x86_64-gcc.c revision 4969cc9b0ab2905ec478277f50ed3849b37a6c6b
1/* x86_64 BIGNUM accelerator version 0.1, December 2002. 2 * 3 * Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL 4 * project. 5 * 6 * Rights for redistribution and usage in source and binary forms are 7 * granted according to the OpenSSL license. Warranty of any kind is 8 * disclaimed. 9 * 10 * Q. Version 0.1? It doesn't sound like Andy, he used to assign real 11 * versions, like 1.0... 12 * A. Well, that's because this code is basically a quick-n-dirty 13 * proof-of-concept hack. As you can see it's implemented with 14 * inline assembler, which means that you're bound to GCC and that 15 * there might be enough room for further improvement. 16 * 17 * Q. Why inline assembler? 18 * A. x86_64 features own ABI which I'm not familiar with. This is 19 * why I decided to let the compiler take care of subroutine 20 * prologue/epilogue as well as register allocation. For reference. 21 * Win64 implements different ABI for AMD64, different from Linux. 22 * 23 * Q. How much faster does it get? 24 * A. 'apps/openssl speed rsa dsa' output with no-asm: 25 * 26 * sign verify sign/s verify/s 27 * rsa 512 bits 0.0006s 0.0001s 1683.8 18456.2 28 * rsa 1024 bits 0.0028s 0.0002s 356.0 6407.0 29 * rsa 2048 bits 0.0172s 0.0005s 58.0 1957.8 30 * rsa 4096 bits 0.1155s 0.0018s 8.7 555.6 31 * sign verify sign/s verify/s 32 * dsa 512 bits 0.0005s 0.0006s 2100.8 1768.3 33 * dsa 1024 bits 0.0014s 0.0018s 692.3 559.2 34 * dsa 2048 bits 0.0049s 0.0061s 204.7 165.0 35 * 36 * 'apps/openssl speed rsa dsa' output with this module: 37 * 38 * sign verify sign/s verify/s 39 * rsa 512 bits 0.0004s 0.0000s 2767.1 33297.9 40 * rsa 1024 bits 0.0012s 0.0001s 867.4 14674.7 41 * rsa 2048 bits 0.0061s 0.0002s 164.0 5270.0 42 * rsa 4096 bits 0.0384s 0.0006s 26.1 1650.8 43 * sign verify sign/s verify/s 44 * dsa 512 bits 0.0002s 0.0003s 4442.2 3786.3 45 * dsa 1024 bits 0.0005s 0.0007s 1835.1 1497.4 46 * dsa 2048 bits 0.0016s 0.0020s 620.4 504.6 47 * 48 * For the reference. IA-32 assembler implementation performs 49 * very much like 64-bit code compiled with no-asm on the same 50 * machine. 51 */ 52 53#include <openssl/bn.h> 54 55/* TODO(davidben): Get this file working on Windows x64. */ 56#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && defined(__GNUC__) 57 58#include "../internal.h" 59 60 61#undef mul 62#undef mul_add 63 64#define asm __asm__ 65 66/* 67 * "m"(a), "+m"(r) is the way to favor DirectPath µ-code; 68 * "g"(0) let the compiler to decide where does it 69 * want to keep the value of zero; 70 */ 71#define mul_add(r, a, word, carry) \ 72 do { \ 73 register BN_ULONG high, low; \ 74 asm("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "m"(a) : "cc"); \ 75 asm("addq %2,%0; adcq %3,%1" \ 76 : "+r"(carry), "+d"(high) \ 77 : "a"(low), "g"(0) \ 