774ff8fed6
Montgomery multiplication post-conditions in some of code paths were formally non-constant time. Cache access pattern was result-neutral, but a little bit asymmetric, which might have produced a signal [if processor reordered load and stores at run-time]. Reviewed-by: Rich Salz <rsalz@openssl.org> (Merged from https://github.com/openssl/openssl/pull/6141)
1990 lines
48 KiB
Raku
1990 lines
48 KiB
Raku
#! /usr/bin/env perl
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# Copyright 2006-2016 The OpenSSL Project Authors. All Rights Reserved.
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#
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# Licensed under the OpenSSL license (the "License"). You may not use
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# this file except in compliance with the License. You can obtain a copy
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# in the file LICENSE in the source distribution or at
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# https://www.openssl.org/source/license.html
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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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# April 2006
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# "Teaser" Montgomery multiplication module for PowerPC. It's possible
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# to gain a bit more by modulo-scheduling outer loop, then dedicated
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# squaring procedure should give further 20% and code can be adapted
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# for 32-bit application running on 64-bit CPU. As for the latter.
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# It won't be able to achieve "native" 64-bit performance, because in
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# 32-bit application context every addc instruction will have to be
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# expanded as addc, twice right shift by 32 and finally adde, etc.
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# So far RSA *sign* performance improvement over pre-bn_mul_mont asm
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# for 64-bit application running on PPC970/G5 is:
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#
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# 512-bit +65%
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# 1024-bit +35%
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# 2048-bit +18%
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# 4096-bit +4%
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# September 2016
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#
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# Add multiplication procedure operating on lengths divisible by 4
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# and squaring procedure operating on lengths divisible by 8. Length
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# is expressed in number of limbs. RSA private key operations are
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# ~35-50% faster (more for longer keys) on contemporary high-end POWER
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# processors in 64-bit builds, [mysteriously enough] more in 32-bit
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# builds. On low-end 32-bit processors performance improvement turned
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# to be marginal...
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$flavour = shift;
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if ($flavour =~ /32/) {
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$BITS= 32;
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$BNSZ= $BITS/8;
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$SIZE_T=4;
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$RZONE= 224;
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$LD= "lwz"; # load
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$LDU= "lwzu"; # load and update
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$LDX= "lwzx"; # load indexed
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$ST= "stw"; # store
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$STU= "stwu"; # store and update
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$STX= "stwx"; # store indexed
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$STUX= "stwux"; # store indexed and update
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$UMULL= "mullw"; # unsigned multiply low
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$UMULH= "mulhwu"; # unsigned multiply high
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$UCMP= "cmplw"; # unsigned compare
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$SHRI= "srwi"; # unsigned shift right by immediate
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$SHLI= "slwi"; # unsigned shift left by immediate
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$PUSH= $ST;
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$POP= $LD;
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} elsif ($flavour =~ /64/) {
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$BITS= 64;
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$BNSZ= $BITS/8;
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$SIZE_T=8;
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$RZONE= 288;
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# same as above, but 64-bit mnemonics...
