3514 lines
76 KiB
Perl
Executable file
3514 lines
76 KiB
Perl
Executable file
#!/usr/bin/env perl
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# ====================================================================
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# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
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# project. The module is, however, dual licensed under OpenSSL and
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# CRYPTOGAMS licenses depending on where you obtain it. For further
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# details see http://www.openssl.org/~appro/cryptogams/.
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# ====================================================================
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# August 2011.
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#
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# Companion to x86_64-mont.pl that optimizes cache-timing attack
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# countermeasures. The subroutines are produced by replacing bp[i]
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# references in their x86_64-mont.pl counterparts with cache-neutral
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# references to powers table computed in BN_mod_exp_mont_consttime.
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# In addition subroutine that scatters elements of the powers table
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# is implemented, so that scatter-/gathering can be tuned without
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# bn_exp.c modifications.
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# August 2013.
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#
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# Add MULX/AD*X code paths and additional interfaces to optimize for
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# branch prediction unit. For input lengths that are multiples of 8
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# the np argument is not just modulus value, but one interleaved
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# with 0. This is to optimize post-condition...
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$flavour = shift;
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$output = shift;
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if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
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$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
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$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
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( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
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( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
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die "can't locate x86_64-xlate.pl";
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open OUT,"| \"$^X\" $xlate $flavour $output";
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*STDOUT=*OUT;
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if (`$ENV{CC} -Wa,-v -c -o /dev/null -x assembler /dev/null 2>&1`
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=~ /GNU assembler version ([2-9]\.[0-9]+)/) {
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$addx = ($1>=2.23);
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}
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if (!$addx && $win64 && ($flavour =~ /nasm/ || $ENV{ASM} =~ /nasm/) &&
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`nasm -v 2>&1` =~ /NASM version ([2-9]\.[0-9]+)/) {
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$addx = ($1>=2.10);
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}
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if (!$addx && $win64 && ($flavour =~ /masm/ || $ENV{ASM} =~ /ml64/) &&
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`ml64 2>&1` =~ /Version ([0-9]+)\./) {
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$addx = ($1>=11);
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}
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# int bn_mul_mont_gather5(
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$rp="%rdi"; # BN_ULONG *rp,
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$ap="%rsi"; # const BN_ULONG *ap,
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$bp="%rdx"; # const BN_ULONG *bp,
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$np="%rcx"; # const BN_ULONG *np,
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$n0="%r8"; # const BN_ULONG *n0,
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$num="%r9"; # int num,
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# int idx); # 0 to 2^5-1, "index" in $bp holding
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# pre-computed powers of a', interlaced
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# in such manner that b[0] is $bp[idx],
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# b[1] is [2^5+idx], etc.
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$lo0="%r10";
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$hi0="%r11";
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$hi1="%r13";
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$i="%r14";
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$j="%r15";
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$m0="%rbx";
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$m1="%rbp";
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$code=<<___;
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.text
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.extern OPENSSL_ia32cap_P
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.globl bn_mul_mont_gather5
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.type bn_mul_mont_gather5,\@function,6
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.align 64
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bn_mul_mont_gather5:
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test \$7,${num}d
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jnz .Lmul_enter
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___
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$code.=<<___ if ($addx);
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mov OPENSSL_ia32cap_P+8(%rip),%r11d
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___
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$code.=<<___;
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jmp .Lmul4x_enter
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.align 16
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.Lmul_enter:
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mov ${num}d,${num}d
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mov %rsp,%rax
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mov `($win64?56:8)`(%rsp),%r10d # load 7th argument
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push %rbx
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push %rbp
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push %r12
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push %r13
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push %r14
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push %r15
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___
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$code.=<<___ if ($win64);
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lea -0x28(%rsp),%rsp
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movaps %xmm6,(%rsp)
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movaps %xmm7,0x10(%rsp)
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___
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$code.=<<___;
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lea 2($num),%r11
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neg %r11
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lea (%rsp,%r11,8),%rsp # tp=alloca(8*(num+2))
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and \$-1024,%rsp # minimize TLB usage
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mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
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.Lmul_body:
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mov $bp,%r12 # reassign $bp
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___
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$bp="%r12";
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$STRIDE=2**5*8; # 5 is "window size"
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$N=$STRIDE/4; # should match cache line size
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$code.=<<___;
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mov %r10,%r11
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shr \$`log($N/8)/log(2)`,%r10
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and \$`$N/8-1`,%r11
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not %r10
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lea .Lmagic_masks(%rip),%rax
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and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
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lea 96($bp,%r11,8),$bp # pointer within 1st cache line
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movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
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movq 8(%rax,%r10,8),%xmm5 # cache line contains element
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movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
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movq 24(%rax,%r10,8),%xmm7
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movq `0*$STRIDE/4-96`($bp),%xmm0
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movq `1*$STRIDE/4-96`($bp),%xmm1
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pand %xmm4,%xmm0
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movq `2*$STRIDE/4-96`($bp),%xmm2
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pand %xmm5,%xmm1
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movq `3*$STRIDE/4-96`($bp),%xmm3
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pand %xmm6,%xmm2
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por %xmm1,%xmm0
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pand %xmm7,%xmm3
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por %xmm2,%xmm0
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lea $STRIDE($bp),$bp
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por %xmm3,%xmm0
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movq %xmm0,$m0 # m0=bp[0]
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mov ($n0),$n0 # pull n0[0] value
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mov ($ap),%rax
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xor $i,$i # i=0
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xor $j,$j # j=0
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movq `0*$STRIDE/4-96`($bp),%xmm0
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movq `1*$STRIDE/4-96`($bp),%xmm1
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pand %xmm4,%xmm0
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movq `2*$STRIDE/4-96`($bp),%xmm2
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pand %xmm5,%xmm1
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mov $n0,$m1
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mulq $m0 # ap[0]*bp[0]
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mov %rax,$lo0
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mov ($np),%rax
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movq `3*$STRIDE/4-96`($bp),%xmm3
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pand %xmm6,%xmm2
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por %xmm1,%xmm0
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pand %xmm7,%xmm3
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imulq $lo0,$m1 # "tp[0]"*n0
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mov %rdx,$hi0
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por %xmm2,%xmm0
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lea $STRIDE($bp),$bp
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por %xmm3,%xmm0
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mulq $m1 # np[0]*m1
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add %rax,$lo0 # discarded
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mov 8($ap),%rax
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adc \$0,%rdx
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mov %rdx,$hi1
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lea 1($j),$j # j++
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jmp .L1st_enter
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.align 16
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.L1st:
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add %rax,$hi1
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mov ($ap,$j,8),%rax
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adc \$0,%rdx
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add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
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mov $lo0,$hi0
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adc \$0,%rdx
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mov $hi1,-16(%rsp,$j,8) # tp[j-1]
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mov %rdx,$hi1
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.L1st_enter:
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mulq $m0 # ap[j]*bp[0]
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add %rax,$hi0
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mov ($np,$j,8),%rax
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adc \$0,%rdx
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lea 1($j),$j # j++
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mov %rdx,$lo0
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mulq $m1 # np[j]*m1
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cmp $num,$j
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jne .L1st
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movq %xmm0,$m0 # bp[1]
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add %rax,$hi1
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mov ($ap),%rax # ap[0]
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adc \$0,%rdx
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add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
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adc \$0,%rdx
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mov $hi1,-16(%rsp,$j,8) # tp[j-1]
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mov %rdx,$hi1
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mov $lo0,$hi0
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xor %rdx,%rdx
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add $hi0,$hi1
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adc \$0,%rdx
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mov $hi1,-8(%rsp,$num,8)
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mov %rdx,(%rsp,$num,8) # store upmost overflow bit
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lea 1($i),$i # i++
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jmp .Louter
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.align 16
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.Louter:
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xor $j,$j # j=0
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mov $n0,$m1
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mov (%rsp),$lo0
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movq `0*$STRIDE/4-96`($bp),%xmm0
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movq `1*$STRIDE/4-96`($bp),%xmm1
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pand %xmm4,%xmm0
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movq `2*$STRIDE/4-96`($bp),%xmm2
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pand %xmm5,%xmm1
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mulq $m0 # ap[0]*bp[i]
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add %rax,$lo0 # ap[0]*bp[i]+tp[0]
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mov ($np),%rax
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adc \$0,%rdx
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movq `3*$STRIDE/4-96`($bp),%xmm3
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pand %xmm6,%xmm2
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por %xmm1,%xmm0
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pand %xmm7,%xmm3
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imulq $lo0,$m1 # tp[0]*n0
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mov %rdx,$hi0
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por %xmm2,%xmm0
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lea $STRIDE($bp),$bp
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por %xmm3,%xmm0
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mulq $m1 # np[0]*m1
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add %rax,$lo0 # discarded
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mov 8($ap),%rax
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adc \$0,%rdx
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mov 8(%rsp),$lo0 # tp[1]
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mov %rdx,$hi1
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lea 1($j),$j # j++
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jmp .Linner_enter
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.align 16
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.Linner:
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add %rax,$hi1
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mov ($ap,$j,8),%rax
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adc \$0,%rdx
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add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
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mov (%rsp,$j,8),$lo0
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adc \$0,%rdx
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mov $hi1,-16(%rsp,$j,8) # tp[j-1]
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mov %rdx,$hi1
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.Linner_enter:
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mulq $m0 # ap[j]*bp[i]
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add %rax,$hi0
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mov ($np,$j,8),%rax
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adc \$0,%rdx
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add $hi0,$lo0 # ap[j]*bp[i]+tp[j]
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mov %rdx,$hi0
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adc \$0,$hi0
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lea 1($j),$j # j++
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mulq $m1 # np[j]*m1
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cmp $num,$j
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jne .Linner
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movq %xmm0,$m0 # bp[i+1]
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add %rax,$hi1
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mov ($ap),%rax # ap[0]
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adc \$0,%rdx
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add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
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mov (%rsp,$j,8),$lo0
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adc \$0,%rdx
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mov $hi1,-16(%rsp,$j,8) # tp[j-1]
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mov %rdx,$hi1
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xor %rdx,%rdx
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add $hi0,$hi1
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adc \$0,%rdx
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add $lo0,$hi1 # pull upmost overflow bit
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adc \$0,%rdx
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mov $hi1,-8(%rsp,$num,8)
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mov %rdx,(%rsp,$num,8) # store upmost overflow bit
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lea 1($i),$i # i++
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cmp $num,$i
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jb .Louter
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xor $i,$i # i=0 and clear CF!
