);
qp--;
}
return r >> norm;
}
}
mp_limb_t F_mpn_addmul(mp_limb_t * rp, mp_limb_t * s1p, unsigned long s1n,
mp_limb_t * s2p, unsigned long s2n)
{
if (s2n == 0) return 0;
mp_limb_t carry;
carry = mpn_addmul_1(rp, s1p, s1n, s2p[0]);
unsigned long i;
for (i = 1; i < s2n; i++)
{
carry = mpn_add_1(rp+i+s1n-1, rp+i+s1n-1, 1, carry);
if (s2p[i]) carry += mpn_addmul_1(rp+i, s1p, s1n, s2p[i]);
}
carry = mpn_add_1(rp+s2n+s1n-1, rp+s2n+s1n-1, 1, carry);
return carry;
}
/*=====================================================================================
Fast Integer Multiplication Code
=====================================================================================*/
unsigned long MUL_TWK_VALS[MUL_TWK_COUNT][3] =
{
{2000, 2140, 1024},
{2140, 2430, 64},
{2430, 2580, 1024},
{2580, 2700, 64},
{2700, 2880, 4096},
{2880, 3850, 16},
{3850, 4220, 4},
{4220, 4400, 1024},
{4400, 4850, 16},
{4850, 5700, 1024},
{5700, 7900, 4},
{7900, 8900, 1024},
{8900, 97000, 4},
{97000, 127000, 1},
{127000, 262000, 4},
{262000, 517000, 1},
{517000, 1050000, 4},
{1050000, 2060000, 1},
{2060000, 4230000, 4},
{4230000, 8350000, 1}
};
unsigned long SQR_TWK_VALS[SQR_TWK_COUNT][3] =
{
{1564, 1994, 16},
{1994, 2952, 64},
{2952, 5921, 16},
{5921, 32575, 4},
{32575, 40006, 16},
{40006, 66526, 4},
{66526, 127370, 1},
{127370, 257473, 4},
{257473, 520507, 1},
{520507, 1050000, 4},
{1050000, 2060000, 1},
{2060000, 4230000, 4},
{4230000, 8350000, 1}
};
unsigned long FFT_MUL_TWK[FFT_MUL_COUNT][2] =
{
{1734, 8},
{3450, 9},
{3710, 8},
{3840, 9},
{4080, 8},
{4220, 9},
{4480, 8},
{4600, 9},
{4870, 8},
{4980, 9},
{5230, 8},
{5380, 9},
{6140, 10},
{7150, 9},
{7700, 10},
{8700, 9},
{9200, 10},
{12300, 11},
{34800, 10},
{36900, 12},
{41000, 11},
{49200, 12},
{99000, 13},
{130000, 12},
{198000, 13},
{396000, 14},
{526000, 13},
{1040000, 14},
{3150000, 15},
{6300000, 16},
{8400000, 15},
{12700000, 17},
{15900000, 16}
};
unsigned long FFT_SQR_TWK[FFT_SQR_COUNT][2] =
{
{1300, 8},
{2700, 9},
{2950, 8},
{3080, 9},
{4100, 8},
{4240, 9},
{5100, 10},
{5630, 9},
{6150, 10},
{8700, 9},
{9200, 10},
{12300, 11},
{24700, 12},
{29000, 11},
{35000, 10},
{36900, 11},
{49000, 12},
{99000, 13},
{130000, 12},
{198000, 13},
{396000, 14},
{660000, 13},
{780000, 14},
{170000, 15},
{210000, 14},
{420000, 15},
{880000, 16},
{1060000, 15},
{1260000, 17},
{1680000, 16}
};
/*
Splits an mpn into segments of length coeff_limbs and stores in a ZmodF_poly
in zero padded coefficients of length output_limbs, for use in FFT
convolution code. Assumes that the input is total_limbs in length.
