Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1 | #!/usr/bin/env perl |
| 2 | |
| 3 | # ==================================================================== |
| 4 | # Written by Andy Polyakov <appro@openssl.org> for the OpenSSL |
| 5 | # project. The module is, however, dual licensed under OpenSSL and |
| 6 | # CRYPTOGAMS licenses depending on where you obtain it. For further |
| 7 | # details see http://www.openssl.org/~appro/cryptogams/. |
| 8 | # ==================================================================== |
| 9 | |
| 10 | # March 2015 |
| 11 | # |
| 12 | # "Teaser" Montgomery multiplication module for ARMv8. Needs more |
| 13 | # work. While it does improve RSA sign performance by 20-30% (less for |
| 14 | # longer keys) on most processors, for some reason RSA2048 is not |
| 15 | # faster and RSA4096 goes 15-20% slower on Cortex-A57. Multiplication |
| 16 | # instruction issue rate is limited on processor in question, meaning |
| 17 | # that dedicated squaring procedure is a must. Well, actually all |
| 18 | # contemporary AArch64 processors seem to have limited multiplication |
| 19 | # issue rate, i.e. they can't issue multiplication every cycle, which |
| 20 | # explains moderate improvement coefficients in comparison to |
| 21 | # compiler-generated code. Recall that compiler is instructed to use |
| 22 | # umulh and therefore uses same amount of multiplication instructions |
| 23 | # to do the job. Assembly's edge is to minimize number of "collateral" |
| 24 | # instructions and of course instruction scheduling. |
| 25 | # |
| 26 | # April 2015 |
| 27 | # |
| 28 | # Squaring procedure that handles lengths divisible by 8 improves |
| 29 | # RSA/DSA performance by 25-40-60% depending on processor and key |
| 30 | # length. Overall improvement coefficients are always positive in |
| 31 | # comparison to compiler-generated code. On Cortex-A57 improvement |
| 32 | # is still modest on longest key lengths, while others exhibit e.g. |
| 33 | # 50-70% improvement for RSA4096 sign. RSA2048 sign is ~25% faster |
| 34 | # on Cortex-A57 and ~60-100% faster on others. |
| 35 | |
| 36 | $flavour = shift; |
| 37 | $output = shift; |
| 38 | |
| 39 | $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; |
| 40 | ( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or |
| 41 | ( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or |
| 42 | die "can't locate arm-xlate.pl"; |
| 43 | |
| 44 | open OUT,"| \"$^X\" $xlate $flavour $output"; |
| 45 | *STDOUT=*OUT; |
| 46 | |
| 47 | ($lo0,$hi0,$aj,$m0,$alo,$ahi, |
| 48 | $lo1,$hi1,$nj,$m1,$nlo,$nhi, |
| 49 | $ovf, $i,$j,$tp,$tj) = map("x$_",6..17,19..24); |
| 50 | |
| 51 | # int bn_mul_mont( |
| 52 | $rp="x0"; # BN_ULONG *rp, |
| 53 | $ap="x1"; # const BN_ULONG *ap, |
| 54 | $bp="x2"; # const BN_ULONG *bp, |
| 55 | $np="x3"; # const BN_ULONG *np, |
| 56 | $n0="x4"; # const BN_ULONG *n0, |
| 57 | $num="x5"; # int num); |
| 58 | |
| 59 | $code.=<<___; |
| 60 | .text |
| 61 | |
| 62 | .globl bn_mul_mont |
| 63 | .type bn_mul_mont,%function |
| 64 | .align 5 |
| 65 | bn_mul_mont: |
| 66 | tst $num,#7 |
| 67 | b.eq __bn_sqr8x_mont |
| 68 | tst $num,#3 |
| 69 | b.eq __bn_mul4x_mont |
| 70 | .Lmul_mont: |
| 71 | stp x29,x30,[sp,#-64]! |
| 72 | add x29,sp,#0 |
| 73 | stp x19,x20,[sp,#16] |
| 74 | stp x21,x22,[sp,#32] |
| 75 | stp x23,x24,[sp,#48] |
| 76 | |
| 77 | ldr $m0,[$bp],#8 // bp[0] |
| 78 | sub $tp,sp,$num,lsl#3 |
| 79 | ldp $hi0,$aj,[$ap],#16 // ap[0..1] |
| 80 | lsl $num,$num,#3 |
| 81 | ldr $n0,[$n0] // *n0 |
| 82 | and $tp,$tp,#-16 // ABI says so |
| 83 | ldp $hi1,$nj,[$np],#16 // np[0..1] |
| 84 | |
| 85 | mul $lo0,$hi0,$m0 // ap[0]*bp[0] |
| 86 | sub $j,$num,#16 // j=num-2 |
| 87 | umulh $hi0,$hi0,$m0 |
| 88 | mul $alo,$aj,$m0 // ap[1]*bp[0] |
| 89 | umulh $ahi,$aj,$m0 |
| 90 | |
| 91 | mul $m1,$lo0,$n0 // "tp[0]"*n0 |
| 92 | mov sp,$tp // alloca |
| 93 | |
| 94 | // (*) mul $lo1,$hi1,$m1 // np[0]*m1 |
| 95 | umulh $hi1,$hi1,$m1 |
| 96 | mul $nlo,$nj,$m1 // np[1]*m1 |
| 97 | // (*) adds $lo1,$lo1,$lo0 // discarded |
| 98 | // (*) As for removal of first multiplication and addition |
| 99 | // instructions. The outcome of first addition is |
| 100 | // guaranteed to be zero, which leaves two computationally |
| 101 | // significant outcomes: it either carries or not. Then |
| 102 | // question is when does it carry? Is there alternative |
| 103 | // way to deduce it? If you follow operations, you can |
| 104 | // observe that condition for carry is quite simple: |
| 105 | // $lo0 being non-zero. So that carry can be calculated |
| 106 | // by adding -1 to $lo0. That's what next instruction does. |
| 107 | subs xzr,$lo0,#1 // (*) |
| 108 | umulh $nhi,$nj,$m1 |
| 109 | adc $hi1,$hi1,xzr |
| 110 | cbz $j,.L1st_skip |
| 111 | |
| 112 | .L1st: |
| 113 | ldr $aj,[$ap],#8 |
| 114 | adds $lo0,$alo,$hi0 |
| 115 | sub $j,$j,#8 // j-- |
| 116 | adc $hi0,$ahi,xzr |
| 117 | |
| 118 | ldr $nj,[$np],#8 |
| 119 | adds $lo1,$nlo,$hi1 |
| 120 | mul $alo,$aj,$m0 // ap[j]*bp[0] |
| 121 | adc $hi1,$nhi,xzr |
| 122 | umulh $ahi,$aj,$m0 |
| 123 | |
| 124 | adds $lo1,$lo1,$lo0 |
| 125 | mul $nlo,$nj,$m1 // np[j]*m1 |
| 126 | adc $hi1,$hi1,xzr |
| 127 | umulh $nhi,$nj,$m1 |
| 128 | str $lo1,[$tp],#8 // tp[j-1] |
| 129 | cbnz $j,.L1st |
| 130 | |
| 131 | .L1st_skip: |
| 132 | adds $lo0,$alo,$hi0 |
| 133 | sub $ap,$ap,$num // rewind $ap |
| 134 | adc $hi0,$ahi,xzr |
| 135 | |
| 136 | adds $lo1,$nlo,$hi1 |
| 137 | sub $np,$np,$num // rewind $np |
| 138 | adc $hi1,$nhi,xzr |
| 139 | |
| 140 | adds $lo1,$lo1,$lo0 |
| 141 | sub $i,$num,#8 // i=num-1 |
| 142 | adcs $hi1,$hi1,$hi0 |
| 143 | |
| 144 | adc $ovf,xzr,xzr // upmost overflow bit |
| 145 | stp $lo1,$hi1,[$tp] |
| 146 | |
| 147 | .Louter: |
| 148 | ldr $m0,[$bp],#8 // bp[i] |
| 149 | ldp $hi0,$aj,[$ap],#16 |
| 150 | ldr $tj,[sp] // tp[0] |
| 151 | add $tp,sp,#8 |
| 152 | |
| 153 | mul $lo0,$hi0,$m0 // ap[0]*bp[i] |
| 154 | sub $j,$num,#16 // j=num-2 |
| 155 | umulh $hi0,$hi0,$m0 |
| 156 | ldp $hi1,$nj,[$np],#16 |
| 157 | mul $alo,$aj,$m0 // ap[1]*bp[i] |
| 158 | adds $lo0,$lo0,$tj |
