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 # ====================================================================
12 # Montgomery multiplication routine for x86_64. While it gives modest
13 # 9% improvement of rsa4096 sign on Opteron, rsa512 sign runs more
14 # than twice, >2x, as fast. Most common rsa1024 sign is improved by
15 # respectful 50%. It remains to be seen if loop unrolling and
16 # dedicated squaring routine can provide further improvement...
20 # Add dedicated squaring procedure. Performance improvement varies
21 # from platform to platform, but in average it's ~5%/15%/25%/33%
22 # for 512-/1024-/2048-/4096-bit RSA *sign* benchmarks respectively.
26 # Unroll and modulo-schedule inner loops in such manner that they
27 # are "fallen through" for input lengths of 8, which is critical for
28 # 1024-bit RSA *sign*. Average performance improvement in comparison
29 # to *initial* version of this module from 2005 is ~0%/30%/40%/45%
30 # for 512-/1024-/2048-/4096-bit RSA *sign* benchmarks respectively.
34 # Optmize reduction in squaring procedure and improve 1024+-bit RSA
35 # sign performance by 10-16% on Intel Sandy Bridge and later
36 # (virtually same on non-Intel processors).
40 if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
42 $win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
44 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
45 ( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
46 ( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
47 die "can't locate x86_64-xlate.pl";
49 open OUT,"| \"$^X\" $xlate $flavour $output";
53 $rp="%rdi"; # BN_ULONG *rp,
54 $ap="%rsi"; # const BN_ULONG *ap,
55 $bp="%rdx"; # const BN_ULONG *bp,
56 $np="%rcx"; # const BN_ULONG *np,
57 $n0="%r8"; # const BN_ULONG *n0,
58 $num="%r9"; # int num);
71 .type bn_mul_mont,\@function,6
97 lea (%rsp,%r10,8),%rsp # tp=alloca(8*(num+2))
98 and \$-1024,%rsp # minimize TLB usage
100 mov %r11,8(%rsp,$num,8) # tp[num+1]=%rsp
102 mov $bp,%r12 # reassign $bp
106 mov ($n0),$n0 # pull n0[0] value
107 mov ($bp),$m0 # m0=bp[0]
114 mulq $m0 # ap[0]*bp[0]
118 imulq $lo0,$m1 # "tp[0]"*n0
122 add %rax,$lo0 # discarded
135 add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
138 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
142 mulq $m0 # ap[j]*bp[0]
154 mov ($ap),%rax # ap[0]
156 add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
158 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
165 mov $hi1,-8(%rsp,$num,8)
166 mov %rdx,(%rsp,$num,8) # store upmost overflow bit
172 mov ($bp,$i,8),$m0 # m0=bp[i]
176 mulq $m0 # ap[0]*bp[i]
177 add %rax,$lo0 # ap[0]*bp[i]+tp[0]
181 imulq $lo0,$m1 # tp[0]*n0
185 add %rax,$lo0 # discarded
188 mov 8(%rsp),$lo0 # tp[1]
199 add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
202 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
206 mulq $m0 # ap[j]*bp[i]
210 add $hi0,$lo0 # ap[j]*bp[i]+tp[j]
220 mov ($ap),%rax # ap[0]
222 add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
225 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
231 add $lo0,$hi1 # pull upmost overflow bit
233 mov $hi1,-8(%rsp,$num,8)
234 mov %rdx,(%rsp,$num,8) # store upmost overflow bit
240 xor $i,$i # i=0 and clear CF!
241 mov (%rsp),%rax # tp[0]
242 lea (%rsp),$ap # borrow ap for tp
246 .Lsub: sbb ($np,$i,8),%rax
247 mov %rax,($rp,$i,8) # rp[i]=tp[i]-np[i]
248 mov 8($ap,$i,8),%rax # tp[i+1]
250 dec $j # doesnn't affect CF!