Used by the large integer multiplication code
(F_mpn_mul and F_mpn_mul_precache and F_mpn_mul_trunc)
*/
void F_mpn_FFT_split(ZmodF_poly_t poly, const mp_limb_t * limbs, const unsigned long total_limbs,
unsigned long coeff_limbs, unsigned long output_limbs)
{
unsigned long length = (total_limbs-1)/coeff_limbs + 1;
unsigned long i, j, skip;
for (skip = 0, i = 0; skip+coeff_limbs <= total_limbs; skip+=coeff_limbs, i++)
{
if (i + 1 < length)
for (j = 0; j + 8 < output_limbs; j += 8) FLINT_PREFETCH(poly->coeffs[i+1], j);
F_mpn_clear(poly->coeffs[i], output_limbs+1);
// convert a coefficient
F_mpn_copy(poly->coeffs[i], limbs+skip, coeff_limbs);
}
if (i < length) F_mpn_clear(poly->coeffs[i], output_limbs+1);
if (total_limbs > skip) F_mpn_copy(poly->coeffs[i], limbs+skip, total_limbs-skip);
poly->length = length;
}
/*
Splits an mpn into segments of length _bits_ and stores in a ZmodF_poly
in zero padded coefficients of length output_limbs, for use in FFT
convolution code. Assumes that the input is total_limbs in length.
Used by the large integer multiplication code
(F_mpn_mul)
It is assumed that bits is not divisible by FLINT_BITS
*/
void F_mpn_FFT_split_bits(ZmodF_poly_t poly, const mp_limb_t * limbs, const unsigned long total_limbs,
unsigned long bits, unsigned long output_limbs)
{
unsigned long length = (FLINT_BITS*total_limbs-1)/bits + 1;
unsigned long i, j;
unsigned long top_bits = ((FLINT_BITS-1)&bits);
if (top_bits == 0)
{
F_mpn_FFT_split(poly, limbs, total_limbs, bits >> FLINT_LG_BITS_PER_LIMB, output_limbs);
return;
}
unsigned long coeff_limbs = (bits>>FLINT_LG_BITS_PER_LIMB) + 1;
unsigned long mask = (1L<<top_bits)-1L;
unsigned long shift_bits = 0L;
unsigned long const * limb_ptr = limbs;
for (i = 0; i < length - 1; i++)
{
for (j = 0; j + 8 < output_limbs; j += 8) FLINT_PREFETCH(poly->coeffs[i+1], j);
F_mpn_clear(poly->coeffs[i], output_limbs+1);
// convert a coefficient
if (!shift_bits)
{
F_mpn_copy(poly->coeffs[i], limb_ptr, coeff_limbs);
poly->coeffs[i][coeff_limbs-1] &= mask;
limb_ptr += (coeff_limbs-1);
shift_bits += top_bits;
} else
{
mpn_rshift(poly->coeffs[i], limb_ptr, coeff_limbs, shift_bits);
limb_ptr += (coeff_limbs-1);
shift_bits += top_bits;
if (shift_bits >= FLINT_BITS)
{
limb_ptr++;
poly->coeffs[i][coeff_limbs-1] += (limb_ptr[0] << (FLINT_BITS - (shift_bits - top_bits)));
shift_bits -= FLINT_BITS;
}
poly->coeffs[i][coeff_limbs-1] &= mask;
}
}
F_mpn_clear(poly->coeffs[i], output_limbs+1);
unsigned long limbs_left = total_limbs - (limb_ptr - limbs);
if (!shift_bits)
{
F_mpn_copy(poly->coeffs[i], limb_ptr, limbs_left);
} else
{
mpn_rshift(poly->coeffs[i], limb_ptr, limbs_left, shift_bits);
}
poly->length = length;
}
/*
Recombines coefficients of a ZmodF_poly after doing a convolution. Assumes
each of the coefficients of the ZmodF_poly is output_limbs long, that each
of the coefficients is being shifted by a multiple of coeff_limbs and added
to an mpn which is total_limbs long. It is assumed that the mpn has been
zeroed in advance.
