1 /* x86_64 BIGNUM accelerator version 0.1, December 2002. 2 * 3 * Implemented by Andy Polyakov <appro (at) 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 -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); \ 95 (carry) = high; \ 96 } while (0) 97 #undef sqr 98 #define sqr(r0, r1, a) asm("mulq %2" : "=a"(r0), "=d"(r1) : "a"(a) : "cc"); 99 100 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, 101 BN_ULONG w) { 102 BN_ULONG c1 = 0; 103 104 if (num <= 0) { 105 return (c1); 106 } 107 108 while (num & ~3) { 109 mul_add(rp[0], ap[0], w, c1); 110 mul_add(rp[1], ap[1], w, c1); 111 mul_add(rp[2], ap[2], w, c1); 112 mul_add(rp[3], ap[3], w, c1); 113 ap += 4; 114 rp += 4; 115 num -= 4; 116 } 117 if (num) { 118 mul_add(rp[0], ap[0], w, c1); 119 if (--num == 0) { 120 return c1; 121 } 122 mul_add(rp[1], ap[1], w, c1); 123 if (--num == 0) { 124 return c1; 125 } 126 mul_add(rp[2], ap[2], w, c1); 127 return c1; 128 } 129 130 return c1; 131 } 132 133 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) { 134 BN_ULONG c1 = 0; 135 136 if (num <= 0) { 137 return c1; 138 } 139 140 while (num & ~3) { 141 mul(rp[0], ap[0], w, c1); 142 mul(rp[1], ap[1], w, c1); 143 mul(rp[2], ap[2], w, c1); 144 mul(rp[3], ap[3], w, c1); 145 ap += 4; 146 rp += 4; 147 num -= 4; 148 } 149 if (num) { 150 mul(rp[0], ap[0], w, c1); 151 if (--num == 0) { 152 return c1; 153 } 154 mul(rp[1], ap[1], w, c1); 155 if (--num == 0) { 156 return c1; 157 } 158 mul(rp[2], ap[2], w, c1); 159 } 160 return c1; 161 } 162 163 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) { 164 if (n <= 0) { 165 return; 166 } 167 168 while (n & ~3) { 169 sqr(r[0], r[1], a[0]); 170 sqr(r[2], r[3], a[1]); 171 sqr(r[4], r[5], a[2]); 172 sqr(r[6], r[7], a[3]); 173 a += 4; 174 r += 8; 175 n -= 4; 176 } 177 if (n) { 178 sqr(r[0], r[1], a[0]); 179 if (--n == 0) { 180 return; 181 } 182 sqr(r[2], r[3], a[1]); 183 if (--n == 0) { 184 return; 185 } 186 sqr(r[4], r[5], a[2]); 187 } 188 } 189 190 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 191 int n) { 192 BN_ULONG ret; 193 size_t i = 0; 194 195 if (n <= 0) { 196 return 0; 197 } 198 199 asm volatile ( 200 " subq %0,%0 \n" /* clear carry */ 201 " jmp 1f \n" 202 ".p2align 4 \n" 203 "1:" 204 " movq (%4,%2,8),%0 \n" 205 " adcq (%5,%2,8),%0 \n" 206 " movq %0,(%3,%2,8) \n" 207 " lea 1(%2),%2 \n" 208 " loop 1b \n" 209 " sbbq %0,%0 \n" 210 : "=&r"(ret), "+c"(n), "+r"(i) 211 : "r"(rp), "r"(ap), "r"(bp) 212 : "cc", "memory"); 213 214 return ret & 1; 215 } 216 217 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, 218 int n) { 219 BN_ULONG ret; 220 size_t i = 0; 221 222 if (n <= 0) { 223 return 0; 224 } 225 226 asm volatile ( 227 " subq %0,%0 \n" /* clear borrow */ 228 " jmp 1f \n" 229 ".p2align 4 \n" 230 "1:" 231 " movq (%4,%2,8),%0 \n" 232 " sbbq (%5,%2,8),%0 \n" 233 " movq %0,(%3,%2,8) \n" 234 " lea 1(%2),%2 \n" 235 " loop 1b \n" 236 " sbbq %0,%0 \n" 237 : "=&r"(ret), "+c"(n), "+r"(i) 238 : "r"(rp), "r"(ap), "r"(bp) 239 : "cc", "memory"); 240 241 return ret & 1; 242 } 243 244 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */ 245 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */ 246 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */ 247 /* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) 248 */ 249 250 /* Keep in mind that carrying into high part of multiplication result can not 251 * overflow, because it cannot be all-ones. */ 252 #define mul_add_c(a, b, c0, c1, c2) \ 253 do { \ 254 BN_ULONG t1, t2; \ 255 asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \ 256 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 257 : "+r"(c0), "+r"(c1), "+r"(c2) \ 258 : "r"(t1), "r"(t2), "g"(0) \ 259 : "cc"); \ 260 } while (0) 261 262 #define sqr_add_c(a, i, c0, c1, c2) \ 263 do { \ 264 BN_ULONG t1, t2; \ 265 asm("mulq %2" : "=a"(t1), "=d"(t2) : "a"((a)[i]) : "cc"); \ 266 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 267 : "+r"(c0), "+r"(c1), "+r"(c2) \ 268 : "r"(t1), "r"(t2), "g"(0) \ 269 : "cc"); \ 270 } while (0) 271 272 #define mul_add_c2(a, b, c0, c1, c2) \ 273 do { \ 274 BN_ULONG t1, t2; \ 275 asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \ 276 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 277 : "+r"(c0), "+r"(c1), "+r"(c2) \ 278 : "r"(t1), "r"(t2), "g"(0) \ 279 : "cc"); \ 280 asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \ 281 : "+r"(c0), "+r"(c1), "+r"(c2) \ 282 : "r"(t1), "r"(t2), "g"(0) \ 283 : "cc"); \ 284 } while (0) 285 286 #define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2) 287 288 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { 289 BN_ULONG c1, c2, c3; 290 291 c1 = 0; 292 c2 = 0; 293 c3 = 0; 294 mul_add_c(a[0], b[0], c1, c2, c3); 295 r[0] = c1; 296 c1 = 0; 297 mul_add_c(a[0], b[1], c2, c3, c1); 298 mul_add_c(a[1], b[0], c2, c3, c1); 299 r[1] = c2; 300 c2 = 0; 301 mul_add_c(a[2], b[0], c3, c1, c2); 302 mul_add_c(a[1], b[1], c3, c1, c2); 303 mul_add_c(a[0], b[2], c3, c1, c2); 304 r[2] = c3; 305 c3 = 0; 306 mul_add_c(a[0], b[3], c1, c2, c3); 307 mul_add_c(a[1], b[2], c1, c2, c3); 308 mul_add_c(a[2], b[1], c1, c2, c3); 309 mul_add_c(a[3], b[0], c1, c2, c3); 310 r[3] = c1; 311 c1 = 0; 312 mul_add_c(a[4], b[0], c2, c3, c1); 313 mul_add_c(a[3], b[1], c2, c3, c1); 314 mul_add_c(a[2], b[2], c2, c3, c1); 315 mul_add_c(a[1], b[3], c2, c3, c1); 316 mul_add_c(a[0], b[4], c2, c3, c1); 317 r[4] = c2; 318 c2 = 0; 319 mul_add_c(a[0], b[5], c3, c1, c2); 320 mul_add_c(a[1], b[4], c3, c1, c2); 321 mul_add_c(a[2], b[3], c3, c1, c2); 322 mul_add_c(a[3], b[2], c3, c1, c2); 323 mul_add_c(a[4], b[1], c3, c1, c2); 324 mul_add_c(a[5], b[0], c3, c1, c2); 325 r[5] = c3; 326 