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| #! /usr/bin/env perl
| # Copyright 2011-2020 The OpenSSL Project Authors. All Rights Reserved.
| #
| # Licensed under the OpenSSL license (the "License"). You may not use
| # this file except in compliance with the License. You can obtain a copy
| # in the file LICENSE in the source distribution or at
| # https://www.openssl.org/source/license.html
|
|
| # ====================================================================
| # Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
| # project. The module is, however, dual licensed under OpenSSL and
| # CRYPTOGAMS licenses depending on where you obtain it. For further
| # details see http://www.openssl.org/~appro/cryptogams/.
| # ====================================================================
|
| # August 2011.
| #
| # Companion to x86_64-mont.pl that optimizes cache-timing attack
| # countermeasures. The subroutines are produced by replacing bp[i]
| # references in their x86_64-mont.pl counterparts with cache-neutral
| # references to powers table computed in BN_mod_exp_mont_consttime.
| # In addition subroutine that scatters elements of the powers table
| # is implemented, so that scatter-/gathering can be tuned without
| # bn_exp.c modifications.
|
| # August 2013.
| #
| # Add MULX/AD*X code paths and additional interfaces to optimize for
| # branch prediction unit. For input lengths that are multiples of 8
| # the np argument is not just modulus value, but one interleaved
| # with 0. This is to optimize post-condition...
|
| $flavour = shift;
| $output = shift;
| if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
|
| $win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
|
| $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
| ( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
| ( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
| die "can't locate x86_64-xlate.pl";
|
| open OUT,"| \"$^X\" \"$xlate\" $flavour \"$output\"";
| *STDOUT=*OUT;
|
| if (`$ENV{CC} -Wa,-v -c -o /dev/null -x assembler /dev/null 2>&1`
| =~ /GNU assembler version ([2-9]\.[0-9]+)/) {
| $addx = ($1>=2.23);
| }
|
| if (!$addx && $win64 && ($flavour =~ /nasm/ || $ENV{ASM} =~ /nasm/) &&
| `nasm -v 2>&1` =~ /NASM version ([2-9]\.[0-9]+)/) {
| $addx = ($1>=2.10);
| }
|
| if (!$addx && $win64 && ($flavour =~ /masm/ || $ENV{ASM} =~ /ml64/) &&
| `ml64 2>&1` =~ /Version ([0-9]+)\./) {
| $addx = ($1>=12);
| }
|
| if (!$addx && `$ENV{CC} -v 2>&1` =~ /((?:clang|LLVM) version|.*based on LLVM) ([0-9]+)\.([0-9]+)/) {
| my $ver = $2 + $3/100.0; # 3.1->3.01, 3.10->3.10
| $addx = ($ver>=3.03);
| }
|
| # int bn_mul_mont_gather5(
| $rp="%rdi"; # BN_ULONG *rp,
| $ap="%rsi"; # const BN_ULONG *ap,
| $bp="%rdx"; # const BN_ULONG *bp,
| $np="%rcx"; # const BN_ULONG *np,
| $n0="%r8"; # const BN_ULONG *n0,
| $num="%r9"; # int num,
| # int idx); # 0 to 2^5-1, "index" in $bp holding
| # pre-computed powers of a', interlaced
| # in such manner that b[0] is $bp[idx],
| # b[1] is [2^5+idx], etc.
| $lo0="%r10";
| $hi0="%r11";
| $hi1="%r13";
| $i="%r14";
| $j="%r15";
| $m0="%rbx";
| $m1="%rbp";
|
| $code=<<___;
| .text
|
| .extern OPENSSL_ia32cap_P
|
| .globl bn_mul_mont_gather5
| .type bn_mul_mont_gather5,\@function,6
| .align 64
| bn_mul_mont_gather5:
| .cfi_startproc
| mov ${num}d,${num}d
| mov %rsp,%rax
| .cfi_def_cfa_register %rax
| test \$7,${num}d
| jnz .Lmul_enter
| ___
| $code.=<<___ if ($addx);
| mov OPENSSL_ia32cap_P+8(%rip),%r11d
| ___
| $code.=<<___;
| jmp .Lmul4x_enter
|
| .align 16
| .Lmul_enter:
| movd `($win64?56:8)`(%rsp),%xmm5 # load 7th argument
| push %rbx
| .cfi_push %rbx
| push %rbp
| .cfi_push %rbp
| push %r12
| .cfi_push %r12
| push %r13
| .cfi_push %r13
| push %r14
| .cfi_push %r14
| push %r15
| .cfi_push %r15
|
| neg $num
| mov %rsp,%r11
| lea -280(%rsp,$num,8),%r10 # future alloca(8*(num+2)+256+8)
| neg $num # restore $num
| and \$-1024,%r10 # minimize TLB usage
|
| # An OS-agnostic version of __chkstk.
| #
| # Some OSes (Windows) insist on stack being "wired" to
| # physical memory in strictly sequential manner, i.e. if stack
| # allocation spans two pages, then reference to farmost one can
| # be punishable by SEGV. But page walking can do good even on
| # other OSes, because it guarantees that villain thread hits
| # the guard page before it can make damage to innocent one...
| sub %r10,%r11
| and \$-4096,%r11
| lea (%r10,%r11),%rsp
| mov (%rsp),%r11
| cmp %r10,%rsp
| ja .Lmul_page_walk
| jmp .Lmul_page_walk_done
|
| .Lmul_page_walk:
| lea -4096(%rsp),%rsp
| mov (%rsp),%r11
| cmp %r10,%rsp
| ja .Lmul_page_walk
| .Lmul_page_walk_done:
|
| lea .Linc(%rip),%r10
| mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
| .cfi_cfa_expression %rsp+8,$num,8,mul,plus,deref,+8
| .Lmul_body:
|
| lea 128($bp),%r12 # reassign $bp (+size optimization)
| ___
| $bp="%r12";
| $STRIDE=2**5*8; # 5 is "window size"
| $N=$STRIDE/4; # should match cache line size
| $code.=<<___;
| movdqa 0(%r10),%xmm0 # 00000001000000010000000000000000
| movdqa 16(%r10),%xmm1 # 00000002000000020000000200000002
| lea 24-112(%rsp,$num,8),%r10# place the mask after tp[num+3] (+ICache optimization)
| and \$-16,%r10
|
| pshufd \$0,%xmm5,%xmm5 # broadcast index
| movdqa %xmm1,%xmm4
| movdqa %xmm1,%xmm2
| ___
| ########################################################################
| # calculate mask by comparing 0..31 to index and save result to stack
| #
| $code.=<<___;
| paddd %xmm0,%xmm1
| pcmpeqd %xmm5,%xmm0 # compare to 1,0
| .byte 0x67
| movdqa %xmm4,%xmm3
| ___
| for($k=0;$k<$STRIDE/16-4;$k+=4) {
| $code.=<<___;
| paddd %xmm1,%xmm2
| pcmpeqd %xmm5,%xmm1 # compare to 3,2
| movdqa %xmm0,`16*($k+0)+112`(%r10)
| movdqa %xmm4,%xmm0
|
| paddd %xmm2,%xmm3
| pcmpeqd %xmm5,%xmm2 # compare to 5,4
| movdqa %xmm1,`16*($k+1)+112`(%r10)
| movdqa %xmm4,%xmm1
|
| paddd %xmm3,%xmm0
| pcmpeqd %xmm5,%xmm3 # compare to 7,6
| movdqa %xmm2,`16*($k+2)+112`(%r10)
| movdqa %xmm4,%xmm2
|
| paddd %xmm0,%xmm1
| pcmpeqd %xmm5,%xmm0
| movdqa %xmm3,`16*($k+3)+112`(%r10)
| movdqa %xmm4,%xmm3
| ___
| }
| $code.=<<___; # last iteration can be optimized
| paddd %xmm1,%xmm2
| pcmpeqd %xmm5,%xmm1
| movdqa %xmm0,`16*($k+0)+112`(%r10)
|
| paddd %xmm2,%xmm3
| .byte 0x67
| pcmpeqd %xmm5,%xmm2
| movdqa %xmm1,`16*($k+1)+112`(%r10)
|
| pcmpeqd %xmm5,%xmm3
| movdqa %xmm2,`16*($k+2)+112`(%r10)
| pand `16*($k+0)-128`($bp),%xmm0 # while it's still in register
|
| pand `16*($k+1)-128`($bp),%xmm1
| pand `16*($k+2)-128`($bp),%xmm2
| movdqa %xmm3,`16*($k+3)+112`(%r10)
| pand `16*($k+3)-128`($bp),%xmm3
| por %xmm2,%xmm0
| por %xmm3,%xmm1
| ___
| for($k=0;$k<$STRIDE/16-4;$k+=4) {
| $code.=<<___;
| movdqa `16*($k+0)-128`($bp),%xmm4
| movdqa `16*($k+1)-128`($bp),%xmm5
| movdqa `16*($k+2)-128`($bp),%xmm2
| pand `16*($k+0)+112`(%r10),%xmm4
| movdqa `16*($k+3)-128`($bp),%xmm3
| pand `16*($k+1)+112`(%r10),%xmm5
| por %xmm4,%xmm0
| pand `16*($k+2)+112`(%r10),%xmm2
| por %xmm5,%xmm1
| pand `16*($k+3)+112`(%r10),%xmm3
| por %xmm2,%xmm0
| por %xmm3,%xmm1
| ___
| }
| $code.=<<___;
| por %xmm1,%xmm0
| pshufd \$0x4e,%xmm0,%xmm1
| por %xmm1,%xmm0
| lea $STRIDE($bp),$bp
| movq %xmm0,$m0 # m0=bp[0]
|
| mov ($n0),$n0 # pull n0[0] value
| mov ($ap),%rax
|
| xor $i,$i # i=0
| xor $j,$j # j=0
|
| mov $n0,$m1
| mulq $m0 # ap[0]*bp[0]
| mov %rax,$lo0
| mov ($np),%rax
|
| imulq $lo0,$m1 # "tp[0]"*n0
| mov %rdx,$hi0
|
| mulq $m1 # np[0]*m1
| add %rax,$lo0 # discarded
| mov 8($ap),%rax
| adc \$0,%rdx
| mov %rdx,$hi1
|
| lea 1($j),$j # j++
| jmp .L1st_enter
|
| .align 16
| .L1st:
| add %rax,$hi1
| mov ($ap,$j,8),%rax
| adc \$0,%rdx
| add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
| mov $lo0,$hi0
| adc \$0,%rdx
| mov $hi1,-16(%rsp,$j,8) # tp[j-1]
| mov %rdx,$hi1
|
| .L1st_enter:
| mulq $m0 # ap[j]*bp[0]
| add %rax,$hi0
| mov ($np,$j,8),%rax
| adc \$0,%rdx
| lea 1($j),$j # j++
| mov %rdx,$lo0
|
| mulq $m1 # np[j]*m1
| cmp $num,$j
| jne .L1st # note that upon exit $j==$num, so
| # they can be used interchangeably
|
| add %rax,$hi1
| adc \$0,%rdx
| add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
| adc \$0,%rdx
| mov $hi1,-16(%rsp,$num,8) # tp[num-1]
| mov %rdx,$hi1
| mov $lo0,$hi0
|
| xor %rdx,%rdx
| add $hi0,$hi1
| adc \$0,%rdx
| mov $hi1,-8(%rsp,$num,8)
| mov %rdx,(%rsp,$num,8) # store upmost overflow bit
|
| lea 1($i),$i # i++
| jmp .Louter
| .align 16
| .Louter:
| lea 24+128(%rsp,$num,8),%rdx # where 256-byte mask is (+size optimization)
| and \$-16,%rdx
| pxor %xmm4,%xmm4
| pxor %xmm5,%xmm5
| ___
| for($k=0;$k<$STRIDE/16;$k+=4) {
| $code.=<<___;
| movdqa `16*($k+0)-128`($bp),%xmm0
| movdqa `16*($k+1)-128`($bp),%xmm1
| movdqa `16*($k+2)-128`($bp),%xmm2
| movdqa `16*($k+3)-128`($bp),%xmm3
| pand `16*($k+0)-128`(%rdx),%xmm0
| pand `16*($k+1)-128`(%rdx),%xmm1
| por %xmm0,%xmm4
| pand `16*($k+2)-128`(%rdx),%xmm2
| por %xmm1,%xmm5
| pand `16*($k+3)-128`(%rdx),%xmm3
| por %xmm2,%xmm4
| por %xmm3,%xmm5
| ___
| }
| $code.=<<___;
| por %xmm5,%xmm4
| pshufd \$0x4e,%xmm4,%xmm0
| por %xmm4,%xmm0
| lea $STRIDE($bp),$bp
|
| mov ($ap),%rax # ap[0]
| movq %xmm0,$m0 # m0=bp[i]
|
| xor $j,$j # j=0
| mov $n0,$m1
| mov (%rsp),$lo0
|
| mulq $m0 # ap[0]*bp[i]
| add %rax,$lo0 # ap[0]*bp[i]+tp[0]
| mov ($np),%rax
| adc \$0,%rdx
|
| imulq $lo0,$m1 # tp[0]*n0
| mov %rdx,$hi0
|
| mulq $m1 # np[0]*m1
| add %rax,$lo0 # discarded
| mov 8($ap),%rax
| adc \$0,%rdx
| mov 8(%rsp),$lo0 # tp[1]
| mov %rdx,$hi1
|
| lea 1($j),$j # j++
| jmp .Linner_enter
|
| .align 16
| .Linner:
| add %rax,$hi1
| mov ($ap,$j,8),%rax
| adc \$0,%rdx
| add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
| mov (%rsp,$j,8),$lo0
| adc \$0,%rdx
| mov $hi1,-16(%rsp,$j,8) # tp[j-1]
| mov %rdx,$hi1
|
| .Linner_enter:
| mulq $m0 # ap[j]*bp[i]
| add %rax,$hi0
| mov ($np,$j,8),%rax
| adc \$0,%rdx
| add $hi0,$lo0 # ap[j]*bp[i]+tp[j]
| mov %rdx,$hi0
| adc \$0,$hi0
| lea 1($j),$j # j++
|
| mulq $m1 # np[j]*m1
| cmp $num,$j
| jne .Linner # note that upon exit $j==$num, so
| # they can be used interchangeably
| add %rax,$hi1
| adc \$0,%rdx
| add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
| mov (%rsp,$num,8),$lo0
| adc \$0,%rdx
| mov $hi1,-16(%rsp,$num,8) # tp[num-1]
| mov %rdx,$hi1
|
| xor %rdx,%rdx
| add $hi0,$hi1
| adc \$0,%rdx
| add $lo0,$hi1 # pull upmost overflow bit
| adc \$0,%rdx
| mov $hi1,-8(%rsp,$num,8)
| mov %rdx,(%rsp,$num,8) # store upmost overflow bit
|
| lea 1($i),$i # i++
| cmp $num,$i
| jb .Louter
|
| xor $i,$i # i=0 and clear CF!
| mov (%rsp),%rax # tp[0]
| lea (%rsp),$ap # borrow ap for tp
| mov $num,$j # j=num
| jmp .Lsub
| .align 16
| .Lsub: sbb ($np,$i,8),%rax
| mov %rax,($rp,$i,8) # rp[i]=tp[i]-np[i]
| mov 8($ap,$i,8),%rax # tp[i+1]
| lea 1($i),$i # i++
| dec $j # doesn't affect CF!
| jnz .Lsub
|
| sbb \$0,%rax # handle upmost overflow bit
| mov \$-1,%rbx
| xor %rax,%rbx
| xor $i,$i
| mov $num,$j # j=num
|
| .Lcopy: # conditional copy
| mov ($rp,$i,8),%rcx
| mov (%rsp,$i,8),%rdx
| and %rbx,%rcx
| and %rax,%rdx
| mov $i,(%rsp,$i,8) # zap temporary vector
| or %rcx,%rdx
| mov %rdx,($rp,$i,8) # rp[i]=tp[i]
| lea 1($i),$i
| sub \$1,$j
| jnz .Lcopy
|
| mov 8(%rsp,$num,8),%rsi # restore %rsp
| .cfi_def_cfa %rsi,8
| mov \$1,%rax
|
| mov -48(%rsi),%r15
| .cfi_restore %r15
| mov -40(%rsi),%r14
| .cfi_restore %r14
| mov -32(%rsi),%r13
| .cfi_restore %r13
| mov -24(%rsi),%r12
| .cfi_restore %r12
| mov -16(%rsi),%rbp
| .cfi_restore %rbp
| mov -8(%rsi),%rbx
| .cfi_restore %rbx
| lea (%rsi),%rsp
| .cfi_def_cfa_register %rsp
| .Lmul_epilogue:
| ret
| .cfi_endproc
| .size bn_mul_mont_gather5,.-bn_mul_mont_gather5
| ___
| {{{
| my @A=("%r10","%r11");
| my @N=("%r13","%rdi");
| $code.=<<___;
| .type bn_mul4x_mont_gather5,\@function,6
| .align 32
| bn_mul4x_mont_gather5:
| .cfi_startproc
| .byte 0x67
| mov %rsp,%rax
| .cfi_def_cfa_register %rax
| .Lmul4x_enter:
| ___
| $code.=<<___ if ($addx);
| and \$0x80108,%r11d
| cmp \$0x80108,%r11d # check for AD*X+BMI2+BMI1
| je .Lmulx4x_enter
| ___
| $code.=<<___;
| push %rbx
| .cfi_push %rbx
| push %rbp
| .cfi_push %rbp
| push %r12
| .cfi_push %r12
| push %r13
| .cfi_push %r13
| push %r14
| .cfi_push %r14
| push %r15
| .cfi_push %r15
| .Lmul4x_prologue:
|
| .byte 0x67
| shl \$3,${num}d # convert $num to bytes
| lea ($num,$num,2),%r10 # 3*$num in bytes
| neg $num # -$num
|
| ##############################################################
| # Ensure that stack frame doesn't alias with $rptr+3*$num
| # modulo 4096, which covers ret[num], am[num] and n[num]
| # (see bn_exp.c). This is done to allow memory disambiguation
| # logic do its magic. [Extra [num] is allocated in order
| # to align with bn_power5's frame, which is cleansed after
| # completing exponentiation. Extra 256 bytes is for power mask
| # calculated from 7th argument, the index.]