78 : "cc"); \ 79 asm("addq %2,%0; adcq %3,%1" \ 80 : "+m"(r), "+d"(high) \ 81 : "r"(carry), "g"(0) \ 82 : "cc"); \ 83 carry = high; \ 84 } while (0) 85 86#define mul(r, a, word, carry) \ 87 do { \ 88 register BN_ULONG high, low; \ 89 asm("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "g"(a) : "cc"); \ 90 asm("addq %2,%0; adcq %3,%1" \ 91 : "+r"(carry), "+d"(high) \ 92 : "a"(low), "g"(0) \ 93 : "cc"); \ 94 (r) = carry, carry = high; \ 95 } while (0) 96#undef sqr 97#define sqr(r0, r1, a) asm("mulq %2" : "=a"(r0), "=d"(r1) : "a"(a) : "cc"); 98 99BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, 100 BN_ULONG w) { 101 BN_ULONG c1 = 0; 102 103 if (num <= 0) { 104 return (c1); 105 } 106 107 while (num & ~3) { 108 mul_add(rp[0], ap[0], w, c1); 109 mul_add(rp[1], ap[1], w, c1); 110 mul_add(rp[2], ap[2], w, c1); 111 mul_add(rp[3], ap[3], w, c1); 112 ap += 4; 113 rp += 4; 114 num -= 4; 115 } 116 if (num) { 117 mul_add(rp[0], ap[0], w, c1); 118 if (--num == 0) { 119 return c1; 120 } 121 mul_add(rp[1], ap[1], w, c1); 122 if (--num == 0) { 123 return c1; 124 } 125 mul_add(rp[2], ap[2], w, c1); 126 return c1; 127 } 128 129 return c1; 130} 131 132BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) { 133 BN_ULONG c1 = 0; 134 135 if (num <= 0) { 136 return c1; 137 } 138 139 while (num & ~3) { 140 mul(rp[0], ap[0], w, c1); 141 mul(rp[1], ap[1], w, c1); 142 mul(rp[2], ap[2], w, c1); 143 mul(rp[3], ap[3], w, c1); 144 ap += 4; 145 rp += 4; 146 num -= 4; 147 } 148 if (num) { 149 mul(rp[0], ap[0], w, c1); 150 if (--num == 0) { 151 return c1; 152 } 153 mul(rp[1], ap[1], w, c1); 154 if (--num == 0) { 155 return c1; 156 } 157 mul(rp[2], ap[2], w, c1); 158 } 159 return c1; 160} 161 162void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) { 163 if (n <= 0) { 164 return; 165 } 166 167 while (n & ~3) { 168 sqr(r[0], r[1], a[0]); 169 sqr(r[2], r[3], a[1]); 170 sqr(r[4], r[5], a[2]); 171 sqr(r[6], r[7], a[3]); 172 a += 4; 173 r += 8; 174 n -= 4; 175 } 176 if (n) { 177 sqr(r[0], r[1], a[0]); 178 if (--n == 0) { 179 return; 180 } 181 sqr(r[2], r[3], a[1]); 182 if (--n == 0) { 183 return; 184 } 185 sqr(r[4], r[5], a[2]); 186 } 187} 188 189BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 190 int n) { 191 BN_ULONG ret; 192 size_t i = 0; 193 194 if (n <= 0) { 195 return 0; 196 } 197 198 asm volatile ( 199 " subq %0,%0 \n" /* clear carry */ 200 " jmp 1f \n" 201 ".p2align 4 \n" 202 "1: movq (%4,%2,8),%0 \n" 203 " adcq (%5,%2,8),%0 \n" 204 " movq %0,(%3,%2,8) \n" 205 " lea 1(%2),%2 \n" 206 " loop 1b \n" 207 " sbbq %0,%0 \n" 208 : "=&r"(ret), "+c"(n), "+r"(i) 209 : "r"(rp), "r"(ap), "r"(bp) 210 : "cc", "memory"); 211 212 return ret & 1; 213} 214 215BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 216 int n) { 217 BN_ULONG ret; 218 size_t i = 0; 219 220 if (n <= 0) { 221 