Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1 | #if defined(__aarch64__) |
| 2 | .text |
| 3 | |
| 4 | .globl bn_mul_mont |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 5 | .hidden bn_mul_mont |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 6 | .type bn_mul_mont,%function |
| 7 | .align 5 |
| 8 | bn_mul_mont: |
| 9 | tst x5,#7 |
| 10 | b.eq __bn_sqr8x_mont |
| 11 | tst x5,#3 |
| 12 | b.eq __bn_mul4x_mont |
| 13 | .Lmul_mont: |
| 14 | stp x29,x30,[sp,#-64]! |
| 15 | add x29,sp,#0 |
| 16 | stp x19,x20,[sp,#16] |
| 17 | stp x21,x22,[sp,#32] |
| 18 | stp x23,x24,[sp,#48] |
| 19 | |
| 20 | ldr x9,[x2],#8 // bp[0] |
| 21 | sub x22,sp,x5,lsl#3 |
| 22 | ldp x7,x8,[x1],#16 // ap[0..1] |
| 23 | lsl x5,x5,#3 |
| 24 | ldr x4,[x4] // *n0 |
| 25 | and x22,x22,#-16 // ABI says so |
| 26 | ldp x13,x14,[x3],#16 // np[0..1] |
| 27 | |
| 28 | mul x6,x7,x9 // ap[0]*bp[0] |
| 29 | sub x21,x5,#16 // j=num-2 |
| 30 | umulh x7,x7,x9 |
| 31 | mul x10,x8,x9 // ap[1]*bp[0] |
| 32 | umulh x11,x8,x9 |
| 33 | |
| 34 | mul x15,x6,x4 // "tp[0]"*n0 |
| 35 | mov sp,x22 // alloca |
| 36 | |
| 37 | // (*) mul x12,x13,x15 // np[0]*m1 |
| 38 | umulh x13,x13,x15 |
| 39 | mul x16,x14,x15 // np[1]*m1 |
| 40 | // (*) adds x12,x12,x6 // discarded |
| 41 | // (*) As for removal of first multiplication and addition |
| 42 | // instructions. The outcome of first addition is |
| 43 | // guaranteed to be zero, which leaves two computationally |
| 44 | // significant outcomes: it either carries or not. Then |
| 45 | // question is when does it carry? Is there alternative |
| 46 | // way to deduce it? If you follow operations, you can |
| 47 | // observe that condition for carry is quite simple: |
| 48 | // x6 being non-zero. So that carry can be calculated |
| 49 | // by adding -1 to x6. That's what next instruction does. |
| 50 | subs xzr,x6,#1 // (*) |
| 51 | umulh x17,x14,x15 |
| 52 | adc x13,x13,xzr |
| 53 | cbz x21,.L1st_skip |
| 54 | |
| 55 | .L1st: |
| 56 | ldr x8,[x1],#8 |
| 57 | adds x6,x10,x7 |
| 58 | sub x21,x21,#8 // j-- |
| 59 | adc x7,x11,xzr |
| 60 | |
| 61 | ldr x14,[x3],#8 |
| 62 | adds x12,x16,x13 |
| 63 | mul x10,x8,x9 // ap[j]*bp[0] |
| 64 | adc x13,x17,xzr |
| 65 | umulh x11,x8,x9 |
| 66 | |
| 67 | adds x12,x12,x6 |
| 68 | mul x16,x14,x15 // np[j]*m1 |
| 69 | adc x13,x13,xzr |
| 70 | umulh x17,x14,x15 |
| 71 | str x12,[x22],#8 // tp[j-1] |
| 72 | cbnz x21,.L1st |
| 73 | |
| 74 | .L1st_skip: |
| 75 | adds x6,x10,x7 |
| 76 | sub x1,x1,x5 // rewind x1 |
| 77 | adc x7,x11,xzr |
| 78 | |
| 79 | adds x12,x16,x13 |
| 80 | sub x3,x3,x5 // rewind x3 |
| 81 | adc x13,x17,xzr |
| 82 | |
| 83 | adds x12,x12,x6 |
| 84 | sub x20,x5,#8 // i=num-1 |
| 85 | adcs x13,x13,x7 |
| 86 | |
| 87 | adc x19,xzr,xzr // upmost overflow bit |
| 88 | stp x12,x13,[x22] |
| 89 | |
| 90 | .Louter: |
| 91 | ldr x9,[x2],#8 // bp[i] |
| 92 | ldp x7,x8,[x1],#16 |
| 93 | ldr x23,[sp] // tp[0] |
| 94 | add x22,sp,#8 |
| 95 | |
| 96 | mul x6,x7,x9 // ap[0]*bp[i] |
| 97 | sub x21,x5,#16 // j=num-2 |
| 98 | umulh x7,x7,x9 |
| 99 | ldp x13,x14,[x3],#16 |
| 100 | mul x10,x8,x9 // ap[1]*bp[i] |
| 101 | adds x6,x6,x23 |
| 102 | umulh x11,x8,x9 |
| 103 | adc x7,x7,xzr |
| 104 | |
| 105 | mul x15,x6,x4 |
| 106 | sub x20,x20,#8 // i-- |
| 107 | |
| 108 | // (*) mul x12,x13,x15 // np[0]*m1 |
| 109 | umulh x13,x13,x15 |
| 110 | mul x16,x14,x15 // np[1]*m1 |
| 111 | // (*) adds x12,x12,x6 |
| 112 | subs xzr,x6,#1 // (*) |
| 113 | umulh x17,x14,x15 |
| 114 | cbz x21,.Linner_skip |
| 115 | |
| 116 | .Linner: |
| 117 | ldr x8,[x1],#8 |
| 118 | adc x13,x13,xzr |
| 119 | ldr x23,[x22],#8 // tp[j] |
| 120 | adds x6,x10,x7 |
| 121 | sub x21,x21,#8 // j-- |
| 122 | adc x7,x11,xzr |
| 123 | |
| 124 | adds x12,x16,x13 |
| 125 | ldr x14,[x3],#8 |
| 126 | adc x13,x17,xzr |
| 127 | |
| 128 | mul x10,x8,x9 // ap[j]*bp[i] |
| 129 | adds x6,x6,x23 |
| 130 | umulh x11,x8,x9 |
| 131 | adc x7,x7,xzr |
| 132 | |
| 133 | mul x16,x14,x15 // np[j]*m1 |
| 134 | adds x12,x12,x6 |
| 135 | umulh x17,x14,x15 |
| 136 | str x12,[x22,#-16] // tp[j-1] |
| 137 | cbnz x21,.Linner |
| 138 | |
| 139 | .Linner_skip: |
| 140 | ldr x23,[x22],#8 // tp[j] |
| 141 | adc x13,x13,xzr |
| 142 | adds x6,x10,x7 |
| 143 | sub x1,x1,x5 // rewind x1 |
| 144 | adc x7,x11,xzr |
| 145 | |
| 146 | adds x12,x16,x13 |
| 147 | sub x3,x3,x5 // rewind x3 |
| 148 | adcs x13,x17,x19 |
| 149 | adc x19,xzr,xzr |
| 150 | |
| 151 | adds x6,x6,x23 |
| 152 | adc x7,x7,xzr |
| 153 | |
| 154 | adds x12,x12,x6 |
| 155 | adcs x13,x13,x7 |
| 156 | adc x19,x19,xzr // upmost overflow bit |
| 157 | stp x12,x13,[x22,#-16] |
| 158 | |
| 159 | cbnz x20,.Louter |
| 160 | |
| 161 | // Final step. We see if result is larger than modulus, and |
| 162 | // if it is, subtract the modulus. But comparison implies |
| 163 | // subtraction. So we subtract modulus, see if it borrowed, |
| 164 | // and conditionally copy original value. |
| 165 | ldr x23,[sp] // tp[0] |
| 166 | add x22,sp,#8 |
| 167 | ldr x14,[x3],#8 // np[0] |
| 168 | subs x21,x5,#8 // j=num-1 and clear borrow |
| 169 | mov x1,x0 |
| 170 | .Lsub: |
| 171 | sbcs x8,x23,x14 // tp[j]-np[j] |
| 172 | ldr x23,[x22],#8 |
| 173 | sub x21,x21,#8 // j-- |
| 174 | ldr x14,[x3],#8 |
| 175 | str x8,[x1],#8 // rp[j]=tp[j]-np[j] |
