2 # Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved.
4 # Licensed under the Apache License 2.0 (the "License"). You may not use
5 # this file except in compliance with the License. You can obtain a copy
6 # in the file LICENSE in the source distribution or at
7 # https://www.openssl.org/source/license.html
10 # ====================================================================
11 # Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
12 # project. The module is, however, dual licensed under OpenSSL and
13 # CRYPTOGAMS licenses depending on where you obtain it. For further
14 # details see http://www.openssl.org/~appro/cryptogams/.
15 # ====================================================================
19 # Companion to x86_64-mont.pl that optimizes cache-timing attack
20 # countermeasures. The subroutines are produced by replacing bp[i]
21 # references in their x86_64-mont.pl counterparts with cache-neutral
22 # references to powers table computed in BN_mod_exp_mont_consttime.
23 # In addition subroutine that scatters elements of the powers table
24 # is implemented, so that scatter-/gathering can be tuned without
25 # bn_exp.c modifications.
29 # Add MULX/AD*X code paths and additional interfaces to optimize for
30 # branch prediction unit. For input lengths that are multiples of 8
31 # the np argument is not just modulus value, but one interleaved
32 # with 0. This is to optimize post-condition...
36 if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
38 $win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
40 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
41 ( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
42 ( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
43 die "can't locate x86_64-xlate.pl";
45 open OUT,"| \"$^X\" \"$xlate\" $flavour \"$output\"";
48 if (`$ENV{CC} -Wa,-v -c -o /dev/null -x assembler /dev/null 2>&1`
49 =~ /GNU assembler version ([2-9]\.[0-9]+)/) {
53 if (!$addx && $win64 && ($flavour =~ /nasm/ || $ENV{ASM} =~ /nasm/) &&
54 `nasm -v 2>&1` =~ /NASM version ([2-9]\.[0-9]+)/) {
58 if (!$addx && $win64 && ($flavour =~ /masm/ || $ENV{ASM} =~ /ml64/) &&
59 `ml64 2>&1` =~ /Version ([0-9]+)\./) {
63 if (!$addx && `$ENV{CC} -v 2>&1` =~ /((?:^clang|LLVM) version|.*based on LLVM) ([3-9])\.([0-9]+)/) {
64 my $ver = $2 + $3/100.0; # 3.1->3.01, 3.10->3.10
68 # int bn_mul_mont_gather5(
69 $rp="%rdi"; # BN_ULONG *rp,
70 $ap="%rsi"; # const BN_ULONG *ap,
71 $bp="%rdx"; # const BN_ULONG *bp,
72 $np="%rcx"; # const BN_ULONG *np,
73 $n0="%r8"; # const BN_ULONG *n0,
74 $num="%r9"; # int num,
75 # int idx); # 0 to 2^5-1, "index" in $bp holding
76 # pre-computed powers of a', interlaced
77 # in such manner that b[0] is $bp[idx],
78 # b[1] is [2^5+idx], etc.
90 .extern OPENSSL_ia32cap_P
92 .globl bn_mul_mont_gather5
93 .type bn_mul_mont_gather5,\@function,6
99 .cfi_def_cfa_register %rax
103 $code.=<<___ if ($addx);
104 mov OPENSSL_ia32cap_P+8(%rip),%r11d
111 movd `($win64?56:8)`(%rsp),%xmm5 # load 7th argument
127 lea -280(%rsp,$num,8),%r10 # future alloca(8*(num+2)+256+8)
128 neg $num # restore $num
129 and \$-1024,%r10 # minimize TLB usage
131 # An OS-agnostic version of __chkstk.
133 # Some OSes (Windows) insist on stack being "wired" to
134 # physical memory in strictly sequential manner, i.e. if stack
135 # allocation spans two pages, then reference to farmost one can
136 # be punishable by SEGV. But page walking can do good even on
137 # other OSes, because it guarantees that villain thread hits
138 # the guard page before it can make damage to innocent one...
145 jmp .Lmul_page_walk_done
152 .Lmul_page_walk_done:
155 mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
156 .cfi_cfa_expression %rsp+8,$num,8,mul,plus,deref,+8
159 lea 128($bp),%r12 # reassign $bp (+size optimization)
162 $STRIDE=2**5*8; # 5 is "window size"
163 $N=$STRIDE/4; # should match cache line size
165 movdqa 0(%r10),%xmm0 # 00000001000000010000000000000000
166 movdqa 16(%r10),%xmm1 # 00000002000000020000000200000002
167 lea 24-112(%rsp,$num,8),%r10# place the mask after tp[num+3] (+ICache optimization)
170 pshufd \$0,%xmm5,%xmm5 # broadcast index
174 ########################################################################
175 # calculate mask by comparing 0..31 to index and save result to stack
179 pcmpeqd %xmm5,%xmm0 # compare to 1,0
183 for($k=0;$k<$STRIDE/16-4;$k+=4) {
186 pcmpeqd %xmm5,%xmm1 # compare to 3,2
187 movdqa %xmm0,`16*($k+0)+112`(%r10)
191 pcmpeqd %xmm5,%xmm2 # compare to 5,4
192 movdqa %xmm1,`16*($k+1)+112`(%r10)
196 pcmpeqd %xmm5,%xmm3 # compare to 7,6
197 movdqa %xmm2,`16*($k+2)+112`(%r10)
202 movdqa %xmm3,`16*($k+3)+112`(%r10)
206 $code.=<<___; # last iteration can be optimized
209 movdqa %xmm0,`16*($k+0)+112`(%r10)
214 movdqa %xmm1,`16*($k+1)+112`(%r10)
217 movdqa %xmm2,`16*($k+2)+112`(%r10)
218 pand `16*($k+0)-128`($bp),%xmm0 # while it's still in register
220 pand `16*($k+1)-128`($bp),%xmm1
221 pand `16*($k+2)-128`($bp),%xmm2
222 movdqa %xmm3,`16*($k+3)+112`(%r10)
223 pand `16*($k+3)-128`($bp),%xmm3
227 for($k=0;$k<$STRIDE/16-4;$k+=4) {
229 movdqa `16*($k+0)-128`($bp),%xmm4
230 movdqa `16*($k+1)-128`($bp),%xmm5
231 movdqa `16*($k+2)-128`($bp),%xmm2
232 pand `16*($k+0)+112`(%r10),%xmm4
233 movdqa `16*($k+3)-128`($bp),%xmm3
234 pand `16*($k+1)+112`(%r10),%xmm5
236 pand `16*($k+2)+112`(%r10),%xmm2
238 pand `16*($k+3)+112`(%r10),%xmm3
245 pshufd \$0x4e,%xmm0,%xmm1
248 movq %xmm0,$m0 # m0=bp[0]
250 mov ($n0),$n0 # pull n0[0] value
257 mulq $m0 # ap[0]*bp[0]
261 imulq $lo0,$m1 # "tp[0]"*n0
265 add %rax,$lo0 # discarded
278 add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
281 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
285 mulq $m0 # ap[j]*bp[0]
294 jne .L1st # note that upon exit $j==$num, so
295 # they can be used interchangeably
299 add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
301 mov $hi1,-16(%rsp,$num,8) # tp[num-1]
308 mov $hi1,-8(%rsp,$num,8)
309 mov %rdx,(%rsp,$num,8) # store upmost overflow bit
315 lea 24+128(%rsp,$num,8),%rdx # where 256-byte mask is (+size optimization)
320 for($k=0;$k<$STRIDE/16;$k+=4) {
322 movdqa `16*($k+0)-128`($bp),%xmm0
323 movdqa `16*($k+1)-128`($bp),%xmm1
324 movdqa `16*($k+2)-128`($bp),%xmm2
325 movdqa `16*($k+3)-128`($bp),%xmm3
326 pand `16*($k+0)-128`(%rdx),%xmm0
327 pand `16*($k+1)-128`(%rdx),%xmm1
329 pand `16*($k+2)-128`(%rdx),%xmm2
331 pand `16*($k+3)-128`(%rdx),%xmm3
338 pshufd \$0x4e,%xmm4,%xmm0
342 mov ($ap),%rax # ap[0]
343 movq %xmm0,$m0 # m0=bp[i]
349 mulq $m0 # ap[0]*bp[i]
350 add %rax,$lo0 # ap[0]*bp[i]+tp[0]
354 imulq $lo0,$m1 # tp[0]*n0
358 add %rax,$lo0 # discarded
361 mov 8(%rsp),$lo0 # tp[1]
372 add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
375 mov $hi1,-16(%rsp,$j,8) # tp[j-1]
379 mulq $m0 # ap[j]*bp[i]
383 add $hi0,$lo0 # ap[j]*bp[i]+tp[j]
390 jne .Linner # note that upon exit $j==$num, so
391 # they can be used interchangeably
394 add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
395 mov (%rsp,$num,8),$lo0
397 mov $hi1,-16(%rsp,$num,8) # tp[num-1]
403 add $lo0,$hi1 # pull upmost overflow bit
405 mov $hi1,-8(%rsp,$num,8)
406 mov %rdx,(%rsp,$num,8) # store upmost overflow bit
412 xor $i,$i # i=0 and clear CF!
413 mov (%rsp),%rax # tp[0]
414 lea (%rsp),$ap # borrow ap for tp
418 .Lsub: sbb ($np,$i,8),%rax
419 mov %rax,($rp,$i,8) # rp[i]=tp[i]-np[i]
420 mov 8($ap,$i,8),%rax # tp[i+1]
422 dec $j # doesn't affect CF!