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$LD= "ld"; # load
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$LDU= "ldu"; # load and update
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$LDX= "ldx"; # load indexed
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$ST= "std"; # store
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$STU= "stdu"; # store and update
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$STX= "stdx"; # store indexed
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$STUX= "stdux"; # store indexed and update
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$UMULL= "mulld"; # unsigned multiply low
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$UMULH= "mulhdu"; # unsigned multiply high
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$UCMP= "cmpld"; # unsigned compare
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$SHRI= "srdi"; # unsigned shift right by immediate
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$SHLI= "sldi"; # unsigned shift left by immediate
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$PUSH= $ST;
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$POP= $LD;
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} else { die "nonsense $flavour"; }
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$FRAME=8*$SIZE_T+$RZONE;
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$LOCALS=8*$SIZE_T;
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$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
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( $xlate="${dir}ppc-xlate.pl" and -f $xlate ) or
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( $xlate="${dir}../../perlasm/ppc-xlate.pl" and -f $xlate) or
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die "can't locate ppc-xlate.pl";
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open STDOUT,"| $^X $xlate $flavour ".shift || die "can't call $xlate: $!";
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$sp="r1";
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$toc="r2";
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$rp="r3";
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$ap="r4";
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$bp="r5";
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$np="r6";
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$n0="r7";
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$num="r8";
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{
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my $ovf=$rp;
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my $rp="r9"; # $rp is reassigned
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my $aj="r10";
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my $nj="r11";
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my $tj="r12";
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# non-volatile registers
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my $i="r20";
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my $j="r21";
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my $tp="r22";
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my $m0="r23";
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my $m1="r24";
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my $lo0="r25";
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my $hi0="r26";
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my $lo1="r27";
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my $hi1="r28";
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my $alo="r29";
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my $ahi="r30";
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my $nlo="r31";
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#
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my $nhi="r0";
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$code=<<___;
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.machine "any"
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.text
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.globl .bn_mul_mont_int
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.align 5
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.bn_mul_mont_int:
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mr $rp,r3 ; $rp is reassigned
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li r3,0
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___
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$code.=<<___ if ($BNSZ==4);
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cmpwi $num,32 ; longer key performance is not better
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bgelr
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___
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$code.=<<___;
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slwi $num,$num,`log($BNSZ)/log(2)`
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li $tj,-4096
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addi $ovf,$num,$FRAME
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subf $ovf,$ovf,$sp ; $sp-$ovf
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and $ovf,$ovf,$tj ; minimize TLB usage
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subf $ovf,$sp,$ovf ; $ovf-$sp
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mr $tj,$sp
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srwi $num,$num,`log($BNSZ)/log(2)`
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$STUX $sp,$sp,$ovf
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$PUSH r20,`-12*$SIZE_T`($tj)
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$PUSH r21,`-11*$SIZE_T`($tj)
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$PUSH r22,`-10*$SIZE_T`($tj)
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$PUSH r23,`-9*$SIZE_T`($tj)
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$PUSH r24,`-8*$SIZE_T`($tj)
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$PUSH r25,`-7*$SIZE_T`($tj)
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$PUSH r26,`-6*$SIZE_T`($tj)
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$PUSH r27,`-5*$SIZE_T`($tj)
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$PUSH r28,`-4*$SIZE_T`($tj)
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$PUSH r29,`-3*$SIZE_T`($tj)
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$PUSH r30,`-2*$SIZE_T`($tj)
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$PUSH r31,`-1*$SIZE_T`($tj)
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$LD $n0,0($n0) ; pull n0[0] value
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addi $num,$num,-2 ; adjust $num for counter register
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$LD $m0,0($bp) ; m0=bp[0]
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$LD $aj,0($ap) ; ap[0]
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addi $tp,$sp,$LOCALS