Used by the large integer multiplication code (F_mpn_mul and F_mpn_mul_precache
and F_mpn_mul_trunc)
*/
void F_mpn_FFT_combine(mp_limb_t * res, ZmodF_poly_t poly, unsigned long coeff_limbs,
unsigned long output_limbs, unsigned long total_limbs)
{
unsigned long skip, i, j;
unsigned long length = poly->length;
for (skip = 0, i = 0; (i < length) && (skip+output_limbs <= total_limbs); i++, skip+=coeff_limbs)
{
for (j = 0; j < output_limbs; j += 8) FLINT_PREFETCH(poly->coeffs[i+1], j);
mpn_add(res+skip, res+skip, output_limbs+1, poly->coeffs[i], output_limbs);
}
while ((skip < total_limbs) && (i < length))
{
mpn_add(res+skip, res+skip, total_limbs - skip, poly->coeffs[i], FLINT_MIN(total_limbs - skip, output_limbs));
i++;
skip+=coeff_limbs;
}
}
/*
Recombines coefficients of a ZmodF_poly after doing a convolution. Assumes
each of the coefficients of the ZmodF_poly is output_limbs long, that each
of the coefficients is being shifted by a multiple of _bits_ and added
to an mpn which is total_limbs long. It is assumed that the mpn has been
zeroed in advance.
Used by the large integer multiplication code (F_mpn_mul)
It is assumed that bits is not divisible by FLINT_BITS
*/
void F_mpn_FFT_combine_bits(mp_limb_t * res, ZmodF_poly_t poly, unsigned long bits,
unsigned long output_limbs, unsigned long total_limbs)
{
unsigned long top_bits = ((FLINT_BITS-1)&bits);
if (top_bits == 0)
{
F_mpn_FFT_combine(res, poly, bits >> FLINT_LG_BITS_PER_LIMB, output_limbs, total_limbs);
return;
}
unsigned long coeff_limbs = (bits>>FLINT_LG_BITS_PER_LIMB) + 1;
unsigned long i, j;
unsigned long length = poly->length;
unsigned long * temp = (unsigned long *) flint_heap_alloc(output_limbs+1);
unsigned long shift_bits = 0;
unsigned long * limb_ptr = res;
unsigned long * end = res + total_limbs;
for (i = 0; (i < length) && (limb_ptr + output_limbs < end); i++)
{
for (j = 0; j < output_limbs; j += 8) FLINT_PREFETCH(poly->coeffs[i+1], j);
if (shift_bits)
{
mpn_lshift(temp, poly->coeffs[i], output_limbs+1, shift_bits);
mpn_add_n(limb_ptr, limb_ptr, temp, output_limbs+1);
} else
{
mpn_add(limb_ptr, limb_ptr, output_limbs+1, poly->coeffs[i], output_limbs);
}
shift_bits += top_bits;
limb_ptr += (coeff_limbs - 1);
if (shift_bits >= FLINT_BITS)
{
limb_ptr++;
shift_bits -= FLINT_BITS;
}
}
while ((limb_ptr < end) && (i < length))
{
if (shift_bits)
{
mpn_lshift(temp, poly->coeffs[i], output_limbs+1, shift_bits);
mpn_add_n(limb_ptr, limb_ptr, temp, end - limb_ptr);
} else
{
mpn_add_n(limb_ptr, limb_ptr, poly->coeffs[i], end - limb_ptr);
}
shift_bits += top_bits;
limb_ptr += (coeff_limbs - 1);
if (shift_bits >= FLINT_BITS)
{
limb_ptr++;
shift_bits -= FLINT_BITS;
}
i++;
}
flint_heap_free(temp);
}
/*
Compute optimal lengths for the polynomials that coeff1 and coeff2 are broken into
in the convolution based long integer code.