| #
| lea -320(%rsp,$num,2),%r11
| mov %rsp,%rbp
| sub $rp,%r11
| and \$4095,%r11
| cmp %r11,%r10
| jb .Lmul4xsp_alt
| sub %r11,%rbp # align with $rp
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
| jmp .Lmul4xsp_done
|
| .align 32
| .Lmul4xsp_alt:
| lea 4096-320(,$num,2),%r10
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
| sub %r10,%r11
| mov \$0,%r10
| cmovc %r10,%r11
| sub %r11,%rbp
| .Lmul4xsp_done:
| and \$-64,%rbp
| mov %rsp,%r11
| sub %rbp,%r11
| and \$-4096,%r11
| lea (%rbp,%r11),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lmul4x_page_walk
| jmp .Lmul4x_page_walk_done
|
| .Lmul4x_page_walk:
| lea -4096(%rsp),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lmul4x_page_walk
| .Lmul4x_page_walk_done:
|
| neg $num
|
| mov %rax,40(%rsp)
| .cfi_cfa_expression %rsp+40,deref,+8
| .Lmul4x_body:
|
| call mul4x_internal
|
| mov 40(%rsp),%rsi # restore %rsp
| .cfi_def_cfa %rsi,8
| mov \$1,%rax
|
| mov -48(%rsi),%r15
| .cfi_restore %r15
| mov -40(%rsi),%r14
| .cfi_restore %r14
| mov -32(%rsi),%r13
| .cfi_restore %r13
| mov -24(%rsi),%r12
| .cfi_restore %r12
| mov -16(%rsi),%rbp
| .cfi_restore %rbp
| mov -8(%rsi),%rbx
| .cfi_restore %rbx
| lea (%rsi),%rsp
| .cfi_def_cfa_register %rsp
| .Lmul4x_epilogue:
| ret
| .cfi_endproc
| .size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
|
| .type mul4x_internal,\@abi-omnipotent
| .align 32
| mul4x_internal:
| .cfi_startproc
| shl \$5,$num # $num was in bytes
| movd `($win64?56:8)`(%rax),%xmm5 # load 7th argument, index
| lea .Linc(%rip),%rax
| lea 128(%rdx,$num),%r13 # end of powers table (+size optimization)
| shr \$5,$num # restore $num
| ___
| $bp="%r12";
| $STRIDE=2**5*8; # 5 is "window size"
| $N=$STRIDE/4; # should match cache line size
| $tp=$i;
| $code.=<<___;
| movdqa 0(%rax),%xmm0 # 00000001000000010000000000000000
| movdqa 16(%rax),%xmm1 # 00000002000000020000000200000002
| lea 88-112(%rsp,$num),%r10 # place the mask after tp[num+1] (+ICache optimization)
| lea 128(%rdx),$bp # size optimization
|
| pshufd \$0,%xmm5,%xmm5 # broadcast index
| movdqa %xmm1,%xmm4
| .byte 0x67,0x67
| movdqa %xmm1,%xmm2
| ___
| ########################################################################
| # calculate mask by comparing 0..31 to index and save result to stack
| #
| $code.=<<___;
| paddd %xmm0,%xmm1
| pcmpeqd %xmm5,%xmm0 # compare to 1,0
| .byte 0x67
| movdqa %xmm4,%xmm3
| ___
| for($i=0;$i<$STRIDE/16-4;$i+=4) {
| $code.=<<___;
| paddd %xmm1,%xmm2
| pcmpeqd %xmm5,%xmm1 # compare to 3,2
| movdqa %xmm0,`16*($i+0)+112`(%r10)
| movdqa %xmm4,%xmm0
|
| paddd %xmm2,%xmm3
| pcmpeqd %xmm5,%xmm2 # compare to 5,4
| movdqa %xmm1,`16*($i+1)+112`(%r10)
| movdqa %xmm4,%xmm1
|
| paddd %xmm3,%xmm0
| pcmpeqd %xmm5,%xmm3 # compare to 7,6
| movdqa %xmm2,`16*($i+2)+112`(%r10)
| movdqa %xmm4,%xmm2
|
| paddd %xmm0,%xmm1
| pcmpeqd %xmm5,%xmm0
| movdqa %xmm3,`16*($i+3)+112`(%r10)
| movdqa %xmm4,%xmm3
| ___
| }
| $code.=<<___; # last iteration can be optimized
| paddd %xmm1,%xmm2
| pcmpeqd %xmm5,%xmm1
| movdqa %xmm0,`16*($i+0)+112`(%r10)
|
| paddd %xmm2,%xmm3
| .byte 0x67
| pcmpeqd %xmm5,%xmm2
| movdqa %xmm1,`16*($i+1)+112`(%r10)
|
| pcmpeqd %xmm5,%xmm3
| movdqa %xmm2,`16*($i+2)+112`(%r10)
| pand `16*($i+0)-128`($bp),%xmm0 # while it's still in register
|
| pand `16*($i+1)-128`($bp),%xmm1
| pand `16*($i+2)-128`($bp),%xmm2
| movdqa %xmm3,`16*($i+3)+112`(%r10)
| pand `16*($i+3)-128`($bp),%xmm3
| por %xmm2,%xmm0
| por %xmm3,%xmm1
| ___
| for($i=0;$i<$STRIDE/16-4;$i+=4) {
| $code.=<<___;
| movdqa `16*($i+0)-128`($bp),%xmm4
| movdqa `16*($i+1)-128`($bp),%xmm5
| movdqa `16*($i+2)-128`($bp),%xmm2
| pand `16*($i+0)+112`(%r10),%xmm4
| movdqa `16*($i+3)-128`($bp),%xmm3
| pand `16*($i+1)+112`(%r10),%xmm5
| por %xmm4,%xmm0
| pand `16*($i+2)+112`(%r10),%xmm2
| por %xmm5,%xmm1
| pand `16*($i+3)+112`(%r10),%xmm3
| por %xmm2,%xmm0
| por %xmm3,%xmm1
| ___
| }
| $code.=<<___;
| por %xmm1,%xmm0
| pshufd \$0x4e,%xmm0,%xmm1
| por %xmm1,%xmm0
| lea $STRIDE($bp),$bp
| movq %xmm0,$m0 # m0=bp[0]
|
| mov %r13,16+8(%rsp) # save end of b[num]
| mov $rp, 56+8(%rsp) # save $rp
|
| mov ($n0),$n0 # pull n0[0] value
| mov ($ap),%rax
| lea ($ap,$num),$ap # end of a[num]
| neg $num
|
| mov $n0,$m1
| mulq $m0 # ap[0]*bp[0]
| mov %rax,$A[0]
| mov ($np),%rax
|
| imulq $A[0],$m1 # "tp[0]"*n0
| lea 64+8(%rsp),$tp
| mov %rdx,$A[1]
|
| mulq $m1 # np[0]*m1
| add %rax,$A[0] # discarded
| mov 8($ap,$num),%rax
| adc \$0,%rdx
| mov %rdx,$N[1]
|
| mulq $m0
| add %rax,$A[1]
| mov 8*1($np),%rax
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1
| add %rax,$N[1]
| mov 16($ap,$num),%rax
| adc \$0,%rdx
| add $A[1],$N[1]
| lea 4*8($num),$j # j=4
| lea 8*4($np),$np
| adc \$0,%rdx
| mov $N[1],($tp)
| mov %rdx,$N[0]
| jmp .L1st4x
|
| .align 32
| .L1st4x:
| mulq $m0 # ap[j]*bp[0]
| add %rax,$A[0]
| mov -8*2($np),%rax
| lea 32($tp),$tp
| adc \$0,%rdx
| mov %rdx,$A[1]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[0]
| mov -8($ap,$j),%rax
| adc \$0,%rdx
| add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
| adc \$0,%rdx
| mov $N[0],-24($tp) # tp[j-1]
| mov %rdx,$N[1]
|
| mulq $m0 # ap[j]*bp[0]
| add %rax,$A[1]
| mov -8*1($np),%rax
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[1]
| mov ($ap,$j),%rax
| adc \$0,%rdx
| add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
| adc \$0,%rdx
| mov $N[1],-16($tp) # tp[j-1]
| mov %rdx,$N[0]
|
| mulq $m0 # ap[j]*bp[0]
| add %rax,$A[0]
| mov 8*0($np),%rax
| adc \$0,%rdx
| mov %rdx,$A[1]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[0]
| mov 8($ap,$j),%rax
| adc \$0,%rdx
| add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
| adc \$0,%rdx
| mov $N[0],-8($tp) # tp[j-1]
| mov %rdx,$N[1]
|
| mulq $m0 # ap[j]*bp[0]
| add %rax,$A[1]
| mov 8*1($np),%rax
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[1]
| mov 16($ap,$j),%rax
| adc \$0,%rdx
| add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
| lea 8*4($np),$np
| adc \$0,%rdx
| mov $N[1],($tp) # tp[j-1]
| mov %rdx,$N[0]
|
| add \$32,$j # j+=4
| jnz .L1st4x
|
| mulq $m0 # ap[j]*bp[0]
| add %rax,$A[0]
| mov -8*2($np),%rax
| lea 32($tp),$tp
| adc \$0,%rdx
| mov %rdx,$A[1]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[0]
| mov -8($ap),%rax
| adc \$0,%rdx
| add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
| adc \$0,%rdx
| mov $N[0],-24($tp) # tp[j-1]
| mov %rdx,$N[1]
|
| mulq $m0 # ap[j]*bp[0]
| add %rax,$A[1]
| mov -8*1($np),%rax
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[1]
| mov ($ap,$num),%rax # ap[0]
| adc \$0,%rdx
| add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
| adc \$0,%rdx
| mov $N[1],-16($tp) # tp[j-1]
| mov %rdx,$N[0]
|
| lea ($np,$num),$np # rewind $np
|
| xor $N[1],$N[1]
| add $A[0],$N[0]
| adc \$0,$N[1]
| mov $N[0],-8($tp)
|
| jmp .Louter4x
|
| .align 32
| .Louter4x:
| lea 16+128($tp),%rdx # where 256-byte mask is (+size optimization)
| pxor %xmm4,%xmm4
| pxor %xmm5,%xmm5
| ___
| for($i=0;$i<$STRIDE/16;$i+=4) {
| $code.=<<___;
| movdqa `16*($i+0)-128`($bp),%xmm0
| movdqa `16*($i+1)-128`($bp),%xmm1
| movdqa `16*($i+2)-128`($bp),%xmm2
| movdqa `16*($i+3)-128`($bp),%xmm3
| pand `16*($i+0)-128`(%rdx),%xmm0
| pand `16*($i+1)-128`(%rdx),%xmm1
| por %xmm0,%xmm4
| pand `16*($i+2)-128`(%rdx),%xmm2
| por %xmm1,%xmm5
| pand `16*($i+3)-128`(%rdx),%xmm3
| por %xmm2,%xmm4
| por %xmm3,%xmm5
| ___
| }
| $code.=<<___;
| por %xmm5,%xmm4
| pshufd \$0x4e,%xmm4,%xmm0
| por %xmm4,%xmm0
| lea $STRIDE($bp),$bp
| movq %xmm0,$m0 # m0=bp[i]
|
| mov ($tp,$num),$A[0]
| mov $n0,$m1
| mulq $m0 # ap[0]*bp[i]
| add %rax,$A[0] # ap[0]*bp[i]+tp[0]
| mov ($np),%rax
| adc \$0,%rdx
|
| imulq $A[0],$m1 # tp[0]*n0
| mov %rdx,$A[1]
| mov $N[1],($tp) # store upmost overflow bit
|
| lea ($tp,$num),$tp # rewind $tp
|
| mulq $m1 # np[0]*m1
| add %rax,$A[0] # "$N[0]", discarded
| mov 8($ap,$num),%rax
| adc \$0,%rdx
| mov %rdx,$N[1]
|
| mulq $m0 # ap[j]*bp[i]
| add %rax,$A[1]
| mov 8*1($np),%rax
| adc \$0,%rdx
| add 8($tp),$A[1] # +tp[1]
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[1]
| mov 16($ap,$num),%rax
| adc \$0,%rdx
| add $A[1],$N[1] # np[j]*m1+ap[j]*bp[i]+tp[j]
| lea 4*8($num),$j # j=4
| lea 8*4($np),$np
| adc \$0,%rdx
| mov %rdx,$N[0]
| jmp .Linner4x
|
| .align 32
| .Linner4x:
| mulq $m0 # ap[j]*bp[i]
| add %rax,$A[0]
| mov -8*2($np),%rax
| adc \$0,%rdx
| add 16($tp),$A[0] # ap[j]*bp[i]+tp[j]
| lea 32($tp),$tp
| adc \$0,%rdx
| mov %rdx,$A[1]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[0]
| mov -8($ap,$j),%rax
| adc \$0,%rdx
| add $A[0],$N[0]
| adc \$0,%rdx
| mov $N[1],-32($tp) # tp[j-1]
| mov %rdx,$N[1]
|
| mulq $m0 # ap[j]*bp[i]
| add %rax,$A[1]
| mov -8*1($np),%rax
| adc \$0,%rdx
| add -8($tp),$A[1]
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[1]
| mov ($ap,$j),%rax
| adc \$0,%rdx
| add $A[1],$N[1]
| adc \$0,%rdx
| mov $N[0],-24($tp) # tp[j-1]
| mov %rdx,$N[0]
|
| mulq $m0 # ap[j]*bp[i]
| add %rax,$A[0]
| mov 8*0($np),%rax
| adc \$0,%rdx
| add ($tp),$A[0] # ap[j]*bp[i]+tp[j]
| adc \$0,%rdx
| mov %rdx,$A[1]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[0]
| mov 8($ap,$j),%rax
| adc \$0,%rdx
| add $A[0],$N[0]
| adc \$0,%rdx
| mov $N[1],-16($tp) # tp[j-1]
| mov %rdx,$N[1]
|
| mulq $m0 # ap[j]*bp[i]
| add %rax,$A[1]
| mov 8*1($np),%rax
| adc \$0,%rdx
| add 8($tp),$A[1]
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[1]
| mov 16($ap,$j),%rax
| adc \$0,%rdx
| add $A[1],$N[1]
| lea 8*4($np),$np
| adc \$0,%rdx
| mov $N[0],-8($tp) # tp[j-1]
| mov %rdx,$N[0]
|
| add \$32,$j # j+=4
| jnz .Linner4x
|
| mulq $m0 # ap[j]*bp[i]
| add %rax,$A[0]
| mov -8*2($np),%rax
| adc \$0,%rdx
| add 16($tp),$A[0] # ap[j]*bp[i]+tp[j]
| lea 32($tp),$tp
| adc \$0,%rdx
| mov %rdx,$A[1]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[0]
| mov -8($ap),%rax
| adc \$0,%rdx
| add $A[0],$N[0]
| adc \$0,%rdx
| mov $N[1],-32($tp) # tp[j-1]
| mov %rdx,$N[1]
|
| mulq $m0 # ap[j]*bp[i]
| add %rax,$A[1]
| mov $m1,%rax
| mov -8*1($np),$m1
| adc \$0,%rdx
| add -8($tp),$A[1]
| adc \$0,%rdx
| mov %rdx,$A[0]
|
| mulq $m1 # np[j]*m1
| add %rax,$N[1]
| mov ($ap,$num),%rax # ap[0]
| adc \$0,%rdx
| add $A[1],$N[1]
| adc \$0,%rdx
| mov $N[0],-24($tp) # tp[j-1]
| mov %rdx,$N[0]
|
| mov $N[1],-16($tp) # tp[j-1]
| lea ($np,$num),$np # rewind $np
|
| xor $N[1],$N[1]
| add $A[0],$N[0]
| adc \$0,$N[1]
| add ($tp),$N[0] # pull upmost overflow bit
| adc \$0,$N[1] # upmost overflow bit
| mov $N[0],-8($tp)
|
| cmp 16+8(%rsp),$bp
| jb .Louter4x
| ___
| if (1) {
| $code.=<<___;
| xor %rax,%rax
| sub $N[0],$m1 # compare top-most words
| adc $j,$j # $j is zero
| or $j,$N[1]
| sub $N[1],%rax # %rax=-$N[1]
| lea ($tp,$num),%rbx # tptr in .sqr4x_sub
| mov ($np),%r12
| lea ($np),%rbp # nptr in .sqr4x_sub
| mov %r9,%rcx
| sar \$3+2,%rcx
| mov 56+8(%rsp),%rdi # rptr in .sqr4x_sub
| dec %r12 # so that after 'not' we get -n[0]
| xor %r10,%r10
| mov 8*1(%rbp),%r13
| mov 8*2(%rbp),%r14
| mov 8*3(%rbp),%r15
| jmp .Lsqr4x_sub_entry
| ___
| } else {
| my @ri=("%rax",$bp,$m0,$m1);
| my $rp="%rdx";
| $code.=<<___
| xor \$1,$N[1]
| lea ($tp,$num),$tp # rewind $tp
| sar \$5,$num # cf=0
| lea ($np,$N[1],8),$np
| mov 56+8(%rsp),$rp # restore $rp
| jmp .Lsub4x
|
| .align 32
| .Lsub4x:
| .byte 0x66
| mov 8*0($tp),@ri[0]
| mov 8*1($tp),@ri[1]
| .byte 0x66
| sbb 16*0($np),@ri[0]
| mov 8*2($tp),@ri[2]
| sbb 16*1($np),@ri[1]
| mov 3*8($tp),@ri[3]
| lea 4*8($tp),$tp
| sbb 16*2($np),@ri[2]
| mov @ri[0],8*0($rp)
| sbb 16*3($np),@ri[3]
| lea 16*4($np),$np
| mov @ri[1],8*1($rp)
| mov @ri[2],8*2($rp)
| mov @ri[3],8*3($rp)
| lea 8*4($rp),$rp
|
| inc $num
| jnz .Lsub4x
|
| ret
| ___
| }
| $code.=<<___;
| .cfi_endproc
| .size mul4x_internal,.-mul4x_internal
| ___
| }}}
| {{{
| ######################################################################
| # void bn_power5(
| my $rptr="%rdi"; # BN_ULONG *rptr,
| my $aptr="%rsi"; # const BN_ULONG *aptr,
| my $bptr="%rdx"; # const void *table,
| my $nptr="%rcx"; # const BN_ULONG *nptr,
| my $n0 ="%r8"; # const BN_ULONG *n0);
| my $num ="%r9"; # int num, has to be divisible by 8
| # int pwr
|
| my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
| my @A0=("%r10","%r11");
| my @A1=("%r12","%r13");
| my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
|
| $code.=<<___;
| .globl bn_power5
| .type bn_power5,\@function,6
| .align 32
| bn_power5:
| .cfi_startproc
| mov %rsp,%rax
| .cfi_def_cfa_register %rax
| ___
| $code.=<<___ if ($addx);
| mov OPENSSL_ia32cap_P+8(%rip),%r11d
| and \$0x80108,%r11d
| cmp \$0x80108,%r11d # check for AD*X+BMI2+BMI1
| je .Lpowerx5_enter
| ___
| $code.=<<___;
| push %rbx
| .cfi_push %rbx
| push %rbp
| .cfi_push %rbp
| push %r12
| .cfi_push %r12
| push %r13
| .cfi_push %r13
| push %r14
| .cfi_push %r14
| push %r15
| .cfi_push %r15
| .Lpower5_prologue:
|
| shl \$3,${num}d # convert $num to bytes
| lea ($num,$num,2),%r10d # 3*$num
| neg $num
| mov ($n0),$n0 # *n0
|
| ##############################################################
| # Ensure that stack frame doesn't alias with $rptr+3*$num
| # modulo 4096, which covers ret[num], am[num] and n[num]
| # (see bn_exp.c). This is done to allow memory disambiguation
| # logic do its magic. [Extra 256 bytes is for power mask
| # calculated from 7th argument, the index.]
