1 #!/usr/bin/env perl
   2 #
   3 # Copyright (c) 2010-2011 Intel Corp.
   4 #   Author: Vinodh.Gopal@intel.com
   5 #           Jim Guilford
   6 #           Erdinc.Ozturk@intel.com
   7 #           Maxim.Perminov@intel.com
   8 #
   9 # More information about algorithm used can be found at:
  10 #   http://www.cse.buffalo.edu/srds2009/escs2009_submission_Gopal.pdf
  11 #
  12 # ====================================================================
  13 # Copyright (c) 2011 The OpenSSL Project.  All rights reserved.
  14 #
  15 # Redistribution and use in source and binary forms, with or without
  16 # modification, are permitted provided that the following conditions
  17 # are met:
  18 #
  19 # 1. Redistributions of source code must retain the above copyright
  20 #    notice, this list of conditions and the following disclaimer.
  21 #
  22 # 2. Redistributions in binary form must reproduce the above copyright
  23 #    notice, this list of conditions and the following disclaimer in
  24 #    the documentation and/or other materials provided with the
  25 #    distribution.
  26 #
  27 # 3. All advertising materials mentioning features or use of this
  28 #    software must display the following acknowledgment:
  29 #    "This product includes software developed by the OpenSSL Project
  30 #    for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
  31 #
  32 # 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  33 #    endorse or promote products derived from this software without
  34 #    prior written permission. For written permission, please contact
  35 #    licensing@OpenSSL.org.
  36 #
  37 # 5. Products derived from this software may not be called "OpenSSL"
  38 #    nor may "OpenSSL" appear in their names without prior written
  39 #    permission of the OpenSSL Project.
  40 #
  41 # 6. Redistributions of any form whatsoever must retain the following
  42 #    acknowledgment:
  43 #    "This product includes software developed by the OpenSSL Project
  44 #    for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
  45 #
  46 # THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  47 # EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  48 # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  49 # PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  50 # ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  51 # SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  52 # NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  53 # LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  54 # HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  55 # STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  56 # ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  57 # OF THE POSSIBILITY OF SUCH DAMAGE.
  58 # ====================================================================
  59 
  60 $flavour = shift;
  61 $output  = shift;
  62 if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
  63 
  64 my $win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
  65 
  66 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
  67 ( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
  68 ( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
  69 die "can't locate x86_64-xlate.pl";
  70 
  71 open OUT,"| \"$^X\" $xlate $flavour $output";
  72 *STDOUT=*OUT;
  73 
  74 use strict;
  75 my $code=".text\n\n";
  76 my $m=0;
  77 
  78 #
  79 # Define x512 macros
  80 #
  81 
  82 #MULSTEP_512_ADD        MACRO   x7, x6, x5, x4, x3, x2, x1, x0, dst, src1, src2, add_src, tmp1, tmp2
  83 #
  84 # uses rax, rdx, and args
  85 sub MULSTEP_512_ADD
  86 {
  87  my ($x, $DST, $SRC2, $ASRC, $OP, $TMP)=@_;
  88  my @X=@$x;     # make a copy
  89 $code.=<<___;
  90          mov    (+8*0)($SRC2), %rax
  91          mul    $OP                     # rdx:rax = %OP * [0]
  92          mov    ($ASRC), $X[0]
  93          add    %rax, $X[0]
  94          adc    \$0, %rdx
  95          mov    $X[0], $DST
  96 ___
  97 for(my $i=1;$i<8;$i++) {
  98 $code.=<<___;
  99          mov    %rdx, $TMP
 100 
 101          mov    (+8*$i)($SRC2), %rax
 102          mul    $OP                     # rdx:rax = %OP * [$i]
 103          mov    (+8*$i)($ASRC), $X[$i]
 104          add    %rax, $X[$i]
 105          adc    \$0, %rdx
 106          add    $TMP, $X[$i]
 107          adc    \$0, %rdx
 108 ___
 109 }
 110 $code.=<<___;
 111          mov    %rdx, $X[0]
 112 ___
 113 }
 114 
 115 #MULSTEP_512    MACRO   x7, x6, x5, x4, x3, x2, x1, x0, dst, src2, src1_val, tmp
 116 #
 117 # uses rax, rdx, and args
 118 sub MULSTEP_512
 119 {
 120  my ($x, $DST, $SRC2, $OP, $TMP)=@_;
 121  my @X=@$x;     # make a copy
 122 $code.=<<___;
 123          mov    (+8*0)($SRC2), %rax
 124          mul    $OP                     # rdx:rax = %OP * [0]
 125          add    %rax, $X[0]
 126          adc    \$0, %rdx
 127          mov    $X[0], $DST
 128 ___
 129 for(my $i=1;$i<8;$i++) {
 130 $code.=<<___;
 131          mov    %rdx, $TMP
 132 
 133          mov    (+8*$i)($SRC2), %rax
 134          mul    $OP                     # rdx:rax = %OP * [$i]
 135          add    %rax, $X[$i]
 136          adc    \$0, %rdx
 137          add    $TMP, $X[$i]
 138          adc    \$0, %rdx
 139 ___
 140 }
 141 $code.=<<___;
 142          mov    %rdx, $X[0]
 143 ___
 144 }
 145 
 146 #
 147 # Swizzle Macros
 148 #
 149 
 150 # macro to copy data from flat space to swizzled table
 151 #MACRO swizzle  pDst, pSrc, tmp1, tmp2
 152 # pDst and pSrc are modified
 153 sub swizzle
 154 {
 155  my ($pDst, $pSrc, $cnt, $d0)=@_;
 156 $code.=<<___;
 157          mov    \$8, $cnt
 158 loop_$m:
 159          mov    ($pSrc), $d0
 160          mov    $d0#w, ($pDst)
 161          shr    \$16, $d0
 162          mov    $d0#w, (+64*1)($pDst)
 163          shr    \$16, $d0
 164          mov    $d0#w, (+64*2)($pDst)
 165          shr    \$16, $d0
 166          mov    $d0#w, (+64*3)($pDst)
 167          lea    8($pSrc), $pSrc
 168          lea    64*4($pDst), $pDst
 169          dec    $cnt
 170          jnz    loop_$m
 171 ___
 172 
 173  $m++;
 174 }
 175 
 176 # macro to copy data from swizzled table to  flat space
 177 #MACRO unswizzle        pDst, pSrc, tmp*3
 178 sub unswizzle
 179 {
 180  my ($pDst, $pSrc, $cnt, $d0, $d1)=@_;
 181 $code.=<<___;
 182          mov    \$4, $cnt
 183 loop_$m:
 184          movzxw (+64*3+256*0)($pSrc), $d0
 185          movzxw (+64*3+256*1)($pSrc), $d1
 186          shl    \$16, $d0
 187          shl    \$16, $d1
 188          mov    (+64*2+256*0)($pSrc), $d0#w
 189          mov    (+64*2+256*1)($pSrc), $d1#w
 190          shl    \$16, $d0
 191          shl    \$16, $d1
 192          mov    (+64*1+256*0)($pSrc), $d0#w
 193          mov    (+64*1+256*1)($pSrc), $d1#w
 194          shl    \$16, $d0
 195          shl    \$16, $d1
 196          mov    (+64*0+256*0)($pSrc), $d0#w
 197          mov    (+64*0+256*1)($pSrc), $d1#w
 198          mov    $d0, (+8*0)($pDst)
 199          mov    $d1, (+8*1)($pDst)
 200          lea    256*2($pSrc), $pSrc
 201          lea    8*2($pDst), $pDst
 202          sub    \$1, $cnt
 203          jnz    loop_$m
 204 ___
 205 
 206  $m++;
 207 }
 208 
 209 #
 210 # Data Structures
 211 #
 212 
 213 # Reduce Data
 214 #
 215 #
 216 # Offset  Value
 217 # 0C0     Carries
 218 # 0B8     X2[10]
 219 # 0B0     X2[9]
 220 # 0A8     X2[8]
 221 # 0A0     X2[7]
 222 # 098     X2[6]
 223 # 090     X2[5]
 224 # 088     X2[4]
 225 # 080     X2[3]
 226 # 078     X2[2]
 227 # 070     X2[1]
 228 # 068     X2[0]
 229 # 060     X1[12]  P[10]
 230 # 058     X1[11]  P[9]  Z[8]
 231 # 050     X1[10]  P[8]  Z[7]
 232 # 048     X1[9]   P[7]  Z[6]
 233 # 040     X1[8]   P[6]  Z[5]
 234 # 038     X1[7]   P[5]  Z[4]
 235 # 030     X1[6]   P[4]  Z[3]
 236 # 028     X1[5]   P[3]  Z[2]
 237 # 020     X1[4]   P[2]  Z[1]
 238 # 018     X1[3]   P[1]  Z[0]
 239 # 010     X1[2]   P[0]  Y[2]
 240 # 008     X1[1]   Q[1]  Y[1]
 241 # 000     X1[0]   Q[0]  Y[0]
 242 
 243 my $X1_offset           =  0;                   # 13 qwords
 244 my $X2_offset           =  $X1_offset + 13*8;                   # 11 qwords
 245 my $Carries_offset      =  $X2_offset + 11*8;                   # 1 qword
 246 my $Q_offset            =  0;                   # 2 qwords
 247 my $P_offset            =  $Q_offset + 2*8;                     # 11 qwords
 248 my $Y_offset            =  0;                   # 3 qwords
 249 my $Z_offset            =  $Y_offset + 3*8;                     # 9 qwords
 250 
 251 my $Red_Data_Size       =  $Carries_offset + 1*8;                       # (25 qwords)
 252 
 253 #
 254 # Stack Frame
 255 #
 256 #
 257 # offset        value
 258 # ...           <old stack contents>
 259 # ...
