1504 lines
36 KiB
Perl
1504 lines
36 KiB
Perl
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#!/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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# March 2015
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#
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# "Teaser" Montgomery multiplication module for ARMv8. Needs more
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# work. While it does improve RSA sign performance by 20-30% (less for
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# longer keys) on most processors, for some reason RSA2048 is not
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# faster and RSA4096 goes 15-20% slower on Cortex-A57. Multiplication
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# instruction issue rate is limited on processor in question, meaning
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# that dedicated squaring procedure is a must. Well, actually all
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# contemporary AArch64 processors seem to have limited multiplication
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# issue rate, i.e. they can't issue multiplication every cycle, which
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# explains moderate improvement coefficients in comparison to
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# compiler-generated code. Recall that compiler is instructed to use
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# umulh and therefore uses same amount of multiplication instructions
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# to do the job. Assembly's edge is to minimize number of "collateral"
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# instructions and of course instruction scheduling.
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#
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# April 2015
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#
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# Squaring procedure that handles lengths divisible by 8 improves
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# RSA/DSA performance by 25-40-60% depending on processor and key
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# length. Overall improvement coefficients are always positive in
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# comparison to compiler-generated code. On Cortex-A57 improvement
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# is still modest on longest key lengths, while others exhibit e.g.
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# 50-70% improvement for RSA4096 sign. RSA2048 sign is ~25% faster
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# on Cortex-A57 and ~60-100% faster on others.
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$flavour = shift;
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$output = shift;
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$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
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( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or
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( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or
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die "can't locate arm-xlate.pl";
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open OUT,"| \"$^X\" $xlate $flavour $output";
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*STDOUT=*OUT;
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($lo0,$hi0,$aj,$m0,$alo,$ahi,
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$lo1,$hi1,$nj,$m1,$nlo,$nhi,
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$ovf, $i,$j,$tp,$tj) = map("x$_",6..17,19..24);
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# int bn_mul_mont(
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$rp="x0"; # BN_ULONG *rp,
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$ap="x1"; # const BN_ULONG *ap,
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$bp="x2"; # const BN_ULONG *bp,
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$np="x3"; # const BN_ULONG *np,
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$n0="x4"; # const BN_ULONG *n0,
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$num="x5"; # int num);
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$code.=<<___;
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.text
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.globl bn_mul_mont
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.type bn_mul_mont,%function
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.align 5
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bn_mul_mont:
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tst $num,#7
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b.eq __bn_sqr8x_mont
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tst $num,#3
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b.eq __bn_mul4x_mont
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.Lmul_mont:
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stp x29,x30,[sp,#-64]!
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add x29,sp,#0
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stp x19,x20,[sp,#16]
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stp x21,x22,[sp,#32]
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stp x23,x24,[sp,#48]
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ldr $m0,[$bp],#8 // bp[0]
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sub $tp,sp,$num,lsl#3
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ldp $hi0,$aj,[$ap],#16 // ap[0..1]
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lsl $num,$num,#3
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ldr $n0,[$n0] // *n0
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and $tp,$tp,#-16 // ABI says so
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ldp $hi1,$nj,[$np],#16 // np[0..1]
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mul $lo0,$hi0,$m0 // ap[0]*bp[0]
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sub $j,$num,#16 // j=num-2
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umulh $hi0,$hi0,$m0
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mul $alo,$aj,$m0 // ap[1]*bp[0]
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umulh $ahi,$aj,$m0
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mul $m1,$lo0,$n0 // "tp[0]"*n0
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mov sp,$tp // alloca
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// (*) mul $lo1,$hi1,$m1 // np[0]*m1
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umulh $hi1,$hi1,$m1
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mul $nlo,$nj,$m1 // np[1]*m1
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// (*) adds $lo1,$lo1,$lo0 // discarded
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// (*) As for removal of first multiplication and addition
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// instructions. The outcome of first addition is
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// guaranteed to be zero, which leaves two computationally
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// significant outcomes: it either carries or not. Then
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// question is when does it carry? Is there alternative
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// way to deduce it? If you follow operations, you can
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// observe that condition for carry is quite simple:
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// $lo0 being non-zero. So that carry can be calculated
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// by adding -1 to $lo0. That's what next instruction does.
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subs xzr,$lo0,#1 // (*)
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umulh $nhi,$nj,$m1
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adc $hi1,$hi1,xzr
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cbz $j,.L1st_skip
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.L1st:
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ldr $aj,[$ap],#8
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adds $lo0,$alo,$hi0
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sub $j,$j,#8 // j--
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adc $hi0,$ahi,xzr
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ldr $nj,[$np],#8
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adds $lo1,$nlo,$hi1
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mul $alo,$aj,$m0 // ap[j]*bp[0]
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adc $hi1,$nhi,xzr
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umulh $ahi,$aj,$m0
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adds $lo1,$lo1,$lo0
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mul $nlo,$nj,$m1 // np[j]*m1
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adc $hi1,$hi1,xzr
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umulh $nhi,$nj,$m1
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str $lo1,[$tp],#8 // tp[j-1]
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cbnz $j,.L1st
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.L1st_skip:
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adds $lo0,$alo,$hi0
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sub $ap,$ap,$num // rewind $ap
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adc $hi0,$ahi,xzr
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adds $lo1,$nlo,$hi1
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sub $np,$np,$num // rewind $np
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adc $hi1,$nhi,xzr
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adds $lo1,$lo1,$lo0
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sub $i,$num,#8 // i=num-1
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adcs $hi1,$hi1,$hi0
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adc $ovf,xzr,xzr // upmost overflow bit
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stp $lo1,$hi1,[$tp]
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.Louter:
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ldr $m0,[$bp],#8 // bp[i]
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ldp $hi0,$aj,[$ap],#16
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ldr $tj,[sp] // tp[0]
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add $tp,sp,#8
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mul $lo0,$hi0,$m0 // ap[0]*bp[i]
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sub $j,$num,#16 // j=num-2
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umulh $hi0,$hi0,$m0
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ldp $hi1,$nj,[$np],#16
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mul $alo,$aj,$m0 // ap[1]*bp[i]
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adds $lo0,$lo0,$tj
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umulh $ahi,$aj,$m0
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adc $hi0,$hi0,xzr
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mul $m1,$lo0,$n0
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sub $i,$i,#8 // i--
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// (*) mul $lo1,$hi1,$m1 // np[0]*m1
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umulh $hi1,$hi1,$m1
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mul $nlo,$nj,$m1 // np[1]*m1
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// (*) adds $lo1,$lo1,$lo0
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subs xzr,$lo0,#1 // (*)
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umulh $nhi,$nj,$m1
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cbz $j,.Linner_skip
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.Linner:
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ldr $aj,[$ap],#8
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adc $hi1,$hi1,xzr
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ldr $tj,[$tp],#8 // tp[j]
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adds $lo0,$alo,$hi0
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sub $j,$j,#8 // j--
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adc $hi0,$ahi,xzr
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adds $lo1,$nlo,$hi1
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ldr $nj,[$np],#8
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adc $hi1,$nhi,xzr
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mul $alo,$aj,$m0 // ap[j]*bp[i]
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adds $lo0,$lo0,$tj
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umulh $ahi,$aj,$m0
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adc $hi0,$hi0,xzr
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mul $nlo,$nj,$m1 // np[j]*m1
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adds $lo1,$lo1,$lo0
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umulh $nhi,$nj,$m1
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str $lo1,[$tp,#-16] // tp[j-1]
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cbnz $j,.Linner
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.Linner_skip:
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ldr $tj,[$tp],#8 // tp[j]
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adc $hi1,$hi1,xzr
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adds $lo0,$alo,$hi0
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sub $ap,$ap,$num // rewind $ap
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adc $hi0,$ahi,xzr
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adds $lo1,$nlo,$hi1
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sub $np,$np,$num // rewind $np
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adcs $hi1,$nhi,$ovf
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adc $ovf,xzr,xzr
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adds $lo0,$lo0,$tj
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adc $hi0,$hi0,xzr
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adds $lo1,$lo1,$lo0
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adcs $hi1,$hi1,$hi0
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adc $ovf,$ovf,xzr // upmost overflow bit
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stp $lo1,$hi1,[$tp,#-16]
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cbnz $i,.Louter
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// Final step. We see if result is larger than modulus, and
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// if it is, subtract the modulus. But comparison implies
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// subtraction. So we subtract modulus, see if it borrowed,
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// and conditionally copy original value.
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ldr $tj,[sp] // tp[0]
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add $tp,sp,#8
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ldr $nj,[$np],#8 // np[0]
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subs $j,$num,#8 // j=num-1 and clear borrow
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mov $ap,$rp
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.Lsub:
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sbcs $aj,$tj,$nj // tp[j]-np[j]
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ldr $tj,[$tp],#8
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sub $j,$j,#8 // j--
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ldr $nj,[$np],#8
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str $aj,[$ap],#8 // rp[j]=tp[j]-np[j]
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cbnz $j,.Lsub
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sbcs $aj,$tj,$nj
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sbcs $ovf,$ovf,xzr // did it borrow?
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str $aj,[$ap],#8 // rp[num-1]
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ldr $tj,[sp] // tp[0]
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add $tp,sp,#8
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ldr $aj,[$rp],#8 // rp[0]
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sub $num,$num,#8 // num--
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nop
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.Lcond_copy:
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sub $num,$num,#8 // num--
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csel $nj,$tj,$aj,lo // did it borrow?