| #
| lea -320(%rsp,$num,2),%r11
| mov %rsp,%rbp
| sub $rptr,%r11
| and \$4095,%r11
| cmp %r11,%r10
| jb .Lpwr_sp_alt
| sub %r11,%rbp # align with $aptr
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
| jmp .Lpwr_sp_done
|
| .align 32
| .Lpwr_sp_alt:
| lea 4096-320(,$num,2),%r10
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*num*8+256)
| sub %r10,%r11
| mov \$0,%r10
| cmovc %r10,%r11
| sub %r11,%rbp
| .Lpwr_sp_done:
| and \$-64,%rbp
| mov %rsp,%r11
| sub %rbp,%r11
| and \$-4096,%r11
| lea (%rbp,%r11),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lpwr_page_walk
| jmp .Lpwr_page_walk_done
|
| .Lpwr_page_walk:
| lea -4096(%rsp),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lpwr_page_walk
| .Lpwr_page_walk_done:
|
| mov $num,%r10
| neg $num
|
| ##############################################################
| # Stack layout
| #
| # +0 saved $num, used in reduction section
| # +8 &t[2*$num], used in reduction section
| # +32 saved *n0
| # +40 saved %rsp
| # +48 t[2*$num]
| #
| mov $n0, 32(%rsp)
| mov %rax, 40(%rsp) # save original %rsp
| .cfi_cfa_expression %rsp+40,deref,+8
| .Lpower5_body:
| movq $rptr,%xmm1 # save $rptr, used in sqr8x
| movq $nptr,%xmm2 # save $nptr
| movq %r10, %xmm3 # -$num, used in sqr8x
| movq $bptr,%xmm4
|
| call __bn_sqr8x_internal
| call __bn_post4x_internal
| call __bn_sqr8x_internal
| call __bn_post4x_internal
| call __bn_sqr8x_internal
| call __bn_post4x_internal
| call __bn_sqr8x_internal
| call __bn_post4x_internal
| call __bn_sqr8x_internal
| call __bn_post4x_internal
|
| movq %xmm2,$nptr
| movq %xmm4,$bptr
| mov $aptr,$rptr
| mov 40(%rsp),%rax
| lea 32(%rsp),$n0
|
| call mul4x_internal
|
| mov 40(%rsp),%rsi # restore %rsp
| .cfi_def_cfa %rsi,8
| mov \$1,%rax
| mov -48(%rsi),%r15
| .cfi_restore %r15
| mov -40(%rsi),%r14
| .cfi_restore %r14
| mov -32(%rsi),%r13
| .cfi_restore %r13
| mov -24(%rsi),%r12
| .cfi_restore %r12
| mov -16(%rsi),%rbp
| .cfi_restore %rbp
| mov -8(%rsi),%rbx
| .cfi_restore %rbx
| lea (%rsi),%rsp
| .cfi_def_cfa_register %rsp
| .Lpower5_epilogue:
| ret
| .cfi_endproc
| .size bn_power5,.-bn_power5
|
| .globl bn_sqr8x_internal
| .hidden bn_sqr8x_internal
| .type bn_sqr8x_internal,\@abi-omnipotent
| .align 32
| bn_sqr8x_internal:
| __bn_sqr8x_internal:
| .cfi_startproc
| ##############################################################
| # Squaring part:
| #
| # a) multiply-n-add everything but a[i]*a[i];
| # b) shift result of a) by 1 to the left and accumulate
| # a[i]*a[i] products;
| #
| ##############################################################
| # a[1]a[0]
| # a[2]a[0]
| # a[3]a[0]
| # a[2]a[1]
| # a[4]a[0]
| # a[3]a[1]
| # a[5]a[0]
| # a[4]a[1]
| # a[3]a[2]
| # a[6]a[0]
| # a[5]a[1]
| # a[4]a[2]
| # a[7]a[0]
| # a[6]a[1]
| # a[5]a[2]
| # a[4]a[3]
| # a[7]a[1]
| # a[6]a[2]
| # a[5]a[3]
| # a[7]a[2]
| # a[6]a[3]
| # a[5]a[4]
| # a[7]a[3]
| # a[6]a[4]
| # a[7]a[4]
| # a[6]a[5]
| # a[7]a[5]
| # a[7]a[6]
| # a[1]a[0]
| # a[2]a[0]
| # a[3]a[0]
| # a[4]a[0]
| # a[5]a[0]
| # a[6]a[0]
| # a[7]a[0]
| # a[2]a[1]
| # a[3]a[1]
| # a[4]a[1]
| # a[5]a[1]
| # a[6]a[1]
| # a[7]a[1]
| # a[3]a[2]
| # a[4]a[2]
| # a[5]a[2]
| # a[6]a[2]
| # a[7]a[2]
| # a[4]a[3]
| # a[5]a[3]
| # a[6]a[3]
| # a[7]a[3]
| # a[5]a[4]
| # a[6]a[4]
| # a[7]a[4]
| # a[6]a[5]
| # a[7]a[5]
| # a[7]a[6]
| # a[0]a[0]
| # a[1]a[1]
| # a[2]a[2]
| # a[3]a[3]
| # a[4]a[4]
| # a[5]a[5]
| # a[6]a[6]
| # a[7]a[7]
|
| lea 32(%r10),$i # $i=-($num-32)
| lea ($aptr,$num),$aptr # end of a[] buffer, ($aptr,$i)=&ap[2]
|
| mov $num,$j # $j=$num
|
| # comments apply to $num==8 case
| mov -32($aptr,$i),$a0 # a[0]
| lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
| mov -24($aptr,$i),%rax # a[1]
| lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
| mov -16($aptr,$i),$ai # a[2]
| mov %rax,$a1
|
| mul $a0 # a[1]*a[0]
| mov %rax,$A0[0] # a[1]*a[0]
| mov $ai,%rax # a[2]
| mov %rdx,$A0[1]
| mov $A0[0],-24($tptr,$i) # t[1]
|
| mul $a0 # a[2]*a[0]
| add %rax,$A0[1]
| mov $ai,%rax
| adc \$0,%rdx
| mov $A0[1],-16($tptr,$i) # t[2]
| mov %rdx,$A0[0]
|
|
| mov -8($aptr,$i),$ai # a[3]
| mul $a1 # a[2]*a[1]
| mov %rax,$A1[0] # a[2]*a[1]+t[3]
| mov $ai,%rax
| mov %rdx,$A1[1]
|
| lea ($i),$j
| mul $a0 # a[3]*a[0]
| add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
| mov $ai,%rax
| mov %rdx,$A0[1]
| adc \$0,$A0[1]
| add $A1[0],$A0[0]
| adc \$0,$A0[1]
| mov $A0[0],-8($tptr,$j) # t[3]
| jmp .Lsqr4x_1st
|
| .align 32
| .Lsqr4x_1st:
| mov ($aptr,$j),$ai # a[4]
| mul $a1 # a[3]*a[1]
| add %rax,$A1[1] # a[3]*a[1]+t[4]
| mov $ai,%rax
| mov %rdx,$A1[0]
| adc \$0,$A1[0]
|
| mul $a0 # a[4]*a[0]
| add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
| mov $ai,%rax # a[3]
| mov 8($aptr,$j),$ai # a[5]
| mov %rdx,$A0[0]
| adc \$0,$A0[0]
| add $A1[1],$A0[1]
| adc \$0,$A0[0]
|
|
| mul $a1 # a[4]*a[3]
| add %rax,$A1[0] # a[4]*a[3]+t[5]
| mov $ai,%rax
| mov $A0[1],($tptr,$j) # t[4]
| mov %rdx,$A1[1]
| adc \$0,$A1[1]
|
| mul $a0 # a[5]*a[2]
| add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
| mov $ai,%rax
| mov 16($aptr,$j),$ai # a[6]
| mov %rdx,$A0[1]
| adc \$0,$A0[1]
| add $A1[0],$A0[0]
| adc \$0,$A0[1]
|
| mul $a1 # a[5]*a[3]
| add %rax,$A1[1] # a[5]*a[3]+t[6]
| mov $ai,%rax
| mov $A0[0],8($tptr,$j) # t[5]
| mov %rdx,$A1[0]
| adc \$0,$A1[0]
|
| mul $a0 # a[6]*a[2]
| add %rax,$A0[1] # a[6]*a[2]+a[5]*a[3]+t[6]
| mov $ai,%rax # a[3]
| mov 24($aptr,$j),$ai # a[7]
| mov %rdx,$A0[0]
| adc \$0,$A0[0]
| add $A1[1],$A0[1]
| adc \$0,$A0[0]
|
|
| mul $a1 # a[6]*a[5]
| add %rax,$A1[0] # a[6]*a[5]+t[7]
| mov $ai,%rax
| mov $A0[1],16($tptr,$j) # t[6]
| mov %rdx,$A1[1]
| adc \$0,$A1[1]
| lea 32($j),$j
|
| mul $a0 # a[7]*a[4]
| add %rax,$A0[0] # a[7]*a[4]+a[6]*a[5]+t[6]
| mov $ai,%rax
| mov %rdx,$A0[1]
| adc \$0,$A0[1]
| add $A1[0],$A0[0]
| adc \$0,$A0[1]
| mov $A0[0],-8($tptr,$j) # t[7]
|
| cmp \$0,$j
| jne .Lsqr4x_1st
|
| mul $a1 # a[7]*a[5]
| add %rax,$A1[1]
| lea 16($i),$i
| adc \$0,%rdx
| add $A0[1],$A1[1]
| adc \$0,%rdx
|
| mov $A1[1],($tptr) # t[8]
| mov %rdx,$A1[0]
| mov %rdx,8($tptr) # t[9]
| jmp .Lsqr4x_outer
|
| .align 32
| .Lsqr4x_outer: # comments apply to $num==6 case
| mov -32($aptr,$i),$a0 # a[0]
| lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
| mov -24($aptr,$i),%rax # a[1]
| lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
| mov -16($aptr,$i),$ai # a[2]
| mov %rax,$a1
|
| mul $a0 # a[1]*a[0]
| mov -24($tptr,$i),$A0[0] # t[1]
| add %rax,$A0[0] # a[1]*a[0]+t[1]
| mov $ai,%rax # a[2]
| adc \$0,%rdx
| mov $A0[0],-24($tptr,$i) # t[1]
| mov %rdx,$A0[1]
|
| mul $a0 # a[2]*a[0]
| add %rax,$A0[1]
| mov $ai,%rax
| adc \$0,%rdx
| add -16($tptr,$i),$A0[1] # a[2]*a[0]+t[2]
| mov %rdx,$A0[0]
| adc \$0,$A0[0]
| mov $A0[1],-16($tptr,$i) # t[2]
|
| xor $A1[0],$A1[0]
|
| mov -8($aptr,$i),$ai # a[3]
| mul $a1 # a[2]*a[1]
| add %rax,$A1[0] # a[2]*a[1]+t[3]
| mov $ai,%rax
| adc \$0,%rdx
| add -8($tptr,$i),$A1[0]
| mov %rdx,$A1[1]
| adc \$0,$A1[1]
|
| mul $a0 # a[3]*a[0]
| add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
| mov $ai,%rax
| adc \$0,%rdx
| add $A1[0],$A0[0]
| mov %rdx,$A0[1]
| adc \$0,$A0[1]
| mov $A0[0],-8($tptr,$i) # t[3]
|
| lea ($i),$j
| jmp .Lsqr4x_inner
|
| .align 32
| .Lsqr4x_inner:
| mov ($aptr,$j),$ai # a[4]
| mul $a1 # a[3]*a[1]
| add %rax,$A1[1] # a[3]*a[1]+t[4]
| mov $ai,%rax
| mov %rdx,$A1[0]
| adc \$0,$A1[0]
| add ($tptr,$j),$A1[1]
| adc \$0,$A1[0]
|
| .byte 0x67
| mul $a0 # a[4]*a[0]
| add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
| mov $ai,%rax # a[3]
| mov 8($aptr,$j),$ai # a[5]
| mov %rdx,$A0[0]
| adc \$0,$A0[0]
| add $A1[1],$A0[1]
| adc \$0,$A0[0]
|
| mul $a1 # a[4]*a[3]
| add %rax,$A1[0] # a[4]*a[3]+t[5]
| mov $A0[1],($tptr,$j) # t[4]
| mov $ai,%rax
| mov %rdx,$A1[1]
| adc \$0,$A1[1]
| add 8($tptr,$j),$A1[0]
| lea 16($j),$j # j++
| adc \$0,$A1[1]
|
| mul $a0 # a[5]*a[2]
| add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
| mov $ai,%rax
| adc \$0,%rdx
| add $A1[0],$A0[0]
| mov %rdx,$A0[1]
| adc \$0,$A0[1]
| mov $A0[0],-8($tptr,$j) # t[5], "preloaded t[1]" below
|
| cmp \$0,$j
| jne .Lsqr4x_inner
|
| .byte 0x67
| mul $a1 # a[5]*a[3]
| add %rax,$A1[1]
| adc \$0,%rdx
| add $A0[1],$A1[1]
| adc \$0,%rdx
|
| mov $A1[1],($tptr) # t[6], "preloaded t[2]" below
| mov %rdx,$A1[0]
| mov %rdx,8($tptr) # t[7], "preloaded t[3]" below
|
| add \$16,$i
| jnz .Lsqr4x_outer
|
| # comments apply to $num==4 case
| mov -32($aptr),$a0 # a[0]
| lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
| mov -24($aptr),%rax # a[1]
| lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
| mov -16($aptr),$ai # a[2]
| mov %rax,$a1
|
| mul $a0 # a[1]*a[0]
| add %rax,$A0[0] # a[1]*a[0]+t[1], preloaded t[1]
| mov $ai,%rax # a[2]
| mov %rdx,$A0[1]
| adc \$0,$A0[1]
|
| mul $a0 # a[2]*a[0]
| add %rax,$A0[1]
| mov $ai,%rax
| mov $A0[0],-24($tptr) # t[1]
| mov %rdx,$A0[0]
| adc \$0,$A0[0]
| add $A1[1],$A0[1] # a[2]*a[0]+t[2], preloaded t[2]
| mov -8($aptr),$ai # a[3]
| adc \$0,$A0[0]
|
| mul $a1 # a[2]*a[1]
| add %rax,$A1[0] # a[2]*a[1]+t[3], preloaded t[3]
| mov $ai,%rax
| mov $A0[1],-16($tptr) # t[2]
| mov %rdx,$A1[1]
| adc \$0,$A1[1]
|
| mul $a0 # a[3]*a[0]
| add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
| mov $ai,%rax
| mov %rdx,$A0[1]
| adc \$0,$A0[1]
| add $A1[0],$A0[0]
| adc \$0,$A0[1]
| mov $A0[0],-8($tptr) # t[3]
|
| mul $a1 # a[3]*a[1]
| add %rax,$A1[1]
| mov -16($aptr),%rax # a[2]
| adc \$0,%rdx
| add $A0[1],$A1[1]
| adc \$0,%rdx
|
| mov $A1[1],($tptr) # t[4]
| mov %rdx,$A1[0]
| mov %rdx,8($tptr) # t[5]
|
| mul $ai # a[2]*a[3]
| ___
| {
| my ($shift,$carry)=($a0,$a1);
| my @S=(@A1,$ai,$n0);
| $code.=<<___;
| add \$16,$i
| xor $shift,$shift
| sub $num,$i # $i=16-$num
| xor $carry,$carry
|
| add $A1[0],%rax # t[5]
| adc \$0,%rdx
| mov %rax,8($tptr) # t[5]
| mov %rdx,16($tptr) # t[6]
| mov $carry,24($tptr) # t[7]
|
| mov -16($aptr,$i),%rax # a[0]
| lea 48+8(%rsp),$tptr
| xor $A0[0],$A0[0] # t[0]
| mov 8($tptr),$A0[1] # t[1]
|
| lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[1] # | t[2*i]>>63
| mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
| mov $A0[1],$shift # shift=t[2*i+1]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
| adc %rax,$S[0]
| mov -8($aptr,$i),%rax # a[i+1] # prefetch
| mov $S[0],($tptr)
| adc %rdx,$S[1]
|
| lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
| mov $S[1],8($tptr)
| sbb $carry,$carry # mov cf,$carry
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[3] # | t[2*i]>>63
| mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