| 159 | umulh $ahi,$aj,$m0 |
| 160 | adc $hi0,$hi0,xzr |
| 161 | |
| 162 | mul $m1,$lo0,$n0 |
| 163 | sub $i,$i,#8 // i-- |
| 164 | |
| 165 | // (*) mul $lo1,$hi1,$m1 // np[0]*m1 |
| 166 | umulh $hi1,$hi1,$m1 |
| 167 | mul $nlo,$nj,$m1 // np[1]*m1 |
| 168 | // (*) adds $lo1,$lo1,$lo0 |
| 169 | subs xzr,$lo0,#1 // (*) |
| 170 | umulh $nhi,$nj,$m1 |
| 171 | cbz $j,.Linner_skip |
| 172 | |
| 173 | .Linner: |
| 174 | ldr $aj,[$ap],#8 |
| 175 | adc $hi1,$hi1,xzr |
| 176 | ldr $tj,[$tp],#8 // tp[j] |
| 177 | adds $lo0,$alo,$hi0 |
| 178 | sub $j,$j,#8 // j-- |
| 179 | adc $hi0,$ahi,xzr |
| 180 | |
| 181 | adds $lo1,$nlo,$hi1 |
| 182 | ldr $nj,[$np],#8 |
| 183 | adc $hi1,$nhi,xzr |
| 184 | |
| 185 | mul $alo,$aj,$m0 // ap[j]*bp[i] |
| 186 | adds $lo0,$lo0,$tj |
| 187 | umulh $ahi,$aj,$m0 |
| 188 | adc $hi0,$hi0,xzr |
| 189 | |
| 190 | mul $nlo,$nj,$m1 // np[j]*m1 |
| 191 | adds $lo1,$lo1,$lo0 |
| 192 | umulh $nhi,$nj,$m1 |
| 193 | str $lo1,[$tp,#-16] // tp[j-1] |
| 194 | cbnz $j,.Linner |
| 195 | |
| 196 | .Linner_skip: |
| 197 | ldr $tj,[$tp],#8 // tp[j] |
| 198 | adc $hi1,$hi1,xzr |
| 199 | adds $lo0,$alo,$hi0 |
| 200 | sub $ap,$ap,$num // rewind $ap |
| 201 | adc $hi0,$ahi,xzr |
| 202 | |
| 203 | adds $lo1,$nlo,$hi1 |
| 204 | sub $np,$np,$num // rewind $np |
| 205 | adcs $hi1,$nhi,$ovf |
| 206 | adc $ovf,xzr,xzr |
| 207 | |
| 208 | adds $lo0,$lo0,$tj |
| 209 | adc $hi0,$hi0,xzr |
| 210 | |
| 211 | adds $lo1,$lo1,$lo0 |
| 212 | adcs $hi1,$hi1,$hi0 |
| 213 | adc $ovf,$ovf,xzr // upmost overflow bit |
| 214 | stp $lo1,$hi1,[$tp,#-16] |
| 215 | |
| 216 | cbnz $i,.Louter |
| 217 | |
| 218 | // Final step. We see if result is larger than modulus, and |
| 219 | // if it is, subtract the modulus. But comparison implies |
| 220 | // subtraction. So we subtract modulus, see if it borrowed, |
| 221 | // and conditionally copy original value. |
| 222 | ldr $tj,[sp] // tp[0] |
| 223 | add $tp,sp,#8 |
| 224 | ldr $nj,[$np],#8 // np[0] |
| 225 | subs $j,$num,#8 // j=num-1 and clear borrow |
| 226 | mov $ap,$rp |
| 227 | .Lsub: |
| 228 | sbcs $aj,$tj,$nj // tp[j]-np[j] |
| 229 | ldr $tj,[$tp],#8 |
| 230 | sub $j,$j,#8 // j-- |
| 231 | ldr $nj,[$np],#8 |
| 232 | str $aj,[$ap],#8 // rp[j]=tp[j]-np[j] |
| 233 | cbnz $j,.Lsub |
| 234 | |
| 235 | sbcs $aj,$tj,$nj |
| 236 | sbcs $ovf,$ovf,xzr // did it borrow? |
| 237 | str $aj,[$ap],#8 // rp[num-1] |
| 238 | |
| 239 | ldr $tj,[sp] // tp[0] |
| 240 | add $tp,sp,#8 |
| 241 | ldr $aj,[$rp],#8 // rp[0] |
| 242 | sub $num,$num,#8 // num-- |
| 243 | nop |
| 244 | .Lcond_copy: |
| 245 | sub $num,$num,#8 // num-- |
| 246 | csel $nj,$tj,$aj,lo // did it borrow? |
| 247 | ldr $tj,[$tp],#8 |
| 248 | ldr $aj,[$rp],#8 |
| 249 | str xzr,[$tp,#-16] // wipe tp |
| 250 | str $nj,[$rp,#-16] |
| 251 | cbnz $num,.Lcond_copy |
| 252 | |
| 253 | csel $nj,$tj,$aj,lo |
| 254 | str xzr,[$tp,#-8] // wipe tp |
| 255 | str $nj,[$rp,#-8] |
| 256 | |
| 257 | ldp x19,x20,[x29,#16] |
| 258 | mov sp,x29 |
| 259 | ldp x21,x22,[x29,#32] |
| 260 | mov x0,#1 |
| 261 | ldp x23,x24,[x29,#48] |
| 262 | ldr x29,[sp],#64 |
| 263 | ret |
| 264 | .size bn_mul_mont,.-bn_mul_mont |
| 265 | ___ |
| 266 | { |
| 267 | ######################################################################## |
| 268 | # Following is ARMv8 adaptation of sqrx8x_mont from x86_64-mont5 module. |
| 269 | |
| 270 | my ($a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7)=map("x$_",(6..13)); |
| 271 | my ($t0,$t1,$t2,$t3)=map("x$_",(14..17)); |
| 272 | my ($acc0,$acc1,$acc2,$acc3,$acc4,$acc5,$acc6,$acc7)=map("x$_",(19..26)); |
| 273 | my ($cnt,$carry,$topmost)=("x27","x28","x30"); |
| 274 | my ($tp,$ap_end,$na0)=($bp,$np,$carry); |
| 275 | |
| 276 | $code.=<<___; |
| 277 | .type __bn_sqr8x_mont,%function |
| 278 | .align 5 |
| 279 | __bn_sqr8x_mont: |
| 280 | cmp $ap,$bp |
| 281 | b.ne __bn_mul4x_mont |
| 282 | .Lsqr8x_mont: |
| 283 | stp x29,x30,[sp,#-128]! |
| 284 | add x29,sp,#0 |
| 285 | stp x19,x20,[sp,#16] |
| 286 | stp x21,x22,[sp,#32] |
| 287 | stp x23,x24,[sp,#48] |
| 288 | stp x25,x26,[sp,#64] |
| 289 | stp x27,x28,[sp,#80] |
| 290 | stp $rp,$np,[sp,#96] // offload rp and np |
| 291 | |
| 292 | ldp $a0,$a1,[$ap,#8*0] |
| 293 | ldp $a2,$a3,[$ap,#8*2] |
| 294 | ldp $a4,$a5,[$ap,#8*4] |
| 295 | ldp $a6,$a7,[$ap,#8*6] |
| 296 | |
| 297 | sub $tp,sp,$num,lsl#4 |
| 298 | lsl $num,$num,#3 |
| 299 | ldr $n0,[$n0] // *n0 |
| 300 | mov sp,$tp // alloca |
| 301 | sub $cnt,$num,#8*8 |
| 302 | b .Lsqr8x_zero_start |
| 303 | |
| 304 | .Lsqr8x_zero: |
| 305 | sub $cnt,$cnt,#8*8 |
| 306 | stp xzr,xzr,[$tp,#8*0] |
| 307 | stp xzr,xzr,[$tp,#8*2] |
| 308 | stp xzr,xzr,[$tp,#8*4] |
| 309 | stp xzr,xzr,[$tp,#8*6] |
| 310 | .Lsqr8x_zero_start: |
| 311 | stp xzr,xzr,[$tp,#8*8] |
| 312 | stp xzr,xzr,[$tp,#8*10] |
| 313 | stp xzr,xzr,[$tp,#8*12] |
| 314 | stp xzr,xzr,[$tp,#8*14] |
| 315 | add $tp,$tp,#8*16 |
| 316 | cbnz $cnt,.Lsqr8x_zero |
| 317 | |
| 318 | add $ap_end,$ap,$num |
| 319 | add $ap,$ap,#8*8 |
| 320 | mov $acc0,xzr |
| 321 | mov $acc1,xzr |
| 322 | mov $acc2,xzr |
| 323 | mov $acc3,xzr |
| 324 | mov $acc4,xzr |
| 325 | mov $acc5,xzr |
| 326 | mov $acc6,xzr |
| 327 | mov $acc7,xzr |
| 328 | mov $tp,sp |
| 329 | str $n0,[x29,#112] // offload n0 |
| 330 | |
| 331 | // Multiply everything but a[i]*a[i] |
| 332 | .align 4 |
| 333 | .Lsqr8x_outer_loop: |
| 334 | // a[1]a[0] (i) |
| 335 | // a[2]a[0] |
| 336 | // a[3]a[0] |
| 337 | // a[4]a[0] |
| 338 | // a[5]a[0] |
| 339 | // a[6]a[0] |
| 340 | // a[7]a[0] |
| 341 | // a[2]a[1] (ii) |
| 342 | // a[3]a[1] |
| 343 | // a[4]a[1] |
| 344 | // a[5]a[1] |
| 345 | // a[6]a[1] |
| 346 | // a[7]a[1] |
| 347 | // a[3]a[2] (iii) |
| 348 | // a[4]a[2] |
| 349 | // a[5]a[2] |
| 350 | // a[6]a[2] |
| 351 | // a[7]a[2] |
| 352 | // a[4]a[3] (iv) |
| 353 | // a[5]a[3] |
| 354 | // a[6]a[3] |
| 355 | // a[7]a[3] |
| 356 | // a[5]a[4] (v) |
| 357 | // a[6]a[4] |
| 358 | // a[7]a[4] |
| 359 | // a[6]a[5] (vi) |
| 360 | // a[7]a[5] |
| 361 | // a[7]a[6] (vii) |
| 362 | |
| 363 | mul $t0,$a1,$a0 // lo(a[1..7]*a[0]) (i) |
| 364 | mul $t1,$a2,$a0 |
| 365 | mul $t2,$a3,$a0 |
| 366 | mul $t3,$a4,$a0 |