425 sbb \$0,%rax # handle upmost overflow bit
431 .Lcopy: # conditional copy
436 mov $i,(%rsp,$i,8) # zap temporary vector
438 mov %rdx,($rp,$i,8) # rp[i]=tp[i]
443 mov 8(%rsp,$num,8),%rsi # restore %rsp
460 .cfi_def_cfa_register %rsp
464 .size bn_mul_mont_gather5,.-bn_mul_mont_gather5
467 my @A=("%r10","%r11");
468 my @N=("%r13","%rdi");
470 .type bn_mul4x_mont_gather5,\@function,6
472 bn_mul4x_mont_gather5:
476 .cfi_def_cfa_register %rax
479 $code.=<<___ if ($addx);
481 cmp \$0x80108,%r11d # check for AD*X+BMI2+BMI1
500 shl \$3,${num}d # convert $num to bytes
501 lea ($num,$num,2),%r10 # 3*$num in bytes
504 ##############################################################
505 # Ensure that stack frame doesn't alias with $rptr+3*$num
506 # modulo 4096, which covers ret[num], am[num] and n[num]
507 # (see bn_exp.c). This is done to allow memory disambiguation
508 # logic do its magic. [Extra [num] is allocated in order
509 # to align with bn_power5's frame, which is cleansed after
510 # completing exponentiation. Extra 256 bytes is for power mask
511 # calculated from 7th argument, the index.]
513 lea -320(%rsp,$num,2),%r11
519 sub %r11,%rbp # align with $rp
520 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
525 lea 4096-320(,$num,2),%r10
526 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
540 jmp .Lmul4x_page_walk_done
547 .Lmul4x_page_walk_done:
552 .cfi_cfa_expression %rsp+40,deref,+8
557 mov 40(%rsp),%rsi # restore %rsp
574 .cfi_def_cfa_register %rsp
578 .size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
580 .type mul4x_internal,\@abi-omnipotent
583 shl \$5,$num # $num was in bytes
584 movd `($win64?56:8)`(%rax),%xmm5 # load 7th argument, index
586 lea 128(%rdx,$num),%r13 # end of powers table (+size optimization)
587 shr \$5,$num # restore $num
590 $STRIDE=2**5*8; # 5 is "window size"
591 $N=$STRIDE/4; # should match cache line size
594 movdqa 0(%rax),%xmm0 # 00000001000000010000000000000000
595 movdqa 16(%rax),%xmm1 # 00000002000000020000000200000002
596 lea 88-112(%rsp,$num),%r10 # place the mask after tp[num+1] (+ICache optimization)
597 lea 128(%rdx),$bp # size optimization
599 pshufd \$0,%xmm5,%xmm5 # broadcast index
604 ########################################################################
605 # calculate mask by comparing 0..31 to index and save result to stack
609 pcmpeqd %xmm5,%xmm0 # compare to 1,0
613 for($i=0;$i<$STRIDE/16-4;$i+=4) {
616 pcmpeqd %xmm5,%xmm1 # compare to 3,2
617 movdqa %xmm0,`16*($i+0)+112`(%r10)
621 pcmpeqd %xmm5,%xmm2 # compare to 5,4
622 movdqa %xmm1,`16*($i+1)+112`(%r10)
626 pcmpeqd %xmm5,%xmm3 # compare to 7,6
627 movdqa %xmm2,`16*($i+2)+112`(%r10)
632 movdqa %xmm3,`16*($i+3)+112`(%r10)
636 $code.=<<___; # last iteration can be optimized
639 movdqa %xmm0,`16*($i+0)+112`(%r10)
644 movdqa %xmm1,`16*($i+1)+112`(%r10)
647 movdqa %xmm2,`16*($i+2)+112`(%r10)
648 pand `16*($i+0)-128`($bp),%xmm0 # while it's still in register
650 pand `16*($i+1)-128`($bp),%xmm1
651 pand `16*($i+2)-128`($bp),%xmm2
652 movdqa %xmm3,`16*($i+3)+112`(%r10)
653 pand `16*($i+3)-128`($bp),%xmm3
657 for($i=0;$i<$STRIDE/16-4;$i+=4) {
659 movdqa `16*($i+0)-128`($bp),%xmm4
660 movdqa `16*($i+1)-128`($bp),%xmm5
661 movdqa `16*($i+2)-128`($bp),%xmm2
662 pand `16*($i+0)+112`(%r10),%xmm4
663 movdqa `16*($i+3)-128`($bp),%xmm3
664 pand `16*($i+1)+112`(%r10),%xmm5
666 pand `16*($i+2)+112`(%r10),%xmm2
668 pand `16*($i+3)+112`(%r10),%xmm3
675 pshufd \$0x4e,%xmm0,%xmm1
678 movq %xmm0,$m0 # m0=bp[0]
680 mov %r13,16+8(%rsp) # save end of b[num]
681 mov $rp, 56+8(%rsp) # save $rp
683 mov ($n0),$n0 # pull n0[0] value
685 lea ($ap,$num),$ap # end of a[num]
689 mulq $m0 # ap[0]*bp[0]
693 imulq $A[0],$m1 # "tp[0]"*n0
698 add %rax,$A[0] # discarded
711 mov 16($ap,$num),%rax
714 lea 4*8($num),$j # j=4
723 mulq $m0 # ap[j]*bp[0]
734 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
736 mov $N[0],-24($tp) # tp[j-1]
739 mulq $m0 # ap[j]*bp[0]
749 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
751 mov $N[1],-16($tp) # tp[j-1]
754 mulq $m0 # ap[j]*bp[0]
764 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
766 mov $N[0],-8($tp) # tp[j-1]
769 mulq $m0 # ap[j]*bp[0]
779 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
782 mov $N[1],($tp) # tp[j-1]
788 mulq $m0 # ap[j]*bp[0]
799 add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
801 mov $N[0],-24($tp) # tp[j-1]
804 mulq $m0 # ap[j]*bp[0]
812 mov ($ap,$num),%rax # ap[0]
814 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
816 mov $N[1],-16($tp) # tp[j-1]
819 lea ($np,$num),$np # rewind $np
830 lea 16+128($tp),%rdx # where 256-byte mask is (+size optimization)
834 for($i=0;$i<$STRIDE/16;$i+=4) {
836 movdqa `16*($i+0)-128`($bp),%xmm0
837 movdqa `16*($i+1)-128`($bp),%xmm1
838 movdqa `16*($i+2)-128`($bp),%xmm2
839 movdqa `16*($i+3)-128`($bp),%xmm3
840 pand `16*($i+0)-128`(%rdx),%xmm0
841 pand `16*($i+1)-128`(%rdx),%xmm1
843 pand `16*($i+2)-128`(%rdx),%xmm2
845 pand `16*($i+3)-128`(%rdx),%xmm3
852 pshufd \$0x4e,%xmm4,%xmm0
855 movq %xmm0,$m0 # m0=bp[i]
859 mulq $m0 # ap[0]*bp[i]
860 add %rax,$A[0] # ap[0]*bp[i]+tp[0]
864 imulq $A[0],$m1 # tp[0]*n0
866 mov $N[1],($tp) # store upmost overflow bit
868 lea ($tp,$num),$tp # rewind $tp
871 add %rax,$A[0] # "$N[0]", discarded
876 mulq $m0 # ap[j]*bp[i]
880 add 8($tp),$A[1] # +tp[1]
886 mov 16($ap,$num),%rax
888 add $A[1],$N[1] # np[j]*m1+ap[j]*bp[i]+tp[j]
889 lea 4*8($num),$j # j=4
897 mulq $m0 # ap[j]*bp[i]
901 add 16($tp),$A[0] # ap[j]*bp[i]+tp[j]
912 mov $N[1],-32($tp) # tp[j-1]
915 mulq $m0 # ap[j]*bp[i]
929 mov $N[0],-24($tp) # tp[j-1]
932 mulq $m0 # ap[j]*bp[i]
936 add ($tp),$A[0] # ap[j]*bp[i]+tp[j]
946 mov $N[1],-16($tp) # tp[j-1]
949 mulq $m0 # ap[j]*bp[i]
964 mov $N[0],-8($tp) # tp[j-1]
970 mulq $m0 # ap[j]*bp[i]
974 add 16($tp),$A[0] # ap[j]*bp[i]+tp[j]
985 mov $N[1],-32($tp) # tp[j-1]
988 mulq $m0 # ap[j]*bp[i]
999 mov ($ap,$num),%rax # ap[0]
1003 mov $N[0],-24($tp) # tp[j-1]
1006 mov $N[1],-16($tp) # tp[j-1]
1007 lea ($np,$num),$np # rewind $np
1012 add ($tp),$N[0] # pull upmost overflow bit
1013 adc \$0,$N[1] # upmost overflow bit
1022 sub $N[0],$m1 # compare top-most words
1023 adc $j,$j # $j is zero
1025 sub $N[1],%rax # %rax=-$N[1]
1026 lea ($tp,$num),%rbx # tptr in .sqr4x_sub
1028 lea ($np),%rbp # nptr in .sqr4x_sub
1031 mov 56+8(%rsp),%rdi # rptr in .sqr4x_sub
1032 dec %r12 # so that after 'not' we get -n[0]
1037 jmp .Lsqr4x_sub_entry
1040 my @ri=("%rax",$bp,$m0,$m1);
1044 lea ($tp,$num),$tp # rewind $tp
1046 lea ($np,$N[1],8),$np
1047 mov 56+8(%rsp),$rp # restore $rp
1056 sbb 16*0($np),@ri[0]
1058 sbb 16*1($np),@ri[1]
1061 sbb 16*2($np),@ri[2]
1063 sbb 16*3($np),@ri[3]
1077 .size mul4x_internal,.-mul4x_internal
1081 ######################################################################
1083 my $rptr="%rdi"; # BN_ULONG *rptr,
1084 my $aptr="%rsi"; # const BN_ULONG *aptr,
1085 my $bptr="%rdx"; # const void *table,
1086 my $nptr="%rcx"; # const BN_ULONG *nptr,
1087 my $n0 ="%r8"; # const BN_ULONG *n0);
1088 my $num ="%r9"; # int num, has to be divisible by 8
1091 my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
1092 my @A0=("%r10","%r11");
1093 my @A1=("%r12","%r13");
1094 my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
1098 .type bn_power5,\@function,6
1103 .cfi_def_cfa_register %rax
1105 $code.=<<___ if ($addx);
1106 mov OPENSSL_ia32cap_P+8(%rip),%r11d
1108 cmp \$0x80108,%r11d # check for AD*X+BMI2+BMI1
1126 shl \$3,${num}d # convert $num to bytes
1127 lea ($num,$num,2),%r10d # 3*$num
1131 ##############################################################
1132 # Ensure that stack frame doesn't alias with $rptr+3*$num
1133 # modulo 4096, which covers ret[num], am[num] and n[num]
1134 # (see bn_exp.c). This is done to allow memory disambiguation
1135 # logic do its magic. [Extra 256 bytes is for power mask
1136 # calculated from 7th argument, the index.]
