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#!/usr/bin/env perl
# ====================================================================
# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
# project. The module is, however, dual licensed under OpenSSL and
# CRYPTOGAMS licenses depending on where you obtain it. For further
# details see http://www.openssl.org/~appro/cryptogams/.
# ====================================================================
# March 2015
#
# "Teaser" Montgomery multiplication module for ARMv8. Needs more
# work. While it does improve RSA sign performance by 20-30% (less for
# longer keys) on most processors, for some reason RSA2048 is not
# faster and RSA4096 goes 15-20% slower on Cortex-A57. Multiplication
# instruction issue rate is limited on processor in question, meaning
# that dedicated squaring procedure is a must. Well, actually all
# contemporary AArch64 processors seem to have limited multiplication
# issue rate, i.e. they can't issue multiplication every cycle, which
# explains moderate improvement coefficients in comparison to
# compiler-generated code. Recall that compiler is instructed to use
# umulh and therefore uses same amount of multiplication instructions
# to do the job. Assembly's edge is to minimize number of "collateral"
# instructions and of course instruction scheduling.
$flavour = shift;
$output = shift;
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or
( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or
die "can't locate arm-xlate.pl";
open OUT,"| \"$^X\" $xlate $flavour $output";
*STDOUT=*OUT;
($lo0,$hi0,$aj,$m0,$alo,$ahi,
$lo1,$hi1,$nj,$m1,$nlo,$nhi,
$ovf, $i,$j,$tp,$tj) = map("x$_",6..17,19..24);
# int bn_mul_mont(
$rp="x0"; # BN_ULONG *rp,
$ap="x1"; # const BN_ULONG *ap,
$bp="x2"; # const BN_ULONG *bp,
$np="x3"; # const BN_ULONG *np,
$n0="x4"; # const BN_ULONG *n0,
$num="x5"; # int num);
$code.=<<___;
.text
.globl bn_mul_mont
.type bn_mul_mont,%function
.align 5
bn_mul_mont:
stp x29,x30,[sp,#-64]!
add x29,sp,#0
stp x19,x20,[sp,#16]
stp x21,x22,[sp,#32]
stp x23,x24,[sp,#48]
ldr $m0,[$bp],#8 // bp[0]
sub $tp,sp,$num,lsl#3
ldp $hi0,$aj,[$ap],#16 // ap[0..1]
lsl $num,$num,#3
ldr $n0,[$n0] // *n0
and $tp,$tp,#-16 // ABI says so
ldp $hi1,$nj,[$np],#16 // np[0..1]
mul $lo0,$hi0,$m0 // ap[0]*bp[0]
sub $j,$num,#16 // j=num-2
umulh $hi0,$hi0,$m0
mul $alo,$aj,$m0 // ap[1]*bp[0]
umulh $ahi,$aj,$m0
mul $m1,$lo0,$n0 // "tp[0]"*n0
mov sp,$tp // alloca
mul $lo1,$hi1,$m1 // np[0]*m1
umulh $hi1,$hi1,$m1
mul $nlo,$nj,$m1 // np[1]*m1
adds $lo1,$lo1,$lo0 // discarded
umulh $nhi,$nj,$m1
adc $hi1,$hi1,xzr
cbz $j,.L1st_skip
.L1st:
ldr $aj,[$ap],#8
adds $lo0,$alo,$hi0
sub $j,$j,#8 // j--
adc $hi0,$ahi,xzr
ldr $nj,[$np],#8
