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 if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
36 $win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
38 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
39 ( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
40 ( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
41 die "can't locate x86_64-xlate.pl";
43 open OUT,"| \"$^X\" $xlate $flavour $output";
47 $rp="%rdi"; # BN_ULONG *rp,
48 $ap="%rsi"; # const BN_ULONG *ap,
49 $bp="%rdx"; # const BN_ULONG *bp,
50 $np="%rcx"; # const BN_ULONG *np,
51 $n0="%r8"; # const BN_ULONG *n0,
52 $num="%r9"; # int num);
65 .type bn_mul_mont,\@function,6
89 lea (%rsp,%r10,8),%rsp # tp=alloca(8*(num+2))
90 and \$-1024,%rsp # minimize TLB usage
92 mov %r11,8(%rsp,$num,8) # tp[num+1]=%rsp
94 mov $bp,%r12 # reassign $bp
98 mov ($n0),$n0 # pull n0[0] value
99 mov ($bp),$m0 # m0=bp[0]
106 mulq $m0 # ap[0]*bp[0]
110 imulq $lo0,$m1 # "tp[0]"*n0
114 add %rax,$lo0 # discarded
127 add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
130 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
134 mulq $m0 # ap[j]*bp[0]
146 mov ($ap),%rax # ap[0]
148 add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
150 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
157 mov $hi1,-8(%rsp,$num,8)
158 mov %rdx,(%rsp,$num,8) # store upmost overflow bit
164 mov ($bp,$i,8),$m0 # m0=bp[i]
168 mulq $m0 # ap[0]*bp[i]
169 add %rax,$lo0 # ap[0]*bp[i]+tp[0]
173 imulq $lo0,$m1 # tp[0]*n0
177 add %rax,$lo0 # discarded
180 mov 8(%rsp),$lo0 # tp[1]
191 add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
194 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
198 mulq $m0 # ap[j]*bp[i]
202 add $hi0,$lo0 # ap[j]*bp[i]+tp[j]
212 mov ($ap),%rax # ap[0]
214 add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
217 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
223 add $lo0,$hi1 # pull upmost overflow bit
225 mov $hi1,-8(%rsp,$num,8)
226 mov %rdx,(%rsp,$num,8) # store upmost overflow bit
232 xor $i,$i # i=0 and clear CF!
233 mov (%rsp),%rax # tp[0]
234 lea (%rsp),$ap # borrow ap for tp
238 .Lsub: sbb ($np,$i,8),%rax
239 mov %rax,($rp,$i,8) # rp[i]=tp[i]-np[i]
240 mov 8($ap,$i,8),%rax # tp[i+1]
242 dec $j # doesnn't affect CF!
245 sbb \$0,%rax # handle upmost overflow bit
252 or $np,$ap # ap=borrow?tp:rp
254 .Lcopy: # copy or in-place refresh
256 mov $i,(%rsp,$i,8) # zap temporary vector
257 mov %rax,($rp,$i,8) # rp[i]=tp[i]
262 mov 8(%rsp,$num,8),%rsi # restore %rsp
273 .size bn_mul_mont,.-bn_mul_mont
276 my @A=("%r10","%r11");
277 my @N=("%r13","%rdi");
279 .type bn_mul4x_mont,\@function,6
294 lea (%rsp,%r10,8),%rsp # tp=alloca(8*(num+4))
295 and \$-1024,%rsp # minimize TLB usage
297 mov %r11,8(%rsp,$num,8) # tp[num+1]=%rsp
299 mov $rp,16(%rsp,$num,8) # tp[num+2]=$rp
300 mov %rdx,%r12 # reassign $bp
304 mov ($n0),$n0 # pull n0[0] value
305 mov ($bp),$m0 # m0=bp[0]
312 mulq $m0 # ap[0]*bp[0]
316 imulq $A[0],$m1 # "tp[0]"*n0
320 add %rax,$A[0] # discarded
343 mulq $m0 # ap[j]*bp[0]
345 mov -16($np,$j,8),%rax
351 mov -8($ap,$j,8),%rax
353 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