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mov (%rsp),%rax # tp[0]
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lea (%rsp),$ap # borrow ap for tp
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mov $num,$j # j=num
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jmp .Lsub
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.align 16
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.Lsub: sbb ($np,$i,8),%rax
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mov %rax,($rp,$i,8) # rp[i]=tp[i]-np[i]
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mov 8($ap,$i,8),%rax # tp[i+1]
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lea 1($i),$i # i++
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dec $j # doesnn't affect CF!
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jnz .Lsub
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sbb \$0,%rax # handle upmost overflow bit
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xor $i,$i
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and %rax,$ap
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not %rax
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mov $rp,$np
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and %rax,$np
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mov $num,$j # j=num
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or $np,$ap # ap=borrow?tp:rp
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.align 16
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.Lcopy: # copy or in-place refresh
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mov ($ap,$i,8),%rax
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mov $i,(%rsp,$i,8) # zap temporary vector
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mov %rax,($rp,$i,8) # rp[i]=tp[i]
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lea 1($i),$i
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sub \$1,$j
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jnz .Lcopy
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mov 8(%rsp,$num,8),%rsi # restore %rsp
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mov \$1,%rax
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___
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$code.=<<___ if ($win64);
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movaps -88(%rsi),%xmm6
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movaps -72(%rsi),%xmm7
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___
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$code.=<<___;
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mov -48(%rsi),%r15
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mov -40(%rsi),%r14
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mov -32(%rsi),%r13
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mov -24(%rsi),%r12
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mov -16(%rsi),%rbp
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mov -8(%rsi),%rbx
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lea (%rsi),%rsp
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.Lmul_epilogue:
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ret
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.size bn_mul_mont_gather5,.-bn_mul_mont_gather5
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___
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{{{
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my @A=("%r10","%r11");
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my @N=("%r13","%rdi");
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$code.=<<___;
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.type bn_mul4x_mont_gather5,\@function,6
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.align 32
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bn_mul4x_mont_gather5:
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.Lmul4x_enter:
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___
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$code.=<<___ if ($addx);
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and \$0x80100,%r11d
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cmp \$0x80100,%r11d
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je .Lmulx4x_enter
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___
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$code.=<<___;
|
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.byte 0x67
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mov %rsp,%rax
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||
push %rbx
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push %rbp
|
||
push %r12
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push %r13
|
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push %r14
|
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push %r15
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___
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$code.=<<___ if ($win64);
|
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lea -0x28(%rsp),%rsp
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movaps %xmm6,(%rsp)
|
||
movaps %xmm7,0x10(%rsp)
|
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___
|
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$code.=<<___;
|
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.byte 0x67
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mov ${num}d,%r10d
|
||
shl \$3,${num}d
|
||
shl \$3+2,%r10d # 4*$num
|
||
neg $num # -$num
|
||
|
||
##############################################################
|
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# ensure that stack frame doesn't alias with $aptr+4*$num
|
||
# modulo 4096, which covers ret[num], am[num] and n[2*num]
|
||
# (see bn_exp.c). this is done to allow memory disambiguation
|
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# logic do its magic. [excessive frame is allocated in order
|
||
# to allow bn_from_mont8x to clear it.]
|
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#
|
||
lea -64(%rsp,$num,2),%r11
|
||
sub $ap,%r11
|
||
and \$4095,%r11
|
||
cmp %r11,%r10
|
||
jb .Lmul4xsp_alt
|
||
sub %r11,%rsp # align with $ap
|
||
lea -64(%rsp,$num,2),%rsp # alloca(128+num*8)
|
||
jmp .Lmul4xsp_done
|
||
|
||
.align 32
|
||
.Lmul4xsp_alt:
|
||
lea 4096-64(,$num,2),%r10
|
||
lea -64(%rsp,$num,2),%rsp # alloca(128+num*8)
|
||
sub %r10,%r11
|
||
mov \$0,%r10
|
||
cmovc %r10,%r11
|
||
sub %r11,%rsp
|
||
.Lmul4xsp_done:
|
||
and \$-64,%rsp
|
||
neg $num
|
||
|
||
mov %rax,40(%rsp)
|
||
.Lmul4x_body:
|
||
|
||
call mul4x_internal
|
||
|
||
mov 40(%rsp),%rsi # restore %rsp
|
||
mov \$1,%rax
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
movaps -88(%rsi),%xmm6
|
||
movaps -72(%rsi),%xmm7
|
||
___
|
||
$code.=<<___;
|
||
mov -48(%rsi),%r15
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||
mov -40(%rsi),%r14
|
||
mov -32(%rsi),%r13
|
||
mov -24(%rsi),%r12
|
||
mov -16(%rsi),%rbp
|
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mov -8(%rsi),%rbx
|
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lea (%rsi),%rsp
|
||
.Lmul4x_epilogue:
|
||
ret
|
||
.size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
|
||
|
||
.type mul4x_internal,\@abi-omnipotent
|
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.align 32
|
||
mul4x_internal:
|
||
shl \$5,$num
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mov `($win64?56:8)`(%rax),%r10d # load 7th argument
|
||
lea 256(%rdx,$num),%r13
|
||
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;
|
||
$code.=<<___;
|
||
mov %r10,%r11
|
||
shr \$`log($N/8)/log(2)`,%r10
|
||
and \$`$N/8-1`,%r11
|
||
not %r10
|
||
lea .Lmagic_masks(%rip),%rax
|
||
and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
|
||
lea 96(%rdx,%r11,8),$bp # pointer within 1st cache line
|
||
movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
|
||
movq 8(%rax,%r10,8),%xmm5 # cache line contains element
|
||
add \$7,%r11
|
||
movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
|
||
movq 24(%rax,%r10,8),%xmm7
|
||
and \$7,%r11
|
||
|
||
movq `0*$STRIDE/4-96`($bp),%xmm0
|
||
lea $STRIDE($bp),$tp # borrow $tp
|
||
movq `1*$STRIDE/4-96`($bp),%xmm1
|
||
pand %xmm4,%xmm0
|
||
movq `2*$STRIDE/4-96`($bp),%xmm2
|
||
pand %xmm5,%xmm1
|
||
movq `3*$STRIDE/4-96`($bp),%xmm3
|
||
pand %xmm6,%xmm2
|
||
.byte 0x67
|
||
por %xmm1,%xmm0
|
||
movq `0*$STRIDE/4-96`($tp),%xmm1
|
||
.byte 0x67
|
||
pand %xmm7,%xmm3
|
||
.byte 0x67
|
||
por %xmm2,%xmm0
|
||
movq `1*$STRIDE/4-96`($tp),%xmm2
|
||
.byte 0x67
|
||
pand %xmm4,%xmm1
|
||
.byte 0x67
|
||
por %xmm3,%xmm0
|
||
movq `2*$STRIDE/4-96`($tp),%xmm3
|
||
|
||
movq %xmm0,$m0 # m0=bp[0]