We want the sum of the two lengths to satisfy the SS condition (with sqrt2):
if 2^l1 < length1 + length2 <= 2^l2 then 2^(l2-1) divides output_bits
Requires limbs1 and limbs2 are at least 1, ensures length1 and length2 are at least 1
*/
#define F_mpn_mul_ADJUST \
do { \
/* Compute the coefficient size for breaking the two long integers up */ \
coeff_limbs = (limbs1+limbs2-1)/(length)+1; \
if (coeff_limbs == 1L) /* This is as far as we can go */ \
\
{ \
length1 = limbs1; \
length2 = limbs2; \
done = 1; \
} \
while ((limbs1-1)/(coeff_limbs)+(limbs2-1)/(coeff_limbs)+2 > length) coeff_limbs++; \
/* Compute the number of bits for the output coefficients */ \
output_bits = (2*coeff_limbs+1)*FLINT_BITS; \
output_bits = (((output_bits - 1) >> (log_length-1)) + 1) << (log_length-1); \
/* Try and compute a more optimal coefficient size to break up inputs */ \
coeff_limbs = ((output_bits - FLINT_BITS)/FLINT_BITS)/2; \
if ((long) coeff_limbs <= 1L) coeff_limbs = 1; \
/* Compute the lengths of the polys the coefficients will be broken into with this coeff size */ \
length1 = (limbs1-1)/coeff_limbs+1; \
length2 = (limbs2-1)/coeff_limbs+1; \
} while (0)
#define F_mpn_mul_TUNING \
do { \
if (twk > 64) \
{ \
length = 2; \
log_length = 1; \
\
int done = 0; \
\
while ((length < 2*output_bits) && !done) \
{ \
/* We are outside the optimal SS region, so double the length */ \
length<<=1; \
log_length++; \
F_mpn_mul_ADJUST; \
} \
\
while ((twk > 64) && (length >= 4)) \
{ \
log_length--; \
length>>=1; \
twk>>=2; \
} \
\
F_mpn_mul_ADJUST; \
\
} else \
{ \
int done = 0; \
\
while ((twk*length < 2*output_bits) && !done) \
{ \
/* We are outside the optimal SS region, so double the length */ \
length<<=1; \
log_length++; \
F_mpn_mul_ADJUST; \
} \
} \
} while (0)
mp_limb_t __F_mpn_mul(mp_limb_t * res, const mp_limb_t * data1, const unsigned long limbs1,
const mp_limb_t * data2, const unsigned long limbs2, unsigned long log_length)
{
unsigned long coeff_limbs = limbs1 + limbs2;
unsigned long s1 = (FLINT_BIT_COUNT(data1[limbs1-1]) + FLINT_BIT_COUNT(data2[limbs2-1]) <= FLINT_BITS);
unsigned long total_limbs = coeff_limbs - s1;
unsigned long output_bits = coeff_limbs*FLINT_BITS;
unsigned long n = coeff_limbs;
unsigned long length1 = 1;
unsigned long length2 = 1;
unsigned log_length2 = 1;
unsigned long bits;
do
{
bits = (((limbs1 << FLINT_LG_BITS_PER_LIMB)-1) >> (log_length-1)) + 1;
output_bits = 2*bits + log_length2;
output_bits = (((output_bits - 1) >> (log_length-1)) + 1) << (log_length-1);
bits = (output_bits - log_length2)/2;
length1 = ((limbs1 << FLINT_LG_BITS_PER_LIMB)-1)/bits + 1;
length2 = ((limbs2 << FLINT_LG_BITS_PER_LIMB)-1)/bits + 1;
log_length2++;
} while ((length2 > (1L<<(log_length2-1))) || (length1 > (1L<<(log_length-1))));
n = (output_bits-1)/FLINT_BITS+1;
#if DEBUG
printf("%ld, %ld, %ld, %ld, %ld, %ld, %ld\n", bits, length1, length2, output_bits, coeff_limbs, n, log_length);
#endif
ZmodF_poly_t poly1;
ZmodF_poly_init(poly1, log_length, n, 1);
F_mpn_FFT_split_bits(poly1, data1, limbs1, bits, n);