c3 = 0; 327 mul_add_c(a[6], b[0], c1, c2, c3); 328 mul_add_c(a[5], b[1], c1, c2, c3); 329 mul_add_c(a[4], b[2], c1, c2, c3); 330 mul_add_c(a[3], b[3], c1, c2, c3); 331 mul_add_c(a[2], b[4], c1, c2, c3); 332 mul_add_c(a[1], b[5], c1, c2, c3); 333 mul_add_c(a[0], b[6], c1, c2, c3); 334 r[6] = c1; 335 c1 = 0; 336 mul_add_c(a[0], b[7], c2, c3, c1); 337 mul_add_c(a[1], b[6], c2, c3, c1); 338 mul_add_c(a[2], b[5], c2, c3, c1); 339 mul_add_c(a[3], b[4], c2, c3, c1); 340 mul_add_c(a[4], b[3], c2, c3, c1); 341 mul_add_c(a[5], b[2], c2, c3, c1); 342 mul_add_c(a[6], b[1], c2, c3, c1); 343 mul_add_c(a[7], b[0], c2, c3, c1); 344 r[7] = c2; 345 c2 = 0; 346 mul_add_c(a[7], b[1], c3, c1, c2); 347 mul_add_c(a[6], b[2], c3, c1, c2); 348 mul_add_c(a[5], b[3], c3, c1, c2); 349 mul_add_c(a[4], b[4], c3, c1, c2); 350 mul_add_c(a[3], b[5], c3, c1, c2); 351 mul_add_c(a[2], b[6], c3, c1, c2); 352 mul_add_c(a[1], b[7], c3, c1, c2); 353 r[8] = c3; 354 c3 = 0; 355 mul_add_c(a[2], b[7], c1, c2, c3); 356 mul_add_c(a[3], b[6], c1, c2, c3); 357 mul_add_c(a[4], b[5], c1, c2, c3); 358 mul_add_c(a[5], b[4], c1, c2, c3); 359 mul_add_c(a[6], b[3], c1, c2, c3); 360 mul_add_c(a[7], b[2], c1, c2, c3); 361 r[9] = c1; 362 c1 = 0; 363 mul_add_c(a[7], b[3], c2, c3, c1); 364 mul_add_c(a[6], b[4], c2, c3, c1); 365 mul_add_c(a[5], b[5], c2, c3, c1); 366 mul_add_c(a[4], b[6], c2, c3, c1); 367 mul_add_c(a[3], b[7], c2, c3, c1); 368 r[10] = c2; 369 c2 = 0; 370 mul_add_c(a[4], b[7], c3, c1, c2); 371 mul_add_c(a[5], b[6], c3, c1, c2); 372 mul_add_c(a[6], b[5], c3, c1, c2); 373 mul_add_c(a[7], b[4], c3, c1, c2); 374 r[11] = c3; 375 c3 = 0; 376 mul_add_c(a[7], b[5], c1, c2, c3); 377 mul_add_c(a[6], b[6], c1, c2, c3); 378 mul_add_c(a[5], b[7], c1, c2, c3); 379 r[12] = c1; 380 c1 = 0; 381 mul_add_c(a[6], b[7], c2, c3, c1); 382 mul_add_c(a[7], b[6], c2, c3, c1); 383 r[13] = c2; 384 c2 = 0; 385 mul_add_c(a[7], b[7], c3, c1, c2); 386 r[14] = c3; 387 r[15] = c1; 388 } 389 390 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { 391 BN_ULONG c1, c2, c3; 392 393 c1 = 0; 394 c2 = 0; 395 c3 = 0; 396 mul_add_c(a[0], b[0], c1, c2, c3); 397 r[0] = c1; 398 c1 = 0; 399 mul_add_c(a[0], b[1], c2, c3, c1); 400 mul_add_c(a[1], b[0], c2, c3, c1); 401 r[1] = c2; 402 c2 = 0; 403 mul_add_c(a[2], b[0], c3, c1, c2); 404 mul_add_c(a[1], b[1], c3, c1, c2); 405 mul_add_c(a[0], b[2], c3, c1, c2); 406 r[2] = c3; 407 c3 = 0; 408 mul_add_c(a[0], b[3], c1, c2, c3); 409 mul_add_c(a[1], b[2], c1, c2, c3); 410 mul_add_c(a[2], b[1], c1, c2, c3); 411 mul_add_c(a[3], b[0], c1, c2, c3); 412 r[3] = c1; 413 c1 = 0; 414 mul_add_c(a[3], b[1], c2, c3, c1); 415 mul_add_c(a[2], b[2], c2, c3, c1); 416 mul_add_c(a[1], b[3], c2, c3, c1); 417 r[4] = c2; 418 c2 = 0; 419 mul_add_c(a[2], b[3], c3, c1, c2); 420 mul_add_c(a[3], b[2], c3, c1, c2); 421 r[5] = c3; 422 