355 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
358 mulq $m0 # ap[j]*bp[0]
360 mov -8($np,$j,8),%rax
368 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
370 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
373 mulq $m0 # ap[j]*bp[0]
383 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
385 mov $N[0],-8(%rsp,$j,8) # tp[j-1]
388 mulq $m0 # ap[j]*bp[0]
397 mov -16($ap,$j,8),%rax
399 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
401 mov $N[1],-32(%rsp,$j,8) # tp[j-1]
406 mulq $m0 # ap[j]*bp[0]
408 mov -16($np,$j,8),%rax
414 mov -8($ap,$j,8),%rax
416 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
418 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
421 mulq $m0 # ap[j]*bp[0]
423 mov -8($np,$j,8),%rax
429 mov ($ap),%rax # ap[0]
431 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
433 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
439 mov $N[0],-8(%rsp,$j,8)
440 mov $N[1],(%rsp,$j,8) # store upmost overflow bit
445 mov ($bp,$i,8),$m0 # m0=bp[i]
449 mulq $m0 # ap[0]*bp[i]
450 add %rax,$A[0] # ap[0]*bp[i]+tp[0]
454 imulq $A[0],$m1 # tp[0]*n0
458 add %rax,$A[0] # "$N[0]", discarded
463 mulq $m0 # ap[j]*bp[i]
467 add 8(%rsp),$A[1] # +tp[1]
475 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[i]+tp[j]
478 mov $N[1],(%rsp) # tp[j-1]
483 mulq $m0 # ap[j]*bp[i]
485 mov -16($np,$j,8),%rax
487 add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
493 mov -8($ap,$j,8),%rax
497 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
500 mulq $m0 # ap[j]*bp[i]
502 mov -8($np,$j,8),%rax
504 add -8(%rsp,$j,8),$A[1]
514 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
517 mulq $m0 # ap[j]*bp[i]
521 add (%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
531 mov $N[0],-8(%rsp,$j,8) # tp[j-1]
534 mulq $m0 # ap[j]*bp[i]
538 add 8(%rsp,$j,8),$A[1]
545 mov -16($ap,$j,8),%rax
549 mov $N[1],-32(%rsp,$j,8) # tp[j-1]
554 mulq $m0 # ap[j]*bp[i]
556 mov -16($np,$j,8),%rax
558 add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
564 mov -8($ap,$j,8),%rax
568 mov $N[0],-24(%rsp,$j,8) # tp[j-1]
571 mulq $m0 # ap[j]*bp[i]
573 mov -8($np,$j,8),%rax
575 add -8(%rsp,$j,8),$A[1]
582 mov ($ap),%rax # ap[0]
586 mov $N[1],-16(%rsp,$j,8) # tp[j-1]
592 add (%rsp,$num,8),$N[0] # pull upmost overflow bit
594 mov $N[0],-8(%rsp,$j,8)
595 mov $N[1],(%rsp,$j,8) # store upmost overflow bit
601 my @ri=("%rax","%rdx",$m0,$m1);
603 mov 16(%rsp,$num,8),$rp # restore $rp
604 mov 0(%rsp),@ri[0] # tp[0]
606 mov 8(%rsp),@ri[1] # tp[1]
607 shr \$2,$num # num/=4
608 lea (%rsp),$ap # borrow ap for tp
609 xor $i,$i # i=0 and clear CF!
612 mov 16($ap),@ri[2] # tp[2]
613 mov 24($ap),@ri[3] # tp[3]
615 lea -1($num),$j # j=num/4-1
619 mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
620 mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
621 sbb 16($np,$i,8),@ri[2]
622 mov 32($ap,$i,8),@ri[0] # tp[i+1]
623 mov 40($ap,$i,8),@ri[1]
624 sbb 24($np,$i,8),@ri[3]
625 mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
626 mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
627 sbb 32($np,$i,8),@ri[0]
628 mov 48($ap,$i,8),@ri[2]
629 mov 56($ap,$i,8),@ri[3]
630 sbb 40($np,$i,8),@ri[1]
632 dec $j # doesnn't affect CF!