 260 # 280           Garray
 261 
 262 # 278           tmp16[15]
 263 # ...           ...
 264 # 200           tmp16[0]
 265 
 266 # 1F8           tmp[7]
 267 # ...           ...
 268 # 1C0           tmp[0]
 269 
 270 # 1B8           GT[7]
 271 # ...           ...
 272 # 180           GT[0]
 273 
 274 # 178           Reduce Data
 275 # ...           ...
 276 # 0B8           Reduce Data
 277 # 0B0           reserved
 278 # 0A8           reserved
 279 # 0A0           reserved
 280 # 098           reserved
 281 # 090           reserved
 282 # 088           reduce result addr
 283 # 080           exp[8]
 284 
 285 # ...
 286 # 048           exp[1]
 287 # 040           exp[0]
 288 
 289 # 038           reserved
 290 # 030           loop_idx
 291 # 028           pg
 292 # 020           i
 293 # 018           pData   ; arg 4
 294 # 010           pG      ; arg 2
 295 # 008           pResult ; arg 1
 296 # 000           rsp     ; stack pointer before subtract
 297 
 298 my $rsp_offset          =  0;
 299 my $pResult_offset      =  8*1 + $rsp_offset;
 300 my $pG_offset           =  8*1 + $pResult_offset;
 301 my $pData_offset        =  8*1 + $pG_offset;
 302 my $i_offset            =  8*1 + $pData_offset;
 303 my $pg_offset           =  8*1 + $i_offset;
 304 my $loop_idx_offset     =  8*1 + $pg_offset;
 305 my $reserved1_offset    =  8*1 + $loop_idx_offset;
 306 my $exp_offset          =  8*1 + $reserved1_offset;
 307 my $red_result_addr_offset=  8*9 + $exp_offset;
 308 my $reserved2_offset    =  8*1 + $red_result_addr_offset;
 309 my $Reduce_Data_offset  =  8*5 + $reserved2_offset;
 310 my $GT_offset           =  $Red_Data_Size + $Reduce_Data_offset;
 311 my $tmp_offset          =  8*8 + $GT_offset;
 312 my $tmp16_offset        =  8*8 + $tmp_offset;
 313 my $garray_offset       =  8*16 + $tmp16_offset;
 314 my $mem_size            =  8*8*32 + $garray_offset;
 315 
 316 #
 317 # Offsets within Reduce Data
 318 #
 319 #
 320 #       struct MODF_2FOLD_MONT_512_C1_DATA {
 321 #       UINT64 t[8][8];
 322 #       UINT64 m[8];
 323 #       UINT64 m1[8]; /* 2^768 % m */
 324 #       UINT64 m2[8]; /* 2^640 % m */
 325 #       UINT64 k1[2]; /* (- 1/m) % 2^128 */
 326 #       };
 327 
 328 my $T                   =  0;
 329 my $M                   =  512;                 # = 8 * 8 * 8
 330 my $M1                  =  576;                 # = 8 * 8 * 9 /* += 8 * 8 */
 331 my $M2                  =  640;                 # = 8 * 8 * 10 /* += 8 * 8 */
 332 my $K1                  =  704;                 # = 8 * 8 * 11 /* += 8 * 8 */
 333 
 334 #
 335 #   FUNCTIONS
 336 #
 337 
 338 {{{
 339 #
 340 # MULADD_128x512 : Function to multiply 128-bits (2 qwords) by 512-bits (8 qwords)
 341 #                       and add 512-bits (8 qwords)
 342 #                       to get 640 bits (10 qwords)
 343 # Input: 128-bit mul source: [rdi+8*1], rbp
 344 #        512-bit mul source: [rsi+8*n]
 345 #        512-bit add source: r15, r14, ..., r9, r8
 346 # Output: r9, r8, r15, r14, r13, r12, r11, r10, [rcx+8*1], [rcx+8*0]
 347 # Clobbers all regs except: rcx, rsi, rdi
 348 $code.=<<___;
 349 .type   MULADD_128x512,\@abi-omnipotent
 350 .align  16
 351 MULADD_128x512:
 352 ___
 353         &MULSTEP_512([map("%r$_",(8..15))], "(+8*0)(%rcx)", "%rsi", "%rbp", "%rbx");
 354 $code.=<<___;
 355          mov    (+8*1)(%rdi), %rbp
 356 ___
 357         &MULSTEP_512([map("%r$_",(9..15,8))], "(+8*1)(%rcx)", "%rsi", "%rbp", "%rbx");
 358 $code.=<<___;
 359          ret
 360 .size   MULADD_128x512,.-MULADD_128x512
 361 ___
 362 }}}
 363 
 364 {{{
 365 #MULADD_256x512 MACRO   pDst, pA, pB, OP, TMP, X7, X6, X5, X4, X3, X2, X1, X0
 366 #
 367 # Inputs: pDst: Destination  (768 bits, 12 qwords)
 368 #         pA:   Multiplicand (1024 bits, 16 qwords)
 369 #         pB:   Multiplicand (512 bits, 8 qwords)
 370 # Dst = Ah * B + Al
 371 # where Ah is (in qwords) A[15:12] (256 bits) and Al is A[7:0] (512 bits)
 372 # Results in X3 X2 X1 X0 X7 X6 X5 X4 Dst[3:0]
 373 # Uses registers: arguments, RAX, RDX
 374 sub MULADD_256x512
 375 {
 376  my ($pDst, $pA, $pB, $OP, $TMP, $X)=@_;
 377 $code.=<<___;
 378         mov     (+8*12)($pA), $OP
 379 ___
 380         &MULSTEP_512_ADD($X, "(+8*0)($pDst)", $pB, $pA, $OP, $TMP);
 381         push(@$X,shift(@$X));
 382 
 383 $code.=<<___;
 384          mov    (+8*13)($pA), $OP
 385 ___
 386         &MULSTEP_512($X, "(+8*1)($pDst)", $pB, $OP, $TMP);
 387         push(@$X,shift(@$X));
 388 
 389 $code.=<<___;
 390          mov    (+8*14)($pA), $OP
 391 ___
 392         &MULSTEP_512($X, "(+8*2)($pDst)", $pB, $OP, $TMP);
 393         push(@$X,shift(@$X));
 394 
 395 $code.=<<___;
 396          mov    (+8*15)($pA), $OP
 397 ___
 398         &MULSTEP_512($X, "(+8*3)($pDst)", $pB, $OP, $TMP);
 399         push(@$X,shift(@$X));
 400 }
 401 
 402 #
 403 # mont_reduce(UINT64 *x,  /* 1024 bits, 16 qwords */
 404 #              UINT64 *m,  /*  512 bits,  8 qwords */
 405 #              MODF_2FOLD_MONT_512_C1_DATA *data,
 406 #             UINT64 *r)  /*  512 bits,  8 qwords */
 407 # Input:  x (number to be reduced): tmp16 (Implicit)
 408 #         m (modulus):              [pM]  (Implicit)
 409 #         data (reduce data):       [pData] (Implicit)
 410 # Output: r (result):                Address in [red_res_addr]
 411 #         result also in: r9, r8, r15, r14, r13, r12, r11, r10
 412 
 413 my @X=map("%r$_",(8..15));
 414 
 415 $code.=<<___;
 416 .type   mont_reduce,\@abi-omnipotent
 417 .align  16
 418 mont_reduce:
 419 ___
 420 
 421 my $STACK_DEPTH         =  8;
 422         #
 423         # X1 = Xh * M1 + Xl
 424 $code.=<<___;
 425          lea    (+$Reduce_Data_offset+$X1_offset+$STACK_DEPTH)(%rsp), %rdi                      # pX1 (Dst) 769 bits, 13 qwords
 426          mov    (+$pData_offset+$STACK_DEPTH)(%rsp), %rsi                       # pM1 (Bsrc) 512 bits, 8 qwords
 427          add    \$$M1, %rsi
 428          lea    (+$tmp16_offset+$STACK_DEPTH)(%rsp), %rcx                       # X (Asrc) 1024 bits, 16 qwords
 429 
 430 ___
 431 
 432         &MULADD_256x512("%rdi", "%rcx", "%rsi", "%rbp", "%rbx", \@X);       # rotates @X 4 times