| 176 | cbnz x21,.Lsub |
| 177 | |
| 178 | sbcs x8,x23,x14 |
| 179 | sbcs x19,x19,xzr // did it borrow? |
| 180 | str x8,[x1],#8 // rp[num-1] |
| 181 | |
| 182 | ldr x23,[sp] // tp[0] |
| 183 | add x22,sp,#8 |
| 184 | ldr x8,[x0],#8 // rp[0] |
| 185 | sub x5,x5,#8 // num-- |
| 186 | nop |
| 187 | .Lcond_copy: |
| 188 | sub x5,x5,#8 // num-- |
| 189 | csel x14,x23,x8,lo // did it borrow? |
| 190 | ldr x23,[x22],#8 |
| 191 | ldr x8,[x0],#8 |
| 192 | str xzr,[x22,#-16] // wipe tp |
| 193 | str x14,[x0,#-16] |
| 194 | cbnz x5,.Lcond_copy |
| 195 | |
| 196 | csel x14,x23,x8,lo |
| 197 | str xzr,[x22,#-8] // wipe tp |
| 198 | str x14,[x0,#-8] |
| 199 | |
| 200 | ldp x19,x20,[x29,#16] |
| 201 | mov sp,x29 |
| 202 | ldp x21,x22,[x29,#32] |
| 203 | mov x0,#1 |
| 204 | ldp x23,x24,[x29,#48] |
| 205 | ldr x29,[sp],#64 |
| 206 | ret |
| 207 | .size bn_mul_mont,.-bn_mul_mont |
| 208 | .type __bn_sqr8x_mont,%function |
| 209 | .align 5 |
| 210 | __bn_sqr8x_mont: |
| 211 | cmp x1,x2 |
| 212 | b.ne __bn_mul4x_mont |
| 213 | .Lsqr8x_mont: |
| 214 | stp x29,x30,[sp,#-128]! |
| 215 | add x29,sp,#0 |
| 216 | stp x19,x20,[sp,#16] |
| 217 | stp x21,x22,[sp,#32] |
| 218 | stp x23,x24,[sp,#48] |
| 219 | stp x25,x26,[sp,#64] |
| 220 | stp x27,x28,[sp,#80] |
| 221 | stp x0,x3,[sp,#96] // offload rp and np |
| 222 | |
| 223 | ldp x6,x7,[x1,#8*0] |
| 224 | ldp x8,x9,[x1,#8*2] |
| 225 | ldp x10,x11,[x1,#8*4] |
| 226 | ldp x12,x13,[x1,#8*6] |
| 227 | |
| 228 | sub x2,sp,x5,lsl#4 |
| 229 | lsl x5,x5,#3 |
| 230 | ldr x4,[x4] // *n0 |
| 231 | mov sp,x2 // alloca |
| 232 | sub x27,x5,#8*8 |
| 233 | b .Lsqr8x_zero_start |
| 234 | |
| 235 | .Lsqr8x_zero: |
| 236 | sub x27,x27,#8*8 |
| 237 | stp xzr,xzr,[x2,#8*0] |
| 238 | stp xzr,xzr,[x2,#8*2] |
| 239 | stp xzr,xzr,[x2,#8*4] |
| 240 | stp xzr,xzr,[x2,#8*6] |
| 241 | .Lsqr8x_zero_start: |
| 242 | stp xzr,xzr,[x2,#8*8] |
| 243 | stp xzr,xzr,[x2,#8*10] |
| 244 | stp xzr,xzr,[x2,#8*12] |
| 245 | stp xzr,xzr,[x2,#8*14] |
| 246 | add x2,x2,#8*16 |
| 247 | cbnz x27,.Lsqr8x_zero |
| 248 | |
| 249 | add x3,x1,x5 |
| 250 | add x1,x1,#8*8 |
| 251 | mov x19,xzr |
| 252 | mov x20,xzr |
| 253 | mov x21,xzr |
| 254 | mov x22,xzr |
| 255 | mov x23,xzr |
| 256 | mov x24,xzr |
| 257 | mov x25,xzr |
| 258 | mov x26,xzr |
| 259 | mov x2,sp |
| 260 | str x4,[x29,#112] // offload n0 |
| 261 | |
| 262 | // Multiply everything but a[i]*a[i] |
| 263 | .align 4 |
| 264 | .Lsqr8x_outer_loop: |
| 265 | // a[1]a[0] (i) |
| 266 | // a[2]a[0] |
| 267 | // a[3]a[0] |
| 268 | // a[4]a[0] |
| 269 | // a[5]a[0] |
| 270 | // a[6]a[0] |
| 271 | // a[7]a[0] |
| 272 | // a[2]a[1] (ii) |
| 273 | // a[3]a[1] |
| 274 | // a[4]a[1] |
| 275 | // a[5]a[1] |
| 276 | // a[6]a[1] |
| 277 | // a[7]a[1] |
| 278 | // a[3]a[2] (iii) |
| 279 | // a[4]a[2] |
| 280 | // a[5]a[2] |
| 281 | // a[6]a[2] |
| 282 | // a[7]a[2] |
| 283 | // a[4]a[3] (iv) |
| 284 | // a[5]a[3] |
| 285 | // a[6]a[3] |
| 286 | // a[7]a[3] |
| 287 | // a[5]a[4] (v) |
| 288 | // a[6]a[4] |
| 289 | // a[7]a[4] |
| 290 | // a[6]a[5] (vi) |
| 291 | // a[7]a[5] |
| 292 | // a[7]a[6] (vii) |
| 293 | |
| 294 | mul x14,x7,x6 // lo(a[1..7]*a[0]) (i) |
| 295 | mul x15,x8,x6 |
| 296 | mul x16,x9,x6 |
| 297 | mul x17,x10,x6 |
| 298 | adds x20,x20,x14 // t[1]+lo(a[1]*a[0]) |
| 299 | mul x14,x11,x6 |
| 300 | adcs x21,x21,x15 |
| 301 | mul x15,x12,x6 |
| 302 | adcs x22,x22,x16 |
| 303 | mul x16,x13,x6 |
| 304 | adcs x23,x23,x17 |
| 305 | umulh x17,x7,x6 // hi(a[1..7]*a[0]) |
| 306 | adcs x24,x24,x14 |
| 307 | umulh x14,x8,x6 |
| 308 | adcs x25,x25,x15 |
| 309 | umulh x15,x9,x6 |
| 310 | adcs x26,x26,x16 |
| 311 | umulh x16,x10,x6 |
| 312 | stp x19,x20,[x2],#8*2 // t[0..1] |
| 313 | adc x19,xzr,xzr // t[8] |
| 314 | adds x21,x21,x17 // t[2]+lo(a[1]*a[0]) |
| 315 | umulh x17,x11,x6 |
| 316 | adcs x22,x22,x14 |
| 317 | umulh x14,x12,x6 |
| 318 | adcs x23,x23,x15 |
| 319 | umulh x15,x13,x6 |
| 320 | adcs x24,x24,x16 |
| 321 | mul x16,x8,x7 // lo(a[2..7]*a[1]) (ii) |
| 322 | adcs x25,x25,x17 |
| 323 | mul x17,x9,x7 |
| 324 | adcs x26,x26,x14 |
| 325 | mul x14,x10,x7 |
| 326 | adc x19,x19,x15 |
| 327 | |
| 328 | mul x15,x11,x7 |
| 329 | adds x22,x22,x16 |
| 330 | mul x16,x12,x7 |
| 331 | adcs x23,x23,x17 |
| 332 | mul x17,x13,x7 |
| 333 | adcs x24,x24,x14 |
| 334 | umulh x14,x8,x7 // hi(a[2..7]*a[1]) |
| 335 | adcs x25,x25,x15 |
| 336 | umulh x15,x9,x7 |
| 337 | adcs x26,x26,x16 |
| 338 | umulh x16,x10,x7 |
| 339 | adcs x19,x19,x17 |
| 340 | umulh x17,x11,x7 |
| 341 | stp x21,x22,[x2],#8*2 // t[2..3] |
| 342 | adc x20,xzr,xzr // t[9] |
| 343 | adds x23,x23,x14 |
| 344 | umulh x14,x12,x7 |
| 345 | adcs x24,x24,x15 |
| 346 | umulh x15,x13,x7 |
| 347 | adcs x25,x25,x16 |
| 348 | mul x16,x9,x8 // lo(a[3..7]*a[2]) (iii) |
| 349 | adcs x26,x26,x17 |
| 350 | mul x17,x10,x8 |
| 351 | adcs x19,x19,x14 |
| 352 | mul x14,x11,x8 |
| 353 | adc x20,x20,x15 |
| 354 | |
| 355 | mul x15,x12,x8 |
| 356 | adds x24,x24,x16 |
| 357 | mul x16,x13,x8 |
| 358 | adcs x25,x25,x17 |
| 359 | umulh x17,x9,x8 // hi(a[3..7]*a[2]) |
| 360 | adcs x26,x26,x14 |
| 361 | umulh x14,x10,x8 |
| 362 | adcs x19,x19,x15 |
| 363 | umulh x15,x11,x8 |
| 364 | adcs x20,x20,x16 |
| 365 | umulh x16,x12,x8 |
| 366 | stp x23,x24,[x2],#8*2 // t[4..5] |
