#! /usr/bin/env perl
# Copyright 2006-2020 The OpenSSL Project Authors. All Rights Reserved.
#
# Licensed under the OpenSSL license (the "License"). You may not use
# this file except in compliance with the License. You can obtain a copy
# in the file LICENSE in the source distribution or at
# https://www.openssl.org/source/license.html
# ====================================================================
# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
# project. The module is, however, dual licensed under OpenSSL and
# CRYPTOGAMS licenses depending on where you obtain it. For further
# details see http://www.openssl.org/~appro/cryptogams/.
# ====================================================================
# April 2006
# "Teaser" Montgomery multiplication module for PowerPC. It's possible
# to gain a bit more by modulo-scheduling outer loop, then dedicated
# squaring procedure should give further 20% and code can be adapted
# for 32-bit application running on 64-bit CPU. As for the latter.
# It won't be able to achieve "native" 64-bit performance, because in
# 32-bit application context every addc instruction will have to be
# expanded as addc, twice right shift by 32 and finally adde, etc.
# So far RSA *sign* performance improvement over pre-bn_mul_mont asm
# for 64-bit application running on PPC970/G5 is:
#
# 512-bit +65%
# 1024-bit +35%
# 2048-bit +18%
# 4096-bit +4%
# September 2016
#
# Add multiplication procedure operating on lengths divisible by 4
# and squaring procedure operating on lengths divisible by 8. Length
# is expressed in number of limbs. RSA private key operations are
# ~35-50% faster (more for longer keys) on contemporary high-end POWER
# processors in 64-bit builds, [mysteriously enough] more in 32-bit
# builds. On low-end 32-bit processors performance improvement turned
# to be marginal...
$flavour = shift;
if ($flavour =~ /32/) {
$BITS= 32;
$BNSZ= $BITS/8;
$SIZE_T=4;
$RZONE= 224;
$LD= "lwz"; # load
$LDU= "lwzu"; # load and update
$LDX= "lwzx"; # load indexed
$ST= "stw"; # store
$STU= "stwu"; # store and update
$STX= "stwx"; # store indexed
$STUX= "stwux"; # store indexed and update
$UMULL= "mullw"; # unsigned multiply low
$UMULH= "mulhwu"; # unsigned multiply high
$UCMP= "cmplw"; # unsigned compare
$SHRI= "srwi"; # unsigned shift right by immediate
$SHLI= "slwi"; # unsigned shift left by immediate
$PUSH= $ST;
$POP= $LD;
} elsif ($flavour =~ /64/) {
$BITS= 64;
$BNSZ= $BITS/8;
$SIZE_T=8;
$RZONE= 288;
# same as above, but 64-bit mnemonics...
$LD= "ld"; # load
$LDU= "ldu"; # load and update
$LDX= "ldx"; # load indexed
$ST= "std"; # store
$STU= "stdu"; # store and update
$STX= "stdx"; # store indexed
$STUX= "stdux"; # store indexed and update
$UMULL= "mulld"; # unsigned multiply low
$UMULH= "mulhdu"; # unsigned multiply high
$UCMP= "cmpld"; # unsigned compare
$SHRI= "srdi"; # unsigned shift right by immediate
$SHLI= "sldi"; # unsigned shift left by immediate
$PUSH= $ST;
$POP= $LD;
} else { die "nonsense $flavour"; }
$FRAME=8*$SIZE_T+$RZONE;
$LOCALS=8*$SIZE_T;
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
( $xlate="${dir}ppc-xlate.pl" and -f $xlate ) or
( $xlate="${dir}../../perlasm/ppc-xlate.pl" and -f $xlate) or
die "can't locate ppc-xlate.pl";
open STDOUT,"| $^X $xlate $flavour ".shift || die "can't call $xlate: $!";
$sp="r1";
$toc="r2";
$rp="r3";
$ap="r4";
$bp="r5";
$np="r6";
$n0="r7";
$num="r8";
{
my $ovf=$rp;
my $rp="r9"; # $rp is reassigned
my $aj="r10";
my $nj="r11";
my $tj="r12";
# non-volatile registers
my $i="r20";
my $j="r21";
my $tp="r22";
my $m0="r23";
my $m1="r24";
my $lo0="r25";
my $hi0="r26";
my $lo1="r27";
my $hi1="r28";
my $alo="r29";
my $ahi="r30";
my $nlo="r31";
#
my $nhi="r0";
$code=<<___;
.machine "any"
.text
.globl .bn_mul_mont_int
.align 5
.bn_mul_mont_int:
mr $rp,r3 ; $rp is reassigned
li r3,0
___
$code.=<<___ if ($BNSZ==4);
cmpwi $num,32 ; longer key performance is not better
bgelr
___
$code.=<<___;
slwi $num,$num,`log($BNSZ)/log(2)`
li $tj,-4096
addi $ovf,$num,$FRAME
subf $ovf,$ovf,$sp ; $sp-$ovf
and $ovf,$ovf,$tj ; minimize TLB usage
subf $ovf,$sp,$ovf ; $ovf-$sp
mr $tj,$sp
srwi $num,$num,`log($BNSZ)/log(2)`
$STUX $sp,$sp,$ovf
$PUSH r20,`-12*$SIZE_T`($tj)
$PUSH r21,`-11*$SIZE_T`($tj)
$PUSH r22,`-10*$SIZE_T`($tj)
$PUSH r23,`-9*$SIZE_T`($tj)
$PUSH r24,`-8*$SIZE_T`($tj)
$PUSH r25,`-7*$SIZE_T`($tj)
$PUSH r26,`-6*$SIZE_T`($tj)
$PUSH r27,`-5*$SIZE_T`($tj)
$PUSH r28,`-4*$SIZE_T`($tj)
$PUSH r29,`-3*$SIZE_T`($tj)
$PUSH r30,`-2*$SIZE_T`($tj)
$PUSH r31,`-1*$SIZE_T`($tj)
$LD $n0,0($n0) ; pull n0[0] value
addi $num,$num,-2 ; adjust $num for counter register
$LD $m0,0($bp) ; m0=bp[0]
$LD $aj,0($ap) ; ap[0]
addi $tp,$sp,$LOCALS
$UMULL $lo0,$aj,$m0 ; ap[0]*bp[0]
$UMULH $hi0,$aj,$m0
$LD $aj,$BNSZ($ap) ; ap[1]
$LD $nj,0($np) ; np[0]
$UMULL $m1,$lo0,$n0 ; "tp[0]"*n0
$UMULL $alo,$aj,$m0 ; ap[1]*bp[0]
$UMULH $ahi,$aj,$m0
$UMULL $lo1,$nj,$m1 ; np[0]*m1
$UMULH $hi1,$nj,$m1
$LD $nj,$BNSZ($np) ; np[1]
addc $lo1,$lo1,$lo0
addze $hi1,$hi1
$UMULL $nlo,$nj,$m1 ; np[1]*m1
$UMULH $nhi,$nj,$m1
mtctr $num
li $j,`2*$BNSZ`
.align 4
L1st:
$LDX $aj,$ap,$j ; ap[j]
addc $lo0,$alo,$hi0
$LDX $nj,$np,$j ; np[j]
addze $hi0,$ahi
$UMULL $alo,$aj,$m0 ; ap[j]*bp[0]
addc $lo1,$nlo,$hi1
$UMULH $ahi,$aj,$m0
addze $hi1,$nhi
$UMULL $nlo,$nj,$m1 ; np[j]*m1
addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[0]
$UMULH $nhi,$nj,$m1
addze $hi1,$hi1
$ST $lo1,0($tp) ; tp[j-1]
addi $j,$j,$BNSZ ; j++
addi $tp,$tp,$BNSZ ; tp++
bdnz L1st
;L1st
addc $lo0,$alo,$hi0
addze $hi0,$ahi
addc $lo1,$nlo,$hi1
addze $hi1,$nhi
addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[0]
addze $hi1,$hi1
$ST $lo1,0($tp) ; tp[j-1]
li $ovf,0
addc $hi1,$hi1,$hi0
addze $ovf,$ovf ; upmost overflow bit
$ST $hi1,$BNSZ($tp)
li $i,$BNSZ
.align 4
Louter:
$LDX $m0,$bp,$i ; m0=bp[i]
$LD $aj,0($ap) ; ap[0]
addi $tp,$sp,$LOCALS
$LD $tj,$LOCALS($sp); tp[0]
$UMULL $lo0,$aj,$m0 ; ap[0]*bp[i]
$UMULH $hi0,$aj,$m0
$LD $aj,$BNSZ($ap) ; ap[1]
$LD $nj,0($np) ; np[0]
addc $lo0,$lo0,$tj ; ap[0]*bp[i]+tp[0]
$UMULL $alo,$aj,$m0 ; ap[j]*bp[i]
addze $hi0,$hi0
$UMULL $m1,$lo0,$n0 ; tp[0]*n0
$UMULH $ahi,$aj,$m0
$UMULL $lo1,$nj,$m1 ; np[0]*m1
$UMULH $hi1,$nj,$m1
$LD $nj,$BNSZ($np) ; np[1]
addc $lo1,$lo1,$lo0
$UMULL $nlo,$nj,$m1 ; np[1]*m1
addze $hi1,$hi1
$UMULH $nhi,$nj,$m1
mtctr $num
li $j,`2*$BNSZ`
.align 4
Linner:
$LDX $aj,$ap,$j ; ap[j]
addc $lo0,$alo,$hi0
$LD $tj,$BNSZ($tp) ; tp[j]
addze $hi0,$ahi
$LDX $nj,$np,$j ; np[j]
addc $lo1,$nlo,$hi1
$UMULL $alo,$aj,$m0 ; ap[j]*bp[i]
addze $hi1,$nhi
$UMULH $ahi,$aj,$m0
addc $lo0,$lo0,$tj ; ap[j]*bp[i]+tp[j]
$UMULL $nlo,$nj,$m1 ; np[j]*m1
addze $hi0,$hi0
$UMULH $nhi,$nj,$m1
addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[i]+tp[j]
addi $j,$j,$BNSZ ; j++
addze $hi1,$hi1
$ST $lo1,0($tp) ; tp[j-1]
addi $tp,$tp,$BNSZ ; tp++
bdnz Linner
;Linner
$LD $tj,$BNSZ($tp) ; tp[j]
addc $lo0,$alo,$hi0
addze $hi0,$ahi
addc $lo0,$lo0,$tj ; ap[j]*bp[i]+tp[j]
addze $hi0,$hi0
addc $lo1,$nlo,$hi1
addze $hi1,$nhi
addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[i]+tp[j]
addze $hi1,$hi1
$ST $lo1,0($tp) ; tp[j-1]
addic $ovf,$ovf,-1 ; move upmost overflow to XER[CA]
li $ovf,0
adde $hi1,$hi1,$hi0
addze $ovf,$ovf
$ST $hi1,$BNSZ($tp)
;
slwi $tj,$num,`log($BNSZ)/log(2)`
$UCMP $i,$tj
addi $i,$i,$BNSZ
ble Louter
addi $num,$num,2 ; restore $num
subfc $j,$j,$j ; j=0 and "clear" XER[CA]
addi $tp,$sp,$LOCALS
mtctr $num
.align 4
Lsub: $LDX $tj,$tp,$j
$LDX $nj,$np,$j
subfe $aj,$nj,$tj ; tp[j]-np[j]
$STX $aj,$rp,$j
addi $j,$j,$BNSZ
bdnz Lsub
li $j,0
mtctr $num
subfe $ovf,$j,$ovf ; handle upmost overflow bit
.align 4
Lcopy: ; conditional copy
$LDX $tj,$tp,$j
$LDX $aj,$rp,$j
and $tj,$tj,$ovf
andc $aj,$aj,$ovf
$STX $j,$tp,$j ; zap at once
or $aj,$aj,$tj
$STX $aj,$rp,$j
addi $j,$j,$BNSZ
bdnz Lcopy
$POP $tj,0($sp)
li r3,1
$POP r20,`-12*$SIZE_T`($tj)
$POP r21,`-11*$SIZE_T`($tj)
$POP r22,`-10*$SIZE_T`($tj)
$POP r23,`-9*$SIZE_T`($tj)
$POP r24,`-8*$SIZE_T`($tj)
$POP r25,`-7*$SIZE_T`($tj)
$POP r26,`-6*$SIZE_T`($tj)
$POP r27,`-5*$SIZE_T`($tj)
$POP r28,`-4*$SIZE_T`($tj)
$POP r29,`-3*$SIZE_T`($tj)
$POP r30,`-2*$SIZE_T`($tj)
$POP r31,`-1*$SIZE_T`($tj)
mr $sp,$tj
blr
.long 0
.byte 0,12,4,0,0x80,12,6,0
.long 0
.size .bn_mul_mont_int,.-.bn_mul_mont_int
___
}
if (1) {
my ($a0,$a1,$a2,$a3,
$t0,$t1,$t2,$t3,
$m0,$m1,$m2,$m3,
$acc0,$acc1,$acc2,$acc3,$acc4,
$bi,$mi,$tp,$ap_end,$cnt) = map("r$_",(9..12,14..31));
my ($carry,$zero) = ($rp,"r0");