| mov $A0[1],$shift # shift=t[2*i+1]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
| adc %rax,$S[2]
| mov 0($aptr,$i),%rax # a[i+1] # prefetch
| mov $S[2],16($tptr)
| adc %rdx,$S[3]
| lea 16($i),$i
| mov $S[3],24($tptr)
| sbb $carry,$carry # mov cf,$carry
| lea 64($tptr),$tptr
| jmp .Lsqr4x_shift_n_add
|
| .align 32
| .Lsqr4x_shift_n_add:
| lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[1] # | t[2*i]>>63
| mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
| mov $A0[1],$shift # shift=t[2*i+1]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
| adc %rax,$S[0]
| mov -8($aptr,$i),%rax # a[i+1] # prefetch
| mov $S[0],-32($tptr)
| adc %rdx,$S[1]
|
| lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
| mov $S[1],-24($tptr)
| sbb $carry,$carry # mov cf,$carry
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[3] # | t[2*i]>>63
| mov 0($tptr),$A0[0] # t[2*i+2] # prefetch
| mov $A0[1],$shift # shift=t[2*i+1]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| mov 8($tptr),$A0[1] # t[2*i+2+1] # prefetch
| adc %rax,$S[2]
| mov 0($aptr,$i),%rax # a[i+1] # prefetch
| mov $S[2],-16($tptr)
| adc %rdx,$S[3]
|
| lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
| mov $S[3],-8($tptr)
| sbb $carry,$carry # mov cf,$carry
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[1] # | t[2*i]>>63
| mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
| mov $A0[1],$shift # shift=t[2*i+1]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
| adc %rax,$S[0]
| mov 8($aptr,$i),%rax # a[i+1] # prefetch
| mov $S[0],0($tptr)
| adc %rdx,$S[1]
|
| lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
| mov $S[1],8($tptr)
| sbb $carry,$carry # mov cf,$carry
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[3] # | t[2*i]>>63
| mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
| mov $A0[1],$shift # shift=t[2*i+1]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
| adc %rax,$S[2]
| mov 16($aptr,$i),%rax # a[i+1] # prefetch
| mov $S[2],16($tptr)
| adc %rdx,$S[3]
| mov $S[3],24($tptr)
| sbb $carry,$carry # mov cf,$carry
| lea 64($tptr),$tptr
| add \$32,$i
| jnz .Lsqr4x_shift_n_add
|
| lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
| .byte 0x67
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[1] # | t[2*i]>>63
| mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
| mov $A0[1],$shift # shift=t[2*i+1]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
| adc %rax,$S[0]
| mov -8($aptr),%rax # a[i+1] # prefetch
| mov $S[0],-32($tptr)
| adc %rdx,$S[1]
|
| lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1|shift
| mov $S[1],-24($tptr)
| sbb $carry,$carry # mov cf,$carry
| shr \$63,$A0[0]
| lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
| shr \$63,$A0[1]
| or $A0[0],$S[3] # | t[2*i]>>63
| mul %rax # a[i]*a[i]
| neg $carry # mov $carry,cf
| adc %rax,$S[2]
| adc %rdx,$S[3]
| mov $S[2],-16($tptr)
| mov $S[3],-8($tptr)
| ___
| }
| ######################################################################
| # Montgomery reduction part, "word-by-word" algorithm.
| #
| # This new path is inspired by multiple submissions from Intel, by
| # Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
| # Vinodh Gopal...
| {
| my ($nptr,$tptr,$carry,$m0)=("%rbp","%rdi","%rsi","%rbx");
|
| $code.=<<___;
| movq %xmm2,$nptr
| __bn_sqr8x_reduction:
| xor %rax,%rax
| lea ($nptr,$num),%rcx # end of n[]
| lea 48+8(%rsp,$num,2),%rdx # end of t[] buffer
| mov %rcx,0+8(%rsp)
| lea 48+8(%rsp,$num),$tptr # end of initial t[] window
| mov %rdx,8+8(%rsp)
| neg $num
| jmp .L8x_reduction_loop
|
| .align 32
| .L8x_reduction_loop:
| lea ($tptr,$num),$tptr # start of current t[] window
| .byte 0x66
| mov 8*0($tptr),$m0
| mov 8*1($tptr),%r9
| mov 8*2($tptr),%r10
| mov 8*3($tptr),%r11
| mov 8*4($tptr),%r12
| mov 8*5($tptr),%r13
| mov 8*6($tptr),%r14
| mov 8*7($tptr),%r15
| mov %rax,(%rdx) # store top-most carry bit
| lea 8*8($tptr),$tptr
|
| .byte 0x67
| mov $m0,%r8
| imulq 32+8(%rsp),$m0 # n0*a[0]
| mov 8*0($nptr),%rax # n[0]
| mov \$8,%ecx
| jmp .L8x_reduce
|
| .align 32
| .L8x_reduce:
| mulq $m0
| mov 8*1($nptr),%rax # n[1]
| neg %r8
| mov %rdx,%r8
| adc \$0,%r8
|
| mulq $m0
| add %rax,%r9
| mov 8*2($nptr),%rax
| adc \$0,%rdx
| add %r9,%r8
| mov $m0,48-8+8(%rsp,%rcx,8) # put aside n0*a[i]
| mov %rdx,%r9
| adc \$0,%r9
|
| mulq $m0
| add %rax,%r10
| mov 8*3($nptr),%rax
| adc \$0,%rdx
| add %r10,%r9
| mov 32+8(%rsp),$carry # pull n0, borrow $carry
| mov %rdx,%r10
| adc \$0,%r10
|
| mulq $m0
| add %rax,%r11
| mov 8*4($nptr),%rax
| adc \$0,%rdx
| imulq %r8,$carry # modulo-scheduled
| add %r11,%r10
| mov %rdx,%r11
| adc \$0,%r11
|
| mulq $m0
| add %rax,%r12
| mov 8*5($nptr),%rax
| adc \$0,%rdx
| add %r12,%r11
| mov %rdx,%r12
| adc \$0,%r12
|
| mulq $m0
| add %rax,%r13
| mov 8*6($nptr),%rax
| adc \$0,%rdx
| add %r13,%r12
| mov %rdx,%r13
| adc \$0,%r13
|
| mulq $m0
| add %rax,%r14
| mov 8*7($nptr),%rax
| adc \$0,%rdx
| add %r14,%r13
| mov %rdx,%r14
| adc \$0,%r14
|
| mulq $m0
| mov $carry,$m0 # n0*a[i]
| add %rax,%r15
| mov 8*0($nptr),%rax # n[0]
| adc \$0,%rdx
| add %r15,%r14
| mov %rdx,%r15
| adc \$0,%r15
|
| dec %ecx
| jnz .L8x_reduce
|
| lea 8*8($nptr),$nptr
| xor %rax,%rax
| mov 8+8(%rsp),%rdx # pull end of t[]
| cmp 0+8(%rsp),$nptr # end of n[]?
| jae .L8x_no_tail
|
| .byte 0x66
| add 8*0($tptr),%r8
| adc 8*1($tptr),%r9
| adc 8*2($tptr),%r10
| adc 8*3($tptr),%r11
| adc 8*4($tptr),%r12
| adc 8*5($tptr),%r13
| adc 8*6($tptr),%r14
| adc 8*7($tptr),%r15
| sbb $carry,$carry # top carry
|
| mov 48+56+8(%rsp),$m0 # pull n0*a[0]
| mov \$8,%ecx
| mov 8*0($nptr),%rax
| jmp .L8x_tail
|
| .align 32
| .L8x_tail:
| mulq $m0
| add %rax,%r8
| mov 8*1($nptr),%rax
| mov %r8,($tptr) # save result
| mov %rdx,%r8
| adc \$0,%r8
|
| mulq $m0
| add %rax,%r9
| mov 8*2($nptr),%rax
| adc \$0,%rdx
| add %r9,%r8
| lea 8($tptr),$tptr # $tptr++
| mov %rdx,%r9
| adc \$0,%r9
|
| mulq $m0
| add %rax,%r10
| mov 8*3($nptr),%rax
| adc \$0,%rdx
| add %r10,%r9
| mov %rdx,%r10
| adc \$0,%r10
|
| mulq $m0
| add %rax,%r11
| mov 8*4($nptr),%rax
| adc \$0,%rdx
| add %r11,%r10
| mov %rdx,%r11
| adc \$0,%r11
|
| mulq $m0
| add %rax,%r12
| mov 8*5($nptr),%rax
| adc \$0,%rdx
| add %r12,%r11
| mov %rdx,%r12
| adc \$0,%r12
|
| mulq $m0
| add %rax,%r13
| mov 8*6($nptr),%rax
| adc \$0,%rdx
| add %r13,%r12
| mov %rdx,%r13
| adc \$0,%r13
|
| mulq $m0
| add %rax,%r14
| mov 8*7($nptr),%rax
| adc \$0,%rdx
| add %r14,%r13
| mov %rdx,%r14
| adc \$0,%r14
|
| mulq $m0
| mov 48-16+8(%rsp,%rcx,8),$m0# pull n0*a[i]
| add %rax,%r15
| adc \$0,%rdx
| add %r15,%r14
| mov 8*0($nptr),%rax # pull n[0]
| mov %rdx,%r15
| adc \$0,%r15
|
| dec %ecx
| jnz .L8x_tail
|
| lea 8*8($nptr),$nptr
| mov 8+8(%rsp),%rdx # pull end of t[]
| cmp 0+8(%rsp),$nptr # end of n[]?
| jae .L8x_tail_done # break out of loop
|
| mov 48+56+8(%rsp),$m0 # pull n0*a[0]
| neg $carry
| mov 8*0($nptr),%rax # pull n[0]
| adc 8*0($tptr),%r8
| adc 8*1($tptr),%r9
| adc 8*2($tptr),%r10
| adc 8*3($tptr),%r11
| adc 8*4($tptr),%r12
| adc 8*5($tptr),%r13
| adc 8*6($tptr),%r14
| adc 8*7($tptr),%r15
| sbb $carry,$carry # top carry
|
| mov \$8,%ecx
| jmp .L8x_tail
|
| .align 32
| .L8x_tail_done:
| xor %rax,%rax
| add (%rdx),%r8 # can this overflow?
| adc \$0,%r9
| adc \$0,%r10
| adc \$0,%r11
| adc \$0,%r12
| adc \$0,%r13
| adc \$0,%r14
| adc \$0,%r15
| adc \$0,%rax
|
| neg $carry
| .L8x_no_tail:
| adc 8*0($tptr),%r8
| adc 8*1($tptr),%r9
| adc 8*2($tptr),%r10
| adc 8*3($tptr),%r11
| adc 8*4($tptr),%r12
| adc 8*5($tptr),%r13
| adc 8*6($tptr),%r14
| adc 8*7($tptr),%r15
| adc \$0,%rax # top-most carry
| mov -8($nptr),%rcx # np[num-1]
| xor $carry,$carry
|
| movq %xmm2,$nptr # restore $nptr
|
| mov %r8,8*0($tptr) # store top 512 bits
| mov %r9,8*1($tptr)
| movq %xmm3,$num # $num is %r9, can't be moved upwards
| mov %r10,8*2($tptr)
| mov %r11,8*3($tptr)
| mov %r12,8*4($tptr)
| mov %r13,8*5($tptr)
| mov %r14,8*6($tptr)
| mov %r15,8*7($tptr)
| lea 8*8($tptr),$tptr
|
| cmp %rdx,$tptr # end of t[]?
| jb .L8x_reduction_loop
| ret
| .cfi_endproc
| .size bn_sqr8x_internal,.-bn_sqr8x_internal
| ___
| }
| ##############################################################
| # Post-condition, 4x unrolled
| #
| {
| my ($tptr,$nptr)=("%rbx","%rbp");
| $code.=<<___;
| .type __bn_post4x_internal,\@abi-omnipotent
| .align 32
| __bn_post4x_internal:
| .cfi_startproc
| mov 8*0($nptr),%r12
| lea (%rdi,$num),$tptr # %rdi was $tptr above
| mov $num,%rcx
| movq %xmm1,$rptr # restore $rptr
| neg %rax
| movq %xmm1,$aptr # prepare for back-to-back call
| sar \$3+2,%rcx
| dec %r12 # so that after 'not' we get -n[0]
| xor %r10,%r10
| mov 8*1($nptr),%r13
| mov 8*2($nptr),%r14
| mov 8*3($nptr),%r15
| jmp .Lsqr4x_sub_entry
|
| .align 16
| .Lsqr4x_sub:
| mov 8*0($nptr),%r12
| mov 8*1($nptr),%r13
| mov 8*2($nptr),%r14
| mov 8*3($nptr),%r15
| .Lsqr4x_sub_entry:
| lea 8*4($nptr),$nptr
| not %r12
| not %r13
| not %r14
| not %r15
| and %rax,%r12
| and %rax,%r13
| and %rax,%r14
| and %rax,%r15
|
| neg %r10 # mov %r10,%cf
| adc 8*0($tptr),%r12
| adc 8*1($tptr),%r13
| adc 8*2($tptr),%r14
| adc 8*3($tptr),%r15
| mov %r12,8*0($rptr)
| lea 8*4($tptr),$tptr
| mov %r13,8*1($rptr)
| sbb %r10,%r10 # mov %cf,%r10
| mov %r14,8*2($rptr)
| mov %r15,8*3($rptr)
| lea 8*4($rptr),$rptr
|
| inc %rcx # pass %cf
| jnz .Lsqr4x_sub
|
| mov $num,%r10 # prepare for back-to-back call
| neg $num # restore $num
| ret
| .cfi_endproc
| .size __bn_post4x_internal,.-__bn_post4x_internal
| ___
| }
| {
| $code.=<<___;
| .globl bn_from_montgomery
| .type bn_from_montgomery,\@abi-omnipotent
| .align 32
| bn_from_montgomery:
| .cfi_startproc
| testl \$7,`($win64?"48(%rsp)":"%r9d")`
| jz bn_from_mont8x
| xor %eax,%eax
| ret
| .cfi_endproc
| .size bn_from_montgomery,.-bn_from_montgomery
|
| .type bn_from_mont8x,\@function,6
| .align 32
| bn_from_mont8x:
| .cfi_startproc
| .byte 0x67
| mov %rsp,%rax
| .cfi_def_cfa_register %rax
| push %rbx
| .cfi_push %rbx
| push %rbp
| .cfi_push %rbp
| push %r12
| .cfi_push %r12
| push %r13
| .cfi_push %r13
| push %r14
| .cfi_push %r14
| push %r15
| .cfi_push %r15
| .Lfrom_prologue:
|
| shl \$3,${num}d # convert $num to bytes
| lea ($num,$num,2),%r10 # 3*$num in bytes
| neg $num
| mov ($n0),$n0 # *n0
|
| ##############################################################
| # Ensure that stack frame doesn't alias with $rptr+3*$num
| # modulo 4096, which covers ret[num], am[num] and n[num]
| # (see bn_exp.c). The stack is allocated to aligned with
| # bn_power5's frame, and as bn_from_montgomery happens to be
| # last operation, we use the opportunity to cleanse it.
