1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
|
/* mpn_mul_n -- Multiply two natural numbers of length n.
Copyright (C) 1991-2014 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
#if __STDC__
impn_mul_n_basecase (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
#else
impn_mul_n_basecase (prodp, up, vp, size)
mp_ptr prodp;
mp_srcptr up;
mp_srcptr vp;
mp_size_t size;
#endif
{
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
#if __STDC__
impn_mul_n (mp_ptr prodp,
mp_srcptr up, mp_srcptr vp, mp_size_t size, mp_ptr tspace)
#else
impn_mul_n (prodp, up, vp, size, tspace)
mp_ptr prodp;
mp_srcptr up;
mp_srcptr vp;
mp_size_t size;
mp_ptr tspace;
#endif
{
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
#if __STDC__
impn_sqr_n_basecase (mp_ptr prodp, mp_srcptr up, mp_size_t size)
#else
impn_sqr_n_basecase (prodp, up, size)
mp_ptr prodp;
mp_srcptr up;
mp_size_t size;
#endif
{
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
#if __STDC__
impn_sqr_n (mp_ptr prodp,
mp_srcptr up, mp_size_t size, mp_ptr tspace)
#else
impn_sqr_n (prodp, up, size, tspace)
mp_ptr prodp;
mp_srcptr up;
mp_size_t size;
mp_ptr tspace;
#endif
{
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
#if __STDC__
mpn_mul_n (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
#else
mpn_mul_n (prodp, up, vp, size)
mp_ptr prodp;
mp_srcptr up;
mp_srcptr vp;
mp_size_t size;
#endif
{
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);
}
|