# sp----------->+-------------------------------+
# | saved sp |
# +-------------------------------+
# . .
# +8*size_t +-------------------------------+
# | 4 "n0*t0" |
# . .
# . .
# +12*size_t +-------------------------------+
# | size_t tmp[num] |
# . .
# . .
# . .
# +-------------------------------+
# | topmost carry |
# . .
# -18*size_t +-------------------------------+
# | 18 saved gpr, r14-r31 |
# . .
# . .
# +-------------------------------+
$code.=<<___;
.globl .bn_mul4x_mont_int
.align 5
.bn_mul4x_mont_int:
andi. r0,$num,7
bne .Lmul4x_do
$UCMP $ap,$bp
bne .Lmul4x_do
b .Lsqr8x_do
.Lmul4x_do:
slwi $num,$num,`log($SIZE_T)/log(2)`
mr $a0,$sp
li $a1,-32*$SIZE_T
sub $a1,$a1,$num
$STUX $sp,$sp,$a1 # alloca
$PUSH r14,-$SIZE_T*18($a0)
$PUSH r15,-$SIZE_T*17($a0)
$PUSH r16,-$SIZE_T*16($a0)
$PUSH r17,-$SIZE_T*15($a0)
$PUSH r18,-$SIZE_T*14($a0)
$PUSH r19,-$SIZE_T*13($a0)
$PUSH r20,-$SIZE_T*12($a0)
$PUSH r21,-$SIZE_T*11($a0)
$PUSH r22,-$SIZE_T*10($a0)
$PUSH r23,-$SIZE_T*9($a0)
$PUSH r24,-$SIZE_T*8($a0)
$PUSH r25,-$SIZE_T*7($a0)
$PUSH r26,-$SIZE_T*6($a0)
$PUSH r27,-$SIZE_T*5($a0)
$PUSH r28,-$SIZE_T*4($a0)
$PUSH r29,-$SIZE_T*3($a0)
$PUSH r30,-$SIZE_T*2($a0)
$PUSH r31,-$SIZE_T*1($a0)
subi $ap,$ap,$SIZE_T # bias by -1
subi $np,$np,$SIZE_T # bias by -1
subi $rp,$rp,$SIZE_T # bias by -1
$LD $n0,0($n0) # *n0
add $t0,$bp,$num
add $ap_end,$ap,$num
subi $t0,$t0,$SIZE_T*4 # &b[num-4]
$LD $bi,$SIZE_T*0($bp) # b[0]
li $acc0,0
$LD $a0,$SIZE_T*1($ap) # a[0..3]
li $acc1,0
$LD $a1,$SIZE_T*2($ap)
li $acc2,0
$LD $a2,$SIZE_T*3($ap)
li $acc3,0
$LDU $a3,$SIZE_T*4($ap)
$LD $m0,$SIZE_T*1($np) # n[0..3]
$LD $m1,$SIZE_T*2($np)
$LD $m2,$SIZE_T*3($np)
$LDU $m3,$SIZE_T*4($np)
$PUSH $rp,$SIZE_T*6($sp) # offload rp and &b[num-4]
$PUSH $t0,$SIZE_T*7($sp)
li $carry,0
addic $tp,$sp,$SIZE_T*7 # &t[-1], clear carry bit
li $cnt,0
li $zero,0
b .Loop_mul4x_1st_reduction
.align 5
.Loop_mul4x_1st_reduction:
$UMULL $t0,$a0,$bi # lo(a[0..3]*b[0])
addze $carry,$carry # modulo-scheduled
$UMULL $t1,$a1,$bi
addi $cnt,$cnt,$SIZE_T
$UMULL $t2,$a2,$bi
andi. $cnt,$cnt,$SIZE_T*4-1
$UMULL $t3,$a3,$bi
addc $acc0,$acc0,$t0
$UMULH $t0,$a0,$bi # hi(a[0..3]*b[0])
adde $acc1,$acc1,$t1
$UMULH $t1,$a1,$bi
adde $acc2,$acc2,$t2
$UMULL $mi,$acc0,$n0 # t[0]*n0
adde $acc3,$acc3,$t3
$UMULH $t2,$a2,$bi
addze $acc4,$zero
$UMULH $t3,$a3,$bi
$LDX $bi,$bp,$cnt # next b[i] (or b[0])
addc $acc1,$acc1,$t0
# (*) mul $t0,$m0,$mi # lo(n[0..3]*t[0]*n0)
$STU $mi,$SIZE_T($tp) # put aside t[0]*n0 for tail processing
adde $acc2,$acc2,$t1
$UMULL $t1,$m1,$mi
adde $acc3,$acc3,$t2
$UMULL $t2,$m2,$mi
adde $acc4,$acc4,$t3 # can't overflow
$UMULL $t3,$m3,$mi
# (*) addc $acc0,$acc0,$t0
# (*) As for removal of first multiplication and addition
# instructions. The outcome of first addition is
# guaranteed to be zero, which leaves two computationally
# significant outcomes: it either carries or not. Then
# question is when does it carry? Is there alternative
# way to deduce it? If you follow operations, you can
# observe that condition for carry is quite simple:
# $acc0 being non-zero. So that carry can be calculated
# by adding -1 to $acc0. That's what next instruction does.
addic $acc0,$acc0,-1 # (*), discarded
$UMULH $t0,$m0,$mi # hi(n[0..3]*t[0]*n0)
adde $acc0,$acc1,$t1
$UMULH $t1,$m1,$mi
adde $acc1,$acc2,$t2
$UMULH $t2,$m2,$mi
adde $acc2,$acc3,$t3
$UMULH $t3,$m3,$mi
adde $acc3,$acc4,$carry
addze $carry,$zero
addc $acc0,$acc0,$t0
adde $acc1,$acc1,$t1
adde $acc2,$acc2,$t2
adde $acc3,$acc3,$t3
#addze $carry,$carry
bne .Loop_mul4x_1st_reduction
$UCMP $ap_end,$ap
beq .Lmul4x4_post_condition
$LD $a0,$SIZE_T*1($ap) # a[4..7]
$LD $a1,$SIZE_T*2($ap)
$LD $a2,$SIZE_T*3($ap)
$LDU $a3,$SIZE_T*4($ap)
$LD $mi,$SIZE_T*8($sp) # a[0]*n0
$LD $m0,$SIZE_T*1($np) # n[4..7]
$LD $m1,$SIZE_T*2($np)
$LD $m2,$SIZE_T*3($np)
$LDU $m3,$SIZE_T*4($np)
b .Loop_mul4x_1st_tail
.align 5
.Loop_mul4x_1st_tail:
$UMULL $t0,$a0,$bi # lo(a[4..7]*b[i])
addze $carry,$carry # modulo-scheduled
$UMULL $t1,$a1,$bi
addi $cnt,$cnt,$SIZE_T
$UMULL $t2,$a2,$bi
andi. $cnt,$cnt,$SIZE_T*4-1
$UMULL $t3,$a3,$bi
addc $acc0,$acc0,$t0
$UMULH $t0,$a0,$bi # hi(a[4..7]*b[i])
adde $acc1,$acc1,$t1
$UMULH $t1,$a1,$bi
adde $acc2,$acc2,$t2
$UMULH $t2,$a2,$bi
adde $acc3,$acc3,$t3
$UMULH $t3,$a3,$bi
addze $acc4,$zero
$LDX $bi,$bp,$cnt # next b[i] (or b[0])
addc $acc1,$acc1,$t0
$UMULL $t0,$m0,$mi # lo(n[4..7]*a[0]*n0)
adde $acc2,$acc2,$t1
$UMULL $t1,$m1,$mi
adde $acc3,$acc3,$t2
$UMULL $t2,$m2,$mi
adde $acc4,$acc4,$t3 # can't overflow
$UMULL $t3,$m3,$mi
addc $acc0,$acc0,$t0
$UMULH $t0,$m0,$mi # hi(n[4..7]*a[0]*n0)
adde $acc1,$acc1,$t1
$UMULH $t1,$m1,$mi
adde $acc2,$acc2,$t2
$UMULH $t2,$m2,$mi
adde $acc3,$acc3,$t3
adde $acc4,$acc4,$carry
$UMULH $t3,$m3,$mi
addze $carry,$zero
addi $mi,$sp,$SIZE_T*8
$LDX $mi,$mi,$cnt # next t[0]*n0
$STU $acc0,$SIZE_T($tp) # word of result
addc $acc0,$acc1,$t0
adde $acc1,$acc2,$t1
adde $acc2,$acc3,$t2
adde $acc3,$acc4,$t3
#addze $carry,$carry
bne .Loop_mul4x_1st_tail
sub $t1,$ap_end,$num # rewinded $ap
$UCMP $ap_end,$ap # done yet?
