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mpir/mpn/generic/toom4_mul_n.c

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/* mpn_toom4_mul_n -- Internal routine to multiply two natural numbers
of length n.
THIS IS AN INTERNAL FUNCTION WITH A MUTABLE INTERFACE. IT IS ONLY
SAFE TO REACH THIS FUNCTION THROUGH DOCUMENTED INTERFACES.
*/
/* Implementation of the Bodrato-Zanoni algorithm for Toom-Cook 4-way.
Copyright 2001, 2002, 2004, 2005, 2006 Free Software Foundation, Inc.
Copyright 2009 William Hart
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The GNU MP Library 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */
/*
This implementation is based on that of Paul Zimmmermann, which is available
for mpz_t's at http://www.loria.fr/~zimmerma/software/toom4.c
*/
#include "mpir.h"
#include "gmp-impl.h"
#include "longlong.h"
#define TC4_LIB 1 // library build only
#if !TC4_LIB
#include <stdio.h>
#include <stdlib.h>
#define TC4_TEST 0 // test code
#define TC4_TIME 1 // timing code
#else
#define TC4_TEST 0
#define TC4_TIME 0
#endif
void
mpn_toom4_mul_n (mp_ptr rp, mp_srcptr up,
mp_srcptr vp, mp_size_t n);
void _tc4_add(mp_ptr rp, mp_size_t * rn, mp_srcptr r1, mp_size_t r1n, mp_srcptr r2, mp_size_t r2n)
{
mp_limb_t cy;
mp_size_t s1 = ABS(r1n);
mp_size_t s2 = ABS(r2n);
if (!s1)
{
*rn = 0;
} else if (!s2)
{
if (rp != r1) MPN_COPY(rp, r1, s1);
*rn = r1n;
} else if ((r1n ^ r2n) >= 0)
{
*rn = r1n;
cy = mpn_add(rp, r1, s1, r2, s2);
if (cy)
{
rp[s1] = cy;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
} else
{
mp_size_t ct;
if (s1 != s2) ct = 1;
else MPN_CMP(ct, r1, r2, s1);
if (!ct) *rn = 0;
else if (ct > 0)
{
mpn_sub(rp, r1, s1, r2, s2);
*rn = s1;
MPN_NORMALIZE(rp, (*rn));
if (r1n < 0) *rn = -(*rn);
}
else
{
mpn_sub_n(rp, r2, r1, s1);
*rn = s1;
MPN_NORMALIZE(rp, (*rn));
if (r1n > 0) *rn = -(*rn);
}
}
}
void tc4_add(mp_ptr rp, mp_size_t * rn, mp_srcptr r1, mp_size_t r1n, mp_srcptr r2, mp_size_t r2n)
{
mp_size_t s1 = ABS(r1n);
mp_size_t s2 = ABS(r2n);
if (s1 < s2) _tc4_add(rp, rn, r2, r2n, r1, r1n);
else _tc4_add(rp, rn, r1, r1n, r2, r2n);
}
#if HAVE_NATIVE_mpn_sumdiff_n
void tc4_sumdiff(mp_ptr rp, mp_size_t * rn, mp_ptr sp, mp_size_t * sn, mp_ptr r1, mp_size_t r1n, mp_ptr r2, mp_size_t r2n)
{
mp_limb_t cy, cy2;
mp_size_t s1 = ABS(r1n);
mp_size_t s2 = ABS(r2n);
int swapped = 0;
if (s1 < s2)
{
MPN_PTR_SWAP(r1, r1n, r2, r2n);
MP_SIZE_T_SWAP(s1, s2);
swapped = 1;
}
if (!s1)
{
*rn = 0;
*sn = 0;
} else if (!s2)
{
if (rp != r1) MPN_COPY(rp, r1, s1);
if (sp != r1) MPN_COPY(sp, r1, s1);
*rn = r1n;
*sn = (swapped ? -r1n : r1n);
} else
{
mp_size_t ct;
if (s1 != s2) ct = 1;
else MPN_CMP(ct, r1, r2, s1);
if (!ct)
{
if ((r1n ^ r2n) >= 0)
{
*sn = 0;
*rn = r1n;
cy = mpn_lshift(rp, r1, s1, 1);
if (cy)
{
rp[s1] = cy;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
} else
{
*rn = 0;
*sn = (swapped ? -r1n : r1n);
cy = mpn_lshift(sp, r1, s1, 1);
if (cy)
