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glibc/stdlib/mul_n.c
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/* mpn_mul_n -- Multiply two natural numbers of length n. | |
Copyright (C) 1991-2016 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); | |
} |