beq .Lmul4x_proceed
$LD $a0,$SIZE_T*1($ap)
$LD $a1,$SIZE_T*2($ap)
$LD $a2,$SIZE_T*3($ap)
$LDU $a3,$SIZE_T*4($ap)
$LD $m0,$SIZE_T*1($np)
$LD $m1,$SIZE_T*2($np)
$LD $m2,$SIZE_T*3($np)
$LDU $m3,$SIZE_T*4($np)
b .Loop_mul4x_1st_tail
.align 5
.Lmul4x_proceed:
$LDU $bi,$SIZE_T*4($bp) # *++b
addze $carry,$carry # topmost carry
$LD $a0,$SIZE_T*1($t1)
$LD $a1,$SIZE_T*2($t1)
$LD $a2,$SIZE_T*3($t1)
$LD $a3,$SIZE_T*4($t1)
addi $ap,$t1,$SIZE_T*4
sub $np,$np,$num # rewind np
$ST $acc0,$SIZE_T*1($tp) # result
$ST $acc1,$SIZE_T*2($tp)
$ST $acc2,$SIZE_T*3($tp)
$ST $acc3,$SIZE_T*4($tp)
$ST $carry,$SIZE_T*5($tp) # save topmost carry
$LD $acc0,$SIZE_T*12($sp) # t[0..3]
$LD $acc1,$SIZE_T*13($sp)
$LD $acc2,$SIZE_T*14($sp)
$LD $acc3,$SIZE_T*15($sp)
$LD $m0,$SIZE_T*1($np) # n[0..3]
$LD $m1,$SIZE_T*2($np)
$LD $m2,$SIZE_T*3($np)
$LDU $m3,$SIZE_T*4($np)
addic $tp,$sp,$SIZE_T*7 # &t[-1], clear carry bit
li $carry,0
b .Loop_mul4x_reduction
.align 5
.Loop_mul4x_reduction:
$UMULL $t0,$a0,$bi # lo(a[0..3]*b[4])
addze $carry,$carry # modulo-scheduled
$UMULL $t1,$a1,$bi
addi $cnt,$cnt,$SIZE_T
$UMULL $t2,$a2,$bi
andi. $cnt,$cnt,$SIZE_T*4-1
$UMULL $t3,$a3,$bi
addc $acc0,$acc0,$t0
$UMULH $t0,$a0,$bi # hi(a[0..3]*b[4])
adde $acc1,$acc1,$t1
$UMULH $t1,$a1,$bi
adde $acc2,$acc2,$t2
$UMULL $mi,$acc0,$n0 # t[0]*n0
adde $acc3,$acc3,$t3
$UMULH $t2,$a2,$bi
addze $acc4,$zero
$UMULH $t3,$a3,$bi
$LDX $bi,$bp,$cnt # next b[i]
addc $acc1,$acc1,$t0
# (*) mul $t0,$m0,$mi
$STU $mi,$SIZE_T($tp) # put aside t[0]*n0 for tail processing
adde $acc2,$acc2,$t1
$UMULL $t1,$m1,$mi # lo(n[0..3]*t[0]*n0
adde $acc3,$acc3,$t2
$UMULL $t2,$m2,$mi
adde $acc4,$acc4,$t3 # can't overflow
$UMULL $t3,$m3,$mi
# (*) addc $acc0,$acc0,$t0
addic $acc0,$acc0,-1 # (*), discarded
$UMULH $t0,$m0,$mi # hi(n[0..3]*t[0]*n0
adde $acc0,$acc1,$t1
$UMULH $t1,$m1,$mi
adde $acc1,$acc2,$t2
$UMULH $t2,$m2,$mi
adde $acc2,$acc3,$t3
$UMULH $t3,$m3,$mi
adde $acc3,$acc4,$carry
addze $carry,$zero
addc $acc0,$acc0,$t0
adde $acc1,$acc1,$t1
adde $acc2,$acc2,$t2
adde $acc3,$acc3,$t3
#addze $carry,$carry
bne .Loop_mul4x_reduction
$LD $t0,$SIZE_T*5($tp) # t[4..7]
addze $carry,$carry
$LD $t1,$SIZE_T*6($tp)
$LD $t2,$SIZE_T*7($tp)
$LD $t3,$SIZE_T*8($tp)
$LD $a0,$SIZE_T*1($ap) # a[4..7]
$LD $a1,$SIZE_T*2($ap)
$LD $a2,$SIZE_T*3($ap)
$LDU $a3,$SIZE_T*4($ap)
addc $acc0,$acc0,$t0
adde $acc1,$acc1,$t1
adde $acc2,$acc2,$t2
adde $acc3,$acc3,$t3
#addze $carry,$carry
$LD $mi,$SIZE_T*8($sp) # t[0]*n0
$LD $m0,$SIZE_T*1($np) # n[4..7]
$LD $m1,$SIZE_T*2($np)
$LD $m2,$SIZE_T*3($np)
$LDU $m3,$SIZE_T*4($np)
b .Loop_mul4x_tail
.align 5
.Loop_mul4x_tail:
$UMULL $t0,$a0,$bi # lo(a[4..7]*b[4])
addze $carry,$carry # modulo-scheduled
$UMULL $t1,$a1,$bi
addi $cnt,$cnt,$SIZE_T
$UMULL $t2,$a2,$bi
andi. $cnt,$cnt,$SIZE_T*4-1
$UMULL $t3,$a3,$bi
addc $acc0,$acc0,$t0
$UMULH $t0,$a0,$bi # hi(a[4..7]*b[4])
adde $acc1,$acc1,$t1
$UMULH $t1,$a1,$bi
adde $acc2,$acc2,$t2
$UMULH $t2,$a2,$bi
adde $acc3,$acc3,$t3
$UMULH $t3,$a3,$bi
addze $acc4,$zero
$LDX $bi,$bp,$cnt # next b[i]
addc $acc1,$acc1,$t0
$UMULL $t0,$m0,$mi # lo(n[4..7]*t[0]*n0)
adde $acc2,$acc2,$t1
$UMULL $t1,$m1,$mi
adde $acc3,$acc3,$t2
$UMULL $t2,$m2,$mi
adde $acc4,$acc4,$t3 # can't overflow
$UMULL $t3,$m3,$mi
addc $acc0,$acc0,$t0
$UMULH $t0,$m0,$mi # hi(n[4..7]*t[0]*n0)
adde $acc1,$acc1,$t1
$UMULH $t1,$m1,$mi
adde $acc2,$acc2,$t2
$UMULH $t2,$m2,$mi
adde $acc3,$acc3,$t3
$UMULH $t3,$m3,$mi
adde $acc4,$acc4,$carry
addi $mi,$sp,$SIZE_T*8
$LDX $mi,$mi,$cnt # next a[0]*n0
addze $carry,$zero
$STU $acc0,$SIZE_T($tp) # word of result
addc $acc0,$acc1,$t0
adde $acc1,$acc2,$t1
adde $acc2,$acc3,$t2
adde $acc3,$acc4,$t3
#addze $carry,$carry
bne .Loop_mul4x_tail
$LD $t0,$SIZE_T*5($tp) # next t[i] or topmost carry
sub $t1,$np,$num # rewinded np?
addze $carry,$carry
$UCMP $ap_end,$ap # done yet?
beq .Loop_mul4x_break
$LD $t1,$SIZE_T*6($tp)
$LD $t2,$SIZE_T*7($tp)
$LD $t3,$SIZE_T*8($tp)
$LD $a0,$SIZE_T*1($ap)
$LD $a1,$SIZE_T*2($ap)
$LD $a2,$SIZE_T*3($ap)
$LDU $a3,$SIZE_T*4($ap)
addc $acc0,$acc0,$t0
adde $acc1,$acc1,$t1
adde $acc2,$acc2,$t2
adde $acc3,$acc3,$t3
#addze $carry,$carry
$LD $m0,$SIZE_T*1($np) # n[4..7]
$LD $m1,$SIZE_T*2($np)
$LD $m2,$SIZE_T*3($np)
$LDU $m3,$SIZE_T*4($np)
b .Loop_mul4x_tail
.align 5
.Loop_mul4x_break:
$POP $t2,$SIZE_T*6($sp) # pull rp and &b[num-4]
$POP $t3,$SIZE_T*7($sp)
addc $a0,$acc0,$t0 # accumulate topmost carry
$LD $acc0,$SIZE_T*12($sp) # t[0..3]
addze $a1,$acc1
$LD $acc1,$SIZE_T*13($sp)
addze $a2,$acc2
$LD $acc2,$SIZE_T*14($sp)
addze $a3,$acc3
$LD $acc3,$SIZE_T*15($sp)
addze $carry,$carry # topmost carry
$ST $a0,$SIZE_T*1($tp) # result
sub $ap,$ap_end,$num # rewind ap
$ST $a1,$SIZE_T*2($tp)
$ST $a2,$SIZE_T*3($tp)
$ST $a3,$SIZE_T*4($tp)
$ST $carry,$SIZE_T*5($tp) # store topmost carry
$LD $m0,$SIZE_T*1($t1) # n[0..3]
$LD $m1,$SIZE_T*2($t1)
$LD $m2,$SIZE_T*3($t1)
$LD $m3,$SIZE_T*4($t1)
addi $np,$t1,$SIZE_T*4
$UCMP $bp,$t3 # done yet?