| 367 | adds $acc1,$acc1,$t0 // t[1]+lo(a[1]*a[0]) |
| 368 | mul $t0,$a5,$a0 |
| 369 | adcs $acc2,$acc2,$t1 |
| 370 | mul $t1,$a6,$a0 |
| 371 | adcs $acc3,$acc3,$t2 |
| 372 | mul $t2,$a7,$a0 |
| 373 | adcs $acc4,$acc4,$t3 |
| 374 | umulh $t3,$a1,$a0 // hi(a[1..7]*a[0]) |
| 375 | adcs $acc5,$acc5,$t0 |
| 376 | umulh $t0,$a2,$a0 |
| 377 | adcs $acc6,$acc6,$t1 |
| 378 | umulh $t1,$a3,$a0 |
| 379 | adcs $acc7,$acc7,$t2 |
| 380 | umulh $t2,$a4,$a0 |
| 381 | stp $acc0,$acc1,[$tp],#8*2 // t[0..1] |
| 382 | adc $acc0,xzr,xzr // t[8] |
| 383 | adds $acc2,$acc2,$t3 // t[2]+lo(a[1]*a[0]) |
| 384 | umulh $t3,$a5,$a0 |
| 385 | adcs $acc3,$acc3,$t0 |
| 386 | umulh $t0,$a6,$a0 |
| 387 | adcs $acc4,$acc4,$t1 |
| 388 | umulh $t1,$a7,$a0 |
| 389 | adcs $acc5,$acc5,$t2 |
| 390 | mul $t2,$a2,$a1 // lo(a[2..7]*a[1]) (ii) |
| 391 | adcs $acc6,$acc6,$t3 |
| 392 | mul $t3,$a3,$a1 |
| 393 | adcs $acc7,$acc7,$t0 |
| 394 | mul $t0,$a4,$a1 |
| 395 | adc $acc0,$acc0,$t1 |
| 396 | |
| 397 | mul $t1,$a5,$a1 |
| 398 | adds $acc3,$acc3,$t2 |
| 399 | mul $t2,$a6,$a1 |
| 400 | adcs $acc4,$acc4,$t3 |
| 401 | mul $t3,$a7,$a1 |
| 402 | adcs $acc5,$acc5,$t0 |
| 403 | umulh $t0,$a2,$a1 // hi(a[2..7]*a[1]) |
| 404 | adcs $acc6,$acc6,$t1 |
| 405 | umulh $t1,$a3,$a1 |
| 406 | adcs $acc7,$acc7,$t2 |
| 407 | umulh $t2,$a4,$a1 |
| 408 | adcs $acc0,$acc0,$t3 |
| 409 | umulh $t3,$a5,$a1 |
| 410 | stp $acc2,$acc3,[$tp],#8*2 // t[2..3] |
| 411 | adc $acc1,xzr,xzr // t[9] |
| 412 | adds $acc4,$acc4,$t0 |
| 413 | umulh $t0,$a6,$a1 |
| 414 | adcs $acc5,$acc5,$t1 |
| 415 | umulh $t1,$a7,$a1 |
| 416 | adcs $acc6,$acc6,$t2 |
| 417 | mul $t2,$a3,$a2 // lo(a[3..7]*a[2]) (iii) |
| 418 | adcs $acc7,$acc7,$t3 |
| 419 | mul $t3,$a4,$a2 |
| 420 | adcs $acc0,$acc0,$t0 |
| 421 | mul $t0,$a5,$a2 |
| 422 | adc $acc1,$acc1,$t1 |
| 423 | |
| 424 | mul $t1,$a6,$a2 |
| 425 | adds $acc5,$acc5,$t2 |
| 426 | mul $t2,$a7,$a2 |
| 427 | adcs $acc6,$acc6,$t3 |
| 428 | umulh $t3,$a3,$a2 // hi(a[3..7]*a[2]) |
| 429 | adcs $acc7,$acc7,$t0 |
| 430 | umulh $t0,$a4,$a2 |
| 431 | adcs $acc0,$acc0,$t1 |
| 432 | umulh $t1,$a5,$a2 |
| 433 | adcs $acc1,$acc1,$t2 |
| 434 | umulh $t2,$a6,$a2 |
| 435 | stp $acc4,$acc5,[$tp],#8*2 // t[4..5] |
| 436 | adc $acc2,xzr,xzr // t[10] |
| 437 | adds $acc6,$acc6,$t3 |
| 438 | umulh $t3,$a7,$a2 |
| 439 | adcs $acc7,$acc7,$t0 |
| 440 | mul $t0,$a4,$a3 // lo(a[4..7]*a[3]) (iv) |
| 441 | adcs $acc0,$acc0,$t1 |
| 442 | mul $t1,$a5,$a3 |
| 443 | adcs $acc1,$acc1,$t2 |
| 444 | mul $t2,$a6,$a3 |
| 445 | adc $acc2,$acc2,$t3 |
| 446 | |
| 447 | mul $t3,$a7,$a3 |
| 448 | adds $acc7,$acc7,$t0 |
| 449 | umulh $t0,$a4,$a3 // hi(a[4..7]*a[3]) |
| 450 | adcs $acc0,$acc0,$t1 |
| 451 | umulh $t1,$a5,$a3 |
| 452 | adcs $acc1,$acc1,$t2 |
| 453 | umulh $t2,$a6,$a3 |
| 454 | adcs $acc2,$acc2,$t3 |
| 455 | umulh $t3,$a7,$a3 |
| 456 | stp $acc6,$acc7,[$tp],#8*2 // t[6..7] |
| 457 | adc $acc3,xzr,xzr // t[11] |
| 458 | adds $acc0,$acc0,$t0 |
| 459 | mul $t0,$a5,$a4 // lo(a[5..7]*a[4]) (v) |
| 460 | adcs $acc1,$acc1,$t1 |
| 461 | mul $t1,$a6,$a4 |
| 462 | adcs $acc2,$acc2,$t2 |
| 463 | mul $t2,$a7,$a4 |
| 464 | adc $acc3,$acc3,$t3 |
| 465 | |
| 466 | umulh $t3,$a5,$a4 // hi(a[5..7]*a[4]) |
| 467 | adds $acc1,$acc1,$t0 |
| 468 | umulh $t0,$a6,$a4 |
| 469 | adcs $acc2,$acc2,$t1 |
| 470 | umulh $t1,$a7,$a4 |
| 471 | adcs $acc3,$acc3,$t2 |
| 472 | mul $t2,$a6,$a5 // lo(a[6..7]*a[5]) (vi) |
| 473 | adc $acc4,xzr,xzr // t[12] |
| 474 | adds $acc2,$acc2,$t3 |
| 475 | mul $t3,$a7,$a5 |
| 476 | adcs $acc3,$acc3,$t0 |
| 477 | umulh $t0,$a6,$a5 // hi(a[6..7]*a[5]) |
| 478 | adc $acc4,$acc4,$t1 |
| 479 | |
| 480 | umulh $t1,$a7,$a5 |
| 481 | adds $acc3,$acc3,$t2 |
| 482 | mul $t2,$a7,$a6 // lo(a[7]*a[6]) (vii) |
| 483 | adcs $acc4,$acc4,$t3 |
| 484 | umulh $t3,$a7,$a6 // hi(a[7]*a[6]) |
| 485 | adc $acc5,xzr,xzr // t[13] |
| 486 | adds $acc4,$acc4,$t0 |
| 487 | sub $cnt,$ap_end,$ap // done yet? |
| 488 | adc $acc5,$acc5,$t1 |
| 489 | |
| 490 | adds $acc5,$acc5,$t2 |
| 491 | sub $t0,$ap_end,$num // rewinded ap |
| 492 | adc $acc6,xzr,xzr // t[14] |
| 493 | add $acc6,$acc6,$t3 |
| 494 | |
| 495 | cbz $cnt,.Lsqr8x_outer_break |
| 496 | |
| 497 | mov $n0,$a0 |
| 498 | ldp $a0,$a1,[$tp,#8*0] |
| 499 | ldp $a2,$a3,[$tp,#8*2] |
| 500 | ldp $a4,$a5,[$tp,#8*4] |
| 501 | ldp $a6,$a7,[$tp,#8*6] |
| 502 | adds $acc0,$acc0,$a0 |
| 503 | adcs $acc1,$acc1,$a1 |
| 504 | ldp $a0,$a1,[$ap,#8*0] |
| 505 | adcs $acc2,$acc2,$a2 |
| 506 | adcs $acc3,$acc3,$a3 |
| 507 | ldp $a2,$a3,[$ap,#8*2] |
| 508 | adcs $acc4,$acc4,$a4 |
| 509 | adcs $acc5,$acc5,$a5 |
| 510 | ldp $a4,$a5,[$ap,#8*4] |
| 511 | adcs $acc6,$acc6,$a6 |
| 512 | mov $rp,$ap |
| 513 | adcs $acc7,xzr,$a7 |
| 514 | ldp $a6,$a7,[$ap,#8*6] |
| 515 | add $ap,$ap,#8*8 |
| 516 | //adc $carry,xzr,xzr // moved below |
| 517 | mov $cnt,#-8*8 |
| 518 | |
| 519 | // a[8]a[0] |
| 520 | // a[9]a[0] |
| 521 | // a[a]a[0] |
| 522 | // a[b]a[0] |
| 523 | // a[c]a[0] |
| 524 | // a[d]a[0] |
| 525 | // a[e]a[0] |
| 526 | // a[f]a[0] |
| 527 | // a[8]a[1] |
| 528 | // a[f]a[1]........................ |
| 529 | // a[8]a[2] |
| 530 | // a[f]a[2]........................ |
| 531 | // a[8]a[3] |
| 532 | // a[f]a[3]........................ |
| 533 | // a[8]a[4] |
| 534 | // a[f]a[4]........................ |
| 535 | // a[8]a[5] |
| 536 | // a[f]a[5]........................ |
| 537 | // a[8]a[6] |
| 538 | // a[f]a[6]........................ |
| 539 | // a[8]a[7] |
| 540 | // a[f]a[7]........................ |
| 541 | .Lsqr8x_mul: |
| 542 | mul $t0,$a0,$n0 |
| 543 | adc $carry,xzr,xzr // carry bit, modulo-scheduled |
| 544 | mul $t1,$a1,$n0 |
| 545 | add $cnt,$cnt,#8 |
| 546 | mul $t2,$a2,$n0 |
| 547 | mul $t3,$a3,$n0 |
| 548 | adds $acc0,$acc0,$t0 |
| 549 | mul $t0,$a4,$n0 |
| 550 | adcs $acc1,$acc1,$t1 |
| 551 | mul $t1,$a5,$n0 |
| 552 | adcs $acc2,$acc2,$t2 |
| 553 | mul $t2,$a6,$n0 |
| 554 | adcs $acc3,$acc3,$t3 |
| 555 | mul $t3,$a7,$n0 |
| 556 | adcs $acc4,$acc4,$t0 |
| 557 | umulh $t0,$a0,$n0 |
| 558 | adcs $acc5,$acc5,$t1 |
| 559 | umulh $t1,$a1,$n0 |
| 560 | adcs $acc6,$acc6,$t2 |
| 561 | umulh $t2,$a2,$n0 |
| 562 | adcs $acc7,$acc7,$t3 |
| 563 | umulh $t3,$a3,$n0 |