 433         # results in r11, r10, r9, r8, r15, r14, r13, r12, X1[3:0]
 434 
 435 $code.=<<___;
 436          xor    %rax, %rax
 437         # X1 += xl
 438          add    (+8*8)(%rcx), $X[4]
 439          adc    (+8*9)(%rcx), $X[5]
 440          adc    (+8*10)(%rcx), $X[6]
 441          adc    (+8*11)(%rcx), $X[7]
 442          adc    \$0, %rax
 443         # X1 is now rax, r11-r8, r15-r12, tmp16[3:0]
 444 
 445         #
 446         # check for carry ;; carry stored in rax
 447          mov    $X[4], (+8*8)(%rdi)                     # rdi points to X1
 448          mov    $X[5], (+8*9)(%rdi)
 449          mov    $X[6], %rbp
 450          mov    $X[7], (+8*11)(%rdi)
 451 
 452          mov    %rax, (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp)
 453 
 454          mov    (+8*0)(%rdi), $X[4]
 455          mov    (+8*1)(%rdi), $X[5]
 456          mov    (+8*2)(%rdi), $X[6]
 457          mov    (+8*3)(%rdi), $X[7]
 458 
 459         # X1 is now stored in: X1[11], rbp, X1[9:8], r15-r8
 460         # rdi -> X1
 461         # rsi -> M1
 462 
 463         #
 464         # X2 = Xh * M2 + Xl
 465         # do first part (X2 = Xh * M2)
 466          add    \$8*10, %rdi                    # rdi -> pXh ; 128 bits, 2 qwords
 467                                 #        Xh is actually { [rdi+8*1], rbp }
 468          add    \$`$M2-$M1`, %rsi                       # rsi -> M2
 469          lea    (+$Reduce_Data_offset+$X2_offset+$STACK_DEPTH)(%rsp), %rcx                      # rcx -> pX2 ; 641 bits, 11 qwords
 470 ___
 471         unshift(@X,pop(@X));    unshift(@X,pop(@X));
 472 $code.=<<___;
 473 
 474          call   MULADD_128x512                  # args in rcx, rdi / rbp, rsi, r15-r8
 475         # result in r9, r8, r15, r14, r13, r12, r11, r10, X2[1:0]
 476          mov    (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp), %rax
 477 
 478         # X2 += Xl
 479          add    (+8*8-8*10)(%rdi), $X[6]                # (-8*10) is to adjust rdi -> Xh to Xl
 480          adc    (+8*9-8*10)(%rdi), $X[7]
 481          mov    $X[6], (+8*8)(%rcx)
 482          mov    $X[7], (+8*9)(%rcx)
 483 
 484          adc    %rax, %rax
 485          mov    %rax, (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp)
 486 
 487          lea    (+$Reduce_Data_offset+$Q_offset+$STACK_DEPTH)(%rsp), %rdi                       # rdi -> pQ ; 128 bits, 2 qwords
 488          add    \$`$K1-$M2`, %rsi                       # rsi -> pK1 ; 128 bits, 2 qwords
 489 
 490         # MUL_128x128t128       rdi, rcx, rsi   ; Q = X2 * K1 (bottom half)
 491         # B1:B0 = rsi[1:0] = K1[1:0]
 492         # A1:A0 = rcx[1:0] = X2[1:0]
 493         # Result = rdi[1],rbp = Q[1],rbp
 494          mov    (%rsi), %r8                     # B0
 495          mov    (+8*1)(%rsi), %rbx                      # B1
 496 
 497          mov    (%rcx), %rax                    # A0
 498          mul    %r8                     # B0
 499          mov    %rax, %rbp
 500          mov    %rdx, %r9
 501 
 502          mov    (+8*1)(%rcx), %rax                      # A1
 503          mul    %r8                     # B0
 504          add    %rax, %r9
 505 
 506          mov    (%rcx), %rax                    # A0
 507          mul    %rbx                    # B1
 508          add    %rax, %r9
 509 
 510          mov    %r9, (+8*1)(%rdi)
 511         # end MUL_128x128t128
 512 
 513          sub    \$`$K1-$M`, %rsi
 514 
 515          mov    (%rcx), $X[6]
 516          mov    (+8*1)(%rcx), $X[7]                     # r9:r8 = X2[1:0]
 517 
 518          call   MULADD_128x512                  # args in rcx, rdi / rbp, rsi, r15-r8
 519         # result in r9, r8, r15, r14, r13, r12, r11, r10, X2[1:0]
 520 
 521         # load first half of m to rdx, rdi, rbx, rax
 522         # moved this here for efficiency
 523          mov    (+8*0)(%rsi), %rax
 524          mov    (+8*1)(%rsi), %rbx
 525          mov    (+8*2)(%rsi), %rdi
 526          mov    (+8*3)(%rsi), %rdx
 527 
 528         # continue with reduction
 529          mov    (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp), %rbp
 530 
 531          add    (+8*8)(%rcx), $X[6]
 532          adc    (+8*9)(%rcx), $X[7]
 533 
 534         #accumulate the final carry to rbp
 535          adc    %rbp, %rbp
 536 
 537         # Add in overflow corrections: R = (X2>>128) += T[overflow]
 538         # R = {r9, r8, r15, r14, ..., r10}
 539          shl    \$3, %rbp
 540          mov    (+$pData_offset+$STACK_DEPTH)(%rsp), %rcx                       # rsi -> Data (and points to T)
 541          add    %rcx, %rbp                      # pT ; 512 bits, 8 qwords, spread out
 542 
 543         # rsi will be used to generate a mask after the addition
 544          xor    %rsi, %rsi
 545 
 546          add    (+8*8*0)(%rbp), $X[0]
 547          adc    (+8*8*1)(%rbp), $X[1]
 548          adc    (+8*8*2)(%rbp), $X[2]
 549          adc    (+8*8*3)(%rbp), $X[3]
 550          adc    (+8*8*4)(%rbp), $X[4]
 551          adc    (+8*8*5)(%rbp), $X[5]
 552          adc    (+8*8*6)(%rbp), $X[6]
 553          adc    (+8*8*7)(%rbp), $X[7]
 554 
 555         # if there is a carry:  rsi = 0xFFFFFFFFFFFFFFFF
 556         # if carry is clear:    rsi = 0x0000000000000000
 557          sbb    \$0, %rsi
 558 
 559         # if carry is clear, subtract 0. Otherwise, subtract 256 bits of m
 560          and    %rsi, %rax
 561          and    %rsi, %rbx
 562          and    %rsi, %rdi
 563          and    %rsi, %rdx
 564 
 565          mov    \$1, %rbp
 566          sub    %rax, $X[0]
 567          sbb    %rbx, $X[1]
 568          sbb    %rdi, $X[2]
 569          sbb    %rdx, $X[3]
 570 
 571         # if there is a borrow:         rbp = 0
 572         # if there is no borrow:        rbp = 1
 573         # this is used to save the borrows in between the first half and the 2nd half of the subtraction of m
 574          sbb    \$0, %rbp
 575 
 576         #load second half of m to rdx, rdi, rbx, rax
 577 
 578          add    \$$M, %rcx
 579          mov    (+8*4)(%rcx), %rax