| #
| lea -320(%rsp,$num,2),%r11
| mov %rsp,%rbp
| sub $rptr,%r11
| and \$4095,%r11
| cmp %r11,%r10
| jb .Lfrom_sp_alt
| sub %r11,%rbp # align with $aptr
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
| jmp .Lfrom_sp_done
|
| .align 32
| .Lfrom_sp_alt:
| lea 4096-320(,$num,2),%r10
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
| sub %r10,%r11
| mov \$0,%r10
| cmovc %r10,%r11
| sub %r11,%rbp
| .Lfrom_sp_done:
| and \$-64,%rbp
| mov %rsp,%r11
| sub %rbp,%r11
| and \$-4096,%r11
| lea (%rbp,%r11),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lfrom_page_walk
| jmp .Lfrom_page_walk_done
|
| .Lfrom_page_walk:
| lea -4096(%rsp),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lfrom_page_walk
| .Lfrom_page_walk_done:
|
| mov $num,%r10
| neg $num
|
| ##############################################################
| # Stack layout
| #
| # +0 saved $num, used in reduction section
| # +8 &t[2*$num], used in reduction section
| # +32 saved *n0
| # +40 saved %rsp
| # +48 t[2*$num]
| #
| mov $n0, 32(%rsp)
| mov %rax, 40(%rsp) # save original %rsp
| .cfi_cfa_expression %rsp+40,deref,+8
| .Lfrom_body:
| mov $num,%r11
| lea 48(%rsp),%rax
| pxor %xmm0,%xmm0
| jmp .Lmul_by_1
|
| .align 32
| .Lmul_by_1:
| movdqu ($aptr),%xmm1
| movdqu 16($aptr),%xmm2
| movdqu 32($aptr),%xmm3
| movdqa %xmm0,(%rax,$num)
| movdqu 48($aptr),%xmm4
| movdqa %xmm0,16(%rax,$num)
| .byte 0x48,0x8d,0xb6,0x40,0x00,0x00,0x00 # lea 64($aptr),$aptr
| movdqa %xmm1,(%rax)
| movdqa %xmm0,32(%rax,$num)
| movdqa %xmm2,16(%rax)
| movdqa %xmm0,48(%rax,$num)
| movdqa %xmm3,32(%rax)
| movdqa %xmm4,48(%rax)
| lea 64(%rax),%rax
| sub \$64,%r11
| jnz .Lmul_by_1
|
| movq $rptr,%xmm1
| movq $nptr,%xmm2
| .byte 0x67
| mov $nptr,%rbp
| movq %r10, %xmm3 # -num
| ___
| $code.=<<___ if ($addx);
| mov OPENSSL_ia32cap_P+8(%rip),%r11d
| and \$0x80108,%r11d
| cmp \$0x80108,%r11d # check for AD*X+BMI2+BMI1
| jne .Lfrom_mont_nox
|
| lea (%rax,$num),$rptr
| call __bn_sqrx8x_reduction
| call __bn_postx4x_internal
|
| pxor %xmm0,%xmm0
| lea 48(%rsp),%rax
| jmp .Lfrom_mont_zero
|
| .align 32
| .Lfrom_mont_nox:
| ___
| $code.=<<___;
| call __bn_sqr8x_reduction
| call __bn_post4x_internal
|
| pxor %xmm0,%xmm0
| lea 48(%rsp),%rax
| jmp .Lfrom_mont_zero
|
| .align 32
| .Lfrom_mont_zero:
| mov 40(%rsp),%rsi # restore %rsp
| .cfi_def_cfa %rsi,8
| movdqa %xmm0,16*0(%rax)
| movdqa %xmm0,16*1(%rax)
| movdqa %xmm0,16*2(%rax)
| movdqa %xmm0,16*3(%rax)
| lea 16*4(%rax),%rax
| sub \$32,$num
| jnz .Lfrom_mont_zero
|
| mov \$1,%rax
| mov -48(%rsi),%r15
| .cfi_restore %r15
| mov -40(%rsi),%r14
| .cfi_restore %r14
| mov -32(%rsi),%r13
| .cfi_restore %r13
| mov -24(%rsi),%r12
| .cfi_restore %r12
| mov -16(%rsi),%rbp
| .cfi_restore %rbp
| mov -8(%rsi),%rbx
| .cfi_restore %rbx
| lea (%rsi),%rsp
| .cfi_def_cfa_register %rsp
| .Lfrom_epilogue:
| ret
| .cfi_endproc
| .size bn_from_mont8x,.-bn_from_mont8x
| ___
| }
| }}}
|
| if ($addx) {{{
| my $bp="%rdx"; # restore original value
|
| $code.=<<___;
| .type bn_mulx4x_mont_gather5,\@function,6
| .align 32
| bn_mulx4x_mont_gather5:
| .cfi_startproc
| mov %rsp,%rax
| .cfi_def_cfa_register %rax
| .Lmulx4x_enter:
| push %rbx
| .cfi_push %rbx
| push %rbp
| .cfi_push %rbp
| push %r12
| .cfi_push %r12
| push %r13
| .cfi_push %r13
| push %r14
| .cfi_push %r14
| push %r15
| .cfi_push %r15
| .Lmulx4x_prologue:
|
| shl \$3,${num}d # convert $num to bytes
| lea ($num,$num,2),%r10 # 3*$num in bytes
| neg $num # -$num
| mov ($n0),$n0 # *n0
|
| ##############################################################
| # Ensure that stack frame doesn't alias with $rptr+3*$num
| # modulo 4096, which covers ret[num], am[num] and n[num]
| # (see bn_exp.c). This is done to allow memory disambiguation
| # logic do its magic. [Extra [num] is allocated in order
| # to align with bn_power5's frame, which is cleansed after
| # completing exponentiation. Extra 256 bytes is for power mask
| # calculated from 7th argument, the index.]
| #
| lea -320(%rsp,$num,2),%r11
| mov %rsp,%rbp
| sub $rp,%r11
| and \$4095,%r11
| cmp %r11,%r10
| jb .Lmulx4xsp_alt
| sub %r11,%rbp # align with $aptr
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
| jmp .Lmulx4xsp_done
|
| .Lmulx4xsp_alt:
| lea 4096-320(,$num,2),%r10
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
| sub %r10,%r11
| mov \$0,%r10
| cmovc %r10,%r11
| sub %r11,%rbp
| .Lmulx4xsp_done:
| and \$-64,%rbp # ensure alignment
| mov %rsp,%r11
| sub %rbp,%r11
| and \$-4096,%r11
| lea (%rbp,%r11),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lmulx4x_page_walk
| jmp .Lmulx4x_page_walk_done
|
| .Lmulx4x_page_walk:
| lea -4096(%rsp),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lmulx4x_page_walk
| .Lmulx4x_page_walk_done:
|
| ##############################################################
| # Stack layout
| # +0 -num
| # +8 off-loaded &b[i]
| # +16 end of b[num]
| # +24 inner counter
| # +32 saved n0
| # +40 saved %rsp
| # +48
| # +56 saved rp
| # +64 tmp[num+1]
| #
| mov $n0, 32(%rsp) # save *n0
| mov %rax,40(%rsp) # save original %rsp
| .cfi_cfa_expression %rsp+40,deref,+8
| .Lmulx4x_body:
| call mulx4x_internal
|
| mov 40(%rsp),%rsi # restore %rsp
| .cfi_def_cfa %rsi,8
| mov \$1,%rax
|
| mov -48(%rsi),%r15
| .cfi_restore %r15
| mov -40(%rsi),%r14
| .cfi_restore %r14
| mov -32(%rsi),%r13
| .cfi_restore %r13
| mov -24(%rsi),%r12
| .cfi_restore %r12
| mov -16(%rsi),%rbp
| .cfi_restore %rbp
| mov -8(%rsi),%rbx
| .cfi_restore %rbx
| lea (%rsi),%rsp
| .cfi_def_cfa_register %rsp
| .Lmulx4x_epilogue:
| ret
| .cfi_endproc
| .size bn_mulx4x_mont_gather5,.-bn_mulx4x_mont_gather5
|
| .type mulx4x_internal,\@abi-omnipotent
| .align 32
| mulx4x_internal:
| .cfi_startproc
| mov $num,8(%rsp) # save -$num (it was in bytes)
| mov $num,%r10
| neg $num # restore $num
| shl \$5,$num
| neg %r10 # restore $num
| lea 128($bp,$num),%r13 # end of powers table (+size optimization)
| shr \$5+5,$num
| movd `($win64?56:8)`(%rax),%xmm5 # load 7th argument
| sub \$1,$num
| lea .Linc(%rip),%rax
| mov %r13,16+8(%rsp) # end of b[num]
| mov $num,24+8(%rsp) # inner counter
| mov $rp, 56+8(%rsp) # save $rp
| ___
| my ($aptr, $bptr, $nptr, $tptr, $mi, $bi, $zero, $num)=
| ("%rsi","%rdi","%rcx","%rbx","%r8","%r9","%rbp","%rax");
| my $rptr=$bptr;
| my $STRIDE=2**5*8; # 5 is "window size"
| my $N=$STRIDE/4; # should match cache line size
| $code.=<<___;
| movdqa 0(%rax),%xmm0 # 00000001000000010000000000000000
| movdqa 16(%rax),%xmm1 # 00000002000000020000000200000002
| lea 88-112(%rsp,%r10),%r10 # place the mask after tp[num+1] (+ICache optimization)
| lea 128($bp),$bptr # size optimization
|
| pshufd \$0,%xmm5,%xmm5 # broadcast index
| movdqa %xmm1,%xmm4
| .byte 0x67
| movdqa %xmm1,%xmm2
| ___
| ########################################################################
| # calculate mask by comparing 0..31 to index and save result to stack
| #
| $code.=<<___;
| .byte 0x67
| paddd %xmm0,%xmm1
| pcmpeqd %xmm5,%xmm0 # compare to 1,0
| movdqa %xmm4,%xmm3
| ___
| for($i=0;$i<$STRIDE/16-4;$i+=4) {
| $code.=<<___;
| paddd %xmm1,%xmm2
| pcmpeqd %xmm5,%xmm1 # compare to 3,2
| movdqa %xmm0,`16*($i+0)+112`(%r10)
| movdqa %xmm4,%xmm0
|
| paddd %xmm2,%xmm3
| pcmpeqd %xmm5,%xmm2 # compare to 5,4
| movdqa %xmm1,`16*($i+1)+112`(%r10)
| movdqa %xmm4,%xmm1
|
| paddd %xmm3,%xmm0
| pcmpeqd %xmm5,%xmm3 # compare to 7,6
| movdqa %xmm2,`16*($i+2)+112`(%r10)
| movdqa %xmm4,%xmm2
|
| paddd %xmm0,%xmm1
| pcmpeqd %xmm5,%xmm0
| movdqa %xmm3,`16*($i+3)+112`(%r10)
| movdqa %xmm4,%xmm3
| ___
| }
| $code.=<<___; # last iteration can be optimized
| .byte 0x67
| paddd %xmm1,%xmm2
| pcmpeqd %xmm5,%xmm1
| movdqa %xmm0,`16*($i+0)+112`(%r10)
|
| paddd %xmm2,%xmm3
| pcmpeqd %xmm5,%xmm2
| movdqa %xmm1,`16*($i+1)+112`(%r10)
|
| pcmpeqd %xmm5,%xmm3
| movdqa %xmm2,`16*($i+2)+112`(%r10)
|
| pand `16*($i+0)-128`($bptr),%xmm0 # while it's still in register
| pand `16*($i+1)-128`($bptr),%xmm1
| pand `16*($i+2)-128`($bptr),%xmm2
| movdqa %xmm3,`16*($i+3)+112`(%r10)
| pand `16*($i+3)-128`($bptr),%xmm3
| por %xmm2,%xmm0
| por %xmm3,%xmm1
| ___
| for($i=0;$i<$STRIDE/16-4;$i+=4) {
| $code.=<<___;
| movdqa `16*($i+0)-128`($bptr),%xmm4
| movdqa `16*($i+1)-128`($bptr),%xmm5
| movdqa `16*($i+2)-128`($bptr),%xmm2
| pand `16*($i+0)+112`(%r10),%xmm4
| movdqa `16*($i+3)-128`($bptr),%xmm3
| pand `16*($i+1)+112`(%r10),%xmm5
| por %xmm4,%xmm0
| pand `16*($i+2)+112`(%r10),%xmm2
| por %xmm5,%xmm1
| pand `16*($i+3)+112`(%r10),%xmm3
| por %xmm2,%xmm0
| por %xmm3,%xmm1
| ___
| }
| $code.=<<___;
| pxor %xmm1,%xmm0
| pshufd \$0x4e,%xmm0,%xmm1
| por %xmm1,%xmm0
| lea $STRIDE($bptr),$bptr
| movq %xmm0,%rdx # bp[0]
| lea 64+8*4+8(%rsp),$tptr
|
| mov %rdx,$bi
| mulx 0*8($aptr),$mi,%rax # a[0]*b[0]
| mulx 1*8($aptr),%r11,%r12 # a[1]*b[0]
| add %rax,%r11
| mulx 2*8($aptr),%rax,%r13 # ...
| adc %rax,%r12
| adc \$0,%r13
| mulx 3*8($aptr),%rax,%r14
|
| mov $mi,%r15
| imulq 32+8(%rsp),$mi # "t[0]"*n0
| xor $zero,$zero # cf=0, of=0
| mov $mi,%rdx
|
| mov $bptr,8+8(%rsp) # off-load &b[i]
|
| lea 4*8($aptr),$aptr
| adcx %rax,%r13
| adcx $zero,%r14 # cf=0
|
| mulx 0*8($nptr),%rax,%r10
| adcx %rax,%r15 # discarded
| adox %r11,%r10
| mulx 1*8($nptr),%rax,%r11
| adcx %rax,%r10
| adox %r12,%r11
| mulx 2*8($nptr),%rax,%r12
| mov 24+8(%rsp),$bptr # counter value
| mov %r10,-8*4($tptr)
| adcx %rax,%r11
| adox %r13,%r12
| mulx 3*8($nptr),%rax,%r15
| mov $bi,%rdx
| mov %r11,-8*3($tptr)
| adcx %rax,%r12
| adox $zero,%r15 # of=0
| lea 4*8($nptr),$nptr
| mov %r12,-8*2($tptr)
| jmp .Lmulx4x_1st
|
| .align 32
| .Lmulx4x_1st:
| adcx $zero,%r15 # cf=0, modulo-scheduled
| mulx 0*8($aptr),%r10,%rax # a[4]*b[0]
| adcx %r14,%r10
| mulx 1*8($aptr),%r11,%r14 # a[5]*b[0]
| adcx %rax,%r11
| mulx 2*8($aptr),%r12,%rax # ...