return 0; 222 } 223 224 asm volatile ( 225 " subq %0,%0 \n" /* clear borrow */ 226 " jmp 1f \n" 227 ".p2align 4 \n" 228 "1: movq (%4,%2,8),%0 \n" 229 " sbbq (%5,%2,8),%0 \n" 230 " movq %0,(%3,%2,8) \n" 231 " lea 1(%2),%2 \n" 232 " loop 1b \n" 233 " sbbq %0,%0 \n" 234 : "=&r"(ret), "+c"(n), "+r"(i) 235 : "r"(rp), "r"(ap), "r"(bp) 236 : "cc", "memory"); 237 238 return ret & 1; 239} 240 241/* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */ 242/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */ 243/* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */ 244/* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) 245 */ 246 247/* Keep in mind that carrying into high part of multiplication result can not 248 * overflow, because it cannot be all-ones. */ 249#define mul_add_c(a, b, c0, c1, c2) \ 250 do { \ 251 BN_ULONG t1, t2; \ 252 asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \ 253 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 254 : "+r"(c0), "+r"(c1), "+r"(c2) \ 255 : "r"(t1), "r"(t2), "g"(0) \ 256 : "cc"); \ 257 } while (0) 258 259#define sqr_add_c(a, i, c0, c1, c2) \ 260 do { \ 261 BN_ULONG t1, t2; \ 262 asm("mulq %2" : "=a"(t1), "=d"(t2) : "a"(a[i]) : "cc"); \ 263 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 264 : "+r"(c0), "+r"(c1), "+r"(c2) \ 265 : "r"(t1), "r"(t2), "g"(0) \ 266 : "cc"); \ 267 } while (0) 268 269#define mul_add_c2(a, b, c0, c1, c2) \ 270 do { \ 271 BN_ULONG t1, t2; \ 272 asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \ 273 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 274 : "+r"(c0), "+r"(c1), "+r"(c2) \ 275 : "r"(t1), "r"(t2), "g"(0) \ 276 : "cc"); \ 277 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 278 : "+r"(c0), "+r"(c1), "+r"(c2) \ 279 : "r"(t1), "r"(t2), "g"(0) \ 280 : "cc"); \ 281 } while (0) 282 283#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2) 284 285void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { 286 BN_ULONG c1, c2, c3; 287 288 c1 = 0; 289 c2 = 0; 290 c3 = 0; 291 mul_add_c(a[0], b[0], c1, c2, c3); 292 r[0] = c1; 293 c1 = 0; 294 mul_add_c(a[0], b[1], c2, c3, c1); 295 mul_add_c(a[1], b[0], c2, c3, c1); 296 r[1] = c2; 297 c2 = 0; 298 mul_add_c(a[2], b[0], c3, c1, c2); 299 mul_add_c(a[1], b[1], c3, c1, c2); 300 mul_add_c(a[0], b[2], c3, c1, c2); 301 r[2] = c3; 302 c3 = 0; 303 mul_add_c(a[0], b[3], c1, c2, c3); 304 mul_add_c(a[1], b[2], c1, c2, c3); 305 mul_add_c(a[2], b[1], c1, c2, c3); 306 mul_add_c(a[3], b[0], c1, c2, c3); 307 r[3] = c1; 308 c1 = 0; 309 mul_add_c(a[4], b[0], c2, c3, c1); 310 mul_add_c(a[3], b[1], c2, c3, c1); 311 mul_add_c(a[2], b[2], c2, c3, c1); 312 mul_add_c(a[1], b[3], c2, c3, c1); 313 mul_add_c(a[0], b[4], c2, c3, c1); 314 r[4] = c2; 315 c2 = 0; 316 mul_add_c(a[0], b[5], c3, c1, c2); 317 mul_add_c(a[1], b[4], c3, c1, c2); 318 