 580          mov    (+8*5)(%rcx), %rbx
 581          mov    (+8*6)(%rcx), %rdi
 582          mov    (+8*7)(%rcx), %rdx
 583 
 584         # use the rsi mask as before
 585         # if carry is clear, subtract 0. Otherwise, subtract 256 bits of m
 586          and    %rsi, %rax
 587          and    %rsi, %rbx
 588          and    %rsi, %rdi
 589          and    %rsi, %rdx
 590 
 591         # if rbp = 0, there was a borrow before, it is moved to the carry flag
 592         # if rbp = 1, there was not a borrow before, carry flag is cleared
 593          sub    \$1, %rbp
 594 
 595          sbb    %rax, $X[4]
 596          sbb    %rbx, $X[5]
 597          sbb    %rdi, $X[6]
 598          sbb    %rdx, $X[7]
 599 
 600         # write R back to memory
 601 
 602          mov    (+$red_result_addr_offset+$STACK_DEPTH)(%rsp), %rsi
 603          mov    $X[0], (+8*0)(%rsi)
 604          mov    $X[1], (+8*1)(%rsi)
 605          mov    $X[2], (+8*2)(%rsi)
 606          mov    $X[3], (+8*3)(%rsi)
 607          mov    $X[4], (+8*4)(%rsi)
 608          mov    $X[5], (+8*5)(%rsi)
 609          mov    $X[6], (+8*6)(%rsi)
 610          mov    $X[7], (+8*7)(%rsi)
 611 
 612          ret
 613 .size   mont_reduce,.-mont_reduce
 614 ___
 615 }}}
 616 
 617 {{{
 618 #MUL_512x512    MACRO   pDst, pA, pB, x7, x6, x5, x4, x3, x2, x1, x0, tmp*2
 619 #
 620 # Inputs: pDst: Destination  (1024 bits, 16 qwords)
 621 #         pA:   Multiplicand (512 bits, 8 qwords)
 622 #         pB:   Multiplicand (512 bits, 8 qwords)
 623 # Uses registers rax, rdx, args
 624 #   B operand in [pB] and also in x7...x0
 625 sub MUL_512x512
 626 {
 627  my ($pDst, $pA, $pB, $x, $OP, $TMP, $pDst_o)=@_;
 628  my ($pDst,  $pDst_o) = ($pDst =~ m/([^+]*)\+?(.*)?/);
 629  my @X=@$x;     # make a copy
 630 
 631 $code.=<<___;
 632          mov    (+8*0)($pA), $OP
 633 
 634          mov    $X[0], %rax
 635          mul    $OP                     # rdx:rax = %OP * [0]
 636          mov    %rax, (+$pDst_o+8*0)($pDst)
 637          mov    %rdx, $X[0]
 638 ___
 639 for(my $i=1;$i<8;$i++) {
 640 $code.=<<___;
 641          mov    $X[$i], %rax
 642          mul    $OP                     # rdx:rax = %OP * [$i]
 643          add    %rax, $X[$i-1]
 644          adc    \$0, %rdx
 645          mov    %rdx, $X[$i]
 646 ___
 647 }
 648 
 649 for(my $i=1;$i<8;$i++) {
 650 $code.=<<___;
 651          mov    (+8*$i)($pA), $OP
 652 ___
 653 
 654         &MULSTEP_512(\@X, "(+$pDst_o+8*$i)($pDst)", $pB, $OP, $TMP);
 655         push(@X,shift(@X));
 656 }
 657 
 658 $code.=<<___;
 659          mov    $X[0], (+$pDst_o+8*8)($pDst)
 660          mov    $X[1], (+$pDst_o+8*9)($pDst)
 661          mov    $X[2], (+$pDst_o+8*10)($pDst)
 662          mov    $X[3], (+$pDst_o+8*11)($pDst)
 663          mov    $X[4], (+$pDst_o+8*12)($pDst)
 664          mov    $X[5], (+$pDst_o+8*13)($pDst)
 665          mov    $X[6], (+$pDst_o+8*14)($pDst)
 666          mov    $X[7], (+$pDst_o+8*15)($pDst)
 667 ___
 668 }
 669 
 670 #
 671 # mont_mul_a3b : subroutine to compute (Src1 * Src2) % M (all 512-bits)
 672 # Input:  src1: Address of source 1: rdi
 673 #         src2: Address of source 2: rsi
 674 # Output: dst:  Address of destination: [red_res_addr]
 675 #    src2 and result also in: r9, r8, r15, r14, r13, r12, r11, r10
 676 # Temp:   Clobbers [tmp16], all registers
 677 $code.=<<___;
 678 .type   mont_mul_a3b,\@abi-omnipotent
 679 .align  16
 680 mont_mul_a3b:
 681         #
 682         # multiply tmp = src1 * src2
 683         # For multiply: dst = rcx, src1 = rdi, src2 = rsi
 684         # stack depth is extra 8 from call
 685 ___
 686         &MUL_512x512("%rsp+$tmp16_offset+8", "%rdi", "%rsi", [map("%r$_",(10..15,8..9))], "%rbp", "%rbx");
 687 $code.=<<___;
 688         #
 689         # Dst = tmp % m
 690         # Call reduce(tmp, m, data, dst)
 691 
 692         # tail recursion optimization: jmp to mont_reduce and return from there
 693          jmp    mont_reduce
 694         # call  mont_reduce
 695         # ret
 696 .size   mont_mul_a3b,.-mont_mul_a3b
 697 ___
 698 }}}
 699 
 700 {{{
 701 #SQR_512 MACRO pDest, pA, x7, x6, x5, x4, x3, x2, x1, x0, tmp*4
 702 #
 703 # Input in memory [pA] and also in x7...x0
 704 # Uses all argument registers plus rax and rdx
 705 #
 706 # This version computes all of the off-diagonal terms into memory,
 707 # and then it adds in the diagonal terms
 708 
 709 sub SQR_512
 710 {
 711  my ($pDst, $pA, $x, $A, $tmp, $x7, $x6, $pDst_o)=@_;
 712  my ($pDst,  $pDst_o) = ($pDst =~ m/([^+]*)\+?(.*)?/);
 713  my @X=@$x;     # make a copy
 714 $code.=<<___;
 715         # ------------------
 716         # first pass 01...07
 717         # ------------------
 718          mov    $X[0], $A
 719 
 720          mov    $X[1],%rax
 721          mul    $A
 722          mov    %rax, (+$pDst_o+8*1)($pDst)
 723 ___
 724 for(my $i=2;$i<8;$i++) {
 725 $code.=<<___;
 726          mov    %rdx, $X[$i-2]
 727          mov    $X[$i],%rax
 728          mul    $A
 729          add    %rax, $X[$i-2]
 730          adc    \$0, %rdx
 731 ___
 732 }
 733 $code.=<<___;
 734          mov    %rdx, $x7
 735 
 736          mov    $X[0], (+$pDst_o+8*2)($pDst)
 737 
 738         # ------------------
 739         # second pass 12...17
 740         # ------------------
 741 
 742          mov    (+8*1)($pA), $A
 743 
 744          mov    (+8*2)($pA),%rax
 745          mul    $A
 746          add    %rax, $X[1]
 747          adc    \$0, %rdx
 748          mov    $X[1], (+$pDst_o+8*3)($pDst)
 749 
 750          mov    %rdx, $X[0]
 751          mov    (+8*3)($pA),%rax
 752          mul    $A
 753          add    %rax, $X[2]
 754          adc    \$0, %rdx
 755          add    $X[0], $X[2]
 756          adc    \$0, %rdx
 757          mov    $X[2], (+$pDst_o+8*4)($pDst)
 758 
 759          mov    %rdx, $X[0]
 760          mov    (+8*4)($pA),%rax
 761          mul    $A
 762          add    %rax, $X[3]
 763          adc    \$0, %rdx
 764          add    $X[0], $X[3]
 765          adc    \$0, %rdx
 766 
 767          mov    %rdx, $X[0]
 768          mov    (+8*5)($pA),%rax