c3 = 0; 423 mul_add_c(a[3], b[3], c1, c2, c3); 424 r[6] = c1; 425 r[7] = c2; 426 } 427 428 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) { 429 BN_ULONG c1, c2, c3; 430 431 c1 = 0; 432 c2 = 0; 433 c3 = 0; 434 sqr_add_c(a, 0, c1, c2, c3); 435 r[0] = c1; 436 c1 = 0; 437 sqr_add_c2(a, 1, 0, c2, c3, c1); 438 r[1] = c2; 439 c2 = 0; 440 sqr_add_c(a, 1, c3, c1, c2); 441 sqr_add_c2(a, 2, 0, c3, c1, c2); 442 r[2] = c3; 443 c3 = 0; 444 sqr_add_c2(a, 3, 0, c1, c2, c3); 445 sqr_add_c2(a, 2, 1, c1, c2, c3); 446 r[3] = c1; 447 c1 = 0; 448 sqr_add_c(a, 2, c2, c3, c1); 449 sqr_add_c2(a, 3, 1, c2, c3, c1); 450 sqr_add_c2(a, 4, 0, c2, c3, c1); 451 r[4] = c2; 452 c2 = 0; 453 sqr_add_c2(a, 5, 0, c3, c1, c2); 454 sqr_add_c2(a, 4, 1, c3, c1, c2); 455 sqr_add_c2(a, 3, 2, c3, c1, c2); 456 r[5] = c3; 457 c3 = 0; 458 sqr_add_c(a, 3, c1, c2, c3); 459 sqr_add_c2(a, 4, 2, c1, c2, c3); 460 sqr_add_c2(a, 5, 1, c1, c2, c3); 461 sqr_add_c2(a, 6, 0, c1, c2, c3); 462 r[6] = c1; 463 c1 = 0; 464 sqr_add_c2(a, 7, 0, c2, c3, c1); 465 sqr_add_c2(a, 6, 1, c2, c3, c1); 466 sqr_add_c2(a, 5, 2, c2, c3, c1); 467 sqr_add_c2(a, 4, 3, c2, c3, c1); 468 r[7] = c2; 469 c2 = 0; 470 sqr_add_c(a, 4, c3, c1, c2); 471 sqr_add_c2(a, 5, 3, c3, c1, c2); 472 sqr_add_c2(a, 6, 2, c3, c1, c2); 473 sqr_add_c2(a, 7, 1, c3, c1, c2); 474 r[8] = c3; 475 c3 = 0; 476 sqr_add_c2(a, 7, 2, c1, c2, c3); 477 sqr_add_c2(a, 6, 3, c1, c2, c3); 478 sqr_add_c2(a, 5, 4, c1, c2, c3); 479 r[9] = c1; 480 c1 = 0; 481 sqr_add_c(a, 5, c2, c3, c1); 482 sqr_add_c2(a, 6, 4, c2, c3, c1); 483 sqr_add_c2(a, 7, 3, c2, c3, c1); 484 r[10] = c2; 485 c2 = 0; 486 sqr_add_c2(a, 7, 4, c3, c1, c2); 487 sqr_add_c2(a, 6, 5, c3, c1, c2); 488 r[11] = c3; 489 c3 = 0; 490 sqr_add_c(a, 6, c1, c2, c3); 491 sqr_add_c2(a, 7, 5, c1, c2, c3); 492 r[12] = c1; 493 c1 = 0; 494 sqr_add_c2(a, 7, 6, c2, c3, c1); 495 r[13] = c2; 496 c2 = 0; 497 sqr_add_c(a, 7, c3, c1, c2); 498 r[14] = c3; 499 r[15] = c1; 500 } 501 502 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) { 503 BN_ULONG c1, c2, c3; 504 505 c1 = 0; 506 c2 = 0; 507 c3 = 0; 508 sqr_add_c(a, 0, c1, c2, c3); 509 r[0] = c1; 510 c1 = 0; 511 sqr_add_c2(a, 1, 0, c2, c3, c1); 512 r[1] = c2; 513 c2 = 0; 514 sqr_add_c(a, 1, c3, c1, c2); 515 sqr_add_c2(a, 2, 0, c3, c1, c2); 516 r[2] = c3; 517 c3 = 0; 518 sqr_add_c2(a, 3, 0, c1, c2, c3); 519 sqr_add_c2(a, 2, 1, c1, c2, c3); 520 r[3] = c1; 521 c1 = 0; 522 sqr_add_c(a, 2, c2, c3, c1); 523 sqr_add_c2(a, 3, 1, c2, c3, c1); 524 r[4] = c2; 525 c2 = 0; 526 sqr_add_c2(a, 3, 2, c3, c1, c2); 527 r[5] = c3; 528 c3 = 0; 529 sqr_add_c(a, 3, c1, c2, c3); 530 r[6] = c1; 531 r[7] = c2; 532 } 533 534 #undef mul_add 535 #undef mul 536 #undef sqr 537 #undef mul_add_c 538 #undef sqr_add_c 539 #undef mul_add_c2 540 #undef sqr_add_c2 541 542 #endif /* !NO_ASM && X86_64 && __GNUC__ */ 543