mul_add_c(a[2], b[3], c3, c1, c2); 319 mul_add_c(a[3], b[2], c3, c1, c2); 320 mul_add_c(a[4], b[1], c3, c1, c2); 321 mul_add_c(a[5], b[0], c3, c1, c2); 322 r[5] = c3; 323 c3 = 0; 324 mul_add_c(a[6], b[0], c1, c2, c3); 325 mul_add_c(a[5], b[1], c1, c2, c3); 326 mul_add_c(a[4], b[2], c1, c2, c3); 327 mul_add_c(a[3], b[3], c1, c2, c3); 328 mul_add_c(a[2], b[4], c1, c2, c3); 329 mul_add_c(a[1], b[5], c1, c2, c3); 330 mul_add_c(a[0], b[6], c1, c2, c3); 331 r[6] = c1; 332 c1 = 0; 333 mul_add_c(a[0], b[7], c2, c3, c1); 334 mul_add_c(a[1], b[6], c2, c3, c1); 335 mul_add_c(a[2], b[5], c2, c3, c1); 336 mul_add_c(a[3], b[4], c2, c3, c1); 337 mul_add_c(a[4], b[3], c2, c3, c1); 338 mul_add_c(a[5], b[2], c2, c3, c1); 339 mul_add_c(a[6], b[1], c2, c3, c1); 340 mul_add_c(a[7], b[0], c2, c3, c1); 341 r[7] = c2; 342 c2 = 0; 343 mul_add_c(a[7], b[1], c3, c1, c2); 344 mul_add_c(a[6], b[2], c3, c1, c2); 345 mul_add_c(a[5], b[3], c3, c1, c2); 346 mul_add_c(a[4], b[4], c3, c1, c2); 347 mul_add_c(a[3], b[5], c3, c1, c2); 348 mul_add_c(a[2], b[6], c3, c1, c2); 349 mul_add_c(a[1], b[7], c3, c1, c2); 350 r[8] = c3; 351 c3 = 0; 352 mul_add_c(a[2], b[7], c1, c2, c3); 353 mul_add_c(a[3], b[6], c1, c2, c3); 354 mul_add_c(a[4], b[5], c1, c2, c3); 355 mul_add_c(a[5], b[4], c1, c2, c3); 356 mul_add_c(a[6], b[3], c1, c2, c3); 357 mul_add_c(a[7], b[2], c1, c2, c3); 358 r[9] = c1; 359 c1 = 0; 360 mul_add_c(a[7], b[3], c2, c3, c1); 361 mul_add_c(a[6], b[4], c2, c3, c1); 362 mul_add_c(a[5], b[5], c2, c3, c1); 363 mul_add_c(a[4], b[6], c2, c3, c1); 364 mul_add_c(a[3], b[7], c2, c3, c1); 365 r[10] = c2; 366 c2 = 0; 367 mul_add_c(a[4], b[7], c3, c1, c2); 368 mul_add_c(a[5], b[6], c3, c1, c2); 369 mul_add_c(a[6], b[5], c3, c1, c2); 370 mul_add_c(a[7], b[4], c3, c1, c2); 371 r[11] = c3; 372 c3 = 0; 373 mul_add_c(a[7], b[5], c1, c2, c3); 374 mul_add_c(a[6], b[6], c1, c2, c3); 375 mul_add_c(a[5], b[7], c1, c2, c3); 376 r[12] = c1; 377 c1 = 0; 378 mul_add_c(a[6], b[7], c2, c3, c1); 379 mul_add_c(a[7], b[6], c2, c3, c1); 380 r[13] = c2; 381 c2 = 0; 382 mul_add_c(a[7], b[7], c3, c1, c2); 383 r[14] = c3; 384 r[15] = c1; 385} 386 387void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { 388 BN_ULONG c1, c2, c3; 389 390 c1 = 0; 391 c2 = 0; 392 c3 = 0; 393 mul_add_c(a[0], b[0], c1, c2, c3); 394 r[0] = c1; 395 c1 = 0; 396 mul_add_c(a[0], b[1], c2, c3, c1); 397 mul_add_c(a[1], b[0], c2, c3, c1); 398 r[1] = c2; 399 c2 = 0; 400 mul_add_c(a[2], b[0], c3, c1, c2); 401 mul_add_c(a[1], b[1], c3, c1, c2); 402 mul_add_c(a[0], b[2], c3, c1, c2); 403 r[2] = c3; 404 c3 = 0; 405 mul_add_c(a[0], b[3], c1, c2, c3); 406 mul_add_c(a[1], b[2], c1, c2, c3); 407 mul_add_c(a[2], b[1], c1, c2, c3); 408 mul_add_c(a[3], b[0], c1, c2, c3); 409 r[3] = c1; 410 c1 = 0; 411 mul_add_c(a[3], b[1], c2, c3, c1); 412 mul_add_c(a[2], b[2], c2, c3, c1); 413 