253 sbb \$0,%rax # handle upmost overflow bit
260 or $np,$ap # ap=borrow?tp:rp
262 .Lcopy: # copy or in-place refresh
264 mov $i,(%rsp,$i,8) # zap temporary vector
265 mov %rax,($rp,$i,8) # rp[i]=tp[i]
270 mov 8(%rsp,$num,8),%rsi # restore %rsp
281 .size bn_mul_mont,.-bn_mul_mont
284 my @A=("%r10","%r11");
285 my @N=("%r13","%rdi");
287 .type bn_mul4x_mont,\@function,6
302 lea (%rsp,%r10,8),%rsp # tp=alloca(8*(num+4))
303 and \$-1024,%rsp # minimize TLB usage
305 mov %r11,8(%rsp,$num,8) # tp[num+1]=%rsp
307 mov $rp,16(%rsp,$num,8) # tp[num+2]=$rp
308 mov %rdx,%r12 # reassign $bp
312 mov ($n0),$n0 # pull n0[0] value
313 mov ($bp),$m0 # m0=bp[0]
320 mulq $m0 # ap[0]*bp[0]
324 imulq $A[0],$m1 # "tp[0]"*n0
328 add %rax,$A[0] # discarded
351 mulq $m0 # ap[j]*bp[0]
353 mov -16($np,$j,8),%rax
359 mov -8($ap,$j,8),%rax
361 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
363 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
366 mulq $m0 # ap[j]*bp[0]
368 mov -8($np,$j,8),%rax
376 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
378 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
381 mulq $m0 # ap[j]*bp[0]
391 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
393 mov $N[0],-8(%rsp,$j,8) # tp[j-1]
396 mulq $m0 # ap[j]*bp[0]
405 mov -16($ap,$j,8),%rax
407 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
409 mov $N[1],-32(%rsp,$j,8) # tp[j-1]
414 mulq $m0 # ap[j]*bp[0]
416 mov -16($np,$j,8),%rax
422 mov -8($ap,$j,8),%rax
424 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
426 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
429 mulq $m0 # ap[j]*bp[0]
431 mov -8($np,$j,8),%rax
437 mov ($ap),%rax # ap[0]
439 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
441 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
447 mov $N[0],-8(%rsp,$j,8)
448 mov $N[1],(%rsp,$j,8) # store upmost overflow bit
453 mov ($bp,$i,8),$m0 # m0=bp[i]
457 mulq $m0 # ap[0]*bp[i]
458 add %rax,$A[0] # ap[0]*bp[i]+tp[0]
462 imulq $A[0],$m1 # tp[0]*n0
466 add %rax,$A[0] # "$N[0]", discarded
471 mulq $m0 # ap[j]*bp[i]
475 add 8(%rsp),$A[1] # +tp[1]
483 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[i]+tp[j]
486 mov $N[1],(%rsp) # tp[j-1]
491 mulq $m0 # ap[j]*bp[i]
493 mov -16($np,$j,8),%rax
495 add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
501 mov -8($ap,$j,8),%rax
505 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
508 mulq $m0 # ap[j]*bp[i]
510 mov -8($np,$j,8),%rax
512 add -8(%rsp,$j,8),$A[1]
522 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
525 mulq $m0 # ap[j]*bp[i]
529 add (%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
539 mov $N[0],-8(%rsp,$j,8) # tp[j-1]
542 mulq $m0 # ap[j]*bp[i]
546 add 8(%rsp,$j,8),$A[1]
553 mov -16($ap,$j,8),%rax
557 mov $N[1],-32(%rsp,$j,8) # tp[j-1]
562 mulq $m0 # ap[j]*bp[i]
564 mov -16($np,$j,8),%rax
566 add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
572 mov -8($ap,$j,8),%rax
576 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
579 mulq $m0 # ap[j]*bp[i]
581 mov -8($np,$j,8),%rax
583 add -8(%rsp,$j,8),$A[1]
590 mov ($ap),%rax # ap[0]
594 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
600 add (%rsp,$num,8),$N[0] # pull upmost overflow bit
602 mov $N[0],-8(%rsp,$j,8)
603 mov $N[1],(%rsp,$j,8) # store upmost overflow bit
609 my @ri=("%rax","%rdx",$m0,$m1);
611 mov 16(%rsp,$num,8),$rp # restore $rp
612 mov 0(%rsp),@ri[0] # tp[0]
614 mov 8(%rsp),@ri[1] # tp[1]
615 shr \$2,$num # num/=4
616 lea (%rsp),$ap # borrow ap for tp
617 xor $i,$i # i=0 and clear CF!