{
sp[s1] = cy;
if ((*sn) < 0) (*sn)--;
else (*sn)++;
}
}
} else if (ct > 0) // r1 is bigger than r2
{
if ((r1n ^ r2n) >= 0) // both inputs are same sign
{
cy = mpn_sumdiff_n(rp, sp, r1, r2, s2);
if (s1 > s2) // r1 has more limbs than r2
{
*rn = r1n;
cy2 = mpn_add_1(rp + s2, r1 + s2, s1 - s2, cy>>1);
if (cy2)
{
rp[s1] = cy2;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
mpn_sub_1(sp + s2, r1 + s2, s1 - s2, cy&1);
} else // both inputs have same number of limbs
{
*rn = r1n;
if (cy>>1)
{
rp[s1] = 1;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
}
*sn = s1;
MPN_NORMALIZE(sp, (*sn));
if (r1n ^ (~swapped) < 0) *sn = -(*sn);
} else // inputs are different sign
{
cy = mpn_sumdiff_n(sp, rp, r1, r2, s2);
if (s1 > s2) // r1 has more limbs than r2
{
*sn = r1n;
cy2 = mpn_add_1(sp + s2, r1 + s2, s1 - s2, cy>>1);
if (cy2)
{
sp[s1] = cy2;
if ((*sn) < 0) (*sn)--;
else (*sn)++;
}
mpn_sub_1(rp + s2, r1 + s2, s1 - s2, cy&1);
} else // both inputs have same number of limbs
{
*sn = r1n;
if (cy>>1)
{
sp[s1] = 1;
if ((*sn) < 0) (*sn)--;
else (*sn)++;
}
}
*rn = s1;
MPN_NORMALIZE(rp, (*rn));
if (r1n ^ (~swapped) < 0) *rn = -(*rn);
}
} else // r2 is bigger than r1 (but same number of limbs)
{
if ((r1n ^ r2n) >= 0) // both inputs are same sign
{
cy = mpn_sumdiff_n(rp, sp, r2, r1, s1);
*rn = r1n;
if (cy>>1)
{
rp[s1] = 1;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
*sn = s1;
MPN_NORMALIZE(sp, (*sn));
if (r1n ^ (~swapped) > 0) *sn = -(*sn);
} else // inputs are different sign
{
cy = mpn_sumdiff_n(sp, rp, r2, r1, s1);
*sn = r1n;
if (cy>>1)
{
sp[s1] = 1;
if ((*sn) < 0) (*sn)--;
else (*sn)++;
}
*rn = s1;
MPN_NORMALIZE(rp, (*rn));
if (r1n ^ (~swapped) > 0) *rn = -(*rn);
}
}
}
}
void tc4_sumdiff_unsigned(mp_ptr rp, mp_size_t * rn, mp_ptr sp, mp_size_t * sn, mp_ptr r1, mp_size_t r1n, mp_ptr r2, mp_size_t r2n)
{
mp_limb_t cy, cy2;
mp_size_t s1 = ABS(r1n);
mp_size_t s2 = ABS(r2n);
int swapped = 0;
if (s1 < s2)
{
MPN_PTR_SWAP(r1, r1n, r2, r2n);
MP_SIZE_T_SWAP(s1, s2);
swapped = 1;
}
if (!s1)
{
*rn = 0;
*sn = 0;
} else if (!s2)
{
if (rp != r1) MPN_COPY(rp, r1, s1);
if (sp != r1) MPN_COPY(sp, r1, s1);
*rn = r1n;
*sn = (swapped ? -r1n : r1n);
} else
{
mp_size_t ct;
if (s1 != s2) ct = 1;
else MPN_CMP(ct, r1, r2, s1);
if (!ct)
{
*sn = 0;
*rn = r1n;
cy = mpn_lshift(rp, r1, s1, 1);
if (cy)
{
rp[s1] = cy;
(*rn)++;
}
} else if (ct > 0) // r1 is bigger than r2
{
cy = mpn_sumdiff_n(rp, sp, r1, r2, s2);
if (s1 > s2) // r1 has more limbs than r2
{
*rn = r1n;
cy2 = mpn_add_1(rp + s2, r1 + s2, s1 - s2, cy>>1);
if (cy2)
{
rp[s1] = cy2;
(*rn)++;
}
mpn_sub_1(sp + s2, r1 + s2, s1 - s2, cy&1);
} else // both inputs have same number of limbs
{
*rn = r1n;
if (cy>>1)
{
rp[s1] = 1;
(*rn)++;
}
}
*sn = s1;
MPN_NORMALIZE(sp, (*sn));
if (swapped) *sn = -(*sn);
} else // r2 is bigger than r1 (but same number of limbs)
{
cy = mpn_sumdiff_n(rp, sp, r2, r1, s1);
*rn = r1n;
if (cy>>1)
{
rp[s1] = 1;