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ldr $tj,[$tp],#8
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ldr $aj,[$rp],#8
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str xzr,[$tp,#-16] // wipe tp
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str $nj,[$rp,#-16]
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cbnz $num,.Lcond_copy
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csel $nj,$tj,$aj,lo
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str xzr,[$tp,#-8] // wipe tp
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str $nj,[$rp,#-8]
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ldp x19,x20,[x29,#16]
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mov sp,x29
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ldp x21,x22,[x29,#32]
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mov x0,#1
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ldp x23,x24,[x29,#48]
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ldr x29,[sp],#64
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ret
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.size bn_mul_mont,.-bn_mul_mont
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___
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{
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########################################################################
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# Following is ARMv8 adaptation of sqrx8x_mont from x86_64-mont5 module.
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my ($a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7)=map("x$_",(6..13));
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my ($t0,$t1,$t2,$t3)=map("x$_",(14..17));
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my ($acc0,$acc1,$acc2,$acc3,$acc4,$acc5,$acc6,$acc7)=map("x$_",(19..26));
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my ($cnt,$carry,$topmost)=("x27","x28","x30");
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my ($tp,$ap_end,$na0)=($bp,$np,$carry);
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$code.=<<___;
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.type __bn_sqr8x_mont,%function
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.align 5
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__bn_sqr8x_mont:
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cmp $ap,$bp
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b.ne __bn_mul4x_mont
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.Lsqr8x_mont:
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stp x29,x30,[sp,#-128]!
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add x29,sp,#0
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stp x19,x20,[sp,#16]
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stp x21,x22,[sp,#32]
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stp x23,x24,[sp,#48]
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stp x25,x26,[sp,#64]
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stp x27,x28,[sp,#80]
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stp $rp,$np,[sp,#96] // offload rp and np
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ldp $a0,$a1,[$ap,#8*0]
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ldp $a2,$a3,[$ap,#8*2]
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ldp $a4,$a5,[$ap,#8*4]
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ldp $a6,$a7,[$ap,#8*6]
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sub $tp,sp,$num,lsl#4
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lsl $num,$num,#3
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ldr $n0,[$n0] // *n0
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mov sp,$tp // alloca
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sub $cnt,$num,#8*8
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b .Lsqr8x_zero_start
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.Lsqr8x_zero:
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sub $cnt,$cnt,#8*8
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stp xzr,xzr,[$tp,#8*0]
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stp xzr,xzr,[$tp,#8*2]
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stp xzr,xzr,[$tp,#8*4]
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stp xzr,xzr,[$tp,#8*6]
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.Lsqr8x_zero_start:
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stp xzr,xzr,[$tp,#8*8]
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stp xzr,xzr,[$tp,#8*10]
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stp xzr,xzr,[$tp,#8*12]
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stp xzr,xzr,[$tp,#8*14]
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add $tp,$tp,#8*16
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cbnz $cnt,.Lsqr8x_zero
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add $ap_end,$ap,$num
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add $ap,$ap,#8*8
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mov $acc0,xzr
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mov $acc1,xzr
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mov $acc2,xzr
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mov $acc3,xzr
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mov $acc4,xzr
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mov $acc5,xzr
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mov $acc6,xzr
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mov $acc7,xzr
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mov $tp,sp
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str $n0,[x29,#112] // offload n0
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// Multiply everything but a[i]*a[i]
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.align 4
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.Lsqr8x_outer_loop:
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// a[1]a[0] (i)
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// a[2]a[0]
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// a[3]a[0]
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// a[4]a[0]
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// a[5]a[0]
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// a[6]a[0]
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// a[7]a[0]
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|
|
// a[2]a[1] (ii)
|
||
|
|
// a[3]a[1]
|
||
|
|
// a[4]a[1]
|
||
|
|
// a[5]a[1]
|
||
|
|
// a[6]a[1]
|
||
|
|
// a[7]a[1]
|
||
|
|
// a[3]a[2] (iii)
|
||
|
|
// a[4]a[2]
|
||
|
|
// a[5]a[2]
|
||
|
|
// a[6]a[2]
|
||
|
|
// a[7]a[2]
|
||
|
|
// a[4]a[3] (iv)
|
||
|
|
// a[5]a[3]
|
||
|
|
// a[6]a[3]
|
||
|
|
// a[7]a[3]
|
||
|
|
// a[5]a[4] (v)
|
||
|
|
// a[6]a[4]
|
||
|
|
// a[7]a[4]
|
||
|
|
// a[6]a[5] (vi)
|
||
|
|
// a[7]a[5]
|
||
|
|
// a[7]a[6] (vii)
|
||
|
|
|
||
|
|
mul $t0,$a1,$a0 // lo(a[1..7]*a[0]) (i)
|
||
|
|
mul $t1,$a2,$a0
|
||
|
|
mul $t2,$a3,$a0
|
||
|
|
mul $t3,$a4,$a0
|
||
|
|
adds $acc1,$acc1,$t0 // t[1]+lo(a[1]*a[0])
|
||
|
|
mul $t0,$a5,$a0
|
||
|
|
adcs $acc2,$acc2,$t1
|
||
|
|
mul $t1,$a6,$a0
|
||
|
|
adcs $acc3,$acc3,$t2
|
||
|
|
mul $t2,$a7,$a0
|
||
|
|
adcs $acc4,$acc4,$t3
|
||
|
|
umulh $t3,$a1,$a0 // hi(a[1..7]*a[0])
|
||
|
|
adcs $acc5,$acc5,$t0
|
||
|
|
umulh $t0,$a2,$a0
|
||
|
|
adcs $acc6,$acc6,$t1
|
||
|
|
umulh $t1,$a3,$a0
|
||
|
|
adcs $acc7,$acc7,$t2
|
||
|
|
umulh $t2,$a4,$a0
|
||
|
|
stp $acc0,$acc1,[$tp],#8*2 // t[0..1]
|
||
|
|
adc $acc0,xzr,xzr // t[8]
|
||
|
|
adds $acc2,$acc2,$t3 // t[2]+lo(a[1]*a[0])
|
||
|
|
umulh $t3,$a5,$a0
|
||
|
|
adcs $acc3,$acc3,$t0
|
||
|
|
umulh $t0,$a6,$a0
|
||
|
|
adcs $acc4,$acc4,$t1
|
||
|
|
umulh $t1,$a7,$a0
|
||
|
|
adcs $acc5,$acc5,$t2
|
||
|
|
mul $t2,$a2,$a1 // lo(a[2..7]*a[1]) (ii)
|
||
|
|
adcs $acc6,$acc6,$t3
|
||
|
|
mul $t3,$a3,$a1
|
||
|
|
adcs $acc7,$acc7,$t0
|
||
|
|
mul $t0,$a4,$a1
|
||
|
|
adc $acc0,$acc0,$t1
|
||
|
|
|
||
|
|
mul $t1,$a5,$a1
|
||
|
|
adds $acc3,$acc3,$t2
|
||
|
|
mul $t2,$a6,$a1
|
||
|
|
adcs $acc4,$acc4,$t3
|
||
|
|
mul $t3,$a7,$a1
|
||
|
|
adcs $acc5,$acc5,$t0
|
||
|
|
umulh $t0,$a2,$a1 // hi(a[2..7]*a[1])
|
||
|
|
adcs $acc6,$acc6,$t1
|
||
|
|
umulh $t1,$a3,$a1
|
||
|
|
adcs $acc7,$acc7,$t2
|
||
|
|
umulh $t2,$a4,$a1
|
||
|
|
adcs $acc0,$acc0,$t3
|
||
|
|
umulh $t3,$a5,$a1
|
||
|
|
stp $acc2,$acc3,[$tp],#8*2 // t[2..3]
|
||
|
|
adc $acc1,xzr,xzr // t[9]
|
||
|
|
adds $acc4,$acc4,$t0
|
||
|
|
umulh $t0,$a6,$a1
|
||
|
|
adcs $acc5,$acc5,$t1
|
||
|
|
umulh $t1,$a7,$a1
|
||
|
|
adcs $acc6,$acc6,$t2
|
||
|
|
mul $t2,$a3,$a2 // lo(a[3..7]*a[2]) (iii)
|
||
|
|
adcs $acc7,$acc7,$t3
|
||
|
|
mul $t3,$a4,$a2
|
||
|
|
adcs $acc0,$acc0,$t0
|
||
|
|
mul $t0,$a5,$a2
|
||
|
|
adc $acc1,$acc1,$t1
|
||
|
|
|
||
|
|
mul $t1,$a6,$a2
|
||
|
|
adds $acc5,$acc5,$t2
|
||
|
|
mul $t2,$a7,$a2
|
||
|
|
adcs $acc6,$acc6,$t3
|
||
|
|
umulh $t3,$a3,$a2 // hi(a[3..7]*a[2])
|
||
|
|
adcs $acc7,$acc7,$t0
|
||
|
|
umulh $t0,$a4,$a2
|
||
|
|
adcs $acc0,$acc0,$t1
|
||
|
|
umulh $t1,$a5,$a2
|
||
|
|
adcs $acc1,$acc1,$t2
|
||
|
|
umulh $t2,$a6,$a2
|
||
|
|
stp $acc4,$acc5,[$tp],#8*2 // t[4..5]
|
||
|
|
adc $acc2,xzr,xzr // t[10]
|
||
|
|
adds $acc6,$acc6,$t3
|
||
|
|
umulh $t3,$a7,$a2
|
||
|
|
adcs $acc7,$acc7,$t0
|
||
|
|
mul $t0,$a4,$a3 // lo(a[4..7]*a[3]) (iv)
|
||
|
|
adcs $acc0,$acc0,$t1
|
||
|
|
mul $t1,$a5,$a3
|
||
|
|
adcs $acc1,$acc1,$t2
|
||
|
|
mul $t2,$a6,$a3
|
||
|
|
adc $acc2,$acc2,$t3
|
||
|
|
|
||
|
|
mul $t3,$a7,$a3
|
||
|
|
adds $acc7,$acc7,$t0
|
||
|
|
umulh $t0,$a4,$a3 // hi(a[4..7]*a[3])
|
||
|
|
adcs $acc0,$acc0,$t1
|
||
|
|
umulh $t1,$a5,$a3
|
||
|
|
adcs $acc1,$acc1,$t2
|
||
|
|
umulh $t2,$a6,$a3
|
||
|
|
adcs $acc2,$acc2,$t3
|
||
|
|
umulh $t3,$a7,$a3
|
||
|
|
stp $acc6,$acc7,[$tp],#8*2 // t[6..7]
|
||
|
|
adc $acc3,xzr,xzr // t[11]
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
mul $t0,$a5,$a4 // lo(a[5..7]*a[4]) (v)
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
mul $t1,$a6,$a4
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
mul $t2,$a7,$a4
|
||
|
|
adc $acc3,$acc3,$t3
|
||
|
|
|
||
|
|
umulh $t3,$a5,$a4 // hi(a[5..7]*a[4])
|
||
|
|
adds $acc1,$acc1,$t0
|
||
|
|
umulh $t0,$a6,$a4
|
||
|
|
adcs $acc2,$acc2,$t1
|
||
|
|
umulh $t1,$a7,$a4
|
||
|
|
adcs $acc3,$acc3,$t2
|
||
|
|
mul $t2,$a6,$a5 // lo(a[6..7]*a[5]) (vi)
|
||
|
|
adc $acc4,xzr,xzr // t[12]
|
||
|
|
adds $acc2,$acc2,$t3
|
||
|
|
mul $t3,$a7,$a5
|
||
|
|
adcs $acc3,$acc3,$t0
|
||
|
|
umulh $t0,$a6,$a5 // hi(a[6..7]*a[5])
|
||
|
|
adc $acc4,$acc4,$t1
|
||
|
|
|
||
|
|
umulh $t1,$a7,$a5
|
||
|
|
adds $acc3,$acc3,$t2
|
||
|
|
mul $t2,$a7,$a6 // lo(a[7]*a[6]) (vii)
|
||
|
|
adcs $acc4,$acc4,$t3
|
||
|
|
umulh $t3,$a7,$a6 // hi(a[7]*a[6])
|
||
|
|
adc $acc5,xzr,xzr // t[13]
|
||
|
|
adds $acc4,$acc4,$t0
|
||
|
|
sub $cnt,$ap_end,$ap // done yet?