|
||
movq `3*$STRIDE/4-96`($tp),%xmm0
|
||
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
|
||
|
||
pand %xmm5,%xmm2
|
||
pand %xmm6,%xmm3
|
||
por %xmm2,%xmm1
|
||
|
||
imulq $A[0],$m1 # "tp[0]"*n0
|
||
##############################################################
|
||
# $tp is chosen so that writing to top-most element of the
|
||
# vector occurs just "above" references to powers table,
|
||
# "above" modulo cache-line size, which effectively precludes
|
||
# possibility of memory disambiguation logic failure when
|
||
# accessing the table.
|
||
#
|
||
lea 64+8(%rsp,%r11,8),$tp
|
||
mov %rdx,$A[1]
|
||
|
||
pand %xmm7,%xmm0
|
||
por %xmm3,%xmm1
|
||
lea 2*$STRIDE($bp),$bp
|
||
por %xmm1,%xmm0
|
||
|
||
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 16*1($np),%rax # interleaved with 0, therefore 16*n
|
||
adc \$0,%rdx
|
||
mov %rdx,$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 16*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 -16*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 -16*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 16*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 16*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 16*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 -16*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 -16*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,$N[0]
|
||
|
||
movq %xmm0,$m0 # bp[1]
|
||
lea ($np,$num,2),$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:
|
||
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 ($np),%rax
|
||
adc \$0,%rdx
|
||
|
||
movq `0*$STRIDE/4-96`($bp),%xmm0
|
||
movq `1*$STRIDE/4-96`($bp),%xmm1
|
||
pand %xmm4,%xmm0
|
||
movq `2*$STRIDE/4-96`($bp),%xmm2
|
||
pand %xmm5,%xmm1
|
||
movq `3*$STRIDE/4-96`($bp),%xmm3
|
||
|
||
imulq $A[0],$m1 # tp[0]*n0
|
||
.byte 0x67
|
||
mov %rdx,$A[1]
|
||
mov $N[1],($tp) # store upmost overflow bit
|
||
|
||
pand %xmm6,%xmm2
|
||
por %xmm1,%xmm0
|
||
pand %xmm7,%xmm3
|
||
por %xmm2,%xmm0
|
||
lea ($tp,$num),$tp # rewind $tp
|
||
lea $STRIDE($bp),$bp
|
||
por %xmm3,%xmm0
|
||
|
||
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 16*1($np),%rax # interleaved with 0, therefore 16*n
|
||
adc \$0,%rdx
|
||
add 8($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 16*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 -16*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 -16*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 16*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 16*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 16*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 -16*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 $m1,%rax
|
||
mov -16*1($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,$N[0]
|
||
|
||
movq %xmm0,$m0 # bp[i+1]
|
||
mov $N[1],-16($tp) # tp[j-1]
|
||
lea ($np,$num,2),$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.=<<___;
|
||
sub $N[0],$m1 # compare top-most words
|
||
adc $j,$j # $j is zero
|
||
or $j,$N[1]
|
||
xor \$1,$N[1]
|
||
lea ($tp,$num),%rbx # tptr in .sqr4x_sub
|
||
lea ($np,$N[1],8),%rbp # nptr in .sqr4x_sub
|
||
mov %r9,%rcx
|
||
sar \$3+2,%rcx # cf=0
|
||
mov 56+8(%rsp),%rdi # rptr in .sqr4x_sub
|
||
jmp .Lsqr4x_sub
|
||
___
|
||
} else {
|
||
my @ri=("%rax",$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.=<<___;
|
||
.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:
|
||
___
|
||
$code.=<<___ if ($addx);
|
||
mov OPENSSL_ia32cap_P+8(%rip),%r11d
|
||
and \$0x80100,%r11d
|
||
cmp \$0x80100,%r11d
|
||
je .Lpowerx5_enter
|
||
___
|
||
$code.=<<___;
|
||
mov %rsp,%rax
|
||
push %rbx
|
||
push %rbp
|
||
push %r12
|
||
push %r13
|
||
push %r14
|
||
push %r15
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
lea -0x28(%rsp),%rsp
|
||
movaps %xmm6,(%rsp)
|
||
movaps %xmm7,0x10(%rsp)
|
||
___
|
||
$code.=<<___;
|
||
mov ${num}d,%r10d
|
||
shl \$3,${num}d # convert $num to bytes
|
||
shl \$3+2,%r10d # 4*$num
|
||
neg $num
|
||
mov ($n0),$n0 # *n0
|
||
|
||
##############################################################
|
||
# ensure that stack frame doesn't alias with $aptr+4*$num
|
||
# modulo 4096, which covers ret[num], am[num] and n[2*num]
|
||
# (see bn_exp.c). this is done to allow memory disambiguation
|
||
# logic do its magic.
|
||
#
|
||
lea -64(%rsp,$num,2),%r11
|
||
sub $aptr,%r11
|
||
and \$4095,%r11
|
||
cmp %r11,%r10
|
||
jb .Lpwr_sp_alt
|
||
sub %r11,%rsp # align with $aptr
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
|
||
jmp .Lpwr_sp_done
|
||
|
||
.align 32
|
||
.Lpwr_sp_alt:
|
||
lea 4096-64(,$num,2),%r10 # 4096-frame-2*$num
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
|
||
sub %r10,%r11
|
||
mov \$0,%r10
|
||
cmovc %r10,%r11
|
||
sub %r11,%rsp
|
||
.Lpwr_sp_done:
|
||
and \$-64,%rsp
|
||
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
|
||
.Lpower5_body:
|
||
movq $rptr,%xmm1 # save $rptr
|
||
movq $nptr,%xmm2 # save $nptr
|
||
movq %r10, %xmm3 # -$num
|
||
movq $bptr,%xmm4
|
||
|
||
call __bn_sqr8x_internal
|
||
call __bn_sqr8x_internal
|
||
call __bn_sqr8x_internal
|
||
call __bn_sqr8x_internal
|
||
call __bn_sqr8x_internal
|
||
|
||
movq %xmm2,$nptr
|
||
movq %xmm4,$bptr
|
||
mov $aptr,$rptr
|
||
mov 40(%rsp),%rax
|
||
lea 32(%rsp),$n0
|
||
|
||
call mul4x_internal
|
||
|
||
mov 40(%rsp),%rsi # restore %rsp
|
||
mov \$1,%rax
|
||
mov -48(%rsi),%r15
|
||
mov -40(%rsi),%r14
|
||
mov -32(%rsi),%r13
|
||
mov -24(%rsi),%r12
|
||
mov -16(%rsi),%rbp
|
||
mov -8(%rsi),%rbx
|
||
lea (%rsi),%rsp
|
||
.Lpower5_epilogue:
|
||
ret
|
||
.size bn_power5,.-bn_power5
|
||
|
||
.globl bn_sqr8x_internal
|
||
.hidden bn_sqr8x_internal
|
||
.type bn_sqr8x_internal,\@abi-omnipotent
|
||
.align 32
|
||
bn_sqr8x_internal:
|
||
__bn_sqr8x_internal:
|
||
##############################################################
|
||
# Squaring part:
|
||
#
|
||
# a) multiply-n-add everything but a[i]*a[i];
|
||
# b) shift result of a) by 1 to the left and accumulate
|
||
# a[i]*a[i] products;
|
||
#
|
||