620 mov 16($ap),@ri[2] # tp[2]
621 mov 24($ap),@ri[3] # tp[3]
623 lea -1($num),$j # j=num/4-1
627 mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
628 mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
629 sbb 16($np,$i,8),@ri[2]
630 mov 32($ap,$i,8),@ri[0] # tp[i+1]
631 mov 40($ap,$i,8),@ri[1]
632 sbb 24($np,$i,8),@ri[3]
633 mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
634 mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
635 sbb 32($np,$i,8),@ri[0]
636 mov 48($ap,$i,8),@ri[2]
637 mov 56($ap,$i,8),@ri[3]
638 sbb 40($np,$i,8),@ri[1]
640 dec $j # doesnn't affect CF!
643 mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
644 mov 32($ap,$i,8),@ri[0] # load overflow bit
645 sbb 16($np,$i,8),@ri[2]
646 mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
647 sbb 24($np,$i,8),@ri[3]
648 mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
650 sbb \$0,@ri[0] # handle upmost overflow bit
651 mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
658 or $np,$ap # ap=borrow?tp:rp
665 .Lcopy4x: # copy or in-place refresh
666 movdqu 16($ap,$i),%xmm2
667 movdqu 32($ap,$i),%xmm1
668 movdqa %xmm0,16(%rsp,$i)
669 movdqu %xmm2,16($rp,$i)
670 movdqa %xmm0,32(%rsp,$i)
671 movdqu %xmm1,32($rp,$i)
677 movdqu 16($ap,$i),%xmm2
678 movdqa %xmm0,16(%rsp,$i)
679 movdqu %xmm2,16($rp,$i)
683 mov 8(%rsp,$num,8),%rsi # restore %rsp
694 .size bn_mul4x_mont,.-bn_mul4x_mont
698 ######################################################################
699 # void bn_sqr8x_mont(
700 my $rptr="%rdi"; # const BN_ULONG *rptr,
701 my $aptr="%rsi"; # const BN_ULONG *aptr,
702 my $bptr="%rdx"; # not used
703 my $nptr="%rcx"; # const BN_ULONG *nptr,
704 my $n0 ="%r8"; # const BN_ULONG *n0);
705 my $num ="%r9"; # int num, has to be divisible by 8
707 my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
708 my @A0=("%r10","%r11");
709 my @A1=("%r12","%r13");
710 my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
713 .type bn_sqr8x_mont,\@function,6
724 shl \$3,${num}d # convert $num to bytes
726 mov %rsp,%r11 # put aside %rsp
727 sub $num,%r10 # -$num
729 lea -72(%rsp,%r10,2),%rsp # alloca(frame+2*$num)
730 and \$-1024,%rsp # minimize TLB usage
731 ##############################################################
734 # +0 saved $num, used in reduction section
735 # +8 &t[2*$num], used in reduction section
742 mov $rptr,32(%rsp) # save $rptr
745 mov %r11, 56(%rsp) # save original %rsp
747 ##############################################################
750 # a) multiply-n-add everything but a[i]*a[i];
751 # b) shift result of a) by 1 to the left and accumulate
752 # a[i]*a[i] products;
754 ##############################################################
820 lea 32(%r10),$i # $i=-($num-32)
821 lea ($aptr,$num),$aptr # end of a[] buffer, ($aptr,$i)=&ap[2]
823 mov $num,$j # $j=$num
825 # comments apply to $num==8 case
826 mov -32($aptr,$i),$a0 # a[0]
827 lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
828 mov -24($aptr,$i),%rax # a[1]
829 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
830 mov -16($aptr,$i),$ai # a[2]
834 mov %rax,$A0[0] # a[1]*a[0]
837 mov $A0[0],-24($tptr,$i) # t[1]
843 mov $A0[1],-16($tptr,$i) # t[2]
846 lea -16($i),$j # j=-16
849 mov 8($aptr,$j),$ai # a[3]
851 mov %rax,$A1[0] # a[2]*a[1]+t[3]
857 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
863 mov $A0[0],-8($tptr,$j) # t[3]
868 mov ($aptr,$j),$ai # a[4]
870 add %rax,$A1[1] # a[3]*a[1]+t[4]
876 add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
