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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...
$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";
$fp="%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 $rp,0($num,$rp) # pointers to point at the vectors' ends
la $ap,0($num,$ap)
la $bp,0($num,$bp)
la $np,0($num,$np)
stmg %r2,%r15,16($sp)
cghi $num,16 #
lghi %r2,0 #
blr %r14 # if($num<16) return 0;
lcgr $num,$num # -$num
lgr %r0,$sp
lgr $fp,$sp
aghi $fp,-160-8 # leave room for carry bit
la $sp,0($num,$fp) # alloca
stg %r0,0($sp)
aghi $fp,160-8 # $fp to point at tp[$num-1]
la $bp,0($num,$bp) # restore $bp
lg $n0,0($n0) # pull n0
lg $bi,0($bp)
lg $alo,0($num,$ap)
mlgr $ahi,$bi # ap[0]*bp[0]
lgr $AHI,$ahi
lgr $mn0,$alo # "tp[0]"*n0
msgr $mn0,$n0
lg $nlo,0($num,$np)#
mlgr $nhi,$mn0 # np[0]*m1
algr $nlo,$alo # +="tp[0]"
lghi $NHI,0
alcgr $NHI,$nhi
lgr $j,$num
aghi $j,8 # j=1
.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 $nlo,0($j,$fp) # tp[j-1]=
aghi $j,8 # j++
jnz .L1st
algr $NHI,$AHI
lghi $AHI,0
alcgr $AHI,$AHI # upmost overflow bit
stg $NHI,0($fp)
stg $AHI,8($fp)
la $bp,8($bp) # bp++
.Louter:
lg $bi,0($bp) # bp[i]
lg $alo,0($num,$ap)
mlgr $ahi,$bi # ap[0]*bp[i]
alg $alo,8($num,$fp)# +=tp[0]
lghi $AHI,0
alcgr $AHI,$ahi
lgr $mn0,$alo
msgr $mn0,$n0 # tp[0]*n0
lg $nlo,0($num,$np)# np[0]
mlgr $nhi,$mn0 # np[0]*m1
algr $nlo,$alo # +="tp[0]"
lghi $NHI,0
alcgr $NHI,$nhi
lgr $j,$num
aghi $j,8 # j=1
.Linner:
lg $alo,0($j,$ap)
mlgr $ahi,$bi # ap[j]*bp[i]
algr $alo,$AHI
lghi $AHI,0
alcgr $ahi,$AHI
alg $alo,8($j,$fp) # +=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 $nlo,0($j,$fp) # tp[j-1]=
aghi $j,8 # j++
jnz .Linner
algr $NHI,$AHI
lghi $AHI,0
alcgr $AHI,$AHI
alg $NHI,8($fp) # accumulate previous upmost overflow bit
lghi $ahi,0
alcgr $AHI,$ahi # new upmost overflow bit
stg $NHI,0($fp)
stg $AHI,8($fp)
la $bp,8($bp) # bp++
clg $bp,16+32($fp) # compare to &bp[num]
jne .Louter
___
undef $bi;
$count=$ap; undef $ap;
$code.=<<___;
lg $rp,16+16($fp) # reincarnate rp
lgr $j,$num
ltgr $AHI,$AHI
jnz .Lsub # upmost overflow bit is not zero
#slg $NHI,-8($np) # tp[num-1]-np[num-1]
lghi $count,-8 # buggy assembler
slg $NHI,0($count,$np) # buggy assembler
jnle .Lsub # branch if not borrow
.Lcopy: lg $alo,8($j,$fp)
stg $j,8($j,$fp)
stg $alo,0($j,$rp)
aghi $j,8
jnz .Lcopy
.Lexit:
lmg %r6,%r15,16+48($fp)
lghi %r2,1 # signal "processed"
br %r14
.Lsub: lcgr $count,$num
sra $count,3 # incidentally clears "borrow"
.Lsubloop:
lg $alo,8($j,$fp)
slbg $alo,0($j,$np)
stg $alo,0($j,$rp)
la $j,8($j)
brct $count,.Lsubloop
lghi $ahi,0
slbgr $AHI,$ahi
lgr $j,$num
jle .Lcopy # branch if borrow
.Lzap: stg $j,8($j,$fp)
aghi $j,8
jnz .Lzap
j .Lexit
.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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