|
||
|
|
adc $acc5,$acc5,$t1
|
||
|
|
|
||
|
|
adds $acc5,$acc5,$t2
|
||
|
|
sub $t0,$ap_end,$num // rewinded ap
|
||
|
|
adc $acc6,xzr,xzr // t[14]
|
||
|
|
add $acc6,$acc6,$t3
|
||
|
|
|
||
|
|
cbz $cnt,.Lsqr8x_outer_break
|
||
|
|
|
||
|
|
mov $n0,$a0
|
||
|
|
ldp $a0,$a1,[$tp,#8*0]
|
||
|
|
ldp $a2,$a3,[$tp,#8*2]
|
||
|
|
ldp $a4,$a5,[$tp,#8*4]
|
||
|
|
ldp $a6,$a7,[$tp,#8*6]
|
||
|
|
adds $acc0,$acc0,$a0
|
||
|
|
adcs $acc1,$acc1,$a1
|
||
|
|
ldp $a0,$a1,[$ap,#8*0]
|
||
|
|
adcs $acc2,$acc2,$a2
|
||
|
|
adcs $acc3,$acc3,$a3
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
adcs $acc4,$acc4,$a4
|
||
|
|
adcs $acc5,$acc5,$a5
|
||
|
|
ldp $a4,$a5,[$ap,#8*4]
|
||
|
|
adcs $acc6,$acc6,$a6
|
||
|
|
mov $rp,$ap
|
||
|
|
adcs $acc7,xzr,$a7
|
||
|
|
ldp $a6,$a7,[$ap,#8*6]
|
||
|
|
add $ap,$ap,#8*8
|
||
|
|
//adc $carry,xzr,xzr // moved below
|
||
|
|
mov $cnt,#-8*8
|
||
|
|
|
||
|
|
// a[8]a[0]
|
||
|
|
// a[9]a[0]
|
||
|
|
// a[a]a[0]
|
||
|
|
// a[b]a[0]
|
||
|
|
// a[c]a[0]
|
||
|
|
// a[d]a[0]
|
||
|
|
// a[e]a[0]
|
||
|
|
// a[f]a[0]
|
||
|
|
// a[8]a[1]
|
||
|
|
// a[f]a[1]........................
|
||
|
|
// a[8]a[2]
|
||
|
|
// a[f]a[2]........................
|
||
|
|
// a[8]a[3]
|
||
|
|
// a[f]a[3]........................
|
||
|
|
// a[8]a[4]
|
||
|
|
// a[f]a[4]........................
|
||
|
|
// a[8]a[5]
|
||
|
|
// a[f]a[5]........................
|
||
|
|
// a[8]a[6]
|
||
|
|
// a[f]a[6]........................
|
||
|
|
// a[8]a[7]
|
||
|
|
// a[f]a[7]........................
|
||
|
|
.Lsqr8x_mul:
|
||
|
|
mul $t0,$a0,$n0
|
||
|
|
adc $carry,xzr,xzr // carry bit, modulo-scheduled
|
||
|
|
mul $t1,$a1,$n0
|
||
|
|
add $cnt,$cnt,#8
|
||
|
|
mul $t2,$a2,$n0
|
||
|
|
mul $t3,$a3,$n0
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
mul $t0,$a4,$n0
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
mul $t1,$a5,$n0
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
mul $t2,$a6,$n0
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
mul $t3,$a7,$n0
|
||
|
|
adcs $acc4,$acc4,$t0
|
||
|
|
umulh $t0,$a0,$n0
|
||
|
|
adcs $acc5,$acc5,$t1
|
||
|
|
umulh $t1,$a1,$n0
|
||
|
|
adcs $acc6,$acc6,$t2
|
||
|
|
umulh $t2,$a2,$n0
|
||
|
|
adcs $acc7,$acc7,$t3
|
||
|
|
umulh $t3,$a3,$n0
|
||
|
|
adc $carry,$carry,xzr
|
||
|
|
str $acc0,[$tp],#8
|
||
|
|
adds $acc0,$acc1,$t0
|
||
|
|
umulh $t0,$a4,$n0
|
||
|
|
adcs $acc1,$acc2,$t1
|
||
|
|
umulh $t1,$a5,$n0
|
||
|
|
adcs $acc2,$acc3,$t2
|
||
|
|
umulh $t2,$a6,$n0
|
||
|
|
adcs $acc3,$acc4,$t3
|
||
|
|
umulh $t3,$a7,$n0
|
||
|
|
ldr $n0,[$rp,$cnt]
|
||
|
|
adcs $acc4,$acc5,$t0
|
||
|
|
adcs $acc5,$acc6,$t1
|
||
|
|
adcs $acc6,$acc7,$t2
|
||
|
|
adcs $acc7,$carry,$t3
|
||
|
|
//adc $carry,xzr,xzr // moved above
|
||
|
|
cbnz $cnt,.Lsqr8x_mul
|
||
|
|
// note that carry flag is guaranteed
|
||
|
|
// to be zero at this point
|
||
|
|
cmp $ap,$ap_end // done yet?
|
||
|
|
b.eq .Lsqr8x_break
|
||
|
|
|
||
|
|
ldp $a0,$a1,[$tp,#8*0]
|
||
|
|
ldp $a2,$a3,[$tp,#8*2]
|
||
|
|
ldp $a4,$a5,[$tp,#8*4]
|
||
|
|
ldp $a6,$a7,[$tp,#8*6]
|
||
|
|
adds $acc0,$acc0,$a0
|
||
|
|
ldr $n0,[$rp,#-8*8]
|
||
|
|
adcs $acc1,$acc1,$a1
|
||
|
|
ldp $a0,$a1,[$ap,#8*0]
|
||
|
|
adcs $acc2,$acc2,$a2
|
||
|
|
adcs $acc3,$acc3,$a3
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
adcs $acc4,$acc4,$a4
|
||
|
|
adcs $acc5,$acc5,$a5
|
||
|
|
ldp $a4,$a5,[$ap,#8*4]
|
||
|
|
adcs $acc6,$acc6,$a6
|
||
|
|
mov $cnt,#-8*8
|
||
|
|
adcs $acc7,$acc7,$a7
|
||
|
|
ldp $a6,$a7,[$ap,#8*6]
|
||
|
|
add $ap,$ap,#8*8
|
||
|
|
//adc $carry,xzr,xzr // moved above
|
||
|
|
b .Lsqr8x_mul
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Lsqr8x_break:
|
||
|
|
ldp $a0,$a1,[$rp,#8*0]
|
||
|
|
add $ap,$rp,#8*8
|
||
|
|
ldp $a2,$a3,[$rp,#8*2]
|
||
|
|
sub $t0,$ap_end,$ap // is it last iteration?