635 mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
636 mov 32($ap,$i,8),@ri[0] # load overflow bit
637 sbb 16($np,$i,8),@ri[2]
638 mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
639 sbb 24($np,$i,8),@ri[3]
640 mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
642 sbb \$0,@ri[0] # handle upmost overflow bit
643 mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
650 or $np,$ap # ap=borrow?tp:rp
657 .Lcopy4x: # copy or in-place refresh
658 movdqu 16($ap,$i),%xmm2
659 movdqu 32($ap,$i),%xmm1
660 movdqa %xmm0,16(%rsp,$i)
661 movdqu %xmm2,16($rp,$i)
662 movdqa %xmm0,32(%rsp,$i)
663 movdqu %xmm1,32($rp,$i)
669 movdqu 16($ap,$i),%xmm2
670 movdqa %xmm0,16(%rsp,$i)
671 movdqu %xmm2,16($rp,$i)
675 mov 8(%rsp,$num,8),%rsi # restore %rsp
686 .size bn_mul4x_mont,.-bn_mul4x_mont
690 ######################################################################
691 # void bn_sqr4x_mont(
692 my $rptr="%rdi"; # const BN_ULONG *rptr,
693 my $aptr="%rsi"; # const BN_ULONG *aptr,
694 my $bptr="%rdx"; # not used
695 my $nptr="%rcx"; # const BN_ULONG *nptr,
696 my $n0 ="%r8"; # const BN_ULONG *n0);
697 my $num ="%r9"; # int num, has to be divisible by 4 and
700 my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
701 my @A0=("%r10","%r11");
702 my @A1=("%r12","%r13");
703 my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
706 .type bn_sqr4x_mont,\@function,6
717 shl \$3,${num}d # convert $num to bytes
719 mov %rsp,%r11 # put aside %rsp
720 sub $num,%r10 # -$num
722 lea -72(%rsp,%r10,2),%rsp # alloca(frame+2*$num)
723 and \$-1024,%rsp # minimize TLB usage
724 ##############################################################
727 # +0 saved $num, used in reduction section
728 # +8 &t[2*$num], used in reduction section
735 mov $rptr,32(%rsp) # save $rptr
738 mov %r11, 56(%rsp) # save original %rsp
740 ##############################################################
743 # a) multiply-n-add everything but a[i]*a[i];
744 # b) shift result of a) by 1 to the left and accumulate
745 # a[i]*a[i] products;
747 lea 32(%r10),$i # $i=-($num-32)
748 lea ($aptr,$num),$aptr # end of a[] buffer, ($aptr,$i)=&ap[2]
750 mov $num,$j # $j=$num
752 # comments apply to $num==8 case
753 mov -32($aptr,$i),$a0 # a[0]
754 lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
755 mov -24($aptr,$i),%rax # a[1]
756 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
757 mov -16($aptr,$i),$ai # a[2]
761 mov %rax,$A0[0] # a[1]*a[0]
764 mov $A0[0],-24($tptr,$i) # t[1]
771 mov $A0[1],-16($tptr,$i) # t[2]
773 lea -16($i),$j # j=-16
776 mov 8($aptr,$j),$ai # a[3]
778 mov %rax,$A1[0] # a[2]*a[1]+t[3]
787 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
790 mov $A0[0],-8($tptr,$j) # t[3]
795 mov ($aptr,$j),$ai # a[4]
798 add %rax,$A1[1] # a[3]*a[1]+t[4]
806 add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
809 mov $A0[1],($tptr,$j) # t[4]
812 mov 8($aptr,$j),$ai # a[5]
815 add %rax,$A1[0] # a[4]*a[3]+t[5]
823 add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
826 mov $A0[0],8($tptr,$j) # t[5]
828 mov 16($aptr,$j),$ai # a[6]
831 add %rax,$A1[1] # a[5]*a[3]+t[6]
839 add %rax,$A0[1] # a[6]*a[2]+a[5]*a[3]+t[6]
842 mov $A0[1],16($tptr,$j) # t[6]
845 mov 24($aptr,$j),$ai # a[7]
848 add %rax,$A1[0] # a[6]*a[5]+t[7]