| adcx %r14,%r12
| mulx 3*8($aptr),%r13,%r14
| .byte 0x67,0x67
| mov $mi,%rdx
| adcx %rax,%r13
| adcx $zero,%r14 # cf=0
| lea 4*8($aptr),$aptr
| lea 4*8($tptr),$tptr
|
| adox %r15,%r10
| mulx 0*8($nptr),%rax,%r15
| adcx %rax,%r10
| adox %r15,%r11
| mulx 1*8($nptr),%rax,%r15
| adcx %rax,%r11
| adox %r15,%r12
| mulx 2*8($nptr),%rax,%r15
| mov %r10,-5*8($tptr)
| adcx %rax,%r12
| mov %r11,-4*8($tptr)
| adox %r15,%r13
| mulx 3*8($nptr),%rax,%r15
| mov $bi,%rdx
| mov %r12,-3*8($tptr)
| adcx %rax,%r13
| adox $zero,%r15
| lea 4*8($nptr),$nptr
| mov %r13,-2*8($tptr)
|
| dec $bptr # of=0, pass cf
| jnz .Lmulx4x_1st
|
| mov 8(%rsp),$num # load -num
| adc $zero,%r15 # modulo-scheduled
| lea ($aptr,$num),$aptr # rewind $aptr
| add %r15,%r14
| mov 8+8(%rsp),$bptr # re-load &b[i]
| adc $zero,$zero # top-most carry
| mov %r14,-1*8($tptr)
| jmp .Lmulx4x_outer
|
| .align 32
| .Lmulx4x_outer:
| lea 16-256($tptr),%r10 # where 256-byte mask is (+density control)
| pxor %xmm4,%xmm4
| .byte 0x67,0x67
| pxor %xmm5,%xmm5
| ___
| for($i=0;$i<$STRIDE/16;$i+=4) {
| $code.=<<___;
| movdqa `16*($i+0)-128`($bptr),%xmm0
| movdqa `16*($i+1)-128`($bptr),%xmm1
| movdqa `16*($i+2)-128`($bptr),%xmm2
| pand `16*($i+0)+256`(%r10),%xmm0
| movdqa `16*($i+3)-128`($bptr),%xmm3
| pand `16*($i+1)+256`(%r10),%xmm1
| por %xmm0,%xmm4
| pand `16*($i+2)+256`(%r10),%xmm2
| por %xmm1,%xmm5
| pand `16*($i+3)+256`(%r10),%xmm3
| por %xmm2,%xmm4
| por %xmm3,%xmm5
| ___
| }
| $code.=<<___;
| por %xmm5,%xmm4
| pshufd \$0x4e,%xmm4,%xmm0
| por %xmm4,%xmm0
| lea $STRIDE($bptr),$bptr
| movq %xmm0,%rdx # m0=bp[i]
|
| mov $zero,($tptr) # save top-most carry
| lea 4*8($tptr,$num),$tptr # rewind $tptr
| mulx 0*8($aptr),$mi,%r11 # a[0]*b[i]
| xor $zero,$zero # cf=0, of=0
| mov %rdx,$bi
| mulx 1*8($aptr),%r14,%r12 # a[1]*b[i]
| adox -4*8($tptr),$mi # +t[0]
| adcx %r14,%r11
| mulx 2*8($aptr),%r15,%r13 # ...
| adox -3*8($tptr),%r11
| adcx %r15,%r12
| mulx 3*8($aptr),%rdx,%r14
| adox -2*8($tptr),%r12
| adcx %rdx,%r13
| lea ($nptr,$num),$nptr # rewind $nptr
| lea 4*8($aptr),$aptr
| adox -1*8($tptr),%r13
| adcx $zero,%r14
| adox $zero,%r14
|
| mov $mi,%r15
| imulq 32+8(%rsp),$mi # "t[0]"*n0
|
| mov $mi,%rdx
| xor $zero,$zero # cf=0, of=0
| mov $bptr,8+8(%rsp) # off-load &b[i]
|
| mulx 0*8($nptr),%rax,%r10
| adcx %rax,%r15 # discarded
| adox %r11,%r10
| mulx 1*8($nptr),%rax,%r11
| adcx %rax,%r10
| adox %r12,%r11
| mulx 2*8($nptr),%rax,%r12
| adcx %rax,%r11
| adox %r13,%r12
| mulx 3*8($nptr),%rax,%r15
| mov $bi,%rdx
| mov 24+8(%rsp),$bptr # counter value
| mov %r10,-8*4($tptr)
| adcx %rax,%r12
| mov %r11,-8*3($tptr)
| adox $zero,%r15 # of=0
| mov %r12,-8*2($tptr)
| lea 4*8($nptr),$nptr
| jmp .Lmulx4x_inner
|
| .align 32
| .Lmulx4x_inner:
| mulx 0*8($aptr),%r10,%rax # a[4]*b[i]
| adcx $zero,%r15 # cf=0, modulo-scheduled
| adox %r14,%r10
| mulx 1*8($aptr),%r11,%r14 # a[5]*b[i]
| adcx 0*8($tptr),%r10
| adox %rax,%r11
| mulx 2*8($aptr),%r12,%rax # ...
| adcx 1*8($tptr),%r11
| adox %r14,%r12
| mulx 3*8($aptr),%r13,%r14
| mov $mi,%rdx
| adcx 2*8($tptr),%r12
| adox %rax,%r13
| adcx 3*8($tptr),%r13
| adox $zero,%r14 # of=0
| lea 4*8($aptr),$aptr
| lea 4*8($tptr),$tptr
| adcx $zero,%r14 # cf=0
|
| adox %r15,%r10
| mulx 0*8($nptr),%rax,%r15
| adcx %rax,%r10
| adox %r15,%r11
| mulx 1*8($nptr),%rax,%r15
| adcx %rax,%r11
| adox %r15,%r12
| mulx 2*8($nptr),%rax,%r15
| mov %r10,-5*8($tptr)
| adcx %rax,%r12
| adox %r15,%r13
| mov %r11,-4*8($tptr)
| mulx 3*8($nptr),%rax,%r15
| mov $bi,%rdx
| lea 4*8($nptr),$nptr
| mov %r12,-3*8($tptr)
| adcx %rax,%r13
| adox $zero,%r15
| mov %r13,-2*8($tptr)
|
| dec $bptr # of=0, pass cf
| jnz .Lmulx4x_inner
|
| mov 0+8(%rsp),$num # load -num
| adc $zero,%r15 # modulo-scheduled
| sub 0*8($tptr),$bptr # pull top-most carry to %cf
| mov 8+8(%rsp),$bptr # re-load &b[i]
| mov 16+8(%rsp),%r10
| adc %r15,%r14
| lea ($aptr,$num),$aptr # rewind $aptr
| adc $zero,$zero # top-most carry
| mov %r14,-1*8($tptr)
|
| cmp %r10,$bptr
| jb .Lmulx4x_outer
|
| mov -8($nptr),%r10
| mov $zero,%r8
| mov ($nptr,$num),%r12
| lea ($nptr,$num),%rbp # rewind $nptr
| mov $num,%rcx
| lea ($tptr,$num),%rdi # rewind $tptr
| xor %eax,%eax
| xor %r15,%r15
| sub %r14,%r10 # compare top-most words
| adc %r15,%r15
| or %r15,%r8
| sar \$3+2,%rcx
| sub %r8,%rax # %rax=-%r8
| mov 56+8(%rsp),%rdx # restore rp
| dec %r12 # so that after 'not' we get -n[0]
| mov 8*1(%rbp),%r13
| xor %r8,%r8
| mov 8*2(%rbp),%r14
| mov 8*3(%rbp),%r15
| jmp .Lsqrx4x_sub_entry # common post-condition
| .cfi_endproc
| .size mulx4x_internal,.-mulx4x_internal
| ___
| } {
| ######################################################################
| # void bn_power5(
| my $rptr="%rdi"; # BN_ULONG *rptr,
| my $aptr="%rsi"; # const BN_ULONG *aptr,
| my $bptr="%rdx"; # const void *table,
| my $nptr="%rcx"; # const BN_ULONG *nptr,
| my $n0 ="%r8"; # const BN_ULONG *n0);
| my $num ="%r9"; # int num, has to be divisible by 8
| # int pwr);
|
| my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
| my @A0=("%r10","%r11");
| my @A1=("%r12","%r13");
| my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
|
| $code.=<<___;
| .type bn_powerx5,\@function,6
| .align 32
| bn_powerx5:
| .cfi_startproc
| mov %rsp,%rax
| .cfi_def_cfa_register %rax
| .Lpowerx5_enter:
| push %rbx
| .cfi_push %rbx
| push %rbp
| .cfi_push %rbp
| push %r12
| .cfi_push %r12
| push %r13
| .cfi_push %r13
| push %r14
| .cfi_push %r14
| push %r15
| .cfi_push %r15
| .Lpowerx5_prologue:
|
| shl \$3,${num}d # convert $num to bytes
| lea ($num,$num,2),%r10 # 3*$num in bytes
| neg $num
| mov ($n0),$n0 # *n0
|
| ##############################################################
| # Ensure that stack frame doesn't alias with $rptr+3*$num
| # modulo 4096, which covers ret[num], am[num] and n[num]
| # (see bn_exp.c). This is done to allow memory disambiguation
| # logic do its magic. [Extra 256 bytes is for power mask
| # calculated from 7th argument, the index.]
| #
| lea -320(%rsp,$num,2),%r11
| mov %rsp,%rbp
| sub $rptr,%r11
| and \$4095,%r11
| cmp %r11,%r10
| jb .Lpwrx_sp_alt
| sub %r11,%rbp # align with $aptr
| lea -320(%rbp,$num,2),%rbp # future alloca(frame+2*$num*8+256)
| jmp .Lpwrx_sp_done
|
| .align 32
| .Lpwrx_sp_alt:
| lea 4096-320(,$num,2),%r10
| lea -320(%rbp,$num,2),%rbp # alloca(frame+2*$num*8+256)
| sub %r10,%r11
| mov \$0,%r10
| cmovc %r10,%r11
| sub %r11,%rbp
| .Lpwrx_sp_done:
| and \$-64,%rbp
| mov %rsp,%r11
| sub %rbp,%r11
| and \$-4096,%r11
| lea (%rbp,%r11),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lpwrx_page_walk
| jmp .Lpwrx_page_walk_done
|
| .Lpwrx_page_walk:
| lea -4096(%rsp),%rsp
| mov (%rsp),%r10
| cmp %rbp,%rsp
| ja .Lpwrx_page_walk
| .Lpwrx_page_walk_done:
|
| mov $num,%r10
| neg $num
|
| ##############################################################
| # Stack layout
| #
| # +0 saved $num, used in reduction section
| # +8 &t[2*$num], used in reduction section
| # +16 intermediate carry bit
| # +24 top-most carry bit, used in reduction section
| # +32 saved *n0
| # +40 saved %rsp
| # +48 t[2*$num]
| #
| pxor %xmm0,%xmm0
| movq $rptr,%xmm1 # save $rptr
| movq $nptr,%xmm2 # save $nptr
| movq %r10, %xmm3 # -$num
| movq $bptr,%xmm4
| mov $n0, 32(%rsp)
| mov %rax, 40(%rsp) # save original %rsp
| .cfi_cfa_expression %rsp+40,deref,+8
| .Lpowerx5_body:
|
| call __bn_sqrx8x_internal
| call __bn_postx4x_internal
| call __bn_sqrx8x_internal
| call __bn_postx4x_internal
| call __bn_sqrx8x_internal
| call __bn_postx4x_internal
| call __bn_sqrx8x_internal
| call __bn_postx4x_internal
| call __bn_sqrx8x_internal
| call __bn_postx4x_internal
|
| mov %r10,$num # -num
| mov $aptr,$rptr
| movq %xmm2,$nptr
| movq %xmm4,$bptr
| mov 40(%rsp),%rax
|
| call mulx4x_internal
|
| mov 40(%rsp),%rsi # restore %rsp
| .cfi_def_cfa %rsi,8
| mov \$1,%rax
|
| mov -48(%rsi),%r15
| .cfi_restore %r15
| mov -40(%rsi),%r14
| .cfi_restore %r14
| mov -32(%rsi),%r13
| .cfi_restore %r13
| mov -24(%rsi),%r12
| .cfi_restore %r12
| mov -16(%rsi),%rbp
| .cfi_restore %rbp
| mov -8(%rsi),%rbx
| .cfi_restore %rbx
| lea (%rsi),%rsp
| .cfi_def_cfa_register %rsp
| .Lpowerx5_epilogue:
| ret
| .cfi_endproc
| .size bn_powerx5,.-bn_powerx5
|
| .globl bn_sqrx8x_internal
| .hidden bn_sqrx8x_internal
| .type bn_sqrx8x_internal,\@abi-omnipotent
| .align 32
| bn_sqrx8x_internal:
| __bn_sqrx8x_internal:
| .cfi_startproc
| ##################################################################
| # Squaring part:
| #
| # a) multiply-n-add everything but a[i]*a[i];
| # b) shift result of a) by 1 to the left and accumulate
| # a[i]*a[i] products;
| #
| ##################################################################
| # 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]
| # a[1]a[0]
| # a[2]a[0]
| # a[3]a[0]
| # a[2]a[1]
| # a[3]a[1]
| # a[3]a[2]
| #
| # a[4]a[0]
| # a[5]a[0]
| # a[6]a[0]
| # a[7]a[0]
| # a[4]a[1]
| # a[5]a[1]
| # a[6]a[1]
| # a[7]a[1]
| # a[4]a[2]
| # a[5]a[2]
| # a[6]a[2]
| # a[7]a[2]
| # a[4]a[3]
| # a[5]a[3]
| # a[6]a[3]
| # a[7]a[3]
| #
| # a[5]a[4]
| # a[6]a[4]
| # a[7]a[4]
| # a[6]a[5]
| # a[7]a[5]
| # a[7]a[6]
| # 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]
| ___
| {
| my ($zero,$carry)=("%rbp","%rcx");
| my $aaptr=$zero;
| $code.=<<___;
| lea 48+8(%rsp),$tptr
| lea ($aptr,$num),$aaptr
| mov $num,0+8(%rsp) # save $num
| mov $aaptr,8+8(%rsp) # save end of $aptr
| jmp .Lsqr8x_zero_start
|
| .align 32
| .byte 0x66,0x66,0x66,0x2e,0x0f,0x1f,0x84,0x00,0x00,0x00,0x00,0x00
| .Lsqrx8x_zero:
| .byte 0x3e
| movdqa %xmm0,0*8($tptr)
| movdqa %xmm0,2*8($tptr)
| movdqa %xmm0,4*8($tptr)
| movdqa %xmm0,6*8($tptr)
| .Lsqr8x_zero_start: # aligned at 32
| movdqa %xmm0,8*8($tptr)
| movdqa %xmm0,10*8($tptr)
| movdqa %xmm0,12*8($tptr)
| movdqa %xmm0,14*8($tptr)
| lea 16*8($tptr),$tptr
| sub \$64,$num
| jnz .Lsqrx8x_zero
|
| mov 0*8($aptr),%rdx # a[0], modulo-scheduled
| #xor %r9,%r9 # t[1], ex-$num, zero already
| xor %r10,%r10
| xor %r11,%r11
| xor %r12,%r12
| xor %r13,%r13
| xor %r14,%r14
| xor %r15,%r15
| lea 48+8(%rsp),$tptr
| xor $zero,$zero # cf=0, cf=0
| jmp .Lsqrx8x_outer_loop
|
| .align 32
| .Lsqrx8x_outer_loop:
| mulx 1*8($aptr),%r8,%rax # a[1]*a[0]
| adcx %r9,%r8 # a[1]*a[0]+=t[1]
| adox %rax,%r10
| mulx 2*8($aptr),%r9,%rax # a[2]*a[0]
| adcx %r10,%r9
| adox %rax,%r11
| .byte 0xc4,0xe2,0xab,0xf6,0x86,0x18,0x00,0x00,0x00 # mulx 3*8($aptr),%r10,%rax # ...
| adcx %r11,%r10
| adox %rax,%r12
| .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x20,0x00,0x00,0x00 # mulx 4*8($aptr),%r11,%rax
| adcx %r12,%r11
| adox %rax,%r13
| mulx 5*8($aptr),%r12,%rax
| adcx %r13,%r12
| adox %rax,%r14
| mulx 6*8($aptr),%r13,%rax
| adcx %r14,%r13
| adox %r15,%rax
| mulx 7*8($aptr),%r14,%r15
| mov 1*8($aptr),%rdx # a[1]
| adcx %rax,%r14
| adox $zero,%r15
| adc 8*8($tptr),%r15
| mov %r8,1*8($tptr) # t[1]
| mov %r9,2*8($tptr) # t[2]
| sbb $carry,$carry # mov %cf,$carry
| xor $zero,$zero # cf=0, of=0
|
|
| mulx 2*8($aptr),%r8,%rbx # a[2]*a[1]
| mulx 3*8($aptr),%r9,%rax # a[3]*a[1]
| adcx %r10,%r8
| adox %rbx,%r9
| mulx 4*8($aptr),%r10,%rbx # ...
| adcx %r11,%r9
| adox %rax,%r10
| .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x28,0x00,0x00,0x00 # mulx 5*8($aptr),%r11,%rax
| adcx %r12,%r10
| adox %rbx,%r11
| .byte 0xc4,0xe2,0x9b,0xf6,0x9e,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r12,%rbx
| adcx %r13,%r11
| adox %r14,%r12
| .byte 0xc4,0x62,0x93,0xf6,0xb6,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r13,%r14
| mov 2*8($aptr),%rdx # a[2]
| adcx %rax,%r12
| adox %rbx,%r13
| adcx %r15,%r13
| adox $zero,%r14 # of=0
| adcx $zero,%r14 # cf=0
|
| mov %r8,3*8($tptr) # t[3]
| mov %r9,4*8($tptr) # t[4]
|
| mulx 3*8($aptr),%r8,%rbx # a[3]*a[2]
| mulx 4*8($aptr),%r9,%rax # a[4]*a[2]
| adcx %r10,%r8
| adox %rbx,%r9
| mulx 5*8($aptr),%r10,%rbx # ...