1138 lea -320(%rsp,$num,2),%r11
1144 sub %r11,%rbp # align with $aptr
1145 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
1150 lea 4096-320(,$num,2),%r10
1151 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
1161 lea (%rbp,%r11),%rsp
1165 jmp .Lpwr_page_walk_done
1168 lea -4096(%rsp),%rsp
1172 .Lpwr_page_walk_done:
1177 ##############################################################
1180 # +0 saved $num, used in reduction section
1181 # +8 &t[2*$num], used in reduction section
1187 mov %rax, 40(%rsp) # save original %rsp
1188 .cfi_cfa_expression %rsp+40,deref,+8
1190 movq $rptr,%xmm1 # save $rptr, used in sqr8x
1191 movq $nptr,%xmm2 # save $nptr
1192 movq %r10, %xmm3 # -$num, used in sqr8x
1195 call __bn_sqr8x_internal
1196 call __bn_post4x_internal
1197 call __bn_sqr8x_internal
1198 call __bn_post4x_internal
1199 call __bn_sqr8x_internal
1200 call __bn_post4x_internal
1201 call __bn_sqr8x_internal
1202 call __bn_post4x_internal
1203 call __bn_sqr8x_internal
1204 call __bn_post4x_internal
1214 mov 40(%rsp),%rsi # restore %rsp
1230 .cfi_def_cfa_register %rsp
1234 .size bn_power5,.-bn_power5
1236 .globl bn_sqr8x_internal
1237 .hidden bn_sqr8x_internal
1238 .type bn_sqr8x_internal,\@abi-omnipotent
1241 __bn_sqr8x_internal:
1242 ##############################################################
1245 # a) multiply-n-add everything but a[i]*a[i];
1246 # b) shift result of a) by 1 to the left and accumulate
1247 # a[i]*a[i] products;
1249 ##############################################################
1315 lea 32(%r10),$i # $i=-($num-32)
1316 lea ($aptr,$num),$aptr # end of a[] buffer, ($aptr,$i)=&ap[2]
1318 mov $num,$j # $j=$num
1320 # comments apply to $num==8 case
1321 mov -32($aptr,$i),$a0 # a[0]
1322 lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
1323 mov -24($aptr,$i),%rax # a[1]
1324 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
1325 mov -16($aptr,$i),$ai # a[2]
1329 mov %rax,$A0[0] # a[1]*a[0]
1332 mov $A0[0],-24($tptr,$i) # t[1]
1338 mov $A0[1],-16($tptr,$i) # t[2]
1342 mov -8($aptr,$i),$ai # a[3]
1344 mov %rax,$A1[0] # a[2]*a[1]+t[3]
1350 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
1356 mov $A0[0],-8($tptr,$j) # t[3]
1361 mov ($aptr,$j),$ai # a[4]
1363 add %rax,$A1[1] # a[3]*a[1]+t[4]
1369 add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
1371 mov 8($aptr,$j),$ai # a[5]
1379 add %rax,$A1[0] # a[4]*a[3]+t[5]
1381 mov $A0[1],($tptr,$j) # t[4]
1386 add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
1388 mov 16($aptr,$j),$ai # a[6]
1395 add %rax,$A1[1] # a[5]*a[3]+t[6]
1397 mov $A0[0],8($tptr,$j) # t[5]
1402 add %rax,$A0[1] # a[6]*a[2]+a[5]*a[3]+t[6]
1404 mov 24($aptr,$j),$ai # a[7]
1412 add %rax,$A1[0] # a[6]*a[5]+t[7]
1414 mov $A0[1],16($tptr,$j) # t[6]
1420 add %rax,$A0[0] # a[7]*a[4]+a[6]*a[5]+t[6]
1426 mov $A0[0],-8($tptr,$j) # t[7]
1438 mov $A1[1],($tptr) # t[8]
1440 mov %rdx,8($tptr) # t[9]
1444 .Lsqr4x_outer: # comments apply to $num==6 case
1445 mov -32($aptr,$i),$a0 # a[0]
1446 lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
1447 mov -24($aptr,$i),%rax # a[1]
1448 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
1449 mov -16($aptr,$i),$ai # a[2]
1453 mov -24($tptr,$i),$A0[0] # t[1]
1454 add %rax,$A0[0] # a[1]*a[0]+t[1]
1457 mov $A0[0],-24($tptr,$i) # t[1]
1464 add -16($tptr,$i),$A0[1] # a[2]*a[0]+t[2]
1467 mov $A0[1],-16($tptr,$i) # t[2]
1471 mov -8($aptr,$i),$ai # a[3]
1473 add %rax,$A1[0] # a[2]*a[1]+t[3]
1476 add -8($tptr,$i),$A1[0]
1481 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
1487 mov $A0[0],-8($tptr,$i) # t[3]
1494 mov ($aptr,$j),$ai # a[4]
1496 add %rax,$A1[1] # a[3]*a[1]+t[4]
1500 add ($tptr,$j),$A1[1]
1505 add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
1507 mov 8($aptr,$j),$ai # a[5]
1514 add %rax,$A1[0] # a[4]*a[3]+t[5]
1515 mov $A0[1],($tptr,$j) # t[4]
1519 add 8($tptr,$j),$A1[0]
1524 add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
1530 mov $A0[0],-8($tptr,$j) # t[5], "preloaded t[1]" below
1542 mov $A1[1],($tptr) # t[6], "preloaded t[2]" below
1544 mov %rdx,8($tptr) # t[7], "preloaded t[3]" below
1549 # comments apply to $num==4 case
1550 mov -32($aptr),$a0 # a[0]
1551 lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
1552 mov -24($aptr),%rax # a[1]
1553 lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
1554 mov -16($aptr),$ai # a[2]
1558 add %rax,$A0[0] # a[1]*a[0]+t[1], preloaded t[1]
1566 mov $A0[0],-24($tptr) # t[1]
1569 add $A1[1],$A0[1] # a[2]*a[0]+t[2], preloaded t[2]
1570 mov -8($aptr),$ai # a[3]
1574 add %rax,$A1[0] # a[2]*a[1]+t[3], preloaded t[3]
1576 mov $A0[1],-16($tptr) # t[2]
1581 add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
1587 mov $A0[0],-8($tptr) # t[3]
1591 mov -16($aptr),%rax # a[2]
1596 mov $A1[1],($tptr) # t[4]
1598 mov %rdx,8($tptr) # t[5]
1603 my ($shift,$carry)=($a0,$a1);
1604 my @S=(@A1,$ai,$n0);
1608 sub $num,$i # $i=16-$num
1611 add $A1[0],%rax # t[5]
1613 mov %rax,8($tptr) # t[5]
1614 mov %rdx,16($tptr) # t[6]
1615 mov $carry,24($tptr) # t[7]
1617 mov -16($aptr,$i),%rax # a[0]
1618 lea 48+8(%rsp),$tptr
1619 xor $A0[0],$A0[0] # t[0]
1620 mov 8($tptr),$A0[1] # t[1]
1622 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1624 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1626 or $A0[0],$S[1] # | t[2*i]>>63
1627 mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
1628 mov $A0[1],$shift # shift=t[2*i+1]>>63
1629 mul %rax # a[i]*a[i]
1630 neg $carry # mov $carry,cf
1631 mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
1633 mov -8($aptr,$i),%rax # a[i+1] # prefetch
1637 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1639 sbb $carry,$carry # mov cf,$carry
1641 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1643 or $A0[0],$S[3] # | t[2*i]>>63
1644 mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
1645 mov $A0[1],$shift # shift=t[2*i+1]>>63
1646 mul %rax # a[i]*a[i]
1647 neg $carry # mov $carry,cf
1648 mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
1650 mov 0($aptr,$i),%rax # a[i+1] # prefetch
1655 sbb $carry,$carry # mov cf,$carry
1657 jmp .Lsqr4x_shift_n_add
1660 .Lsqr4x_shift_n_add:
1661 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1663 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1665 or $A0[0],$S[1] # | t[2*i]>>63
1666 mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
1667 mov $A0[1],$shift # shift=t[2*i+1]>>63
1668 mul %rax # a[i]*a[i]
1669 neg $carry # mov $carry,cf
1670 mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
1672 mov -8($aptr,$i),%rax # a[i+1] # prefetch
1673 mov $S[0],-32($tptr)
1676 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1677 mov $S[1],-24($tptr)
1678 sbb $carry,$carry # mov cf,$carry
1680 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1682 or $A0[0],$S[3] # | t[2*i]>>63
1683 mov 0($tptr),$A0[0] # t[2*i+2] # prefetch
1684 mov $A0[1],$shift # shift=t[2*i+1]>>63
1685 mul %rax # a[i]*a[i]
1686 neg $carry # mov $carry,cf
1687 mov 8($tptr),$A0[1] # t[2*i+2+1] # prefetch
1689 mov 0($aptr,$i),%rax # a[i+1] # prefetch
1690 mov $S[2],-16($tptr)
1693 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1695 sbb $carry,$carry # mov cf,$carry
1697 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1699 or $A0[0],$S[1] # | t[2*i]>>63
1700 mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
1701 mov $A0[1],$shift # shift=t[2*i+1]>>63
1702 mul %rax # a[i]*a[i]
1703 neg $carry # mov $carry,cf
1704 mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
1706 mov 8($aptr,$i),%rax # a[i+1] # prefetch
1710 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
1712 sbb $carry,$carry # mov cf,$carry
1714 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1716 or $A0[0],$S[3] # | t[2*i]>>63
1717 mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
1718 mov $A0[1],$shift # shift=t[2*i+1]>>63
1719 mul %rax # a[i]*a[i]
1720 neg $carry # mov $carry,cf
1721 mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
1723 mov 16($aptr,$i),%rax # a[i+1] # prefetch
1727 sbb $carry,$carry # mov cf,$carry
1730 jnz .Lsqr4x_shift_n_add
1732 lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
1735 lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
1737 or $A0[0],$S[1] # | t[2*i]>>63
1738 mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
1739 mov $A0[1],$shift # shift=t[2*i+1]>>63
1740 mul %rax # a[i]*a[i]
1741 neg $carry # mov $carry,cf
1742 mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
1744 mov -8($aptr),%rax # a[i+1] # prefetch
1745 mov $S[0],-32($tptr)
1748 lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1|shift
1749 mov $S[1],-24($tptr)
1750 sbb $carry,$carry # mov cf,$carry
1752 lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
1754 or $A0[0],$S[3] # | t[2*i]>>63
1755 mul %rax # a[i]*a[i]
1756 neg $carry # mov $carry,cf
1759 mov $S[2],-16($tptr)
1763 ######################################################################
1764 # Montgomery reduction part, "word-by-word" algorithm.