| 367 | adc x21,xzr,xzr // t[10] |
| 368 | adds x25,x25,x17 |
| 369 | umulh x17,x13,x8 |
| 370 | adcs x26,x26,x14 |
| 371 | mul x14,x10,x9 // lo(a[4..7]*a[3]) (iv) |
| 372 | adcs x19,x19,x15 |
| 373 | mul x15,x11,x9 |
| 374 | adcs x20,x20,x16 |
| 375 | mul x16,x12,x9 |
| 376 | adc x21,x21,x17 |
| 377 | |
| 378 | mul x17,x13,x9 |
| 379 | adds x26,x26,x14 |
| 380 | umulh x14,x10,x9 // hi(a[4..7]*a[3]) |
| 381 | adcs x19,x19,x15 |
| 382 | umulh x15,x11,x9 |
| 383 | adcs x20,x20,x16 |
| 384 | umulh x16,x12,x9 |
| 385 | adcs x21,x21,x17 |
| 386 | umulh x17,x13,x9 |
| 387 | stp x25,x26,[x2],#8*2 // t[6..7] |
| 388 | adc x22,xzr,xzr // t[11] |
| 389 | adds x19,x19,x14 |
| 390 | mul x14,x11,x10 // lo(a[5..7]*a[4]) (v) |
| 391 | adcs x20,x20,x15 |
| 392 | mul x15,x12,x10 |
| 393 | adcs x21,x21,x16 |
| 394 | mul x16,x13,x10 |
| 395 | adc x22,x22,x17 |
| 396 | |
| 397 | umulh x17,x11,x10 // hi(a[5..7]*a[4]) |
| 398 | adds x20,x20,x14 |
| 399 | umulh x14,x12,x10 |
| 400 | adcs x21,x21,x15 |
| 401 | umulh x15,x13,x10 |
| 402 | adcs x22,x22,x16 |
| 403 | mul x16,x12,x11 // lo(a[6..7]*a[5]) (vi) |
| 404 | adc x23,xzr,xzr // t[12] |
| 405 | adds x21,x21,x17 |
| 406 | mul x17,x13,x11 |
| 407 | adcs x22,x22,x14 |
| 408 | umulh x14,x12,x11 // hi(a[6..7]*a[5]) |
| 409 | adc x23,x23,x15 |
| 410 | |
| 411 | umulh x15,x13,x11 |
| 412 | adds x22,x22,x16 |
| 413 | mul x16,x13,x12 // lo(a[7]*a[6]) (vii) |
| 414 | adcs x23,x23,x17 |
| 415 | umulh x17,x13,x12 // hi(a[7]*a[6]) |
| 416 | adc x24,xzr,xzr // t[13] |
| 417 | adds x23,x23,x14 |
| 418 | sub x27,x3,x1 // done yet? |
| 419 | adc x24,x24,x15 |
| 420 | |
| 421 | adds x24,x24,x16 |
| 422 | sub x14,x3,x5 // rewinded ap |
| 423 | adc x25,xzr,xzr // t[14] |
| 424 | add x25,x25,x17 |
| 425 | |
| 426 | cbz x27,.Lsqr8x_outer_break |
| 427 | |
| 428 | mov x4,x6 |
| 429 | ldp x6,x7,[x2,#8*0] |
| 430 | ldp x8,x9,[x2,#8*2] |
| 431 | ldp x10,x11,[x2,#8*4] |
| 432 | ldp x12,x13,[x2,#8*6] |
| 433 | adds x19,x19,x6 |
| 434 | adcs x20,x20,x7 |
| 435 | ldp x6,x7,[x1,#8*0] |
| 436 | adcs x21,x21,x8 |
| 437 | adcs x22,x22,x9 |
| 438 | ldp x8,x9,[x1,#8*2] |
| 439 | adcs x23,x23,x10 |
| 440 | adcs x24,x24,x11 |
| 441 | ldp x10,x11,[x1,#8*4] |
| 442 | adcs x25,x25,x12 |
| 443 | mov x0,x1 |
| 444 | adcs x26,xzr,x13 |
| 445 | ldp x12,x13,[x1,#8*6] |
| 446 | add x1,x1,#8*8 |
| 447 | //adc x28,xzr,xzr // moved below |
| 448 | mov x27,#-8*8 |
| 449 | |
| 450 | // a[8]a[0] |
| 451 | // a[9]a[0] |
| 452 | // a[a]a[0] |
| 453 | // a[b]a[0] |
| 454 | // a[c]a[0] |
| 455 | // a[d]a[0] |
| 456 | // a[e]a[0] |
| 457 | // a[f]a[0] |
| 458 | // a[8]a[1] |
| 459 | // a[f]a[1]........................ |
| 460 | // a[8]a[2] |
| 461 | // a[f]a[2]........................ |
| 462 | // a[8]a[3] |
| 463 | // a[f]a[3]........................ |
| 464 | // a[8]a[4] |
| 465 | // a[f]a[4]........................ |
| 466 | // a[8]a[5] |
| 467 | // a[f]a[5]........................ |
| 468 | // a[8]a[6] |
| 469 | // a[f]a[6]........................ |
| 470 | // a[8]a[7] |
| 471 | // a[f]a[7]........................ |
| 472 | .Lsqr8x_mul: |
| 473 | mul x14,x6,x4 |
| 474 | adc x28,xzr,xzr // carry bit, modulo-scheduled |
| 475 | mul x15,x7,x4 |
| 476 | add x27,x27,#8 |
| 477 | mul x16,x8,x4 |
| 478 | mul x17,x9,x4 |
| 479 | adds x19,x19,x14 |
| 480 | mul x14,x10,x4 |
| 481 | adcs x20,x20,x15 |
| 482 | mul x15,x11,x4 |
| 483 | adcs x21,x21,x16 |
| 484 | mul x16,x12,x4 |
| 485 | adcs x22,x22,x17 |
| 486 | mul x17,x13,x4 |
| 487 | adcs x23,x23,x14 |
| 488 | umulh x14,x6,x4 |
| 489 | adcs x24,x24,x15 |
| 490 | umulh x15,x7,x4 |
| 491 | adcs x25,x25,x16 |
| 492 | umulh x16,x8,x4 |
| 493 | adcs x26,x26,x17 |
| 494 | umulh x17,x9,x4 |
| 495 | adc x28,x28,xzr |
| 496 | str x19,[x2],#8 |
| 497 | adds x19,x20,x14 |
| 498 | umulh x14,x10,x4 |
| 499 | adcs x20,x21,x15 |
| 500 | umulh x15,x11,x4 |
| 501 | adcs x21,x22,x16 |
| 502 | umulh x16,x12,x4 |
| 503 | adcs x22,x23,x17 |
| 504 | umulh x17,x13,x4 |
| 505 | ldr x4,[x0,x27] |
| 506 | adcs x23,x24,x14 |
| 507 | adcs x24,x25,x15 |
| 508 | adcs x25,x26,x16 |
| 509 | adcs x26,x28,x17 |
| 510 | //adc x28,xzr,xzr // moved above |
| 511 | cbnz x27,.Lsqr8x_mul |
| 512 | // note that carry flag is guaranteed |
| 513 | // to be zero at this point |
| 514 | cmp x1,x3 // done yet? |
| 515 | b.eq .Lsqr8x_break |
| 516 | |
| 517 | ldp x6,x7,[x2,#8*0] |
| 518 | ldp x8,x9,[x2,#8*2] |
| 519 | ldp x10,x11,[x2,#8*4] |
| 520 | ldp x12,x13,[x2,#8*6] |
| 521 | adds x19,x19,x6 |
| 522 | ldr x4,[x0,#-8*8] |
| 523 | adcs x20,x20,x7 |
| 524 | ldp x6,x7,[x1,#8*0] |
| 525 | adcs x21,x21,x8 |
| 526 | adcs x22,x22,x9 |
| 527 | ldp x8,x9,[x1,#8*2] |
| 528 | adcs x23,x23,x10 |
| 529 | adcs x24,x24,x11 |
| 530 | ldp x10,x11,[x1,#8*4] |
| 531 | adcs x25,x25,x12 |
| 532 | mov x27,#-8*8 |
| 533 | adcs x26,x26,x13 |
| 534 | ldp x12,x13,[x1,#8*6] |
| 535 | add x1,x1,#8*8 |
| 536 | //adc x28,xzr,xzr // moved above |
| 537 | b .Lsqr8x_mul |
| 538 | |
| 539 | .align 4 |
| 540 | .Lsqr8x_break: |
| 541 | ldp x6,x7,[x0,#8*0] |
| 542 | add x1,x0,#8*8 |
| 543 | ldp x8,x9,[x0,#8*2] |
| 544 | sub x14,x3,x1 // is it last iteration? |
| 545 | ldp x10,x11,[x0,#8*4] |
| 546 | sub x15,x2,x14 |
| 547 | ldp x12,x13,[x0,#8*6] |
| 548 | cbz x14,.Lsqr8x_outer_loop |
| 549 | |