857 add %rax,$A0[0] # a[7]*a[4]+a[6]*a[5]+t[6]
860 mov $A0[0],-8($tptr,$j) # t[7]
872 mov $A1[1],($tptr) # t[8]
874 mov $A1[0],8($tptr) # t[9]
878 .Lsqr4x_outer: # comments apply to $num==6 case
879 mov -32($aptr,$i),$a0 # a[0]
880 lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
881 mov -24($aptr,$i),%rax # a[1]
882 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
883 mov -16($aptr,$i),$ai # a[2]
886 mov -24($tptr,$i),$A0[0] # t[1]
889 add %rax,$A0[0] # a[1]*a[0]+t[1]
892 mov $A0[0],-24($tptr,$i) # t[1]
895 add -16($tptr,$i),$A0[1] # a[2]*a[0]+t[2]
901 mov $A0[1],-16($tptr,$i) # t[2]
903 lea -16($i),$j # j=-16
907 mov 8($aptr,$j),$ai # a[3]
909 add 8($tptr,$j),$A1[0]
912 add %rax,$A1[0] # a[2]*a[1]+t[3]
920 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
923 mov $A0[0],8($tptr,$j) # t[3]
930 mov ($aptr,$j),$ai # a[4]
932 add ($tptr,$j),$A1[1]
935 add %rax,$A1[1] # a[3]*a[1]+t[4]
943 add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
946 mov $A0[1],($tptr,$j) # t[4]
948 mov 8($aptr,$j),$ai # a[5]
950 add 8($tptr,$j),$A1[0]
953 add %rax,$A1[0] # a[4]*a[3]+t[5]
962 add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
965 mov $A0[0],-8($tptr,$j) # t[5], "preloaded t[1]" below
977 mov $A1[1],($tptr) # t[6], "preloaded t[2]" below
978 mov $A1[0],8($tptr) # t[7], "preloaded t[3]" below
983 # comments apply to $num==4 case
984 mov -32($aptr),$a0 # a[0]
985 lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
986 mov -24($aptr),%rax # a[1]
987 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
988 mov -16($aptr),$ai # a[2]
993 add %rax,$A0[0] # a[1]*a[0]+t[1], preloaded t[1]
996 mov $A0[0],-24($tptr) # t[1]
999 add $A1[1],$A0[1] # a[2]*a[0]+t[2], preloaded t[2]
1005 mov $A0[1],-16($tptr) # t[2]
1007 mov -8($aptr),$ai # a[3]
1009 add %rax,$A1[0] # a[2]*a[1]+t[3], preloaded t[3]
1018 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
1021 mov $A0[0],-8($tptr) # t[3]
1028 mov -16($aptr),%rax # a[2]
1031 mov $A1[1],($tptr) # t[4]
1032 mov $A1[0],8($tptr) # t[5]
1037 my ($shift,$carry)=($a0,$a1);
1038 my @S=(@A1,$ai,$n0);
1042 sub $num,$i # $i=16-$num
1045 add $A1[0],%rax # t[5]
1047 mov %rax,8($tptr) # t[5]
1048 mov %rdx,16($tptr) # t[6]
1049 mov $carry,24($tptr) # t[7]
1051 mov -16($aptr,$i),%rax # a[0]
1052 lea 64(%rsp,$num,2),$tptr
1053 xor $A0[0],$A0[0] # t[0]
1054 mov -24($tptr,$i,2),$A0[1] # t[1]
1056 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1058 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1060 or $A0[0],$S[1] # | t[2*i]>>63
1061 mov -16($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1062 mov $A0[1],$shift # shift=t[2*i+1]>>63
1063 mul %rax # a[i]*a[i]
1064 neg $carry # mov $carry,cf
1065 mov -8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1067 mov -8($aptr,$i),%rax # a[i+1] # prefetch
1068 mov $S[0],-32($tptr,$i,2)
1071 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1072 mov $S[1],-24($tptr,$i,2)
1073 sbb $carry,$carry # mov cf,$carry
1075 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1077 or $A0[0],$S[3] # | t[2*i]>>63
1078 mov 0($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1079 mov $A0[1],$shift # shift=t[2*i+1]>>63
1080 mul %rax # a[i]*a[i]
1081 neg $carry # mov $carry,cf