1766 # This new path is inspired by multiple submissions from Intel, by
1767 # Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
1770 my ($nptr,$tptr,$carry,$m0)=("%rbp","%rdi","%rsi","%rbx");
1774 __bn_sqr8x_reduction:
1776 lea ($nptr,$num),%rcx # end of n[]
1777 lea 48+8(%rsp,$num,2),%rdx # end of t[] buffer
1779 lea 48+8(%rsp,$num),$tptr # end of initial t[] window
1782 jmp .L8x_reduction_loop
1785 .L8x_reduction_loop:
1786 lea ($tptr,$num),$tptr # start of current t[] window
1796 mov %rax,(%rdx) # store top-most carry bit
1797 lea 8*8($tptr),$tptr
1801 imulq 32+8(%rsp),$m0 # n0*a[0]
1802 mov 8*0($nptr),%rax # n[0]
1809 mov 8*1($nptr),%rax # n[1]
1819 mov $m0,48-8+8(%rsp,%rcx,8) # put aside n0*a[i]
1828 mov 32+8(%rsp),$carry # pull n0, borrow $carry
1836 imulq %r8,$carry # modulo-scheduled
1866 mov $carry,$m0 # n0*a[i]
1868 mov 8*0($nptr),%rax # n[0]
1877 lea 8*8($nptr),$nptr
1879 mov 8+8(%rsp),%rdx # pull end of t[]
1880 cmp 0+8(%rsp),$nptr # end of n[]?
1892 sbb $carry,$carry # top carry
1894 mov 48+56+8(%rsp),$m0 # pull n0*a[0]
1904 mov %r8,($tptr) # save result
1913 lea 8($tptr),$tptr # $tptr++
1958 mov 48-16+8(%rsp,%rcx,8),$m0# pull n0*a[i]
1962 mov 8*0($nptr),%rax # pull n[0]
1969 lea 8*8($nptr),$nptr
1970 mov 8+8(%rsp),%rdx # pull end of t[]
1971 cmp 0+8(%rsp),$nptr # end of n[]?
1972 jae .L8x_tail_done # break out of loop
1974 mov 48+56+8(%rsp),$m0 # pull n0*a[0]
1976 mov 8*0($nptr),%rax # pull n[0]
1985 sbb $carry,$carry # top carry
1993 add (%rdx),%r8 # can this overflow?
2013 adc \$0,%rax # top-most carry
2014 mov -8($nptr),%rcx # np[num-1]
2017 movq %xmm2,$nptr # restore $nptr
2019 mov %r8,8*0($tptr) # store top 512 bits
2021 movq %xmm3,$num # $num is %r9, can't be moved upwards
2028 lea 8*8($tptr),$tptr
2030 cmp %rdx,$tptr # end of t[]?
2031 jb .L8x_reduction_loop
2033 .size bn_sqr8x_internal,.-bn_sqr8x_internal
2036 ##############################################################
2037 # Post-condition, 4x unrolled
2040 my ($tptr,$nptr)=("%rbx","%rbp");
2042 .type __bn_post4x_internal,\@abi-omnipotent
2044 __bn_post4x_internal:
2046 lea (%rdi,$num),$tptr # %rdi was $tptr above
2048 movq %xmm1,$rptr # restore $rptr
2050 movq %xmm1,$aptr # prepare for back-to-back call
2052 dec %r12 # so that after 'not' we get -n[0]
2057 jmp .Lsqr4x_sub_entry
2066 lea 8*4($nptr),$nptr
2076 neg %r10 # mov %r10,%cf
2082 lea 8*4($tptr),$tptr
2084 sbb %r10,%r10 # mov %cf,%r10
2087 lea 8*4($rptr),$rptr
2092 mov $num,%r10 # prepare for back-to-back call
2093 neg $num # restore $num
2095 .size __bn_post4x_internal,.-__bn_post4x_internal
2100 .globl bn_from_montgomery
2101 .type bn_from_montgomery,\@abi-omnipotent
2104 testl \$7,`($win64?"48(%rsp)":"%r9d")`
2108 .size bn_from_montgomery,.-bn_from_montgomery
2110 .type bn_from_mont8x,\@function,6
2116 .cfi_def_cfa_register %rax
2131 shl \$3,${num}d # convert $num to bytes
2132 lea ($num,$num,2),%r10 # 3*$num in bytes
2136 ##############################################################
2137 # Ensure that stack frame doesn't alias with $rptr+3*$num
2138 # modulo 4096, which covers ret[num], am[num] and n[num]
2139 # (see bn_exp.c). The stack is allocated to aligned with
2140 # bn_power5's frame, and as bn_from_montgomery happens to be
2141 # last operation, we use the opportunity to cleanse it.
2143 lea -320(%rsp,$num,2),%r11
2149 sub %r11,%rbp # align with $aptr
2150 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
2155 lea 4096-320(,$num,2),%r10
2156 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
2166 lea (%rbp,%r11),%rsp
2170 jmp .Lfrom_page_walk_done
2173 lea -4096(%rsp),%rsp
2177 .Lfrom_page_walk_done:
2182 ##############################################################
2185 # +0 saved $num, used in reduction section
2186 # +8 &t[2*$num], used in reduction section
2192 mov %rax, 40(%rsp) # save original %rsp
2193 .cfi_cfa_expression %rsp+40,deref,+8
2202 movdqu ($aptr),%xmm1
2203 movdqu 16($aptr),%xmm2
2204 movdqu 32($aptr),%xmm3
2205 movdqa %xmm0,(%rax,$num)
2206 movdqu 48($aptr),%xmm4
2207 movdqa %xmm0,16(%rax,$num)
2208 .byte 0x48,0x8d,0xb6,0x40,0x00,0x00,0x00 # lea 64($aptr),$aptr
2210 movdqa %xmm0,32(%rax,$num)
2211 movdqa %xmm2,16(%rax)
2212 movdqa %xmm0,48(%rax,$num)
2213 movdqa %xmm3,32(%rax)
2214 movdqa %xmm4,48(%rax)
2223 movq %r10, %xmm3 # -num
2225 $code.=<<___ if ($addx);
2226 mov OPENSSL_ia32cap_P+8(%rip),%r11d
2228 cmp \$0x80108,%r11d # check for AD*X+BMI2+BMI1
2231 lea (%rax,$num),$rptr
2232 call __bn_sqrx8x_reduction
2233 call __bn_postx4x_internal
2237 jmp .Lfrom_mont_zero
2243 call __bn_sqr8x_reduction
2244 call __bn_post4x_internal
2248 jmp .Lfrom_mont_zero
2252 mov 40(%rsp),%rsi # restore %rsp
2254 movdqa %xmm0,16*0(%rax)
2255 movdqa %xmm0,16*1(%rax)
2256 movdqa %xmm0,16*2(%rax)
2257 movdqa %xmm0,16*3(%rax)
2260 jnz .Lfrom_mont_zero
2276 .cfi_def_cfa_register %rsp
2280 .size bn_from_mont8x,.-bn_from_mont8x
2286 my $bp="%rdx"; # restore original value
2289 .type bn_mulx4x_mont_gather5,\@function,6
2291 bn_mulx4x_mont_gather5:
2294 .cfi_def_cfa_register %rax
2310 shl \$3,${num}d # convert $num to bytes
2311 lea ($num,$num,2),%r10 # 3*$num in bytes
2315 ##############################################################
2316 # Ensure that stack frame doesn't alias with $rptr+3*$num
2317 # modulo 4096, which covers ret[num], am[num] and n[num]
2318 # (see bn_exp.c). This is done to allow memory disambiguation
2319 # logic do its magic. [Extra [num] is allocated in order
2320 # to align with bn_power5's frame, which is cleansed after
2321 # completing exponentiation. Extra 256 bytes is for power mask
2322 # calculated from 7th argument, the index.]