| 550 | stp x19,x20,[x2,#8*0] |
| 551 | ldp x19,x20,[x15,#8*0] |
| 552 | stp x21,x22,[x2,#8*2] |
| 553 | ldp x21,x22,[x15,#8*2] |
| 554 | stp x23,x24,[x2,#8*4] |
| 555 | ldp x23,x24,[x15,#8*4] |
| 556 | stp x25,x26,[x2,#8*6] |
| 557 | mov x2,x15 |
| 558 | ldp x25,x26,[x15,#8*6] |
| 559 | b .Lsqr8x_outer_loop |
| 560 | |
| 561 | .align 4 |
| 562 | .Lsqr8x_outer_break: |
| 563 | // Now multiply above result by 2 and add a[n-1]*a[n-1]|...|a[0]*a[0] |
| 564 | ldp x7,x9,[x14,#8*0] // recall that x14 is &a[0] |
| 565 | ldp x15,x16,[sp,#8*1] |
| 566 | ldp x11,x13,[x14,#8*2] |
| 567 | add x1,x14,#8*4 |
| 568 | ldp x17,x14,[sp,#8*3] |
| 569 | |
| 570 | stp x19,x20,[x2,#8*0] |
| 571 | mul x19,x7,x7 |
| 572 | stp x21,x22,[x2,#8*2] |
| 573 | umulh x7,x7,x7 |
| 574 | stp x23,x24,[x2,#8*4] |
| 575 | mul x8,x9,x9 |
| 576 | stp x25,x26,[x2,#8*6] |
| 577 | mov x2,sp |
| 578 | umulh x9,x9,x9 |
| 579 | adds x20,x7,x15,lsl#1 |
| 580 | extr x15,x16,x15,#63 |
| 581 | sub x27,x5,#8*4 |
| 582 | |
| 583 | .Lsqr4x_shift_n_add: |
| 584 | adcs x21,x8,x15 |
| 585 | extr x16,x17,x16,#63 |
| 586 | sub x27,x27,#8*4 |
| 587 | adcs x22,x9,x16 |
| 588 | ldp x15,x16,[x2,#8*5] |
| 589 | mul x10,x11,x11 |
| 590 | ldp x7,x9,[x1],#8*2 |
| 591 | umulh x11,x11,x11 |
| 592 | mul x12,x13,x13 |
| 593 | umulh x13,x13,x13 |
| 594 | extr x17,x14,x17,#63 |
| 595 | stp x19,x20,[x2,#8*0] |
| 596 | adcs x23,x10,x17 |
| 597 | extr x14,x15,x14,#63 |
| 598 | stp x21,x22,[x2,#8*2] |
| 599 | adcs x24,x11,x14 |
| 600 | ldp x17,x14,[x2,#8*7] |
| 601 | extr x15,x16,x15,#63 |
| 602 | adcs x25,x12,x15 |
| 603 | extr x16,x17,x16,#63 |
| 604 | adcs x26,x13,x16 |
| 605 | ldp x15,x16,[x2,#8*9] |
| 606 | mul x6,x7,x7 |
| 607 | ldp x11,x13,[x1],#8*2 |
| 608 | umulh x7,x7,x7 |
| 609 | mul x8,x9,x9 |
| 610 | umulh x9,x9,x9 |
| 611 | stp x23,x24,[x2,#8*4] |
| 612 | extr x17,x14,x17,#63 |
| 613 | stp x25,x26,[x2,#8*6] |
| 614 | add x2,x2,#8*8 |
| 615 | adcs x19,x6,x17 |
| 616 | extr x14,x15,x14,#63 |
| 617 | adcs x20,x7,x14 |
| 618 | ldp x17,x14,[x2,#8*3] |
| 619 | extr x15,x16,x15,#63 |
| 620 | cbnz x27,.Lsqr4x_shift_n_add |
| 621 | ldp x1,x4,[x29,#104] // pull np and n0 |
| 622 | |
| 623 | adcs x21,x8,x15 |
| 624 | extr x16,x17,x16,#63 |
| 625 | adcs x22,x9,x16 |
| 626 | ldp x15,x16,[x2,#8*5] |
| 627 | mul x10,x11,x11 |
| 628 | umulh x11,x11,x11 |
| 629 | stp x19,x20,[x2,#8*0] |
| 630 | mul x12,x13,x13 |
| 631 | umulh x13,x13,x13 |
| 632 | stp x21,x22,[x2,#8*2] |
| 633 | extr x17,x14,x17,#63 |
| 634 | adcs x23,x10,x17 |
| 635 | extr x14,x15,x14,#63 |
| 636 | ldp x19,x20,[sp,#8*0] |
| 637 | adcs x24,x11,x14 |
| 638 | extr x15,x16,x15,#63 |
| 639 | ldp x6,x7,[x1,#8*0] |
| 640 | adcs x25,x12,x15 |
| 641 | extr x16,xzr,x16,#63 |
| 642 | ldp x8,x9,[x1,#8*2] |
| 643 | adc x26,x13,x16 |
| 644 | ldp x10,x11,[x1,#8*4] |
| 645 | |
| 646 | // Reduce by 512 bits per iteration |
| 647 | mul x28,x4,x19 // t[0]*n0 |
| 648 | ldp x12,x13,[x1,#8*6] |
| 649 | add x3,x1,x5 |
| 650 | ldp x21,x22,[sp,#8*2] |
| 651 | stp x23,x24,[x2,#8*4] |
| 652 | ldp x23,x24,[sp,#8*4] |
| 653 | stp x25,x26,[x2,#8*6] |
| 654 | ldp x25,x26,[sp,#8*6] |
| 655 | add x1,x1,#8*8 |
| 656 | mov x30,xzr // initial top-most carry |
| 657 | mov x2,sp |
| 658 | mov x27,#8 |
| 659 | |
| 660 | .Lsqr8x_reduction: |
| 661 | // (*) mul x14,x6,x28 // lo(n[0-7])*lo(t[0]*n0) |
| 662 | mul x15,x7,x28 |
| 663 | sub x27,x27,#1 |
| 664 | mul x16,x8,x28 |
| 665 | str x28,[x2],#8 // put aside t[0]*n0 for tail processing |
| 666 | mul x17,x9,x28 |
| 667 | // (*) adds xzr,x19,x14 |
| 668 | subs xzr,x19,#1 // (*) |
| 669 | mul x14,x10,x28 |
| 670 | adcs x19,x20,x15 |
| 671 | mul x15,x11,x28 |
| 672 | adcs x20,x21,x16 |
| 673 | mul x16,x12,x28 |
| 674 | adcs x21,x22,x17 |
| 675 | mul x17,x13,x28 |
| 676 | adcs x22,x23,x14 |
| 677 | umulh x14,x6,x28 // hi(n[0-7])*lo(t[0]*n0) |
| 678 | adcs x23,x24,x15 |
| 679 | umulh x15,x7,x28 |
| 680 | adcs x24,x25,x16 |
| 681 | umulh x16,x8,x28 |
| 682 | adcs x25,x26,x17 |
| 683 | umulh x17,x9,x28 |
| 684 | adc x26,xzr,xzr |
| 685 | adds x19,x19,x14 |
| 686 | umulh x14,x10,x28 |
| 687 | adcs x20,x20,x15 |
| 688 | umulh x15,x11,x28 |
| 689 | adcs x21,x21,x16 |
| 690 | umulh x16,x12,x28 |
| 691 | adcs x22,x22,x17 |
| 692 | umulh x17,x13,x28 |
| 693 | mul x28,x4,x19 // next t[0]*n0 |
| 694 | adcs x23,x23,x14 |
| 695 | adcs x24,x24,x15 |
| 696 | adcs x25,x25,x16 |
| 697 | adc x26,x26,x17 |
| 698 | cbnz x27,.Lsqr8x_reduction |
| 699 | |
| 700 | ldp x14,x15,[x2,#8*0] |
| 701 | ldp x16,x17,[x2,#8*2] |
| 702 | mov x0,x2 |
| 703 | sub x27,x3,x1 // done yet? |
| 704 | adds x19,x19,x14 |
| 705 | adcs x20,x20,x15 |
| 706 | ldp x14,x15,[x2,#8*4] |
| 707 | adcs x21,x21,x16 |
| 708 | adcs x22,x22,x17 |
| 709 | ldp x16,x17,[x2,#8*6] |
| 710 | adcs x23,x23,x14 |
| 711 | adcs x24,x24,x15 |
| 712 | adcs x25,x25,x16 |
| 713 | adcs x26,x26,x17 |
| 714 | //adc x28,xzr,xzr // moved below |
| 715 | cbz x27,.Lsqr8x8_post_condition |
| 716 | |
| 717 | ldr x4,[x2,#-8*8] |
| 718 | ldp x6,x7,[x1,#8*0] |
| 719 | ldp x8,x9,[x1,#8*2] |
| 720 | ldp x10,x11,[x1,#8*4] |
| 721 | mov x27,#-8*8 |
| 722 | ldp x12,x13,[x1,#8*6] |
| 723 | add x1,x1,#8*8 |
| 724 | |
| 725 | .Lsqr8x_tail: |
| 726 | mul x14,x6,x4 |
| 727 | adc x28,xzr,xzr // carry bit, modulo-scheduled |
| 728 | mul x15,x7,x4 |