(*rn)++;
}
*sn = s1;
MPN_NORMALIZE(sp, (*sn));
if (!swapped) *sn = -(*sn);
}
}
}
#endif
/* ~~~~~~~~~~~~~~~~~~~~UNTESTED CODE~~~~~~~~~~~~~~~~~~~~~~~~~~
#define MPN_ADDSUB_CMP(cyxx, r1xx, r2xx, r3xx, snxx) \
do { \
mp_limb_t t[2]; \
add_ssaaaa(t[1], t[0], CNST_LIMB(0), r1xx[snxx - 1], CNST_LIMB(0), r2xx[snxx - 1]); \
if (t[1]) cyxx = 1; \
else if (t[0] > r3xx[snxx - 1]) cyxx = 1; \
else if (t[0] < r3xx[snxx - 1] - CNST_LIMB(1)) cyxx = -1; \
else cyxx = 0; \
} while (0)
void tc4_addadd(mp_ptr rp, mp_size_t * rn, mp_ptr r1, mp_size_t r1n, mp_ptr r2, mp_size_t r2n, mp_ptr r3, mp_size_t r3n)
{
mp_size_t s1 = ABS(r1n);
mp_size_t s2 = ABS(r2n);
mp_size_t s3 = ABS(r3n);
if ((s1 != s2) || (s1 != s3))
{
tc4_add(rp, rn, r1, r1n, r2, r2n);
tc4_add(rp, rn, rp, *rn, r3, r3n);
} else
{
mp_limb_t cy;
mp_size_t cy2;
if (((r1n ^ r2n) >= 0) && ((r1n ^ r3n) >= 0)) // all same sign addadd
{
cy = mpn_addadd_n(rp, r1, r2, r3, s1);
*rn = r1n;
if (cy)
{
rp[s1] = cy;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
} else if (((r1n ^ r2n) >= 0) && ((r1n ^ r3n) < 0)) // addsub
{
MPN_ADDSUB_CMP(cy2, r1, r2, r3, s1);
if (cy2 > 0)
{
cy = mpn_addsub_n(rp, r1, r2, r3, s1);
*rn = r1n;
if (cy)
{
rp[s1] = cy;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
} else if (cy2 < 0)
{
cy = mpn_subadd_n(rp, r3, r1, r2, s1);
if (cy) abort();
*rn = s1;
MPN_NORMALIZE(rp, (*rn));
if (r1n < 0) *rn = -(*rn);
} else
{
tc4_add(rp, rn, r1, r1n, r2, r2n);
tc4_add(rp, rn, rp, *rn, r3, r3n);
}
} else if (((r1n ^ r2n) < 0) && ((r1n ^ r3n) >= 0)) // subadd
{
MPN_ADDSUB_CMP(cy2, r1, r3, r2, s1);
if (cy2 > 0)
{
cy = mpn_addsub_n(rp, r1, r3, r2, s1);
*rn = r1n;
if (cy)
{
rp[s1] = cy;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
} else if (cy2 < 0)
{
mpn_subadd_n(rp, r2, r1, r3, s1);
*rn = s1;
MPN_NORMALIZE(rp, (*rn));
if (r1n > 0) *rn = -(*rn);
} else
{
tc4_add(rp, rn, r1, r1n, r2, r2n);
tc4_add(rp, rn, rp, *rn, r3, r3n);
}
} else // add final two and subtract first
{
MPN_ADDSUB_CMP(cy2, r2, r3, r1, s1);
if (cy2 > 0)
{
cy = mpn_addsub_n(rp, r2, r3, r1, s1);
*rn = r1n;
if (cy)
{
rp[s1] = cy;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
} else if (cy2 < 0)
{
mpn_subadd_n(rp, r1, r2, r3, s1);
*rn = s1;
MPN_NORMALIZE(rp, (*rn));
if (r1n < 0) *rn = -(*rn);
} else
{
tc4_add(rp, rn, r1, r1n, r2, r2n);
tc4_add(rp, rn, rp, *rn, r3, r3n);
}
}
}
}
void tc4_addsub(mp_ptr rp, mp_size_t * rn, mp_ptr r1, mp_size_t r1n, mp_ptr r2, mp_size_t r2n, mp_ptr r3, mp_size_t r3n)
{
tc4_addadd(rp, rn, r1, r1n, r2, r2n, r3, -r3n);
}
void tc4_subsub(mp_ptr rp, mp_size_t * rn, mp_ptr r1, mp_size_t r1n, mp_ptr r2, mp_size_t r2n, mp_ptr r3, mp_size_t r3n)
{
tc4_addadd(rp, rn, r1, r1n, r2, -r2n, r3, -r3n);
}
*/
void _tc4_add_unsigned(mp_ptr rp, mp_size_t * rn, mp_srcptr r1, mp_size_t r1n, mp_srcptr r2, mp_size_t r2n)
{
mp_limb_t cy;
mp_size_t s1 = r1n;
mp_size_t s2 = r2n;
if (!s2)
{
if (!s1) *rn = 0;
else
{