 769          mul    $A
 770          add    %rax, $X[4]
 771          adc    \$0, %rdx
 772          add    $X[0], $X[4]
 773          adc    \$0, %rdx
 774 
 775          mov    %rdx, $X[0]
 776          mov    $X[6],%rax
 777          mul    $A
 778          add    %rax, $X[5]
 779          adc    \$0, %rdx
 780          add    $X[0], $X[5]
 781          adc    \$0, %rdx
 782 
 783          mov    %rdx, $X[0]
 784          mov    $X[7],%rax
 785          mul    $A
 786          add    %rax, $x7
 787          adc    \$0, %rdx
 788          add    $X[0], $x7
 789          adc    \$0, %rdx
 790 
 791          mov    %rdx, $X[1]
 792 
 793         # ------------------
 794         # third pass 23...27
 795         # ------------------
 796          mov    (+8*2)($pA), $A
 797 
 798          mov    (+8*3)($pA),%rax
 799          mul    $A
 800          add    %rax, $X[3]
 801          adc    \$0, %rdx
 802          mov    $X[3], (+$pDst_o+8*5)($pDst)
 803 
 804          mov    %rdx, $X[0]
 805          mov    (+8*4)($pA),%rax
 806          mul    $A
 807          add    %rax, $X[4]
 808          adc    \$0, %rdx
 809          add    $X[0], $X[4]
 810          adc    \$0, %rdx
 811          mov    $X[4], (+$pDst_o+8*6)($pDst)
 812 
 813          mov    %rdx, $X[0]
 814          mov    (+8*5)($pA),%rax
 815          mul    $A
 816          add    %rax, $X[5]
 817          adc    \$0, %rdx
 818          add    $X[0], $X[5]
 819          adc    \$0, %rdx
 820 
 821          mov    %rdx, $X[0]
 822          mov    $X[6],%rax
 823          mul    $A
 824          add    %rax, $x7
 825          adc    \$0, %rdx
 826          add    $X[0], $x7
 827          adc    \$0, %rdx
 828 
 829          mov    %rdx, $X[0]
 830          mov    $X[7],%rax
 831          mul    $A
 832          add    %rax, $X[1]
 833          adc    \$0, %rdx
 834          add    $X[0], $X[1]
 835          adc    \$0, %rdx
 836 
 837          mov    %rdx, $X[2]
 838 
 839         # ------------------
 840         # fourth pass 34...37
 841         # ------------------
 842 
 843          mov    (+8*3)($pA), $A
 844 
 845          mov    (+8*4)($pA),%rax
 846          mul    $A
 847          add    %rax, $X[5]
 848          adc    \$0, %rdx
 849          mov    $X[5], (+$pDst_o+8*7)($pDst)
 850 
 851          mov    %rdx, $X[0]
 852          mov    (+8*5)($pA),%rax
 853          mul    $A
 854          add    %rax, $x7
 855          adc    \$0, %rdx
 856          add    $X[0], $x7
 857          adc    \$0, %rdx
 858          mov    $x7, (+$pDst_o+8*8)($pDst)
 859 
 860          mov    %rdx, $X[0]
 861          mov    $X[6],%rax
 862          mul    $A
 863          add    %rax, $X[1]
 864          adc    \$0, %rdx
 865          add    $X[0], $X[1]
 866          adc    \$0, %rdx
 867 
 868          mov    %rdx, $X[0]
 869          mov    $X[7],%rax
 870          mul    $A
 871          add    %rax, $X[2]
 872          adc    \$0, %rdx
 873          add    $X[0], $X[2]
 874          adc    \$0, %rdx
 875 
 876          mov    %rdx, $X[5]
 877 
 878         # ------------------
 879         # fifth pass 45...47
 880         # ------------------
 881          mov    (+8*4)($pA), $A
 882 
 883          mov    (+8*5)($pA),%rax
 884          mul    $A
 885          add    %rax, $X[1]
 886          adc    \$0, %rdx
 887          mov    $X[1], (+$pDst_o+8*9)($pDst)
 888 
 889          mov    %rdx, $X[0]
 890          mov    $X[6],%rax
 891          mul    $A
 892          add    %rax, $X[2]
 893          adc    \$0, %rdx
 894          add    $X[0], $X[2]
 895          adc    \$0, %rdx
 896          mov    $X[2], (+$pDst_o+8*10)($pDst)
 897 
 898          mov    %rdx, $X[0]
 899          mov    $X[7],%rax
 900          mul    $A
 901          add    %rax, $X[5]
 902          adc    \$0, %rdx
 903          add    $X[0], $X[5]
 904          adc    \$0, %rdx
 905 
 906          mov    %rdx, $X[1]
 907 
 908         # ------------------
 909         # sixth pass 56...57
 910         # ------------------
 911          mov    (+8*5)($pA), $A
 912 
 913          mov    $X[6],%rax
 914          mul    $A
 915          add    %rax, $X[5]
 916          adc    \$0, %rdx
 917          mov    $X[5], (+$pDst_o+8*11)($pDst)
 918 
 919          mov    %rdx, $X[0]
 920          mov    $X[7],%rax
 921          mul    $A
 922          add    %rax, $X[1]
 923          adc    \$0, %rdx
 924          add    $X[0], $X[1]
 925          adc    \$0, %rdx
 926          mov    $X[1], (+$pDst_o+8*12)($pDst)
 927 
 928          mov    %rdx, $X[2]
 929 
 930         # ------------------
 931         # seventh pass 67
 932         # ------------------
 933          mov    $X[6], $A
 934 
 935          mov    $X[7],%rax
 936          mul    $A
 937          add    %rax, $X[2]
 938          adc    \$0, %rdx
 939          mov    $X[2], (+$pDst_o+8*13)($pDst)
 940 
 941          mov    %rdx, (+$pDst_o+8*14)($pDst)
 942 
 943         # start finalize (add   in squares, and double off-terms)
 944          mov    (+$pDst_o+8*1)($pDst), $X[0]
 945          mov    (+$pDst_o+8*2)($pDst), $X[1]
 946          mov    (+$pDst_o+8*3)($pDst), $X[2]
 947          mov    (+$pDst_o+8*4)($pDst), $X[3]
 948          mov    (+$pDst_o+8*5)($pDst), $X[4]
 949          mov    (+$pDst_o+8*6)($pDst), $X[5]
 950 
 951          mov    (+8*3)($pA), %rax
 952          mul    %rax
 953          mov    %rax, $x6
 954          mov    %rdx, $X[6]
 955 
 956          add    $X[0], $X[0]
 957          adc    $X[1], $X[1]
 958          adc    $X[2], $X[2]
 959          adc    $X[3], $X[3]
 960          adc    $X[4], $X[4]
 961          adc    $X[5], $X[5]
 962          adc    \$0, $X[6]
 963 
 964          mov    (+8*0)($pA), %rax
 965          mul    %rax
 966          mov    %rax, (+$pDst_o+8*0)($pDst)
 967          mov    %rdx, $A
 968 
 969          mov    (+8*1)($pA), %rax
 970          mul    %rax
 971 
 972          add    $A, $X[0]
 973          adc    %rax, $X[1]
 974          adc    \$0, %rdx
 975 
 976          mov    %rdx, $A
 977          mov    $X[0], (+$pDst_o+8*1)($pDst)