beq .Lmul4x_post
$LDU $bi,$SIZE_T*4($bp)
$LD $a0,$SIZE_T*1($ap) # a[0..3]
$LD $a1,$SIZE_T*2($ap)
$LD $a2,$SIZE_T*3($ap)
$LDU $a3,$SIZE_T*4($ap)
li $carry,0
addic $tp,$sp,$SIZE_T*7 # &t[-1], clear carry bit
b .Loop_mul4x_reduction
.align 5
.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.
srwi $cnt,$num,`log($SIZE_T)/log(2)+2`
mr $bp,$t2 # &rp[-1]
subi $cnt,$cnt,1
mr $ap_end,$t2 # &rp[-1] copy
subfc $t0,$m0,$acc0
addi $tp,$sp,$SIZE_T*15
subfe $t1,$m1,$acc1
mtctr $cnt
.Lmul4x_sub:
$LD $m0,$SIZE_T*1($np)
$LD $acc0,$SIZE_T*1($tp)
subfe $t2,$m2,$acc2
$LD $m1,$SIZE_T*2($np)
$LD $acc1,$SIZE_T*2($tp)
subfe $t3,$m3,$acc3
$LD $m2,$SIZE_T*3($np)
$LD $acc2,$SIZE_T*3($tp)
$LDU $m3,$SIZE_T*4($np)
$LDU $acc3,$SIZE_T*4($tp)
$ST $t0,$SIZE_T*1($bp)
$ST $t1,$SIZE_T*2($bp)
subfe $t0,$m0,$acc0
$ST $t2,$SIZE_T*3($bp)
$STU $t3,$SIZE_T*4($bp)
subfe $t1,$m1,$acc1
bdnz .Lmul4x_sub
$LD $a0,$SIZE_T*1($ap_end)
$ST $t0,$SIZE_T*1($bp)
$LD $t0,$SIZE_T*12($sp)
subfe $t2,$m2,$acc2
$LD $a1,$SIZE_T*2($ap_end)
$ST $t1,$SIZE_T*2($bp)
$LD $t1,$SIZE_T*13($sp)
subfe $t3,$m3,$acc3
subfe $carry,$zero,$carry # did it borrow?
addi $tp,$sp,$SIZE_T*12
$LD $a2,$SIZE_T*3($ap_end)
$ST $t2,$SIZE_T*3($bp)
$LD $t2,$SIZE_T*14($sp)
$LD $a3,$SIZE_T*4($ap_end)
$ST $t3,$SIZE_T*4($bp)
$LD $t3,$SIZE_T*15($sp)
mtctr $cnt
.Lmul4x_cond_copy:
and $t0,$t0,$carry
andc $a0,$a0,$carry
$ST $zero,$SIZE_T*0($tp) # wipe stack clean
and $t1,$t1,$carry
andc $a1,$a1,$carry
$ST $zero,$SIZE_T*1($tp)
and $t2,$t2,$carry
andc $a2,$a2,$carry
$ST $zero,$SIZE_T*2($tp)
and $t3,$t3,$carry
andc $a3,$a3,$carry
$ST $zero,$SIZE_T*3($tp)
or $acc0,$t0,$a0
$LD $a0,$SIZE_T*5($ap_end)
$LD $t0,$SIZE_T*4($tp)
or $acc1,$t1,$a1
$LD $a1,$SIZE_T*6($ap_end)
$LD $t1,$SIZE_T*5($tp)
or $acc2,$t2,$a2
$LD $a2,$SIZE_T*7($ap_end)
$LD $t2,$SIZE_T*6($tp)
or $acc3,$t3,$a3
$LD $a3,$SIZE_T*8($ap_end)
$LD $t3,$SIZE_T*7($tp)
addi $tp,$tp,$SIZE_T*4
$ST $acc0,$SIZE_T*1($ap_end)
$ST $acc1,$SIZE_T*2($ap_end)
$ST $acc2,$SIZE_T*3($ap_end)
$STU $acc3,$SIZE_T*4($ap_end)
bdnz .Lmul4x_cond_copy
$POP $bp,0($sp) # pull saved sp
and $t0,$t0,$carry
andc $a0,$a0,$carry
$ST $zero,$SIZE_T*0($tp)
and $t1,$t1,$carry
andc $a1,$a1,$carry
$ST $zero,$SIZE_T*1($tp)
and $t2,$t2,$carry
andc $a2,$a2,$carry
$ST $zero,$SIZE_T*2($tp)
and $t3,$t3,$carry
andc $a3,$a3,$carry
$ST $zero,$SIZE_T*3($tp)
or $acc0,$t0,$a0
or $acc1,$t1,$a1
$ST $zero,$SIZE_T*4($tp)
or $acc2,$t2,$a2
or $acc3,$t3,$a3
$ST $acc0,$SIZE_T*1($ap_end)
$ST $acc1,$SIZE_T*2($ap_end)
$ST $acc2,$SIZE_T*3($ap_end)
$ST $acc3,$SIZE_T*4($ap_end)
b .Lmul4x_done
.align 4
.Lmul4x4_post_condition:
$POP $ap,$SIZE_T*6($sp) # pull &rp[-1]
$POP $bp,0($sp) # pull saved sp
addze $carry,$carry # modulo-scheduled
# $acc0-3,$carry hold result, $m0-3 hold modulus
subfc $a0,$m0,$acc0
subfe $a1,$m1,$acc1
subfe $a2,$m2,$acc2
subfe $a3,$m3,$acc3
subfe $carry,$zero,$carry # did it borrow?
and $m0,$m0,$carry
and $m1,$m1,$carry
addc $a0,$a0,$m0
and $m2,$m2,$carry
adde $a1,$a1,$m1
and $m3,$m3,$carry
adde $a2,$a2,$m2
adde $a3,$a3,$m3
$ST $a0,$SIZE_T*1($ap) # write result
$ST $a1,$SIZE_T*2($ap)
$ST $a2,$SIZE_T*3($ap)
$ST $a3,$SIZE_T*4($ap)
.Lmul4x_done:
$ST $zero,$SIZE_T*8($sp) # wipe stack clean
$ST $zero,$SIZE_T*9($sp)
$ST $zero,$SIZE_T*10($sp)
$ST $zero,$SIZE_T*11($sp)
li r3,1 # signal "done"
$POP r14,-$SIZE_T*18($bp)
$POP r15,-$SIZE_T*17($bp)
$POP r16,-$SIZE_T*16($bp)
$POP r17,-$SIZE_T*15($bp)
$POP r18,-$SIZE_T*14($bp)
$POP r19,-$SIZE_T*13($bp)
$POP r20,-$SIZE_T*12($bp)
$POP r21,-$SIZE_T*11($bp)
$POP r22,-$SIZE_T*10($bp)
$POP r23,-$SIZE_T*9($bp)
$POP r24,-$SIZE_T*8($bp)
$POP r25,-$SIZE_T*7($bp)
$POP r26,-$SIZE_T*6($bp)
$POP r27,-$SIZE_T*5($bp)
$POP r28,-$SIZE_T*4($bp)
$POP r29,-$SIZE_T*3($bp)
$POP r30,-$SIZE_T*2($bp)
$POP r31,-$SIZE_T*1($bp)
mr $sp,$bp
blr
.long 0
.byte 0,12,4,0x20,0x80,18,6,0
.long 0
.size .bn_mul4x_mont_int,.-.bn_mul4x_mont_int
___
}
if (1) {
########################################################################
# Following is PPC adaptation of sqrx8x_mont from x86_64-mont5 module.
my ($a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7)=map("r$_",(9..12,14..17));
my ($t0,$t1,$t2,$t3)=map("r$_",(18..21));
my ($acc0,$acc1,$acc2,$acc3,$acc4,$acc5,$acc6,$acc7)=map("r$_",(22..29));
my ($cnt,$carry,$zero)=("r30","r31","r0");
my ($tp,$ap_end,$na0)=($bp,$np,$carry);