if (rp != r1) MPN_COPY(rp, r1, s1);
*rn = r1n;
}
} else
{
*rn = r1n;
cy = mpn_add(rp, r1, s1, r2, s2);
if (cy)
{
rp[s1] = cy;
if ((*rn) < 0) (*rn)--;
else (*rn)++;
}
}
}
void tc4_add_unsigned(mp_ptr rp, mp_size_t * rn, mp_srcptr r1, mp_size_t r1n, mp_srcptr r2, mp_size_t r2n)
{
if (r1n < r2n) _tc4_add_unsigned(rp, rn, r2, r2n, r1, r1n);
else _tc4_add_unsigned(rp, rn, r1, r1n, r2, r2n);
}
void tc4_sub(mp_ptr rp, mp_size_t * rn, mp_ptr r1, mp_size_t r1n, mp_ptr r2, mp_size_t r2n)
{
tc4_add(rp, rn, r1, r1n, r2, -r2n);
}
void tc4_lshift(mp_ptr rp, mp_size_t * rn, mp_srcptr xp, mp_size_t xn, mp_size_t bits)
{
if (xn == 0) *rn = 0;
else
{
mp_size_t xu = ABS(xn);
mp_limb_t msl = mpn_lshift(rp, xp, xu, bits);
if (msl)
{
rp[xu] = msl;
*rn = (xn >= 0 ? xn + 1 : xn - 1);
} else
*rn = xn;
}
}
void tc4_rshift_inplace(mp_ptr rp, mp_size_t * rn, mp_size_t bits)
{
if (*rn)
{
if ((*rn) > 0)
{
mpn_rshift(rp, rp, *rn, bits);
if (rp[(*rn) - 1] == CNST_LIMB(0)) (*rn)--;
} else
{
mpn_rshift(rp, rp, -(*rn), bits);
if (rp[-(*rn) - 1] == CNST_LIMB(0)) (*rn)++;
}
}
}
#if HAVE_NATIVE_mpn_addlsh1_n
void tc4_addlsh1_unsigned(mp_ptr rp, mp_size_t * rn, mp_srcptr xp, mp_size_t xn)
{
if (xn)
{
if (xn >= *rn)
{
mp_limb_t cy;
if (xn > *rn) MPN_ZERO(rp + *rn, xn - *rn);
cy = mpn_addlsh1_n(rp, rp, xp, xn);
if (cy)
{
rp[xn] = cy;
*rn = xn + 1;
} else *rn = xn;
} else
{
mp_limb_t cy = mpn_addlsh1_n(rp, rp, xp, xn);
if (cy) cy = mpn_add_1(rp + xn, rp + xn, *rn - xn, cy);
if (cy)
{
rp[*rn] = cy;
(*rn)++;
}
}
}
}
#endif
/*
void tc4_divexact_ui(mp_ptr rp, mp_size_t * rn, mp_srcptr x, mp_size_t xn, mp_limb_t c)
{
if (xn)
{
mp_size_t xu = ABS(xn);
mp_limb_t cy = mpn_divmod_1(rp, x, xu, c);
if (xn > 0)
{
if (rp[xu - 1] == 0) *rn = xn - 1;
else *rn = xn;
} else
{
if (rp[xu - 1] == 0) *rn = xn + 1;
else *rn = xn;
}
} else *rn = 0;
}
*/
void tc4_divexact_ui(mp_ptr rp, mp_size_t * rn, mp_ptr x, mp_size_t xn, mp_limb_t c)
{
mpz_t xm, rm;
xm->_mp_d = x;
xm->_mp_size = xn;
rm->_mp_d = rp;
rm->_mp_size = *rn;
rm->_mp_alloc = ABS(xn);
mpz_divexact_ui(rm, xm, c);
(*rn) = rm->_mp_size;
}
void tc4_divexact_by3(mp_ptr rp, mp_size_t * rn, mp_ptr x, mp_size_t xn)
{
if (xn)
{
mp_size_t xu = ABS(xn);
mpn_divexact_by3(rp, x, xu);
if (xn > 0)
{
if (rp[xu - 1] == CNST_LIMB(0)) *rn = xn - 1;
else *rn = xn;
} else
{
if (rp[xu - 1] == CNST_LIMB(0)) *rn = xn + 1;
else *rn = xn;
}
} else *rn = 0;
}
#if HAVE_NATIVE_mpn_divexact_byBm1of
void tc4_divexact_by15(mp_ptr rp, mp_size_t * rn, mp_ptr x, mp_size_t xn)
{
if (xn)
{
mp_size_t xu = ABS(xn);
mpn_divexact_byBm1of(rp, x, xu, CNST_LIMB(15), CNST_LIMB((~0)/15)); // works for 32 and 64 bits
if (xn > 0)
{
if (rp[xu - 1] == CNST_LIMB(0)) *rn = xn - 1;
else *rn = xn;
} else
{
if (rp[xu - 1] == CNST_LIMB(0)) *rn = xn + 1;
else *rn = xn;
}
} else *rn = 0;
}
#endif
#if HAVE_NATIVE_mpn_mul_1c
#define MPN_MUL_1C(cout, dst, src, size, n, cin) \
do { \
(cout) = mpn_mul_1c (dst, src, size, n, cin); \
} while (0)
#else
#define MPN_MUL_1C(cout, dst, src, size, n, cin) \
do { \
mp_limb_t __cy; \
__cy = mpn_mul_1 (dst, src, size, n); \
(cout) = __cy + mpn_add_1 (dst, dst, size, cin); \
} while (0)
#endif
void tc4_addmul_1(mp_ptr wp, mp_size_t * wn, mp_srcptr xp, mp_size_t xn, mp_limb_t y)
{
mp_size_t sign, wu, xu, ws, new_wn, min_size, dsize;
mp_limb_t cy;
/* w unaffected if x==0 or y==0 */
if (xn == 0 || y == 0)
return;
sign = xn;
xu = ABS (xn);
ws = *wn;
if (*wn == 0)
{
/* nothing to add to, just set x*y, "sign" gives the sign */
cy = mpn_mul_1 (wp, xp, xu, y);
wp[xu] = cy;
xu = xu + (cy != 0);
*wn = (sign >= 0 ? xu : -xu);
return;
}
sign ^= *wn;
wu = ABS (*wn);
new_wn = MAX (wu, xu);
min_size = MIN (wu, xu);
if (sign >= 0)
{
/* addmul of absolute values */
cy = mpn_addmul_1 (wp, xp, min_size, y);
dsize = xu - wu;
#if HAVE_NATIVE_mpn_mul_1c
if (dsize > 0)
cy = mpn_mul_1c (wp + min_size, xp + min_size, dsize, y, cy);
else if (dsize < 0)
{
dsize = -dsize;
cy = mpn_add_1 (wp + min_size, wp + min_size, dsize, cy);
}
#else
if (dsize != 0)
{
mp_limb_t cy2;
if (dsize > 0)
cy2 = mpn_mul_1 (wp + min_size, xp + min_size, dsize, y);
else
{
dsize = -dsize;
cy2 = 0;
}
cy = cy2 + mpn_add_1 (wp + min_size, wp + min_size, dsize, cy);
}
#endif
wp[dsize + min_size] = cy;
new_wn += (cy != 0);
} else
{
/* submul of absolute values */
cy = mpn_submul_1 (wp, xp, min_size, y);
if (wu >= xu)
{
/* if w bigger than x, then propagate borrow through it */
if (wu != xu)
cy = mpn_sub_1 (wp + xu, wp + xu, wu - xu, cy);
if (cy != 0)
{
/* Borrow out of w, take twos complement negative to get
absolute value, flip sign of w. */
wp[new_wn] = ~-cy; /* extra limb is 0-cy */
mpn_com_n (wp, wp, new_wn);
new_wn++;
MPN_INCR_U (wp, new_wn, CNST_LIMB(1));
ws = -*wn;
}
} else /* wu < xu */
{
/* x bigger than w, so want x*y-w. Submul has given w-x*y, so
take twos complement and use an mpn_mul_1 for the rest. */
mp_limb_t cy2;
/* -(-cy*b^n + w-x*y) = (cy-1)*b^n + ~(w-x*y) + 1 */
mpn_com_n (wp, wp, wu);
cy += mpn_add_1 (wp, wp, wu, CNST_LIMB(1));
cy -= 1;
/* If cy-1 == -1 then hold that -1 for latter. mpn_submul_1 never
returns cy==MP_LIMB_T_MAX so that value always indicates a -1. */
cy2 = (cy == MP_LIMB_T_MAX);
cy += cy2;
MPN_MUL_1C (cy, wp + wu, xp + wu, xu - wu, y, cy);
wp[new_wn] = cy;
new_wn += (cy != 0);
/* Apply any -1 from above. The value at wp+wsize is non-zero
because y!=0 and the high limb of x will be non-zero. */
if (cy2)
MPN_DECR_U (wp+wu, new_wn - wu, CNST_LIMB(1));
ws = -*wn;
}
/* submul can produce high zero limbs due to cancellation, both when w
has more limbs or x has more */
MPN_NORMALIZE (wp, new_wn);
}
*wn = (ws >= 0 ? new_wn : -new_wn);
ASSERT (new_wn == 0 || wp[new_wn - 1] != 0);
}
void tc4_submul_1(mp_ptr wp, mp_size_t * wn, mp_srcptr x, mp_size_t xn, mp_limb_t y)
{
tc4_addmul_1(wp, wn, x, -xn, y);
}
void tc4_copy (mp_ptr yp, mp_size_t * yn, mp_size_t offset, mp_srcptr xp, mp_size_t xn)
{
mp_size_t yu = ABS(*yn);
mp_size_t xu = ABS(xn);
mp_limb_t cy = 0;
if (xn == 0)
return;
if (offset < yu) /* low part of x overlaps with y */
{
if (offset + xu <= yu) /* x entirely inside y */
{
cy = mpn_add_n (yp + offset, yp + offset, xp, xu);
if (offset + xu < yu)
cy = mpn_add_1 (yp + offset + xu, yp + offset + xu,
yu - (offset + xu), cy);
} else
cy = mpn_add_n (yp + offset, yp + offset, xp, yu - offset);
/* now cy is the carry at yp + yu */
if (xu + offset > yu) /* high part of x exceeds y */
{
MPN_COPY (yp + yu, xp + yu - offset, xu + offset - yu);
cy = mpn_add_1 (yp + yu, yp + yu, xu + offset - yu, cy);
yu = xu + offset;
}
/* now cy is the carry at yp + yn */
if (cy)
yp[yu++] = cy;
MPN_NORMALIZE(yp, yu);
*yn = yu;
} else /* x does not overlap */
{
if (offset > yu)
MPN_ZERO (yp + yu, offset - yu);
MPN_COPY (yp + offset, xp, xu);
*yn = offset + xu;
}
}
#define tc4_mpn_mul_n(r3xx, r1xx, r2xx, n1xx, tempxx) \
do \
{ \
if ((r3xx == r1xx) || (r3xx == r2xx)) \
{ \
mpn_mul_n(tempxx, r1xx, r2xx, n1xx); \
MPN_COPY(r3xx, tempxx, 2*n1xx); \
} else \
{ \
mpn_mul_n(r3xx, r1xx, r2xx, n1xx); \
} \
} while (0)
#define tc4_mpn_mul(r3xx, r1xx, n1xx, r2xx, n2xx, tempxx) \
do \
{ \
if ((r3xx == r1xx) || (r3xx == r2xx)) \
{ \
mpn_mul(tempxx, r1xx, n1xx, r2xx, n2xx); \
MPN_COPY(r3xx, tempxx, n1xx + n2xx); \
} else \
{ \
mpn_mul(r3xx, r1xx, n1xx, r2xx, n2xx); \
} \
} while (0)
#define MUL_TC4_UNSIGNED(r3xx, n3xx, r1xx, n1xx, r2xx, n2xx, tempxx) \
do \
{ \
if ((n1xx != 0) && (n2xx != 0)) \
{ mp_size_t len; \
if (n1xx == n2xx) \
{ \
if (n1xx > MUL_TOOM4_INTERNAL_THRESHOLD) mpn_toom4_mul_n(r3xx, r1xx, r2xx, n1xx); \
else tc4_mpn_mul_n(r3xx, r1xx, r2xx, n1xx, tempxx); \
} else if (n1xx > n2xx) \
tc4_mpn_mul(r3xx, r1xx, n1xx, r2xx, n2xx, tempxx); \
else \
tc4_mpn_mul(r3xx, r2xx, n2xx, r1xx, n1xx, tempxx); \
len = n1xx + n2xx; \
MPN_NORMALIZE(r3xx, len); \
n3xx = len; \
} else \
n3xx = 0; \
} while (0)
#define MUL_TC4(r3xx, n3xx, r1xx, n1xx, r2xx, n2xx, tempxx) \
do \
{ \
mp_size_t sign = n1xx ^ n2xx; \
mp_size_t un1 = ABS(n1xx); \
mp_size_t un2 = ABS(n2xx); \
MUL_TC4_UNSIGNED(r3xx, n3xx, r1xx, un1, r2xx, un2, tempxx); \
if (sign < 0) n3xx = -n3xx; \
} while (0)
#define TC4_NORM(rxx, nxx, sxx) \
do \
{ \
nxx = sxx; \
MPN_NORMALIZE(rxx, nxx); \
} while(0)
#if TC4_TEST || TC4_TIME
#define p2(axx, anxx, bxx, bnxx) \
do \
{ \
printf("s1 = "); \
if (anxx < 0) printf("-"); \
if (anxx == 0) printf("0, "); \
else printf("%ld, ", axx[0]); \
printf("s2 = "); \
if (bnxx < 0) printf("-"); \
if (bnxx == 0) printf("0"); \
else printf("%ld\n", bxx[0]); \
} while (0)
#define p(axx, anxx) \
do \
{ \
printf("r = "); \
if (anxx < 0) printf("-"); \
if (anxx == 0) printf("0\n"); \
else printf("%ld\n", axx[0]); \
} while (0)
#endif
/* Multiply {up, n} by {vp, n} and write the result to
{prodp, 2n}.
Note that prodp gets 2n limbs stored, even if the actual result
only needs 2n - 1.
*/
void
mpn_toom4_mul_n (mp_ptr rp, mp_srcptr up,
mp_srcptr vp, mp_size_t n)
{
mp_size_t len1, len2;
mp_limb_t cy;
mp_ptr tp;
mp_size_t a0n, a1n, a2n, a3n, b0n, b1n, b2n, b3n, sn, n1, n2, n3, n4, n5, n6, n7, rpn;
len1 = n;
len2 = n;
ASSERT (n >= 1);
ASSERT (!MPN_OVERLAP_P(rp, 2*n, up, n));
ASSERT (!MPN_OVERLAP_P(rp, 2*n, vp, n));
MPN_NORMALIZE(up, len1);
MPN_NORMALIZE(vp, len2);
sn = (n - 1) / 4 + 1;
#define a0 (up)
#define a1 (up + sn)
#define a2 (up + 2*sn)
#define a3 (up + 3*sn)
#define b0 (vp)
#define b1 (vp + sn)
#define b2 (vp + 2*sn)
#define b3 (vp + 3*sn)
TC4_NORM(a0, a0n, sn);
TC4_NORM(a1, a1n, sn);
TC4_NORM(a2, a2n, sn);
TC4_NORM(a3, a3n, n - 3*sn);
TC4_NORM(b0, b0n, sn);
TC4_NORM(b1, b1n, sn);
TC4_NORM(b2, b2n, sn);
TC4_NORM(b3, b3n, n - 3*sn);
#define t4 (2*sn+2) // allows mult of 2 integers of sn + 1 limbs
tp = __GMP_ALLOCATE_FUNC_LIMBS(8*t4);
#define r1 (tp)
#define r2 (tp + t4)
#define r3 (tp + 2*t4)
#define r4 (tp + 3*t4)
#define r5 (tp + 4*t4)
#define r6 (tp + 5*t4)
#define r7 (tp + 6*t4)
#define temp (tp + 7*t4)
tc4_add_unsigned(r6, &n6, a3, a3n, a1, a1n);
tc4_add_unsigned(r5, &n5, a2, a2n, a0, a0n);
#if HAVE_NATIVE_mpn_sumdiff_n
tc4_sumdiff_unsigned(r3, &n3, r4, &n4, r5, n5, r6, n6);
#else
tc4_add_unsigned(r3, &n3, r5, n5, r6, n6);
tc4_sub(r4, &n4, r5, n5, r6, n6);
#endif
tc4_add_unsigned(r6, &n6, b3, b3n, b1, b1n);
tc4_add_unsigned(r5, &n5, b2, b2n, b0, b0n);
#if HAVE_NATIVE_mpn_sumdiff_n
tc4_sumdiff_unsigned(r7, &n7, r5, &n5, r5, n5, r6, n6);
#else
tc4_add_unsigned(r7, &n7, r5, n5, r6, n6);
tc4_sub(r5, &n5, r5, n5, r6, n6);
#endif
MUL_TC4_UNSIGNED(r3, n3, r3, n3, r7, n7, temp);
MUL_TC4(r4, n4, r4, n4, r5, n5, temp);
tc4_lshift(r1, &n1, a0, a0n, 3);
#if HAVE_NATIVE_mpn_addlsh1_n
tc4_addlsh1_unsigned(r1, &n1, a2, a2n);
#else
tc4_addmul_1(r1, &n1, a2, a2n, 2);
#endif
tc4_lshift(r7, &n7, a1, a1n, 2);
tc4_add(r7, &n7, r7, n7, a3, a3n);
tc4_add(r5, &n5, r1, n1, r7, n7);
tc4_sub(r6, &n6, r1, n1, r7, n7);
tc4_lshift(r1, &n1, b0, b0n, 3);
#if HAVE_NATIVE_mpn_addlsh1_n
tc4_addlsh1_unsigned(r1, &n1, b2, b2n);
#else
tc4_addmul_1(r1, &n1, b2, b2n, 2);
#endif
tc4_lshift(r7, &n7, b1, b1n, 2);
tc4_add(r7, &n7, r7, n7, b3, b3n);
tc4_add(r2, &n2, r1, n1, r7, n7);
tc4_sub(r7, &n7, r1, n1, r7, n7);
MUL_TC4_UNSIGNED(r5, n5, r5, n5, r2, n2, temp);
MUL_TC4(r6, n6, r6, n6, r7, n7, temp);
tc4_lshift(r2, &n2, a3, a3n, 3);
tc4_addmul_1(r2, &n2, a2, a2n, 4);
#if HAVE_NATIVE_mpn_addlsh1_n
tc4_addlsh1_unsigned(r2, &n2, a1, a1n);
#else
tc4_addmul_1(r2, &n2, a1, a1n, 2);
#endif
tc4_add(r2, &n2, r2, n2, a0, a0n);
tc4_lshift(r7, &n7, b3, b3n, 3);
tc4_addmul_1(r7, &n7, b2, b2n, 4);
#if HAVE_NATIVE_mpn_addlsh1_n
tc4_addlsh1_unsigned(r7, &n7, b1, b1n);
#else
tc4_addmul_1(r7, &n7, b1, b1n, 2);
#endif
tc4_add(r7, &n7, r7, n7, b0, b0n);
MUL_TC4_UNSIGNED(r2, n2, r2, n2, r7, n7, temp);
MUL_TC4_UNSIGNED(r1, n1, a3, a3n, b3, b3n, temp);
MUL_TC4_UNSIGNED(r7, n7, a0, a0n, b0, b0n, temp);