878 mov 8($aptr,$j),$ai # a[5]
886 add %rax,$A1[0] # a[4]*a[3]+t[5]
888 mov $A0[1],($tptr,$j) # t[4]
893 add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
895 mov 16($aptr,$j),$ai # a[6]
902 add %rax,$A1[1] # a[5]*a[3]+t[6]
904 mov $A0[0],8($tptr,$j) # t[5]
909 add %rax,$A0[1] # a[6]*a[2]+a[5]*a[3]+t[6]
911 mov 24($aptr,$j),$ai # a[7]
919 add %rax,$A1[0] # a[6]*a[5]+t[7]
921 mov $A0[1],16($tptr,$j) # t[6]
926 add %rax,$A0[0] # a[7]*a[4]+a[6]*a[5]+t[6]
933 mov $A0[0],-8($tptr,$j) # t[7]
945 mov $A1[1],($tptr) # t[8]
947 mov %rdx,8($tptr) # t[9]
951 .Lsqr4x_outer: # comments apply to $num==6 case
952 mov -32($aptr,$i),$a0 # a[0]
953 lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
954 mov -24($aptr,$i),%rax # a[1]
955 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
956 mov -16($aptr,$i),$ai # a[2]
959 mov -24($tptr,$i),$A0[0] # t[1]
961 add %rax,$A0[0] # a[1]*a[0]+t[1]
964 mov $A0[0],-24($tptr,$i) # t[1]
971 add -16($tptr,$i),$A0[1] # a[2]*a[0]+t[2]
974 mov $A0[1],-16($tptr,$i) # t[2]
976 lea -16($i),$j # j=-16
980 mov 8($aptr,$j),$ai # a[3]
982 add %rax,$A1[0] # a[2]*a[1]+t[3]
985 add 8($tptr,$j),$A1[0]
990 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
996 mov $A0[0],8($tptr,$j) # t[3]
1003 mov ($aptr,$j),$ai # a[4]
1005 add %rax,$A1[1] # a[3]*a[1]+t[4]
1009 add ($tptr,$j),$A1[1]
1013 add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
1015 mov 8($aptr,$j),$ai # a[5]
1022 add %rax,$A1[0] # a[4]*a[3]+t[5]
1023 mov $A0[1],($tptr,$j) # t[4]
1027 add 8($tptr,$j),$A1[0]
1032 add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
1038 mov $A0[0],-8($tptr,$j) # t[5], "preloaded t[1]" below
1049 mov $A1[1],($tptr) # t[6], "preloaded t[2]" below
1051 mov %rdx,8($tptr) # t[7], "preloaded t[3]" below
1056 # comments apply to $num==4 case
1057 mov -32($aptr),$a0 # a[0]
1058 lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
1059 mov -24($aptr),%rax # a[1]
1060 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
1061 mov -16($aptr),$ai # a[2]
1065 add %rax,$A0[0] # a[1]*a[0]+t[1], preloaded t[1]
1073 mov $A0[0],-24($tptr) # t[1]
1076 add $A1[1],$A0[1] # a[2]*a[0]+t[2], preloaded t[2]
1077 mov -8($aptr),$ai # a[3]
1081 add %rax,$A1[0] # a[2]*a[1]+t[3], preloaded t[3]
1083 mov $A0[1],-16($tptr) # t[2]
1088 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
1094 mov $A0[0],-8($tptr) # t[3]
1098 mov -16($aptr),%rax # a[2]
1103 mov $A1[1],($tptr) # t[4]
1105 mov %rdx,8($tptr) # t[5]
1110 my ($shift,$carry)=($a0,$a1);
1111 my @S=(@A1,$ai,$n0);
1115 sub $num,$i # $i=16-$num
1118 add $A1[0],%rax # t[5]
1120 mov %rax,8($tptr) # t[5]
1121 mov %rdx,16($tptr) # t[6]
1122 mov $carry,24($tptr) # t[7]
1124 mov -16($aptr,$i),%rax # a[0]
1125 lea 64(%rsp,$num,2),$tptr
1126 xor $A0[0],$A0[0] # t[0]
1127 mov -24($tptr,$i,2),$A0[1] # t[1]
1129 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1131 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1133 or $A0[0],$S[1] # | t[2*i]>>63
1134 mov -16($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1135 mov $A0[1],$shift # shift=t[2*i+1]>>63
1136 mul %rax # a[i]*a[i]
1137 neg $carry # mov $carry,cf
1138 mov -8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1140 mov -8($aptr,$i),%rax # a[i+1] # prefetch
1141 mov $S[0],-32($tptr,$i,2)
1144 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1145 mov $S[1],-24($tptr,$i,2)
1146 sbb $carry,$carry # mov cf,$carry
1148 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1150 or $A0[0],$S[3] # | t[2*i]>>63