 978          mov    $X[1], (+$pDst_o+8*2)($pDst)
 979 
 980          mov    (+8*2)($pA), %rax
 981          mul    %rax
 982 
 983          add    $A, $X[2]
 984          adc    %rax, $X[3]
 985          adc    \$0, %rdx
 986 
 987          mov    %rdx, $A
 988 
 989          mov    $X[2], (+$pDst_o+8*3)($pDst)
 990          mov    $X[3], (+$pDst_o+8*4)($pDst)
 991 
 992          xor    $tmp, $tmp
 993          add    $A, $X[4]
 994          adc    $x6, $X[5]
 995          adc    \$0, $tmp
 996 
 997          mov    $X[4], (+$pDst_o+8*5)($pDst)
 998          mov    $X[5], (+$pDst_o+8*6)($pDst)
 999 
1000         # %%tmp has 0/1 in column 7
1001         # %%A6 has a full value in column 7
1002 
1003          mov    (+$pDst_o+8*7)($pDst), $X[0]
1004          mov    (+$pDst_o+8*8)($pDst), $X[1]
1005          mov    (+$pDst_o+8*9)($pDst), $X[2]
1006          mov    (+$pDst_o+8*10)($pDst), $X[3]
1007          mov    (+$pDst_o+8*11)($pDst), $X[4]
1008          mov    (+$pDst_o+8*12)($pDst), $X[5]
1009          mov    (+$pDst_o+8*13)($pDst), $x6
1010          mov    (+$pDst_o+8*14)($pDst), $x7
1011 
1012          mov    $X[7], %rax
1013          mul    %rax
1014          mov    %rax, $X[7]
1015          mov    %rdx, $A
1016 
1017          add    $X[0], $X[0]
1018          adc    $X[1], $X[1]
1019          adc    $X[2], $X[2]
1020          adc    $X[3], $X[3]
1021          adc    $X[4], $X[4]
1022          adc    $X[5], $X[5]
1023          adc    $x6, $x6
1024          adc    $x7, $x7
1025          adc    \$0, $A
1026 
1027          add    $tmp, $X[0]
1028 
1029          mov    (+8*4)($pA), %rax
1030          mul    %rax
1031 
1032          add    $X[6], $X[0]
1033          adc    %rax, $X[1]
1034          adc    \$0, %rdx
1035 
1036          mov    %rdx, $tmp
1037 
1038          mov    $X[0], (+$pDst_o+8*7)($pDst)
1039          mov    $X[1], (+$pDst_o+8*8)($pDst)
1040 
1041          mov    (+8*5)($pA), %rax
1042          mul    %rax
1043 
1044          add    $tmp, $X[2]
1045          adc    %rax, $X[3]
1046          adc    \$0, %rdx
1047 
1048          mov    %rdx, $tmp
1049 
1050          mov    $X[2], (+$pDst_o+8*9)($pDst)
1051          mov    $X[3], (+$pDst_o+8*10)($pDst)
1052 
1053          mov    (+8*6)($pA), %rax
1054          mul    %rax
1055 
1056          add    $tmp, $X[4]
1057          adc    %rax, $X[5]
1058          adc    \$0, %rdx
1059 
1060          mov    $X[4], (+$pDst_o+8*11)($pDst)
1061          mov    $X[5], (+$pDst_o+8*12)($pDst)
1062 
1063          add    %rdx, $x6
1064          adc    $X[7], $x7
1065          adc    \$0, $A
1066 
1067          mov    $x6, (+$pDst_o+8*13)($pDst)
1068          mov    $x7, (+$pDst_o+8*14)($pDst)
1069          mov    $A, (+$pDst_o+8*15)($pDst)
1070 ___
1071 }
1072 
1073 #
1074 # sqr_reduce: subroutine to compute Result = reduce(Result * Result)
1075 #
1076 # input and result also in: r9, r8, r15, r14, r13, r12, r11, r10
1077 #
1078 $code.=<<___;
1079 .type   sqr_reduce,\@abi-omnipotent
1080 .align  16
1081 sqr_reduce:
1082          mov    (+$pResult_offset+8)(%rsp), %rcx
1083 ___
1084         &SQR_512("%rsp+$tmp16_offset+8", "%rcx", [map("%r$_",(10..15,8..9))], "%rbx", "%rbp", "%rsi", "%rdi");
1085 $code.=<<___;
1086         # tail recursion optimization: jmp to mont_reduce and return from there
1087          jmp    mont_reduce
1088         # call  mont_reduce
1089         # ret
1090 .size   sqr_reduce,.-sqr_reduce
1091 ___
1092 }}}
1093 
1094 #
1095 # MAIN FUNCTION
1096 #
1097 
1098 #mod_exp_512(UINT64 *result, /* 512 bits, 8 qwords */
1099 #           UINT64 *g,   /* 512 bits, 8 qwords */
1100 #           UINT64 *exp, /* 512 bits, 8 qwords */
1101 #           struct mod_ctx_512 *data)
1102 
1103 # window size = 5
1104 # table size = 2^5 = 32
1105 #table_entries  equ     32
1106 #table_size     equ     table_entries * 8
1107 $code.=<<___;
1108 .globl  mod_exp_512
1109 .type   mod_exp_512,\@function,4
1110 mod_exp_512:
1111          push   %rbp
1112          push   %rbx
1113          push   %r12
1114          push   %r13
1115          push   %r14
1116          push   %r15
1117 
1118         # adjust stack down and then align it with cache boundary
1119          mov    %rsp, %r8
1120          sub    \$$mem_size, %rsp
1121          and    \$-64, %rsp
1122 
1123         # store previous stack pointer and arguments
1124          mov    %r8, (+$rsp_offset)(%rsp)
1125          mov    %rdi, (+$pResult_offset)(%rsp)
1126          mov    %rsi, (+$pG_offset)(%rsp)
1127          mov    %rcx, (+$pData_offset)(%rsp)
1128 .Lbody:
1129         # transform g into montgomery space
1130         # GT = reduce(g * C2) = reduce(g * (2^256))
1131         # reduce expects to have the input in [tmp16]
1132          pxor   %xmm4, %xmm4
1133          movdqu (+16*0)(%rsi), %xmm0
1134          movdqu (+16*1)(%rsi), %xmm1
1135          movdqu (+16*2)(%rsi), %xmm2
1136          movdqu (+16*3)(%rsi), %xmm3
1137          movdqa %xmm4, (+$tmp16_offset+16*0)(%rsp)
1138          movdqa %xmm4, (+$tmp16_offset+16*1)(%rsp)
1139          movdqa %xmm4, (+$tmp16_offset+16*6)(%rsp)
1140          movdqa %xmm4, (+$tmp16_offset+16*7)(%rsp)
1141          movdqa %xmm0, (+$tmp16_offset+16*2)(%rsp)
1142          movdqa %xmm1, (+$tmp16_offset+16*3)(%rsp)
1143          movdqa %xmm2, (+$tmp16_offset+16*4)(%rsp)
1144          movdqa %xmm3, (+$tmp16_offset+16*5)(%rsp)
1145 
1146         # load pExp before rdx gets blown away
1147          movdqu (+16*0)(%rdx), %xmm0
1148          movdqu (+16*1)(%rdx), %xmm1
1149          movdqu (+16*2)(%rdx), %xmm2
1150          movdqu (+16*3)(%rdx), %xmm3
1151 
1152          lea    (+$GT_offset)(%rsp), %rbx
1153          mov    %rbx, (+$red_result_addr_offset)(%rsp)
1154          call   mont_reduce
1155 
1156         # Initialize tmp = C
1157          lea    (+$tmp_offset)(%rsp), %rcx
1158          xor    %rax, %rax
1159          mov    %rax, (+8*0)(%rcx)
1160          mov    %rax, (+8*1)(%rcx)
1161          mov    %rax, (+8*3)(%rcx)
1162          mov    %rax, (+8*4)(%rcx)
1163          mov    %rax, (+8*5)(%rcx)
1164          mov    %rax, (+8*6)(%rcx)