adds $lo1,$nlo,$hi1
mul $alo,$aj,$m0 // ap[j]*bp[0]
adc $hi1,$nhi,xzr
umulh $ahi,$aj,$m0
adds $lo1,$lo1,$lo0
mul $nlo,$nj,$m1 // np[j]*m1
adc $hi1,$hi1,xzr
umulh $nhi,$nj,$m1
str $lo1,[$tp],#8 // tp[j-1]
cbnz $j,.L1st
.L1st_skip:
adds $lo0,$alo,$hi0
sub $ap,$ap,$num // rewind $ap
adc $hi0,$ahi,xzr
adds $lo1,$nlo,$hi1
sub $np,$np,$num // rewind $np
adc $hi1,$nhi,xzr
adds $lo1,$lo1,$lo0
sub $i,$num,#8 // i=num-1
adcs $hi1,$hi1,$hi0
adc $ovf,xzr,xzr // upmost overflow bit
stp $lo1,$hi1,[$tp]
.Louter:
ldr $m0,[$bp],#8 // bp[i]
ldp $hi0,$aj,[$ap],#16
ldr $tj,[sp] // tp[0]
add $tp,sp,#8
mul $lo0,$hi0,$m0 // ap[0]*bp[i]
sub $j,$num,#16 // j=num-2
umulh $hi0,$hi0,$m0
ldp $hi1,$nj,[$np],#16
mul $alo,$aj,$m0 // ap[1]*bp[i]
adds $lo0,$lo0,$tj
umulh $ahi,$aj,$m0
adc $hi0,$hi0,xzr
mul $m1,$lo0,$n0
sub $i,$i,#8 // i--
mul $lo1,$hi1,$m1 // np[0]*m1
umulh $hi1,$hi1,$m1
mul $nlo,$nj,$m1 // np[1]*m1
adds $lo1,$lo1,$lo0
umulh $nhi,$nj,$m1
cbz $j,.Linner_skip
.Linner:
ldr $aj,[$ap],#8
adc $hi1,$hi1,xzr
ldr $tj,[$tp],#8 // tp[j]
adds $lo0,$alo,$hi0
sub $j,$j,#8 // j--
adc $hi0,$ahi,xzr
adds $lo1,$nlo,$hi1
ldr $nj,[$np],#8
adc $hi1,$nhi,xzr
mul $alo,$aj,$m0 // ap[j]*bp[i]
adds $lo0,$lo0,$tj
umulh $ahi,$aj,$m0
adc $hi0,$hi0,xzr
mul $nlo,$nj,$m1 // np[j]*m1
adds $lo1,$lo1,$lo0
umulh $nhi,$nj,$m1
str $lo1,[$tp,#-16] // tp[j-1]
cbnz $j,.Linner
.Linner_skip:
ldr $tj,[$tp],#8 // tp[j]
adc $hi1,$hi1,xzr
adds $lo0,$alo,$hi0
sub $ap,$ap,$num // rewind $ap
adc $hi0,$ahi,xzr
adds $lo1,$nlo,$hi1
sub $np,$np,$num // rewind $np
adc $hi1,$nhi,$ovf
adds $lo0,$lo0,$tj
adc $hi0,$hi0,xzr
adds $lo1,$lo1,$lo0
adcs $hi1,$hi1,$hi0
adc $ovf,xzr,xzr // upmost overflow bit
stp $lo1,$hi1,[$tp,#-16]
cbnz $i,.Louter
// 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 $tj,[sp] // tp[0]
add $tp,sp,#8
ldr $nj,[$np],#8 // np[0]
subs $j,$num,#8 // j=num-1 and clear borrow
mov $ap,$rp
.Lsub:
sbcs $aj,$tj,$nj // tp[j]-np[j]
ldr $tj,[$tp],#8
sub $j,$j,#8 // j--
ldr $nj,[$np],#8
str $aj,[$ap],#8 // rp[j]=tp[j]-np[j]
cbnz $j,.Lsub
sbcs $aj,$tj,$nj
sbcs $ovf,$ovf,xzr // did it borrow?
str $aj,[$ap],#8 // rp[num-1]
ldr $tj,[sp] // tp[0]
add $tp,sp,#8
ldr $aj,[$rp],#8 // rp[0]
sub $num,$num,#8 // num--
nop
.Lcond_copy:
sub $num,$num,#8 // num--
csel $nj,$aj,$tj,cs // did it borrow?
ldr $tj,[$tp],#8
ldr $aj,[$rp],#8
str xzr,[$tp,#-16] // wipe tp
str $nj,[$rp,#-16]
cbnz $num,.Lcond_copy
csel $nj,$aj,$tj,cs
str xzr,[$tp,#-8] // wipe tp
str $nj,[$rp,#-8]
ldp x19,x20,[x29,#16]
mov sp,x29
ldp x21,x22,[x29,#32]
ldp x23,x24,[x29,#48]
ldr x29,[sp],#64
ret
.size bn_mul_mont,.-bn_mul_mont
.asciz "Montgomery Multiplication for ARMv8, CRYPTOGAMS by <appro\@openssl.org>"
.align 4
___
print $code;
close STDOUT;
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