1#include <openssl/bn.h> 2 3#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && !defined(OPENSSL_WINDOWS) 4 5#include "../internal.h" 6 7/* x86_64 BIGNUM accelerator version 0.1, December 2002. 8 * 9 * Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL 10 * project. 11 * 12 * Rights for redistribution and usage in source and binary forms are 13 * granted according to the OpenSSL license. Warranty of any kind is 14 * disclaimed. 15 * 16 * Q. Version 0.1? It doesn't sound like Andy, he used to assign real 17 * versions, like 1.0... 18 * A. Well, that's because this code is basically a quick-n-dirty 19 * proof-of-concept hack. As you can see it's implemented with 20 * inline assembler, which means that you're bound to GCC and that 21 * there might be enough room for further improvement. 22 * 23 * Q. Why inline assembler? 24 * A. x86_64 features own ABI which I'm not familiar with. This is 25 * why I decided to let the compiler take care of subroutine 26 * prologue/epilogue as well as register allocation. For reference. 27 * Win64 implements different ABI for AMD64, different from Linux. 28 * 29 * Q. How much faster does it get? 30 * A. 'apps/openssl speed rsa dsa' output with no-asm: 31 * 32 * sign verify sign/s verify/s 33 * rsa 512 bits 0.0006s 0.0001s 1683.8 18456.2 34 * rsa 1024 bits 0.0028s 0.0002s 356.0 6407.0 35 * rsa 2048 bits 0.0172s 0.0005s 58.0 1957.8 36 * rsa 4096 bits 0.1155s 0.0018s 8.7 555.6 37 * sign verify sign/s verify/s 38 * dsa 512 bits 0.0005s 0.0006s 2100.8 1768.3 39 * dsa 1024 bits 0.0014s 0.0018s 692.3 559.2 40 * dsa 2048 bits 0.0049s 0.0061s 204.7 165.0 41 * 42 * 'apps/openssl speed rsa dsa' output with this module: 43 * 44 * sign verify sign/s verify/s 45 * rsa 512 bits 0.0004s 0.0000s 2767.1 33297.9 46 * rsa 1024 bits 0.0012s 0.0001s 867.4 14674.7 47 * rsa 2048 bits 0.0061s 0.0002s 164.0 5270.0 48 * rsa 4096 bits 0.0384s 0.0006s 26.1 1650.8 49 * sign verify sign/s verify/s 50 * dsa 512 bits 0.0002s 0.0003s 4442.2 3786.3 51 * dsa 1024 bits 0.0005s 0.0007s 1835.1 1497.4 52 * dsa 2048 bits 0.0016s 0.0020s 620.4 504.6 53 * 54 * For the reference. IA-32 assembler implementation performs 55 * very much like 64-bit code compiled with no-asm on the same 56 * machine. 