| adcx %r11,%r9
| adox %rax,%r10
| .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r11,%rax
| adcx %r12,%r10
| adox %r13,%r11
| .byte 0xc4,0x62,0x9b,0xf6,0xae,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r12,%r13
| .byte 0x3e
| mov 3*8($aptr),%rdx # a[3]
| adcx %rbx,%r11
| adox %rax,%r12
| adcx %r14,%r12
| mov %r8,5*8($tptr) # t[5]
| mov %r9,6*8($tptr) # t[6]
| mulx 4*8($aptr),%r8,%rax # a[4]*a[3]
| adox $zero,%r13 # of=0
| adcx $zero,%r13 # cf=0
|
| mulx 5*8($aptr),%r9,%rbx # a[5]*a[3]
| adcx %r10,%r8
| adox %rax,%r9
| mulx 6*8($aptr),%r10,%rax # ...
| adcx %r11,%r9
| adox %r12,%r10
| mulx 7*8($aptr),%r11,%r12
| mov 4*8($aptr),%rdx # a[4]
| mov 5*8($aptr),%r14 # a[5]
| adcx %rbx,%r10
| adox %rax,%r11
| mov 6*8($aptr),%r15 # a[6]
| adcx %r13,%r11
| adox $zero,%r12 # of=0
| adcx $zero,%r12 # cf=0
|
| mov %r8,7*8($tptr) # t[7]
| mov %r9,8*8($tptr) # t[8]
|
| mulx %r14,%r9,%rax # a[5]*a[4]
| mov 7*8($aptr),%r8 # a[7]
| adcx %r10,%r9
| mulx %r15,%r10,%rbx # a[6]*a[4]
| adox %rax,%r10
| adcx %r11,%r10
| mulx %r8,%r11,%rax # a[7]*a[4]
| mov %r14,%rdx # a[5]
| adox %rbx,%r11
| adcx %r12,%r11
| #adox $zero,%rax # of=0
| adcx $zero,%rax # cf=0
|
| mulx %r15,%r14,%rbx # a[6]*a[5]
| mulx %r8,%r12,%r13 # a[7]*a[5]
| mov %r15,%rdx # a[6]
| lea 8*8($aptr),$aptr
| adcx %r14,%r11
| adox %rbx,%r12
| adcx %rax,%r12
| adox $zero,%r13
|
| .byte 0x67,0x67
| mulx %r8,%r8,%r14 # a[7]*a[6]
| adcx %r8,%r13
| adcx $zero,%r14
|
| cmp 8+8(%rsp),$aptr
| je .Lsqrx8x_outer_break
|
| neg $carry # mov $carry,%cf
| mov \$-8,%rcx
| mov $zero,%r15
| mov 8*8($tptr),%r8
| adcx 9*8($tptr),%r9 # +=t[9]
| adcx 10*8($tptr),%r10 # ...
| adcx 11*8($tptr),%r11
| adc 12*8($tptr),%r12
| adc 13*8($tptr),%r13
| adc 14*8($tptr),%r14
| adc 15*8($tptr),%r15
| lea ($aptr),$aaptr
| lea 2*64($tptr),$tptr
| sbb %rax,%rax # mov %cf,$carry
|
| mov -64($aptr),%rdx # a[0]
| mov %rax,16+8(%rsp) # offload $carry
| mov $tptr,24+8(%rsp)
|
| #lea 8*8($tptr),$tptr # see 2*8*8($tptr) above
| xor %eax,%eax # cf=0, of=0
| jmp .Lsqrx8x_loop
|
| .align 32
| .Lsqrx8x_loop:
| mov %r8,%rbx
| mulx 0*8($aaptr),%rax,%r8 # a[8]*a[i]
| adcx %rax,%rbx # +=t[8]
| adox %r9,%r8
|
| mulx 1*8($aaptr),%rax,%r9 # ...
| adcx %rax,%r8
| adox %r10,%r9
|
| mulx 2*8($aaptr),%rax,%r10
| adcx %rax,%r9
| adox %r11,%r10
|
| mulx 3*8($aaptr),%rax,%r11
| adcx %rax,%r10
| adox %r12,%r11
|
| .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 4*8($aaptr),%rax,%r12
| adcx %rax,%r11
| adox %r13,%r12
|
| mulx 5*8($aaptr),%rax,%r13
| adcx %rax,%r12
| adox %r14,%r13
|
| mulx 6*8($aaptr),%rax,%r14
| mov %rbx,($tptr,%rcx,8) # store t[8+i]
| mov \$0,%ebx
| adcx %rax,%r13
| adox %r15,%r14
|
| .byte 0xc4,0x62,0xfb,0xf6,0xbd,0x38,0x00,0x00,0x00 # mulx 7*8($aaptr),%rax,%r15
| mov 8($aptr,%rcx,8),%rdx # a[i]
| adcx %rax,%r14
| adox %rbx,%r15 # %rbx is 0, of=0
| adcx %rbx,%r15 # cf=0
|
| .byte 0x67
| inc %rcx # of=0
| jnz .Lsqrx8x_loop
|
| lea 8*8($aaptr),$aaptr
| mov \$-8,%rcx
| cmp 8+8(%rsp),$aaptr # done?
| je .Lsqrx8x_break
|
| sub 16+8(%rsp),%rbx # mov 16(%rsp),%cf
| .byte 0x66
| mov -64($aptr),%rdx
| adcx 0*8($tptr),%r8
| adcx 1*8($tptr),%r9
| adc 2*8($tptr),%r10
| adc 3*8($tptr),%r11
| adc 4*8($tptr),%r12
| adc 5*8($tptr),%r13
| adc 6*8($tptr),%r14
| adc 7*8($tptr),%r15
| lea 8*8($tptr),$tptr
| .byte 0x67
| sbb %rax,%rax # mov %cf,%rax
| xor %ebx,%ebx # cf=0, of=0
| mov %rax,16+8(%rsp) # offload carry
| jmp .Lsqrx8x_loop
|
| .align 32
| .Lsqrx8x_break:
| xor $zero,$zero
| sub 16+8(%rsp),%rbx # mov 16(%rsp),%cf
| adcx $zero,%r8
| mov 24+8(%rsp),$carry # initial $tptr, borrow $carry
| adcx $zero,%r9
| mov 0*8($aptr),%rdx # a[8], modulo-scheduled
| adc \$0,%r10
| mov %r8,0*8($tptr)
| adc \$0,%r11
| adc \$0,%r12
| adc \$0,%r13
| adc \$0,%r14
| adc \$0,%r15
| cmp $carry,$tptr # cf=0, of=0
| je .Lsqrx8x_outer_loop
|
| mov %r9,1*8($tptr)
| mov 1*8($carry),%r9
| mov %r10,2*8($tptr)
| mov 2*8($carry),%r10
| mov %r11,3*8($tptr)
| mov 3*8($carry),%r11
| mov %r12,4*8($tptr)
| mov 4*8($carry),%r12
| mov %r13,5*8($tptr)
| mov 5*8($carry),%r13
| mov %r14,6*8($tptr)
| mov 6*8($carry),%r14
| mov %r15,7*8($tptr)
| mov 7*8($carry),%r15
| mov $carry,$tptr
| jmp .Lsqrx8x_outer_loop
|
| .align 32
| .Lsqrx8x_outer_break:
| mov %r9,9*8($tptr) # t[9]
| movq %xmm3,%rcx # -$num
| mov %r10,10*8($tptr) # ...
| mov %r11,11*8($tptr)
| mov %r12,12*8($tptr)
| mov %r13,13*8($tptr)
| mov %r14,14*8($tptr)
| ___
| } {
| my $i="%rcx";
| $code.=<<___;
| lea 48+8(%rsp),$tptr
| mov ($aptr,$i),%rdx # a[0]
|
| mov 8($tptr),$A0[1] # t[1]
| xor $A0[0],$A0[0] # t[0], of=0, cf=0
| mov 0+8(%rsp),$num # restore $num
| adox $A0[1],$A0[1]
| mov 16($tptr),$A1[0] # t[2] # prefetch
| mov 24($tptr),$A1[1] # t[3] # prefetch
| #jmp .Lsqrx4x_shift_n_add # happens to be aligned
|
| .align 32
| .Lsqrx4x_shift_n_add:
| mulx %rdx,%rax,%rbx
| adox $A1[0],$A1[0]
| adcx $A0[0],%rax
| .byte 0x48,0x8b,0x94,0x0e,0x08,0x00,0x00,0x00 # mov 8($aptr,$i),%rdx # a[i+1] # prefetch
| .byte 0x4c,0x8b,0x97,0x20,0x00,0x00,0x00 # mov 32($tptr),$A0[0] # t[2*i+4] # prefetch
| adox $A1[1],$A1[1]
| adcx $A0[1],%rbx
| mov 40($tptr),$A0[1] # t[2*i+4+1] # prefetch
| mov %rax,0($tptr)
| mov %rbx,8($tptr)
|
| mulx %rdx,%rax,%rbx
| adox $A0[0],$A0[0]
| adcx $A1[0],%rax
| mov 16($aptr,$i),%rdx # a[i+2] # prefetch
| mov 48($tptr),$A1[0] # t[2*i+6] # prefetch
| adox $A0[1],$A0[1]
| adcx $A1[1],%rbx
| mov 56($tptr),$A1[1] # t[2*i+6+1] # prefetch
| mov %rax,16($tptr)
| mov %rbx,24($tptr)
|
| mulx %rdx,%rax,%rbx
| adox $A1[0],$A1[0]
| adcx $A0[0],%rax
| mov 24($aptr,$i),%rdx # a[i+3] # prefetch
| lea 32($i),$i
| mov 64($tptr),$A0[0] # t[2*i+8] # prefetch
| adox $A1[1],$A1[1]
| adcx $A0[1],%rbx
| mov 72($tptr),$A0[1] # t[2*i+8+1] # prefetch
| mov %rax,32($tptr)
| mov %rbx,40($tptr)
|
| mulx %rdx,%rax,%rbx
| adox $A0[0],$A0[0]
| adcx $A1[0],%rax
| jrcxz .Lsqrx4x_shift_n_add_break
| .byte 0x48,0x8b,0x94,0x0e,0x00,0x00,0x00,0x00 # mov 0($aptr,$i),%rdx # a[i+4] # prefetch
| adox $A0[1],$A0[1]
| adcx $A1[1],%rbx
| mov 80($tptr),$A1[0] # t[2*i+10] # prefetch
| mov 88($tptr),$A1[1] # t[2*i+10+1] # prefetch
| mov %rax,48($tptr)
| mov %rbx,56($tptr)
| lea 64($tptr),$tptr
| nop
| jmp .Lsqrx4x_shift_n_add
|
| .align 32
| .Lsqrx4x_shift_n_add_break:
| adcx $A1[1],%rbx
| mov %rax,48($tptr)
| mov %rbx,56($tptr)
| lea 64($tptr),$tptr # end of t[] buffer
| ___
| }
| ######################################################################
| # Montgomery reduction part, "word-by-word" algorithm.
| #
| # This new path is inspired by multiple submissions from Intel, by
| # Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
| # Vinodh Gopal...
| {
| my ($nptr,$carry,$m0)=("%rbp","%rsi","%rdx");
|
| $code.=<<___;
| movq %xmm2,$nptr
| __bn_sqrx8x_reduction:
| xor %eax,%eax # initial top-most carry bit
| mov 32+8(%rsp),%rbx # n0
| mov 48+8(%rsp),%rdx # "%r8", 8*0($tptr)
| lea -8*8($nptr,$num),%rcx # end of n[]
| #lea 48+8(%rsp,$num,2),$tptr # end of t[] buffer
| mov %rcx, 0+8(%rsp) # save end of n[]
| mov $tptr,8+8(%rsp) # save end of t[]
|
| lea 48+8(%rsp),$tptr # initial t[] window
| jmp .Lsqrx8x_reduction_loop
|
| .align 32
| .Lsqrx8x_reduction_loop:
| mov 8*1($tptr),%r9
| mov 8*2($tptr),%r10
| mov 8*3($tptr),%r11
| mov 8*4($tptr),%r12
| mov %rdx,%r8
| imulq %rbx,%rdx # n0*a[i]
| mov 8*5($tptr),%r13
| mov 8*6($tptr),%r14
| mov 8*7($tptr),%r15
| mov %rax,24+8(%rsp) # store top-most carry bit
|
| lea 8*8($tptr),$tptr
| xor $carry,$carry # cf=0,of=0
| mov \$-8,%rcx
| jmp .Lsqrx8x_reduce
|
| .align 32
| .Lsqrx8x_reduce:
| mov %r8, %rbx
| mulx 8*0($nptr),%rax,%r8 # n[0]
| adcx %rbx,%rax # discarded
| adox %r9,%r8
|
| mulx 8*1($nptr),%rbx,%r9 # n[1]
| adcx %rbx,%r8
| adox %r10,%r9
|
| mulx 8*2($nptr),%rbx,%r10
| adcx %rbx,%r9
| adox %r11,%r10
|
| mulx 8*3($nptr),%rbx,%r11
| adcx %rbx,%r10
| adox %r12,%r11
|
| .byte 0xc4,0x62,0xe3,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 8*4($nptr),%rbx,%r12
| mov %rdx,%rax
| mov %r8,%rdx
| adcx %rbx,%r11
| adox %r13,%r12
|
| mulx 32+8(%rsp),%rbx,%rdx # %rdx discarded
| mov %rax,%rdx
| mov %rax,64+48+8(%rsp,%rcx,8) # put aside n0*a[i]
|
| mulx 8*5($nptr),%rax,%r13
| adcx %rax,%r12
| adox %r14,%r13
|
| mulx 8*6($nptr),%rax,%r14
| adcx %rax,%r13
| adox %r15,%r14
|
| mulx 8*7($nptr),%rax,%r15
| mov %rbx,%rdx
| adcx %rax,%r14
| adox $carry,%r15 # $carry is 0
| adcx $carry,%r15 # cf=0
|
| .byte 0x67,0x67,0x67
| inc %rcx # of=0
| jnz .Lsqrx8x_reduce
|
| mov $carry,%rax # xor %rax,%rax
| cmp 0+8(%rsp),$nptr # end of n[]?
| jae .Lsqrx8x_no_tail
|
| mov 48+8(%rsp),%rdx # pull n0*a[0]
| add 8*0($tptr),%r8
| lea 8*8($nptr),$nptr
| mov \$-8,%rcx
| adcx 8*1($tptr),%r9
| adcx 8*2($tptr),%r10
| adc 8*3($tptr),%r11
| adc 8*4($tptr),%r12
| adc 8*5($tptr),%r13
| adc 8*6($tptr),%r14
| adc 8*7($tptr),%r15
| lea 8*8($tptr),$tptr
| sbb %rax,%rax # top carry
|
| xor $carry,$carry # of=0, cf=0
| mov %rax,16+8(%rsp)
| jmp .Lsqrx8x_tail
|
| .align 32
| .Lsqrx8x_tail:
| mov %r8,%rbx
| mulx 8*0($nptr),%rax,%r8
| adcx %rax,%rbx
| adox %r9,%r8
|
| mulx 8*1($nptr),%rax,%r9
| adcx %rax,%r8
| adox %r10,%r9
|
| mulx 8*2($nptr),%rax,%r10
| adcx %rax,%r9
| adox %r11,%r10
|
| mulx 8*3($nptr),%rax,%r11
| adcx %rax,%r10
| adox %r12,%r11
|
| .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 8*4($nptr),%rax,%r12
| adcx %rax,%r11
| adox %r13,%r12
|
| mulx 8*5($nptr),%rax,%r13
| adcx %rax,%r12
| adox %r14,%r13
|
| mulx 8*6($nptr),%rax,%r14
| adcx %rax,%r13
| adox %r15,%r14
|
| mulx 8*7($nptr),%rax,%r15
| mov 72+48+8(%rsp,%rcx,8),%rdx # pull n0*a[i]
| adcx %rax,%r14
| adox $carry,%r15
| mov %rbx,($tptr,%rcx,8) # save result
| mov %r8,%rbx
| adcx $carry,%r15 # cf=0
|
| inc %rcx # of=0
| jnz .Lsqrx8x_tail
|
| cmp 0+8(%rsp),$nptr # end of n[]?