|
||
|
|
ldp $a4,$a5,[$rp,#8*4]
|
||
|
|
sub $t1,$tp,$t0
|
||
|
|
ldp $a6,$a7,[$rp,#8*6]
|
||
|
|
cbz $t0,.Lsqr8x_outer_loop
|
||
|
|
|
||
|
|
stp $acc0,$acc1,[$tp,#8*0]
|
||
|
|
ldp $acc0,$acc1,[$t1,#8*0]
|
||
|
|
stp $acc2,$acc3,[$tp,#8*2]
|
||
|
|
ldp $acc2,$acc3,[$t1,#8*2]
|
||
|
|
stp $acc4,$acc5,[$tp,#8*4]
|
||
|
|
ldp $acc4,$acc5,[$t1,#8*4]
|
||
|
|
stp $acc6,$acc7,[$tp,#8*6]
|
||
|
|
mov $tp,$t1
|
||
|
|
ldp $acc6,$acc7,[$t1,#8*6]
|
||
|
|
b .Lsqr8x_outer_loop
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Lsqr8x_outer_break:
|
||
|
|
// Now multiply above result by 2 and add a[n-1]*a[n-1]|...|a[0]*a[0]
|
||
|
|
ldp $a1,$a3,[$t0,#8*0] // recall that $t0 is &a[0]
|
||
|
|
ldp $t1,$t2,[sp,#8*1]
|
||
|
|
ldp $a5,$a7,[$t0,#8*2]
|
||
|
|
add $ap,$t0,#8*4
|
||
|
|
ldp $t3,$t0,[sp,#8*3]
|
||
|
|
|
||
|
|
stp $acc0,$acc1,[$tp,#8*0]
|
||
|
|
mul $acc0,$a1,$a1
|
||
|
|
stp $acc2,$acc3,[$tp,#8*2]
|
||
|
|
umulh $a1,$a1,$a1
|
||
|
|
stp $acc4,$acc5,[$tp,#8*4]
|
||
|
|
mul $a2,$a3,$a3
|
||
|
|
stp $acc6,$acc7,[$tp,#8*6]
|
||
|
|
mov $tp,sp
|
||
|
|
umulh $a3,$a3,$a3
|
||
|
|
adds $acc1,$a1,$t1,lsl#1
|
||
|
|
extr $t1,$t2,$t1,#63
|
||
|
|
sub $cnt,$num,#8*4
|
||
|
|
|
||
|
|
.Lsqr4x_shift_n_add:
|
||
|
|
adcs $acc2,$a2,$t1
|
||
|
|
extr $t2,$t3,$t2,#63
|
||
|
|
sub $cnt,$cnt,#8*4
|
||
|
|
adcs $acc3,$a3,$t2
|
||
|
|
ldp $t1,$t2,[$tp,#8*5]
|
||
|
|
mul $a4,$a5,$a5
|
||
|
|
ldp $a1,$a3,[$ap],#8*2
|
||
|
|
umulh $a5,$a5,$a5
|
||
|
|
mul $a6,$a7,$a7
|
||
|
|
umulh $a7,$a7,$a7
|
||
|
|
extr $t3,$t0,$t3,#63
|
||
|
|
stp $acc0,$acc1,[$tp,#8*0]
|
||
|
|
adcs $acc4,$a4,$t3
|
||
|
|
extr $t0,$t1,$t0,#63
|
||
|
|
stp $acc2,$acc3,[$tp,#8*2]
|
||
|
|
adcs $acc5,$a5,$t0
|
||
|
|
ldp $t3,$t0,[$tp,#8*7]
|
||
|
|
extr $t1,$t2,$t1,#63
|
||
|
|
adcs $acc6,$a6,$t1
|
||
|
|
extr $t2,$t3,$t2,#63
|
||
|
|
adcs $acc7,$a7,$t2
|
||
|
|
ldp $t1,$t2,[$tp,#8*9]
|
||
|
|
mul $a0,$a1,$a1
|
||
|
|
ldp $a5,$a7,[$ap],#8*2
|
||
|
|
umulh $a1,$a1,$a1
|
||
|
|
mul $a2,$a3,$a3
|
||
|
|
umulh $a3,$a3,$a3
|
||
|
|
stp $acc4,$acc5,[$tp,#8*4]
|
||
|
|
extr $t3,$t0,$t3,#63
|
||
|
|
stp $acc6,$acc7,[$tp,#8*6]
|
||
|
|
add $tp,$tp,#8*8
|
||
|
|
adcs $acc0,$a0,$t3
|
||
|
|
extr $t0,$t1,$t0,#63
|
||
|
|
adcs $acc1,$a1,$t0
|
||
|
|
ldp $t3,$t0,[$tp,#8*3]
|
||
|
|
extr $t1,$t2,$t1,#63
|
||
|
|
cbnz $cnt,.Lsqr4x_shift_n_add
|
||
|
|
___
|
||
|
|
my ($np,$np_end)=($ap,$ap_end);
|
||
|
|
$code.=<<___;
|
||
|
|
ldp $np,$n0,[x29,#104] // pull np and n0
|
||
|
|
|
||
|
|
adcs $acc2,$a2,$t1
|
||
|
|
extr $t2,$t3,$t2,#63
|
||
|
|
adcs $acc3,$a3,$t2
|
||
|
|
ldp $t1,$t2,[$tp,#8*5]
|
||
|
|
mul $a4,$a5,$a5
|
||
|
|
umulh $a5,$a5,$a5
|
||
|
|
stp $acc0,$acc1,[$tp,#8*0]
|
||
|
|
mul $a6,$a7,$a7
|
||
|
|
umulh $a7,$a7,$a7
|
||
|
|
stp $acc2,$acc3,[$tp,#8*2]
|
||
|
|
extr $t3,$t0,$t3,#63
|
||
|
|
adcs $acc4,$a4,$t3
|
||
|
|
extr $t0,$t1,$t0,#63
|
||
|
|
ldp $acc0,$acc1,[sp,#8*0]
|
||
|
|
adcs $acc5,$a5,$t0
|
||
|
|
extr $t1,$t2,$t1,#63
|
||
|
|
ldp $a0,$a1,[$np,#8*0]
|
||
|
|
adcs $acc6,$a6,$t1
|
||
|
|
extr $t2,xzr,$t2,#63
|
||
|
|
ldp $a2,$a3,[$np,#8*2]
|
||
|
|
adc $acc7,$a7,$t2
|
||
|
|
ldp $a4,$a5,[$np,#8*4]
|
||
|
|
|
||
|
|
// Reduce by 512 bits per iteration
|
||
|
|
mul $na0,$n0,$acc0 // t[0]*n0
|
||
|
|
ldp $a6,$a7,[$np,#8*6]
|
||
|
|
add $np_end,$np,$num
|
||
|
|
ldp $acc2,$acc3,[sp,#8*2]
|
||
|
|
stp $acc4,$acc5,[$tp,#8*4]
|
||
|
|
ldp $acc4,$acc5,[sp,#8*4]
|
||
|
|
stp $acc6,$acc7,[$tp,#8*6]
|
||
|
|
ldp $acc6,$acc7,[sp,#8*6]
|
||
|
|
add $np,$np,#8*8
|
||
|
|
mov $topmost,xzr // initial top-most carry
|
||
|
|
mov $tp,sp
|
||
|
|
mov $cnt,#8
|
||
|
|
|
||
|
|
.Lsqr8x_reduction:
|
||
|
|
// (*) mul $t0,$a0,$na0 // lo(n[0-7])*lo(t[0]*n0)
|
||
|
|
mul $t1,$a1,$na0
|
||
|
|
sub $cnt,$cnt,#1
|
||
|
|
mul $t2,$a2,$na0
|
||
|
|
str $na0,[$tp],#8 // put aside t[0]*n0 for tail processing
|
||
|
|
mul $t3,$a3,$na0
|
||
|
|
// (*) adds xzr,$acc0,$t0
|
||
|
|
subs xzr,$acc0,#1 // (*)
|
||
|
|
mul $t0,$a4,$na0
|
||
|
|
adcs $acc0,$acc1,$t1
|
||
|
|
mul $t1,$a5,$na0
|
||
|
|
adcs $acc1,$acc2,$t2
|
||
|
|
mul $t2,$a6,$na0
|
||
|
|
adcs $acc2,$acc3,$t3
|
||
|
|
mul $t3,$a7,$na0
|
||
|
|
adcs $acc3,$acc4,$t0
|
||
|
|
umulh $t0,$a0,$na0 // hi(n[0-7])*lo(t[0]*n0)
|
||
|
|
adcs $acc4,$acc5,$t1
|
||
|
|
umulh $t1,$a1,$na0
|
||
|
|
adcs $acc5,$acc6,$t2
|
||
|
|
umulh $t2,$a2,$na0
|
||
|
|
adcs $acc6,$acc7,$t3
|
||
|
|
umulh $t3,$a3,$na0
|
||
|
|
adc $acc7,xzr,xzr
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
umulh $t0,$a4,$na0
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
umulh $t1,$a5,$na0
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
umulh $t2,$a6,$na0
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
umulh $t3,$a7,$na0
|
||
|
|
mul $na0,$n0,$acc0 // next t[0]*n0
|
||
|
|
adcs $acc4,$acc4,$t0
|
||
|
|
adcs $acc5,$acc5,$t1
|
||
|
|
adcs $acc6,$acc6,$t2
|
||
|
|
adc $acc7,$acc7,$t3
|
||
|
|
cbnz $cnt,.Lsqr8x_reduction
|
||
|
|
|
||
|
|
ldp $t0,$t1,[$tp,#8*0]
|
||
|
|
ldp $t2,$t3,[$tp,#8*2]
|
||
|
|
mov $rp,$tp
|
||
|
|
sub $cnt,$np_end,$np // done yet?