1151 mov 0($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1152 mov $A0[1],$shift # shift=t[2*i+1]>>63
1153 mul %rax # a[i]*a[i]
1154 neg $carry # mov $carry,cf
1155 mov 8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1157 mov 0($aptr,$i),%rax # a[i+1] # prefetch
1158 mov $S[2],-16($tptr,$i,2)
1161 mov $S[3],-40($tptr,$i,2)
1162 sbb $carry,$carry # mov cf,$carry
1163 jmp .Lsqr4x_shift_n_add
1166 .Lsqr4x_shift_n_add:
1167 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1169 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1171 or $A0[0],$S[1] # | t[2*i]>>63
1172 mov -16($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1173 mov $A0[1],$shift # shift=t[2*i+1]>>63
1174 mul %rax # a[i]*a[i]
1175 neg $carry # mov $carry,cf
1176 mov -8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1178 mov -8($aptr,$i),%rax # a[i+1] # prefetch
1179 mov $S[0],-32($tptr,$i,2)
1182 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1183 mov $S[1],-24($tptr,$i,2)
1184 sbb $carry,$carry # mov cf,$carry
1186 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1188 or $A0[0],$S[3] # | t[2*i]>>63
1189 mov 0($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1190 mov $A0[1],$shift # shift=t[2*i+1]>>63
1191 mul %rax # a[i]*a[i]
1192 neg $carry # mov $carry,cf
1193 mov 8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1195 mov 0($aptr,$i),%rax # a[i+1] # prefetch
1196 mov $S[2],-16($tptr,$i,2)
1199 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1200 mov $S[3],-8($tptr,$i,2)
1201 sbb $carry,$carry # mov cf,$carry
1203 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1205 or $A0[0],$S[1] # | t[2*i]>>63
1206 mov 16($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1207 mov $A0[1],$shift # shift=t[2*i+1]>>63
1208 mul %rax # a[i]*a[i]
1209 neg $carry # mov $carry,cf
1210 mov 24($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1212 mov 8($aptr,$i),%rax # a[i+1] # prefetch
1213 mov $S[0],0($tptr,$i,2)
1216 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1217 mov $S[1],8($tptr,$i,2)
1218 sbb $carry,$carry # mov cf,$carry
1220 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1222 or $A0[0],$S[3] # | t[2*i]>>63
1223 mov 32($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1224 mov $A0[1],$shift # shift=t[2*i+1]>>63
1225 mul %rax # a[i]*a[i]
1226 neg $carry # mov $carry,cf
1227 mov 40($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1229 mov 16($aptr,$i),%rax # a[i+1] # prefetch
1230 mov $S[2],16($tptr,$i,2)
1232 mov $S[3],24($tptr,$i,2)
1233 sbb $carry,$carry # mov cf,$carry
1235 jnz .Lsqr4x_shift_n_add
1237 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1239 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1241 or $A0[0],$S[1] # | t[2*i]>>63
1242 mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
1243 mov $A0[1],$shift # shift=t[2*i+1]>>63
1244 mul %rax # a[i]*a[i]
1245 neg $carry # mov $carry,cf
1246 mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
1248 mov -8($aptr),%rax # a[i+1] # prefetch
1249 mov $S[0],-32($tptr)
1252 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1|shift
1253 mov $S[1],-24($tptr)
1254 sbb $carry,$carry # mov cf,$carry
1256 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1258 or $A0[0],$S[3] # | t[2*i]>>63
1259 mul %rax # a[i]*a[i]
1260 neg $carry # mov $carry,cf
1263 mov $S[2],-16($tptr)
1267 ######################################################################
1268 # Montgomery reduction part, "word-by-word" algorithm.