| 729 | add x27,x27,#8 |
| 730 | mul x16,x8,x4 |
| 731 | mul x17,x9,x4 |
| 732 | adds x19,x19,x14 |
| 733 | mul x14,x10,x4 |
| 734 | adcs x20,x20,x15 |
| 735 | mul x15,x11,x4 |
| 736 | adcs x21,x21,x16 |
| 737 | mul x16,x12,x4 |
| 738 | adcs x22,x22,x17 |
| 739 | mul x17,x13,x4 |
| 740 | adcs x23,x23,x14 |
| 741 | umulh x14,x6,x4 |
| 742 | adcs x24,x24,x15 |
| 743 | umulh x15,x7,x4 |
| 744 | adcs x25,x25,x16 |
| 745 | umulh x16,x8,x4 |
| 746 | adcs x26,x26,x17 |
| 747 | umulh x17,x9,x4 |
| 748 | adc x28,x28,xzr |
| 749 | str x19,[x2],#8 |
| 750 | adds x19,x20,x14 |
| 751 | umulh x14,x10,x4 |
| 752 | adcs x20,x21,x15 |
| 753 | umulh x15,x11,x4 |
| 754 | adcs x21,x22,x16 |
| 755 | umulh x16,x12,x4 |
| 756 | adcs x22,x23,x17 |
| 757 | umulh x17,x13,x4 |
| 758 | ldr x4,[x0,x27] |
| 759 | adcs x23,x24,x14 |
| 760 | adcs x24,x25,x15 |
| 761 | adcs x25,x26,x16 |
| 762 | adcs x26,x28,x17 |
| 763 | //adc x28,xzr,xzr // moved above |
| 764 | cbnz x27,.Lsqr8x_tail |
| 765 | // note that carry flag is guaranteed |
| 766 | // to be zero at this point |
| 767 | ldp x6,x7,[x2,#8*0] |
| 768 | sub x27,x3,x1 // done yet? |
| 769 | sub x16,x3,x5 // rewinded np |
| 770 | ldp x8,x9,[x2,#8*2] |
| 771 | ldp x10,x11,[x2,#8*4] |
| 772 | ldp x12,x13,[x2,#8*6] |
| 773 | cbz x27,.Lsqr8x_tail_break |
| 774 | |
| 775 | ldr x4,[x0,#-8*8] |
| 776 | adds x19,x19,x6 |
| 777 | adcs x20,x20,x7 |
| 778 | ldp x6,x7,[x1,#8*0] |
| 779 | adcs x21,x21,x8 |
| 780 | adcs x22,x22,x9 |
| 781 | ldp x8,x9,[x1,#8*2] |
| 782 | adcs x23,x23,x10 |
| 783 | adcs x24,x24,x11 |
| 784 | ldp x10,x11,[x1,#8*4] |
| 785 | adcs x25,x25,x12 |
| 786 | mov x27,#-8*8 |
| 787 | adcs x26,x26,x13 |
| 788 | ldp x12,x13,[x1,#8*6] |
| 789 | add x1,x1,#8*8 |
| 790 | //adc x28,xzr,xzr // moved above |
| 791 | b .Lsqr8x_tail |
| 792 | |
| 793 | .align 4 |
| 794 | .Lsqr8x_tail_break: |
| 795 | ldr x4,[x29,#112] // pull n0 |
| 796 | add x27,x2,#8*8 // end of current t[num] window |
| 797 | |
| 798 | subs xzr,x30,#1 // "move" top-most carry to carry bit |
| 799 | adcs x14,x19,x6 |
| 800 | adcs x15,x20,x7 |
| 801 | ldp x19,x20,[x0,#8*0] |
| 802 | adcs x21,x21,x8 |
| 803 | ldp x6,x7,[x16,#8*0] // recall that x16 is &n[0] |
| 804 | adcs x22,x22,x9 |
| 805 | ldp x8,x9,[x16,#8*2] |
| 806 | adcs x23,x23,x10 |
| 807 | adcs x24,x24,x11 |
| 808 | ldp x10,x11,[x16,#8*4] |
| 809 | adcs x25,x25,x12 |
| 810 | adcs x26,x26,x13 |
| 811 | ldp x12,x13,[x16,#8*6] |
| 812 | add x1,x16,#8*8 |
| 813 | adc x30,xzr,xzr // top-most carry |
| 814 | mul x28,x4,x19 |
| 815 | stp x14,x15,[x2,#8*0] |
| 816 | stp x21,x22,[x2,#8*2] |
| 817 | ldp x21,x22,[x0,#8*2] |
| 818 | stp x23,x24,[x2,#8*4] |
| 819 | ldp x23,x24,[x0,#8*4] |
| 820 | cmp x27,x29 // did we hit the bottom? |
| 821 | stp x25,x26,[x2,#8*6] |
| 822 | mov x2,x0 // slide the window |
| 823 | ldp x25,x26,[x0,#8*6] |
| 824 | mov x27,#8 |
| 825 | b.ne .Lsqr8x_reduction |
| 826 | |
| 827 | // Final step. We see if result is larger than modulus, and |
| 828 | // if it is, subtract the modulus. But comparison implies |
| 829 | // subtraction. So we subtract modulus, see if it borrowed, |
| 830 | // and conditionally copy original value. |
| 831 | ldr x0,[x29,#96] // pull rp |
| 832 | add x2,x2,#8*8 |
| 833 | subs x14,x19,x6 |
| 834 | sbcs x15,x20,x7 |
| 835 | sub x27,x5,#8*8 |
| 836 | mov x3,x0 // x0 copy |
| 837 | |
| 838 | .Lsqr8x_sub: |
| 839 | sbcs x16,x21,x8 |
| 840 | ldp x6,x7,[x1,#8*0] |
| 841 | sbcs x17,x22,x9 |
| 842 | stp x14,x15,[x0,#8*0] |
| 843 | sbcs x14,x23,x10 |
| 844 | ldp x8,x9,[x1,#8*2] |
| 845 | sbcs x15,x24,x11 |
| 846 | stp x16,x17,[x0,#8*2] |
| 847 | sbcs x16,x25,x12 |
| 848 | ldp x10,x11,[x1,#8*4] |
| 849 | sbcs x17,x26,x13 |
| 850 | ldp x12,x13,[x1,#8*6] |
| 851 | add x1,x1,#8*8 |
| 852 | ldp x19,x20,[x2,#8*0] |
| 853 | sub x27,x27,#8*8 |
| 854 | ldp x21,x22,[x2,#8*2] |
| 855 | ldp x23,x24,[x2,#8*4] |
| 856 | ldp x25,x26,[x2,#8*6] |
| 857 | add x2,x2,#8*8 |
| 858 | stp x14,x15,[x0,#8*4] |
| 859 | sbcs x14,x19,x6 |
| 860 | stp x16,x17,[x0,#8*6] |
| 861 | add x0,x0,#8*8 |
| 862 | sbcs x15,x20,x7 |
| 863 | cbnz x27,.Lsqr8x_sub |
| 864 | |
| 865 | sbcs x16,x21,x8 |
| 866 | mov x2,sp |
| 867 | add x1,sp,x5 |
| 868 | ldp x6,x7,[x3,#8*0] |
| 869 | sbcs x17,x22,x9 |
| 870 | stp x14,x15,[x0,#8*0] |
| 871 | sbcs x14,x23,x10 |
| 872 | ldp x8,x9,[x3,#8*2] |
| 873 | sbcs x15,x24,x11 |
| 874 | stp x16,x17,[x0,#8*2] |
| 875 | sbcs x16,x25,x12 |
| 876 | ldp x19,x20,[x1,#8*0] |
| 877 | sbcs x17,x26,x13 |
| 878 | ldp x21,x22,[x1,#8*2] |
| 879 | sbcs xzr,x30,xzr // did it borrow? |
| 880 | ldr x30,[x29,#8] // pull return address |
| 881 | stp x14,x15,[x0,#8*4] |
| 882 | stp x16,x17,[x0,#8*6] |
| 883 | |
| 884 | sub x27,x5,#8*4 |
| 885 | .Lsqr4x_cond_copy: |
| 886 | sub x27,x27,#8*4 |
| 887 | csel x14,x19,x6,lo |
| 888 | stp xzr,xzr,[x2,#8*0] |
| 889 | csel x15,x20,x7,lo |
| 890 | ldp x6,x7,[x3,#8*4] |
| 891 | ldp x19,x20,[x1,#8*4] |
| 892 | csel x16,x21,x8,lo |
| 893 | stp xzr,xzr,[x2,#8*2] |
| 894 | add x2,x2,#8*4 |
| 895 | csel x17,x22,x9,lo |
| 896 | ldp x8,x9,[x3,#8*6] |
| 897 | ldp x21,x22,[x1,#8*6] |
| 898 | add x1,x1,#8*4 |
| 899 | stp x14,x15,[x3,#8*0] |
| 900 | stp x16,x17,[x3,#8*2] |
| 901 | add x3,x3,#8*4 |
| 902 | stp xzr,xzr,[x1,#8*0] |
| 903 | stp xzr,xzr,[x1,#8*2] |