| jae .Lsqrx8x_tail_done # break out of loop
|
| sub 16+8(%rsp),$carry # mov 16(%rsp),%cf
| mov 48+8(%rsp),%rdx # pull n0*a[0]
| lea 8*8($nptr),$nptr
| adc 8*0($tptr),%r8
| adc 8*1($tptr),%r9
| adc 8*2($tptr),%r10
| adc 8*3($tptr),%r11
| adc 8*4($tptr),%r12
| adc 8*5($tptr),%r13
| adc 8*6($tptr),%r14
| adc 8*7($tptr),%r15
| lea 8*8($tptr),$tptr
| sbb %rax,%rax
| sub \$8,%rcx # mov \$-8,%rcx
|
| xor $carry,$carry # of=0, cf=0
| mov %rax,16+8(%rsp)
| jmp .Lsqrx8x_tail
|
| .align 32
| .Lsqrx8x_tail_done:
| xor %rax,%rax
| add 24+8(%rsp),%r8 # can this overflow?
| adc \$0,%r9
| adc \$0,%r10
| adc \$0,%r11
| adc \$0,%r12
| adc \$0,%r13
| adc \$0,%r14
| adc \$0,%r15
| adc \$0,%rax
|
| sub 16+8(%rsp),$carry # mov 16(%rsp),%cf
| .Lsqrx8x_no_tail: # %cf is 0 if jumped here
| adc 8*0($tptr),%r8
| movq %xmm3,%rcx
| adc 8*1($tptr),%r9
| mov 8*7($nptr),$carry
| movq %xmm2,$nptr # restore $nptr
| adc 8*2($tptr),%r10
| adc 8*3($tptr),%r11
| adc 8*4($tptr),%r12
| adc 8*5($tptr),%r13
| adc 8*6($tptr),%r14
| adc 8*7($tptr),%r15
| adc \$0,%rax # top-most carry
|
| mov 32+8(%rsp),%rbx # n0
| mov 8*8($tptr,%rcx),%rdx # modulo-scheduled "%r8"
|
| mov %r8,8*0($tptr) # store top 512 bits
| lea 8*8($tptr),%r8 # borrow %r8
| mov %r9,8*1($tptr)
| mov %r10,8*2($tptr)
| mov %r11,8*3($tptr)
| mov %r12,8*4($tptr)
| mov %r13,8*5($tptr)
| mov %r14,8*6($tptr)
| mov %r15,8*7($tptr)
|
| lea 8*8($tptr,%rcx),$tptr # start of current t[] window
| cmp 8+8(%rsp),%r8 # end of t[]?
| jb .Lsqrx8x_reduction_loop
| ret
| .cfi_endproc
| .size bn_sqrx8x_internal,.-bn_sqrx8x_internal
| ___
| }
| ##############################################################
| # Post-condition, 4x unrolled
| #
| {
| my ($rptr,$nptr)=("%rdx","%rbp");
| $code.=<<___;
| .align 32
| __bn_postx4x_internal:
| .cfi_startproc
| mov 8*0($nptr),%r12
| mov %rcx,%r10 # -$num
| mov %rcx,%r9 # -$num
| neg %rax
| sar \$3+2,%rcx
| #lea 48+8(%rsp,%r9),$tptr
| movq %xmm1,$rptr # restore $rptr
| movq %xmm1,$aptr # prepare for back-to-back call
| dec %r12 # so that after 'not' we get -n[0]
| mov 8*1($nptr),%r13
| xor %r8,%r8
| mov 8*2($nptr),%r14
| mov 8*3($nptr),%r15
| jmp .Lsqrx4x_sub_entry
|
| .align 16
| .Lsqrx4x_sub:
| mov 8*0($nptr),%r12
| mov 8*1($nptr),%r13
| mov 8*2($nptr),%r14
| mov 8*3($nptr),%r15
| .Lsqrx4x_sub_entry:
| andn %rax,%r12,%r12
| lea 8*4($nptr),$nptr
| andn %rax,%r13,%r13
| andn %rax,%r14,%r14
| andn %rax,%r15,%r15
|
| neg %r8 # mov %r8,%cf
| adc 8*0($tptr),%r12
| adc 8*1($tptr),%r13
| adc 8*2($tptr),%r14
| adc 8*3($tptr),%r15
| mov %r12,8*0($rptr)
| lea 8*4($tptr),$tptr
| mov %r13,8*1($rptr)
| sbb %r8,%r8 # mov %cf,%r8
| mov %r14,8*2($rptr)
| mov %r15,8*3($rptr)
| lea 8*4($rptr),$rptr
|
| inc %rcx
| jnz .Lsqrx4x_sub
|
| neg %r9 # restore $num
|
| ret
| .cfi_endproc
| .size __bn_postx4x_internal,.-__bn_postx4x_internal
| ___
| }
| }}}
| {
| my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%edx","%r8", "%r9d") : # Win64 order
| ("%rdi","%esi","%rdx","%ecx"); # Unix order
| my $out=$inp;
| my $STRIDE=2**5*8;
| my $N=$STRIDE/4;
|
| $code.=<<___;
| .globl bn_get_bits5
| .type bn_get_bits5,\@abi-omnipotent
| .align 16
| bn_get_bits5:
| .cfi_startproc
| lea 0($inp),%r10
| lea 1($inp),%r11
| mov $num,%ecx
| shr \$4,$num
| and \$15,%ecx
| lea -8(%ecx),%eax
| cmp \$11,%ecx
| cmova %r11,%r10
| cmova %eax,%ecx
| movzw (%r10,$num,2),%eax
| shrl %cl,%eax
| and \$31,%eax
| ret
| .cfi_endproc
| .size bn_get_bits5,.-bn_get_bits5
|
| .globl bn_scatter5
| .type bn_scatter5,\@abi-omnipotent
| .align 16
| bn_scatter5:
| .cfi_startproc
| cmp \$0, $num
| jz .Lscatter_epilogue
| lea ($tbl,$idx,8),$tbl
| .Lscatter:
| mov ($inp),%rax
| lea 8($inp),$inp
| mov %rax,($tbl)
| lea 32*8($tbl),$tbl
| sub \$1,$num
| jnz .Lscatter
| .Lscatter_epilogue:
| ret
| .cfi_endproc
| .size bn_scatter5,.-bn_scatter5
|
| .globl bn_gather5
| .type bn_gather5,\@abi-omnipotent
| .align 32
| bn_gather5:
| .LSEH_begin_bn_gather5: # Win64 thing, but harmless in other cases
| .cfi_startproc
| # I can't trust assembler to use specific encoding:-(
| .byte 0x4c,0x8d,0x14,0x24 #lea (%rsp),%r10
| .byte 0x48,0x81,0xec,0x08,0x01,0x00,0x00 #sub $0x108,%rsp
| lea .Linc(%rip),%rax
| and \$-16,%rsp # shouldn't be formally required
|
| movd $idx,%xmm5
| movdqa 0(%rax),%xmm0 # 00000001000000010000000000000000
| movdqa 16(%rax),%xmm1 # 00000002000000020000000200000002
| lea 128($tbl),%r11 # size optimization
| lea 128(%rsp),%rax # size optimization
|
| pshufd \$0,%xmm5,%xmm5 # broadcast $idx
| movdqa %xmm1,%xmm4
| movdqa %xmm1,%xmm2
| ___
| ########################################################################
| # calculate mask by comparing 0..31 to $idx and save result to stack
| #
| for($i=0;$i<$STRIDE/16;$i+=4) {
| $code.=<<___;
| paddd %xmm0,%xmm1
| pcmpeqd %xmm5,%xmm0 # compare to 1,0
| ___
| $code.=<<___ if ($i);
| movdqa %xmm3,`16*($i-1)-128`(%rax)
| ___
| $code.=<<___;
| movdqa %xmm4,%xmm3
|
| paddd %xmm1,%xmm2
| pcmpeqd %xmm5,%xmm1 # compare to 3,2
| movdqa %xmm0,`16*($i+0)-128`(%rax)
| movdqa %xmm4,%xmm0
|
| paddd %xmm2,%xmm3
| pcmpeqd %xmm5,%xmm2 # compare to 5,4
| movdqa %xmm1,`16*($i+1)-128`(%rax)
| movdqa %xmm4,%xmm1
|
| paddd %xmm3,%xmm0
| pcmpeqd %xmm5,%xmm3 # compare to 7,6
| movdqa %xmm2,`16*($i+2)-128`(%rax)
| movdqa %xmm4,%xmm2
| ___
| }
| $code.=<<___;
| movdqa %xmm3,`16*($i-1)-128`(%rax)
| jmp .Lgather
|
| .align 32
| .Lgather:
| pxor %xmm4,%xmm4
| pxor %xmm5,%xmm5
| ___
| for($i=0;$i<$STRIDE/16;$i+=4) {
| $code.=<<___;
| movdqa `16*($i+0)-128`(%r11),%xmm0
| movdqa `16*($i+1)-128`(%r11),%xmm1
| movdqa `16*($i+2)-128`(%r11),%xmm2
| pand `16*($i+0)-128`(%rax),%xmm0
| movdqa `16*($i+3)-128`(%r11),%xmm3
| pand `16*($i+1)-128`(%rax),%xmm1
| por %xmm0,%xmm4
| pand `16*($i+2)-128`(%rax),%xmm2
| por %xmm1,%xmm5
| pand `16*($i+3)-128`(%rax),%xmm3
| por %xmm2,%xmm4
| por %xmm3,%xmm5
| ___
| }
| $code.=<<___;
| por %xmm5,%xmm4
| lea $STRIDE(%r11),%r11
| pshufd \$0x4e,%xmm4,%xmm0
| por %xmm4,%xmm0
| movq %xmm0,($out) # m0=bp[0]
| lea 8($out),$out
| sub \$1,$num
| jnz .Lgather
|
| lea (%r10),%rsp
| ret
| .LSEH_end_bn_gather5:
| .cfi_endproc
| .size bn_gather5,.-bn_gather5
| ___
| }
| $code.=<<___;
| .align 64
| .Linc:
| .long 0,0, 1,1
| .long 2,2, 2,2
| .asciz "Montgomery Multiplication with scatter/gather for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
| ___
|
| # EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
| # CONTEXT *context,DISPATCHER_CONTEXT *disp)
| if ($win64) {
| $rec="%rcx";
| $frame="%rdx";
| $context="%r8";
| $disp="%r9";
|
| $code.=<<___;
| .extern __imp_RtlVirtualUnwind
| .type mul_handler,\@abi-omnipotent
| .align 16
| mul_handler:
| push %rsi
| push %rdi
| push %rbx
| push %rbp
| push %r12
| push %r13
| push %r14
| push %r15
| pushfq
| sub \$64,%rsp
|
| mov 120($context),%rax # pull context->Rax
| mov 248($context),%rbx # pull context->Rip
|
| mov 8($disp),%rsi # disp->ImageBase
| mov 56($disp),%r11 # disp->HandlerData
|
| mov 0(%r11),%r10d # HandlerData[0]
| lea (%rsi,%r10),%r10 # end of prologue label
| cmp %r10,%rbx # context->Rip<end of prologue label
| jb .Lcommon_seh_tail
|
| mov 4(%r11),%r10d # HandlerData[1]
| lea (%rsi,%r10),%r10 # beginning of body label
| cmp %r10,%rbx # context->Rip<body label
| jb .Lcommon_pop_regs
|
| mov 152($context),%rax # pull context->Rsp
|
| mov 8(%r11),%r10d # HandlerData[2]
| lea (%rsi,%r10),%r10 # epilogue label
| cmp %r10,%rbx # context->Rip>=epilogue label
| jae .Lcommon_seh_tail
|
| lea .Lmul_epilogue(%rip),%r10
| cmp %r10,%rbx
| ja .Lbody_40
|
| mov 192($context),%r10 # pull $num
| mov 8(%rax,%r10,8),%rax # pull saved stack pointer
|
| jmp .Lcommon_pop_regs
|
| .Lbody_40:
| mov 40(%rax),%rax # pull saved stack pointer
| .Lcommon_pop_regs:
| mov -8(%rax),%rbx
| mov -16(%rax),%rbp
| mov -24(%rax),%r12
| mov -32(%rax),%r13
| mov -40(%rax),%r14
| mov -48(%rax),%r15
| mov %rbx,144($context) # restore context->Rbx
| mov %rbp,160($context) # restore context->Rbp
| mov %r12,216($context) # restore context->R12
| mov %r13,224($context) # restore context->R13
| mov %r14,232($context) # restore context->R14
| mov %r15,240($context) # restore context->R15
|
| .Lcommon_seh_tail:
| mov 8(%rax),%rdi
| mov 16(%rax),%rsi
| mov %rax,152($context) # restore context->Rsp
| mov %rsi,168($context) # restore context->Rsi
| mov %rdi,176($context) # restore context->Rdi
|
| mov 40($disp),%rdi # disp->ContextRecord
| mov $context,%rsi # context
| mov \$154,%ecx # sizeof(CONTEXT)
| .long 0xa548f3fc # cld; rep movsq
|
| mov $disp,%rsi
| xor %rcx,%rcx # arg1, UNW_FLAG_NHANDLER
| mov 8(%rsi),%rdx # arg2, disp->ImageBase
| mov 0(%rsi),%r8 # arg3, disp->ControlPc
| mov 16(%rsi),%r9 # arg4, disp->FunctionEntry
| mov 40(%rsi),%r10 # disp->ContextRecord
| lea 56(%rsi),%r11 # &disp->HandlerData
| lea 24(%rsi),%r12 # &disp->EstablisherFrame
| mov %r10,32(%rsp) # arg5
| mov %r11,40(%rsp) # arg6
| mov %r12,48(%rsp) # arg7
| mov %rcx,56(%rsp) # arg8, (NULL)
| call *__imp_RtlVirtualUnwind(%rip)
|
| mov \$1,%eax # ExceptionContinueSearch
| add \$64,%rsp
| popfq
| pop %r15
| pop %r14
| pop %r13
| pop %r12
| pop %rbp
| pop %rbx
| pop %rdi
| pop %rsi
| ret
| .size mul_handler,.-mul_handler
|
| .section .pdata
| .align 4
| .rva .LSEH_begin_bn_mul_mont_gather5
| .rva .LSEH_end_bn_mul_mont_gather5
| .rva .LSEH_info_bn_mul_mont_gather5
|
| .rva .LSEH_begin_bn_mul4x_mont_gather5
| .rva .LSEH_end_bn_mul4x_mont_gather5
| .rva .LSEH_info_bn_mul4x_mont_gather5
|
| .rva .LSEH_begin_bn_power5
| .rva .LSEH_end_bn_power5
| .rva .LSEH_info_bn_power5
|
| .rva .LSEH_begin_bn_from_mont8x
| .rva .LSEH_end_bn_from_mont8x
| .rva .LSEH_info_bn_from_mont8x
| ___
| $code.=<<___ if ($addx);
| .rva .LSEH_begin_bn_mulx4x_mont_gather5
| .rva .LSEH_end_bn_mulx4x_mont_gather5
| .rva .LSEH_info_bn_mulx4x_mont_gather5
|
| .rva .LSEH_begin_bn_powerx5
| .rva .LSEH_end_bn_powerx5
| .rva .LSEH_info_bn_powerx5
| ___
| $code.=<<___;
| .rva .LSEH_begin_bn_gather5
| .rva .LSEH_end_bn_gather5
| .rva .LSEH_info_bn_gather5
|
| .section .xdata
| .align 8
| .LSEH_info_bn_mul_mont_gather5:
| .byte 9,0,0,0
| .rva mul_handler
| .rva .Lmul_body,.Lmul_body,.Lmul_epilogue # HandlerData[]
| .align 8
| .LSEH_info_bn_mul4x_mont_gather5:
| .byte 9,0,0,0
| .rva mul_handler
| .rva .Lmul4x_prologue,.Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
| .align 8
| .LSEH_info_bn_power5:
| .byte 9,0,0,0
| .rva mul_handler
| .rva .Lpower5_prologue,.Lpower5_body,.Lpower5_epilogue # HandlerData[]
| .align 8
| .LSEH_info_bn_from_mont8x:
| .byte 9,0,0,0
| .rva mul_handler
| .rva .Lfrom_prologue,.Lfrom_body,.Lfrom_epilogue # HandlerData[]
| ___
| $code.=<<___ if ($addx);
| .align 8
| .LSEH_info_bn_mulx4x_mont_gather5:
| .byte 9,0,0,0
| .rva mul_handler
| .rva .Lmulx4x_prologue,.Lmulx4x_body,.Lmulx4x_epilogue # HandlerData[]
| .align 8
| .LSEH_info_bn_powerx5:
| .byte 9,0,0,0
| .rva mul_handler
| .rva .Lpowerx5_prologue,.Lpowerx5_body,.Lpowerx5_epilogue # HandlerData[]
| ___
| $code.=<<___;
| .align 8
| .LSEH_info_bn_gather5:
| .byte 0x01,0x0b,0x03,0x0a
| .byte 0x0b,0x01,0x21,0x00 # sub rsp,0x108
| .byte 0x04,0xa3,0x00,0x00 # lea r10,(rsp)
| .align 8
| ___
| }
|
| $code =~ s/\`([^\`]*)\`/eval($1)/gem;
|
| print $code;
| close STDOUT or die "error closing STDOUT: $!";
|
|