##############################################################
|
||
# a[1]a[0]
|
||
# a[2]a[0]
|
||
# a[3]a[0]
|
||
# a[2]a[1]
|
||
# a[4]a[0]
|
||
# a[3]a[1]
|
||
# a[5]a[0]
|
||
# a[4]a[1]
|
||
# a[3]a[2]
|
||
# a[6]a[0]
|
||
# a[5]a[1]
|
||
# a[4]a[2]
|
||
# a[7]a[0]
|
||
# a[6]a[1]
|
||
# a[5]a[2]
|
||
# a[4]a[3]
|
||
# a[7]a[1]
|
||
# a[6]a[2]
|
||
# a[5]a[3]
|
||
# a[7]a[2]
|
||
# a[6]a[3]
|
||
# a[5]a[4]
|
||
# a[7]a[3]
|
||
# a[6]a[4]
|
||
# a[7]a[4]
|
||
# a[6]a[5]
|
||
# a[7]a[5]
|
||
# a[7]a[6]
|
||
# a[1]a[0]
|
||
# a[2]a[0]
|
||
# a[3]a[0]
|
||
# a[4]a[0]
|
||
# a[5]a[0]
|
||
# a[6]a[0]
|
||
# a[7]a[0]
|
||
# a[2]a[1]
|
||
# a[3]a[1]
|
||
# a[4]a[1]
|
||
# a[5]a[1]
|
||
# a[6]a[1]
|
||
# a[7]a[1]
|
||
# a[3]a[2]
|
||
# a[4]a[2]
|
||
# a[5]a[2]
|
||
# a[6]a[2]
|
||
# a[7]a[2]
|
||
# a[4]a[3]
|
||
# a[5]a[3]
|
||
# a[6]a[3]
|
||
# a[7]a[3]
|
||
# a[5]a[4]
|
||
# a[6]a[4]
|
||
# a[7]a[4]
|
||
# a[6]a[5]
|
||
# a[7]a[5]
|
||
# a[7]a[6]
|
||
# a[0]a[0]
|
||
# a[1]a[1]
|
||
# a[2]a[2]
|
||
# a[3]a[3]
|
||
# a[4]a[4]
|
||
# a[5]a[5]
|
||
# a[6]a[6]
|
||
# a[7]a[7]
|
||
|
||
lea 32(%r10),$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
|
||
sqr8x_reduction:
|
||
xor %rax,%rax
|
||
lea ($nptr,$num,2),%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 16*0($nptr),%rax # n[0]
|
||
mov \$8,%ecx
|
||
jmp .L8x_reduce
|
||
|
||
.align 32
|
||
.L8x_reduce:
|
||
mulq $m0
|
||
mov 16*1($nptr),%rax # n[1]
|
||
neg %r8
|
||
mov %rdx,%r8
|
||
adc \$0,%r8
|
||
|
||
mulq $m0
|
||
add %rax,%r9
|
||
mov 16*2($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 $m0
|
||
add %rax,%r10
|
||
mov 16*3($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r10,%r9
|
||
mov 32+8(%rsp),$carry # pull n0, borrow $carry
|
||
mov %rdx,%r10
|
||
adc \$0,%r10
|
||
|
||
mulq $m0
|
||
add %rax,%r11
|
||
mov 16*4($nptr),%rax
|
||
adc \$0,%rdx
|
||
imulq %r8,$carry # modulo-scheduled
|
||
add %r11,%r10
|
||
mov %rdx,%r11
|
||
adc \$0,%r11
|
||
|
||
mulq $m0
|
||
add %rax,%r12
|
||
mov 16*5($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r12,%r11
|
||
mov %rdx,%r12
|
||
adc \$0,%r12
|
||
|
||
mulq $m0
|
||
add %rax,%r13
|
||
mov 16*6($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r13,%r12
|
||
mov %rdx,%r13
|
||
adc \$0,%r13
|
||
|
||
mulq $m0
|
||
add %rax,%r14
|
||
mov 16*7($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 16*0($nptr),%rax # n[0]
|
||
adc \$0,%rdx
|
||
add %r15,%r14
|
||
mov %rdx,%r15
|
||
adc \$0,%r15
|
||
|
||
dec %ecx
|
||
jnz .L8x_reduce
|
||
|
||
lea 16*8($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),$m0 # pull n0*a[0]
|
||
mov \$8,%ecx
|
||
mov 16*0($nptr),%rax
|
||
jmp .L8x_tail
|
||
|
||
.align 32
|
||
.L8x_tail:
|
||
mulq $m0
|
||
add %rax,%r8
|
||
mov 16*1($nptr),%rax
|
||
mov %r8,($tptr) # save result
|
||
mov %rdx,%r8
|
||
adc \$0,%r8
|
||
|
||
mulq $m0
|
||
add %rax,%r9
|
||
mov 16*2($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r9,%r8
|
||
lea 8($tptr),$tptr # $tptr++
|
||
mov %rdx,%r9
|
||
adc \$0,%r9
|
||
|
||
mulq $m0
|
||
add %rax,%r10
|
||
mov 16*3($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r10,%r9
|
||
mov %rdx,%r10
|
||
adc \$0,%r10
|
||
|
||
mulq $m0
|
||
add %rax,%r11
|
||
mov 16*4($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r11,%r10
|
||
mov %rdx,%r11
|
||
adc \$0,%r11
|
||
|
||
mulq $m0
|
||
add %rax,%r12
|
||
mov 16*5($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r12,%r11
|
||
mov %rdx,%r12
|
||
adc \$0,%r12
|
||
|
||
mulq $m0
|
||
add %rax,%r13
|
||
mov 16*6($nptr),%rax
|
||
adc \$0,%rdx
|
||
add %r13,%r12
|
||
mov %rdx,%r13
|
||
adc \$0,%r13
|
||
|
||
mulq $m0
|
||
add %rax,%r14
|
||
mov 16*7($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 16*0($nptr),%rax # pull n[0]
|
||
mov %rdx,%r15
|
||
adc \$0,%r15
|
||
|
||
dec %ecx
|
||
jnz .L8x_tail
|
||
|
||
lea 16*8($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:
|
||
add (%rdx),%r8 # can this overflow?
|
||
xor %rax,%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($tptr),%r15
|
||
adc \$0,%rax # top-most carry
|
||
mov -16($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
|
||
___
|
||
}
|
||
##############################################################
|
||
# Post-condition, 4x unrolled
|
||
#
|
||
{
|
||
my ($tptr,$nptr)=("%rbx","%rbp");
|
||
$code.=<<___;
|
||
#xor %rsi,%rsi # %rsi was $carry above
|
||
sub %r15,%rcx # compare top-most words
|
||
lea (%rdi,$num),$tptr # %rdi was $tptr above
|
||
adc %rsi,%rsi
|
||
mov $num,%rcx
|
||
or %rsi,%rax
|
||
movq %xmm1,$rptr # restore $rptr
|
||
xor \$1,%rax
|
||
movq %xmm1,$aptr # prepare for back-to-back call
|
||
lea ($nptr,%rax,8),$nptr
|
||
sar \$3+2,%rcx # cf=0
|
||
jmp .Lsqr4x_sub
|
||
|
||
.align 32
|
||
.Lsqr4x_sub:
|
||
.byte 0x66
|
||
mov 8*0($tptr),%r12
|
||
mov 8*1($tptr),%r13
|
||
sbb 16*0($nptr),%r12
|
||
mov 8*2($tptr),%r14
|
||
sbb 16*1($nptr),%r13
|
||
mov 8*3($tptr),%r15
|
||
lea 8*4($tptr),$tptr
|
||
sbb 16*2($nptr),%r14
|
||
mov %r12,8*0($rptr)
|
||
sbb 16*3($nptr),%r15
|
||
lea 16*4($nptr),$nptr
|
||
mov %r13,8*1($rptr)
|
||
mov %r14,8*2($rptr)
|
||
mov %r15,8*3($rptr)
|
||
lea 8*4($rptr),$rptr
|
||
|
||
inc %rcx # pass %cf
|
||
jnz .Lsqr4x_sub
|
||
___
|
||
}
|
||
$code.=<<___;
|
||
mov $num,%r10 # prepare for back-to-back call
|
||
neg $num # restore $num
|
||
ret
|
||
.size bn_sqr8x_internal,.-bn_sqr8x_internal
|
||
___
|
||
{
|
||
$code.=<<___;
|
||
.globl bn_from_montgomery
|
||
.type bn_from_montgomery,\@abi-omnipotent
|
||
.align 32
|
||
bn_from_montgomery:
|
||
testl \$7,`($win64?"48(%rsp)":"%r9d")`
|
||
jz bn_from_mont8x
|
||
xor %eax,%eax
|
||
ret
|
||
.size bn_from_montgomery,.-bn_from_montgomery
|
||
|
||
.type bn_from_mont8x,\@function,6
|
||
.align 32
|
||
bn_from_mont8x:
|
||
.byte 0x67
|
||
mov %rsp,%rax
|
||
push %rbx
|
||
push %rbp
|
||
push %r12
|
||
push %r13
|
||
push %r14
|
||
push %r15
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
lea -0x28(%rsp),%rsp
|
||
movaps %xmm6,(%rsp)
|
||
movaps %xmm7,0x10(%rsp)
|
||
___
|
||
$code.=<<___;
