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#!/usr/bin/env perl
# ====================================================================
# Written by Andy Polyakov <appro@fy.chalmers.se> 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 2007.
#
# Performance improvement over vanilla C code varies from 85% to 45%
# depending on key length and benchmark. Unfortunately in this context
# these are not very impressive results [for code that utilizes "wide"
# 64x64=128-bit multiplication, which is not commonly available to C
# programmers], at least hand-coded bn_asm.c replacement is known to
# provide 30-40% better results for longest keys. Well, on a second
# thought it's not very surprising, because z-CPUs are single-issue
# and _strictly_ in-order execution, while bn_mul_mont is more or less
# dependent on CPU ability to pipe-line instructions and have several
# of them "in-flight" at the same time. I mean while other methods,
# for example Karatsuba, aim to minimize amount of multiplications at
# the cost of other operations increase, bn_mul_mont aim to neatly
# "overlap" multiplications and the other operations [and on most
# platforms even minimize the amount of the other operations, in
# particular references to memory]. But it's possible to improve this
# module performance by implementing dedicated squaring code-path and
# possibly by unrolling loops...
# January 2009.
#
# Reschedule to minimize/avoid Address Generation Interlock hazard,
# make inner loops counter-based.
$mn0="%r0";
$num="%r1";
# int bn_mul_mont(
$rp="%r2"; # BN_ULONG *rp,
$ap="%r3"; # const BN_ULONG *ap,
$bp="%r4"; # const BN_ULONG *bp,
$np="%r5"; # const BN_ULONG *np,
$n0="%r6"; # const BN_ULONG *n0,
#$num="160(%r15)" # int num);
$bi="%r2"; # zaps rp
$j="%r7";
$ahi="%r8";
$alo="%r9";
$nhi="%r10";
$nlo="%r11";
$AHI="%r12";
$NHI="%r13";
$count="%r14";
$sp="%r15";
$code.=<<___;
.text
.globl bn_mul_mont
.type bn_mul_mont,\@function
bn_mul_mont:
lgf $num,164($sp) # pull $num
sla $num,3 # $num to enumerate bytes
la $bp,0($num,$bp)
stg %r2,16($sp)
cghi $num,16 #
lghi %r2,0 #
blr %r14 # if($num<16) return 0;
cghi $num,96 #
bhr %r14 # if($num>96) return 0;
stmg %r3,%r15,24($sp)
lghi $rp,-160-8 # leave room for carry bit
lcgr $j,$num # -$num
lgr %r0,$sp
la $rp,0($rp,$sp)
la $sp,0($j,$rp) # alloca
stg %r0,0($sp) # back chain
sra $num,3 # restore $num
la $bp,0($j,$bp) # restore $bp
ahi $num,-1 # adjust $num for inner loop
lg $n0,0($n0) # pull n0
lg $bi,0($bp)
lg $alo,0($ap)
mlgr $ahi,$bi # ap[0]*bp[0]
lgr $AHI,$ahi
lgr $mn0,$alo # "tp[0]"*n0
msgr $mn0,$n0
lg $nlo,0($np) #
mlgr $nhi,$mn0 # np[0]*m1
algr $nlo,$alo # +="tp[0]"
lghi $NHI,0
alcgr $NHI,$nhi
la $j,8(%r0) # j=1
lr $count,$num
.align 16
.L1st:
lg $alo,0($j,$ap)
mlgr $ahi,$bi # ap[j]*bp[0]
algr $alo,$AHI
lghi $AHI,0
alcgr $AHI,$ahi
lg $nlo,0($j,$np)
mlgr $nhi,$mn0 # np[j]*m1
algr $nlo,$NHI
lghi $NHI,0
alcgr $nhi,$NHI # +="tp[j]"
algr $nlo,$alo
alcgr $NHI,$nhi
stg $nlo,160-8($j,$sp) # tp[j-1]=
la $j,8($j) # j++
brct $count,.L1st
algr $NHI,$AHI
lghi $AHI,0
alcgr $AHI,$AHI # upmost overflow bit
stg $NHI,160-8($j,$sp)
stg $AHI,160($j,$sp)
la $bp,8($bp) # bp++
.Louter:
lg $bi,0($bp) # bp[i]
lg $alo,0($ap)
mlgr $ahi,$bi # ap[0]*bp[i]
alg $alo,160($sp) # +=tp[0]
lghi $AHI,0
alcgr $AHI,$ahi
lgr $mn0,$alo
msgr $mn0,$n0 # tp[0]*n0
lg $nlo,0($np) # np[0]
mlgr $nhi,$mn0 # np[0]*m1
algr $nlo,$alo # +="tp[0]"
lghi $NHI,0
alcgr $NHI,$nhi
la $j,8(%r0) # j=1
lr $count,$num
.align 16
.Linner:
lg $alo,0($j,$ap)
mlgr $ahi,$bi # ap[j]*bp[i]
algr $alo,$AHI
lghi $AHI,0
alcgr $ahi,$AHI
alg $alo,160($j,$sp)# +=tp[j]
alcgr $AHI,$ahi
lg $nlo,0($j,$np)
mlgr $nhi,$mn0 # np[j]*m1
algr $nlo,$NHI
lghi $NHI,0
alcgr $nhi,$NHI
algr $nlo,$alo # +="tp[j]"
alcgr $NHI,$nhi
stg $nlo,160-8($j,$sp) # tp[j-1]=
la $j,8($j) # j++
brct $count,.Linner
algr $NHI,$AHI
lghi $AHI,0
alcgr $AHI,$AHI
alg $NHI,160($j,$sp)# accumulate previous upmost overflow bit
lghi $ahi,0
alcgr $AHI,$ahi # new upmost overflow bit
stg $NHI,160-8($j,$sp)
stg $AHI,160($j,$sp)
la $bp,8($bp) # bp++
clg $bp,160+8+32($j,$sp) # compare to &bp[num]
jne .Louter
lg $rp,160+8+16($j,$sp) # reincarnate rp
la $ap,160($sp)
ahi $num,1 # restore $num, incidentally clears "borrow"
la $j,0(%r0)
lr $count,$num
.Lsub: lg $alo,0($j,$ap)
slbg $alo,0($j,$np)
stg $alo,0($j,$rp)
la $j,8($j)
brct $count,.Lsub
lghi $ahi,0
slbgr $AHI,$ahi # handle upmost carry
ngr $ap,$AHI
lghi $np,-1
xgr $np,$AHI
ngr $np,$rp
ogr $ap,$np # ap=borrow?tp:rp
la $j,0(%r0)
lgr $count,$num
.Lcopy: lg $alo,0($j,$ap) # copy or in-place refresh
stg $j,160($j,$sp) # zap tp
stg $alo,0($j,$rp)
la $j,8($j)
brct $count,.Lcopy
la %r1,160+8+48($j,$sp)
lmg %r6,%r15,0(%r1)
lghi %r2,1 # signal "processed"
br %r14
.size bn_mul_mont,.-bn_mul_mont
.string "Montgomery Multiplication for s390x, CRYPTOGAMS by <appro\@openssl.org>"
___
print $code;
close STDOUT;
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