57 */ 58 59 /* TODO(davidben): Get this file working on Windows x64. */ 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_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) { 190 BN_ULONG ret, waste; 191 192 asm("divq %4" : "=a"(ret), "=d"(waste) : "a"(l), "d"(h), "g"(d) : "cc"); 193 194 return ret; 195} 196 197BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 198 int n) { 199 BN_ULONG ret; 200 size_t i = 0; 201 202 if (n <= 0) { 203 return 0; 204 } 205 206 asm volatile ( 207 " subq %0,%0 \n" /* clear carry */ 208 " jmp 1f \n" 209 ".p2align 4 \n" 210 "1: movq (%4,%2,8),%0 \n" 211 " adcq (%5,%2,8),%0 \n" 212 " movq %0,(%3,%2,8) \n" 213 " lea 1(%2),%2 \n" 214 " loop 1b \n" 215 " sbbq %0,%0 \n" 216 : "=&r"(ret), "+c"(n), "+r"(i) 217 : "r"(rp), "r"(ap), "r"(bp) 218 : "cc", "memory"); 219 220 return ret & 1; 221} 222 223#ifndef SIMICS 224BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 225 int n) { 226 BN_ULONG ret; 227 size_t i = 0; 228 229 if (n <= 0) { 230 return 0; 231 } 232 233 asm volatile ( 234 " subq %0,%0 \n" /* clear borrow */ 235 " jmp 1f \n" 236 ".p2align 4 \n" 237 "1: movq (%4,%2,8),%0 \n" 238 " sbbq (%5,%2,8),%0 \n" 239 " movq %0,(%3,%2,8) \n" 240 " lea 1(%2),%2 \n" 241 " loop 1b \n" 242 " sbbq %0,%0 \n" 243 : "=&r"(ret), "+c"(n), "+r"(i) 244 : "r"(rp), "r"(ap), "r"(bp) 245 : "cc", "memory"); 246 247 return ret & 1; 248} 249#else 250/* Simics 1.4<7 has buggy sbbq:-( */ 251#define BN_MASK2 0xffffffffffffffffL 252BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) { 253 BN_ULONG t1, t2; 254 int c = 0; 255 256 if (n <= 0) { 257 return (BN_ULONG)0; 258 } 259 260 for (;;) { 261 t1 = a[0]; 262 t2 = b[0]; 263 r[0] = (t1 - t2 - c) & BN_MASK2; 264 if (t1 != t2) { 265 c = (t1 < t2); 266 } 267 if (--n <= 0) { 268 break; 269 } 270 271 t1 = a[1]; 272 t2 = b[1]; 273 r[1] = (t1 - t2 - c) & BN_MASK2; 274 if (t1 != t2) { 275 c = (t1 < t2); 276 } 277 if (--n <= 0) { 278 break; 279 } 280 281 t1 = a[2]; 282 t2 = b[2]; 283 r[2] = (t1 - t2 - c) & BN_MASK2; 284 if (t1 != t2) { 285 c = (t1 < t2); 286 } 287 if (--n <= 0) { 288 break; 289 } 290 291 t1 = a[3]; 292 t2 = b[3]; 293 r[3] = (t1 - t2 - c) & BN_MASK2; 294 if (t1 != t2) { 295 c = (t1 < t2); 296 } 297 if (--n <= 0) { 298 break; 299 } 300 301 a += 4; 302 b += 4; 303 r += 4; 304 } 305 return c; 306} 307#endif 308 309/* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */ 310/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */ 311/* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */ 312/* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) 313 */ 314 315/* Keep in mind that carrying into high part of multiplication result can not 316 * overflow, because it cannot be all-ones. */ 317#define mul_add_c(a, b, c0, c1, c2) \ 318 do { \ 319 BN_ULONG t1, t2; \ 320 asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \ 321 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 322 : "+r"(c0), "+r"(c1), "+r"(c2) \ 323 : "r"(t1), "r"(t2), "g"(0) \ 324 : "cc"); \ 325 } while (0) 326 327#define sqr_add_c(a, i, c0, c1, c2) \ 328 do { \ 329 BN_ULONG t1, t2; \ 330 asm("mulq %2" : "=a"(t1), "=d"(t2) : "a"(a[i]) : "cc"); \ 331 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 332 : "+r"(c0), "+r"(c1), "+r"(c2) \ 333 : "r"(t1), "r"(t2), "g"(0) \ 334 : "cc"); \ 335 } while (0) 336 337#define mul_add_c2(a, b, c0, c1, c2) \ 338 do { \ 339 BN_ULONG t1, t2; \ 340 asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \ 341 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 342 : "+r"(c0), "+r"(c1), "+r"(c2) \ 343 : "r"(t1), "r"(t2), "g"(0) \ 344 : "cc"); \ 345 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 346 : "+r"(c0), "+r"(c1), "+r"(c2) \ 347 : "r"(t1), "r"(t2), "g"(0) \ 348 : "cc"); \ 349 } while (0) 350 351#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2) 352 353void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { 354 BN_ULONG c1, c2, c3; 355 356 c1 = 0; 357 c2 = 0; 358 c3 = 0; 359 mul_add_c(a[0], b[0], c1, c2, c3); 360 r[0] = c1; 361 c1 = 0; 362 mul_add_c(a[0], b[1], c2, c3, c1); 363 mul_add_c(a[1], b[0], c2, c3, c1); 364 r[1] = c2; 365 c2 = 0; 366 mul_add_c(a[2], b[0], c3, c1, c2); 367 mul_add_c(a[1], b[1], c3, c1, c2); 368 mul_add_c(a[0], b[2], c3, c1, c2); 369 r[2] = c3; 370 c3 = 0; 371 mul_add_c(a[0], b[3], c1, c2, c3); 372 mul_add_c(a[1], b[2], c1, c2, c3); 373 mul_add_c(a[2], b[1], c1, c2, c3); 374 mul_add_c(a[3], b[0], c1, c2, c3); 375 r[3] = c1; 376 c1 = 0; 377 mul_add_c(a[4], b[0], c2, c3, c1); 378 mul_add_c(a[3], b[1], c2, c3, c1); 379 mul_add_c(a[2], b[2], c2, c3, c1); 380 mul_add_c(a[1], b[3], c2, c3, c1); 381 mul_add_c(a[0], b[4], c2, c3, c1); 382 r[4] = c2; 383 c2 = 0; 384 mul_add_c(a[0], b[5], c3, c1, c2); 385 mul_add_c(a[1], b[4], c3, c1, c2); 386 mul_add_c(a[2], b[3], c3, c1, c2); 387 mul_add_c(a[3], b[2], c3, c1, c2); 388 mul_add_c(a[4], b[1], c3, c1, c2); 389 mul_add_c(a[5], b[0], c3, c1, c2); 390 r[5] = c3; 391 c3 = 0; 392 mul_add_c(a[6], b[0], c1, c2, c3); 393 mul_add_c(a[5], b[1], c1, c2, c3); 394 mul_add_c(a[4], b[2], c1, c2, c3); 395 mul_add_c(a[3], b[3], c1, c2, c3); 396 mul_add_c(a[2], b[4], c1, c2, c3); 397 mul_add_c(a[1], b[5], c1, c2, c3); 398 mul_add_c(a[0], b[6], c1, c2, c3); 399 r[6] = c1; 400 c1 = 0; 401 mul_add_c(a[0], b[7], c2, c3, c1); 402 mul_add_c(a[1], b[6], c2, c3, c1); 403 mul_add_c(a[2], b[5], c2, c3, c1); 404 