1082 mov 8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1084 mov 0($aptr,$i),%rax # a[i+1] # prefetch
1085 mov $S[2],-16($tptr,$i,2)
1088 mov $S[3],-40($tptr,$i,2)
1089 sbb $carry,$carry # mov cf,$carry
1090 jmp .Lsqr4x_shift_n_add
1093 .Lsqr4x_shift_n_add:
1094 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1096 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1098 or $A0[0],$S[1] # | t[2*i]>>63
1099 mov -16($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1100 mov $A0[1],$shift # shift=t[2*i+1]>>63
1101 mul %rax # a[i]*a[i]
1102 neg $carry # mov $carry,cf
1103 mov -8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1105 mov -8($aptr,$i),%rax # a[i+1] # prefetch
1106 mov $S[0],-32($tptr,$i,2)
1109 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1110 mov $S[1],-24($tptr,$i,2)
1111 sbb $carry,$carry # mov cf,$carry
1113 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1115 or $A0[0],$S[3] # | t[2*i]>>63
1116 mov 0($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1117 mov $A0[1],$shift # shift=t[2*i+1]>>63
1118 mul %rax # a[i]*a[i]
1119 neg $carry # mov $carry,cf
1120 mov 8($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1122 mov 0($aptr,$i),%rax # a[i+1] # prefetch
1123 mov $S[2],-16($tptr,$i,2)
1126 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1127 mov $S[3],-8($tptr,$i,2)
1128 sbb $carry,$carry # mov cf,$carry
1130 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1132 or $A0[0],$S[1] # | t[2*i]>>63
1133 mov 16($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1134 mov $A0[1],$shift # shift=t[2*i+1]>>63
1135 mul %rax # a[i]*a[i]
1136 neg $carry # mov $carry,cf
1137 mov 24($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1139 mov 8($aptr,$i),%rax # a[i+1] # prefetch
1140 mov $S[0],0($tptr,$i,2)
1143 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1144 mov $S[1],8($tptr,$i,2)
1145 sbb $carry,$carry # mov cf,$carry
1147 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1149 or $A0[0],$S[3] # | t[2*i]>>63
1150 mov 32($tptr,$i,2),$A0[0] # t[2*i+2] # prefetch
1151 mov $A0[1],$shift # shift=t[2*i+1]>>63
1152 mul %rax # a[i]*a[i]
1153 neg $carry # mov $carry,cf
1154 mov 40($tptr,$i,2),$A0[1] # t[2*i+2+1] # prefetch
1156 mov 16($aptr,$i),%rax # a[i+1] # prefetch
1157 mov $S[2],16($tptr,$i,2)
1159 mov $S[3],24($tptr,$i,2)
1160 sbb $carry,$carry # mov cf,$carry
1162 jnz .Lsqr4x_shift_n_add
1164 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1166 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1168 or $A0[0],$S[1] # | t[2*i]>>63
1169 mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
1170 mov $A0[1],$shift # shift=t[2*i+1]>>63
1171 mul %rax # a[i]*a[i]
1172 neg $carry # mov $carry,cf
1173 mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
1175 mov -8($aptr),%rax # a[i+1] # prefetch
1176 mov $S[0],-32($tptr)
1179 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1|shift
1180 mov $S[1],-24($tptr)
1181 sbb $carry,$carry # mov cf,$carry
1183 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1185 or $A0[0],$S[3] # | t[2*i]>>63
1186 mul %rax # a[i]*a[i]
1187 neg $carry # mov $carry,cf
1190 mov $S[2],-16($tptr)
1194 ##############################################################
1195 # Montgomery reduction part, "word-by-word" algorithm.