| 904 | cbnz x27,.Lsqr4x_cond_copy |
| 905 | |
| 906 | csel x14,x19,x6,lo |
| 907 | stp xzr,xzr,[x2,#8*0] |
| 908 | csel x15,x20,x7,lo |
| 909 | stp xzr,xzr,[x2,#8*2] |
| 910 | csel x16,x21,x8,lo |
| 911 | csel x17,x22,x9,lo |
| 912 | stp x14,x15,[x3,#8*0] |
| 913 | stp x16,x17,[x3,#8*2] |
| 914 | |
| 915 | b .Lsqr8x_done |
| 916 | |
| 917 | .align 4 |
| 918 | .Lsqr8x8_post_condition: |
| 919 | adc x28,xzr,xzr |
| 920 | ldr x30,[x29,#8] // pull return address |
| 921 | // x19-7,x28 hold result, x6-7 hold modulus |
| 922 | subs x6,x19,x6 |
| 923 | ldr x1,[x29,#96] // pull rp |
| 924 | sbcs x7,x20,x7 |
| 925 | stp xzr,xzr,[sp,#8*0] |
| 926 | sbcs x8,x21,x8 |
| 927 | stp xzr,xzr,[sp,#8*2] |
| 928 | sbcs x9,x22,x9 |
| 929 | stp xzr,xzr,[sp,#8*4] |
| 930 | sbcs x10,x23,x10 |
| 931 | stp xzr,xzr,[sp,#8*6] |
| 932 | sbcs x11,x24,x11 |
| 933 | stp xzr,xzr,[sp,#8*8] |
| 934 | sbcs x12,x25,x12 |
| 935 | stp xzr,xzr,[sp,#8*10] |
| 936 | sbcs x13,x26,x13 |
| 937 | stp xzr,xzr,[sp,#8*12] |
| 938 | sbcs x28,x28,xzr // did it borrow? |
| 939 | stp xzr,xzr,[sp,#8*14] |
| 940 | |
| 941 | // x6-7 hold result-modulus |
| 942 | csel x6,x19,x6,lo |
| 943 | csel x7,x20,x7,lo |
| 944 | csel x8,x21,x8,lo |
| 945 | csel x9,x22,x9,lo |
| 946 | stp x6,x7,[x1,#8*0] |
| 947 | csel x10,x23,x10,lo |
| 948 | csel x11,x24,x11,lo |
| 949 | stp x8,x9,[x1,#8*2] |
| 950 | csel x12,x25,x12,lo |
| 951 | csel x13,x26,x13,lo |
| 952 | stp x10,x11,[x1,#8*4] |
| 953 | stp x12,x13,[x1,#8*6] |
| 954 | |
| 955 | .Lsqr8x_done: |
| 956 | ldp x19,x20,[x29,#16] |
| 957 | mov sp,x29 |
| 958 | ldp x21,x22,[x29,#32] |
| 959 | mov x0,#1 |
| 960 | ldp x23,x24,[x29,#48] |
| 961 | ldp x25,x26,[x29,#64] |
| 962 | ldp x27,x28,[x29,#80] |
| 963 | ldr x29,[sp],#128 |
| 964 | ret |
| 965 | .size __bn_sqr8x_mont,.-__bn_sqr8x_mont |
| 966 | .type __bn_mul4x_mont,%function |
| 967 | .align 5 |
| 968 | __bn_mul4x_mont: |
| 969 | stp x29,x30,[sp,#-128]! |
| 970 | add x29,sp,#0 |
| 971 | stp x19,x20,[sp,#16] |
| 972 | stp x21,x22,[sp,#32] |
| 973 | stp x23,x24,[sp,#48] |
| 974 | stp x25,x26,[sp,#64] |
| 975 | stp x27,x28,[sp,#80] |
| 976 | |
| 977 | sub x26,sp,x5,lsl#3 |
| 978 | lsl x5,x5,#3 |
| 979 | ldr x4,[x4] // *n0 |
| 980 | sub sp,x26,#8*4 // alloca |
| 981 | |
| 982 | add x10,x2,x5 |
| 983 | add x27,x1,x5 |
| 984 | stp x0,x10,[x29,#96] // offload rp and &b[num] |
| 985 | |
| 986 | ldr x24,[x2,#8*0] // b[0] |
| 987 | ldp x6,x7,[x1,#8*0] // a[0..3] |
| 988 | ldp x8,x9,[x1,#8*2] |
| 989 | add x1,x1,#8*4 |
| 990 | mov x19,xzr |
| 991 | mov x20,xzr |
| 992 | mov x21,xzr |
| 993 | mov x22,xzr |
| 994 | ldp x14,x15,[x3,#8*0] // n[0..3] |
| 995 | ldp x16,x17,[x3,#8*2] |
| 996 | adds x3,x3,#8*4 // clear carry bit |
| 997 | mov x0,xzr |
| 998 | mov x28,#0 |
| 999 | mov x26,sp |
| 1000 | |
| 1001 | .Loop_mul4x_1st_reduction: |
| 1002 | mul x10,x6,x24 // lo(a[0..3]*b[0]) |
| 1003 | adc x0,x0,xzr // modulo-scheduled |
| 1004 | mul x11,x7,x24 |
| 1005 | add x28,x28,#8 |
| 1006 | mul x12,x8,x24 |
| 1007 | and x28,x28,#31 |
| 1008 | mul x13,x9,x24 |
| 1009 | adds x19,x19,x10 |
| 1010 | umulh x10,x6,x24 // hi(a[0..3]*b[0]) |
| 1011 | adcs x20,x20,x11 |
| 1012 | mul x25,x19,x4 // t[0]*n0 |
| 1013 | adcs x21,x21,x12 |
| 1014 | umulh x11,x7,x24 |
| 1015 | adcs x22,x22,x13 |
| 1016 | umulh x12,x8,x24 |
| 1017 | adc x23,xzr,xzr |
| 1018 | umulh x13,x9,x24 |
| 1019 | ldr x24,[x2,x28] // next b[i] (or b[0]) |
| 1020 | adds x20,x20,x10 |
| 1021 | // (*) mul x10,x14,x25 // lo(n[0..3]*t[0]*n0) |
| 1022 | str x25,[x26],#8 // put aside t[0]*n0 for tail processing |
| 1023 | adcs x21,x21,x11 |
| 1024 | mul x11,x15,x25 |
| 1025 | adcs x22,x22,x12 |
| 1026 | mul x12,x16,x25 |
| 1027 | adc x23,x23,x13 // can't overflow |
| 1028 | mul x13,x17,x25 |
| 1029 | // (*) adds xzr,x19,x10 |
| 1030 | subs xzr,x19,#1 // (*) |
| 1031 | umulh x10,x14,x25 // hi(n[0..3]*t[0]*n0) |
| 1032 | adcs x19,x20,x11 |
| 1033 | umulh x11,x15,x25 |
| 1034 | adcs x20,x21,x12 |
| 1035 | umulh x12,x16,x25 |
| 1036 | adcs x21,x22,x13 |
| 1037 | umulh x13,x17,x25 |
| 1038 | adcs x22,x23,x0 |
| 1039 | adc x0,xzr,xzr |
| 1040 | adds x19,x19,x10 |
| 1041 | sub x10,x27,x1 |
| 1042 | adcs x20,x20,x11 |
| 1043 | adcs x21,x21,x12 |
| 1044 | adcs x22,x22,x13 |
| 1045 | //adc x0,x0,xzr |
| 1046 | cbnz x28,.Loop_mul4x_1st_reduction |
| 1047 | |
| 1048 | cbz x10,.Lmul4x4_post_condition |
| 1049 | |
| 1050 | ldp x6,x7,[x1,#8*0] // a[4..7] |
| 1051 | ldp x8,x9,[x1,#8*2] |
| 1052 | add x1,x1,#8*4 |
| 1053 | ldr x25,[sp] // a[0]*n0 |
| 1054 | ldp x14,x15,[x3,#8*0] // n[4..7] |
| 1055 | ldp x16,x17,[x3,#8*2] |
| 1056 | add x3,x3,#8*4 |
| 1057 | |
| 1058 | .Loop_mul4x_1st_tail: |
| 1059 | mul x10,x6,x24 // lo(a[4..7]*b[i]) |
| 1060 | adc x0,x0,xzr // modulo-scheduled |
| 1061 | mul x11,x7,x24 |
| 1062 | add x28,x28,#8 |
| 1063 | mul x12,x8,x24 |
| 1064 | and x28,x28,#31 |
| 1065 | mul x13,x9,x24 |
| 1066 | adds x19,x19,x10 |
| 1067 | umulh x10,x6,x24 // hi(a[4..7]*b[i]) |
| 1068 | adcs x20,x20,x11 |
| 1069 | umulh x11,x7,x24 |
| 1070 | adcs x21,x21,x12 |
| 1071 | umulh x12,x8,x24 |
| 1072 | adcs x22,x22,x13 |
| 1073 | umulh x13,x9,x24 |
| 1074 | adc x23,xzr,xzr |
| 1075 | ldr x24,[x2,x28] // next b[i] (or b[0]) |
| 1076 | adds x20,x20,x10 |
| 1077 | mul x10,x14,x25 // lo(n[4..7]*a[0]*n0) |