mul_add_c(a[3], b[4], c2, c3, c1); 405 mul_add_c(a[4], b[3], c2, c3, c1); 406 mul_add_c(a[5], b[2], c2, c3, c1); 407 mul_add_c(a[6], b[1], c2, c3, c1); 408 mul_add_c(a[7], b[0], c2, c3, c1); 409 r[7] = c2; 410 c2 = 0; 411 mul_add_c(a[7], b[1], c3, c1, c2); 412 mul_add_c(a[6], b[2], c3, c1, c2); 413 mul_add_c(a[5], b[3], c3, c1, c2); 414 mul_add_c(a[4], b[4], c3, c1, c2); 415 mul_add_c(a[3], b[5], c3, c1, c2); 416 mul_add_c(a[2], b[6], c3, c1, c2); 417 mul_add_c(a[1], b[7], c3, c1, c2); 418 r[8] = c3; 419 c3 = 0; 420 mul_add_c(a[2], b[7], c1, c2, c3); 421 mul_add_c(a[3], b[6], c1, c2, c3); 422 mul_add_c(a[4], b[5], c1, c2, c3); 423 mul_add_c(a[5], b[4], c1, c2, c3); 424 mul_add_c(a[6], b[3], c1, c2, c3); 425 mul_add_c(a[7], b[2], c1, c2, c3); 426 r[9] = c1; 427 c1 = 0; 428 mul_add_c(a[7], b[3], c2, c3, c1); 429 mul_add_c(a[6], b[4], c2, c3, c1); 430 mul_add_c(a[5], b[5], c2, c3, c1); 431 mul_add_c(a[4], b[6], c2, c3, c1); 432 mul_add_c(a[3], b[7], c2, c3, c1); 433 r[10] = c2; 434 c2 = 0; 435 mul_add_c(a[4], b[7], c3, c1, c2); 436 mul_add_c(a[5], b[6], c3, c1, c2); 437 mul_add_c(a[6], b[5], c3, c1, c2); 438 mul_add_c(a[7], b[4], c3, c1, c2); 439 r[11] = c3; 440 c3 = 0; 441 mul_add_c(a[7], b[5], c1, c2, c3); 442 mul_add_c(a[6], b[6], c1, c2, c3); 443 mul_add_c(a[5], b[7], c1, c2, c3); 444 r[12] = c1; 445 c1 = 0; 446 mul_add_c(a[6], b[7], c2, c3, c1); 447 mul_add_c(a[7], b[6], c2, c3, c1); 448 r[13] = c2; 449 c2 = 0; 450 mul_add_c(a[7], b[7], c3, c1, c2); 451 r[14] = c3; 452 r[15] = c1; 453} 454 455void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { 456 BN_ULONG c1, c2, c3; 457 458 c1 = 0; 459 c2 = 0; 460 c3 = 0; 461 mul_add_c(a[0], b[0], c1, c2, c3); 462 r[0] = c1; 463 c1 = 0; 464 mul_add_c(a[0], b[1], c2, c3, c1); 465 mul_add_c(a[1], b[0], c2, c3, c1); 466 r[1] = c2; 467 c2 = 0; 468 mul_add_c(a[2], b[0], c3, c1, c2); 469 mul_add_c(a[1], b[1], c3, c1, c2); 470 mul_add_c(a[0], b[2], c3, c1, c2); 471 r[2] = c3; 472 c3 = 0; 473 mul_add_c(a[0], b[3], c1, c2, c3); 474 mul_add_c(a[1], b[2], c1, c2, c3); 475 mul_add_c(a[2], b[1], c1, c2, c3); 476 mul_add_c(a[3], b[0], c1, c2, c3); 477 r[3] = c1; 478 c1 = 0; 479 mul_add_c(a[3], b[1], c2, c3, c1); 480 mul_add_c(a[2], b[2], c2, c3, c1); 481 mul_add_c(a[1], b[3], c2, c3, c1); 482 r[4] = c2; 483 c2 = 0; 484 mul_add_c(a[2], b[3], c3, c1, c2); 485 mul_add_c(a[3], b[2], c3, c1, c2); 486 r[5] = c3; 487 c3 = 0; 488 mul_add_c(a[3], b[3], c1, c2, c3); 489 r[6] = c1; 490 r[7] = c2; 491} 492 493void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) { 