1198 my ($topbit,$nptr)=("%rbp",$aptr);
1199 my ($m0,$m1)=($a0,$a1);
1200 my @Ni=("%rbx","%r9");
1202 mov 40(%rsp),$nptr # restore $nptr
1203 mov 48(%rsp),$n0 # restore *n0
1205 mov $num,0(%rsp) # save $num
1206 sub $num,$j # $j=-$num
1207 mov 64(%rsp),$A0[0] # t[0] # modsched #
1208 mov $n0,$m0 # # modsched #
1209 lea 64(%rsp,$num,2),%rax # end of t[] buffer
1210 lea 64(%rsp,$num),$tptr # end of t[] window
1211 mov %rax,8(%rsp) # save end of t[] buffer
1212 lea ($nptr,$num),$nptr # end of n[] buffer
1213 xor $topbit,$topbit # $topbit=0
1215 mov 0($nptr,$j),%rax # n[0] # modsched #
1216 mov 8($nptr,$j),$Ni[1] # n[1] # modsched #
1217 imulq $A0[0],$m0 # m0=t[0]*n0 # modsched #
1218 mov %rax,$Ni[0] # # modsched #
1219 jmp .Lsqr4x_mont_outer
1225 add %rax,$A0[0] # n[0]*m0+t[0]
1231 add 8($tptr,$j),$A0[1]
1234 add %rax,$A0[1] # n[1]*m0+t[1]
1240 mov 16($nptr,$j),$Ni[0] # n[2]
1245 add %rax,$A1[0] # n[0]*m1+"t[1]"
1248 mov $A1[0],8($tptr,$j) # "t[1]"
1251 add 16($tptr,$j),$A0[0]
1254 add %rax,$A0[0] # n[2]*m0+t[2]
1258 mov 24($nptr,$j),$Ni[1] # n[3]
1263 add %rax,$A1[1] # n[1]*m1+"t[2]"
1266 mov $A1[1],16($tptr,$j) # "t[2]"
1269 add 24($tptr,$j),$A0[1]
1273 add %rax,$A0[1] # n[3]*m0+t[3]
1276 jmp .Lsqr4x_mont_inner
1280 mov ($nptr,$j),$Ni[0] # n[4]
1285 add %rax,$A1[0] # n[2]*m1+"t[3]"
1288 mov $A1[0],-8($tptr,$j) # "t[3]"
1291 add ($tptr,$j),$A0[0]
1294 add %rax,$A0[0] # n[4]*m0+t[4]
1298 mov 8($nptr,$j),$Ni[1] # n[5]
1303 add %rax,$A1[1] # n[3]*m1+"t[4]"
1306 mov $A1[1],($tptr,$j) # "t[4]"
1309 add 8($tptr,$j),$A0[1]
1312 add %rax,$A0[1] # n[5]*m0+t[5]
1317 mov 16($nptr,$j),$Ni[0] # n[6]
1322 add %rax,$A1[0] # n[4]*m1+"t[5]"
1325 mov $A1[0],8($tptr,$j) # "t[5]"
1328 add 16($tptr,$j),$A0[0]
1331 add %rax,$A0[0] # n[6]*m0+t[6]
1335 mov 24($nptr,$j),$Ni[1] # n[7]
1340 add %rax,$A1[1] # n[5]*m1+"t[6]"
1343 mov $A1[1],16($tptr,$j) # "t[6]"
1346 add 24($tptr,$j),$A0[1]
1350 add %rax,$A0[1] # n[7]*m0+t[7]
1354 jne .Lsqr4x_mont_inner
1356 sub 0(%rsp),$j # $j=-$num # modsched #
1357 mov $n0,$m0 # # modsched #
1363 add %rax,$A1[0] # n[6]*m1+"t[7]"
1366 mov $A1[0],-8($tptr) # "t[7]"
1369 add ($tptr),$A0[0] # +t[8]
1371 mov 0($nptr,$j),$Ni[0] # n[0] # modsched #
1375 imulq 16($tptr,$j),$m0 # m0=t[0]*n0 # modsched #
1377 mov 8($nptr,$j),$Ni[1] # n[1] # modsched #
1379 mov 16($tptr,$j),$A0[0] # t[0] # modsched #
1382 add %rax,$A1[1] # n[7]*m1+"t[8]"
1383 mov $Ni[0],%rax # # modsched #
1385 mov $A1[1],($tptr) # "t[8]"
1388 add 8($tptr),$A1[0] # +t[9]
1391 lea 16($tptr),$tptr # "t[$num]>>128"
1393 mov $A1[0],-8($tptr) # "t[9]"
1394 cmp 8(%rsp),$tptr # are we done?
1395 jb .Lsqr4x_mont_outer
1397 mov 0(%rsp),$num # restore $num
1398 mov $topbit,($tptr) # save $topbit
1401 ##############################################################
1402 # Post-condition, 4x unrolled copy from bn_mul_mont
1405 my ($tptr,$nptr)=("%rbx",$aptr);
1406 my @ri=("%rax","%rdx","%r10","%r11");
1408 mov 64(%rsp,$num),@ri[0] # tp[0]
1409 lea 64(%rsp,$num),$tptr # upper half of t[2*$num] holds result
1410 mov 40(%rsp),$nptr # restore $nptr
1411 shr \$5,$num # num/4
1412 mov 8($tptr),@ri[1] # t[1]
1413 xor $i,$i # i=0 and clear CF!