2324 lea -320(%rsp,$num,2),%r11
2330 sub %r11,%rbp # align with $aptr
2331 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
2335 lea 4096-320(,$num,2),%r10
2336 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
2342 and \$-64,%rbp # ensure alignment
2346 lea (%rbp,%r11),%rsp
2349 ja .Lmulx4x_page_walk
2350 jmp .Lmulx4x_page_walk_done
2353 lea -4096(%rsp),%rsp
2356 ja .Lmulx4x_page_walk
2357 .Lmulx4x_page_walk_done:
2359 ##############################################################
2362 # +8 off-loaded &b[i]
2371 mov $n0, 32(%rsp) # save *n0
2372 mov %rax,40(%rsp) # save original %rsp
2373 .cfi_cfa_expression %rsp+40,deref,+8
2375 call mulx4x_internal
2377 mov 40(%rsp),%rsi # restore %rsp
2394 .cfi_def_cfa_register %rsp
2398 .size bn_mulx4x_mont_gather5,.-bn_mulx4x_mont_gather5
2400 .type mulx4x_internal,\@abi-omnipotent
2403 mov $num,8(%rsp) # save -$num (it was in bytes)
2405 neg $num # restore $num
2407 neg %r10 # restore $num
2408 lea 128($bp,$num),%r13 # end of powers table (+size optimization)
2410 movd `($win64?56:8)`(%rax),%xmm5 # load 7th argument
2412 lea .Linc(%rip),%rax
2413 mov %r13,16+8(%rsp) # end of b[num]
2414 mov $num,24+8(%rsp) # inner counter
2415 mov $rp, 56+8(%rsp) # save $rp
2417 my ($aptr, $bptr, $nptr, $tptr, $mi, $bi, $zero, $num)=
2418 ("%rsi","%rdi","%rcx","%rbx","%r8","%r9","%rbp","%rax");
2420 my $STRIDE=2**5*8; # 5 is "window size"
2421 my $N=$STRIDE/4; # should match cache line size
2423 movdqa 0(%rax),%xmm0 # 00000001000000010000000000000000
2424 movdqa 16(%rax),%xmm1 # 00000002000000020000000200000002
2425 lea 88-112(%rsp,%r10),%r10 # place the mask after tp[num+1] (+ICache optimization)
2426 lea 128($bp),$bptr # size optimization
2428 pshufd \$0,%xmm5,%xmm5 # broadcast index
2433 ########################################################################
2434 # calculate mask by comparing 0..31 to index and save result to stack
2439 pcmpeqd %xmm5,%xmm0 # compare to 1,0
2442 for($i=0;$i<$STRIDE/16-4;$i+=4) {
2445 pcmpeqd %xmm5,%xmm1 # compare to 3,2
2446 movdqa %xmm0,`16*($i+0)+112`(%r10)
2450 pcmpeqd %xmm5,%xmm2 # compare to 5,4
2451 movdqa %xmm1,`16*($i+1)+112`(%r10)
2455 pcmpeqd %xmm5,%xmm3 # compare to 7,6
2456 movdqa %xmm2,`16*($i+2)+112`(%r10)
2461 movdqa %xmm3,`16*($i+3)+112`(%r10)
2465 $code.=<<___; # last iteration can be optimized
2469 movdqa %xmm0,`16*($i+0)+112`(%r10)
2473 movdqa %xmm1,`16*($i+1)+112`(%r10)
2476 movdqa %xmm2,`16*($i+2)+112`(%r10)
2478 pand `16*($i+0)-128`($bptr),%xmm0 # while it's still in register
2479 pand `16*($i+1)-128`($bptr),%xmm1
2480 pand `16*($i+2)-128`($bptr),%xmm2
2481 movdqa %xmm3,`16*($i+3)+112`(%r10)
2482 pand `16*($i+3)-128`($bptr),%xmm3
2486 for($i=0;$i<$STRIDE/16-4;$i+=4) {
2488 movdqa `16*($i+0)-128`($bptr),%xmm4
2489 movdqa `16*($i+1)-128`($bptr),%xmm5
2490 movdqa `16*($i+2)-128`($bptr),%xmm2
2491 pand `16*($i+0)+112`(%r10),%xmm4
2492 movdqa `16*($i+3)-128`($bptr),%xmm3
2493 pand `16*($i+1)+112`(%r10),%xmm5
2495 pand `16*($i+2)+112`(%r10),%xmm2
2497 pand `16*($i+3)+112`(%r10),%xmm3
2504 pshufd \$0x4e,%xmm0,%xmm1
2506 lea $STRIDE($bptr),$bptr
2507 movq %xmm0,%rdx # bp[0]
2508 lea 64+8*4+8(%rsp),$tptr
2511 mulx 0*8($aptr),$mi,%rax # a[0]*b[0]
2512 mulx 1*8($aptr),%r11,%r12 # a[1]*b[0]
2514 mulx 2*8($aptr),%rax,%r13 # ...
2517 mulx 3*8($aptr),%rax,%r14
2520 imulq 32+8(%rsp),$mi # "t[0]"*n0
2521 xor $zero,$zero # cf=0, of=0
2524 mov $bptr,8+8(%rsp) # off-load &b[i]
2526 lea 4*8($aptr),$aptr
2528 adcx $zero,%r14 # cf=0
2530 mulx 0*8($nptr),%rax,%r10
2531 adcx %rax,%r15 # discarded
2533 mulx 1*8($nptr),%rax,%r11
2536 mulx 2*8($nptr),%rax,%r12
2537 mov 24+8(%rsp),$bptr # counter value
2538 mov %r10,-8*4($tptr)
2541 mulx 3*8($nptr),%rax,%r15
2543 mov %r11,-8*3($tptr)
2545 adox $zero,%r15 # of=0
2546 lea 4*8($nptr),$nptr
2547 mov %r12,-8*2($tptr)
2552 adcx $zero,%r15 # cf=0, modulo-scheduled
2553 mulx 0*8($aptr),%r10,%rax # a[4]*b[0]
2555 mulx 1*8($aptr),%r11,%r14 # a[5]*b[0]
2557 mulx 2*8($aptr),%r12,%rax # ...
2559 mulx 3*8($aptr),%r13,%r14
2563 adcx $zero,%r14 # cf=0
2564 lea 4*8($aptr),$aptr
2565 lea 4*8($tptr),$tptr
2568 mulx 0*8($nptr),%rax,%r15
2571 mulx 1*8($nptr),%rax,%r15
2574 mulx 2*8($nptr),%rax,%r15
2575 mov %r10,-5*8($tptr)
2577 mov %r11,-4*8($tptr)
2579 mulx 3*8($nptr),%rax,%r15
2581 mov %r12,-3*8($tptr)
2584 lea 4*8($nptr),$nptr
2585 mov %r13,-2*8($tptr)
2587 dec $bptr # of=0, pass cf
2590 mov 8(%rsp),$num # load -num
2591 adc $zero,%r15 # modulo-scheduled
2592 lea ($aptr,$num),$aptr # rewind $aptr
2594 mov 8+8(%rsp),$bptr # re-load &b[i]
2595 adc $zero,$zero # top-most carry
2596 mov %r14,-1*8($tptr)
2601 lea 16-256($tptr),%r10 # where 256-byte mask is (+density control)
2606 for($i=0;$i<$STRIDE/16;$i+=4) {
2608 movdqa `16*($i+0)-128`($bptr),%xmm0
2609 movdqa `16*($i+1)-128`($bptr),%xmm1
2610 movdqa `16*($i+2)-128`($bptr),%xmm2
2611 pand `16*($i+0)+256`(%r10),%xmm0
2612 movdqa `16*($i+3)-128`($bptr),%xmm3
2613 pand `16*($i+1)+256`(%r10),%xmm1
2615 pand `16*($i+2)+256`(%r10),%xmm2
2617 pand `16*($i+3)+256`(%r10),%xmm3
2624 pshufd \$0x4e,%xmm4,%xmm0
2626 lea $STRIDE($bptr),$bptr
2627 movq %xmm0,%rdx # m0=bp[i]
2629 mov $zero,($tptr) # save top-most carry
2630 lea 4*8($tptr,$num),$tptr # rewind $tptr
2631 mulx 0*8($aptr),$mi,%r11 # a[0]*b[i]
2632 xor $zero,$zero # cf=0, of=0
2634 mulx 1*8($aptr),%r14,%r12 # a[1]*b[i]
2635 adox -4*8($tptr),$mi # +t[0]
2637 mulx 2*8($aptr),%r15,%r13 # ...
2638 adox -3*8($tptr),%r11
2640 mulx 3*8($aptr),%rdx,%r14
2641 adox -2*8($tptr),%r12
2643 lea ($nptr,$num),$nptr # rewind $nptr
2644 lea 4*8($aptr),$aptr
2645 adox -1*8($tptr),%r13
2650 imulq 32+8(%rsp),$mi # "t[0]"*n0
2653 xor $zero,$zero # cf=0, of=0
2654 mov $bptr,8+8(%rsp) # off-load &b[i]
2656 mulx 0*8($nptr),%rax,%r10
2657 adcx %rax,%r15 # discarded
2659 mulx 1*8($nptr),%rax,%r11
2662 mulx 2*8($nptr),%rax,%r12
2665 mulx 3*8($nptr),%rax,%r15
2667 mov 24+8(%rsp),$bptr # counter value
2668 mov %r10,-8*4($tptr)
2670 mov %r11,-8*3($tptr)
2671 adox $zero,%r15 # of=0
2672 mov %r12,-8*2($tptr)
2673 lea 4*8($nptr),$nptr
2678 mulx 0*8($aptr),%r10,%rax # a[4]*b[i]
2679 adcx $zero,%r15 # cf=0, modulo-scheduled
2681 mulx 1*8($aptr),%r11,%r14 # a[5]*b[i]
2682 adcx 0*8($tptr),%r10
2684 mulx 2*8($aptr),%r12,%rax # ...