| 1078 | adcs x21,x21,x11 |
| 1079 | mul x11,x15,x25 |
| 1080 | adcs x22,x22,x12 |
| 1081 | mul x12,x16,x25 |
| 1082 | adc x23,x23,x13 // can't overflow |
| 1083 | mul x13,x17,x25 |
| 1084 | adds x19,x19,x10 |
| 1085 | umulh x10,x14,x25 // hi(n[4..7]*a[0]*n0) |
| 1086 | adcs x20,x20,x11 |
| 1087 | umulh x11,x15,x25 |
| 1088 | adcs x21,x21,x12 |
| 1089 | umulh x12,x16,x25 |
| 1090 | adcs x22,x22,x13 |
| 1091 | adcs x23,x23,x0 |
| 1092 | umulh x13,x17,x25 |
| 1093 | adc x0,xzr,xzr |
| 1094 | ldr x25,[sp,x28] // next t[0]*n0 |
| 1095 | str x19,[x26],#8 // result!!! |
| 1096 | adds x19,x20,x10 |
| 1097 | sub x10,x27,x1 // done yet? |
| 1098 | adcs x20,x21,x11 |
| 1099 | adcs x21,x22,x12 |
| 1100 | adcs x22,x23,x13 |
| 1101 | //adc x0,x0,xzr |
| 1102 | cbnz x28,.Loop_mul4x_1st_tail |
| 1103 | |
| 1104 | sub x11,x27,x5 // rewinded x1 |
| 1105 | cbz x10,.Lmul4x_proceed |
| 1106 | |
| 1107 | ldp x6,x7,[x1,#8*0] |
| 1108 | ldp x8,x9,[x1,#8*2] |
| 1109 | add x1,x1,#8*4 |
| 1110 | ldp x14,x15,[x3,#8*0] |
| 1111 | ldp x16,x17,[x3,#8*2] |
| 1112 | add x3,x3,#8*4 |
| 1113 | b .Loop_mul4x_1st_tail |
| 1114 | |
| 1115 | .align 5 |
| 1116 | .Lmul4x_proceed: |
| 1117 | ldr x24,[x2,#8*4]! // *++b |
| 1118 | adc x30,x0,xzr |
| 1119 | ldp x6,x7,[x11,#8*0] // a[0..3] |
| 1120 | sub x3,x3,x5 // rewind np |
| 1121 | ldp x8,x9,[x11,#8*2] |
| 1122 | add x1,x11,#8*4 |
| 1123 | |
| 1124 | stp x19,x20,[x26,#8*0] // result!!! |
| 1125 | ldp x19,x20,[sp,#8*4] // t[0..3] |
| 1126 | stp x21,x22,[x26,#8*2] // result!!! |
| 1127 | ldp x21,x22,[sp,#8*6] |
| 1128 | |
| 1129 | ldp x14,x15,[x3,#8*0] // n[0..3] |
| 1130 | mov x26,sp |
| 1131 | ldp x16,x17,[x3,#8*2] |
| 1132 | adds x3,x3,#8*4 // clear carry bit |
| 1133 | mov x0,xzr |
| 1134 | |
| 1135 | .align 4 |
| 1136 | .Loop_mul4x_reduction: |
| 1137 | mul x10,x6,x24 // lo(a[0..3]*b[4]) |
| 1138 | adc x0,x0,xzr // modulo-scheduled |
| 1139 | mul x11,x7,x24 |
| 1140 | add x28,x28,#8 |
| 1141 | mul x12,x8,x24 |
| 1142 | and x28,x28,#31 |
| 1143 | mul x13,x9,x24 |
| 1144 | adds x19,x19,x10 |
| 1145 | umulh x10,x6,x24 // hi(a[0..3]*b[4]) |
| 1146 | adcs x20,x20,x11 |
| 1147 | mul x25,x19,x4 // t[0]*n0 |
| 1148 | adcs x21,x21,x12 |
| 1149 | umulh x11,x7,x24 |
| 1150 | adcs x22,x22,x13 |
| 1151 | umulh x12,x8,x24 |
| 1152 | adc x23,xzr,xzr |
| 1153 | umulh x13,x9,x24 |
| 1154 | ldr x24,[x2,x28] // next b[i] |
| 1155 | adds x20,x20,x10 |
| 1156 | // (*) mul x10,x14,x25 |
| 1157 | str x25,[x26],#8 // put aside t[0]*n0 for tail processing |
| 1158 | adcs x21,x21,x11 |
| 1159 | mul x11,x15,x25 // lo(n[0..3]*t[0]*n0 |
| 1160 | adcs x22,x22,x12 |
| 1161 | mul x12,x16,x25 |
| 1162 | adc x23,x23,x13 // can't overflow |
| 1163 | mul x13,x17,x25 |
| 1164 | // (*) adds xzr,x19,x10 |
| 1165 | subs xzr,x19,#1 // (*) |
| 1166 | umulh x10,x14,x25 // hi(n[0..3]*t[0]*n0 |
| 1167 | adcs x19,x20,x11 |
| 1168 | umulh x11,x15,x25 |
| 1169 | adcs x20,x21,x12 |
| 1170 | umulh x12,x16,x25 |
| 1171 | adcs x21,x22,x13 |
| 1172 | umulh x13,x17,x25 |
| 1173 | adcs x22,x23,x0 |
| 1174 | adc x0,xzr,xzr |
| 1175 | adds x19,x19,x10 |
| 1176 | adcs x20,x20,x11 |
| 1177 | adcs x21,x21,x12 |
| 1178 | adcs x22,x22,x13 |
| 1179 | //adc x0,x0,xzr |
| 1180 | cbnz x28,.Loop_mul4x_reduction |
| 1181 | |
| 1182 | adc x0,x0,xzr |
| 1183 | ldp x10,x11,[x26,#8*4] // t[4..7] |
| 1184 | ldp x12,x13,[x26,#8*6] |
| 1185 | ldp x6,x7,[x1,#8*0] // a[4..7] |
| 1186 | ldp x8,x9,[x1,#8*2] |
| 1187 | add x1,x1,#8*4 |
| 1188 | adds x19,x19,x10 |
| 1189 | adcs x20,x20,x11 |
| 1190 | adcs x21,x21,x12 |
| 1191 | adcs x22,x22,x13 |
| 1192 | //adc x0,x0,xzr |
| 1193 | |
| 1194 | ldr x25,[sp] // t[0]*n0 |
| 1195 | ldp x14,x15,[x3,#8*0] // n[4..7] |
| 1196 | ldp x16,x17,[x3,#8*2] |
| 1197 | add x3,x3,#8*4 |
| 1198 | |
| 1199 | .align 4 |
| 1200 | .Loop_mul4x_tail: |
| 1201 | mul x10,x6,x24 // lo(a[4..7]*b[4]) |
| 1202 | adc x0,x0,xzr // modulo-scheduled |
| 1203 | mul x11,x7,x24 |
| 1204 | add x28,x28,#8 |
| 1205 | mul x12,x8,x24 |
| 1206 | and x28,x28,#31 |
| 1207 | mul x13,x9,x24 |
| 1208 | adds x19,x19,x10 |
| 1209 | umulh x10,x6,x24 // hi(a[4..7]*b[4]) |
| 1210 | adcs x20,x20,x11 |
| 1211 | umulh x11,x7,x24 |
| 1212 | adcs x21,x21,x12 |
| 1213 | umulh x12,x8,x24 |
| 1214 | adcs x22,x22,x13 |
| 1215 | umulh x13,x9,x24 |
| 1216 | adc x23,xzr,xzr |
| 1217 | ldr x24,[x2,x28] // next b[i] |
| 1218 | adds x20,x20,x10 |
| 1219 | mul x10,x14,x25 // lo(n[4..7]*t[0]*n0) |
| 1220 | adcs x21,x21,x11 |
| 1221 | mul x11,x15,x25 |
| 1222 | adcs x22,x22,x12 |
| 1223 | mul x12,x16,x25 |
| 1224 | adc x23,x23,x13 // can't overflow |
| 1225 | mul x13,x17,x25 |
| 1226 | adds x19,x19,x10 |
| 1227 | umulh x10,x14,x25 // hi(n[4..7]*t[0]*n0) |
| 1228 | adcs x20,x20,x11 |
| 1229 | umulh x11,x15,x25 |
| 1230 | adcs x21,x21,x12 |
| 1231 | umulh x12,x16,x25 |
| 1232 | adcs x22,x22,x13 |
| 1233 | umulh x13,x17,x25 |
| 1234 | adcs x23,x23,x0 |
| 1235 | ldr x25,[sp,x28] // next a[0]*n0 |
| 1236 | adc x0,xzr,xzr |
| 1237 | str x19,[x26],#8 // result!!! |
| 1238 | adds x19,x20,x10 |
| 1239 | sub x10,x27,x1 // done yet? |
| 1240 | adcs x20,x21,x11 |
| 1241 | adcs x21,x22,x12 |
| 1242 | adcs x22,x23,x13 |
| 1243 | //adc x0,x0,xzr |
| 1244 | cbnz x28,.Loop_mul4x_tail |
| 1245 | |