1415 mov 32(%rsp),$rptr # restore $rptr
1417 mov 16($tptr),@ri[2] # t[2]
1418 mov 24($tptr),@ri[3] # t[3]
1420 lea -1($num),$j # j=num/4-1
1424 mov @ri[0],0($rptr,$i,8) # rp[i]=tp[i]-np[i]
1425 mov @ri[1],8($rptr,$i,8) # rp[i]=tp[i]-np[i]
1426 sbb 16($nptr,$i,8),@ri[2]
1427 mov 32($tptr,$i,8),@ri[0] # tp[i+1]
1428 mov 40($tptr,$i,8),@ri[1]
1429 sbb 24($nptr,$i,8),@ri[3]
1430 mov @ri[2],16($rptr,$i,8) # rp[i]=tp[i]-np[i]
1431 mov @ri[3],24($rptr,$i,8) # rp[i]=tp[i]-np[i]
1432 sbb 32($nptr,$i,8),@ri[0]
1433 mov 48($tptr,$i,8),@ri[2]
1434 mov 56($tptr,$i,8),@ri[3]
1435 sbb 40($nptr,$i,8),@ri[1]
1437 dec $j # doesn't affect CF!
1440 mov @ri[0],0($rptr,$i,8) # rp[i]=tp[i]-np[i]
1441 mov 32($tptr,$i,8),@ri[0] # load overflow bit
1442 sbb 16($nptr,$i,8),@ri[2]
1443 mov @ri[1],8($rptr,$i,8) # rp[i]=tp[i]-np[i]
1444 sbb 24($nptr,$i,8),@ri[3]
1445 mov @ri[2],16($rptr,$i,8) # rp[i]=tp[i]-np[i]
1447 sbb \$0,@ri[0] # handle upmost overflow bit
1448 mov @ri[3],24($rptr,$i,8) # rp[i]=tp[i]-np[i]
1455 or $nptr,$tptr # tp=borrow?tp:rp
1458 lea 64(%rsp,$num,8),$nptr
1459 movdqu ($tptr),%xmm1
1460 lea ($nptr,$num,8),$nptr
1461 movdqa %xmm0,64(%rsp) # zap lower half of temporary vector
1462 movdqa %xmm0,($nptr) # zap upper half of temporary vector
1463 movdqu %xmm1,($rptr)
1466 .Lsqr4x_copy: # copy or in-place refresh
1467 movdqu 16($tptr,$i),%xmm2
1468 movdqu 32($tptr,$i),%xmm1
1469 movdqa %xmm0,80(%rsp,$i) # zap lower half of temporary vector
1470 movdqa %xmm0,96(%rsp,$i) # zap lower half of temporary vector
1471 movdqa %xmm0,16($nptr,$i) # zap upper half of temporary vector
1472 movdqa %xmm0,32($nptr,$i) # zap upper half of temporary vector
1473 movdqu %xmm2,16($rptr,$i)
1474 movdqu %xmm1,32($rptr,$i)
1479 movdqu 16($tptr,$i),%xmm2
1480 movdqa %xmm0,80(%rsp,$i) # zap lower half of temporary vector
1481 movdqa %xmm0,16($nptr,$i) # zap upper half of temporary vector
1482 movdqu %xmm2,16($rptr,$i)
1486 mov 56(%rsp),%rsi # restore %rsp
1497 .size bn_sqr4x_mont,.-bn_sqr4x_mont
1501 .asciz "Montgomery Multiplication for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
1505 # EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
1506 # CONTEXT *context,DISPATCHER_CONTEXT *disp)
1514 .extern __imp_RtlVirtualUnwind
1515 .type mul_handler,\@abi-omnipotent
1529 mov 120($context),%rax # pull context->Rax
1530 mov 248($context),%rbx # pull context->Rip
1532 mov 8($disp),%rsi # disp->ImageBase
1533 mov 56($disp),%r11 # disp->HandlerData
1535 mov 0(%r11),%r10d # HandlerData[0]
1536 lea (%rsi,%r10),%r10 # end of prologue label
1537 cmp %r10,%rbx # context->Rip<end of prologue label
1538 jb .Lcommon_seh_tail
1540 mov 152($context),%rax # pull context->Rsp
1542 mov 4(%r11),%r10d # HandlerData[1]