ulong length = length1 + length2 - 1;
ulong size = 1UL << log_length;
if (length > size)
length = size;
ZmodF_poly_FFT(poly1, length);
if ((data1 == data2) && (limbs1 == limbs2))
{
ZmodF_poly_pointwise_mul(poly1, poly1, poly1);
} else
{
ZmodF_poly_t poly2;
ZmodF_poly_init(poly2, log_length, n, 1);
F_mpn_FFT_split_bits(poly2, data2, limbs2, bits, n);
ZmodF_poly_FFT(poly2, length);
ZmodF_poly_pointwise_mul(poly1, poly1, poly2);
ZmodF_poly_clear(poly2);
}
ZmodF_poly_IFFT(poly1);
ZmodF_poly_rescale(poly1);
ZmodF_poly_normalise(poly1);
F_mpn_clear(res, limbs1+limbs2);
F_mpn_FFT_combine_bits(res, poly1, bits, n, total_limbs);
ZmodF_poly_clear(poly1);
return res[limbs1+limbs2-1];
}
mp_limb_t __F_mpn_mul_trunc(mp_limb_t * res, mp_limb_t * data1, unsigned long limbs1,
mp_limb_t * data2, unsigned long limbs2,
unsigned long log_length, unsigned long trunc)
{
unsigned long length = 1;
unsigned long coeff_limbs = limbs1 + limbs2;
unsigned long s1 = (FLINT_BIT_COUNT(data1[limbs1-1]) + FLINT_BIT_COUNT(data2[limbs2-1]) <= FLINT_BITS);
unsigned long total_limbs = coeff_limbs - s1;
unsigned long output_bits = coeff_limbs*FLINT_BITS;
unsigned long n = coeff_limbs;
unsigned long length1 = 1;
unsigned long length2 = 1;
unsigned log_length2 = 1;
unsigned long bits;
do
{
bits = (((limbs1 << FLINT_LG_BITS_PER_LIMB)-1) >> (log_length-1)) + 1;
output_bits = 2*bits + log_length2;
output_bits = (((output_bits - 1) >> (log_length-1)) + 1) << (log_length-1);
bits = (output_bits - log_length2)/2;
length1 = ((limbs1 << FLINT_LG_BITS_PER_LIMB)-1)/bits + 1;
length2 = ((limbs2 << FLINT_LG_BITS_PER_LIMB)-1)/bits + 1;
log_length2++;
} while ((length2 > (1L<<(log_length2-1))) || (length1 > (1L<<(log_length-1))));
n = (output_bits-1)/FLINT_BITS+1;
#if DEBUG
printf("%ld, %ld, %ld, %ld, %ld, %ld\n", bits, length1, length2, output_bits, coeff_limbs, n);
#endif
ZmodF_poly_t poly1;
ZmodF_poly_stack_init(poly1, log_length, n, 1);
F_mpn_FFT_split_bits(poly1, data1, limbs1, bits, n);
if ((data1 == data2) && (limbs1 == limbs2))
{
// identical operands case
ZmodF_poly_convolution_range(poly1, poly1, poly1, 0, (trunc*FLINT_BITS-1)/bits+1);
}
else
{
// distinct operands case
ZmodF_poly_t poly2;
ZmodF_poly_stack_init(poly2, log_length, n, 1);
F_mpn_FFT_split_bits(poly2, data2, limbs2, bits, n);
ZmodF_poly_convolution_range(poly1, poly1, poly2, 0, (trunc*FLINT_BITS-1)/bits+1);
ZmodF_poly_stack_clear(poly2);
}
poly1->length = FLINT_MIN(poly1->length, (trunc*FLINT_BITS-1)/bits+1);
ZmodF_poly_normalise(poly1);
F_mpn_clear(res, trunc);
F_mpn_FFT_combine_bits(res, poly1, bits, n, trunc);
ZmodF_poly_stack_clear(poly1);
return res[trunc-1];
}
/*
Multiply two integers in mpn format
WARNING: This function requires limbs1+limbs2 output limbs when limbs1+limbs2
< FLINT_FFT_LIMBS_CROSSOVER but may require one less limb otherwise. The function
will return 0 if it did not require (and indeed did not zero) the extra limb,
otherwise it returns the (non zero) value of this high limb after multiplication.