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
ldp $t0,$t1,[$tp,#8*4]
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
ldp $t2,$t3,[$tp,#8*6]
|
||
|
|
adcs $acc4,$acc4,$t0
|
||
|
|
adcs $acc5,$acc5,$t1
|
||
|
|
adcs $acc6,$acc6,$t2
|
||
|
|
adcs $acc7,$acc7,$t3
|
||
|
|
//adc $carry,xzr,xzr // moved below
|
||
|
|
cbz $cnt,.Lsqr8x8_post_condition
|
||
|
|
|
||
|
|
ldr $n0,[$tp,#-8*8]
|
||
|
|
ldp $a0,$a1,[$np,#8*0]
|
||
|
|
ldp $a2,$a3,[$np,#8*2]
|
||
|
|
ldp $a4,$a5,[$np,#8*4]
|
||
|
|
mov $cnt,#-8*8
|
||
|
|
ldp $a6,$a7,[$np,#8*6]
|
||
|
|
add $np,$np,#8*8
|
||
|
|
|
||
|
|
.Lsqr8x_tail:
|
||
|
|
mul $t0,$a0,$n0
|
||
|
|
adc $carry,xzr,xzr // carry bit, modulo-scheduled
|
||
|
|
mul $t1,$a1,$n0
|
||
|
|
add $cnt,$cnt,#8
|
||
|
|
mul $t2,$a2,$n0
|
||
|
|
mul $t3,$a3,$n0
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
mul $t0,$a4,$n0
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
mul $t1,$a5,$n0
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
mul $t2,$a6,$n0
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
mul $t3,$a7,$n0
|
||
|
|
adcs $acc4,$acc4,$t0
|
||
|
|
umulh $t0,$a0,$n0
|
||
|
|
adcs $acc5,$acc5,$t1
|
||
|
|
umulh $t1,$a1,$n0
|
||
|
|
adcs $acc6,$acc6,$t2
|
||
|
|
umulh $t2,$a2,$n0
|
||
|
|
adcs $acc7,$acc7,$t3
|
||
|
|
umulh $t3,$a3,$n0
|
||
|
|
adc $carry,$carry,xzr
|
||
|
|
str $acc0,[$tp],#8
|
||
|
|
adds $acc0,$acc1,$t0
|
||
|
|
umulh $t0,$a4,$n0
|
||
|
|
adcs $acc1,$acc2,$t1
|
||
|
|
umulh $t1,$a5,$n0
|
||
|
|
adcs $acc2,$acc3,$t2
|
||
|
|
umulh $t2,$a6,$n0
|
||
|
|
adcs $acc3,$acc4,$t3
|
||
|
|
umulh $t3,$a7,$n0
|
||
|
|
ldr $n0,[$rp,$cnt]
|
||
|
|
adcs $acc4,$acc5,$t0
|
||
|
|
adcs $acc5,$acc6,$t1
|
||
|
|
adcs $acc6,$acc7,$t2
|
||
|
|
adcs $acc7,$carry,$t3
|
||
|
|
//adc $carry,xzr,xzr // moved above
|
||
|
|
cbnz $cnt,.Lsqr8x_tail
|
||
|
|
// note that carry flag is guaranteed
|
||
|
|
// to be zero at this point
|
||
|
|
ldp $a0,$a1,[$tp,#8*0]
|
||
|
|
sub $cnt,$np_end,$np // done yet?
|
||
|
|
sub $t2,$np_end,$num // rewinded np
|
||
|
|
ldp $a2,$a3,[$tp,#8*2]
|
||
|
|
ldp $a4,$a5,[$tp,#8*4]
|
||
|
|
ldp $a6,$a7,[$tp,#8*6]
|
||
|
|
cbz $cnt,.Lsqr8x_tail_break
|
||
|
|
|
||
|
|
ldr $n0,[$rp,#-8*8]
|
||
|
|
adds $acc0,$acc0,$a0
|
||
|
|
adcs $acc1,$acc1,$a1
|
||
|
|
ldp $a0,$a1,[$np,#8*0]
|
||
|
|
adcs $acc2,$acc2,$a2
|
||
|
|
adcs $acc3,$acc3,$a3
|
||
|
|
ldp $a2,$a3,[$np,#8*2]
|
||
|
|
adcs $acc4,$acc4,$a4
|
||
|
|
adcs $acc5,$acc5,$a5
|
||
|
|
ldp $a4,$a5,[$np,#8*4]
|
||
|
|
adcs $acc6,$acc6,$a6
|
||
|
|
mov $cnt,#-8*8
|
||
|
|
adcs $acc7,$acc7,$a7
|
||
|
|
ldp $a6,$a7,[$np,#8*6]
|
||
|
|
add $np,$np,#8*8
|
||
|
|
//adc $carry,xzr,xzr // moved above
|
||
|
|
b .Lsqr8x_tail
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Lsqr8x_tail_break:
|
||
|
|
ldr $n0,[x29,#112] // pull n0
|
||
|
|
add $cnt,$tp,#8*8 // end of current t[num] window
|
||
|
|
|
||
|
|
subs xzr,$topmost,#1 // "move" top-most carry to carry bit
|
||
|
|
adcs $t0,$acc0,$a0
|
||
|
|
adcs $t1,$acc1,$a1
|
||
|
|
ldp $acc0,$acc1,[$rp,#8*0]
|
||
|
|
adcs $acc2,$acc2,$a2
|
||
|
|
ldp $a0,$a1,[$t2,#8*0] // recall that $t2 is &n[0]
|
||
|
|
adcs $acc3,$acc3,$a3
|
||
|
|
ldp $a2,$a3,[$t2,#8*2]
|
||
|
|
adcs $acc4,$acc4,$a4
|
||
|
|
adcs $acc5,$acc5,$a5
|
||
|
|
ldp $a4,$a5,[$t2,#8*4]
|
||
|
|
adcs $acc6,$acc6,$a6
|
||
|
|
adcs $acc7,$acc7,$a7
|
||
|
|
ldp $a6,$a7,[$t2,#8*6]
|
||
|
|
add $np,$t2,#8*8
|
||
|
|
adc $topmost,xzr,xzr // top-most carry
|
||
|
|
mul $na0,$n0,$acc0
|
||
|
|
stp $t0,$t1,[$tp,#8*0]
|
||
|
|
stp $acc2,$acc3,[$tp,#8*2]
|
||
|
|
ldp $acc2,$acc3,[$rp,#8*2]
|
||
|
|
stp $acc4,$acc5,[$tp,#8*4]
|
||
|
|
ldp $acc4,$acc5,[$rp,#8*4]
|
||
|
|
cmp $cnt,x29 // did we hit the bottom?
|
||
|
|
stp $acc6,$acc7,[$tp,#8*6]
|
||
|
|
mov $tp,$rp // slide the window
|
||
|
|
ldp $acc6,$acc7,[$rp,#8*6]
|
||
|
|
mov $cnt,#8
|
||
|
|
b.ne .Lsqr8x_reduction
|
||
|
|
|
||
|
|
// Final step. We see if result is larger than modulus, and
|
||
|
|
// if it is, subtract the modulus. But comparison implies
|
||
|
|
// subtraction. So we subtract modulus, see if it borrowed,
|
||
|
|
// and conditionally copy original value.
|
||
|
|
ldr $rp,[x29,#96] // pull rp
|
||
|
|
add $tp,$tp,#8*8
|
||
|
|
subs $t0,$acc0,$a0
|
||
|
|
sbcs $t1,$acc1,$a1
|
||
|
|
sub $cnt,$num,#8*8
|
||
|
|
mov $ap_end,$rp // $rp copy
|
||
|
|
|
||
|
|
.Lsqr8x_sub:
|
||
|
|
sbcs $t2,$acc2,$a2
|
||
|
|
ldp $a0,$a1,[$np,#8*0]
|
||
|
|
sbcs $t3,$acc3,$a3
|
||
|
|
stp $t0,$t1,[$rp,#8*0]
|
||
|
|
sbcs $t0,$acc4,$a4
|
||
|
|
ldp $a2,$a3,[$np,#8*2]
|
||
|
|
sbcs $t1,$acc5,$a5
|
||
|
|
stp $t2,$t3,[$rp,#8*2]
|
||
|
|
sbcs $t2,$acc6,$a6
|
||
|
|
ldp $a4,$a5,[$np,#8*4]
|
||
|
|
sbcs $t3,$acc7,$a7
|
||
|
|
ldp $a6,$a7,[$np,#8*6]
|
||
|
|
add $np,$np,#8*8
|
||
|
|
ldp $acc0,$acc1,[$tp,#8*0]
|
||
|
|
sub $cnt,$cnt,#8*8
|
||
|
|
ldp $acc2,$acc3,[$tp,#8*2]
|
||
|
|
ldp $acc4,$acc5,[$tp,#8*4]
|
||
|
|
ldp $acc6,$acc7,[$tp,#8*6]
|
||
|
|
add $tp,$tp,#8*8
|
||
|
|
stp $t0,$t1,[$rp,#8*4]
|
||
|
|
sbcs $t0,$acc0,$a0
|
||
|
|
stp $t2,$t3,[$rp,#8*6]
|
||
|
|
add $rp,$rp,#8*8
|
||
|
|
sbcs $t1,$acc1,$a1
|
||
|
|
cbnz $cnt,.Lsqr8x_sub
|
||
|
|
|
||
|
|
sbcs $t2,$acc2,$a2
|
||
|
|
mov $tp,sp
|
||
|
|
add $ap,sp,$num
|
||
|
|
ldp $a0,$a1,[$ap_end,#8*0]
|
||
|
|
sbcs $t3,$acc3,$a3
|
||
|
|
stp $t0,$t1,[$rp,#8*0]
|
||
|
|
sbcs $t0,$acc4,$a4
|
||
|
|
ldp $a2,$a3,[$ap_end,#8*2]
|
||
|
|
sbcs $t1,$acc5,$a5
|
||
|
|
stp $t2,$t3,[$rp,#8*2]
|
||
|
|
sbcs $t2,$acc6,$a6
|
||
|
|
ldp $acc0,$acc1,[$ap,#8*0]
|
||
|
|
sbcs $t3,$acc7,$a7
|
||
|
|
ldp $acc2,$acc3,[$ap,#8*2]
|
||
|
|
sbcs xzr,$topmost,xzr // did it borrow?