| 564 | adc $carry,$carry,xzr |
| 565 | str $acc0,[$tp],#8 |
| 566 | adds $acc0,$acc1,$t0 |
| 567 | umulh $t0,$a4,$n0 |
| 568 | adcs $acc1,$acc2,$t1 |
| 569 | umulh $t1,$a5,$n0 |
| 570 | adcs $acc2,$acc3,$t2 |
| 571 | umulh $t2,$a6,$n0 |
| 572 | adcs $acc3,$acc4,$t3 |
| 573 | umulh $t3,$a7,$n0 |
| 574 | ldr $n0,[$rp,$cnt] |
| 575 | adcs $acc4,$acc5,$t0 |
| 576 | adcs $acc5,$acc6,$t1 |
| 577 | adcs $acc6,$acc7,$t2 |
| 578 | adcs $acc7,$carry,$t3 |
| 579 | //adc $carry,xzr,xzr // moved above |
| 580 | cbnz $cnt,.Lsqr8x_mul |
| 581 | // note that carry flag is guaranteed |
| 582 | // to be zero at this point |
| 583 | cmp $ap,$ap_end // done yet? |
| 584 | b.eq .Lsqr8x_break |
| 585 | |
| 586 | ldp $a0,$a1,[$tp,#8*0] |
| 587 | ldp $a2,$a3,[$tp,#8*2] |
| 588 | ldp $a4,$a5,[$tp,#8*4] |
| 589 | ldp $a6,$a7,[$tp,#8*6] |
| 590 | adds $acc0,$acc0,$a0 |
| 591 | ldr $n0,[$rp,#-8*8] |
| 592 | adcs $acc1,$acc1,$a1 |
| 593 | ldp $a0,$a1,[$ap,#8*0] |
| 594 | adcs $acc2,$acc2,$a2 |
| 595 | adcs $acc3,$acc3,$a3 |
| 596 | ldp $a2,$a3,[$ap,#8*2] |
| 597 | adcs $acc4,$acc4,$a4 |
| 598 | adcs $acc5,$acc5,$a5 |
| 599 | ldp $a4,$a5,[$ap,#8*4] |
| 600 | adcs $acc6,$acc6,$a6 |
| 601 | mov $cnt,#-8*8 |
| 602 | adcs $acc7,$acc7,$a7 |
| 603 | ldp $a6,$a7,[$ap,#8*6] |
| 604 | add $ap,$ap,#8*8 |
| 605 | //adc $carry,xzr,xzr // moved above |
| 606 | b .Lsqr8x_mul |
| 607 | |
| 608 | .align 4 |
| 609 | .Lsqr8x_break: |
| 610 | ldp $a0,$a1,[$rp,#8*0] |
| 611 | add $ap,$rp,#8*8 |
| 612 | ldp $a2,$a3,[$rp,#8*2] |
| 613 | sub $t0,$ap_end,$ap // is it last iteration? |
| 614 | ldp $a4,$a5,[$rp,#8*4] |
| 615 | sub $t1,$tp,$t0 |
| 616 | ldp $a6,$a7,[$rp,#8*6] |
| 617 | cbz $t0,.Lsqr8x_outer_loop |
| 618 | |
| 619 | stp $acc0,$acc1,[$tp,#8*0] |
| 620 | ldp $acc0,$acc1,[$t1,#8*0] |
| 621 | stp $acc2,$acc3,[$tp,#8*2] |
| 622 | ldp $acc2,$acc3,[$t1,#8*2] |
| 623 | stp $acc4,$acc5,[$tp,#8*4] |
| 624 | ldp $acc4,$acc5,[$t1,#8*4] |
| 625 | stp $acc6,$acc7,[$tp,#8*6] |
| 626 | mov $tp,$t1 |
| 627 | ldp $acc6,$acc7,[$t1,#8*6] |
| 628 | b .Lsqr8x_outer_loop |
| 629 | |
| 630 | .align 4 |
| 631 | .Lsqr8x_outer_break: |
| 632 | // Now multiply above result by 2 and add a[n-1]*a[n-1]|...|a[0]*a[0] |
| 633 | ldp $a1,$a3,[$t0,#8*0] // recall that $t0 is &a[0] |
| 634 | ldp $t1,$t2,[sp,#8*1] |
| 635 | ldp $a5,$a7,[$t0,#8*2] |
| 636 | add $ap,$t0,#8*4 |
| 637 | ldp $t3,$t0,[sp,#8*3] |
| 638 | |
| 639 | stp $acc0,$acc1,[$tp,#8*0] |
| 640 | mul $acc0,$a1,$a1 |
| 641 | stp $acc2,$acc3,[$tp,#8*2] |
| 642 | umulh $a1,$a1,$a1 |
| 643 | stp $acc4,$acc5,[$tp,#8*4] |
| 644 | mul $a2,$a3,$a3 |
| 645 | stp $acc6,$acc7,[$tp,#8*6] |
| 646 | mov $tp,sp |
| 647 | umulh $a3,$a3,$a3 |
| 648 | adds $acc1,$a1,$t1,lsl#1 |
| 649 | extr $t1,$t2,$t1,#63 |
| 650 | sub $cnt,$num,#8*4 |
| 651 | |
| 652 | .Lsqr4x_shift_n_add: |
| 653 | adcs $acc2,$a2,$t1 |
| 654 | extr $t2,$t3,$t2,#63 |
| 655 | sub $cnt,$cnt,#8*4 |
| 656 | adcs $acc3,$a3,$t2 |
| 657 | ldp $t1,$t2,[$tp,#8*5] |
| 658 | mul $a4,$a5,$a5 |
| 659 | ldp $a1,$a3,[$ap],#8*2 |
| 660 | umulh $a5,$a5,$a5 |
| 661 | mul $a6,$a7,$a7 |
| 662 | umulh $a7,$a7,$a7 |
| 663 | extr $t3,$t0,$t3,#63 |
| 664 | stp $acc0,$acc1,[$tp,#8*0] |
| 665 | adcs $acc4,$a4,$t3 |
| 666 | extr $t0,$t1,$t0,#63 |
| 667 | stp $acc2,$acc3,[$tp,#8*2] |
| 668 | adcs $acc5,$a5,$t0 |
| 669 | ldp $t3,$t0,[$tp,#8*7] |
| 670 | extr $t1,$t2,$t1,#63 |
| 671 | adcs $acc6,$a6,$t1 |
| 672 | extr $t2,$t3,$t2,#63 |
| 673 | adcs $acc7,$a7,$t2 |
| 674 | ldp $t1,$t2,[$tp,#8*9] |
| 675 | mul $a0,$a1,$a1 |
| 676 | ldp $a5,$a7,[$ap],#8*2 |
| 677 | umulh $a1,$a1,$a1 |
| 678 | mul $a2,$a3,$a3 |
| 679 | umulh $a3,$a3,$a3 |
| 680 | stp $acc4,$acc5,[$tp,#8*4] |
| 681 | extr $t3,$t0,$t3,#63 |
| 682 | stp $acc6,$acc7,[$tp,#8*6] |
| 683 | add $tp,$tp,#8*8 |
| 684 | adcs $acc0,$a0,$t3 |
| 685 | extr $t0,$t1,$t0,#63 |
| 686 | adcs $acc1,$a1,$t0 |
| 687 | ldp $t3,$t0,[$tp,#8*3] |
| 688 | extr $t1,$t2,$t1,#63 |
| 689 | cbnz $cnt,.Lsqr4x_shift_n_add |
| 690 | ___ |
| 691 | my ($np,$np_end)=($ap,$ap_end); |
| 692 | $code.=<<___; |
| 693 | ldp $np,$n0,[x29,#104] // pull np and n0 |
| 694 | |
| 695 | adcs $acc2,$a2,$t1 |
| 696 | extr $t2,$t3,$t2,#63 |
| 697 | adcs $acc3,$a3,$t2 |
| 698 | ldp $t1,$t2,[$tp,#8*5] |
| 699 | mul $a4,$a5,$a5 |
| 700 | umulh $a5,$a5,$a5 |
| 701 | stp $acc0,$acc1,[$tp,#8*0] |
| 702 | mul $a6,$a7,$a7 |
| 703 | umulh $a7,$a7,$a7 |
| 704 | stp $acc2,$acc3,[$tp,#8*2] |
| 705 | extr $t3,$t0,$t3,#63 |
| 706 | adcs $acc4,$a4,$t3 |
| 707 | extr $t0,$t1,$t0,#63 |
| 708 | ldp $acc0,$acc1,[sp,#8*0] |
| 709 | adcs $acc5,$a5,$t0 |
| 710 | extr $t1,$t2,$t1,#63 |
| 711 | ldp $a0,$a1,[$np,#8*0] |
| 712 | adcs $acc6,$a6,$t1 |
| 713 | extr $t2,xzr,$t2,#63 |
| 714 | ldp $a2,$a3,[$np,#8*2] |
| 715 | adc $acc7,$a7,$t2 |
| 716 | ldp $a4,$a5,[$np,#8*4] |
| 717 | |
| 718 | // Reduce by 512 bits per iteration |
| 719 | mul $na0,$n0,$acc0 // t[0]*n0 |
| 720 | ldp $a6,$a7,[$np,#8*6] |
| 721 | add $np_end,$np,$num |
| 722 | ldp $acc2,$acc3,[sp,#8*2] |
| 723 | stp $acc4,$acc5,[$tp,#8*4] |
| 724 | ldp $acc4,$acc5,[sp,#8*4] |
| 725 | stp $acc6,$acc7,[$tp,#8*6] |
| 726 | ldp $acc6,$acc7,[sp,#8*6] |
| 727 | add $np,$np,#8*8 |
| 728 | mov $topmost,xzr // initial top-most carry |
| 729 | mov $tp,sp |
| 730 | mov $cnt,#8 |
| 731 | |
| 732 | .Lsqr8x_reduction: |
| 733 | // (*) mul $t0,$a0,$na0 // lo(n[0-7])*lo(t[0]*n0) |
| 734 | mul $t1,$a1,$na0 |
| 735 | sub $cnt,$cnt,#1 |
| 736 | mul $t2,$a2,$na0 |
| 737 | str $na0,[$tp],#8 // put aside t[0]*n0 for tail processing |
| 738 | mul $t3,$a3,$na0 |
| 739 | // (*) adds xzr,$acc0,$t0 |
| 740 | subs xzr,$acc0,#1 // (*) |
| 741 | mul $t0,$a4,$na0 |
| 742 | adcs $acc0,$acc1,$t1 |
| 743 | mul $t1,$a5,$na0 |
| 744 | adcs $acc1,$acc2,$t2 |
| 745 | mul $t2,$a6,$na0 |
| 746 | adcs $acc2,$acc3,$t3 |
| 747 | mul $t3,$a7,$na0 |
| 748 | adcs $acc3,$acc4,$t0 |
| 749 | umulh $t0,$a0,$na0 // hi(n[0-7])*lo(t[0]*n0) |
| 750 | adcs $acc4,$acc5,$t1 |
| 751 | umulh $t1,$a1,$na0 |
| 752 | adcs $acc5,$acc6,$t2 |
| 753 | umulh $t2,$a2,$na0 |
| 754 | adcs $acc6,$acc7,$t3 |
| 755 | umulh $t3,$a3,$na0 |
| 756 | adc $acc7,xzr,xzr |
| 757 | adds $acc0,$acc0,$t0 |