Assumes neither of limbs1, limbs2 is zero.
*/
mp_limb_t F_mpn_mul(mp_limb_t * res, const mp_limb_t * data1, const unsigned long limbs1,
const mp_limb_t * data2, const unsigned long limbs2)
{
unsigned long coeff_limbs = limbs1 + limbs2;
unsigned long twk;
if (coeff_limbs/2 > FFT_TUNE_CUTOFF)
{
twk = 0;
while ((1L<<(2*twk)) < FLINT_BITS*coeff_limbs)
{
twk++;
}
} else if ((data1 != data2) || (limbs1 != limbs2))
{
if (coeff_limbs/2 < FFT_MUL_TWK[0][0])
return mpn_mul(res, data1, limbs1, data2, limbs2);
else
{
unsigned long i = 0;
while ((i < FFT_MUL_COUNT-1) && (coeff_limbs/2 > FFT_MUL_TWK[i+1][0])) i++;
twk = FFT_MUL_TWK[i][1];
}
} else
{
if (coeff_limbs/2 < FFT_SQR_TWK[0][0])
return mpn_mul(res, data1, limbs1, data1, limbs1);
else
{
unsigned long i = 0;
while ((i < FFT_SQR_COUNT-1) && (coeff_limbs/2 > FFT_SQR_TWK[i+1][0])) i++;
twk = FFT_SQR_TWK[i][1];
}
}
return __F_mpn_mul(res, data1, limbs1, data2, limbs2, twk);
}
/*
Multiply two integers in mpn format truncating to _trunc_ output limbs
Assumes none of limbs1, limbs2 and trunc is zero.
WARNING: the output "res" needs to have "limbs1+limbs2"
limbs allocated and we must have limbs1 >= limbs2 >= 1.
*/
mp_limb_t F_mpn_mul_trunc(mp_limb_t * res, mp_limb_t * data1, unsigned long limbs1,
mp_limb_t * data2, unsigned long limbs2, unsigned long trunc)
{
unsigned long coeff_limbs = limbs1 + limbs2;
if (trunc > coeff_limbs) trunc = coeff_limbs;
unsigned long twk;
if (coeff_limbs/2 > FFT_TUNE_CUTOFF)
{
twk = 0;
while ((1L<<(2*twk)) < FLINT_BITS*coeff_limbs)
{
twk++;
}
} else if ((data1 != data2) || (limbs1 != limbs2))
{
if (coeff_limbs/2 < FFT_MUL_TWK[0][0])
{
mpn_mul(res, data1, limbs1, data2, limbs2);
return res[trunc-1];
} else
{
unsigned long i = 0;
while ((i < FFT_MUL_COUNT-1) && (coeff_limbs/2 > FFT_MUL_TWK[i+1][0])) i++;
twk = FFT_MUL_TWK[i][1];
}
} else
{
if (coeff_limbs/2 < FFT_SQR_TWK[0][0])
{
mpn_mul(res, data1, limbs1, data1, limbs1);
return res[trunc-1];
} else
{
unsigned long i = 0;
while ((i < FFT_SQR_COUNT-1) && (coeff_limbs/2 > FFT_SQR_TWK[i+1][0])) i++;
twk = FFT_SQR_TWK[i][1];
}
}
return __F_mpn_mul_trunc(res, data1, limbs1, data2, limbs2, twk, trunc);
}
/*
Precompute an FFT for integer multiplication.
Assumes neither of limbs1, limbs2 is zero.