|
||
.byte 0x67
|
||
mov ${num}d,%r10d
|
||
shl \$3,${num}d # convert $num to bytes
|
||
shl \$3+2,%r10d # 4*$num
|
||
neg $num
|
||
mov ($n0),$n0 # *n0
|
||
|
||
##############################################################
|
||
# ensure that stack frame doesn't alias with $aptr+4*$num
|
||
# modulo 4096, which covers ret[num], am[num] and n[2*num]
|
||
# (see bn_exp.c). this is done to allow memory disambiguation
|
||
# logic do its magic.
|
||
#
|
||
lea -64(%rsp,$num,2),%r11
|
||
sub $aptr,%r11
|
||
and \$4095,%r11
|
||
cmp %r11,%r10
|
||
jb .Lfrom_sp_alt
|
||
sub %r11,%rsp # align with $aptr
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
|
||
jmp .Lfrom_sp_done
|
||
|
||
.align 32
|
||
.Lfrom_sp_alt:
|
||
lea 4096-64(,$num,2),%r10 # 4096-frame-2*$num
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
|
||
sub %r10,%r11
|
||
mov \$0,%r10
|
||
cmovc %r10,%r11
|
||
sub %r11,%rsp
|
||
.Lfrom_sp_done:
|
||
and \$-64,%rsp
|
||
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
|
||
.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 \$0x80100,%r11d
|
||
cmp \$0x80100,%r11d
|
||
jne .Lfrom_mont_nox
|
||
|
||
lea (%rax,$num),$rptr
|
||
call sqrx8x_reduction
|
||
|
||
pxor %xmm0,%xmm0
|
||
lea 48(%rsp),%rax
|
||
mov 40(%rsp),%rsi # restore %rsp
|
||
jmp .Lfrom_mont_zero
|
||
|
||
.align 32
|
||
.Lfrom_mont_nox:
|
||
___
|
||
$code.=<<___;
|
||
call sqr8x_reduction
|
||
|
||
pxor %xmm0,%xmm0
|
||
lea 48(%rsp),%rax
|
||
mov 40(%rsp),%rsi # restore %rsp
|
||
jmp .Lfrom_mont_zero
|
||
|
||
.align 32
|
||
.Lfrom_mont_zero:
|
||
movdqa %xmm0,16*0(%rax)
|
||
movdqa %xmm0,16*1(%rax)
|
||
movdqa %xmm0,16*2(%rax)
|
||
movdqa %xmm0,16*3(%rax)
|
||
lea 16*4(%rax),%rax
|
||
sub \$32,$num
|
||
jnz .Lfrom_mont_zero
|
||
|
||
mov \$1,%rax
|
||
mov -48(%rsi),%r15
|
||
mov -40(%rsi),%r14
|
||
mov -32(%rsi),%r13
|
||
mov -24(%rsi),%r12
|
||
mov -16(%rsi),%rbp
|
||
mov -8(%rsi),%rbx
|
||
lea (%rsi),%rsp
|
||
.Lfrom_epilogue:
|
||
ret
|
||
.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:
|
||
.Lmulx4x_enter:
|
||
.byte 0x67
|
||
mov %rsp,%rax
|
||
push %rbx
|
||
push %rbp
|
||
push %r12
|
||
push %r13
|
||
push %r14
|
||
push %r15
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
lea -0x28(%rsp),%rsp
|
||
movaps %xmm6,(%rsp)
|
||
movaps %xmm7,0x10(%rsp)
|
||
___
|
||
$code.=<<___;
|
||
.byte 0x67
|
||
mov ${num}d,%r10d
|
||
shl \$3,${num}d # convert $num to bytes
|
||
shl \$3+2,%r10d # 4*$num
|
||
neg $num # -$num
|
||
mov ($n0),$n0 # *n0
|
||
|
||
##############################################################
|
||
# ensure that stack frame doesn't alias with $aptr+4*$num
|
||
# modulo 4096, which covers a[num], ret[num] and n[2*num]
|
||
# (see bn_exp.c). this is done to allow memory disambiguation
|
||
# logic do its magic. [excessive frame is allocated in order
|
||
# to allow bn_from_mont8x to clear it.]
|
||
#
|
||
lea -64(%rsp,$num,2),%r11
|
||
sub $ap,%r11
|
||
and \$4095,%r11
|
||
cmp %r11,%r10
|
||
jb .Lmulx4xsp_alt
|
||
sub %r11,%rsp # align with $aptr
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+$num)
|
||
jmp .Lmulx4xsp_done
|
||
|
||
.align 32
|
||
.Lmulx4xsp_alt:
|
||
lea 4096-64(,$num,2),%r10 # 4096-frame-$num
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+$num)
|
||
sub %r10,%r11
|
||
mov \$0,%r10
|
||
cmovc %r10,%r11
|
||
sub %r11,%rsp
|
||
.Lmulx4xsp_done:
|
||
and \$-64,%rsp # ensure alignment
|
||
##############################################################
|
||
# 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
|
||
.Lmulx4x_body:
|
||
call mulx4x_internal
|
||
|
||
mov 40(%rsp),%rsi # restore %rsp
|
||
mov \$1,%rax
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
movaps -88(%rsi),%xmm6
|
||
movaps -72(%rsi),%xmm7
|
||
___
|
||
$code.=<<___;
|
||
mov -48(%rsi),%r15
|
||
mov -40(%rsi),%r14
|
||
mov -32(%rsi),%r13
|
||
mov -24(%rsi),%r12
|
||
mov -16(%rsi),%rbp
|
||
mov -8(%rsi),%rbx
|
||
lea (%rsi),%rsp
|
||
.Lmulx4x_epilogue:
|
||
ret
|
||
.size bn_mulx4x_mont_gather5,.-bn_mulx4x_mont_gather5
|
||
|
||
.type mulx4x_internal,\@abi-omnipotent
|
||
.align 32
|
||
mulx4x_internal:
|
||
.byte 0x4c,0x89,0x8c,0x24,0x08,0x00,0x00,0x00 # mov $num,8(%rsp) # save -$num
|
||
.byte 0x67
|
||
neg $num # restore $num
|
||
shl \$5,$num
|
||
lea 256($bp,$num),%r13
|
||
shr \$5+5,$num
|
||
mov `($win64?56:8)`(%rax),%r10d # load 7th argument
|
||
sub \$1,$num
|
||
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
|
||
$code.=<<___;
|
||
mov %r10,%r11
|
||
shr \$`log($N/8)/log(2)`,%r10
|
||
and \$`$N/8-1`,%r11
|
||
not %r10
|
||
lea .Lmagic_masks(%rip),%rax
|
||
and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
|
||
lea 96($bp,%r11,8),$bptr # pointer within 1st cache line
|
||
movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
|
||
movq 8(%rax,%r10,8),%xmm5 # cache line contains element
|
||
add \$7,%r11
|
||
movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
|
||
movq 24(%rax,%r10,8),%xmm7
|
||
and \$7,%r11
|
||
|
||
movq `0*$STRIDE/4-96`($bptr),%xmm0
|
||
lea $STRIDE($bptr),$tptr # borrow $tptr
|
||
movq `1*$STRIDE/4-96`($bptr),%xmm1
|
||
pand %xmm4,%xmm0
|
||
movq `2*$STRIDE/4-96`($bptr),%xmm2
|
||
pand %xmm5,%xmm1
|
||
movq `3*$STRIDE/4-96`($bptr),%xmm3
|
||
pand %xmm6,%xmm2
|
||
por %xmm1,%xmm0
|
||
movq `0*$STRIDE/4-96`($tptr),%xmm1
|
||
pand %xmm7,%xmm3
|
||
por %xmm2,%xmm0
|
||
movq `1*$STRIDE/4-96`($tptr),%xmm2
|
||
por %xmm3,%xmm0
|
||
.byte 0x67,0x67
|
||
pand %xmm4,%xmm1
|
||
movq `2*$STRIDE/4-96`($tptr),%xmm3
|
||
|
||
movq %xmm0,%rdx # bp[0]
|
||
movq `3*$STRIDE/4-96`($tptr),%xmm0
|
||
lea 2*$STRIDE($bptr),$bptr # next &b[i]