1270 # This new path is inspired by multiple submissions from Intel, by
1271 # Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
1274 my ($nptr,$tptr,$carry,$m0)=("%rbp","%rdi","%rsi","%rbx");
1277 mov 40(%rsp),$nptr # pull $nptr
1279 lea ($nptr,$num),%rdx # end of n[]
1280 lea 64(%rsp,$num,2),$tptr # end of t[] buffer
1283 mov %rax,($tptr) # clear top-most carry bit
1284 lea 64(%rsp,$num),$tptr # end of initial t[] window
1286 jmp .L8x_reduction_loop
1289 .L8x_reduction_loop:
1290 lea ($tptr,$num),$tptr # start of current t[] window
1299 lea 8*8($tptr),$tptr
1302 imulq 48(%rsp),$m0 # n0*a[0]
1303 mov 8*0($nptr),%rax # n[0]
1310 mov 8*1($nptr),%rax # n[1]
1320 mov $m0,64-8(%rsp,%rcx,8) # put aside n0*a[i]
1329 mov 48(%rsp),$carry # pull n0, borrow $carry
1337 imulq %r8,$carry # modulo-scheduled
1367 mov $carry,$m0 # n0*a[i]
1369 mov 8*0($nptr),%rax # n[0]
1378 lea 8*8($nptr),$nptr
1380 mov 8(%rsp),%rdx # pull end of t[]
1381 cmp 0(%rsp),$nptr # end of n[]?
1392 sbb $carry,$carry # top carry
1394 mov 64+56(%rsp),$m0 # pull n0*a[0]
1404 mov %r8,($tptr) # save result
1413 lea 8($tptr),$tptr # $tptr++
1458 mov 64-16(%rsp,%rcx,8),$m0 # pull n0*a[i]
1462 mov 8*0($nptr),%rax # pull n[0]
1469 lea 8*8($nptr),$nptr
1470 mov 8(%rsp),%rdx # pull end of t[]
1471 cmp 0(%rsp),$nptr # end of n[]?
1472 jae .L8x_tail_done # break out of loop
1474 mov 64+56(%rsp),$m0 # pull n0*a[0]
1476 mov 8*0($nptr),%rax # pull n[0]
1485 sbb $carry,$carry # top carry
1492 add (%rdx),%r8 # can this overflow?
1505 adc \$0,%rax # top-most carry
1507 mov 40(%rsp),$nptr # restore $nptr
1509 mov %r8,8*0($tptr) # store top 512 bits
1511 mov $nptr,$num # $num is %r9, can't be moved upwards
1513 sub 0(%rsp),$num # -$num
1519 lea 8*8($tptr),$tptr
1520 mov %rax,(%rdx) # store top-most carry
1522 cmp %rdx,$tptr # end of t[]?
1523 jb .L8x_reduction_loop
1525 neg $num # restore $num
1528 ##############################################################
1529 # Post-condition, 4x unrolled copy from bn_mul_mont
1532 my ($tptr,$nptr)=("%rbx",$aptr);
1533 my @ri=("%rax","%rdx","%r10","%r11");
1535 mov 64(%rsp,$num),@ri[0] # tp[0]
1536 lea 64(%rsp,$num),$tptr # upper half of t[2*$num] holds result
1537 mov 40(%rsp),$nptr # restore $nptr
1538 shr \$5,$num # num/4
1539 mov 8($tptr),@ri[1] # t[1]
1540 xor $i,$i # i=0 and clear CF!