494 BN_ULONG c1, c2, c3; 495 496 c1 = 0; 497 c2 = 0; 498 c3 = 0; 499 sqr_add_c(a, 0, c1, c2, c3); 500 r[0] = c1; 501 c1 = 0; 502 sqr_add_c2(a, 1, 0, c2, c3, c1); 503 r[1] = c2; 504 c2 = 0; 505 sqr_add_c(a, 1, c3, c1, c2); 506 sqr_add_c2(a, 2, 0, c3, c1, c2); 507 r[2] = c3; 508 c3 = 0; 509 sqr_add_c2(a, 3, 0, c1, c2, c3); 510 sqr_add_c2(a, 2, 1, c1, c2, c3); 511 r[3] = c1; 512 c1 = 0; 513 sqr_add_c(a, 2, c2, c3, c1); 514 sqr_add_c2(a, 3, 1, c2, c3, c1); 515 sqr_add_c2(a, 4, 0, c2, c3, c1); 516 r[4] = c2; 517 c2 = 0; 518 sqr_add_c2(a, 5, 0, c3, c1, c2); 519 sqr_add_c2(a, 4, 1, c3, c1, c2); 520 sqr_add_c2(a, 3, 2, c3, c1, c2); 521 r[5] = c3; 522 c3 = 0; 523 sqr_add_c(a, 3, c1, c2, c3); 524 sqr_add_c2(a, 4, 2, c1, c2, c3); 525 sqr_add_c2(a, 5, 1, c1, c2, c3); 526 sqr_add_c2(a, 6, 0, c1, c2, c3); 527 r[6] = c1; 528 c1 = 0; 529 sqr_add_c2(a, 7, 0, c2, c3, c1); 530 sqr_add_c2(a, 6, 1, c2, c3, c1); 531 sqr_add_c2(a, 5, 2, c2, c3, c1); 532 sqr_add_c2(a, 4, 3, c2, c3, c1); 533 r[7] = c2; 534 c2 = 0; 535 sqr_add_c(a, 4, c3, c1, c2); 536 sqr_add_c2(a, 5, 3, c3, c1, c2); 537 sqr_add_c2(a, 6, 2, c3, c1, c2); 538 sqr_add_c2(a, 7, 1, c3, c1, c2); 539 r[8] = c3; 540 c3 = 0; 541 sqr_add_c2(a, 7, 2, c1, c2, c3); 542 sqr_add_c2(a, 6, 3, c1, c2, c3); 543 sqr_add_c2(a, 5, 4, c1, c2, c3); 544 r[9] = c1; 545 c1 = 0; 546 sqr_add_c(a, 5, c2, c3, c1); 547 sqr_add_c2(a, 6, 4, c2, c3, c1); 548 sqr_add_c2(a, 7, 3, c2, c3, c1); 549 r[10] = c2; 550 c2 = 0; 551 sqr_add_c2(a, 7, 4, c3, c1, c2); 552 sqr_add_c2(a, 6, 5, c3, c1, c2); 553 r[11] = c3; 554 c3 = 0; 555 sqr_add_c(a, 6, c1, c2, c3); 556 sqr_add_c2(a, 7, 5, c1, c2, c3); 557 r[12] = c1; 558 c1 = 0; 559 sqr_add_c2(a, 7, 6, c2, c3, c1); 560 r[13] = c2; 561 c2 = 0; 562 sqr_add_c(a, 7, c3, c1, c2); 563 r[14] = c3; 564 r[15] = c1; 565} 566 567void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) { 568 BN_ULONG c1, c2, c3; 569 570 c1 = 0; 571 c2 = 0; 572 c3 = 0; 573 sqr_add_c(a, 0, c1, c2, c3); 574 r[0] = c1; 575 c1 = 0; 576 sqr_add_c2(a, 1, 0, c2, c3, c1); 577 r[1] = c2; 578 c2 = 0; 579 sqr_add_c(a, 1, c3, c1, c2); 580 sqr_add_c2(a, 2, 0, c3, c1, c2); 581 r[2] = c3; 582 c3 = 0; 583 sqr_add_c2(a, 3, 0, c1, c2, c3); 584 sqr_add_c2(a, 2, 1, c1, c2, c3); 585 r[3] = c1; 586 c1 = 0; 587 sqr_add_c(a, 2, c2, c3, c1); 588 sqr_add_c2(a, 3, 1, c2, c3, c1); 589 r[4] = c2; 590 c2 = 0; 591 sqr_add_c2(a, 3, 2, c3, c1, c2); 592 r[5] = c3; 593 c3 = 0; 594 sqr_add_c(a, 3, c1, c2, c3); 595 r[6] = c1; 596 r[7] = c2; 597} 598 599#endif /* !NO_ASM && X86_64 && !WINDOWS */ 600