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$UMULL $lo0,$aj,$m0 ; ap[0]*bp[0]
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$UMULH $hi0,$aj,$m0
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$LD $aj,$BNSZ($ap) ; ap[1]
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$LD $nj,0($np) ; np[0]
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$UMULL $m1,$lo0,$n0 ; "tp[0]"*n0
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$UMULL $alo,$aj,$m0 ; ap[1]*bp[0]
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$UMULH $ahi,$aj,$m0
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$UMULL $lo1,$nj,$m1 ; np[0]*m1
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$UMULH $hi1,$nj,$m1
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$LD $nj,$BNSZ($np) ; np[1]
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addc $lo1,$lo1,$lo0
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addze $hi1,$hi1
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$UMULL $nlo,$nj,$m1 ; np[1]*m1
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$UMULH $nhi,$nj,$m1
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mtctr $num
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li $j,`2*$BNSZ`
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.align 4
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L1st:
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$LDX $aj,$ap,$j ; ap[j]
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addc $lo0,$alo,$hi0
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$LDX $nj,$np,$j ; np[j]
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addze $hi0,$ahi
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$UMULL $alo,$aj,$m0 ; ap[j]*bp[0]
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addc $lo1,$nlo,$hi1
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$UMULH $ahi,$aj,$m0
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addze $hi1,$nhi
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$UMULL $nlo,$nj,$m1 ; np[j]*m1
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addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[0]
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$UMULH $nhi,$nj,$m1
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addze $hi1,$hi1
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$ST $lo1,0($tp) ; tp[j-1]
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addi $j,$j,$BNSZ ; j++
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addi $tp,$tp,$BNSZ ; tp++
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bdnz L1st
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;L1st
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addc $lo0,$alo,$hi0
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addze $hi0,$ahi
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addc $lo1,$nlo,$hi1
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addze $hi1,$nhi
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addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[0]
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addze $hi1,$hi1
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$ST $lo1,0($tp) ; tp[j-1]
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li $ovf,0
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addc $hi1,$hi1,$hi0
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addze $ovf,$ovf ; upmost overflow bit
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$ST $hi1,$BNSZ($tp)
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li $i,$BNSZ
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.align 4
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Louter:
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$LDX $m0,$bp,$i ; m0=bp[i]
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$LD $aj,0($ap) ; ap[0]
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addi $tp,$sp,$LOCALS
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$LD $tj,$LOCALS($sp); tp[0]
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$UMULL $lo0,$aj,$m0 ; ap[0]*bp[i]
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$UMULH $hi0,$aj,$m0
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$LD $aj,$BNSZ($ap) ; ap[1]
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$LD $nj,0($np) ; np[0]
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addc $lo0,$lo0,$tj ; ap[0]*bp[i]+tp[0]
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$UMULL $alo,$aj,$m0 ; ap[j]*bp[i]
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addze $hi0,$hi0
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$UMULL $m1,$lo0,$n0 ; tp[0]*n0
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$UMULH $ahi,$aj,$m0
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$UMULL $lo1,$nj,$m1 ; np[0]*m1
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$UMULH $hi1,$nj,$m1
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$LD $nj,$BNSZ($np) ; np[1]
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addc $lo1,$lo1,$lo0
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$UMULL $nlo,$nj,$m1 ; np[1]*m1
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addze $hi1,$hi1
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$UMULH $nhi,$nj,$m1
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mtctr $num
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li $j,`2*$BNSZ`
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.align 4
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Linner:
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$LDX $aj,$ap,$j ; ap[j]
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addc $lo0,$alo,$hi0
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$LD $tj,$BNSZ($tp) ; tp[j]
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addze $hi0,$ahi
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$LDX $nj,$np,$j ; np[j]
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addc $lo1,$nlo,$hi1
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$UMULL $alo,$aj,$m0 ; ap[j]*bp[i]
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addze $hi1,$nhi
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$UMULH $ahi,$aj,$m0
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addc $lo0,$lo0,$tj ; ap[j]*bp[i]+tp[j]
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$UMULL $nlo,$nj,$m1 ; np[j]*m1
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addze $hi0,$hi0
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$UMULH $nhi,$nj,$m1
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addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[i]+tp[j]
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addi $j,$j,$BNSZ ; j++
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addze $hi1,$hi1
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$ST $lo1,0($tp) ; tp[j-1]
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addi $tp,$tp,$BNSZ ; tp++
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bdnz Linner