# sp----------->+-------------------------------+
# | saved sp |
# +-------------------------------+
# . .
# +12*size_t +-------------------------------+
# | size_t tmp[2*num] |
# . .
# . .
# . .
# +-------------------------------+
# . .
# -18*size_t +-------------------------------+
# | 18 saved gpr, r14-r31 |
# . .
# . .
# +-------------------------------+
$code.=<<___;
.align 5
__bn_sqr8x_mont:
.Lsqr8x_do:
mr $a0,$sp
slwi $a1,$num,`log($SIZE_T)/log(2)+1`
li $a2,-32*$SIZE_T
sub $a1,$a2,$a1
slwi $num,$num,`log($SIZE_T)/log(2)`
$STUX $sp,$sp,$a1 # alloca
$PUSH r14,-$SIZE_T*18($a0)
$PUSH r15,-$SIZE_T*17($a0)
$PUSH r16,-$SIZE_T*16($a0)
$PUSH r17,-$SIZE_T*15($a0)
$PUSH r18,-$SIZE_T*14($a0)
$PUSH r19,-$SIZE_T*13($a0)
$PUSH r20,-$SIZE_T*12($a0)
$PUSH r21,-$SIZE_T*11($a0)
$PUSH r22,-$SIZE_T*10($a0)
$PUSH r23,-$SIZE_T*9($a0)
$PUSH r24,-$SIZE_T*8($a0)
$PUSH r25,-$SIZE_T*7($a0)
$PUSH r26,-$SIZE_T*6($a0)
$PUSH r27,-$SIZE_T*5($a0)
$PUSH r28,-$SIZE_T*4($a0)
$PUSH r29,-$SIZE_T*3($a0)
$PUSH r30,-$SIZE_T*2($a0)
$PUSH r31,-$SIZE_T*1($a0)
subi $ap,$ap,$SIZE_T # bias by -1
subi $t0,$np,$SIZE_T # bias by -1
subi $rp,$rp,$SIZE_T # bias by -1
$LD $n0,0($n0) # *n0
li $zero,0
add $ap_end,$ap,$num
$LD $a0,$SIZE_T*1($ap)
#li $acc0,0
$LD $a1,$SIZE_T*2($ap)
li $acc1,0
$LD $a2,$SIZE_T*3($ap)
li $acc2,0
$LD $a3,$SIZE_T*4($ap)
li $acc3,0
$LD $a4,$SIZE_T*5($ap)
li $acc4,0
$LD $a5,$SIZE_T*6($ap)
li $acc5,0
$LD $a6,$SIZE_T*7($ap)
li $acc6,0
$LDU $a7,$SIZE_T*8($ap)
li $acc7,0
addi $tp,$sp,$SIZE_T*11 # &tp[-1]
subic. $cnt,$num,$SIZE_T*8
b .Lsqr8x_zero_start
.align 5
.Lsqr8x_zero:
subic. $cnt,$cnt,$SIZE_T*8
$ST $zero,$SIZE_T*1($tp)
$ST $zero,$SIZE_T*2($tp)
$ST $zero,$SIZE_T*3($tp)
$ST $zero,$SIZE_T*4($tp)
$ST $zero,$SIZE_T*5($tp)
$ST $zero,$SIZE_T*6($tp)
$ST $zero,$SIZE_T*7($tp)
$ST $zero,$SIZE_T*8($tp)
.Lsqr8x_zero_start:
$ST $zero,$SIZE_T*9($tp)
$ST $zero,$SIZE_T*10($tp)
$ST $zero,$SIZE_T*11($tp)
$ST $zero,$SIZE_T*12($tp)
$ST $zero,$SIZE_T*13($tp)
$ST $zero,$SIZE_T*14($tp)
$ST $zero,$SIZE_T*15($tp)
$STU $zero,$SIZE_T*16($tp)
bne .Lsqr8x_zero
$PUSH $rp,$SIZE_T*6($sp) # offload &rp[-1]
$PUSH $t0,$SIZE_T*7($sp) # offload &np[-1]
$PUSH $n0,$SIZE_T*8($sp) # offload n0
$PUSH $tp,$SIZE_T*9($sp) # &tp[2*num-1]
$PUSH $zero,$SIZE_T*10($sp) # initial top-most carry
addi $tp,$sp,$SIZE_T*11 # &tp[-1]
# Multiply everything but a[i]*a[i]
.align 5
.Lsqr8x_outer_loop:
# a[1]a[0] (i)
# 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] (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)
$UMULL $t0,$a1,$a0 # lo(a[1..7]*a[0]) (i)
$UMULL $t1,$a2,$a0
$UMULL $t2,$a3,$a0
$UMULL $t3,$a4,$a0
addc $acc1,$acc1,$t0 # t[1]+lo(a[1]*a[0])
$UMULL $t0,$a5,$a0
adde $acc2,$acc2,$t1
$UMULL $t1,$a6,$a0
adde $acc3,$acc3,$t2
$UMULL $t2,$a7,$a0
adde $acc4,$acc4,$t3
$UMULH $t3,$a1,$a0 # hi(a[1..7]*a[0])
adde $acc5,$acc5,$t0
$UMULH $t0,$a2,$a0
adde $acc6,$acc6,$t1
$UMULH $t1,$a3,$a0
adde $acc7,$acc7,$t2
$UMULH $t2,$a4,$a0
$ST $acc0,$SIZE_T*1($tp) # t[0]
addze $acc0,$zero # t[8]
$ST $acc1,$SIZE_T*2($tp) # t[1]
addc $acc2,$acc2,$t3 # t[2]+lo(a[1]*a[0])
$UMULH $t3,$a5,$a0
adde $acc3,$acc3,$t0
$UMULH $t0,$a6,$a0
adde $acc4,$acc4,$t1
$UMULH $t1,$a7,$a0
adde $acc5,$acc5,$t2
$UMULL $t2,$a2,$a1 # lo(a[2..7]*a[1]) (ii)
adde $acc6,$acc6,$t3
$UMULL $t3,$a3,$a1
adde $acc7,$acc7,$t0
$UMULL $t0,$a4,$a1
adde $acc0,$acc0,$t1
$UMULL $t1,$a5,$a1
addc $acc3,$acc3,$t2
$UMULL $t2,$a6,$a1
adde $acc4,$acc4,$t3
$UMULL $t3,$a7,$a1
adde $acc5,$acc5,$t0
$UMULH $t0,$a2,$a1 # hi(a[2..7]*a[1])
adde $acc6,$acc6,$t1
$UMULH $t1,$a3,$a1
adde $acc7,$acc7,$t2
$UMULH $t2,$a4,$a1
adde $acc0,$acc0,$t3
$UMULH $t3,$a5,$a1
$ST $acc2,$SIZE_T*3($tp) # t[2]
addze $acc1,$zero # t[9]
$ST $acc3,$SIZE_T*4($tp) # t[3]
addc $acc4,$acc4,$t0
$UMULH $t0,$a6,$a1
adde $acc5,$acc5,$t1
$UMULH $t1,$a7,$a1
adde $acc6,$acc6,$t2
$UMULL $t2,$a3,$a2 # lo(a[3..7]*a[2]) (iii)
adde $acc7,$acc7,$t3
$UMULL $t3,$a4,$a2
adde $acc0,$acc0,$t0
$UMULL $t0,$a5,$a2
adde $acc1,$acc1,$t1
$UMULL $t1,$a6,$a2
addc $acc5,$acc5,$t2
$UMULL $t2,$a7,$a2
adde $acc6,$acc6,$t3
$UMULH $t3,$a3,$a2 # hi(a[3..7]*a[2])
adde $acc7,$acc7,$t0
$UMULH $t0,$a4,$a2
adde $acc0,$acc0,$t1
$UMULH $t1,$a5,$a2
adde $acc1,$acc1,$t2
$UMULH $t2,$a6,$a2
$ST $acc4,$SIZE_T*5($tp) # t[4]
addze $acc2,$zero # t[10]
$ST $acc5,$SIZE_T*6($tp) # t[5]
addc $acc6,$acc6,$t3
$UMULH $t3,$a7,$a2
adde $acc7,$acc7,$t0
$UMULL $t0,$a4,$a3 # lo(a[4..7]*a[3]) (iv)
adde $acc0,$acc0,$t1
$UMULL $t1,$a5,$a3
adde $acc1,$acc1,$t2
$UMULL $t2,$a6,$a3
adde $acc2,$acc2,$t3
$UMULL $t3,$a7,$a3
addc $acc7,$acc7,$t0
$UMULH $t0,$a4,$a3 # hi(a[4..7]*a[3])
adde $acc0,$acc0,$t1
$UMULH $t1,$a5,$a3
adde $acc1,$acc1,$t2
$UMULH $t2,$a6,$a3
adde $acc2,$acc2,$t3
$UMULH $t3,$a7,$a3
$ST $acc6,$SIZE_T*7($tp) # t[6]
addze $acc3,$zero # t[11]
$STU $acc7,$SIZE_T*8($tp) # t[7]
addc $acc0,$acc0,$t0
$UMULL $t0,$a5,$a4 # lo(a[5..7]*a[4]) (v)
adde $acc1,$acc1,$t1
$UMULL $t1,$a6,$a4
adde $acc2,$acc2,$t2
$UMULL $t2,$a7,$a4
adde $acc3,$acc3,$t3
$UMULH $t3,$a5,$a4 # hi(a[5..7]*a[4])
addc $acc1,$acc1,$t0
$UMULH $t0,$a6,$a4
adde $acc2,$acc2,$t1
$UMULH $t1,$a7,$a4
adde $acc3,$acc3,$t2
$UMULL $t2,$a6,$a5 # lo(a[6..7]*a[5]) (vi)
addze $acc4,$zero # t[12]
addc $acc2,$acc2,$t3
$UMULL $t3,$a7,$a5
adde $acc3,$acc3,$t0
$UMULH $t0,$a6,$a5 # hi(a[6..7]*a[5])
adde $acc4,$acc4,$t1
$UMULH $t1,$a7,$a5
addc $acc3,$acc3,$t2
$UMULL $t2,$a7,$a6 # lo(a[7]*a[6]) (vii)
adde $acc4,$acc4,$t3
$UMULH $t3,$a7,$a6 # hi(a[7]*a[6])
addze $acc5,$zero # t[13]
addc $acc4,$acc4,$t0
$UCMP $ap_end,$ap # done yet?
adde $acc5,$acc5,$t1
addc $acc5,$acc5,$t2
sub $t0,$ap_end,$num # rewinded ap
addze $acc6,$zero # t[14]
add $acc6,$acc6,$t3
beq .Lsqr8x_outer_break
mr $n0,$a0
$LD $a0,$SIZE_T*1($tp)
$LD $a1,$SIZE_T*2($tp)
$LD $a2,$SIZE_T*3($tp)
$LD $a3,$SIZE_T*4($tp)
$LD $a4,$SIZE_T*5($tp)
$LD $a5,$SIZE_T*6($tp)
$LD $a6,$SIZE_T*7($tp)
$LD $a7,$SIZE_T*8($tp)
addc $acc0,$acc0,$a0
$LD $a0,$SIZE_T*1($ap)
adde $acc1,$acc1,$a1
$LD $a1,$SIZE_T*2($ap)
adde $acc2,$acc2,$a2
$LD $a2,$SIZE_T*3($ap)
adde $acc3,$acc3,$a3
$LD $a3,$SIZE_T*4($ap)
adde $acc4,$acc4,$a4
$LD $a4,$SIZE_T*5($ap)
adde $acc5,$acc5,$a5
$LD $a5,$SIZE_T*6($ap)
adde $acc6,$acc6,$a6
$LD $a6,$SIZE_T*7($ap)
subi $rp,$ap,$SIZE_T*7
addze $acc7,$a7
$LDU $a7,$SIZE_T*8($ap)
#addze $carry,$zero # moved below
li $cnt,0
b .Lsqr8x_mul
# 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]........................
.align 5
.Lsqr8x_mul:
$UMULL $t0,$a0,$n0
addze $carry,$zero # carry bit, modulo-scheduled
$UMULL $t1,$a1,$n0
addi $cnt,$cnt,$SIZE_T
$UMULL $t2,$a2,$n0
andi. $cnt,$cnt,$SIZE_T*8-1
$UMULL $t3,$a3,$n0
addc $acc0,$acc0,$t0
$UMULL $t0,$a4,$n0
adde $acc1,$acc1,$t1
$UMULL $t1,$a5,$n0
adde $acc2,$acc2,$t2
$UMULL $t2,$a6,$n0
adde $acc3,$acc3,$t3
$UMULL $t3,$a7,$n0
adde $acc4,$acc4,$t0
$UMULH $t0,$a0,$n0
adde $acc5,$acc5,$t1
$UMULH $t1,$a1,$n0
adde $acc6,$acc6,$t2
$UMULH $t2,$a2,$n0
adde $acc7,$acc7,$t3
$UMULH $t3,$a3,$n0
addze $carry,$carry
$STU $acc0,$SIZE_T($tp)
addc $acc0,$acc1,$t0
$UMULH $t0,$a4,$n0
adde $acc1,$acc2,$t1
$UMULH $t1,$a5,$n0
adde $acc2,$acc3,$t2
$UMULH $t2,$a6,$n0
adde $acc3,$acc4,$t3
$UMULH $t3,$a7,$n0
$LDX $n0,$rp,$cnt
adde $acc4,$acc5,$t0
adde $acc5,$acc6,$t1
adde $acc6,$acc7,$t2
adde $acc7,$carry,$t3
#addze $carry,$zero # moved above
bne .Lsqr8x_mul
# note that carry flag is guaranteed
# to be zero at this point
$UCMP $ap,$ap_end # done yet?