| 758 | umulh $t0,$a4,$na0 |
| 759 | adcs $acc1,$acc1,$t1 |
| 760 | umulh $t1,$a5,$na0 |
| 761 | adcs $acc2,$acc2,$t2 |
| 762 | umulh $t2,$a6,$na0 |
| 763 | adcs $acc3,$acc3,$t3 |
| 764 | umulh $t3,$a7,$na0 |
| 765 | mul $na0,$n0,$acc0 // next t[0]*n0 |
| 766 | adcs $acc4,$acc4,$t0 |
| 767 | adcs $acc5,$acc5,$t1 |
| 768 | adcs $acc6,$acc6,$t2 |
| 769 | adc $acc7,$acc7,$t3 |
| 770 | cbnz $cnt,.Lsqr8x_reduction |
| 771 | |
| 772 | ldp $t0,$t1,[$tp,#8*0] |
| 773 | ldp $t2,$t3,[$tp,#8*2] |
| 774 | mov $rp,$tp |
| 775 | sub $cnt,$np_end,$np // done yet? |
| 776 | adds $acc0,$acc0,$t0 |
| 777 | adcs $acc1,$acc1,$t1 |
| 778 | ldp $t0,$t1,[$tp,#8*4] |
| 779 | adcs $acc2,$acc2,$t2 |
| 780 | adcs $acc3,$acc3,$t3 |
| 781 | ldp $t2,$t3,[$tp,#8*6] |
| 782 | adcs $acc4,$acc4,$t0 |
| 783 | adcs $acc5,$acc5,$t1 |
| 784 | adcs $acc6,$acc6,$t2 |
| 785 | adcs $acc7,$acc7,$t3 |
| 786 | //adc $carry,xzr,xzr // moved below |
| 787 | cbz $cnt,.Lsqr8x8_post_condition |
| 788 | |
| 789 | ldr $n0,[$tp,#-8*8] |
| 790 | ldp $a0,$a1,[$np,#8*0] |
| 791 | ldp $a2,$a3,[$np,#8*2] |
| 792 | ldp $a4,$a5,[$np,#8*4] |
| 793 | mov $cnt,#-8*8 |
| 794 | ldp $a6,$a7,[$np,#8*6] |
| 795 | add $np,$np,#8*8 |
| 796 | |
| 797 | .Lsqr8x_tail: |
| 798 | mul $t0,$a0,$n0 |
| 799 | adc $carry,xzr,xzr // carry bit, modulo-scheduled |
| 800 | mul $t1,$a1,$n0 |
| 801 | add $cnt,$cnt,#8 |
| 802 | mul $t2,$a2,$n0 |
| 803 | mul $t3,$a3,$n0 |
| 804 | adds $acc0,$acc0,$t0 |
| 805 | mul $t0,$a4,$n0 |
| 806 | adcs $acc1,$acc1,$t1 |
| 807 | mul $t1,$a5,$n0 |
| 808 | adcs $acc2,$acc2,$t2 |
| 809 | mul $t2,$a6,$n0 |
| 810 | adcs $acc3,$acc3,$t3 |
| 811 | mul $t3,$a7,$n0 |
| 812 | adcs $acc4,$acc4,$t0 |
| 813 | umulh $t0,$a0,$n0 |
| 814 | adcs $acc5,$acc5,$t1 |
| 815 | umulh $t1,$a1,$n0 |
| 816 | adcs $acc6,$acc6,$t2 |
| 817 | umulh $t2,$a2,$n0 |
| 818 | adcs $acc7,$acc7,$t3 |
| 819 | umulh $t3,$a3,$n0 |
| 820 | adc $carry,$carry,xzr |
| 821 | str $acc0,[$tp],#8 |
| 822 | adds $acc0,$acc1,$t0 |
| 823 | umulh $t0,$a4,$n0 |
| 824 | adcs $acc1,$acc2,$t1 |
| 825 | umulh $t1,$a5,$n0 |
| 826 | adcs $acc2,$acc3,$t2 |
| 827 | umulh $t2,$a6,$n0 |
| 828 | adcs $acc3,$acc4,$t3 |
| 829 | umulh $t3,$a7,$n0 |
| 830 | ldr $n0,[$rp,$cnt] |
| 831 | adcs $acc4,$acc5,$t0 |
| 832 | adcs $acc5,$acc6,$t1 |
| 833 | adcs $acc6,$acc7,$t2 |
| 834 | adcs $acc7,$carry,$t3 |
| 835 | //adc $carry,xzr,xzr // moved above |
| 836 | cbnz $cnt,.Lsqr8x_tail |
| 837 | // note that carry flag is guaranteed |
| 838 | // to be zero at this point |
| 839 | ldp $a0,$a1,[$tp,#8*0] |
| 840 | sub $cnt,$np_end,$np // done yet? |
| 841 | sub $t2,$np_end,$num // rewinded np |
| 842 | ldp $a2,$a3,[$tp,#8*2] |
| 843 | ldp $a4,$a5,[$tp,#8*4] |
| 844 | ldp $a6,$a7,[$tp,#8*6] |
| 845 | cbz $cnt,.Lsqr8x_tail_break |
| 846 | |
| 847 | ldr $n0,[$rp,#-8*8] |
| 848 | adds $acc0,$acc0,$a0 |
| 849 | adcs $acc1,$acc1,$a1 |
| 850 | ldp $a0,$a1,[$np,#8*0] |
| 851 | adcs $acc2,$acc2,$a2 |
| 852 | adcs $acc3,$acc3,$a3 |
| 853 | ldp $a2,$a3,[$np,#8*2] |
| 854 | adcs $acc4,$acc4,$a4 |
| 855 | adcs $acc5,$acc5,$a5 |
| 856 | ldp $a4,$a5,[$np,#8*4] |
| 857 | adcs $acc6,$acc6,$a6 |
| 858 | mov $cnt,#-8*8 |
| 859 | adcs $acc7,$acc7,$a7 |
| 860 | ldp $a6,$a7,[$np,#8*6] |
| 861 | add $np,$np,#8*8 |
| 862 | //adc $carry,xzr,xzr // moved above |
| 863 | b .Lsqr8x_tail |
| 864 | |
| 865 | .align 4 |
| 866 | .Lsqr8x_tail_break: |
| 867 | ldr $n0,[x29,#112] // pull n0 |
| 868 | add $cnt,$tp,#8*8 // end of current t[num] window |
| 869 | |
| 870 | subs xzr,$topmost,#1 // "move" top-most carry to carry bit |
| 871 | adcs $t0,$acc0,$a0 |
| 872 | adcs $t1,$acc1,$a1 |
| 873 | ldp $acc0,$acc1,[$rp,#8*0] |
| 874 | adcs $acc2,$acc2,$a2 |
| 875 | ldp $a0,$a1,[$t2,#8*0] // recall that $t2 is &n[0] |
| 876 | adcs $acc3,$acc3,$a3 |
| 877 | ldp $a2,$a3,[$t2,#8*2] |
| 878 | adcs $acc4,$acc4,$a4 |
| 879 | adcs $acc5,$acc5,$a5 |
| 880 | ldp $a4,$a5,[$t2,#8*4] |
| 881 | adcs $acc6,$acc6,$a6 |
| 882 | adcs $acc7,$acc7,$a7 |
| 883 | ldp $a6,$a7,[$t2,#8*6] |
| 884 | add $np,$t2,#8*8 |
| 885 | adc $topmost,xzr,xzr // top-most carry |
| 886 | mul $na0,$n0,$acc0 |
| 887 | stp $t0,$t1,[$tp,#8*0] |
| 888 | stp $acc2,$acc3,[$tp,#8*2] |
| 889 | ldp $acc2,$acc3,[$rp,#8*2] |
| 890 | stp $acc4,$acc5,[$tp,#8*4] |
| 891 | ldp $acc4,$acc5,[$rp,#8*4] |
| 892 | cmp $cnt,x29 // did we hit the bottom? |
| 893 | stp $acc6,$acc7,[$tp,#8*6] |
| 894 | mov $tp,$rp // slide the window |
| 895 | ldp $acc6,$acc7,[$rp,#8*6] |
| 896 | mov $cnt,#8 |
| 897 | b.ne .Lsqr8x_reduction |
| 898 | |
| 899 | // Final step. We see if result is larger than modulus, and |
| 900 | // if it is, subtract the modulus. But comparison implies |
| 901 | // subtraction. So we subtract modulus, see if it borrowed, |
| 902 | // and conditionally copy original value. |
| 903 | ldr $rp,[x29,#96] // pull rp |
| 904 | add $tp,$tp,#8*8 |
| 905 | subs $t0,$acc0,$a0 |
| 906 | sbcs $t1,$acc1,$a1 |
| 907 | sub $cnt,$num,#8*8 |
| 908 | mov $ap_end,$rp // $rp copy |
| 909 | |
| 910 | .Lsqr8x_sub: |
| 911 | sbcs $t2,$acc2,$a2 |
| 912 | ldp $a0,$a1,[$np,#8*0] |
| 913 | sbcs $t3,$acc3,$a3 |
| 914 | stp $t0,$t1,[$rp,#8*0] |
| 915 | sbcs $t0,$acc4,$a4 |
| 916 | ldp $a2,$a3,[$np,#8*2] |
| 917 | sbcs $t1,$acc5,$a5 |
| 918 | stp $t2,$t3,[$rp,#8*2] |
| 919 | sbcs $t2,$acc6,$a6 |
| 920 | ldp $a4,$a5,[$np,#8*4] |
| 921 | sbcs $t3,$acc7,$a7 |
| 922 | ldp $a6,$a7,[$np,#8*6] |
| 923 | add $np,$np,#8*8 |
| 924 | ldp $acc0,$acc1,[$tp,#8*0] |
| 925 | sub $cnt,$cnt,#8*8 |
| 926 | ldp $acc2,$acc3,[$tp,#8*2] |
| 927 | ldp $acc4,$acc5,[$tp,#8*4] |
| 928 | ldp $acc6,$acc7,[$tp,#8*6] |
| 929 | add $tp,$tp,#8*8 |
| 930 | stp $t0,$t1,[$rp,#8*4] |
| 931 | sbcs $t0,$acc0,$a0 |
| 932 | stp $t2,$t3,[$rp,#8*6] |
| 933 | add $rp,$rp,#8*8 |
| 934 | sbcs $t1,$acc1,$a1 |
| 935 | cbnz $cnt,.Lsqr8x_sub |
| 936 | |
| 937 | sbcs $t2,$acc2,$a2 |
| 938 | mov $tp,sp |
| 939 | add $ap,sp,$num |
| 940 | ldp $a0,$a1,[$ap_end,#8*0] |
| 941 | sbcs $t3,$acc3,$a3 |
| 942 | stp $t0,$t1,[$rp,#8*0] |
| 943 | sbcs $t0,$acc4,$a4 |
| 944 | ldp $a2,$a3,[$ap_end,#8*2] |
| 945 | sbcs $t1,$acc5,$a5 |
| 946 | stp $t2,$t3,[$rp,#8*2] |
| 947 | sbcs $t2,$acc6,$a6 |
| 948 | ldp $acc0,$acc1,[$ap,#8*0] |
| 949 | sbcs $t3,$acc7,$a7 |
| 950 | ldp $acc2,$acc3,[$ap,#8*2] |
| 951 | sbcs xzr,$topmost,xzr // did it borrow? |
| 952 | ldr x30,[x29,#8] // pull return address |
| 953 | stp $t0,$t1,[$rp,#8*4] |
| 954 | stp $t2,$t3,[$rp,#8*6] |
| 955 | |
| 956 | sub $cnt,$num,#8*4 |
| 957 | .Lsqr4x_cond_copy: |
| 958 | sub $cnt,$cnt,#8*4 |
| 959 | csel $t0,$acc0,$a0,lo |
| 960 | stp xzr,xzr,[$tp,#8*0] |
| 961 | csel $t1,$acc1,$a1,lo |
| 962 | ldp $a0,$a1,[$ap_end,#8*4] |
| 963 | ldp $acc0,$acc1,[$ap,#8*4] |
| 964 | csel $t2,$acc2,$a2,lo |
| 965 | stp xzr,xzr,[$tp,#8*2] |
| 966 | add $tp,$tp,#8*4 |
| 967 | csel $t3,$acc3,$a3,lo |
| 968 | ldp $a2,$a3,[$ap_end,#8*6] |
| 969 | ldp $acc2,$acc3,[$ap,#8*6] |
| 970 | add $ap,$ap,#8*4 |
| 971 | stp $t0,$t1,[$ap_end,#8*0] |
| 972 | stp $t2,$t3,[$ap_end,#8*2] |
| 973 | add $ap_end,$ap_end,#8*4 |
| 974 | stp xzr,xzr,[$ap,#8*0] |
| 975 | stp xzr,xzr,[$ap,#8*2] |
| 976 | cbnz $cnt,.Lsqr4x_cond_copy |
| 977 | |
| 978 | csel $t0,$acc0,$a0,lo |
| 979 | stp xzr,xzr,[$tp,#8*0] |
| 980 | csel $t1,$acc1,$a1,lo |
| 981 | stp xzr,xzr,[$tp,#8*2] |
| 982 | csel $t2,$acc2,$a2,lo |
| 983 | csel $t3,$acc3,$a3,lo |
| 984 | stp $t0,$t1,[$ap_end,#8*0] |
| 985 | stp $t2,$t3,[$ap_end,#8*2] |
| 986 | |
| 987 | b .Lsqr8x_done |
| 988 | |
| 989 | .align 4 |
| 990 | .Lsqr8x8_post_condition: |
| 991 | adc $carry,xzr,xzr |
| 992 | ldr x30,[x29,#8] // pull return address |
| 993 | // $acc0-7,$carry hold result, $a0-7 hold modulus |
| 994 | subs $a0,$acc0,$a0 |
| 995 | ldr $ap,[x29,#96] // pull rp |
| 996 | sbcs $a1,$acc1,$a1 |
| 997 | stp xzr,xzr,[sp,#8*0] |
| 998 | sbcs $a2,$acc2,$a2 |
| 999 | stp xzr,xzr,[sp,#8*2] |
| 1000 | sbcs $a3,$acc3,$a3 |
| 1001 | stp xzr,xzr,[sp,#8*4] |
| 1002 | sbcs $a4,$acc4,$a4 |
| 1003 | stp xzr,xzr,[sp,#8*6] |
| 1004 | sbcs $a5,$acc5,$a5 |
| 1005 | stp xzr,xzr,[sp,#8*8] |
| 1006 | sbcs $a6,$acc6,$a6 |
| 1007 | stp xzr,xzr,[sp,#8*10] |
| 1008 | sbcs $a7,$acc7,$a7 |
| 1009 | stp xzr,xzr,[sp,#8*12] |
| 1010 | sbcs $carry,$carry,xzr // did it borrow? |
| 1011 | stp xzr,xzr,[sp,#8*14] |
| 1012 | |
| 1013 | // $a0-7 hold result-modulus |
| 1014 | csel $a0,$acc0,$a0,lo |
| 1015 | csel $a1,$acc1,$a1,lo |
| 1016 | csel $a2,$acc2,$a2,lo |
| 1017 | csel $a3,$acc3,$a3,lo |
| 1018 | stp $a0,$a1,[$ap,#8*0] |
| 1019 | csel $a4,$acc4,$a4,lo |
| 1020 | csel $a5,$acc5,$a5,lo |
| 1021 | stp $a2,$a3,[$ap,#8*2] |
| 1022 | csel $a6,$acc6,$a6,lo |
| 1023 | csel $a7,$acc7,$a7,lo |
| 1024 | stp $a4,$a5,[$ap,#8*4] |
| 1025 | stp $a6,$a7,[$ap,#8*6] |
| 1026 | |
| 1027 | .Lsqr8x_done: |
| 1028 | ldp x19,x20,[x29,#16] |
| 1029 | mov sp,x29 |
| 1030 | ldp x21,x22,[x29,#32] |
| 1031 | mov x0,#1 |
| 1032 | ldp x23,x24,[x29,#48] |
| 1033 | ldp x25,x26,[x29,#64] |
| 1034 | ldp x27,x28,[x29,#80] |
| 1035 | ldr x29,[sp],#128 |
| 1036 | ret |
| 1037 | .size __bn_sqr8x_mont,.-__bn_sqr8x_mont |
| 1038 | ___ |
| 1039 | } |
| 1040 | |
| 1041 | { |
| 1042 | ######################################################################## |
| 1043 | # Even though this might look as ARMv8 adaptation of mulx4x_mont from |
| 1044 | # x86_64-mont5 module, it's different in sense that it performs |
| 1045 | # reduction 256 bits at a time. |
| 1046 | |
| 1047 | my ($a0,$a1,$a2,$a3, |
| 1048 | $t0,$t1,$t2,$t3, |
| 1049 | $m0,$m1,$m2,$m3, |
| 1050 | $acc0,$acc1,$acc2,$acc3,$acc4, |
| 1051 | $bi,$mi,$tp,$ap_end,$cnt) = map("x$_",(6..17,19..28)); |
| 1052 | my $bp_end=$rp; |
| 1053 | my ($carry,$topmost) = ($rp,"x30"); |
| 1054 | |
| 1055 | $code.=<<___; |
| 1056 | .type __bn_mul4x_mont,%function |
| 1057 | .align 5 |
| 1058 | __bn_mul4x_mont: |
| 1059 | stp x29,x30,[sp,#-128]! |
| 1060 | add x29,sp,#0 |
| 1061 | stp x19,x20,[sp,#16] |
| 1062 | stp x21,x22,[sp,#32] |
| 1063 | stp x23,x24,[sp,#48] |
| 1064 | stp x25,x26,[sp,#64] |
| 1065 | stp x27,x28,[sp,#80] |
| 1066 | |
| 1067 | sub $tp,sp,$num,lsl#3 |
| 1068 | lsl $num,$num,#3 |
| 1069 | ldr $n0,[$n0] // *n0 |
| 1070 | sub sp,$tp,#8*4 // alloca |
| 1071 | |
| 1072 | add $t0,$bp,$num |
| 1073 | add $ap_end,$ap,$num |
| 1074 | stp $rp,$t0,[x29,#96] // offload rp and &b[num] |
| 1075 | |
| 1076 | ldr $bi,[$bp,#8*0] // b[0] |
| 1077 | ldp $a0,$a1,[$ap,#8*0] // a[0..3] |
| 1078 | ldp $a2,$a3,[$ap,#8*2] |
| 1079 | add $ap,$ap,#8*4 |
| 1080 | mov $acc0,xzr |
| 1081 | mov $acc1,xzr |
| 1082 | mov $acc2,xzr |
| 1083 | mov $acc3,xzr |
| 1084 | ldp $m0,$m1,[$np,#8*0] // n[0..3] |
| 1085 | ldp $m2,$m3,[$np,#8*2] |
| 1086 | adds $np,$np,#8*4 // clear carry bit |
| 1087 | mov $carry,xzr |
| 1088 | mov $cnt,#0 |
| 1089 | mov $tp,sp |
| 1090 | |
| 1091 | .Loop_mul4x_1st_reduction: |
| 1092 | mul $t0,$a0,$bi // lo(a[0..3]*b[0]) |
| 1093 | adc $carry,$carry,xzr // modulo-scheduled |
| 1094 | mul $t1,$a1,$bi |
| 1095 | add $cnt,$cnt,#8 |
| 1096 | mul $t2,$a2,$bi |
| 1097 | and $cnt,$cnt,#31 |
| 1098 | mul $t3,$a3,$bi |
| 1099 | adds $acc0,$acc0,$t0 |
| 1100 | umulh $t0,$a0,$bi // hi(a[0..3]*b[0]) |
| 1101 | adcs $acc1,$acc1,$t1 |
| 1102 | mul $mi,$acc0,$n0 // t[0]*n0 |
| 1103 | adcs $acc2,$acc2,$t2 |
| 1104 | umulh $t1,$a1,$bi |
| 1105 | adcs $acc3,$acc3,$t3 |
| 1106 | umulh $t2,$a2,$bi |
| 1107 | adc $acc4,xzr,xzr |
| 1108 | umulh $t3,$a3,$bi |
| 1109 | ldr $bi,[$bp,$cnt] // next b[i] (or b[0]) |
| 1110 | adds $acc1,$acc1,$t0 |
| 1111 | // (*) mul $t0,$m0,$mi // lo(n[0..3]*t[0]*n0) |
| 1112 | str $mi,[$tp],#8 // put aside t[0]*n0 for tail processing |
| 1113 | adcs $acc2,$acc2,$t1 |
| 1114 | mul $t1,$m1,$mi |
| 1115 | adcs $acc3,$acc3,$t2 |
| 1116 | mul $t2,$m2,$mi |
| 1117 | adc $acc4,$acc4,$t3 // can't overflow |
| 1118 | mul $t3,$m3,$mi |
| 1119 | // (*) adds xzr,$acc0,$t0 |
| 1120 | subs xzr,$acc0,#1 // (*) |
| 1121 | umulh $t0,$m0,$mi // hi(n[0..3]*t[0]*n0) |
| 1122 | adcs $acc0,$acc1,$t1 |
| 1123 | umulh $t1,$m1,$mi |
| 1124 | adcs $acc1,$acc2,$t2 |
| 1125 | umulh $t2,$m2,$mi |
| 1126 | adcs $acc2,$acc3,$t3 |
| 1127 | umulh $t3,$m3,$mi |
| 1128 | adcs $acc3,$acc4,$carry |
| 1129 | adc $carry,xzr,xzr |
| 1130 | adds $acc0,$acc0,$t0 |
| 1131 | sub $t0,$ap_end,$ap |
| 1132 | adcs $acc1,$acc1,$t1 |
| 1133 | adcs $acc2,$acc2,$t2 |
