278d34234f
Since we pre-generate our perlasm, having the output of these files be sensitive to the environment the run in is unhelpful. It would be bad to suddenly change what features we do or don't compile in whenever workstations' toolchains change or if developers do or don't have CC variables set. Previously, all compiler-version-gated features were turned on in https://boringssl-review.googlesource.com/6260, but this broke the build. I also wasn't thorough enough in gathering performance numbers. So, flip them all to off instead. I'll enable them one-by-one as they're tested. This should result in no change to generated assembly. Change-Id: Ib4259b3f97adc4939cb0557c5580e8def120d5bc Reviewed-on: https://boringssl-review.googlesource.com/6383 Reviewed-by: Adam Langley <agl@google.com>
3492 lines
75 KiB
Perl
3492 lines
75 KiB
Perl
#!/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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# In upstream, this is controlled by shelling out to the compiler to check
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# versions, but BoringSSL is intended to be used with pre-generated perlasm
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# output, so this isn't useful anyway.
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#
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# TODO(davidben): Enable this after testing. $addx goes up to 1.
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$addx = 0;
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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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mov $num,$j # j=num
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.align 16
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.Lcopy: # copy or in-place refresh
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mov (%rsp,$i,8),$ap
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mov ($rp,$i,8),$np
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xor $np,$ap # conditional select:
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and %rax,$ap # ((ap ^ np) & %rax) ^ np
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xor $np,$ap # ap = borrow?tp:rp
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mov $i,(%rsp,$i,8) # zap temporary vector
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mov $ap,($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
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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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.byte 0x67
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mov ${num}d,%r10d
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shl \$3,${num}d
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shl \$3+2,%r10d # 4*$num
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neg $num # -$num
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|
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##############################################################
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# ensure that stack frame doesn't alias with $aptr+4*$num
|
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# modulo 4096, which covers ret[num], am[num] and n[2*num]
|
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# (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
|
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sub $ap,%r11
|
||
and \$4095,%r11
|
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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
|
||
___
|
||
$code.=<<___;
|
||
mov -48(%rsi),%r15
|
||
mov -40(%rsi),%r14
|
||
mov -32(%rsi),%r13
|
||
mov -24(%rsi),%r12
|
||
mov -16(%rsi),%rbp
|
||
mov -8(%rsi),%rbx
|
||
lea (%rsi),%rsp
|
||
.Lmul4x_epilogue:
|
||
ret
|
||
.size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
|
||
|
||
.type mul4x_internal,\@abi-omnipotent
|
||
.align 32
|
||
mul4x_internal:
|
||
shl \$5,$num
|
||
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_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;
|