1542 mov 32(%rsp),$rptr # restore $rptr
1544 mov 16($tptr),@ri[2] # t[2]
1545 mov 24($tptr),@ri[3] # t[3]
1547 lea -1($num),$j # j=num/4-1
1551 mov @ri[0],0($rptr,$i,8) # rp[i]=tp[i]-np[i]
1552 mov @ri[1],8($rptr,$i,8) # rp[i]=tp[i]-np[i]
1553 sbb 16($nptr,$i,8),@ri[2]
1554 mov 32($tptr,$i,8),@ri[0] # tp[i+1]
1555 mov 40($tptr,$i,8),@ri[1]
1556 sbb 24($nptr,$i,8),@ri[3]
1557 mov @ri[2],16($rptr,$i,8) # rp[i]=tp[i]-np[i]
1558 mov @ri[3],24($rptr,$i,8) # rp[i]=tp[i]-np[i]
1559 sbb 32($nptr,$i,8),@ri[0]
1560 mov 48($tptr,$i,8),@ri[2]
1561 mov 56($tptr,$i,8),@ri[3]
1562 sbb 40($nptr,$i,8),@ri[1]
1564 dec $j # doesn't affect CF!
1567 mov @ri[0],0($rptr,$i,8) # rp[i]=tp[i]-np[i]
1568 mov 32($tptr,$i,8),@ri[0] # load overflow bit
1569 sbb 16($nptr,$i,8),@ri[2]
1570 mov @ri[1],8($rptr,$i,8) # rp[i]=tp[i]-np[i]
1571 sbb 24($nptr,$i,8),@ri[3]
1572 mov @ri[2],16($rptr,$i,8) # rp[i]=tp[i]-np[i]
1574 sbb \$0,@ri[0] # handle upmost overflow bit
1575 mov @ri[3],24($rptr,$i,8) # rp[i]=tp[i]-np[i]
1582 or $nptr,$tptr # tp=borrow?tp:rp
1585 lea 64(%rsp,$num,8),$nptr
1586 movdqu ($tptr),%xmm1
1587 lea ($nptr,$num,8),$nptr
1588 movdqa %xmm0,64(%rsp) # zap lower half of temporary vector
1589 movdqa %xmm0,($nptr) # zap upper half of temporary vector
1590 movdqu %xmm1,($rptr)
1593 .Lsqr4x_copy: # copy or in-place refresh
1594 movdqu 16($tptr,$i),%xmm2
1595 movdqu 32($tptr,$i),%xmm1
1596 movdqa %xmm0,80(%rsp,$i) # zap lower half of temporary vector
1597 movdqa %xmm0,96(%rsp,$i) # zap lower half of temporary vector
1598 movdqa %xmm0,16($nptr,$i) # zap upper half of temporary vector
1599 movdqa %xmm0,32($nptr,$i) # zap upper half of temporary vector
1600 movdqu %xmm2,16($rptr,$i)
1601 movdqu %xmm1,32($rptr,$i)
1606 movdqu 16($tptr,$i),%xmm2
1607 movdqa %xmm0,80(%rsp,$i) # zap lower half of temporary vector
1608 movdqa %xmm0,16($nptr,$i) # zap upper half of temporary vector
1609 movdqu %xmm2,16($rptr,$i)
1613 mov 56(%rsp),%rsi # restore %rsp
1624 .size bn_sqr8x_mont,.-bn_sqr8x_mont
1628 .asciz "Montgomery Multiplication for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
1632 # EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
1633 # CONTEXT *context,DISPATCHER_CONTEXT *disp)
1641 .extern __imp_RtlVirtualUnwind
1642 .type mul_handler,\@abi-omnipotent
1656 mov 120($context),%rax # pull context->Rax
1657 mov 248($context),%rbx # pull context->Rip
1659 mov 8($disp),%rsi # disp->ImageBase
1660 mov 56($disp),%r11 # disp->HandlerData
1662 mov 0(%r11),%r10d # HandlerData[0]
1663 lea (%rsi,%r10),%r10 # end of prologue label
1664 cmp %r10,%rbx # context->Rip<end of prologue label
1665 jb .Lcommon_seh_tail
1667 mov 152($context),%rax # pull context->Rsp
1669 mov 4(%r11),%r10d # HandlerData[1]