mul_add_c(a[1], b[3], c2, c3, c1); 414 r[4] = c2; 415 c2 = 0; 416 mul_add_c(a[2], b[3], c3, c1, c2); 417 mul_add_c(a[3], b[2], c3, c1, c2); 418 r[5] = c3; 419 c3 = 0; 420 mul_add_c(a[3], b[3], c1, c2, c3); 421 r[6] = c1; 422 r[7] = c2; 423} 424 425void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) { 426 BN_ULONG c1, c2, c3; 427 428 c1 = 0; 429 c2 = 0; 430 c3 = 0; 431 sqr_add_c(a, 0, c1, c2, c3); 432 r[0] = c1; 433 c1 = 0; 434 sqr_add_c2(a, 1, 0, c2, c3, c1); 435 r[1] = c2; 436 c2 = 0; 437 sqr_add_c(a, 1, c3, c1, c2); 438 sqr_add_c2(a, 2, 0, c3, c1, c2); 439 r[2] = c3; 440 c3 = 0; 441 sqr_add_c2(a, 3, 0, c1, c2, c3); 442 sqr_add_c2(a, 2, 1, c1, c2, c3); 443 r[3] = c1; 444 c1 = 0; 445 sqr_add_c(a, 2, c2, c3, c1); 446 sqr_add_c2(a, 3, 1, c2, c3, c1); 447 sqr_add_c2(a, 4, 0, c2, c3, c1); 448 r[4] = c2; 449 c2 = 0; 450 sqr_add_c2(a, 5, 0, c3, c1, c2); 451 sqr_add_c2(a, 4, 1, c3, c1, c2); 452 sqr_add_c2(a, 3, 2, c3, c1, c2); 453 r[5] = c3; 454 c3 = 0; 455 sqr_add_c(a, 3, c1, c2, c3); 456 sqr_add_c2(a, 4, 2, c1, c2, c3); 457 sqr_add_c2(a, 5, 1, c1, c2, c3); 458 sqr_add_c2(a, 6, 0, c1, c2, c3); 459 r[6] = c1; 460 c1 = 0; 461 sqr_add_c2(a, 7, 0, c2, c3, c1); 462 sqr_add_c2(a, 6, 1, c2, c3, c1); 463 sqr_add_c2(a, 5, 2, c2, c3, c1); 464 sqr_add_c2(a, 4, 3, c2, c3, c1); 465 r[7] = c2; 466 c2 = 0; 467 sqr_add_c(a, 4, c3, c1, c2); 468 sqr_add_c2(a, 5, 3, c3, c1, c2); 469 sqr_add_c2(a, 6, 2, c3, c1, c2); 470 sqr_add_c2(a, 7, 1, c3, c1, c2); 471 r[8] = c3; 472 c3 = 0; 473 sqr_add_c2(a, 7, 2, c1, c2, c3); 474 sqr_add_c2(a, 6, 3, c1, c2, c3); 475 sqr_add_c2(a, 5, 4, c1, c2, c3); 476 r[9] = c1; 477 c1 = 0; 478 sqr_add_c(a, 5, c2, c3, c1); 479 sqr_add_c2(a, 6, 4, c2, c3, c1); 480 sqr_add_c2(a, 7, 3, c2, c3, c1); 481 r[10] = c2; 482 c2 = 0; 483 sqr_add_c2(a, 7, 4, c3, c1, c2); 484 sqr_add_c2(a, 6, 5, c3, c1, c2); 485 r[11] = c3; 486 c3 = 0; 487 sqr_add_c(a, 6, c1, c2, c3); 488 sqr_add_c2(a, 7, 5, c1, c2, c3); 489 r[12] = c1; 490 c1 = 0; 491 sqr_add_c2(a, 7, 6, c2, c3, c1); 492 r[13] = c2; 493 c2 = 0; 494 sqr_add_c(a, 7, c3, c1, c2); 495 r[14] = c3; 496 r[15] = c1; 497} 498 499void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) { 500 BN_ULONG c1, c2, c3; 501 502 c1 = 0; 503 c2 = 0; 504 c3 = 0; 505 sqr_add_c(a, 0, c1, c2, c3); 506 r[0] = c1; 507 c1 = 0; 508 sqr_add_c2(a, 1, 0, c2, c3, c1); 509 r[1] = c2; 510 c2 = 0; 511 sqr_add_c(a, 1, c3, c1, c2); 512 sqr_add_c2(a, 2, 0, c3, c1, c2); 513 r[2] = c3; 514 c3 = 0; 515 sqr_add_c2(a, 3, 0, c1, c2, c3); 516 sqr_add_c2(a, 2, 1, c1, c2, c3); 517 r[3] = c1; 518 c1 = 0; 519 sqr_add_c(a, 2, c2, c3, c1); 520 sqr_add_c2(a, 3, 1, c2, c3, c1); 521 r[4] = c2; 522 c2 = 0; 523 sqr_add_c2(a, 3, 2, c3, c1, c2); 524 r[5] = c3; 525 c3 = 0; 526 sqr_add_c(a, 3, c1, c2, c3); 527 r[6] = c1; 528 r[7] = c2; 529} 530 531#endif /* !NO_ASM && X86_64 && __GNUC__ */ 532