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;Linner
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$LD $tj,$BNSZ($tp) ; tp[j]
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addc $lo0,$alo,$hi0
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addze $hi0,$ahi
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addc $lo0,$lo0,$tj ; ap[j]*bp[i]+tp[j]
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addze $hi0,$hi0
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addc $lo1,$nlo,$hi1
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addze $hi1,$nhi
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addc $lo1,$lo1,$lo0 ; np[j]*m1+ap[j]*bp[i]+tp[j]
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addze $hi1,$hi1
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$ST $lo1,0($tp) ; tp[j-1]
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addic $ovf,$ovf,-1 ; move upmost overflow to XER[CA]
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li $ovf,0
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adde $hi1,$hi1,$hi0
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addze $ovf,$ovf
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$ST $hi1,$BNSZ($tp)
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;
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slwi $tj,$num,`log($BNSZ)/log(2)`
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$UCMP $i,$tj
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addi $i,$i,$BNSZ
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ble Louter
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addi $num,$num,2 ; restore $num
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subfc $j,$j,$j ; j=0 and "clear" XER[CA]
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addi $tp,$sp,$LOCALS
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mtctr $num
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.align 4
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Lsub: $LDX $tj,$tp,$j
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$LDX $nj,$np,$j
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subfe $aj,$nj,$tj ; tp[j]-np[j]
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$STX $aj,$rp,$j
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addi $j,$j,$BNSZ
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bdnz Lsub
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li $j,0
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mtctr $num
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subfe $ovf,$j,$ovf ; handle upmost overflow bit
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.align 4
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Lcopy: ; conditional copy
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$LDX $tj,$tp,$j
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$LDX $aj,$rp,$j
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and $tj,$tj,$ovf
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andc $aj,$aj,$ovf
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$STX $j,$tp,$j ; zap at once
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or $aj,$aj,$tj
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$STX $aj,$rp,$j
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addi $j,$j,$BNSZ
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bdnz Lcopy
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$POP $tj,0($sp)
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li r3,1
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$POP r20,`-12*$SIZE_T`($tj)
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$POP r21,`-11*$SIZE_T`($tj)
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$POP r22,`-10*$SIZE_T`($tj)
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$POP r23,`-9*$SIZE_T`($tj)
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$POP r24,`-8*$SIZE_T`($tj)
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$POP r25,`-7*$SIZE_T`($tj)
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$POP r26,`-6*$SIZE_T`($tj)
|
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$POP r27,`-5*$SIZE_T`($tj)
|
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$POP r28,`-4*$SIZE_T`($tj)
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$POP r29,`-3*$SIZE_T`($tj)
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$POP r30,`-2*$SIZE_T`($tj)
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$POP r31,`-1*$SIZE_T`($tj)
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mr $sp,$tj
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blr
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.long 0
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.byte 0,12,4,0,0x80,12,6,0
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.long 0
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.size .bn_mul_mont_int,.-.bn_mul_mont_int
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___
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}
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if (1) {
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my ($a0,$a1,$a2,$a3,
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$t0,$t1,$t2,$t3,
|
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$m0,$m1,$m2,$m3,
|
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$acc0,$acc1,$acc2,$acc3,$acc4,
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$bi,$mi,$tp,$ap_end,$cnt) = map("r$_",(9..12,14..31));
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my ($carry,$zero) = ($rp,"r0");
|
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|
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# sp----------->+-------------------------------+
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# | saved sp |
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# +-------------------------------+
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||
# . .
|
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# +8*size_t +-------------------------------+
|
||
# | 4 "n0*t0" |
|
||
# . .
|
||
# . .
|
||
# +12*size_t +-------------------------------+
|
||
# | size_t tmp[num] |
|
||
# . .
|
||
# . .
|
||
# . .
|
||
# +-------------------------------+
|
||
# | topmost carry |
|
||
# . .
|
||
# -18*size_t +-------------------------------+
|
||
# | 18 saved gpr, r14-r31 |
|
||
# . .
|
||
# . .
|
||
# +-------------------------------+
|
||
$code.=<<___;
|
||
.globl .bn_mul4x_mont_int
|
||
.align 5
|
||
.bn_mul4x_mont_int:
|
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andi. r0,$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
|
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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($ap)
|
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$LD $m0,$SIZE_T*1($np) # n[0..3]
|
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$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;
|