2685 adcx 1*8($tptr),%r11
2687 mulx 3*8($aptr),%r13,%r14
2689 adcx 2*8($tptr),%r12
2691 adcx 3*8($tptr),%r13
2692 adox $zero,%r14 # of=0
2693 lea 4*8($aptr),$aptr
2694 lea 4*8($tptr),$tptr
2695 adcx $zero,%r14 # cf=0
2698 mulx 0*8($nptr),%rax,%r15
2701 mulx 1*8($nptr),%rax,%r15
2704 mulx 2*8($nptr),%rax,%r15
2705 mov %r10,-5*8($tptr)
2708 mov %r11,-4*8($tptr)
2709 mulx 3*8($nptr),%rax,%r15
2711 lea 4*8($nptr),$nptr
2712 mov %r12,-3*8($tptr)
2715 mov %r13,-2*8($tptr)
2717 dec $bptr # of=0, pass cf
2720 mov 0+8(%rsp),$num # load -num
2721 adc $zero,%r15 # modulo-scheduled
2722 sub 0*8($tptr),$bptr # pull top-most carry to %cf
2723 mov 8+8(%rsp),$bptr # re-load &b[i]
2726 lea ($aptr,$num),$aptr # rewind $aptr
2727 adc $zero,$zero # top-most carry
2728 mov %r14,-1*8($tptr)
2735 mov ($nptr,$num),%r12
2736 lea ($nptr,$num),%rbp # rewind $nptr
2738 lea ($tptr,$num),%rdi # rewind $tptr
2741 sub %r14,%r10 # compare top-most words
2745 sub %r8,%rax # %rax=-%r8
2746 mov 56+8(%rsp),%rdx # restore rp
2747 dec %r12 # so that after 'not' we get -n[0]
2752 jmp .Lsqrx4x_sub_entry # common post-condition
2753 .size mulx4x_internal,.-mulx4x_internal
2756 ######################################################################
2758 my $rptr="%rdi"; # BN_ULONG *rptr,
2759 my $aptr="%rsi"; # const BN_ULONG *aptr,
2760 my $bptr="%rdx"; # const void *table,
2761 my $nptr="%rcx"; # const BN_ULONG *nptr,
2762 my $n0 ="%r8"; # const BN_ULONG *n0);
2763 my $num ="%r9"; # int num, has to be divisible by 8
2766 my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
2767 my @A0=("%r10","%r11");
2768 my @A1=("%r12","%r13");
2769 my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
2772 .type bn_powerx5,\@function,6
2777 .cfi_def_cfa_register %rax
2793 shl \$3,${num}d # convert $num to bytes
2794 lea ($num,$num,2),%r10 # 3*$num in bytes
2798 ##############################################################
2799 # Ensure that stack frame doesn't alias with $rptr+3*$num
2800 # modulo 4096, which covers ret[num], am[num] and n[num]
2801 # (see bn_exp.c). This is done to allow memory disambiguation
2802 # logic do its magic. [Extra 256 bytes is for power mask
2803 # calculated from 7th argument, the index.]
2805 lea -320(%rsp,$num,2),%r11
2811 sub %r11,%rbp # align with $aptr
2812 lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
2817 lea 4096-320(,$num,2),%r10
2818 lea -320(%rbp,$num,2),%rbp # alloca(frame+2*$num*8+256)
2828 lea (%rbp,%r11),%rsp
2832 jmp .Lpwrx_page_walk_done
2835 lea -4096(%rsp),%rsp
2839 .Lpwrx_page_walk_done:
2844 ##############################################################
2847 # +0 saved $num, used in reduction section
2848 # +8 &t[2*$num], used in reduction section
2849 # +16 intermediate carry bit
2850 # +24 top-most carry bit, used in reduction section
2856 movq $rptr,%xmm1 # save $rptr
2857 movq $nptr,%xmm2 # save $nptr
2858 movq %r10, %xmm3 # -$num
2861 mov %rax, 40(%rsp) # save original %rsp
2862 .cfi_cfa_expression %rsp+40,deref,+8
2865 call __bn_sqrx8x_internal
2866 call __bn_postx4x_internal
2867 call __bn_sqrx8x_internal
2868 call __bn_postx4x_internal
2869 call __bn_sqrx8x_internal
2870 call __bn_postx4x_internal
2871 call __bn_sqrx8x_internal
2872 call __bn_postx4x_internal
2873 call __bn_sqrx8x_internal
2874 call __bn_postx4x_internal
2876 mov %r10,$num # -num
2882 call mulx4x_internal
2884 mov 40(%rsp),%rsi # restore %rsp
2901 .cfi_def_cfa_register %rsp
2905 .size bn_powerx5,.-bn_powerx5
2907 .globl bn_sqrx8x_internal
2908 .hidden bn_sqrx8x_internal
2909 .type bn_sqrx8x_internal,\@abi-omnipotent
2912 __bn_sqrx8x_internal:
2913 ##################################################################
2916 # a) multiply-n-add everything but a[i]*a[i];
2917 # b) shift result of a) by 1 to the left and accumulate
2918 # a[i]*a[i] products;
2920 ##################################################################
2921 # a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
2952 # a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
2955 my ($zero,$carry)=("%rbp","%rcx");
2958 lea 48+8(%rsp),$tptr
2959 lea ($aptr,$num),$aaptr
2960 mov $num,0+8(%rsp) # save $num
2961 mov $aaptr,8+8(%rsp) # save end of $aptr
2962 jmp .Lsqr8x_zero_start
2965 .byte 0x66,0x66,0x66,0x2e,0x0f,0x1f,0x84,0x00,0x00,0x00,0x00,0x00
2968 movdqa %xmm0,0*8($tptr)
2969 movdqa %xmm0,2*8($tptr)
2970 movdqa %xmm0,4*8($tptr)
2971 movdqa %xmm0,6*8($tptr)
2972 .Lsqr8x_zero_start: # aligned at 32
2973 movdqa %xmm0,8*8($tptr)
2974 movdqa %xmm0,10*8($tptr)
2975 movdqa %xmm0,12*8($tptr)
2976 movdqa %xmm0,14*8($tptr)
2977 lea 16*8($tptr),$tptr
2981 mov 0*8($aptr),%rdx # a[0], modulo-scheduled
2982 #xor %r9,%r9 # t[1], ex-$num, zero already
2989 lea 48+8(%rsp),$tptr
2990 xor $zero,$zero # cf=0, cf=0
2991 jmp .Lsqrx8x_outer_loop
2994 .Lsqrx8x_outer_loop:
2995 mulx 1*8($aptr),%r8,%rax # a[1]*a[0]
2996 adcx %r9,%r8 # a[1]*a[0]+=t[1]
2998 mulx 2*8($aptr),%r9,%rax # a[2]*a[0]
3001 .byte 0xc4,0xe2,0xab,0xf6,0x86,0x18,0x00,0x00,0x00 # mulx 3*8($aptr),%r10,%rax # ...
3004 .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x20,0x00,0x00,0x00 # mulx 4*8($aptr),%r11,%rax
3007 mulx 5*8($aptr),%r12,%rax
3010 mulx 6*8($aptr),%r13,%rax
3013 mulx 7*8($aptr),%r14,%r15
3014 mov 1*8($aptr),%rdx # a[1]
3018 mov %r8,1*8($tptr) # t[1]
3019 mov %r9,2*8($tptr) # t[2]
3020 sbb $carry,$carry # mov %cf,$carry
3021 xor $zero,$zero # cf=0, of=0
3024 mulx 2*8($aptr),%r8,%rbx # a[2]*a[1]
3025 mulx 3*8($aptr),%r9,%rax # a[3]*a[1]
3028 mulx 4*8($aptr),%r10,%rbx # ...
3031 .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x28,0x00,0x00,0x00 # mulx 5*8($aptr),%r11,%rax
3034 .byte 0xc4,0xe2,0x9b,0xf6,0x9e,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r12,%rbx
3037 .byte 0xc4,0x62,0x93,0xf6,0xb6,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r13,%r14
3038 mov 2*8($aptr),%rdx # a[2]
3042 adox $zero,%r14 # of=0
3043 adcx $zero,%r14 # cf=0
3045 mov %r8,3*8($tptr) # t[3]
3046 mov %r9,4*8($tptr) # t[4]
3048 mulx 3*8($aptr),%r8,%rbx # a[3]*a[2]
3049 mulx 4*8($aptr),%r9,%rax # a[4]*a[2]
3052 mulx 5*8($aptr),%r10,%rbx # ...
3055 .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r11,%rax
3058 .byte 0xc4,0x62,0x9b,0xf6,0xae,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r12,%r13
3060 mov 3*8($aptr),%rdx # a[3]
3064 mov %r8,5*8($tptr) # t[5]
3065 mov %r9,6*8($tptr) # t[6]
3066 mulx 4*8($aptr),%r8,%rax # a[4]*a[3]
3067 adox $zero,%r13 # of=0
3068 adcx $zero,%r13 # cf=0
3070 mulx 5*8($aptr),%r9,%rbx # a[5]*a[3]
3073 mulx 6*8($aptr),%r10,%rax # ...
3076 mulx 7*8($aptr),%r11,%r12
3077 mov 4*8($aptr),%rdx # a[4]
3078 mov 5*8($aptr),%r14 # a[5]
3081 mov 6*8($aptr),%r15 # a[6]
3083 adox $zero,%r12 # of=0
3084 adcx $zero,%r12 # cf=0
3086 mov %r8,7*8($tptr) # t[7]
3087 mov %r9,8*8($tptr) # t[8]
3089 mulx %r14,%r9,%rax # a[5]*a[4]
3090 mov 7*8($aptr),%r8 # a[7]
3092 mulx %r15,%r10,%rbx # a[6]*a[4]
3095 mulx %r8,%r11,%rax # a[7]*a[4]
3096 mov %r14,%rdx # a[5]
3099 #adox $zero,%rax # of=0
3100 adcx $zero,%rax # cf=0
3102 mulx %r15,%r14,%rbx # a[6]*a[5]
3103 mulx %r8,%r12,%r13 # a[7]*a[5]
3104 mov %r15,%rdx # a[6]
3105 lea 8*8($aptr),$aptr
3112 mulx %r8,%r8,%r14 # a[7]*a[6]
3117 je .Lsqrx8x_outer_break
3119 neg $carry # mov $carry,%cf
3123 adcx 9*8($tptr),%r9 # +=t[9]
3124 adcx 10*8($tptr),%r10 # ...