| 1134 | adcs $acc3,$acc3,$t3 |
| 1135 | //adc $carry,$carry,xzr |
| 1136 | cbnz $cnt,.Loop_mul4x_1st_reduction |
| 1137 | |
| 1138 | cbz $t0,.Lmul4x4_post_condition |
| 1139 | |
| 1140 | ldp $a0,$a1,[$ap,#8*0] // a[4..7] |
| 1141 | ldp $a2,$a3,[$ap,#8*2] |
| 1142 | add $ap,$ap,#8*4 |
| 1143 | ldr $mi,[sp] // a[0]*n0 |
| 1144 | ldp $m0,$m1,[$np,#8*0] // n[4..7] |
| 1145 | ldp $m2,$m3,[$np,#8*2] |
| 1146 | add $np,$np,#8*4 |
| 1147 | |
| 1148 | .Loop_mul4x_1st_tail: |
| 1149 | mul $t0,$a0,$bi // lo(a[4..7]*b[i]) |
| 1150 | adc $carry,$carry,xzr // modulo-scheduled |
| 1151 | mul $t1,$a1,$bi |
| 1152 | add $cnt,$cnt,#8 |
| 1153 | mul $t2,$a2,$bi |
| 1154 | and $cnt,$cnt,#31 |
| 1155 | mul $t3,$a3,$bi |
| 1156 | adds $acc0,$acc0,$t0 |
| 1157 | umulh $t0,$a0,$bi // hi(a[4..7]*b[i]) |
| 1158 | adcs $acc1,$acc1,$t1 |
| 1159 | umulh $t1,$a1,$bi |
| 1160 | adcs $acc2,$acc2,$t2 |
| 1161 | umulh $t2,$a2,$bi |
| 1162 | adcs $acc3,$acc3,$t3 |
| 1163 | umulh $t3,$a3,$bi |
| 1164 | adc $acc4,xzr,xzr |
| 1165 | ldr $bi,[$bp,$cnt] // next b[i] (or b[0]) |
| 1166 | adds $acc1,$acc1,$t0 |
| 1167 | mul $t0,$m0,$mi // lo(n[4..7]*a[0]*n0) |
| 1168 | adcs $acc2,$acc2,$t1 |
| 1169 | mul $t1,$m1,$mi |
| 1170 | adcs $acc3,$acc3,$t2 |
| 1171 | mul $t2,$m2,$mi |
| 1172 | adc $acc4,$acc4,$t3 // can't overflow |
| 1173 | mul $t3,$m3,$mi |
| 1174 | adds $acc0,$acc0,$t0 |
| 1175 | umulh $t0,$m0,$mi // hi(n[4..7]*a[0]*n0) |
| 1176 | adcs $acc1,$acc1,$t1 |
| 1177 | umulh $t1,$m1,$mi |
| 1178 | adcs $acc2,$acc2,$t2 |
| 1179 | umulh $t2,$m2,$mi |
| 1180 | adcs $acc3,$acc3,$t3 |
| 1181 | adcs $acc4,$acc4,$carry |
| 1182 | umulh $t3,$m3,$mi |
| 1183 | adc $carry,xzr,xzr |
| 1184 | ldr $mi,[sp,$cnt] // next t[0]*n0 |
| 1185 | str $acc0,[$tp],#8 // result!!! |
| 1186 | adds $acc0,$acc1,$t0 |
| 1187 | sub $t0,$ap_end,$ap // done yet? |
| 1188 | adcs $acc1,$acc2,$t1 |
| 1189 | adcs $acc2,$acc3,$t2 |
| 1190 | adcs $acc3,$acc4,$t3 |
| 1191 | //adc $carry,$carry,xzr |
| 1192 | cbnz $cnt,.Loop_mul4x_1st_tail |
| 1193 | |
| 1194 | sub $t1,$ap_end,$num // rewinded $ap |
| 1195 | cbz $t0,.Lmul4x_proceed |
| 1196 | |
| 1197 | ldp $a0,$a1,[$ap,#8*0] |
| 1198 | ldp $a2,$a3,[$ap,#8*2] |
| 1199 | add $ap,$ap,#8*4 |
| 1200 | ldp $m0,$m1,[$np,#8*0] |
| 1201 | ldp $m2,$m3,[$np,#8*2] |
| 1202 | add $np,$np,#8*4 |
| 1203 | b .Loop_mul4x_1st_tail |
| 1204 | |
| 1205 | .align 5 |
| 1206 | .Lmul4x_proceed: |
| 1207 | ldr $bi,[$bp,#8*4]! // *++b |
| 1208 | adc $topmost,$carry,xzr |
| 1209 | ldp $a0,$a1,[$t1,#8*0] // a[0..3] |
| 1210 | sub $np,$np,$num // rewind np |
| 1211 | ldp $a2,$a3,[$t1,#8*2] |
| 1212 | add $ap,$t1,#8*4 |
| 1213 | |
| 1214 | stp $acc0,$acc1,[$tp,#8*0] // result!!! |
| 1215 | ldp $acc0,$acc1,[sp,#8*4] // t[0..3] |
| 1216 | stp $acc2,$acc3,[$tp,#8*2] // result!!! |
| 1217 | ldp $acc2,$acc3,[sp,#8*6] |
| 1218 | |
| 1219 | ldp $m0,$m1,[$np,#8*0] // n[0..3] |
| 1220 | mov $tp,sp |
| 1221 | ldp $m2,$m3,[$np,#8*2] |
| 1222 | adds $np,$np,#8*4 // clear carry bit |
| 1223 | mov $carry,xzr |
| 1224 | |
| 1225 | .align 4 |
| 1226 | .Loop_mul4x_reduction: |
| 1227 | mul $t0,$a0,$bi // lo(a[0..3]*b[4]) |
| 1228 | adc $carry,$carry,xzr // modulo-scheduled |
| 1229 | mul $t1,$a1,$bi |
| 1230 | add $cnt,$cnt,#8 |
| 1231 | mul $t2,$a2,$bi |
| 1232 | and $cnt,$cnt,#31 |
| 1233 | mul $t3,$a3,$bi |
| 1234 | adds $acc0,$acc0,$t0 |
| 1235 | umulh $t0,$a0,$bi // hi(a[0..3]*b[4]) |
| 1236 | adcs $acc1,$acc1,$t1 |
| 1237 | mul $mi,$acc0,$n0 // t[0]*n0 |
| 1238 | adcs $acc2,$acc2,$t2 |
| 1239 | umulh $t1,$a1,$bi |
| 1240 | adcs $acc3,$acc3,$t3 |
| 1241 | umulh $t2,$a2,$bi |
| 1242 | adc $acc4,xzr,xzr |
| 1243 | umulh $t3,$a3,$bi |
| 1244 | ldr $bi,[$bp,$cnt] // next b[i] |
| 1245 | adds $acc1,$acc1,$t0 |
| 1246 | // (*) mul $t0,$m0,$mi |
| 1247 | str $mi,[$tp],#8 // put aside t[0]*n0 for tail processing |
| 1248 | adcs $acc2,$acc2,$t1 |
| 1249 | mul $t1,$m1,$mi // lo(n[0..3]*t[0]*n0 |
| 1250 | adcs $acc3,$acc3,$t2 |
| 1251 | mul $t2,$m2,$mi |
| 1252 | adc $acc4,$acc4,$t3 // can't overflow |
| 1253 | mul $t3,$m3,$mi |
| 1254 | // (*) adds xzr,$acc0,$t0 |
| 1255 | subs xzr,$acc0,#1 // (*) |
| 1256 | umulh $t0,$m0,$mi // hi(n[0..3]*t[0]*n0 |
| 1257 | adcs $acc0,$acc1,$t1 |
| 1258 | umulh $t1,$m1,$mi |
| 1259 | adcs $acc1,$acc2,$t2 |
| 1260 | umulh $t2,$m2,$mi |
| 1261 | adcs $acc2,$acc3,$t3 |
| 1262 | umulh $t3,$m3,$mi |
| 1263 | adcs $acc3,$acc4,$carry |
| 1264 | adc $carry,xzr,xzr |
| 1265 | adds $acc0,$acc0,$t0 |
| 1266 | adcs $acc1,$acc1,$t1 |
| 1267 | adcs $acc2,$acc2,$t2 |
| 1268 | adcs $acc3,$acc3,$t3 |
| 1269 | //adc $carry,$carry,xzr |
| 1270 | cbnz $cnt,.Loop_mul4x_reduction |
| 1271 | |
| 1272 | adc $carry,$carry,xzr |
| 1273 | ldp $t0,$t1,[$tp,#8*4] // t[4..7] |
| 1274 | ldp $t2,$t3,[$tp,#8*6] |
| 1275 | ldp $a0,$a1,[$ap,#8*0] // a[4..7] |
| 1276 | ldp $a2,$a3,[$ap,#8*2] |
| 1277 | add $ap,$ap,#8*4 |
| 1278 | adds $acc0,$acc0,$t0 |
| 1279 | adcs $acc1,$acc1,$t1 |
| 1280 | adcs $acc2,$acc2,$t2 |
| 1281 | adcs $acc3,$acc3,$t3 |
| 1282 | //adc $carry,$carry,xzr |
| 1283 | |
| 1284 | ldr $mi,[sp] // t[0]*n0 |
| 1285 | ldp $m0,$m1,[$np,#8*0] // n[4..7] |
| 1286 | ldp $m2,$m3,[$np,#8*2] |
| 1287 | add $np,$np,#8*4 |
| 1288 | |
| 1289 | .align 4 |
| 1290 | .Loop_mul4x_tail: |
| 1291 | mul $t0,$a0,$bi // lo(a[4..7]*b[4]) |
| 1292 | adc $carry,$carry,xzr // modulo-scheduled |
| 1293 | mul $t1,$a1,$bi |
| 1294 | add $cnt,$cnt,#8 |
| 1295 | mul $t2,$a2,$bi |
| 1296 | and $cnt,$cnt,#31 |
| 1297 | mul $t3,$a3,$bi |
| 1298 | adds $acc0,$acc0,$t0 |
| 1299 | umulh $t0,$a0,$bi // hi(a[4..7]*b[4]) |
| 1300 | adcs $acc1,$acc1,$t1 |
| 1301 | umulh $t1,$a1,$bi |
| 1302 | adcs $acc2,$acc2,$t2 |
| 1303 | umulh $t2,$a2,$bi |
| 1304 | adcs $acc3,$acc3,$t3 |
| 1305 | umulh $t3,$a3,$bi |
| 1306 | adc $acc4,xzr,xzr |
| 1307 | ldr $bi,[$bp,$cnt] // next b[i] |
| 1308 | adds $acc1,$acc1,$t0 |
| 1309 | mul $t0,$m0,$mi // lo(n[4..7]*t[0]*n0) |
| 1310 | adcs $acc2,$acc2,$t1 |
| 1311 | mul $t1,$m1,$mi |
| 1312 | adcs $acc3,$acc3,$t2 |
| 1313 | mul $t2,$m2,$mi |
| 1314 | adc $acc4,$acc4,$t3 // can't overflow |
| 1315 | mul $t3,$m3,$mi |
| 1316 | adds $acc0,$acc0,$t0 |