|
||
|
|
ldr x30,[x29,#8] // pull return address
|
||
|
|
stp $t0,$t1,[$rp,#8*4]
|
||
|
|
stp $t2,$t3,[$rp,#8*6]
|
||
|
|
|
||
|
|
sub $cnt,$num,#8*4
|
||
|
|
.Lsqr4x_cond_copy:
|
||
|
|
sub $cnt,$cnt,#8*4
|
||
|
|
csel $t0,$acc0,$a0,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*0]
|
||
|
|
csel $t1,$acc1,$a1,lo
|
||
|
|
ldp $a0,$a1,[$ap_end,#8*4]
|
||
|
|
ldp $acc0,$acc1,[$ap,#8*4]
|
||
|
|
csel $t2,$acc2,$a2,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*2]
|
||
|
|
add $tp,$tp,#8*4
|
||
|
|
csel $t3,$acc3,$a3,lo
|
||
|
|
ldp $a2,$a3,[$ap_end,#8*6]
|
||
|
|
ldp $acc2,$acc3,[$ap,#8*6]
|
||
|
|
add $ap,$ap,#8*4
|
||
|
|
stp $t0,$t1,[$ap_end,#8*0]
|
||
|
|
stp $t2,$t3,[$ap_end,#8*2]
|
||
|
|
add $ap_end,$ap_end,#8*4
|
||
|
|
stp xzr,xzr,[$ap,#8*0]
|
||
|
|
stp xzr,xzr,[$ap,#8*2]
|
||
|
|
cbnz $cnt,.Lsqr4x_cond_copy
|
||
|
|
|
||
|
|
csel $t0,$acc0,$a0,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*0]
|
||
|
|
csel $t1,$acc1,$a1,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*2]
|
||
|
|
csel $t2,$acc2,$a2,lo
|
||
|
|
csel $t3,$acc3,$a3,lo
|
||
|
|
stp $t0,$t1,[$ap_end,#8*0]
|
||
|
|
stp $t2,$t3,[$ap_end,#8*2]
|
||
|
|
|
||
|
|
b .Lsqr8x_done
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Lsqr8x8_post_condition:
|
||
|
|
adc $carry,xzr,xzr
|
||
|
|
ldr x30,[x29,#8] // pull return address
|
||
|
|
// $acc0-7,$carry hold result, $a0-7 hold modulus
|
||
|
|
subs $a0,$acc0,$a0
|
||
|
|
ldr $ap,[x29,#96] // pull rp
|
||
|
|
sbcs $a1,$acc1,$a1
|
||
|
|
stp xzr,xzr,[sp,#8*0]
|
||
|
|
sbcs $a2,$acc2,$a2
|
||
|
|
stp xzr,xzr,[sp,#8*2]
|
||
|
|
sbcs $a3,$acc3,$a3
|
||
|
|
stp xzr,xzr,[sp,#8*4]
|
||
|
|
sbcs $a4,$acc4,$a4
|
||
|
|
stp xzr,xzr,[sp,#8*6]
|
||
|
|
sbcs $a5,$acc5,$a5
|
||
|
|
stp xzr,xzr,[sp,#8*8]
|
||
|
|
sbcs $a6,$acc6,$a6
|
||
|
|
stp xzr,xzr,[sp,#8*10]
|
||
|
|
sbcs $a7,$acc7,$a7
|
||
|
|
stp xzr,xzr,[sp,#8*12]
|
||
|
|
sbcs $carry,$carry,xzr // did it borrow?
|
||
|
|
stp xzr,xzr,[sp,#8*14]
|
||
|
|
|
||
|
|
// $a0-7 hold result-modulus
|
||
|
|
csel $a0,$acc0,$a0,lo
|
||
|
|
csel $a1,$acc1,$a1,lo
|
||
|
|
csel $a2,$acc2,$a2,lo
|
||
|
|
csel $a3,$acc3,$a3,lo
|
||
|
|
stp $a0,$a1,[$ap,#8*0]
|
||
|
|
csel $a4,$acc4,$a4,lo
|
||
|
|
csel $a5,$acc5,$a5,lo
|
||
|
|
stp $a2,$a3,[$ap,#8*2]
|
||
|
|
csel $a6,$acc6,$a6,lo
|
||
|
|
csel $a7,$acc7,$a7,lo
|
||
|
|
stp $a4,$a5,[$ap,#8*4]
|
||
|
|
stp $a6,$a7,[$ap,#8*6]
|
||
|
|
|
||
|
|
.Lsqr8x_done:
|
||
|
|
ldp x19,x20,[x29,#16]
|
||
|
|
mov sp,x29
|
||
|
|
ldp x21,x22,[x29,#32]
|
||
|
|
mov x0,#1
|
||
|
|
ldp x23,x24,[x29,#48]
|
||
|
|
ldp x25,x26,[x29,#64]
|
||
|
|
ldp x27,x28,[x29,#80]
|
||
|
|
ldr x29,[sp],#128
|
||
|
|
ret
|
||
|
|
.size __bn_sqr8x_mont,.-__bn_sqr8x_mont
|
||
|
|
___
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
########################################################################
|
||
|
|
# Even though this might look as ARMv8 adaptation of mulx4x_mont from
|
||
|
|
# x86_64-mont5 module, it's different in sense that it performs
|
||
|
|
# reduction 256 bits at a time.
|
||
|
|
|
||
|
|
my ($a0,$a1,$a2,$a3,
|
||
|
|
$t0,$t1,$t2,$t3,
|
||
|
|
$m0,$m1,$m2,$m3,
|
||
|
|
$acc0,$acc1,$acc2,$acc3,$acc4,
|
||
|
|
$bi,$mi,$tp,$ap_end,$cnt) = map("x$_",(6..17,19..28));
|
||
|
|
my $bp_end=$rp;
|
||
|
|
my ($carry,$topmost) = ($rp,"x30");
|
||
|
|
|
||
|
|
$code.=<<___;
|
||
|
|
.type __bn_mul4x_mont,%function
|
||
|
|
.align 5
|
||
|
|
__bn_mul4x_mont:
|
||
|
|
stp x29,x30,[sp,#-128]!
|
||
|
|
add x29,sp,#0
|
||
|
|
stp x19,x20,[sp,#16]
|
||
|
|
stp x21,x22,[sp,#32]
|
||
|
|
stp x23,x24,[sp,#48]
|
||
|
|
stp x25,x26,[sp,#64]
|
||
|
|
stp x27,x28,[sp,#80]
|
||
|
|
|
||
|
|
sub $tp,sp,$num,lsl#3
|
||
|
|
lsl $num,$num,#3
|
||
|
|
ldr $n0,[$n0] // *n0
|
||
|
|
sub sp,$tp,#8*4 // alloca
|
||
|
|
|
||
|
|
add $t0,$bp,$num
|
||
|
|
add $ap_end,$ap,$num
|
||
|
|
stp $rp,$t0,[x29,#96] // offload rp and &b[num]
|
||
|
|
|
||
|
|
ldr $bi,[$bp,#8*0] // b[0]
|
||
|
|
ldp $a0,$a1,[$ap,#8*0] // a[0..3]
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
add $ap,$ap,#8*4
|
||
|
|
mov $acc0,xzr
|
||
|
|
mov $acc1,xzr
|
||
|
|
mov $acc2,xzr
|
||
|
|
mov $acc3,xzr
|
||
|
|
ldp $m0,$m1,[$np,#8*0] // n[0..3]
|
||
|
|
ldp $m2,$m3,[$np,#8*2]
|
||
|
|
adds $np,$np,#8*4 // clear carry bit
|
||
|
|
mov $carry,xzr
|
||
|
|
mov $cnt,#0
|
||
|
|
mov $tp,sp
|
||
|
|
|
||
|
|
.Loop_mul4x_1st_reduction:
|
||
|
|
mul $t0,$a0,$bi // lo(a[0..3]*b[0])
|
||
|
|
adc $carry,$carry,xzr // modulo-scheduled
|
||
|
|
mul $t1,$a1,$bi
|
||
|
|
add $cnt,$cnt,#8
|
||
|
|
mul $t2,$a2,$bi
|
||
|
|
and $cnt,$cnt,#31
|
||
|
|
mul $t3,$a3,$bi
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
umulh $t0,$a0,$bi // hi(a[0..3]*b[0])
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
mul $mi,$acc0,$n0 // t[0]*n0
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
umulh $t1,$a1,$bi
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
umulh $t2,$a2,$bi
|
||
|
|
adc $acc4,xzr,xzr
|
||
|
|
umulh $t3,$a3,$bi
|
||
|
|
ldr $bi,[$bp,$cnt] // next b[i] (or b[0])
|
||
|
|
adds $acc1,$acc1,$t0
|
||
|
|
// (*) mul $t0,$m0,$mi // lo(n[0..3]*t[0]*n0)
|
||
|
|
str $mi,[$tp],#8 // put aside t[0]*n0 for tail processing
|
||
|
|
adcs $acc2,$acc2,$t1
|
||
|
|
mul $t1,$m1,$mi
|
||
|
|
adcs $acc3,$acc3,$t2
|
||
|
|
mul $t2,$m2,$mi
|
||
|
|
adc $acc4,$acc4,$t3 // can't overflow
|
||
|
|
mul $t3,$m3,$mi
|
||
|
|
// (*) adds xzr,$acc0,$t0
|
||
|
|
subs xzr,$acc0,#1 // (*)
|
||
|
|
umulh $t0,$m0,$mi // hi(n[0..3]*t[0]*n0)
|
||
|
|
adcs $acc0,$acc1,$t1
|
||
|
|
umulh $t1,$m1,$mi
|
||
|
|
adcs $acc1,$acc2,$t2
|
||
|
|
umulh $t2,$m2,$mi
|
||
|
|
adcs $acc2,$acc3,$t3
|
||
|
|
umulh $t3,$m3,$mi
|
||
|
|
adcs $acc3,$acc4,$carry
|
||
|
|
adc $carry,xzr,xzr
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
sub $t0,$ap_end,$ap
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
//adc $carry,$carry,xzr
|
||
|
|
cbnz $cnt,.Loop_mul4x_1st_reduction
|
||
|
|
|
||
|
|
cbz $t0,.Lmul4x4_post_condition
|
||
|
|
|
||
|
|
ldp $a0,$a1,[$ap,#8*0] // a[4..7]
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
add $ap,$ap,#8*4
|
||
|
|
ldr $mi,[sp] // a[0]*n0
|
||
|
|
ldp $m0,$m1,[$np,#8*0] // n[4..7]
|
||
|
|
ldp $m2,$m3,[$np,#8*2]
|
||
|
|
add $np,$np,#8*4
|
||
|
|
|
||
|
|
.Loop_mul4x_1st_tail:
|
||
|
|
mul $t0,$a0,$bi // lo(a[4..7]*b[i])
|
||
|
|
adc $carry,$carry,xzr // modulo-scheduled
|
||
|
|
mul $t1,$a1,$bi
|
||
|
|
add $cnt,$cnt,#8
|
||
|
|
mul $t2,$a2,$bi
|
||
|
|
and $cnt,$cnt,#31
|
||
|
|
mul $t3,$a3,$bi
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
umulh $t0,$a0,$bi // hi(a[4..7]*b[i])
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
umulh $t1,$a1,$bi
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
umulh $t2,$a2,$bi
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
umulh $t3,$a3,$bi
|
||
|
|
adc $acc4,xzr,xzr
|
||
|
|
ldr $bi,[$bp,$cnt] // next b[i] (or b[0])
|
||
|
|
adds $acc1,$acc1,$t0
|
||
|
|
mul $t0,$m0,$mi // lo(n[4..7]*a[0]*n0)
|
||
|
|
adcs $acc2,$acc2,$t1
|
||
|
|
mul $t1,$m1,$mi
|
||
|
|
adcs $acc3,$acc3,$t2
|
||
|
|
mul $t2,$m2,$mi
|
||
|
|
adc $acc4,$acc4,$t3 // can't overflow
|
||
|
|
mul $t3,$m3,$mi
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
umulh $t0,$m0,$mi // hi(n[4..7]*a[0]*n0)
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
umulh $t1,$m1,$mi
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
umulh $t2,$m2,$mi
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
adcs $acc4,$acc4,$carry
|
||
|
|
umulh $t3,$m3,$mi
|
||
|
|
adc $carry,xzr,xzr
|
||
|
|
ldr $mi,[sp,$cnt] // next t[0]*n0
|
||
|
|
str $acc0,[$tp],#8 // result!!!
|
||
|
|
adds $acc0,$acc1,$t0
|
||
|
|
sub $t0,$ap_end,$ap // done yet?
|
||
|
|
adcs $acc1,$acc2,$t1
|
||
|
|
adcs $acc2,$acc3,$t2
|
||
|
|
adcs $acc3,$acc4,$t3
|
||
|
|
//adc $carry,$carry,xzr
|
||
|
|
cbnz $cnt,.Loop_mul4x_1st_tail
|
||
|
|
|
||
|
|
sub $t1,$ap_end,$num // rewinded $ap
|
||
|
|
cbz $t0,.Lmul4x_proceed
|
||
|
|
|
||
|
|
ldp $a0,$a1,[$ap,#8*0]
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
add $ap,$ap,#8*4
|
||
|
|
ldp $m0,$m1,[$np,#8*0]
|
||
|
|
ldp $m2,$m3,[$np,#8*2]
|
||
|
|
add $np,$np,#8*4
|
||
|
|
b .Loop_mul4x_1st_tail
|
||
|
|
|
||
|
|
.align 5
|
||
|
|
.Lmul4x_proceed:
|
||
|
|
ldr $bi,[$bp,#8*4]! // *++b
|
||
|
|
adc $topmost,$carry,xzr
|
||
|
|
ldp $a0,$a1,[$t1,#8*0] // a[0..3]
|
||
|
|
sub $np,$np,$num // rewind np
|
||
|
|
ldp $a2,$a3,[$t1,#8*2]
|
||
|
|
add $ap,$t1,#8*4
|
||
|
|
|
||
|
|
stp $acc0,$acc1,[$tp,#8*0] // result!!!
|
||
|
|
ldp $acc0,$acc1,[sp,#8*4] // t[0..3]
|
||
|
|
stp $acc2,$acc3,[$tp,#8*2] // result!!!
|
||
|
|
ldp $acc2,$acc3,[sp,#8*6]
|
||
|
|
|
||
|
|
ldp $m0,$m1,[$np,#8*0] // n[0..3]
|
||
|
|
mov $tp,sp
|
||
|
|
ldp $m2,$m3,[$np,#8*2]
|
||
|
|
adds $np,$np,#8*4 // clear carry bit
|
||
|
|
mov $carry,xzr
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Loop_mul4x_reduction:
|
||
|
|
mul $t0,$a0,$bi // lo(a[0..3]*b[4])
|
||
|
|
adc $carry,$carry,xzr // modulo-scheduled
|
||
|
|
mul $t1,$a1,$bi
|
||
|
|
add $cnt,$cnt,#8
|
||
|
|
mul $t2,$a2,$bi
|
||
|
|
and $cnt,$cnt,#31
|
||
|
|
mul $t3,$a3,$bi
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
umulh $t0,$a0,$bi // hi(a[0..3]*b[4])
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
mul $mi,$acc0,$n0 // t[0]*n0
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
umulh $t1,$a1,$bi
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
umulh $t2,$a2,$bi
|
||
|
|
adc $acc4,xzr,xzr
|
||
|
|
umulh $t3,$a3,$bi
|
||
|
|
ldr $bi,[$bp,$cnt] // next b[i]
|
||
|
|
adds $acc1,$acc1,$t0
|
||
|
|
// (*) mul $t0,$m0,$mi
|
||
|
|
str $mi,[$tp],#8 // put aside t[0]*n0 for tail processing
|
||
|
|
adcs $acc2,$acc2,$t1
|
||
|
|
mul $t1,$m1,$mi // lo(n[0..3]*t[0]*n0
|
||
|
|
adcs $acc3,$acc3,$t2
|
||
|
|
mul $t2,$m2,$mi
|
||
|
|
adc $acc4,$acc4,$t3 // can't overflow
|
||
|
|
mul $t3,$m3,$mi
|
||
|
|
// (*) adds xzr,$acc0,$t0
|
||
|
|
subs xzr,$acc0,#1 // (*)
|
||
|
|
umulh $t0,$m0,$mi // hi(n[0..3]*t[0]*n0
|
||
|
|
adcs $acc0,$acc1,$t1
|
||
|
|
umulh $t1,$m1,$mi
|
||
|
|
adcs $acc1,$acc2,$t2
|
||
|
|
umulh $t2,$m2,$mi
|
||
|
|
adcs $acc2,$acc3,$t3
|
||
|
|
umulh $t3,$m3,$mi
|
||
|
|
adcs $acc3,$acc4,$carry
|
||
|
|
adc $carry,xzr,xzr
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
//adc $carry,$carry,xzr
|
||
|
|
cbnz $cnt,.Loop_mul4x_reduction
|
||
|
|
|
||
|
|
adc $carry,$carry,xzr
|
||
|
|
ldp $t0,$t1,[$tp,#8*4] // t[4..7]
|
||
|
|
ldp $t2,$t3,[$tp,#8*6]
|
||
|
|
ldp $a0,$a1,[$ap,#8*0] // a[4..7]
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
add $ap,$ap,#8*4
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
//adc $carry,$carry,xzr
|
||
|
|
|
||
|
|
ldr $mi,[sp] // t[0]*n0
|
||
|
|
ldp $m0,$m1,[$np,#8*0] // n[4..7]
|
||
|
|
ldp $m2,$m3,[$np,#8*2]
|
||
|
|
add $np,$np,#8*4
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Loop_mul4x_tail:
|
||
|
|
mul $t0,$a0,$bi // lo(a[4..7]*b[4])
|
||
|
|
adc $carry,$carry,xzr // modulo-scheduled
|
||
|
|
mul $t1,$a1,$bi
|
||
|
|
add $cnt,$cnt,#8
|
||
|
|
mul $t2,$a2,$bi
|
||
|
|
and $cnt,$cnt,#31
|
||
|
|
mul $t3,$a3,$bi
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
umulh $t0,$a0,$bi // hi(a[4..7]*b[4])
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
umulh $t1,$a1,$bi
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
umulh $t2,$a2,$bi
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
umulh $t3,$a3,$bi
|
||
|
|
adc $acc4,xzr,xzr
|
||
|
|
ldr $bi,[$bp,$cnt] // next b[i]
|
||
|
|
adds $acc1,$acc1,$t0
|
||
|
|
mul $t0,$m0,$mi // lo(n[4..7]*t[0]*n0)
|
||
|
|
adcs $acc2,$acc2,$t1
|
||
|
|
mul $t1,$m1,$mi
|
||
|
|
adcs $acc3,$acc3,$t2
|
||
|
|
mul $t2,$m2,$mi
|
||
|
|
adc $acc4,$acc4,$t3 // can't overflow
|
||
|
|
mul $t3,$m3,$mi
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
umulh $t0,$m0,$mi // hi(n[4..7]*t[0]*n0)
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
umulh $t1,$m1,$mi
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
umulh $t2,$m2,$mi
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
umulh $t3,$m3,$mi
|
||
|
|
adcs $acc4,$acc4,$carry
|
||
|
|
ldr $mi,[sp,$cnt] // next a[0]*n0
|
||
|
|
adc $carry,xzr,xzr
|
||
|
|
str $acc0,[$tp],#8 // result!!!
|
||
|
|
adds $acc0,$acc1,$t0
|
||
|
|
sub $t0,$ap_end,$ap // done yet?