1543 lea (%rsi,%r10),%r10 # epilogue label
1544 cmp %r10,%rbx # context->Rip>=epilogue label
1545 jae .Lcommon_seh_tail
1547 mov 192($context),%r10 # pull $num
1548 mov 8(%rax,%r10,8),%rax # pull saved stack pointer
1557 mov %rbx,144($context) # restore context->Rbx
1558 mov %rbp,160($context) # restore context->Rbp
1559 mov %r12,216($context) # restore context->R12
1560 mov %r13,224($context) # restore context->R13
1561 mov %r14,232($context) # restore context->R14
1562 mov %r15,240($context) # restore context->R15
1564 jmp .Lcommon_seh_tail
1565 .size mul_handler,.-mul_handler
1567 .type sqr_handler,\@abi-omnipotent
1581 mov 120($context),%rax # pull context->Rax
1582 mov 248($context),%rbx # pull context->Rip
1584 lea .Lsqr4x_body(%rip),%r10
1585 cmp %r10,%rbx # context->Rip<.Lsqr_body
1586 jb .Lcommon_seh_tail
1588 mov 152($context),%rax # pull context->Rsp
1590 lea .Lsqr4x_epilogue(%rip),%r10
1591 cmp %r10,%rbx # context->Rip>=.Lsqr_epilogue
1592 jae .Lcommon_seh_tail
1594 mov 56(%rax),%rax # pull saved stack pointer
1603 mov %rbx,144($context) # restore context->Rbx
1604 mov %rbp,160($context) # restore context->Rbp
1605 mov %r12,216($context) # restore context->R12
1606 mov %r13,224($context) # restore context->R13
1607 mov %r14,232($context) # restore context->R14
1608 mov %r15,240($context) # restore context->R15
1613 mov %rax,152($context) # restore context->Rsp
1614 mov %rsi,168($context) # restore context->Rsi
1615 mov %rdi,176($context) # restore context->Rdi
1617 mov 40($disp),%rdi # disp->ContextRecord
1618 mov $context,%rsi # context
1619 mov \$154,%ecx # sizeof(CONTEXT)
1620 .long 0xa548f3fc # cld; rep movsq
1623 xor %rcx,%rcx # arg1, UNW_FLAG_NHANDLER
1624 mov 8(%rsi),%rdx # arg2, disp->ImageBase
1625 mov 0(%rsi),%r8 # arg3, disp->ControlPc
1626 mov 16(%rsi),%r9 # arg4, disp->FunctionEntry
1627 mov 40(%rsi),%r10 # disp->ContextRecord
1628 lea 56(%rsi),%r11 # &disp->HandlerData
1629 lea 24(%rsi),%r12 # &disp->EstablisherFrame
1630 mov %r10,32(%rsp) # arg5
1631 mov %r11,40(%rsp) # arg6
1632 mov %r12,48(%rsp) # arg7
1633 mov %rcx,56(%rsp) # arg8, (NULL)
1634 call *__imp_RtlVirtualUnwind(%rip)
1636 mov \$1,%eax # ExceptionContinueSearch
1648 .size sqr_handler,.-sqr_handler
1652 .rva .LSEH_begin_bn_mul_mont
1653 .rva .LSEH_end_bn_mul_mont
1654 .rva .LSEH_info_bn_mul_mont
1656 .rva .LSEH_begin_bn_mul4x_mont
1657 .rva .LSEH_end_bn_mul4x_mont
1658 .rva .LSEH_info_bn_mul4x_mont
1660 .rva .LSEH_begin_bn_sqr4x_mont
1661 .rva .LSEH_end_bn_sqr4x_mont
1662 .rva .LSEH_info_bn_sqr4x_mont
1666 .LSEH_info_bn_mul_mont:
1669 .rva .Lmul_body,.Lmul_epilogue # HandlerData[]
1670 .LSEH_info_bn_mul4x_mont:
1673 .rva .Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
1674 .LSEH_info_bn_sqr4x_mont: