mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-24 22:10:13 +00:00
688903eb3e
* All files with FSF copyright notices: Update copyright dates using scripts/update-copyrights. * locale/programs/charmap-kw.h: Regenerated. * locale/programs/locfile-kw.h: Likewise.
361 lines
10 KiB
C
361 lines
10 KiB
C
/* mpn_mul_n -- Multiply two natural numbers of length n.
|
|
|
|
Copyright (C) 1991-2018 Free Software Foundation, Inc.
|
|
|
|
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, see
|
|
<http://www.gnu.org/licenses/>. */
|
|
|
|
#include <gmp.h>
|
|
#include "gmp-impl.h"
|
|
|
|
/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
|
|
both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
|
|
always stored. Return the most significant limb.
|
|
|
|
Argument constraints:
|
|
1. PRODP != UP and PRODP != VP, i.e. the destination
|
|
must be distinct from the multiplier and the multiplicand. */
|
|
|
|
/* If KARATSUBA_THRESHOLD is not already defined, define it to a
|
|
value which is good on most machines. */
|
|
#ifndef KARATSUBA_THRESHOLD
|
|
#define KARATSUBA_THRESHOLD 32
|
|
#endif
|
|
|
|
/* The code can't handle KARATSUBA_THRESHOLD smaller than 2. */
|
|
#if KARATSUBA_THRESHOLD < 2
|
|
#undef KARATSUBA_THRESHOLD
|
|
#define KARATSUBA_THRESHOLD 2
|
|
#endif
|
|
|
|
/* Handle simple cases with traditional multiplication.
|
|
|
|
This is the most critical code of multiplication. All multiplies rely
|
|
on this, both small and huge. Small ones arrive here immediately. Huge
|
|
ones arrive here as this is the base case for Karatsuba's recursive
|
|
algorithm below. */
|
|
|
|
void
|
|
impn_mul_n_basecase (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
|
|
{
|
|
mp_size_t i;
|
|
mp_limb_t cy_limb;
|
|
mp_limb_t v_limb;
|
|
|
|
/* Multiply by the first limb in V separately, as the result can be
|
|
stored (not added) to PROD. We also avoid a loop for zeroing. */
|
|
v_limb = vp[0];
|
|
if (v_limb <= 1)
|
|
{
|
|
if (v_limb == 1)
|
|
MPN_COPY (prodp, up, size);
|
|
else
|
|
MPN_ZERO (prodp, size);
|
|
cy_limb = 0;
|
|
}
|
|
else
|
|
cy_limb = mpn_mul_1 (prodp, up, size, v_limb);
|
|
|
|
prodp[size] = cy_limb;
|
|
prodp++;
|
|
|
|
/* For each iteration in the outer loop, multiply one limb from
|
|
U with one limb from V, and add it to PROD. */
|
|
for (i = 1; i < size; i++)
|
|
{
|
|
v_limb = vp[i];
|
|
if (v_limb <= 1)
|
|
{
|
|
cy_limb = 0;
|
|
if (v_limb == 1)
|
|
cy_limb = mpn_add_n (prodp, prodp, up, size);
|
|
}
|
|
else
|
|
cy_limb = mpn_addmul_1 (prodp, up, size, v_limb);
|
|
|
|
prodp[size] = cy_limb;
|
|
prodp++;
|
|
}
|
|
}
|
|
|
|
void
|
|
impn_mul_n (mp_ptr prodp,
|
|
mp_srcptr up, mp_srcptr vp, mp_size_t size, mp_ptr tspace)
|
|
{
|
|
if ((size & 1) != 0)
|
|
{
|
|
/* The size is odd, the code code below doesn't handle that.
|
|
Multiply the least significant (size - 1) limbs with a recursive
|
|
call, and handle the most significant limb of S1 and S2
|
|
separately. */
|
|
/* A slightly faster way to do this would be to make the Karatsuba
|
|
code below behave as if the size were even, and let it check for
|
|
odd size in the end. I.e., in essence move this code to the end.
|
|
Doing so would save us a recursive call, and potentially make the
|
|
stack grow a lot less. */
|
|
|
|
mp_size_t esize = size - 1; /* even size */
|
|
mp_limb_t cy_limb;
|
|
|
|
MPN_MUL_N_RECURSE (prodp, up, vp, esize, tspace);
|
|
cy_limb = mpn_addmul_1 (prodp + esize, up, esize, vp[esize]);
|
|
prodp[esize + esize] = cy_limb;
|
|
cy_limb = mpn_addmul_1 (prodp + esize, vp, size, up[esize]);
|
|
|
|
prodp[esize + size] = cy_limb;
|
|
}
|
|
else
|
|
{
|
|
/* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
|
|
|
|
Split U in two pieces, U1 and U0, such that
|
|
U = U0 + U1*(B**n),
|
|
and V in V1 and V0, such that
|
|
V = V0 + V1*(B**n).
|
|
|
|
UV is then computed recursively using the identity
|
|
|
|
2n n n n
|
|
UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
|
|
1 1 1 0 0 1 0 0
|
|
|
|
Where B = 2**BITS_PER_MP_LIMB. */
|
|
|
|
mp_size_t hsize = size >> 1;
|
|
mp_limb_t cy;
|
|
int negflg;
|
|
|
|
/*** Product H. ________________ ________________
|
|
|_____U1 x V1____||____U0 x V0_____| */
|
|
/* Put result in upper part of PROD and pass low part of TSPACE
|
|
as new TSPACE. */
|
|
MPN_MUL_N_RECURSE (prodp + size, up + hsize, vp + hsize, hsize, tspace);
|
|
|
|
/*** Product M. ________________
|
|
|_(U1-U0)(V0-V1)_| */
|
|
if (mpn_cmp (up + hsize, up, hsize) >= 0)
|
|
{
|
|
mpn_sub_n (prodp, up + hsize, up, hsize);
|
|
negflg = 0;
|
|
}
|
|
else
|
|
{
|
|
mpn_sub_n (prodp, up, up + hsize, hsize);
|
|
negflg = 1;
|
|
}
|
|
if (mpn_cmp (vp + hsize, vp, hsize) >= 0)
|
|
{
|
|
mpn_sub_n (prodp + hsize, vp + hsize, vp, hsize);
|
|
negflg ^= 1;
|
|
}
|
|
else
|
|
{
|
|
mpn_sub_n (prodp + hsize, vp, vp + hsize, hsize);
|
|
/* No change of NEGFLG. */
|
|
}
|
|
/* Read temporary operands from low part of PROD.
|
|
Put result in low part of TSPACE using upper part of TSPACE
|
|
as new TSPACE. */
|
|
MPN_MUL_N_RECURSE (tspace, prodp, prodp + hsize, hsize, tspace + size);
|
|
|
|
/*** Add/copy product H. */
|
|
MPN_COPY (prodp + hsize, prodp + size, hsize);
|
|
cy = mpn_add_n (prodp + size, prodp + size, prodp + size + hsize, hsize);
|
|
|
|
/*** Add product M (if NEGFLG M is a negative number). */
|
|
if (negflg)
|
|
cy -= mpn_sub_n (prodp + hsize, prodp + hsize, tspace, size);
|
|
else
|
|
cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
|
|
|
|
/*** Product L. ________________ ________________
|
|
|________________||____U0 x V0_____| */
|
|
/* Read temporary operands from low part of PROD.
|
|
Put result in low part of TSPACE using upper part of TSPACE
|
|
as new TSPACE. */
|
|
MPN_MUL_N_RECURSE (tspace, up, vp, hsize, tspace + size);
|
|
|
|
/*** Add/copy Product L (twice). */
|
|
|
|
cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
|
|
if (cy)
|
|
mpn_add_1 (prodp + hsize + size, prodp + hsize + size, hsize, cy);
|
|
|
|
MPN_COPY (prodp, tspace, hsize);
|
|
cy = mpn_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
|
|
if (cy)
|
|
mpn_add_1 (prodp + size, prodp + size, size, 1);
|
|
}
|
|
}
|
|
|
|
void
|
|
impn_sqr_n_basecase (mp_ptr prodp, mp_srcptr up, mp_size_t size)
|
|
{
|
|
mp_size_t i;
|
|
mp_limb_t cy_limb;
|
|
mp_limb_t v_limb;
|
|
|
|
/* Multiply by the first limb in V separately, as the result can be
|
|
stored (not added) to PROD. We also avoid a loop for zeroing. */
|
|
v_limb = up[0];
|
|
if (v_limb <= 1)
|
|
{
|
|
if (v_limb == 1)
|
|
MPN_COPY (prodp, up, size);
|
|
else
|
|
MPN_ZERO (prodp, size);
|
|
cy_limb = 0;
|
|
}
|
|
else
|
|
cy_limb = mpn_mul_1 (prodp, up, size, v_limb);
|
|
|
|
prodp[size] = cy_limb;
|
|
prodp++;
|
|
|
|
/* For each iteration in the outer loop, multiply one limb from
|
|
U with one limb from V, and add it to PROD. */
|
|
for (i = 1; i < size; i++)
|
|
{
|
|
v_limb = up[i];
|
|
if (v_limb <= 1)
|
|
{
|
|
cy_limb = 0;
|
|
if (v_limb == 1)
|
|
cy_limb = mpn_add_n (prodp, prodp, up, size);
|
|
}
|
|
else
|
|
cy_limb = mpn_addmul_1 (prodp, up, size, v_limb);
|
|
|
|
prodp[size] = cy_limb;
|
|
prodp++;
|
|
}
|
|
}
|
|
|
|
void
|
|
impn_sqr_n (mp_ptr prodp,
|
|
mp_srcptr up, mp_size_t size, mp_ptr tspace)
|
|
{
|
|
if ((size & 1) != 0)
|
|
{
|
|
/* The size is odd, the code code below doesn't handle that.
|
|
Multiply the least significant (size - 1) limbs with a recursive
|
|
call, and handle the most significant limb of S1 and S2
|
|
separately. */
|
|
/* A slightly faster way to do this would be to make the Karatsuba
|
|
code below behave as if the size were even, and let it check for
|
|
odd size in the end. I.e., in essence move this code to the end.
|
|
Doing so would save us a recursive call, and potentially make the
|
|
stack grow a lot less. */
|
|
|
|
mp_size_t esize = size - 1; /* even size */
|
|
mp_limb_t cy_limb;
|
|
|
|
MPN_SQR_N_RECURSE (prodp, up, esize, tspace);
|
|
cy_limb = mpn_addmul_1 (prodp + esize, up, esize, up[esize]);
|
|
prodp[esize + esize] = cy_limb;
|
|
cy_limb = mpn_addmul_1 (prodp + esize, up, size, up[esize]);
|
|
|
|
prodp[esize + size] = cy_limb;
|
|
}
|
|
else
|
|
{
|
|
mp_size_t hsize = size >> 1;
|
|
mp_limb_t cy;
|
|
|
|
/*** Product H. ________________ ________________
|
|
|_____U1 x U1____||____U0 x U0_____| */
|
|
/* Put result in upper part of PROD and pass low part of TSPACE
|
|
as new TSPACE. */
|
|
MPN_SQR_N_RECURSE (prodp + size, up + hsize, hsize, tspace);
|
|
|
|
/*** Product M. ________________
|
|
|_(U1-U0)(U0-U1)_| */
|
|
if (mpn_cmp (up + hsize, up, hsize) >= 0)
|
|
{
|
|
mpn_sub_n (prodp, up + hsize, up, hsize);
|
|
}
|
|
else
|
|
{
|
|
mpn_sub_n (prodp, up, up + hsize, hsize);
|
|
}
|
|
|
|
/* Read temporary operands from low part of PROD.
|
|
Put result in low part of TSPACE using upper part of TSPACE
|
|
as new TSPACE. */
|
|
MPN_SQR_N_RECURSE (tspace, prodp, hsize, tspace + size);
|
|
|
|
/*** Add/copy product H. */
|
|
MPN_COPY (prodp + hsize, prodp + size, hsize);
|
|
cy = mpn_add_n (prodp + size, prodp + size, prodp + size + hsize, hsize);
|
|
|
|
/*** Add product M (if NEGFLG M is a negative number). */
|
|
cy -= mpn_sub_n (prodp + hsize, prodp + hsize, tspace, size);
|
|
|
|
/*** Product L. ________________ ________________
|
|
|________________||____U0 x U0_____| */
|
|
/* Read temporary operands from low part of PROD.
|
|
Put result in low part of TSPACE using upper part of TSPACE
|
|
as new TSPACE. */
|
|
MPN_SQR_N_RECURSE (tspace, up, hsize, tspace + size);
|
|
|
|
/*** Add/copy Product L (twice). */
|
|
|
|
cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
|
|
if (cy)
|
|
mpn_add_1 (prodp + hsize + size, prodp + hsize + size, hsize, cy);
|
|
|
|
MPN_COPY (prodp, tspace, hsize);
|
|
cy = mpn_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
|
|
if (cy)
|
|
mpn_add_1 (prodp + size, prodp + size, size, 1);
|
|
}
|
|
}
|
|
|
|
/* This should be made into an inline function in gmp.h. */
|
|
void
|
|
mpn_mul_n (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
|
|
{
|
|
TMP_DECL (marker);
|
|
TMP_MARK (marker);
|
|
if (up == vp)
|
|
{
|
|
if (size < KARATSUBA_THRESHOLD)
|
|
{
|
|
impn_sqr_n_basecase (prodp, up, size);
|
|
}
|
|
else
|
|
{
|
|
mp_ptr tspace;
|
|
tspace = (mp_ptr) TMP_ALLOC (2 * size * BYTES_PER_MP_LIMB);
|
|
impn_sqr_n (prodp, up, size, tspace);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if (size < KARATSUBA_THRESHOLD)
|
|
{
|
|
impn_mul_n_basecase (prodp, up, vp, size);
|
|
}
|
|
else
|
|
{
|
|
mp_ptr tspace;
|
|
tspace = (mp_ptr) TMP_ALLOC (2 * size * BYTES_PER_MP_LIMB);
|
|
impn_mul_n (prodp, up, vp, size, tspace);
|
|
}
|
|
}
|
|
TMP_FREE (marker);
|
|
}
|