|
||
|
|
adcs $acc1,$acc2,$t1
|
||
|
|
adcs $acc2,$acc3,$t2
|
||
|
|
adcs $acc3,$acc4,$t3
|
||
|
|
//adc $carry,$carry,xzr
|
||
|
|
cbnz $cnt,.Loop_mul4x_tail
|
||
|
|
|
||
|
|
sub $t1,$np,$num // rewinded np?
|
||
|
|
adc $carry,$carry,xzr
|
||
|
|
cbz $t0,.Loop_mul4x_break
|
||
|
|
|
||
|
|
ldp $t0,$t1,[$tp,#8*4]
|
||
|
|
ldp $t2,$t3,[$tp,#8*6]
|
||
|
|
ldp $a0,$a1,[$ap,#8*0]
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
add $ap,$ap,#8*4
|
||
|
|
adds $acc0,$acc0,$t0
|
||
|
|
adcs $acc1,$acc1,$t1
|
||
|
|
adcs $acc2,$acc2,$t2
|
||
|
|
adcs $acc3,$acc3,$t3
|
||
|
|
//adc $carry,$carry,xzr
|
||
|
|
ldp $m0,$m1,[$np,#8*0]
|
||
|
|
ldp $m2,$m3,[$np,#8*2]
|
||
|
|
add $np,$np,#8*4
|
||
|
|
b .Loop_mul4x_tail
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Loop_mul4x_break:
|
||
|
|
ldp $t2,$t3,[x29,#96] // pull rp and &b[num]
|
||
|
|
adds $acc0,$acc0,$topmost
|
||
|
|
add $bp,$bp,#8*4 // bp++
|
||
|
|
adcs $acc1,$acc1,xzr
|
||
|
|
sub $ap,$ap,$num // rewind ap
|
||
|
|
adcs $acc2,$acc2,xzr
|
||
|
|
stp $acc0,$acc1,[$tp,#8*0] // result!!!
|
||
|
|
adcs $acc3,$acc3,xzr
|
||
|
|
ldp $acc0,$acc1,[sp,#8*4] // t[0..3]
|
||
|
|
adc $topmost,$carry,xzr
|
||
|
|
stp $acc2,$acc3,[$tp,#8*2] // result!!!
|
||
|
|
cmp $bp,$t3 // done yet?
|
||
|
|
ldp $acc2,$acc3,[sp,#8*6]
|
||
|
|
ldp $m0,$m1,[$t1,#8*0] // n[0..3]
|
||
|
|
ldp $m2,$m3,[$t1,#8*2]
|
||
|
|
add $np,$t1,#8*4
|
||
|
|
b.eq .Lmul4x_post
|
||
|
|
|
||
|
|
ldr $bi,[$bp]
|
||
|
|
ldp $a0,$a1,[$ap,#8*0] // a[0..3]
|
||
|
|
ldp $a2,$a3,[$ap,#8*2]
|
||
|
|
adds $ap,$ap,#8*4 // clear carry bit
|
||
|
|
mov $carry,xzr
|
||
|
|
mov $tp,sp
|
||
|
|
b .Loop_mul4x_reduction
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Lmul4x_post:
|
||
|
|
// Final step. We see if result is larger than modulus, and
|
||
|
|
// if it is, subtract the modulus. But comparison implies
|
||
|
|
// subtraction. So we subtract modulus, see if it borrowed,
|
||
|
|
// and conditionally copy original value.
|
||
|
|
mov $rp,$t2
|
||
|
|
mov $ap_end,$t2 // $rp copy
|
||
|
|
subs $t0,$acc0,$m0
|
||
|
|
add $tp,sp,#8*8
|
||
|
|
sbcs $t1,$acc1,$m1
|
||
|
|
sub $cnt,$num,#8*4
|
||
|
|
|
||
|
|
.Lmul4x_sub:
|
||
|
|
sbcs $t2,$acc2,$m2
|
||
|
|
ldp $m0,$m1,[$np,#8*0]
|
||
|
|
sub $cnt,$cnt,#8*4
|
||
|
|
ldp $acc0,$acc1,[$tp,#8*0]
|
||
|
|
sbcs $t3,$acc3,$m3
|
||
|
|
ldp $m2,$m3,[$np,#8*2]
|
||
|
|
add $np,$np,#8*4
|
||
|
|
ldp $acc2,$acc3,[$tp,#8*2]
|
||
|
|
add $tp,$tp,#8*4
|
||
|
|
stp $t0,$t1,[$rp,#8*0]
|
||
|
|
sbcs $t0,$acc0,$m0
|
||
|
|
stp $t2,$t3,[$rp,#8*2]
|
||
|
|
add $rp,$rp,#8*4
|
||
|
|
sbcs $t1,$acc1,$m1
|
||
|
|
cbnz $cnt,.Lmul4x_sub
|
||
|
|
|
||
|
|
sbcs $t2,$acc2,$m2
|
||
|
|
mov $tp,sp
|
||
|
|
add $ap,sp,#8*4
|
||
|
|
ldp $a0,$a1,[$ap_end,#8*0]
|
||
|
|
sbcs $t3,$acc3,$m3
|
||
|
|
stp $t0,$t1,[$rp,#8*0]
|
||
|
|
ldp $a2,$a3,[$ap_end,#8*2]
|
||
|
|
stp $t2,$t3,[$rp,#8*2]
|
||
|
|
ldp $acc0,$acc1,[$ap,#8*0]
|
||
|
|
ldp $acc2,$acc3,[$ap,#8*2]
|
||
|
|
sbcs xzr,$topmost,xzr // did it borrow?
|
||
|
|
ldr x30,[x29,#8] // pull return address
|
||
|
|
|
||
|
|
sub $cnt,$num,#8*4
|
||
|
|
.Lmul4x_cond_copy:
|
||
|
|
sub $cnt,$cnt,#8*4
|
||
|
|
csel $t0,$acc0,$a0,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*0]
|
||
|
|
csel $t1,$acc1,$a1,lo
|
||
|
|
ldp $a0,$a1,[$ap_end,#8*4]
|
||
|
|
ldp $acc0,$acc1,[$ap,#8*4]
|
||
|
|
csel $t2,$acc2,$a2,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*2]
|
||
|
|
add $tp,$tp,#8*4
|
||
|
|
csel $t3,$acc3,$a3,lo
|
||
|
|
ldp $a2,$a3,[$ap_end,#8*6]
|
||
|
|
ldp $acc2,$acc3,[$ap,#8*6]
|
||
|
|
add $ap,$ap,#8*4
|
||
|
|
stp $t0,$t1,[$ap_end,#8*0]
|
||
|
|
stp $t2,$t3,[$ap_end,#8*2]
|
||
|
|
add $ap_end,$ap_end,#8*4
|
||
|
|
cbnz $cnt,.Lmul4x_cond_copy
|
||
|
|
|
||
|
|
csel $t0,$acc0,$a0,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*0]
|
||
|
|
csel $t1,$acc1,$a1,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*2]
|
||
|
|
csel $t2,$acc2,$a2,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*3]
|
||
|
|
csel $t3,$acc3,$a3,lo
|
||
|
|
stp xzr,xzr,[$tp,#8*4]
|
||
|
|
stp $t0,$t1,[$ap_end,#8*0]
|
||
|
|
stp $t2,$t3,[$ap_end,#8*2]
|
||
|
|
|
||
|
|
b .Lmul4x_done
|
||
|
|
|
||
|
|
.align 4
|
||
|
|
.Lmul4x4_post_condition:
|
||
|
|
adc $carry,$carry,xzr
|
||
|
|
ldr $ap,[x29,#96] // pull rp
|
||
|
|
// $acc0-3,$carry hold result, $m0-7 hold modulus
|
||
|
|
subs $a0,$acc0,$m0
|
||
|
|
ldr x30,[x29,#8] // pull return address
|
||
|
|
sbcs $a1,$acc1,$m1
|
||
|
|
stp xzr,xzr,[sp,#8*0]
|
||
|
|
sbcs $a2,$acc2,$m2
|
||
|
|
stp xzr,xzr,[sp,#8*2]
|
||
|
|
sbcs $a3,$acc3,$m3
|
||
|
|
stp xzr,xzr,[sp,#8*4]
|
||
|
|
sbcs xzr,$carry,xzr // did it borrow?
|
||
|
|
stp xzr,xzr,[sp,#8*6]
|
||
|
|
|
||
|
|
// $a0-3 hold result-modulus
|
||
|
|
csel $a0,$acc0,$a0,lo
|
||
|
|
csel $a1,$acc1,$a1,lo
|
||
|
|
csel $a2,$acc2,$a2,lo
|
||
|
|
csel $a3,$acc3,$a3,lo
|
||
|
|
stp $a0,$a1,[$ap,#8*0]
|
||
|
|
stp $a2,$a3,[$ap,#8*2]
|
||
|
|
|
||
|
|
.Lmul4x_done:
|
||
|
|
ldp x19,x20,[x29,#16]
|
||
|
|
mov sp,x29
|
||
|
|
ldp x21,x22,[x29,#32]
|
||
|
|
mov x0,#1
|
||
|
|
ldp x23,x24,[x29,#48]
|
||
|
|
ldp x25,x26,[x29,#64]
|
||
|
|
ldp x27,x28,[x29,#80]
|
||
|
|
ldr x29,[sp],#128
|
||
|
|
ret
|
||
|
|
.size __bn_mul4x_mont,.-__bn_mul4x_mont
|
||
|
|
___
|
||
|
|
}
|
||
|
|
$code.=<<___;
|
||
|
|
.asciz "Montgomery Multiplication for ARMv8, CRYPTOGAMS by <appro\@openssl.org>"
|
||
|
|
.align 4
|
||
|
|
___
|
||
|
|
|
||
|
|
print $code;
|
||
|
|
|
||
|
|
close STDOUT;
|