*/
void F_mpn_mul_precache_init(F_mpn_precache_t precache, mp_limb_t * data1, unsigned long limbs1, unsigned long limbs2)
{
if (limbs1 == 0)
{
precache->poly = NULL;
return;
}
int swapped = 0;
if (limbs2 > limbs1)
{
unsigned long temp = limbs1;
limbs1 = limbs2;
limbs2 = temp;
swapped = 1;
}
unsigned long coeff_limbs = limbs1 + limbs2;
unsigned long log_length;
if (coeff_limbs/2 > FFT_TUNE_CUTOFF)
{
log_length = 0;
while ((1L<<(2*log_length)) < FLINT_BITS*coeff_limbs)
{
log_length++;
}
} else
{
unsigned long i = 0;
while ((i < FFT_SQR_COUNT-1) && (coeff_limbs/2 > FFT_SQR_TWK[i+1][0])) i++;
log_length = FFT_SQR_TWK[i][1];
}
unsigned long length = 1;
unsigned long total_limbs = coeff_limbs;
unsigned long output_bits = coeff_limbs*FLINT_BITS;
unsigned long n = coeff_limbs;
unsigned long length1 = 1;
unsigned long length2 = 1;
unsigned log_length2 = 1;
unsigned long bits;
do
{
bits = (((limbs1 << FLINT_LG_BITS_PER_LIMB)-1) >> (log_length-1)) + 1;
output_bits = 2*bits + log_length2;
output_bits = (((output_bits - 1) >> (log_length-1)) + 1) << (log_length-1);
bits = (output_bits - log_length2)/2;
length1 = ((limbs1 << FLINT_LG_BITS_PER_LIMB)-1)/bits + 1;
length2 = ((limbs2 << FLINT_LG_BITS_PER_LIMB)-1)/bits + 1;
log_length2++;
} while ((length2 > (1L<<(log_length2-1))) || (length1 > (1L<<(log_length-1))));
n = (output_bits-1)/FLINT_BITS+1;
if (swapped)
{
unsigned long temp = limbs1;
limbs1 = limbs2;
limbs2 = temp;
temp = length1;
length1 = length2;
length2 = temp;
}
#if DEBUG
printf("%ld, %ld, %ld, %ld, %ld\n", length1, length2, output_bits, coeff_limbs, log_length);
#endif
ZmodF_poly_p poly1;
poly1 = (ZmodF_poly_p) malloc(sizeof(ZmodF_poly_struct));
ZmodF_poly_init(poly1, log_length, n, 1);
F_mpn_FFT_split_bits(poly1, data1, limbs1, bits, n);
unsigned long size = (1L<<poly1->depth);
ZmodF_poly_FFT(poly1, size);
precache->type = FFT_PRE;
precache->bits = bits;
precache->length = length1;
precache->length2 = length2;
precache->coeff_limbs = coeff_limbs;
precache->limbs1 = limbs1;
precache->limbs2 = limbs2;
precache->poly = poly1;
precache->msl_bits = FLINT_BIT_COUNT(data1[limbs1-1]);
}
void F_mpn_mul_precache_clear(F_mpn_precache_t precache)
{
if (precache->type == FFT_PRE)
{
if (precache->poly)
{
ZmodF_poly_clear(precache->poly);
free(precache->poly);
}
}
}
/*
Compute an integer multiplication given a precomputed FFT for
one of the integers.
Assumes neither of limbs1, limbs2 is zero.