| 1246 | sub x11,x3,x5 // rewinded np? |
| 1247 | adc x0,x0,xzr |
| 1248 | cbz x10,.Loop_mul4x_break |
| 1249 | |
| 1250 | ldp x10,x11,[x26,#8*4] |
| 1251 | ldp x12,x13,[x26,#8*6] |
| 1252 | ldp x6,x7,[x1,#8*0] |
| 1253 | ldp x8,x9,[x1,#8*2] |
| 1254 | add x1,x1,#8*4 |
| 1255 | adds x19,x19,x10 |
| 1256 | adcs x20,x20,x11 |
| 1257 | adcs x21,x21,x12 |
| 1258 | adcs x22,x22,x13 |
| 1259 | //adc x0,x0,xzr |
| 1260 | ldp x14,x15,[x3,#8*0] |
| 1261 | ldp x16,x17,[x3,#8*2] |
| 1262 | add x3,x3,#8*4 |
| 1263 | b .Loop_mul4x_tail |
| 1264 | |
| 1265 | .align 4 |
| 1266 | .Loop_mul4x_break: |
| 1267 | ldp x12,x13,[x29,#96] // pull rp and &b[num] |
| 1268 | adds x19,x19,x30 |
| 1269 | add x2,x2,#8*4 // bp++ |
| 1270 | adcs x20,x20,xzr |
| 1271 | sub x1,x1,x5 // rewind ap |
| 1272 | adcs x21,x21,xzr |
| 1273 | stp x19,x20,[x26,#8*0] // result!!! |
| 1274 | adcs x22,x22,xzr |
| 1275 | ldp x19,x20,[sp,#8*4] // t[0..3] |
| 1276 | adc x30,x0,xzr |
| 1277 | stp x21,x22,[x26,#8*2] // result!!! |
| 1278 | cmp x2,x13 // done yet? |
| 1279 | ldp x21,x22,[sp,#8*6] |
| 1280 | ldp x14,x15,[x11,#8*0] // n[0..3] |
| 1281 | ldp x16,x17,[x11,#8*2] |
| 1282 | add x3,x11,#8*4 |
| 1283 | b.eq .Lmul4x_post |
| 1284 | |
| 1285 | ldr x24,[x2] |
| 1286 | ldp x6,x7,[x1,#8*0] // a[0..3] |
| 1287 | ldp x8,x9,[x1,#8*2] |
| 1288 | adds x1,x1,#8*4 // clear carry bit |
| 1289 | mov x0,xzr |
| 1290 | mov x26,sp |
| 1291 | b .Loop_mul4x_reduction |
| 1292 | |
| 1293 | .align 4 |
| 1294 | .Lmul4x_post: |
| 1295 | // Final step. We see if result is larger than modulus, and |
| 1296 | // if it is, subtract the modulus. But comparison implies |
| 1297 | // subtraction. So we subtract modulus, see if it borrowed, |
| 1298 | // and conditionally copy original value. |
| 1299 | mov x0,x12 |
| 1300 | mov x27,x12 // x0 copy |
| 1301 | subs x10,x19,x14 |
| 1302 | add x26,sp,#8*8 |
| 1303 | sbcs x11,x20,x15 |
| 1304 | sub x28,x5,#8*4 |
| 1305 | |
| 1306 | .Lmul4x_sub: |
| 1307 | sbcs x12,x21,x16 |
| 1308 | ldp x14,x15,[x3,#8*0] |
| 1309 | sub x28,x28,#8*4 |
| 1310 | ldp x19,x20,[x26,#8*0] |
| 1311 | sbcs x13,x22,x17 |
| 1312 | ldp x16,x17,[x3,#8*2] |
| 1313 | add x3,x3,#8*4 |
| 1314 | ldp x21,x22,[x26,#8*2] |
| 1315 | add x26,x26,#8*4 |
| 1316 | stp x10,x11,[x0,#8*0] |
| 1317 | sbcs x10,x19,x14 |
| 1318 | stp x12,x13,[x0,#8*2] |
| 1319 | add x0,x0,#8*4 |
| 1320 | sbcs x11,x20,x15 |
| 1321 | cbnz x28,.Lmul4x_sub |
| 1322 | |
| 1323 | sbcs x12,x21,x16 |
| 1324 | mov x26,sp |
| 1325 | add x1,sp,#8*4 |
| 1326 | ldp x6,x7,[x27,#8*0] |
| 1327 | sbcs x13,x22,x17 |
| 1328 | stp x10,x11,[x0,#8*0] |
| 1329 | ldp x8,x9,[x27,#8*2] |
| 1330 | stp x12,x13,[x0,#8*2] |
| 1331 | ldp x19,x20,[x1,#8*0] |
| 1332 | ldp x21,x22,[x1,#8*2] |
| 1333 | sbcs xzr,x30,xzr // did it borrow? |
| 1334 | ldr x30,[x29,#8] // pull return address |
| 1335 | |
| 1336 | sub x28,x5,#8*4 |
| 1337 | .Lmul4x_cond_copy: |
| 1338 | sub x28,x28,#8*4 |
| 1339 | csel x10,x19,x6,lo |
| 1340 | stp xzr,xzr,[x26,#8*0] |
| 1341 | csel x11,x20,x7,lo |
| 1342 | ldp x6,x7,[x27,#8*4] |
| 1343 | ldp x19,x20,[x1,#8*4] |
| 1344 | csel x12,x21,x8,lo |
| 1345 | stp xzr,xzr,[x26,#8*2] |
| 1346 | add x26,x26,#8*4 |
| 1347 | csel x13,x22,x9,lo |
| 1348 | ldp x8,x9,[x27,#8*6] |
| 1349 | ldp x21,x22,[x1,#8*6] |
| 1350 | add x1,x1,#8*4 |
| 1351 | stp x10,x11,[x27,#8*0] |
| 1352 | stp x12,x13,[x27,#8*2] |
| 1353 | add x27,x27,#8*4 |
| 1354 | cbnz x28,.Lmul4x_cond_copy |
| 1355 | |
| 1356 | csel x10,x19,x6,lo |
| 1357 | stp xzr,xzr,[x26,#8*0] |
| 1358 | csel x11,x20,x7,lo |
| 1359 | stp xzr,xzr,[x26,#8*2] |
| 1360 | csel x12,x21,x8,lo |
| 1361 | stp xzr,xzr,[x26,#8*3] |
| 1362 | csel x13,x22,x9,lo |
| 1363 | stp xzr,xzr,[x26,#8*4] |
| 1364 | stp x10,x11,[x27,#8*0] |
| 1365 | stp x12,x13,[x27,#8*2] |
| 1366 | |
| 1367 | b .Lmul4x_done |
| 1368 | |
| 1369 | .align 4 |
| 1370 | .Lmul4x4_post_condition: |
| 1371 | adc x0,x0,xzr |
| 1372 | ldr x1,[x29,#96] // pull rp |
| 1373 | // x19-3,x0 hold result, x14-7 hold modulus |
| 1374 | subs x6,x19,x14 |
| 1375 | ldr x30,[x29,#8] // pull return address |
| 1376 | sbcs x7,x20,x15 |
| 1377 | stp xzr,xzr,[sp,#8*0] |
| 1378 | sbcs x8,x21,x16 |
| 1379 | stp xzr,xzr,[sp,#8*2] |
| 1380 | sbcs x9,x22,x17 |
| 1381 | stp xzr,xzr,[sp,#8*4] |
| 1382 | sbcs xzr,x0,xzr // did it borrow? |
| 1383 | stp xzr,xzr,[sp,#8*6] |
| 1384 | |
| 1385 | // x6-3 hold result-modulus |
| 1386 | csel x6,x19,x6,lo |
| 1387 | csel x7,x20,x7,lo |
| 1388 | csel x8,x21,x8,lo |
| 1389 | csel x9,x22,x9,lo |
| 1390 | stp x6,x7,[x1,#8*0] |
| 1391 | stp x8,x9,[x1,#8*2] |
| 1392 | |
| 1393 | .Lmul4x_done: |
| 1394 | ldp x19,x20,[x29,#16] |
| 1395 | mov sp,x29 |
| 1396 | ldp x21,x22,[x29,#32] |
| 1397 | mov x0,#1 |
| 1398 | ldp x23,x24,[x29,#48] |
| 1399 | ldp x25,x26,[x29,#64] |
| 1400 | ldp x27,x28,[x29,#80] |
| 1401 | ldr x29,[sp],#128 |
| 1402 | ret |
| 1403 | .size __bn_mul4x_mont,.-__bn_mul4x_mont |
| 1404 | .byte 77,111,110,116,103,111,109,101,114,121,32,77,117,108,116,105,112,108,105,99,97,116,105,111,110,32,102,111,114,32,65,82,77,118,56,44,32,67,82,89,80,84,79,71,65,77,83,32,98,121,32,60,97,112,112,114,111,64,111,112,101,110,115,115,108,46,111,114,103,62,0 |
| 1405 | .align 2 |
| 1406 | .align 4 |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1407 | #endif |