beq .Lsqr8x_break
$LD $a0,$SIZE_T*1($tp)
$LD $a1,$SIZE_T*2($tp)
$LD $a2,$SIZE_T*3($tp)
$LD $a3,$SIZE_T*4($tp)
$LD $a4,$SIZE_T*5($tp)
$LD $a5,$SIZE_T*6($tp)
$LD $a6,$SIZE_T*7($tp)
$LD $a7,$SIZE_T*8($tp)
addc $acc0,$acc0,$a0
$LD $a0,$SIZE_T*1($ap)
adde $acc1,$acc1,$a1
$LD $a1,$SIZE_T*2($ap)
adde $acc2,$acc2,$a2
$LD $a2,$SIZE_T*3($ap)
adde $acc3,$acc3,$a3
$LD $a3,$SIZE_T*4($ap)
adde $acc4,$acc4,$a4
$LD $a4,$SIZE_T*5($ap)
adde $acc5,$acc5,$a5
$LD $a5,$SIZE_T*6($ap)
adde $acc6,$acc6,$a6
$LD $a6,$SIZE_T*7($ap)
adde $acc7,$acc7,$a7
$LDU $a7,$SIZE_T*8($ap)
#addze $carry,$zero # moved above
b .Lsqr8x_mul
.align 5
.Lsqr8x_break:
$LD $a0,$SIZE_T*8($rp)
addi $ap,$rp,$SIZE_T*15
$LD $a1,$SIZE_T*9($rp)
sub. $t0,$ap_end,$ap # is it last iteration?
$LD $a2,$SIZE_T*10($rp)
sub $t1,$tp,$t0
$LD $a3,$SIZE_T*11($rp)
$LD $a4,$SIZE_T*12($rp)
$LD $a5,$SIZE_T*13($rp)
$LD $a6,$SIZE_T*14($rp)
$LD $a7,$SIZE_T*15($rp)
beq .Lsqr8x_outer_loop
$ST $acc0,$SIZE_T*1($tp)
$LD $acc0,$SIZE_T*1($t1)
$ST $acc1,$SIZE_T*2($tp)
$LD $acc1,$SIZE_T*2($t1)
$ST $acc2,$SIZE_T*3($tp)
$LD $acc2,$SIZE_T*3($t1)
$ST $acc3,$SIZE_T*4($tp)
$LD $acc3,$SIZE_T*4($t1)
$ST $acc4,$SIZE_T*5($tp)
$LD $acc4,$SIZE_T*5($t1)
$ST $acc5,$SIZE_T*6($tp)
$LD $acc5,$SIZE_T*6($t1)
$ST $acc6,$SIZE_T*7($tp)
$LD $acc6,$SIZE_T*7($t1)
$ST $acc7,$SIZE_T*8($tp)
$LD $acc7,$SIZE_T*8($t1)
mr $tp,$t1
b .Lsqr8x_outer_loop
.align 5
.Lsqr8x_outer_break:
####################################################################
# Now multiply above result by 2 and add a[n-1]*a[n-1]|...|a[0]*a[0]
$LD $a1,$SIZE_T*1($t0) # recall that $t0 is &a[-1]
$LD $a3,$SIZE_T*2($t0)
$LD $a5,$SIZE_T*3($t0)
$LD $a7,$SIZE_T*4($t0)
addi $ap,$t0,$SIZE_T*4
# "tp[x]" comments are for num==8 case
$LD $t1,$SIZE_T*13($sp) # =tp[1], t[0] is not interesting
$LD $t2,$SIZE_T*14($sp)
$LD $t3,$SIZE_T*15($sp)
$LD $t0,$SIZE_T*16($sp)
$ST $acc0,$SIZE_T*1($tp) # tp[8]=
srwi $cnt,$num,`log($SIZE_T)/log(2)+2`
$ST $acc1,$SIZE_T*2($tp)
subi $cnt,$cnt,1
$ST $acc2,$SIZE_T*3($tp)
$ST $acc3,$SIZE_T*4($tp)
$ST $acc4,$SIZE_T*5($tp)
$ST $acc5,$SIZE_T*6($tp)
$ST $acc6,$SIZE_T*7($tp)
#$ST $acc7,$SIZE_T*8($tp) # tp[15] is not interesting
addi $tp,$sp,$SIZE_T*11 # &tp[-1]
$UMULL $acc0,$a1,$a1
$UMULH $a1,$a1,$a1
add $acc1,$t1,$t1 # <<1
$SHRI $t1,$t1,$BITS-1
$UMULL $a2,$a3,$a3
$UMULH $a3,$a3,$a3
addc $acc1,$acc1,$a1
add $acc2,$t2,$t2
$SHRI $t2,$t2,$BITS-1
add $acc3,$t3,$t3
$SHRI $t3,$t3,$BITS-1
or $acc2,$acc2,$t1
mtctr $cnt
.Lsqr4x_shift_n_add:
$UMULL $a4,$a5,$a5
$UMULH $a5,$a5,$a5
$LD $t1,$SIZE_T*6($tp) # =tp[5]
$LD $a1,$SIZE_T*1($ap)
adde $acc2,$acc2,$a2
add $acc4,$t0,$t0
$SHRI $t0,$t0,$BITS-1
or $acc3,$acc3,$t2
$LD $t2,$SIZE_T*7($tp) # =tp[6]
adde $acc3,$acc3,$a3
$LD $a3,$SIZE_T*2($ap)
add $acc5,$t1,$t1
$SHRI $t1,$t1,$BITS-1
or $acc4,$acc4,$t3
$LD $t3,$SIZE_T*8($tp) # =tp[7]
$UMULL $a6,$a7,$a7
$UMULH $a7,$a7,$a7
adde $acc4,$acc4,$a4
add $acc6,$t2,$t2
$SHRI $t2,$t2,$BITS-1
or $acc5,$acc5,$t0
$LD $t0,$SIZE_T*9($tp) # =tp[8]
adde $acc5,$acc5,$a5
$LD $a5,$SIZE_T*3($ap)
add $acc7,$t3,$t3
$SHRI $t3,$t3,$BITS-1
or $acc6,$acc6,$t1
$LD $t1,$SIZE_T*10($tp) # =tp[9]
$UMULL $a0,$a1,$a1
$UMULH $a1,$a1,$a1
adde $acc6,$acc6,$a6
$ST $acc0,$SIZE_T*1($tp) # tp[0]=
add $acc0,$t0,$t0
$SHRI $t0,$t0,$BITS-1
or $acc7,$acc7,$t2
$LD $t2,$SIZE_T*11($tp) # =tp[10]
adde $acc7,$acc7,$a7
$LDU $a7,$SIZE_T*4($ap)
$ST $acc1,$SIZE_T*2($tp) # tp[1]=
add $acc1,$t1,$t1
$SHRI $t1,$t1,$BITS-1
or $acc0,$acc0,$t3
$LD $t3,$SIZE_T*12($tp) # =tp[11]
$UMULL $a2,$a3,$a3
$UMULH $a3,$a3,$a3
adde $acc0,$acc0,$a0
$ST $acc2,$SIZE_T*3($tp) # tp[2]=
add $acc2,$t2,$t2
$SHRI $t2,$t2,$BITS-1
or $acc1,$acc1,$t0
$LD $t0,$SIZE_T*13($tp) # =tp[12]
adde $acc1,$acc1,$a1
$ST $acc3,$SIZE_T*4($tp) # tp[3]=
$ST $acc4,$SIZE_T*5($tp) # tp[4]=
$ST $acc5,$SIZE_T*6($tp) # tp[5]=
$ST $acc6,$SIZE_T*7($tp) # tp[6]=
$STU $acc7,$SIZE_T*8($tp) # tp[7]=
add $acc3,$t3,$t3
$SHRI $t3,$t3,$BITS-1
or $acc2,$acc2,$t1
bdnz .Lsqr4x_shift_n_add
___
my ($np,$np_end)=($ap,$ap_end);
$code.=<<___;
$POP $np,$SIZE_T*7($sp) # pull &np[-1] and n0
$POP $n0,$SIZE_T*8($sp)
$UMULL $a4,$a5,$a5
$UMULH $a5,$a5,$a5
$ST $acc0,$SIZE_T*1($tp) # tp[8]=
$LD $acc0,$SIZE_T*12($sp) # =tp[0]
$LD $t1,$SIZE_T*6($tp) # =tp[13]
adde $acc2,$acc2,$a2
add $acc4,$t0,$t0
$SHRI $t0,$t0,$BITS-1
or $acc3,$acc3,$t2
$LD $t2,$SIZE_T*7($tp) # =tp[14]
adde $acc3,$acc3,$a3
add $acc5,$t1,$t1
$SHRI $t1,$t1,$BITS-1
or $acc4,$acc4,$t3
$UMULL $a6,$a7,$a7
$UMULH $a7,$a7,$a7
adde $acc4,$acc4,$a4
add $acc6,$t2,$t2
$SHRI $t2,$t2,$BITS-1
or $acc5,$acc5,$t0
$ST $acc1,$SIZE_T*2($tp) # tp[9]=
$LD $acc1,$SIZE_T*13($sp) # =tp[1]
adde $acc5,$acc5,$a5
or $acc6,$acc6,$t1
$LD $a0,$SIZE_T*1($np)
$LD $a1,$SIZE_T*2($np)
adde $acc6,$acc6,$a6
$LD $a2,$SIZE_T*3($np)
$LD $a3,$SIZE_T*4($np)
adde $acc7,$a7,$t2
$LD $a4,$SIZE_T*5($np)
$LD $a5,$SIZE_T*6($np)
################################################################
# Reduce by 8 limbs per iteration
$UMULL $na0,$n0,$acc0 # t[0]*n0
li $cnt,8
$LD $a6,$SIZE_T*7($np)
add $np_end,$np,$num
$LDU $a7,$SIZE_T*8($np)
$ST $acc2,$SIZE_T*3($tp) # tp[10]=