3125 adcx 11*8($tptr),%r11
3126 adc 12*8($tptr),%r12
3127 adc 13*8($tptr),%r13
3128 adc 14*8($tptr),%r14
3129 adc 15*8($tptr),%r15
3131 lea 2*64($tptr),$tptr
3132 sbb %rax,%rax # mov %cf,$carry
3134 mov -64($aptr),%rdx # a[0]
3135 mov %rax,16+8(%rsp) # offload $carry
3136 mov $tptr,24+8(%rsp)
3138 #lea 8*8($tptr),$tptr # see 2*8*8($tptr) above
3139 xor %eax,%eax # cf=0, of=0
3145 mulx 0*8($aaptr),%rax,%r8 # a[8]*a[i]
3146 adcx %rax,%rbx # +=t[8]
3149 mulx 1*8($aaptr),%rax,%r9 # ...
3153 mulx 2*8($aaptr),%rax,%r10
3157 mulx 3*8($aaptr),%rax,%r11
3161 .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 4*8($aaptr),%rax,%r12
3165 mulx 5*8($aaptr),%rax,%r13
3169 mulx 6*8($aaptr),%rax,%r14
3170 mov %rbx,($tptr,%rcx,8) # store t[8+i]
3175 .byte 0xc4,0x62,0xfb,0xf6,0xbd,0x38,0x00,0x00,0x00 # mulx 7*8($aaptr),%rax,%r15
3176 mov 8($aptr,%rcx,8),%rdx # a[i]
3178 adox %rbx,%r15 # %rbx is 0, of=0
3179 adcx %rbx,%r15 # cf=0
3185 lea 8*8($aaptr),$aaptr
3187 cmp 8+8(%rsp),$aaptr # done?
3190 sub 16+8(%rsp),%rbx # mov 16(%rsp),%cf
3201 lea 8*8($tptr),$tptr
3203 sbb %rax,%rax # mov %cf,%rax
3204 xor %ebx,%ebx # cf=0, of=0
3205 mov %rax,16+8(%rsp) # offload carry
3211 sub 16+8(%rsp),%rbx # mov 16(%rsp),%cf
3213 mov 24+8(%rsp),$carry # initial $tptr, borrow $carry
3215 mov 0*8($aptr),%rdx # a[8], modulo-scheduled
3223 cmp $carry,$tptr # cf=0, of=0
3224 je .Lsqrx8x_outer_loop
3229 mov 2*8($carry),%r10
3231 mov 3*8($carry),%r11
3233 mov 4*8($carry),%r12
3235 mov 5*8($carry),%r13
3237 mov 6*8($carry),%r14
3239 mov 7*8($carry),%r15
3241 jmp .Lsqrx8x_outer_loop
3244 .Lsqrx8x_outer_break:
3245 mov %r9,9*8($tptr) # t[9]
3246 movq %xmm3,%rcx # -$num
3247 mov %r10,10*8($tptr) # ...
3248 mov %r11,11*8($tptr)
3249 mov %r12,12*8($tptr)
3250 mov %r13,13*8($tptr)
3251 mov %r14,14*8($tptr)
3256 lea 48+8(%rsp),$tptr
3257 mov ($aptr,$i),%rdx # a[0]
3259 mov 8($tptr),$A0[1] # t[1]
3260 xor $A0[0],$A0[0] # t[0], of=0, cf=0
3261 mov 0+8(%rsp),$num # restore $num
3263 mov 16($tptr),$A1[0] # t[2] # prefetch
3264 mov 24($tptr),$A1[1] # t[3] # prefetch
3265 #jmp .Lsqrx4x_shift_n_add # happens to be aligned
3268 .Lsqrx4x_shift_n_add:
3272 .byte 0x48,0x8b,0x94,0x0e,0x08,0x00,0x00,0x00 # mov 8($aptr,$i),%rdx # a[i+1] # prefetch
3273 .byte 0x4c,0x8b,0x97,0x20,0x00,0x00,0x00 # mov 32($tptr),$A0[0] # t[2*i+4] # prefetch
3276 mov 40($tptr),$A0[1] # t[2*i+4+1] # prefetch
3283 mov 16($aptr,$i),%rdx # a[i+2] # prefetch
3284 mov 48($tptr),$A1[0] # t[2*i+6] # prefetch
3287 mov 56($tptr),$A1[1] # t[2*i+6+1] # prefetch
3294 mov 24($aptr,$i),%rdx # a[i+3] # prefetch
3296 mov 64($tptr),$A0[0] # t[2*i+8] # prefetch
3299 mov 72($tptr),$A0[1] # t[2*i+8+1] # prefetch
3306 jrcxz .Lsqrx4x_shift_n_add_break
3307 .byte 0x48,0x8b,0x94,0x0e,0x00,0x00,0x00,0x00 # mov 0($aptr,$i),%rdx # a[i+4] # prefetch
3310 mov 80($tptr),$A1[0] # t[2*i+10] # prefetch
3311 mov 88($tptr),$A1[1] # t[2*i+10+1] # prefetch
3316 jmp .Lsqrx4x_shift_n_add
3319 .Lsqrx4x_shift_n_add_break:
3323 lea 64($tptr),$tptr # end of t[] buffer
3326 ######################################################################
3327 # Montgomery reduction part, "word-by-word" algorithm.
3329 # This new path is inspired by multiple submissions from Intel, by
3330 # Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
3333 my ($nptr,$carry,$m0)=("%rbp","%rsi","%rdx");
3337 __bn_sqrx8x_reduction:
3338 xor %eax,%eax # initial top-most carry bit
3339 mov 32+8(%rsp),%rbx # n0
3340 mov 48+8(%rsp),%rdx # "%r8", 8*0($tptr)
3341 lea -8*8($nptr,$num),%rcx # end of n[]
3342 #lea 48+8(%rsp,$num,2),$tptr # end of t[] buffer
3343 mov %rcx, 0+8(%rsp) # save end of n[]
3344 mov $tptr,8+8(%rsp) # save end of t[]
3346 lea 48+8(%rsp),$tptr # initial t[] window
3347 jmp .Lsqrx8x_reduction_loop
3350 .Lsqrx8x_reduction_loop:
3356 imulq %rbx,%rdx # n0*a[i]
3360 mov %rax,24+8(%rsp) # store top-most carry bit
3362 lea 8*8($tptr),$tptr
3363 xor $carry,$carry # cf=0,of=0
3370 mulx 8*0($nptr),%rax,%r8 # n[0]
3371 adcx %rbx,%rax # discarded
3374 mulx 8*1($nptr),%rbx,%r9 # n[1]
3378 mulx 8*2($nptr),%rbx,%r10
3382 mulx 8*3($nptr),%rbx,%r11
3386 .byte 0xc4,0x62,0xe3,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 8*4($nptr),%rbx,%r12
3392 mulx 32+8(%rsp),%rbx,%rdx # %rdx discarded
3394 mov %rax,64+48+8(%rsp,%rcx,8) # put aside n0*a[i]
3396 mulx 8*5($nptr),%rax,%r13
3400 mulx 8*6($nptr),%rax,%r14
3404 mulx 8*7($nptr),%rax,%r15
3407 adox $carry,%r15 # $carry is 0
3408 adcx $carry,%r15 # cf=0
3410 .byte 0x67,0x67,0x67
3414 mov $carry,%rax # xor %rax,%rax
3415 cmp 0+8(%rsp),$nptr # end of n[]?
3416 jae .Lsqrx8x_no_tail
3418 mov 48+8(%rsp),%rdx # pull n0*a[0]
3420 lea 8*8($nptr),$nptr
3423 adcx 8*2($tptr),%r10
3429 lea 8*8($tptr),$tptr
3430 sbb %rax,%rax # top carry
3432 xor $carry,$carry # of=0, cf=0
3439 mulx 8*0($nptr),%rax,%r8
3443 mulx 8*1($nptr),%rax,%r9
3447 mulx 8*2($nptr),%rax,%r10
3451 mulx 8*3($nptr),%rax,%r11
3455 .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 8*4($nptr),%rax,%r12
3459 mulx 8*5($nptr),%rax,%r13
3463 mulx 8*6($nptr),%rax,%r14
3467 mulx 8*7($nptr),%rax,%r15
3468 mov 72+48+8(%rsp,%rcx,8),%rdx # pull n0*a[i]
3471 mov %rbx,($tptr,%rcx,8) # save result
3473 adcx $carry,%r15 # cf=0
3478 cmp 0+8(%rsp),$nptr # end of n[]?
3479 jae .Lsqrx8x_tail_done # break out of loop
3481 sub 16+8(%rsp),$carry # mov 16(%rsp),%cf
3482 mov 48+8(%rsp),%rdx # pull n0*a[0]
3483 lea 8*8($nptr),$nptr
3492 lea 8*8($tptr),$tptr
3494 sub \$8,%rcx # mov \$-8,%rcx
3496 xor $carry,$carry # of=0, cf=0
3503 add 24+8(%rsp),%r8 # can this overflow?
3513 sub 16+8(%rsp),$carry # mov 16(%rsp),%cf
3514 .Lsqrx8x_no_tail: # %cf is 0 if jumped here
3518 mov 8*7($nptr),$carry
3519 movq %xmm2,$nptr # restore $nptr
3526 adc \$0,%rax # top-most carry
3528 mov 32+8(%rsp),%rbx # n0
3529 mov 8*8($tptr,%rcx),%rdx # modulo-scheduled "%r8"
3531 mov %r8,8*0($tptr) # store top 512 bits
3532 lea 8*8($tptr),%r8 # borrow %r8
3541 lea 8*8($tptr,%rcx),$tptr # start of current t[] window
3542 cmp 8+8(%rsp),%r8 # end of t[]?