|
||
pand %xmm5,%xmm2
|
||
.byte 0x67,0x67
|
||
pand %xmm6,%xmm3
|
||
##############################################################
|
||
# $tptr is chosen so that writing to top-most element of the
|
||
# vector occurs just "above" references to powers table,
|
||
# "above" modulo cache-line size, which effectively precludes
|
||
# possibility of memory disambiguation logic failure when
|
||
# accessing the table.
|
||
#
|
||
lea 64+8*4+8(%rsp,%r11,8),$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
|
||
|
||
por %xmm2,%xmm1
|
||
pand %xmm7,%xmm0
|
||
por %xmm3,%xmm1
|
||
mov $bptr,8+8(%rsp) # off-load &b[i]
|
||
por %xmm1,%xmm0
|
||
|
||
.byte 0x48,0x8d,0xb6,0x20,0x00,0x00,0x00 # lea 4*8($aptr),$aptr
|
||
adcx %rax,%r13
|
||
adcx $zero,%r14 # cf=0
|
||
|
||
mulx 0*16($nptr),%rax,%r10
|
||
adcx %rax,%r15 # discarded
|
||
adox %r11,%r10
|
||
mulx 1*16($nptr),%rax,%r11
|
||
adcx %rax,%r10
|
||
adox %r12,%r11
|
||
mulx 2*16($nptr),%rax,%r12
|
||
mov 24+8(%rsp),$bptr # counter value
|
||
.byte 0x66
|
||
mov %r10,-8*4($tptr)
|
||
adcx %rax,%r11
|
||
adox %r13,%r12
|
||
mulx 3*16($nptr),%rax,%r15
|
||
.byte 0x67,0x67
|
||
mov $bi,%rdx
|
||
mov %r11,-8*3($tptr)
|
||
adcx %rax,%r12
|
||
adox $zero,%r15 # of=0
|
||
.byte 0x48,0x8d,0x89,0x40,0x00,0x00,0x00 # lea 4*16($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),$tptr
|
||
|
||
adox %r15,%r10
|
||
mulx 0*16($nptr),%rax,%r15
|
||
adcx %rax,%r10
|
||
adox %r15,%r11
|
||
mulx 1*16($nptr),%rax,%r15
|
||
adcx %rax,%r11
|
||
adox %r15,%r12
|
||
mulx 2*16($nptr),%rax,%r15
|
||
mov %r10,-5*8($tptr)
|
||
adcx %rax,%r12
|
||
mov %r11,-4*8($tptr)
|
||
adox %r15,%r13
|
||
mulx 3*16($nptr),%rax,%r15
|
||
mov $bi,%rdx
|
||
mov %r12,-3*8($tptr)
|
||
adcx %rax,%r13
|
||
adox $zero,%r15
|
||
lea 4*16($nptr),$nptr
|
||
mov %r13,-2*8($tptr)
|
||
|
||
dec $bptr # of=0, pass cf
|
||
jnz .Lmulx4x_1st
|
||
|
||
mov 8(%rsp),$num # load -num
|
||
movq %xmm0,%rdx # bp[1]
|
||
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:
|
||
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,2),$nptr # rewind $nptr
|
||
lea 4*8($aptr),$aptr
|
||
adox -1*8($tptr),%r13
|
||
adcx $zero,%r14
|
||
adox $zero,%r14
|
||
|
||
.byte 0x67
|
||
mov $mi,%r15
|
||
imulq 32+8(%rsp),$mi # "t[0]"*n0
|
||
|
||
movq `0*$STRIDE/4-96`($bptr),%xmm0
|
||
.byte 0x67,0x67
|
||
mov $mi,%rdx
|
||
movq `1*$STRIDE/4-96`($bptr),%xmm1
|
||
.byte 0x67
|
||
pand %xmm4,%xmm0
|
||
movq `2*$STRIDE/4-96`($bptr),%xmm2
|
||
.byte 0x67
|
||
pand %xmm5,%xmm1
|
||
movq `3*$STRIDE/4-96`($bptr),%xmm3
|
||
add \$$STRIDE,$bptr # next &b[i]
|
||
.byte 0x67
|
||
pand %xmm6,%xmm2
|
||
por %xmm1,%xmm0
|
||
pand %xmm7,%xmm3
|
||
xor $zero,$zero # cf=0, of=0
|
||
mov $bptr,8+8(%rsp) # off-load &b[i]
|
||
|
||
mulx 0*16($nptr),%rax,%r10
|
||
adcx %rax,%r15 # discarded
|
||
adox %r11,%r10
|
||
mulx 1*16($nptr),%rax,%r11
|
||
adcx %rax,%r10
|
||
adox %r12,%r11
|
||
mulx 2*16($nptr),%rax,%r12
|
||
adcx %rax,%r11
|
||
adox %r13,%r12
|
||
mulx 3*16($nptr),%rax,%r15
|
||
mov $bi,%rdx
|
||
por %xmm2,%xmm0
|
||
mov 24+8(%rsp),$bptr # counter value
|
||
mov %r10,-8*4($tptr)
|
||
por %xmm3,%xmm0
|
||
adcx %rax,%r12
|
||
mov %r11,-8*3($tptr)
|
||
adox $zero,%r15 # of=0
|
||
mov %r12,-8*2($tptr)
|
||
lea 4*16($nptr),$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 $zero,%r14 # cf=0
|
||
|
||
adox %r15,%r10
|
||
mulx 0*16($nptr),%rax,%r15
|
||
adcx %rax,%r10
|
||
adox %r15,%r11
|
||
mulx 1*16($nptr),%rax,%r15
|
||
adcx %rax,%r11
|
||
adox %r15,%r12
|
||
mulx 2*16($nptr),%rax,%r15
|
||
mov %r10,-5*8($tptr)
|
||
adcx %rax,%r12
|
||
adox %r15,%r13
|
||
mov %r11,-4*8($tptr)
|
||
mulx 3*16($nptr),%rax,%r15
|
||
mov $bi,%rdx
|
||
lea 4*16($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
|
||
movq %xmm0,%rdx # bp[i+1]
|
||
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 -16($nptr),%r10
|
||
xor %r15,%r15
|
||
sub %r14,%r10 # compare top-most words
|
||
adc %r15,%r15
|
||
or %r15,$zero
|
||
xor \$1,$zero
|
||
lea ($tptr,$num),%rdi # rewind $tptr
|
||
lea ($nptr,$num,2),$nptr # rewind $nptr
|
||
.byte 0x67,0x67
|
||
sar \$3+2,$num # cf=0
|
||
lea ($nptr,$zero,8),%rbp
|
||
mov 56+8(%rsp),%rdx # restore rp
|
||
mov $num,%rcx
|
||
jmp .Lsqrx4x_sub # common post-condition
|
||
.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:
|
||
.Lpowerx5_enter:
|
||
.byte 0x67
|
||
mov %rsp,%rax
|
||
push %rbx
|
||
push %rbp
|
||
push %r12
|
||
push %r13
|
||
push %r14
|
||
push %r15
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
lea -0x28(%rsp),%rsp
|
||
movaps %xmm6,(%rsp)
|
||
movaps %xmm7,0x10(%rsp)
|
||
___
|
||
$code.=<<___;
|
||
.byte 0x67
|
||
mov ${num}d,%r10d
|
||
shl \$3,${num}d # convert $num to bytes
|
||
shl \$3+2,%r10d # 4*$num
|
||
neg $num
|
||
mov ($n0),$n0 # *n0
|
||
|
||
##############################################################
|
||
# ensure that stack frame doesn't alias with $aptr+4*$num
|
||
# modulo 4096, which covers ret[num], am[num] and n[2*num]
|
||
# (see bn_exp.c). this is done to allow memory disambiguation
|
||
# logic do its magic.
|
||
#
|
||
lea -64(%rsp,$num,2),%r11
|
||
sub $aptr,%r11
|
||
and \$4095,%r11
|
||
cmp %r11,%r10
|
||
jb .Lpwrx_sp_alt
|
||
sub %r11,%rsp # align with $aptr
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
|
||
jmp .Lpwrx_sp_done
|
||
|
||
.align 32
|
||
.Lpwrx_sp_alt:
|
||
lea 4096-64(,$num,2),%r10 # 4096-frame-2*$num
|
||
lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
|
||
sub %r10,%r11
|
||
mov \$0,%r10
|
||
cmovc %r10,%r11
|
||
sub %r11,%rsp
|
||
.Lpwrx_sp_done:
|
||
and \$-64,%rsp
|
||
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 $n0, 32(%rsp)
|
||
mov %rax, 40(%rsp) # save original %rsp
|
||
.Lpowerx5_body:
|
||
|
||
call __bn_sqrx8x_internal
|
||
call __bn_sqrx8x_internal
|
||
call __bn_sqrx8x_internal
|
||
call __bn_sqrx8x_internal
|
||
call __bn_sqrx8x_internal
|
||
|
||
mov %r10,$num # -num
|
||
mov $aptr,$rptr
|
||
movq %xmm2,$nptr
|
||
movq %xmm4,$bptr
|
||
mov 40(%rsp),%rax
|
||
|
||
call mulx4x_internal
|
||
|
||
mov 40(%rsp),%rsi # restore %rsp
|
||
mov \$1,%rax
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
movaps -88(%rsi),%xmm6
|
||
movaps -72(%rsi),%xmm7
|
||
___
|
||
$code.=<<___;
|
||
mov -48(%rsi),%r15
|
||
mov -40(%rsi),%r14
|
||
mov -32(%rsi),%r13
|
||
mov -24(%rsi),%r12
|
||
mov -16(%rsi),%rbp
|
||
mov -8(%rsi),%rbx
|
||
lea (%rsi),%rsp
|
||
.Lpowerx5_epilogue:
|
||
ret
|
||
.size bn_powerx5,.-bn_powerx5
|
||
|
||
.globl bn_sqrx8x_internal
|
||
.hidden bn_sqrx8x_internal
|
||
.type bn_sqrx8x_internal,\@abi-omnipotent
|
||
.align 32
|
||
bn_sqrx8x_internal:
|
||
__bn_sqrx8x_internal:
|
||
##################################################################
|
||
# Squaring part:
|
||
#
|
||
# a) multiply-n-add everything but a[i]*a[i];
|
||
# b) shift result of a) by 1 to the left and accumulate
|
||
# a[i]*a[i] products;
|
||
#
|
||
##################################################################
|
||
# a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
|
||
# a[1]a[0]
|
||
# a[2]a[0]
|
||
# a[3]a[0]
|
||
# a[2]a[1]
|
||
# a[3]a[1]
|
||
# a[3]a[2]
|
||
#
|
||
# a[4]a[0]
|
||
# a[5]a[0]
|
||
# a[6]a[0]
|
||
# a[7]a[0]
|
||
# a[4]a[1]
|
||
# a[5]a[1]
|
||
# a[6]a[1]
|
||
# a[7]a[1]
|
||
# a[4]a[2]
|
||
# a[5]a[2]
|
||
# a[6]a[2]
|
||
# a[7]a[2]
|
||
# a[4]a[3]
|
||
# a[5]a[3]
|
||
# a[6]a[3]
|
||
# a[7]a[3]
|
||
#
|
||
# a[5]a[4]
|
||
# a[6]a[4]
|
||
# a[7]a[4]
|
||
# a[6]a[5]
|
||
# a[7]a[5]
|
||
# a[7]a[6]
|
||
# a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
|
||
___
|
||
{
|
||
my ($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:
|
||
sub 16+8(%rsp),%r8 # consume last carry
|
||
mov 24+8(%rsp),$carry # initial $tptr, borrow $carry
|
||
mov 0*8($aptr),%rdx # a[8], modulo-scheduled
|
||
xor %ebp,%ebp # xor $zero,$zero
|
||
mov %r8,0*8($tptr)
|
||
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
|
||
sqrx8x_reduction:
|
||
xor %eax,%eax # initial top-most carry bit
|
||
mov 32+8(%rsp),%rbx # n0
|
||
mov 48+8(%rsp),%rdx # "%r8", 8*0($tptr)
|
||
lea -128($nptr,$num,2),%rcx # end of n[]
|
||
#lea 48+8(%rsp,$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 16*0($nptr),%rax,%r8 # n[0]
|
||
adcx %rbx,%rax # discarded
|
||
adox %r9,%r8
|
||
|
||
mulx 16*1($nptr),%rbx,%r9 # n[1]
|
||
adcx %rbx,%r8
|
||
adox %r10,%r9
|
||
|
||
mulx 16*2($nptr),%rbx,%r10
|
||
adcx %rbx,%r9
|
||
adox %r11,%r10
|
||
|
||
mulx 16*3($nptr),%rbx,%r11
|
||
adcx %rbx,%r10
|
||
adox %r12,%r11
|
||
|
||
.byte 0xc4,0x62,0xe3,0xf6,0xa5,0x40,0x00,0x00,0x00 # mulx 16*4($nptr),%rbx,%r12
|
||
mov %rdx,%rax
|
||
mov %r8,%rdx
|
||
adcx %rbx,%r11
|
||
adox %r13,%r12
|
||
|
||
mulx 32+8(%rsp),%rbx,%rdx # %rdx discarded
|
||
mov %rax,%rdx
|
||
mov %rax,64+48+8(%rsp,%rcx,8) # put aside n0*a[i]
|
||
|
||
mulx 16*5($nptr),%rax,%r13
|
||
adcx %rax,%r12
|
||
adox %r14,%r13
|
||
|
||
mulx 16*6($nptr),%rax,%r14
|
||
adcx %rax,%r13
|
||
adox %r15,%r14
|
||
|
||
mulx 16*7($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($tptr),%r8
|
||
lea 16*8($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 16*0($nptr),%rax,%r8
|
||
adcx %rax,%rbx
|
||
adox %r9,%r8
|
||
|
||
mulx 16*1($nptr),%rax,%r9
|
||
adcx %rax,%r8
|
||
adox %r10,%r9
|
||
|
||
mulx 16*2($nptr),%rax,%r10
|
||
adcx %rax,%r9
|
||
adox %r11,%r10
|
||
|
||
mulx 16*3($nptr),%rax,%r11
|
||
adcx %rax,%r10
|
||
adox %r12,%r11
|
||
|
||
.byte 0xc4,0x62,0xfb,0xf6,0xa5,0x40,0x00,0x00,0x00 # mulx 16*4($nptr),%rax,%r12
|
||
adcx %rax,%r11
|
||
adox %r13,%r12
|
||
|
||
mulx 16*5($nptr),%rax,%r13
|
||
adcx %rax,%r12
|
||
adox %r14,%r13
|
||
|
||
mulx 16*6($nptr),%rax,%r14
|
||
adcx %rax,%r13
|
||
adox %r15,%r14
|
||
|
||
mulx 16*7($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),$carry # mov 16(%rsp),%cf
|
||
mov 48+8(%rsp),%rdx # pull n0*a[0]
|
||
lea 16*8($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:
|
||
add 24+8(%rsp),%r8 # can this overflow?
|
||
mov $carry,%rax # xor %rax,%rax
|
||
|
||
sub 16+8(%rsp),$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 16*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($tptr),%r15
|
||
adc %rax,%rax # top-most carry
|
||
|
||
mov 32+8(%rsp),%rbx # n0
|
||
mov 8*8($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),$tptr # start of current t[] window
|
||
cmp 8+8(%rsp),%r8 # end of t[]?
|
||
jb .Lsqrx8x_reduction_loop
|
||
___
|
||
}
|
||
##############################################################
|
||
# Post-condition, 4x unrolled
|
||
#
|
||
{
|
||
my ($rptr,$nptr)=("%rdx","%rbp");
|
||
my @ri=map("%r$_",(10..13));
|
||
my @ni=map("%r$_",(14..15));
|
||
$code.=<<___;
|
||
xor %rbx,%rbx
|
||
sub %r15,%rsi # compare top-most words
|
||
adc %rbx,%rbx
|
||
mov %rcx,%r10 # -$num
|
||
.byte 0x67
|
||
or %rbx,%rax
|
||
.byte 0x67
|
||
mov %rcx,%r9 # -$num
|
||
xor \$1,%rax
|
||
sar \$3+2,%rcx # cf=0
|
||
#lea 48+8(%rsp,%r9),$tptr
|
||
lea ($nptr,%rax,8),$nptr
|
||
movq %xmm1,$rptr # restore $rptr
|
||
movq %xmm1,$aptr # prepare for back-to-back call
|
||
jmp .Lsqrx4x_sub
|
||
|
||
.align 32
|
||
.Lsqrx4x_sub:
|
||
.byte 0x66
|
||
mov 8*0($tptr),%r12
|
||
mov 8*1($tptr),%r13
|
||
sbb 16*0($nptr),%r12
|
||
mov 8*2($tptr),%r14
|
||
sbb 16*1($nptr),%r13
|
||
mov 8*3($tptr),%r15
|
||
lea 8*4($tptr),$tptr
|
||
sbb 16*2($nptr),%r14
|
||
mov %r12,8*0($rptr)
|
||
sbb 16*3($nptr),%r15
|
||
lea 16*4($nptr),$nptr
|
||
mov %r13,8*1($rptr)
|
||
mov %r14,8*2($rptr)
|
||
mov %r15,8*3($rptr)
|
||
lea 8*4($rptr),$rptr
|
||
|
||
inc %rcx
|
||
jnz .Lsqrx4x_sub
|
||
___
|
||
}
|
||
$code.=<<___;
|
||
neg %r9 # restore $num
|
||
|
||
ret
|
||
.size bn_sqrx8x_internal,.-bn_sqrx8x_internal
|
||
___
|
||
}}}
|
||
{
|
||
my ($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:
|
||
mov $inp,%r10
|
||
mov $num,%ecx
|
||
shr \$3,$num
|
||
movzw (%r10,$num),%eax
|
||
and \$7,%ecx
|
||
shrl %cl,%eax
|
||
and \$31,%eax
|
||
ret
|
||
.size bn_get_bits5,.-bn_get_bits5
|
||
|
||
.globl bn_scatter5
|
||
.type bn_scatter5,\@abi-omnipotent
|
||
.align 16
|
||
bn_scatter5:
|
||
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
|
||
.size bn_scatter5,.-bn_scatter5
|
||
|
||
.globl bn_gather5
|
||
.type bn_gather5,\@abi-omnipotent
|
||
.align 16
|
||
bn_gather5:
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
.LSEH_begin_bn_gather5:
|
||
# I can't trust assembler to use specific encoding:-(
|
||
.byte 0x48,0x83,0xec,0x28 #sub \$0x28,%rsp
|
||
.byte 0x0f,0x29,0x34,0x24 #movaps %xmm6,(%rsp)
|
||
.byte 0x0f,0x29,0x7c,0x24,0x10 #movdqa %xmm7,0x10(%rsp)
|
||
___
|
||
$code.=<<___;
|
||
mov $idx,%r11d
|
||
shr \$`log($N/8)/log(2)`,$idx
|
||
and \$`$N/8-1`,%r11
|
||
not $idx
|
||
lea .Lmagic_masks(%rip),%rax
|
||
and \$`2**5/($N/8)-1`,$idx # 5 is "window size"
|
||
lea 128($tbl,%r11,8),$tbl # pointer within 1st cache line
|
||
movq 0(%rax,$idx,8),%xmm4 # set of masks denoting which
|
||
movq 8(%rax,$idx,8),%xmm5 # cache line contains element
|
||
movq 16(%rax,$idx,8),%xmm6 # denoted by 7th argument
|
||
movq 24(%rax,$idx,8),%xmm7
|
||
jmp .Lgather
|
||
.align 16
|
||
.Lgather:
|
||
movq `0*$STRIDE/4-128`($tbl),%xmm0
|
||
movq `1*$STRIDE/4-128`($tbl),%xmm1
|
||
pand %xmm4,%xmm0
|
||
movq `2*$STRIDE/4-128`($tbl),%xmm2
|
||
pand %xmm5,%xmm1
|
||
movq `3*$STRIDE/4-128`($tbl),%xmm3
|
||
pand %xmm6,%xmm2
|
||
por %xmm1,%xmm0
|
||
pand %xmm7,%xmm3
|
||
.byte 0x67,0x67
|
||
por %xmm2,%xmm0
|
||
lea $STRIDE($tbl),$tbl
|
||
por %xmm3,%xmm0
|
||
|
||
movq %xmm0,($out) # m0=bp[0]
|
||
lea 8($out),$out
|
||
sub \$1,$num
|
||
jnz .Lgather
|
||
___
|
||
$code.=<<___ if ($win64);
|
||
movaps (%rsp),%xmm6
|
||
movaps 0x10(%rsp),%xmm7
|
||
lea 0x28(%rsp),%rsp
|
||
___
|
||
$code.=<<___;
|
||
ret
|
||
.LSEH_end_bn_gather5:
|
||
.size bn_gather5,.-bn_gather5
|
||
___
|
||
}
|
||
$code.=<<___;
|
||
.align 64
|
||
.Lmagic_masks:
|
||
.long 0,0, 0,0, 0,0, -1,-1
|
||
.long 0,0, 0,0, 0,0, 0,0
|
||
.asciz "Montgomery Multiplication with scatter/gather for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
|
||
___
|
||
|
||
# EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
|
||
# CONTEXT *context,DISPATCHER_CONTEXT *disp)
|
||
if ($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($disp),%r11 # disp->HandlerData
|
||
|
||
mov 0(%r11),%r10d # HandlerData[0]
|
||
lea (%rsi,%r10),%r10 # end of prologue label
|
||
cmp %r10,%rbx # context->Rip<end of prologue label
|
||
jb .Lcommon_seh_tail
|
||
|
||
mov 152($context),%rax # pull context->Rsp
|
||
|
||
mov 4(%r11),%r10d # HandlerData[1]
|
||
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
|
||
jb .Lbody_40
|
||
|
||
mov 192($context),%r10 # pull $num
|
||
mov 8(%rax,%r10,8),%rax # pull saved stack pointer
|
||
jmp .Lbody_proceed
|
||
|
||
.Lbody_40:
|
||
mov 40(%rax),%rax # pull saved stack pointer
|
||
.Lbody_proceed:
|
||
|
||
movaps -88(%rax),%xmm0
|
||
movaps -72(%rax),%xmm1
|
||
|
||
mov -8(%rax),%rbx
|
||
mov -16(%rax),%rbp
|
||
mov -24(%rax),%r12
|
||
mov -32(%rax),%r13
|
||
mov -40(%rax),%r14
|
||
mov -48(%rax),%r15
|
||
mov %rbx,144($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($context) # restore context->R15
|
||
movups %xmm0,512($context) # restore context->Xmm6
|
||
movups %xmm1,528($context) # restore context->Xmm7
|
||
|
||
.Lcommon_seh_tail:
|
||
mov 8(%rax),%rdi
|
||
mov 16(%rax),%rsi
|
||
mov %rax,152($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_epilogue # HandlerData[]
|
||
.align 8
|
||
.LSEH_info_bn_mul4x_mont_gather5:
|
||
.byte 9,0,0,0
|
||
.rva mul_handler
|
||
.rva .Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
|
||
.align 8
|
||
.LSEH_info_bn_power5:
|
||
.byte 9,0,0,0
|
||
.rva mul_handler
|
||
.rva .Lpower5_body,.Lpower5_epilogue # HandlerData[]
|
||
.align 8
|
||
.LSEH_info_bn_from_mont8x:
|
||
.byte 9,0,0,0
|
||
.rva mul_handler
|
||
.rva .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_body,.Lmulx4x_epilogue # HandlerData[]
|
||
.align 8
|
||
.LSEH_info_bn_powerx5:
|
||
.byte 9,0,0,0
|
||
.rva mul_handler
|
||
.rva .Lpowerx5_body,.Lpowerx5_epilogue # HandlerData[]
|
||
___
|
||
$code.=<<___;
|
||
.align 8
|
||
.LSEH_info_bn_gather5:
|
||
.byte 0x01,0x0d,0x05,0x00
|
||
.byte 0x0d,0x78,0x01,0x00 #movaps 0x10(rsp),xmm7
|
||
.byte 0x08,0x68,0x00,0x00 #movaps (rsp),xmm6
|
||
.byte 0x04,0x42,0x00,0x00 #sub rsp,0x28
|
||
.align 8
|
||
___
|
||
}
|
||
|
||
$code =~ s/\`([^\`]*)\`/eval($1)/gem;
|
||
|
||
print $code;
|
||
close STDOUT;
|