| 1317 | umulh $t0,$m0,$mi // hi(n[4..7]*t[0]*n0) |
| 1318 | adcs $acc1,$acc1,$t1 |
| 1319 | umulh $t1,$m1,$mi |
| 1320 | adcs $acc2,$acc2,$t2 |
| 1321 | umulh $t2,$m2,$mi |
| 1322 | adcs $acc3,$acc3,$t3 |
| 1323 | umulh $t3,$m3,$mi |
| 1324 | adcs $acc4,$acc4,$carry |
| 1325 | ldr $mi,[sp,$cnt] // next a[0]*n0 |
| 1326 | adc $carry,xzr,xzr |
| 1327 | str $acc0,[$tp],#8 // result!!! |
| 1328 | adds $acc0,$acc1,$t0 |
| 1329 | sub $t0,$ap_end,$ap // done yet? |
| 1330 | adcs $acc1,$acc2,$t1 |
| 1331 | adcs $acc2,$acc3,$t2 |
| 1332 | adcs $acc3,$acc4,$t3 |
| 1333 | //adc $carry,$carry,xzr |
| 1334 | cbnz $cnt,.Loop_mul4x_tail |
| 1335 | |
| 1336 | sub $t1,$np,$num // rewinded np? |
| 1337 | adc $carry,$carry,xzr |
| 1338 | cbz $t0,.Loop_mul4x_break |
| 1339 | |
| 1340 | ldp $t0,$t1,[$tp,#8*4] |
| 1341 | ldp $t2,$t3,[$tp,#8*6] |
| 1342 | ldp $a0,$a1,[$ap,#8*0] |
| 1343 | ldp $a2,$a3,[$ap,#8*2] |
| 1344 | add $ap,$ap,#8*4 |
| 1345 | adds $acc0,$acc0,$t0 |
| 1346 | adcs $acc1,$acc1,$t1 |
| 1347 | adcs $acc2,$acc2,$t2 |
| 1348 | adcs $acc3,$acc3,$t3 |
| 1349 | //adc $carry,$carry,xzr |
| 1350 | ldp $m0,$m1,[$np,#8*0] |
| 1351 | ldp $m2,$m3,[$np,#8*2] |
| 1352 | add $np,$np,#8*4 |
| 1353 | b .Loop_mul4x_tail |
| 1354 | |
| 1355 | .align 4 |
| 1356 | .Loop_mul4x_break: |
| 1357 | ldp $t2,$t3,[x29,#96] // pull rp and &b[num] |
| 1358 | adds $acc0,$acc0,$topmost |
| 1359 | add $bp,$bp,#8*4 // bp++ |
| 1360 | adcs $acc1,$acc1,xzr |
| 1361 | sub $ap,$ap,$num // rewind ap |
| 1362 | adcs $acc2,$acc2,xzr |
| 1363 | stp $acc0,$acc1,[$tp,#8*0] // result!!! |
| 1364 | adcs $acc3,$acc3,xzr |
| 1365 | ldp $acc0,$acc1,[sp,#8*4] // t[0..3] |
| 1366 | adc $topmost,$carry,xzr |
| 1367 | stp $acc2,$acc3,[$tp,#8*2] // result!!! |
| 1368 | cmp $bp,$t3 // done yet? |
| 1369 | ldp $acc2,$acc3,[sp,#8*6] |
| 1370 | ldp $m0,$m1,[$t1,#8*0] // n[0..3] |
| 1371 | ldp $m2,$m3,[$t1,#8*2] |
| 1372 | add $np,$t1,#8*4 |
| 1373 | b.eq .Lmul4x_post |
| 1374 | |
| 1375 | ldr $bi,[$bp] |
| 1376 | ldp $a0,$a1,[$ap,#8*0] // a[0..3] |
| 1377 | ldp $a2,$a3,[$ap,#8*2] |
| 1378 | adds $ap,$ap,#8*4 // clear carry bit |
| 1379 | mov $carry,xzr |
| 1380 | mov $tp,sp |
| 1381 | b .Loop_mul4x_reduction |
| 1382 | |
| 1383 | .align 4 |
| 1384 | .Lmul4x_post: |
| 1385 | // Final step. We see if result is larger than modulus, and |
| 1386 | // if it is, subtract the modulus. But comparison implies |
| 1387 | // subtraction. So we subtract modulus, see if it borrowed, |
| 1388 | // and conditionally copy original value. |
| 1389 | mov $rp,$t2 |
| 1390 | mov $ap_end,$t2 // $rp copy |
| 1391 | subs $t0,$acc0,$m0 |
| 1392 | add $tp,sp,#8*8 |
| 1393 | sbcs $t1,$acc1,$m1 |
| 1394 | sub $cnt,$num,#8*4 |
| 1395 | |
| 1396 | .Lmul4x_sub: |
| 1397 | sbcs $t2,$acc2,$m2 |
| 1398 | ldp $m0,$m1,[$np,#8*0] |
| 1399 | sub $cnt,$cnt,#8*4 |
| 1400 | ldp $acc0,$acc1,[$tp,#8*0] |
| 1401 | sbcs $t3,$acc3,$m3 |
| 1402 | ldp $m2,$m3,[$np,#8*2] |
| 1403 | add $np,$np,#8*4 |
| 1404 | ldp $acc2,$acc3,[$tp,#8*2] |
| 1405 | add $tp,$tp,#8*4 |
| 1406 | stp $t0,$t1,[$rp,#8*0] |
| 1407 | sbcs $t0,$acc0,$m0 |
| 1408 | stp $t2,$t3,[$rp,#8*2] |
| 1409 | add $rp,$rp,#8*4 |
| 1410 | sbcs $t1,$acc1,$m1 |
| 1411 | cbnz $cnt,.Lmul4x_sub |
| 1412 | |
| 1413 | sbcs $t2,$acc2,$m2 |
| 1414 | mov $tp,sp |
| 1415 | add $ap,sp,#8*4 |
| 1416 | ldp $a0,$a1,[$ap_end,#8*0] |
| 1417 | sbcs $t3,$acc3,$m3 |
| 1418 | stp $t0,$t1,[$rp,#8*0] |
| 1419 | ldp $a2,$a3,[$ap_end,#8*2] |
| 1420 | stp $t2,$t3,[$rp,#8*2] |
| 1421 | ldp $acc0,$acc1,[$ap,#8*0] |
| 1422 | ldp $acc2,$acc3,[$ap,#8*2] |
| 1423 | sbcs xzr,$topmost,xzr // did it borrow? |
| 1424 | ldr x30,[x29,#8] // pull return address |
| 1425 | |
| 1426 | sub $cnt,$num,#8*4 |
| 1427 | .Lmul4x_cond_copy: |
| 1428 | sub $cnt,$cnt,#8*4 |
| 1429 | csel $t0,$acc0,$a0,lo |
| 1430 | stp xzr,xzr,[$tp,#8*0] |
| 1431 | csel $t1,$acc1,$a1,lo |
| 1432 | ldp $a0,$a1,[$ap_end,#8*4] |
| 1433 | ldp $acc0,$acc1,[$ap,#8*4] |
| 1434 | csel $t2,$acc2,$a2,lo |
| 1435 | stp xzr,xzr,[$tp,#8*2] |
| 1436 | add $tp,$tp,#8*4 |
| 1437 | csel $t3,$acc3,$a3,lo |
| 1438 | ldp $a2,$a3,[$ap_end,#8*6] |
| 1439 | ldp $acc2,$acc3,[$ap,#8*6] |
| 1440 | add $ap,$ap,#8*4 |
| 1441 | stp $t0,$t1,[$ap_end,#8*0] |
| 1442 | stp $t2,$t3,[$ap_end,#8*2] |
| 1443 | add $ap_end,$ap_end,#8*4 |
| 1444 | cbnz $cnt,.Lmul4x_cond_copy |
| 1445 | |
| 1446 | csel $t0,$acc0,$a0,lo |
| 1447 | stp xzr,xzr,[$tp,#8*0] |
| 1448 | csel $t1,$acc1,$a1,lo |
| 1449 | stp xzr,xzr,[$tp,#8*2] |
| 1450 | csel $t2,$acc2,$a2,lo |
| 1451 | stp xzr,xzr,[$tp,#8*3] |
| 1452 | csel $t3,$acc3,$a3,lo |
| 1453 | stp xzr,xzr,[$tp,#8*4] |
| 1454 | stp $t0,$t1,[$ap_end,#8*0] |
| 1455 | stp $t2,$t3,[$ap_end,#8*2] |
| 1456 | |
| 1457 | b .Lmul4x_done |
| 1458 | |
| 1459 | .align 4 |
| 1460 | .Lmul4x4_post_condition: |
| 1461 | adc $carry,$carry,xzr |
| 1462 | ldr $ap,[x29,#96] // pull rp |
| 1463 | // $acc0-3,$carry hold result, $m0-7 hold modulus |
| 1464 | subs $a0,$acc0,$m0 |
| 1465 | ldr x30,[x29,#8] // pull return address |
| 1466 | sbcs $a1,$acc1,$m1 |
| 1467 | stp xzr,xzr,[sp,#8*0] |
| 1468 | sbcs $a2,$acc2,$m2 |
| 1469 | stp xzr,xzr,[sp,#8*2] |
| 1470 | sbcs $a3,$acc3,$m3 |
| 1471 | stp xzr,xzr,[sp,#8*4] |
| 1472 | sbcs xzr,$carry,xzr // did it borrow? |
| 1473 | stp xzr,xzr,[sp,#8*6] |
| 1474 | |
| 1475 | // $a0-3 hold result-modulus |
| 1476 | csel $a0,$acc0,$a0,lo |
| 1477 | csel $a1,$acc1,$a1,lo |
| 1478 | csel $a2,$acc2,$a2,lo |
| 1479 | csel $a3,$acc3,$a3,lo |
| 1480 | stp $a0,$a1,[$ap,#8*0] |
| 1481 | stp $a2,$a3,[$ap,#8*2] |
| 1482 | |
| 1483 | .Lmul4x_done: |
| 1484 | ldp x19,x20,[x29,#16] |
| 1485 | mov sp,x29 |
| 1486 | ldp x21,x22,[x29,#32] |
| 1487 | mov x0,#1 |
| 1488 | ldp x23,x24,[x29,#48] |
| 1489 | ldp x25,x26,[x29,#64] |
| 1490 | ldp x27,x28,[x29,#80] |
| 1491 | ldr x29,[sp],#128 |
| 1492 | ret |
| 1493 | .size __bn_mul4x_mont,.-__bn_mul4x_mont |
| 1494 | ___ |
| 1495 | } |
| 1496 | $code.=<<___; |
| 1497 | .asciz "Montgomery Multiplication for ARMv8, CRYPTOGAMS by <appro\@openssl.org>" |
| 1498 | .align 4 |
| 1499 | ___ |
| 1500 | |
| 1501 | print $code; |
| 1502 | |
| 1503 | close STDOUT; |