3543 jb .Lsqrx8x_reduction_loop
3545 .size bn_sqrx8x_internal,.-bn_sqrx8x_internal
3548 ##############################################################
3549 # Post-condition, 4x unrolled
3552 my ($rptr,$nptr)=("%rdx","%rbp");
3555 __bn_postx4x_internal:
3557 mov %rcx,%r10 # -$num
3558 mov %rcx,%r9 # -$num
3561 #lea 48+8(%rsp,%r9),$tptr
3562 movq %xmm1,$rptr # restore $rptr
3563 movq %xmm1,$aptr # prepare for back-to-back call
3564 dec %r12 # so that after 'not' we get -n[0]
3569 jmp .Lsqrx4x_sub_entry
3579 lea 8*4($nptr),$nptr
3584 neg %r8 # mov %r8,%cf
3590 lea 8*4($tptr),$tptr
3592 sbb %r8,%r8 # mov %cf,%r8
3595 lea 8*4($rptr),$rptr
3600 neg %r9 # restore $num
3603 .size __bn_postx4x_internal,.-__bn_postx4x_internal
3608 my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%edx","%r8", "%r9d") : # Win64 order
3609 ("%rdi","%esi","%rdx","%ecx"); # Unix order
3616 .type bn_get_bits5,\@abi-omnipotent
3628 movzw (%r10,$num,2),%eax
3632 .size bn_get_bits5,.-bn_get_bits5
3635 .type bn_scatter5,\@abi-omnipotent
3639 jz .Lscatter_epilogue
3640 lea ($tbl,$idx,8),$tbl
3650 .size bn_scatter5,.-bn_scatter5
3653 .type bn_gather5,\@abi-omnipotent
3656 .LSEH_begin_bn_gather5: # Win64 thing, but harmless in other cases
3657 # I can't trust assembler to use specific encoding:-(
3658 .byte 0x4c,0x8d,0x14,0x24 #lea (%rsp),%r10
3659 .byte 0x48,0x81,0xec,0x08,0x01,0x00,0x00 #sub $0x108,%rsp
3660 lea .Linc(%rip),%rax
3661 and \$-16,%rsp # shouldn't be formally required
3664 movdqa 0(%rax),%xmm0 # 00000001000000010000000000000000
3665 movdqa 16(%rax),%xmm1 # 00000002000000020000000200000002
3666 lea 128($tbl),%r11 # size optimization
3667 lea 128(%rsp),%rax # size optimization
3669 pshufd \$0,%xmm5,%xmm5 # broadcast $idx
3673 ########################################################################
3674 # calculate mask by comparing 0..31 to $idx and save result to stack
3676 for($i=0;$i<$STRIDE/16;$i+=4) {
3679 pcmpeqd %xmm5,%xmm0 # compare to 1,0
3681 $code.=<<___ if ($i);
3682 movdqa %xmm3,`16*($i-1)-128`(%rax)
3688 pcmpeqd %xmm5,%xmm1 # compare to 3,2
3689 movdqa %xmm0,`16*($i+0)-128`(%rax)
3693 pcmpeqd %xmm5,%xmm2 # compare to 5,4
3694 movdqa %xmm1,`16*($i+1)-128`(%rax)
3698 pcmpeqd %xmm5,%xmm3 # compare to 7,6
3699 movdqa %xmm2,`16*($i+2)-128`(%rax)
3704 movdqa %xmm3,`16*($i-1)-128`(%rax)
3712 for($i=0;$i<$STRIDE/16;$i+=4) {
3714 movdqa `16*($i+0)-128`(%r11),%xmm0
3715 movdqa `16*($i+1)-128`(%r11),%xmm1
3716 movdqa `16*($i+2)-128`(%r11),%xmm2
3717 pand `16*($i+0)-128`(%rax),%xmm0
3718 movdqa `16*($i+3)-128`(%r11),%xmm3
3719 pand `16*($i+1)-128`(%rax),%xmm1
3721 pand `16*($i+2)-128`(%rax),%xmm2
3723 pand `16*($i+3)-128`(%rax),%xmm3
3730 lea $STRIDE(%r11),%r11
3731 pshufd \$0x4e,%xmm4,%xmm0
3733 movq %xmm0,($out) # m0=bp[0]
3740 .LSEH_end_bn_gather5:
3741 .size bn_gather5,.-bn_gather5
3749 .asciz "Montgomery Multiplication with scatter/gather for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
3752 # EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
3753 # CONTEXT *context,DISPATCHER_CONTEXT *disp)
3761 .extern __imp_RtlVirtualUnwind
3762 .type mul_handler,\@abi-omnipotent
3776 mov 120($context),%rax # pull context->Rax
3777 mov 248($context),%rbx # pull context->Rip
3779 mov 8($disp),%rsi # disp->ImageBase
3780 mov 56($disp),%r11 # disp->HandlerData
3782 mov 0(%r11),%r10d # HandlerData[0]
3783 lea (%rsi,%r10),%r10 # end of prologue label
3784 cmp %r10,%rbx # context->Rip<end of prologue label
3785 jb .Lcommon_seh_tail
3787 mov 4(%r11),%r10d # HandlerData[1]
3788 lea (%rsi,%r10),%r10 # beginning of body label
3789 cmp %r10,%rbx # context->Rip<body label
3790 jb .Lcommon_pop_regs
3792 mov 152($context),%rax # pull context->Rsp
3794 mov 8(%r11),%r10d # HandlerData[2]
3795 lea (%rsi,%r10),%r10 # epilogue label
3796 cmp %r10,%rbx # context->Rip>=epilogue label
3797 jae .Lcommon_seh_tail
3799 lea .Lmul_epilogue(%rip),%r10
3803 mov 192($context),%r10 # pull $num
3804 mov 8(%rax,%r10,8),%rax # pull saved stack pointer
3806 jmp .Lcommon_pop_regs
3809 mov 40(%rax),%rax # pull saved stack pointer
3817 mov %rbx,144($context) # restore context->Rbx
3818 mov %rbp,160($context) # restore context->Rbp
3819 mov %r12,216($context) # restore context->R12
3820 mov %r13,224($context) # restore context->R13
3821 mov %r14,232($context) # restore context->R14
3822 mov %r15,240($context) # restore context->R15
3827 mov %rax,152($context) # restore context->Rsp
3828 mov %rsi,168($context) # restore context->Rsi
3829 mov %rdi,176($context) # restore context->Rdi
3831 mov 40($disp),%rdi # disp->ContextRecord
3832 mov $context,%rsi # context
3833 mov \$154,%ecx # sizeof(CONTEXT)
3834 .long 0xa548f3fc # cld; rep movsq
3837 xor %rcx,%rcx # arg1, UNW_FLAG_NHANDLER
3838 mov 8(%rsi),%rdx # arg2, disp->ImageBase
3839 mov 0(%rsi),%r8 # arg3, disp->ControlPc
3840 mov 16(%rsi),%r9 # arg4, disp->FunctionEntry
3841 mov 40(%rsi),%r10 # disp->ContextRecord
3842 lea 56(%rsi),%r11 # &disp->HandlerData
3843 lea 24(%rsi),%r12 # &disp->EstablisherFrame
3844 mov %r10,32(%rsp) # arg5
3845 mov %r11,40(%rsp) # arg6
3846 mov %r12,48(%rsp) # arg7
3847 mov %rcx,56(%rsp) # arg8, (NULL)
3848 call *__imp_RtlVirtualUnwind(%rip)
3850 mov \$1,%eax # ExceptionContinueSearch
3862 .size mul_handler,.-mul_handler
3866 .rva .LSEH_begin_bn_mul_mont_gather5
3867 .rva .LSEH_end_bn_mul_mont_gather5
3868 .rva .LSEH_info_bn_mul_mont_gather5
3870 .rva .LSEH_begin_bn_mul4x_mont_gather5
3871 .rva .LSEH_end_bn_mul4x_mont_gather5
3872 .rva .LSEH_info_bn_mul4x_mont_gather5
3874 .rva .LSEH_begin_bn_power5
3875 .rva .LSEH_end_bn_power5
3876 .rva .LSEH_info_bn_power5
3878 .rva .LSEH_begin_bn_from_mont8x
3879 .rva .LSEH_end_bn_from_mont8x
3880 .rva .LSEH_info_bn_from_mont8x
3882 $code.=<<___ if ($addx);
3883 .rva .LSEH_begin_bn_mulx4x_mont_gather5
3884 .rva .LSEH_end_bn_mulx4x_mont_gather5
3885 .rva .LSEH_info_bn_mulx4x_mont_gather5
3887 .rva .LSEH_begin_bn_powerx5
3888 .rva .LSEH_end_bn_powerx5
3889 .rva .LSEH_info_bn_powerx5
3892 .rva .LSEH_begin_bn_gather5
3893 .rva .LSEH_end_bn_gather5
3894 .rva .LSEH_info_bn_gather5
3898 .LSEH_info_bn_mul_mont_gather5:
3901 .rva .Lmul_body,.Lmul_body,.Lmul_epilogue # HandlerData[]
3903 .LSEH_info_bn_mul4x_mont_gather5:
3906 .rva .Lmul4x_prologue,.Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
3908 .LSEH_info_bn_power5:
3911 .rva .Lpower5_prologue,.Lpower5_body,.Lpower5_epilogue # HandlerData[]
3913 .LSEH_info_bn_from_mont8x:
3916 .rva .Lfrom_prologue,.Lfrom_body,.Lfrom_epilogue # HandlerData[]
3918 $code.=<<___ if ($addx);
3920 .LSEH_info_bn_mulx4x_mont_gather5:
3923 .rva .Lmulx4x_prologue,.Lmulx4x_body,.Lmulx4x_epilogue # HandlerData[]
3925 .LSEH_info_bn_powerx5:
3928 .rva .Lpowerx5_prologue,.Lpowerx5_body,.Lpowerx5_epilogue # HandlerData[]
3932 .LSEH_info_bn_gather5:
3933 .byte 0x01,0x0b,0x03,0x0a
3934 .byte 0x0b,0x01,0x21,0x00 # sub rsp,0x108
3935 .byte 0x04,0xa3,0x00,0x00 # lea r10,(rsp)
3940 $code =~ s/\`([^\`]*)\`/eval($1)/gem;