$LD $acc2,$SIZE_T*14($sp)
$ST $acc3,$SIZE_T*4($tp) # tp[11]=
$LD $acc3,$SIZE_T*15($sp)
$ST $acc4,$SIZE_T*5($tp) # tp[12]=
$LD $acc4,$SIZE_T*16($sp)
$ST $acc5,$SIZE_T*6($tp) # tp[13]=
$LD $acc5,$SIZE_T*17($sp)
$ST $acc6,$SIZE_T*7($tp) # tp[14]=
$LD $acc6,$SIZE_T*18($sp)
$ST $acc7,$SIZE_T*8($tp) # tp[15]=
$LD $acc7,$SIZE_T*19($sp)
addi $tp,$sp,$SIZE_T*11 # &tp[-1]
mtctr $cnt
b .Lsqr8x_reduction
.align 5
.Lsqr8x_reduction:
# (*) $UMULL $t0,$a0,$na0 # lo(n[0-7])*lo(t[0]*n0)
$UMULL $t1,$a1,$na0
$UMULL $t2,$a2,$na0
$STU $na0,$SIZE_T($tp) # put aside t[0]*n0 for tail processing
$UMULL $t3,$a3,$na0
# (*) addc $acc0,$acc0,$t0
addic $acc0,$acc0,-1 # (*)
$UMULL $t0,$a4,$na0
adde $acc0,$acc1,$t1
$UMULL $t1,$a5,$na0
adde $acc1,$acc2,$t2
$UMULL $t2,$a6,$na0
adde $acc2,$acc3,$t3
$UMULL $t3,$a7,$na0
adde $acc3,$acc4,$t0
$UMULH $t0,$a0,$na0 # hi(n[0-7])*lo(t[0]*n0)
adde $acc4,$acc5,$t1
$UMULH $t1,$a1,$na0
adde $acc5,$acc6,$t2
$UMULH $t2,$a2,$na0
adde $acc6,$acc7,$t3
$UMULH $t3,$a3,$na0
addze $acc7,$zero
addc $acc0,$acc0,$t0
$UMULH $t0,$a4,$na0
adde $acc1,$acc1,$t1
$UMULH $t1,$a5,$na0
adde $acc2,$acc2,$t2
$UMULH $t2,$a6,$na0
adde $acc3,$acc3,$t3
$UMULH $t3,$a7,$na0
$UMULL $na0,$n0,$acc0 # next t[0]*n0
adde $acc4,$acc4,$t0
adde $acc5,$acc5,$t1
adde $acc6,$acc6,$t2
adde $acc7,$acc7,$t3
bdnz .Lsqr8x_reduction
$LD $t0,$SIZE_T*1($tp)
$LD $t1,$SIZE_T*2($tp)
$LD $t2,$SIZE_T*3($tp)
$LD $t3,$SIZE_T*4($tp)
subi $rp,$tp,$SIZE_T*7
$UCMP $np_end,$np # done yet?
addc $acc0,$acc0,$t0
$LD $t0,$SIZE_T*5($tp)
adde $acc1,$acc1,$t1
$LD $t1,$SIZE_T*6($tp)
adde $acc2,$acc2,$t2
$LD $t2,$SIZE_T*7($tp)
adde $acc3,$acc3,$t3
$LD $t3,$SIZE_T*8($tp)
adde $acc4,$acc4,$t0
adde $acc5,$acc5,$t1
adde $acc6,$acc6,$t2
adde $acc7,$acc7,$t3
#addze $carry,$zero # moved below
beq .Lsqr8x8_post_condition
$LD $n0,$SIZE_T*0($rp)
$LD $a0,$SIZE_T*1($np)
$LD $a1,$SIZE_T*2($np)
$LD $a2,$SIZE_T*3($np)
$LD $a3,$SIZE_T*4($np)
$LD $a4,$SIZE_T*5($np)
$LD $a5,$SIZE_T*6($np)
$LD $a6,$SIZE_T*7($np)
$LDU $a7,$SIZE_T*8($np)
li $cnt,0
.align 5
.Lsqr8x_tail:
$UMULL $t0,$a0,$n0
addze $carry,$zero # carry bit, modulo-scheduled
$UMULL $t1,$a1,$n0
addi $cnt,$cnt,$SIZE_T
$UMULL $t2,$a2,$n0
andi. $cnt,$cnt,$SIZE_T*8-1
$UMULL $t3,$a3,$n0
addc $acc0,$acc0,$t0
$UMULL $t0,$a4,$n0
adde $acc1,$acc1,$t1
$UMULL $t1,$a5,$n0
adde $acc2,$acc2,$t2
$UMULL $t2,$a6,$n0
adde $acc3,$acc3,$t3
$UMULL $t3,$a7,$n0
adde $acc4,$acc4,$t0
$UMULH $t0,$a0,$n0
adde $acc5,$acc5,$t1
$UMULH $t1,$a1,$n0
adde $acc6,$acc6,$t2
$UMULH $t2,$a2,$n0
adde $acc7,$acc7,$t3
$UMULH $t3,$a3,$n0
addze $carry,$carry
$STU $acc0,$SIZE_T($tp)
addc $acc0,$acc1,$t0
$UMULH $t0,$a4,$n0
adde $acc1,$acc2,$t1
$UMULH $t1,$a5,$n0
adde $acc2,$acc3,$t2
$UMULH $t2,$a6,$n0
adde $acc3,$acc4,$t3
$UMULH $t3,$a7,$n0
$LDX $n0,$rp,$cnt
adde $acc4,$acc5,$t0
adde $acc5,$acc6,$t1
adde $acc6,$acc7,$t2
adde $acc7,$carry,$t3
#addze $carry,$zero # moved above
bne .Lsqr8x_tail
# note that carry flag is guaranteed
# to be zero at this point
$LD $a0,$SIZE_T*1($tp)
$POP $carry,$SIZE_T*10($sp) # pull top-most carry in case we break
$UCMP $np_end,$np # done yet?
$LD $a1,$SIZE_T*2($tp)
sub $t2,$np_end,$num # rewinded np
$LD $a2,$SIZE_T*3($tp)
$LD $a3,$SIZE_T*4($tp)
$LD $a4,$SIZE_T*5($tp)
$LD $a5,$SIZE_T*6($tp)
$LD $a6,$SIZE_T*7($tp)
$LD $a7,$SIZE_T*8($tp)
beq .Lsqr8x_tail_break
addc $acc0,$acc0,$a0
$LD $a0,$SIZE_T*1($np)
adde $acc1,$acc1,$a1
$LD $a1,$SIZE_T*2($np)
adde $acc2,$acc2,$a2
$LD $a2,$SIZE_T*3($np)
adde $acc3,$acc3,$a3
$LD $a3,$SIZE_T*4($np)
adde $acc4,$acc4,$a4
$LD $a4,$SIZE_T*5($np)
adde $acc5,$acc5,$a5
$LD $a5,$SIZE_T*6($np)
adde $acc6,$acc6,$a6
$LD $a6,$SIZE_T*7($np)
adde $acc7,$acc7,$a7
$LDU $a7,$SIZE_T*8($np)
#addze $carry,$zero # moved above
b .Lsqr8x_tail
.align 5
.Lsqr8x_tail_break:
$POP $n0,$SIZE_T*8($sp) # pull n0
$POP $t3,$SIZE_T*9($sp) # &tp[2*num-1]
addi $cnt,$tp,$SIZE_T*8 # end of current t[num] window
addic $carry,$carry,-1 # "move" top-most carry to carry bit
adde $t0,$acc0,$a0
$LD $acc0,$SIZE_T*8($rp)
$LD $a0,$SIZE_T*1($t2) # recall that $t2 is &n[-1]
adde $t1,$acc1,$a1
$LD $acc1,$SIZE_T*9($rp)
$LD $a1,$SIZE_T*2($t2)
adde $acc2,$acc2,$a2
$LD $a2,$SIZE_T*3($t2)
adde $acc3,$acc3,$a3
$LD $a3,$SIZE_T*4($t2)
adde $acc4,$acc4,$a4
$LD $a4,$SIZE_T*5($t2)
adde $acc5,$acc5,$a5
$LD $a5,$SIZE_T*6($t2)
adde $acc6,$acc6,$a6
$LD $a6,$SIZE_T*7($t2)
adde $acc7,$acc7,$a7
$LD $a7,$SIZE_T*8($t2)
addi $np,$t2,$SIZE_T*8
addze $t2,$zero # top-most carry
$UMULL $na0,$n0,$acc0
$ST $t0,$SIZE_T*1($tp)
$UCMP $cnt,$t3 # did we hit the bottom?
$ST $t1,$SIZE_T*2($tp)
li $cnt,8
$ST $acc2,$SIZE_T*3($tp)
$LD $acc2,$SIZE_T*10($rp)
$ST $acc3,$SIZE_T*4($tp)
$LD $acc3,$SIZE_T*11($rp)
$ST $acc4,$SIZE_T*5($tp)
$LD $acc4,$SIZE_T*12($rp)
$ST $acc5,$SIZE_T*6($tp)
$LD $acc5,$SIZE_T*13($rp)
$ST $acc6,$SIZE_T*7($tp)
$LD $acc6,$SIZE_T*14($rp)
$ST $acc7,$SIZE_T*8($tp)
$LD $acc7,$SIZE_T*15($rp)
$PUSH $t2,$SIZE_T*10($sp) # off-load top-most carry
addi $tp,$rp,$SIZE_T*7 # slide the window
mtctr $cnt
bne .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.