tc4_add(r2, &n2, r2, n2, r5, n5);
tc4_sub(r6, &n6, r5, n5, r6, n6);
tc4_sub(r4, &n4, r3, n3, r4, n4);
tc4_sub(r5, &n5, r5, n5, r1, n1);
tc4_submul_1(r5, &n5, r7, n7, 64);
tc4_rshift_inplace(r4, &n4, 1);
tc4_sub(r3, &n3, r3, n3, r4, n4);
tc4_lshift(r5, &n5, r5, n5, 1);
tc4_sub(r5, &n5, r5, n5, r6, n6);
tc4_submul_1(r2, &n2, r3, n3, 65);
tc4_sub(r3, &n3, r3, n3, r7, n7);
tc4_sub(r3, &n3, r3, n3, r1, n1);
tc4_addmul_1(r2, &n2, r3, n3, 45);
tc4_submul_1(r5, &n5, r3, n3, 8);
//tc4_divexact_ui(r5, &n5, r5, n5, 24);
tc4_rshift_inplace(r5, &n5, 3);
tc4_divexact_by3(r5, &n5, r5, n5);
tc4_sub(r6, &n6, r6, n6, r2, n2);
tc4_submul_1(r2, &n2, r4, n4, 16);
//tc4_divexact_ui(r2, &n2, r2, n2, 18);
tc4_rshift_inplace(r2, &n2, 1);
tc4_divexact_by3(r2, &n2, r2, n2);
tc4_divexact_by3(r2, &n2, r2, n2);
tc4_sub(r3, &n3, r3, n3, r5, n5);
tc4_sub(r4, &n4, r4, n4, r2, n2);
#if HAVE_NATIVE_mpn_divexact_byBm1of
tc4_divexact_by15(r6, &n6, r6, n6);
tc4_rshift_inplace(r6, &n6, 1);
#else
tc4_divexact_ui(r6, &n6, r6, n6, 30);
#endif
tc4_add(r6, &n6, r6, n6, r2, n2);
tc4_rshift_inplace(r6, &n6, 1);
tc4_sub(r2, &n2, r2, n2, r6, n6);
rpn = 0;
tc4_copy(rp, &rpn, 0, r7, n7);
tc4_copy(rp, &rpn, sn, r6, n6);
tc4_copy(rp, &rpn, 2*sn, r5, n5);
tc4_copy(rp, &rpn, 3*sn, r4, n4);
tc4_copy(rp, &rpn, 4*sn, r3, n3);
tc4_copy(rp, &rpn, 5*sn, r2, n2);
tc4_copy(rp, &rpn, 6*sn, r1, n1);
if (rpn != 2*n)
{
MPN_ZERO((rp + rpn), 2*n - rpn);
}
__GMP_FREE_FUNC_LIMBS (tp, 8*t4);
}
#if TC4_TEST
int tc4_test(mp_ptr up, mp_ptr vp, mp_size_t n)
{
mp_limb_t * rp1 = malloc(2*n*sizeof(mp_limb_t));
mp_limb_t * rp2 = malloc(2*n*sizeof(mp_limb_t));
mpn_mul_n(rp1, up, vp, n);
mpn_toom4_mul_n(rp2, up, vp, n);
mp_size_t i;
for (i = 0; i < 2*n; i++)
{
if (rp1[i] != rp2[i])
{
printf("First error in limb %d\n", i);
free(rp1);
free(rp2);
return 0;
}
}
free(rp1);
free(rp2);
return 1;
}
mp_size_t randsize(mp_size_t limit)
{
static uint64_t randval = 4035456057U;
randval = ((uint64_t)randval*(uint64_t)1025416097U+(uint64_t)286824430U)%(uint64_t)4294967311U;
if (limit == 0L) return (mp_size_t) randval;
return (mp_size_t) randval%limit;
}
int main(void)
{
mp_limb_t * up = malloc(2000*sizeof(mp_limb_t));
mp_limb_t * vp = malloc(2000*sizeof(mp_limb_t));
mp_size_t i, n;
for (i = 0; i < 20000; i++)
{
n = randsize(1500) + 500;
printf("n = %d\n", n);
mpn_random2(up, n);
mpn_random2(vp, n);
if (!tc4_test(up, vp, n)) break;
}
free(up);
free(vp);
return 0;
}
#endif
#if TC4_TIME
int main(void)
{
mp_limb_t * up = malloc(40096*sizeof(mp_limb_t));
mp_limb_t * vp = malloc(40096*sizeof(mp_limb_t));
mp_limb_t * rp = malloc(80192*sizeof(mp_limb_t));
mp_size_t i, n;
n = 2048;
mpn_random(up, n);
mpn_random(vp, n);
for (i = 0; i < 50000; i++)
{
if ((i & 31) == 0)
{
mpn_random(up, n);
mpn_random(vp, n);
}
//mpn_mul_n(rp, up, vp, n);
mpn_toom4_mul_n(rp, up, vp, n);
}
free(up);
free(vp);
free(rp);
return 0;
}
#endif
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