1165          mov    %rax, (+8*7)(%rcx)
1166          mov    %rax, (+$exp_offset+8*8)(%rsp)
1167          movq   \$1, (+8*2)(%rcx)
1168 
1169          lea    (+$garray_offset)(%rsp), %rbp
1170          mov    %rcx, %rsi                      # pTmp
1171          mov    %rbp, %rdi                      # Garray[][0]
1172 ___
1173 
1174         &swizzle("%rdi", "%rcx", "%rax", "%rbx");
1175 
1176         # for (rax = 31; rax != 0; rax--) {
1177         #     tmp = reduce(tmp * G)
1178         #     swizzle(pg, tmp);
1179         #     pg += 2; }
1180 $code.=<<___;
1181          mov    \$31, %rax
1182          mov    %rax, (+$i_offset)(%rsp)
1183          mov    %rbp, (+$pg_offset)(%rsp)
1184         # rsi -> pTmp
1185          mov    %rsi, (+$red_result_addr_offset)(%rsp)
1186          mov    (+8*0)(%rsi), %r10
1187          mov    (+8*1)(%rsi), %r11
1188          mov    (+8*2)(%rsi), %r12
1189          mov    (+8*3)(%rsi), %r13
1190          mov    (+8*4)(%rsi), %r14
1191          mov    (+8*5)(%rsi), %r15
1192          mov    (+8*6)(%rsi), %r8
1193          mov    (+8*7)(%rsi), %r9
1194 init_loop:
1195          lea    (+$GT_offset)(%rsp), %rdi
1196          call   mont_mul_a3b
1197          lea    (+$tmp_offset)(%rsp), %rsi
1198          mov    (+$pg_offset)(%rsp), %rbp
1199          add    \$2, %rbp
1200          mov    %rbp, (+$pg_offset)(%rsp)
1201          mov    %rsi, %rcx                      # rcx = rsi = addr of tmp
1202 ___
1203 
1204         &swizzle("%rbp", "%rcx", "%rax", "%rbx");
1205 $code.=<<___;
1206          mov    (+$i_offset)(%rsp), %rax
1207          sub    \$1, %rax
1208          mov    %rax, (+$i_offset)(%rsp)
1209          jne    init_loop
1210 
1211         #
1212         # Copy exponent onto stack
1213          movdqa %xmm0, (+$exp_offset+16*0)(%rsp)
1214          movdqa %xmm1, (+$exp_offset+16*1)(%rsp)
1215          movdqa %xmm2, (+$exp_offset+16*2)(%rsp)
1216          movdqa %xmm3, (+$exp_offset+16*3)(%rsp)
1217 
1218 
1219         #
1220         # Do exponentiation
1221         # Initialize result to G[exp{511:507}]
1222          mov    (+$exp_offset+62)(%rsp), %eax
1223          mov    %rax, %rdx
1224          shr    \$11, %rax
1225          and    \$0x07FF, %edx
1226          mov    %edx, (+$exp_offset+62)(%rsp)
1227          lea    (+$garray_offset)(%rsp,%rax,2), %rsi
1228          mov    (+$pResult_offset)(%rsp), %rdx
1229 ___
1230 
1231         &unswizzle("%rdx", "%rsi", "%rbp", "%rbx", "%rax");
1232 
1233         #
1234         # Loop variables
1235         # rcx = [loop_idx] = index: 510-5 to 0 by 5
1236 $code.=<<___;
1237          movq   \$505, (+$loop_idx_offset)(%rsp)
1238 
1239          mov    (+$pResult_offset)(%rsp), %rcx
1240          mov    %rcx, (+$red_result_addr_offset)(%rsp)
1241          mov    (+8*0)(%rcx), %r10
1242          mov    (+8*1)(%rcx), %r11
1243          mov    (+8*2)(%rcx), %r12
1244          mov    (+8*3)(%rcx), %r13
1245          mov    (+8*4)(%rcx), %r14
1246          mov    (+8*5)(%rcx), %r15
1247          mov    (+8*6)(%rcx), %r8
1248          mov    (+8*7)(%rcx), %r9
1249          jmp    sqr_2
1250 
1251 main_loop_a3b:
1252          call   sqr_reduce
1253          call   sqr_reduce
1254          call   sqr_reduce
1255 sqr_2:
1256          call   sqr_reduce
1257          call   sqr_reduce
1258 
1259         #
1260         # Do multiply, first look up proper value in Garray
1261          mov    (+$loop_idx_offset)(%rsp), %rcx                 # bit index
1262          mov    %rcx, %rax
1263          shr    \$4, %rax                       # rax is word pointer
1264          mov    (+$exp_offset)(%rsp,%rax,2), %edx
1265          and    \$15, %rcx
1266          shrq   %cl, %rdx
1267          and    \$0x1F, %rdx
1268 
1269          lea    (+$garray_offset)(%rsp,%rdx,2), %rsi
1270          lea    (+$tmp_offset)(%rsp), %rdx
1271          mov    %rdx, %rdi
1272 ___
1273 
1274         &unswizzle("%rdx", "%rsi", "%rbp", "%rbx", "%rax");
1275         # rdi = tmp = pG
1276 
1277         #
1278         # Call mod_mul_a1(pDst,  pSrc1, pSrc2, pM, pData)
1279         #                 result result pG     M   Data
1280 $code.=<<___;
1281          mov    (+$pResult_offset)(%rsp), %rsi
1282          call   mont_mul_a3b
1283 
1284         #
1285         # finish loop
1286          mov    (+$loop_idx_offset)(%rsp), %rcx
1287          sub    \$5, %rcx
1288          mov    %rcx, (+$loop_idx_offset)(%rsp)
1289          jge    main_loop_a3b
1290 
1291         #
1292 
1293 end_main_loop_a3b:
1294         # transform result out of Montgomery space
1295         # result = reduce(result)
1296          mov    (+$pResult_offset)(%rsp), %rdx
1297          pxor   %xmm4, %xmm4
1298          movdqu (+16*0)(%rdx), %xmm0
1299          movdqu (+16*1)(%rdx), %xmm1
1300          movdqu (+16*2)(%rdx), %xmm2
1301          movdqu (+16*3)(%rdx), %xmm3
1302          movdqa %xmm4, (+$tmp16_offset+16*4)(%rsp)
1303          movdqa %xmm4, (+$tmp16_offset+16*5)(%rsp)
1304          movdqa %xmm4, (+$tmp16_offset+16*6)(%rsp)
1305          movdqa %xmm4, (+$tmp16_offset+16*7)(%rsp)
1306          movdqa %xmm0, (+$tmp16_offset+16*0)(%rsp)
1307          movdqa %xmm1, (+$tmp16_offset+16*1)(%rsp)
1308          movdqa %xmm2, (+$tmp16_offset+16*2)(%rsp)
1309          movdqa %xmm3, (+$tmp16_offset+16*3)(%rsp)
1310          call   mont_reduce
1311 
1312         # If result > m, subract m
1313         # load result into r15:r8
1314          mov    (+$pResult_offset)(%rsp), %rax
1315          mov    (+8*0)(%rax), %r8
1316          mov    (+8*1)(%rax), %r9
1317          mov    (+8*2)(%rax), %r10
1318          mov    (+8*3)(%rax), %r11
1319          mov    (+8*4)(%rax), %r12
1320          mov    (+8*5)(%rax), %r13
1321          mov    (+8*6)(%rax), %r14
1322          mov    (+8*7)(%rax), %r15
1323 
1324         # subtract m
1325          mov    (+$pData_offset)(%rsp), %rbx
1326          add    \$$M, %rbx
1327 
1328          sub    (+8*0)(%rbx), %r8
1329          sbb    (+8*1)(%rbx), %r9
1330          sbb    (+8*2)(%rbx), %r10
1331          sbb    (+8*3)(%rbx), %r11