*/
mp_limb_t F_mpn_mul_precache(mp_limb_t * res, mp_limb_t * data2, unsigned long limbs2, F_mpn_precache_t precache)
{
ZmodF_poly_t poly2;
ZmodF_poly_stack_init(poly2, precache->poly->depth, precache->poly->n, 1);
int s1 = (FLINT_BIT_COUNT(data2[limbs2-1]) + precache->msl_bits <= FLINT_BITS);
F_mpn_FFT_split_bits(poly2, data2, limbs2, precache->bits, precache->poly->n);
ZmodF_poly_FFT(poly2, precache->length+poly2->length-1);
ZmodF_poly_pointwise_mul(poly2, poly2, precache->poly);
ZmodF_poly_IFFT(poly2);
ZmodF_poly_rescale(poly2);
ZmodF_poly_normalise(poly2);
F_mpn_clear(res, precache->limbs1 + limbs2 - s1);
F_mpn_FFT_combine_bits(res, poly2, precache->bits, precache->poly->n, precache->limbs1 + limbs2 - s1);
ZmodF_poly_stack_clear(poly2);
if (s1) return 0;
else return res[precache->limbs1+limbs2-1];
}
mp_limb_t F_mpn_mul_precache_trunc(mp_limb_t * res, mp_limb_t * data2, unsigned long limbs2, F_mpn_precache_t precache, unsigned long trunc)
{
if (trunc == 0) return 0;
ZmodF_poly_t poly2;
ZmodF_poly_stack_init(poly2, precache->poly->depth, precache->poly->n, 1);
int s1 = (FLINT_BIT_COUNT(data2[limbs2-1]) + precache->msl_bits <= FLINT_BITS);
if (trunc > precache->limbs1+limbs2 - s1) trunc = precache->limbs1+limbs2 - s1;
F_mpn_FFT_split_bits(poly2, data2, limbs2, precache->bits, precache->poly->n);
ZmodF_poly_FFT(poly2, precache->length+poly2->length-1);
ZmodF_poly_pointwise_mul(poly2, poly2, precache->poly);
ZmodF_poly_IFFT(poly2);
ZmodF_poly_rescale_range(poly2, 0, (trunc*FLINT_BITS-1)/precache->bits+1);
poly2->length = FLINT_MIN(poly2->length,(trunc*FLINT_BITS-1)/precache->bits+1);
ZmodF_poly_normalise(poly2);
F_mpn_clear(res, precache->limbs1 + limbs2);
F_mpn_FFT_combine_bits(res, poly2, precache->bits, precache->poly->n, trunc);
ZmodF_poly_stack_clear(poly2);
return res[trunc-1];
}
/*
Multiply integers data1 of length limbs1 by data2 of length limbs2 and return limbs
[start... trunc) of the output assuming that limbs2 <= limbs1/2
*/
mp_limb_t __F_mpn_mul_middle(mp_limb_t * res, mp_limb_t * data1, unsigned long limbs1,
mp_limb_t * data2, unsigned long limbs2,
unsigned long start, unsigned long trunc)
{
unsigned long coeff_limbs = trunc;
unsigned long twk;
if (coeff_limbs/2 > FFT_TUNE_CUTOFF)
{
twk = 0;
while ((1L<<(2*twk)) < FLINT_BITS*coeff_limbs)
{
twk++;
}
} else if ((data1 != data2) || (limbs1 != limbs2))
{
if (coeff_limbs/2 < FFT_MUL_TWK[0][0])
{
mpn_mul(res, data1, limbs1, data2, limbs2);
return res[trunc-1];
} else
{
unsigned long i = 0;
while ((i < FFT_MUL_COUNT-1) && (coeff_limbs/2 > FFT_MUL_TWK[i+1][0])) i++;
twk = FFT_MUL_TWK[i][1];
}
} else
{
if (coeff_limbs/2 < FFT_SQR_TWK[0][0])
{
mpn_mul(res, data1, limbs1, data1, limbs1);
return res[trunc-1];
} else
{
unsigned long i = 0;
while ((i < FFT_SQR_COUNT-1) && (coeff_limbs/2 > FFT_SQR_TWK[i+1][0])) i++;
twk = FFT_SQR_TWK[i][1];
}
}
unsigned long log_length = twk;
unsigned long length = 1;
unsigned long total_limbs = coeff_limbs;
unsigned long output_bits = coeff_limbs*FLINT_BITS;