$POP $rp,$SIZE_T*6($sp) # pull &rp[-1]
srwi $cnt,$num,`log($SIZE_T)/log(2)+3`
mr $n0,$tp # put tp aside
addi $tp,$tp,$SIZE_T*8
subi $cnt,$cnt,1
subfc $t0,$a0,$acc0
subfe $t1,$a1,$acc1
mr $carry,$t2
mr $ap_end,$rp # $rp copy
mtctr $cnt
b .Lsqr8x_sub
.align 5
.Lsqr8x_sub:
$LD $a0,$SIZE_T*1($np)
$LD $acc0,$SIZE_T*1($tp)
$LD $a1,$SIZE_T*2($np)
$LD $acc1,$SIZE_T*2($tp)
subfe $t2,$a2,$acc2
$LD $a2,$SIZE_T*3($np)
$LD $acc2,$SIZE_T*3($tp)
subfe $t3,$a3,$acc3
$LD $a3,$SIZE_T*4($np)
$LD $acc3,$SIZE_T*4($tp)
$ST $t0,$SIZE_T*1($rp)
subfe $t0,$a4,$acc4
$LD $a4,$SIZE_T*5($np)
$LD $acc4,$SIZE_T*5($tp)
$ST $t1,$SIZE_T*2($rp)
subfe $t1,$a5,$acc5
$LD $a5,$SIZE_T*6($np)
$LD $acc5,$SIZE_T*6($tp)
$ST $t2,$SIZE_T*3($rp)
subfe $t2,$a6,$acc6
$LD $a6,$SIZE_T*7($np)
$LD $acc6,$SIZE_T*7($tp)
$ST $t3,$SIZE_T*4($rp)
subfe $t3,$a7,$acc7
$LDU $a7,$SIZE_T*8($np)
$LDU $acc7,$SIZE_T*8($tp)
$ST $t0,$SIZE_T*5($rp)
subfe $t0,$a0,$acc0
$ST $t1,$SIZE_T*6($rp)
subfe $t1,$a1,$acc1
$ST $t2,$SIZE_T*7($rp)
$STU $t3,$SIZE_T*8($rp)
bdnz .Lsqr8x_sub
srwi $cnt,$num,`log($SIZE_T)/log(2)+2`
$LD $a0,$SIZE_T*1($ap_end) # original $rp
$LD $acc0,$SIZE_T*1($n0) # original $tp
subi $cnt,$cnt,1
$LD $a1,$SIZE_T*2($ap_end)
$LD $acc1,$SIZE_T*2($n0)
subfe $t2,$a2,$acc2
$LD $a2,$SIZE_T*3($ap_end)
$LD $acc2,$SIZE_T*3($n0)
subfe $t3,$a3,$acc3
$LD $a3,$SIZE_T*4($ap_end)
$LDU $acc3,$SIZE_T*4($n0)
$ST $t0,$SIZE_T*1($rp)
subfe $t0,$a4,$acc4
$ST $t1,$SIZE_T*2($rp)
subfe $t1,$a5,$acc5
$ST $t2,$SIZE_T*3($rp)
subfe $t2,$a6,$acc6
$ST $t3,$SIZE_T*4($rp)
subfe $t3,$a7,$acc7
$ST $t0,$SIZE_T*5($rp)
subfe $carry,$zero,$carry # did it borrow?
$ST $t1,$SIZE_T*6($rp)
$ST $t2,$SIZE_T*7($rp)
$ST $t3,$SIZE_T*8($rp)
addi $tp,$sp,$SIZE_T*11
mtctr $cnt
.Lsqr4x_cond_copy:
andc $a0,$a0,$carry
$ST $zero,-$SIZE_T*3($n0) # wipe stack clean
and $acc0,$acc0,$carry
$ST $zero,-$SIZE_T*2($n0)
andc $a1,$a1,$carry
$ST $zero,-$SIZE_T*1($n0)
and $acc1,$acc1,$carry
$ST $zero,-$SIZE_T*0($n0)
andc $a2,$a2,$carry
$ST $zero,$SIZE_T*1($tp)
and $acc2,$acc2,$carry
$ST $zero,$SIZE_T*2($tp)
andc $a3,$a3,$carry
$ST $zero,$SIZE_T*3($tp)
and $acc3,$acc3,$carry
$STU $zero,$SIZE_T*4($tp)
or $t0,$a0,$acc0
$LD $a0,$SIZE_T*5($ap_end)
$LD $acc0,$SIZE_T*1($n0)
or $t1,$a1,$acc1
$LD $a1,$SIZE_T*6($ap_end)
$LD $acc1,$SIZE_T*2($n0)
or $t2,$a2,$acc2
$LD $a2,$SIZE_T*7($ap_end)
$LD $acc2,$SIZE_T*3($n0)
or $t3,$a3,$acc3
$LD $a3,$SIZE_T*8($ap_end)
$LDU $acc3,$SIZE_T*4($n0)
$ST $t0,$SIZE_T*1($ap_end)
$ST $t1,$SIZE_T*2($ap_end)
$ST $t2,$SIZE_T*3($ap_end)
$STU $t3,$SIZE_T*4($ap_end)
bdnz .Lsqr4x_cond_copy
$POP $ap,0($sp) # pull saved sp
andc $a0,$a0,$carry
and $acc0,$acc0,$carry
andc $a1,$a1,$carry
and $acc1,$acc1,$carry
andc $a2,$a2,$carry
and $acc2,$acc2,$carry
andc $a3,$a3,$carry
and $acc3,$acc3,$carry
or $t0,$a0,$acc0
or $t1,$a1,$acc1
or $t2,$a2,$acc2
or $t3,$a3,$acc3
$ST $t0,$SIZE_T*1($ap_end)
$ST $t1,$SIZE_T*2($ap_end)
$ST $t2,$SIZE_T*3($ap_end)
$ST $t3,$SIZE_T*4($ap_end)
b .Lsqr8x_done
.align 5
.Lsqr8x8_post_condition:
$POP $rp,$SIZE_T*6($sp) # pull rp
$POP $ap,0($sp) # pull saved sp
addze $carry,$zero
# $acc0-7,$carry hold result, $a0-7 hold modulus
subfc $acc0,$a0,$acc0
subfe $acc1,$a1,$acc1
$ST $zero,$SIZE_T*12($sp) # wipe stack clean
$ST $zero,$SIZE_T*13($sp)
subfe $acc2,$a2,$acc2
$ST $zero,$SIZE_T*14($sp)
$ST $zero,$SIZE_T*15($sp)
subfe $acc3,$a3,$acc3
$ST $zero,$SIZE_T*16($sp)
$ST $zero,$SIZE_T*17($sp)
subfe $acc4,$a4,$acc4
$ST $zero,$SIZE_T*18($sp)
$ST $zero,$SIZE_T*19($sp)
subfe $acc5,$a5,$acc5
$ST $zero,$SIZE_T*20($sp)
$ST $zero,$SIZE_T*21($sp)
subfe $acc6,$a6,$acc6
$ST $zero,$SIZE_T*22($sp)
$ST $zero,$SIZE_T*23($sp)
subfe $acc7,$a7,$acc7
$ST $zero,$SIZE_T*24($sp)
$ST $zero,$SIZE_T*25($sp)
subfe $carry,$zero,$carry # did it borrow?
$ST $zero,$SIZE_T*26($sp)
$ST $zero,$SIZE_T*27($sp)
and $a0,$a0,$carry
and $a1,$a1,$carry
addc $acc0,$acc0,$a0 # add modulus back if borrowed
and $a2,$a2,$carry
adde $acc1,$acc1,$a1
and $a3,$a3,$carry
adde $acc2,$acc2,$a2
and $a4,$a4,$carry
adde $acc3,$acc3,$a3
and $a5,$a5,$carry
adde $acc4,$acc4,$a4
and $a6,$a6,$carry
adde $acc5,$acc5,$a5
and $a7,$a7,$carry
adde $acc6,$acc6,$a6
adde $acc7,$acc7,$a7
$ST $acc0,$SIZE_T*1($rp)
$ST $acc1,$SIZE_T*2($rp)
$ST $acc2,$SIZE_T*3($rp)
$ST $acc3,$SIZE_T*4($rp)
$ST $acc4,$SIZE_T*5($rp)
$ST $acc5,$SIZE_T*6($rp)
$ST $acc6,$SIZE_T*7($rp)
$ST $acc7,$SIZE_T*8($rp)
.Lsqr8x_done:
$PUSH $zero,$SIZE_T*8($sp)
$PUSH $zero,$SIZE_T*10($sp)
$POP r14,-$SIZE_T*18($ap)
li r3,1 # signal "done"
$POP r15,-$SIZE_T*17($ap)
$POP r16,-$SIZE_T*16($ap)
$POP r17,-$SIZE_T*15($ap)
$POP r18,-$SIZE_T*14($ap)
$POP r19,-$SIZE_T*13($ap)
$POP r20,-$SIZE_T*12($ap)
$POP r21,-$SIZE_T*11($ap)
$POP r22,-$SIZE_T*10($ap)
$POP r23,-$SIZE_T*9($ap)
$POP r24,-$SIZE_T*8($ap)
$POP r25,-$SIZE_T*7($ap)
$POP r26,-$SIZE_T*6($ap)
$POP r27,-$SIZE_T*5($ap)
$POP r28,-$SIZE_T*4($ap)
$POP r29,-$SIZE_T*3($ap)
$POP r30,-$SIZE_T*2($ap)
$POP r31,-$SIZE_T*1($ap)
mr $sp,$ap
blr
.long 0
.byte 0,12,4,0x20,0x80,18,6,0
.long 0
.size __bn_sqr8x_mont,.-__bn_sqr8x_mont
___
}
$code.=<<___;
.asciz "Montgomery Multiplication for PPC, CRYPTOGAMS by <appro\@openssl.org>"
___
$code =~ s/\`([^\`]*)\`/eval $1/gem;
print $code;
close STDOUT or die "error closing STDOUT: $!";