1332          sbb    (+8*4)(%rbx), %r12
1333          sbb    (+8*5)(%rbx), %r13
1334          sbb    (+8*6)(%rbx), %r14
1335          sbb    (+8*7)(%rbx), %r15
1336 
1337         # if Carry is clear, replace result with difference
1338          mov    (+8*0)(%rax), %rsi
1339          mov    (+8*1)(%rax), %rdi
1340          mov    (+8*2)(%rax), %rcx
1341          mov    (+8*3)(%rax), %rdx
1342          cmovnc %r8, %rsi
1343          cmovnc %r9, %rdi
1344          cmovnc %r10, %rcx
1345          cmovnc %r11, %rdx
1346          mov    %rsi, (+8*0)(%rax)
1347          mov    %rdi, (+8*1)(%rax)
1348          mov    %rcx, (+8*2)(%rax)
1349          mov    %rdx, (+8*3)(%rax)
1350 
1351          mov    (+8*4)(%rax), %rsi
1352          mov    (+8*5)(%rax), %rdi
1353          mov    (+8*6)(%rax), %rcx
1354          mov    (+8*7)(%rax), %rdx
1355          cmovnc %r12, %rsi
1356          cmovnc %r13, %rdi
1357          cmovnc %r14, %rcx
1358          cmovnc %r15, %rdx
1359          mov    %rsi, (+8*4)(%rax)
1360          mov    %rdi, (+8*5)(%rax)
1361          mov    %rcx, (+8*6)(%rax)
1362          mov    %rdx, (+8*7)(%rax)
1363 
1364          mov    (+$rsp_offset)(%rsp), %rsi
1365          mov    0(%rsi),%r15
1366          mov    8(%rsi),%r14
1367          mov    16(%rsi),%r13
1368          mov    24(%rsi),%r12
1369          mov    32(%rsi),%rbx
1370          mov    40(%rsi),%rbp
1371          lea    48(%rsi),%rsp
1372 .Lepilogue:
1373          ret
1374 .size mod_exp_512, . - mod_exp_512
1375 ___
1376 
1377 if ($win64) {
1378 # EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
1379 #               CONTEXT *context,DISPATCHER_CONTEXT *disp)
1380 my $rec="%rcx";
1381 my $frame="%rdx";
1382 my $context="%r8";
1383 my $disp="%r9";
1384 
1385 $code.=<<___;
1386 .extern __imp_RtlVirtualUnwind
1387 .type   mod_exp_512_se_handler,\@abi-omnipotent
1388 .align  16
1389 mod_exp_512_se_handler:
1390         push    %rsi
1391         push    %rdi
1392         push    %rbx
1393         push    %rbp
1394         push    %r12
1395         push    %r13
1396         push    %r14
1397         push    %r15
1398         pushfq
1399         sub     \$64,%rsp
1400 
1401         mov     120($context),%rax      # pull context->Rax
1402         mov     248($context),%rbx      # pull context->Rip
1403 
1404         lea     .Lbody(%rip),%r10
1405         cmp     %r10,%rbx               # context->Rip<prologue label
1406         jb      .Lin_prologue
1407 
1408         mov     152($context),%rax      # pull context->Rsp
1409 
1410         lea     .Lepilogue(%rip),%r10
1411         cmp     %r10,%rbx               # context->Rip>=epilogue label
1412         jae     .Lin_prologue
1413 
1414         mov     $rsp_offset(%rax),%rax  # pull saved Rsp
1415 
1416         mov     32(%rax),%rbx
1417         mov     40(%rax),%rbp
1418         mov     24(%rax),%r12
1419         mov     16(%rax),%r13
1420         mov     8(%rax),%r14
1421         mov     0(%rax),%r15
1422         lea     48(%rax),%rax
1423         mov     %rbx,144($context)      # restore context->Rbx
1424         mov     %rbp,160($context)      # restore context->Rbp
1425         mov     %r12,216($context)      # restore context->R12
1426         mov     %r13,224($context)      # restore context->R13
1427         mov     %r14,232($context)      # restore context->R14
1428         mov     %r15,240($context)      # restore context->R15
1429 
1430 .Lin_prologue:
1431         mov     8(%rax),%rdi
1432         mov     16(%rax),%rsi
1433         mov     %rax,152($context)      # restore context->Rsp
1434         mov     %rsi,168($context)      # restore context->Rsi
1435         mov     %rdi,176($context)      # restore context->Rdi
1436 
1437         mov     40($disp),%rdi          # disp->ContextRecord
1438         mov     $context,%rsi           # context
1439         mov     \$154,%ecx              # sizeof(CONTEXT)
1440         .long   0xa548f3fc              # cld; rep movsq
1441 
1442         mov     $disp,%rsi
1443         xor     %rcx,%rcx               # arg1, UNW_FLAG_NHANDLER
1444         mov     8(%rsi),%rdx            # arg2, disp->ImageBase
1445         mov     0(%rsi),%r8             # arg3, disp->ControlPc
1446         mov     16(%rsi),%r9            # arg4, disp->FunctionEntry
1447         mov     40(%rsi),%r10           # disp->ContextRecord
1448         lea     56(%rsi),%r11           # &disp->HandlerData
1449         lea     24(%rsi),%r12           # &disp->EstablisherFrame
1450         mov     %r10,32(%rsp)           # arg5
1451         mov     %r11,40(%rsp)           # arg6
1452         mov     %r12,48(%rsp)           # arg7
1453         mov     %rcx,56(%rsp)           # arg8, (NULL)
1454         call    *__imp_RtlVirtualUnwind(%rip)
1455 
1456         mov     \$1,%eax                # ExceptionContinueSearch
1457         add     \$64,%rsp
1458         popfq
1459         pop     %r15
1460         pop     %r14
1461         pop     %r13
1462         pop     %r12
1463         pop     %rbp
1464         pop     %rbx
1465         pop     %rdi
1466         pop     %rsi
1467         ret
1468 .size   mod_exp_512_se_handler,.-mod_exp_512_se_handler
1469 
1470 .section        .pdata
1471 .align  4
1472         .rva    .LSEH_begin_mod_exp_512
1473         .rva    .LSEH_end_mod_exp_512
1474         .rva    .LSEH_info_mod_exp_512
1475 
1476 .section        .xdata
1477 .align  8
1478 .LSEH_info_mod_exp_512:
1479         .byte   9,0,0,0
1480         .rva    mod_exp_512_se_handler
1481 ___
1482 }
1483 
1484 sub reg_part {
1485 my ($reg,$conv)=@_;
1486     if ($reg =~ /%r[0-9]+/)     { $reg .= $conv; }
1487     elsif ($conv eq "b")        { $reg =~ s/%[er]([^x]+)x?/%$1l/;       }
1488     elsif ($conv eq "w")        { $reg =~ s/%[er](.+)/%$1/;             }
1489     elsif ($conv eq "d")        { $reg =~ s/%[er](.+)/%e$1/;            }
1490     return $reg;
1491 }
1492 
1493 $code =~ s/(%[a-z0-9]+)#([bwd])/reg_part($1,$2)/gem;
1494 $code =~ s/\`([^\`]*)\`/eval $1/gem;
1495 $code =~ s/(\(\+[^)]+\))/eval $1/gem;
1496 print $code;
1497 close STDOUT;