1670 lea (%rsi,%r10),%r10 # epilogue label
1671 cmp %r10,%rbx # context->Rip>=epilogue label
1672 jae .Lcommon_seh_tail
1674 mov 192($context),%r10 # pull $num
1675 mov 8(%rax,%r10,8),%rax # pull saved stack pointer
1684 mov %rbx,144($context) # restore context->Rbx
1685 mov %rbp,160($context) # restore context->Rbp
1686 mov %r12,216($context) # restore context->R12
1687 mov %r13,224($context) # restore context->R13
1688 mov %r14,232($context) # restore context->R14
1689 mov %r15,240($context) # restore context->R15
1691 jmp .Lcommon_seh_tail
1692 .size mul_handler,.-mul_handler
1694 .type sqr_handler,\@abi-omnipotent
1708 mov 120($context),%rax # pull context->Rax
1709 mov 248($context),%rbx # pull context->Rip
1711 lea .Lsqr8x_body(%rip),%r10
1712 cmp %r10,%rbx # context->Rip<.Lsqr_body
1713 jb .Lcommon_seh_tail
1715 mov 152($context),%rax # pull context->Rsp
1717 lea .Lsqr8x_epilogue(%rip),%r10
1718 cmp %r10,%rbx # context->Rip>=.Lsqr_epilogue
1719 jae .Lcommon_seh_tail
1721 mov 56(%rax),%rax # pull saved stack pointer
1730 mov %rbx,144($context) # restore context->Rbx
1731 mov %rbp,160($context) # restore context->Rbp
1732 mov %r12,216($context) # restore context->R12
1733 mov %r13,224($context) # restore context->R13
1734 mov %r14,232($context) # restore context->R14
1735 mov %r15,240($context) # restore context->R15
1740 mov %rax,152($context) # restore context->Rsp
1741 mov %rsi,168($context) # restore context->Rsi
1742 mov %rdi,176($context) # restore context->Rdi
1744 mov 40($disp),%rdi # disp->ContextRecord
1745 mov $context,%rsi # context
1746 mov \$154,%ecx # sizeof(CONTEXT)
1747 .long 0xa548f3fc # cld; rep movsq
1750 xor %rcx,%rcx # arg1, UNW_FLAG_NHANDLER
1751 mov 8(%rsi),%rdx # arg2, disp->ImageBase
1752 mov 0(%rsi),%r8 # arg3, disp->ControlPc
1753 mov 16(%rsi),%r9 # arg4, disp->FunctionEntry
1754 mov 40(%rsi),%r10 # disp->ContextRecord
1755 lea 56(%rsi),%r11 # &disp->HandlerData
1756 lea 24(%rsi),%r12 # &disp->EstablisherFrame
1757 mov %r10,32(%rsp) # arg5
1758 mov %r11,40(%rsp) # arg6
1759 mov %r12,48(%rsp) # arg7
1760 mov %rcx,56(%rsp) # arg8, (NULL)
1761 call *__imp_RtlVirtualUnwind(%rip)
1763 mov \$1,%eax # ExceptionContinueSearch
1775 .size sqr_handler,.-sqr_handler
1779 .rva .LSEH_begin_bn_mul_mont
1780 .rva .LSEH_end_bn_mul_mont
1781 .rva .LSEH_info_bn_mul_mont
1783 .rva .LSEH_begin_bn_mul4x_mont
1784 .rva .LSEH_end_bn_mul4x_mont
1785 .rva .LSEH_info_bn_mul4x_mont
1787 .rva .LSEH_begin_bn_sqr8x_mont
1788 .rva .LSEH_end_bn_sqr8x_mont
1789 .rva .LSEH_info_bn_sqr8x_mont
1793 .LSEH_info_bn_mul_mont:
1796 .rva .Lmul_body,.Lmul_epilogue # HandlerData[]
1797 .LSEH_info_bn_mul4x_mont:
1800 .rva .Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
1801 .LSEH_info_bn_sqr8x_mont: