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#!/usr/bin/env perl |
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# ==================================================================== |
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# Written by Andy Polyakov <appro@fy.chalmers.se> 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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# January 2007. |
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# Montgomery multiplication for ARMv4. |
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# |
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# Performance improvement naturally varies among CPU implementations |
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# and compilers. The code was observed to provide +65-35% improvement |
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# [depending on key length, less for longer keys] on ARM920T, and |
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# +115-80% on Intel IXP425. This is compared to pre-bn_mul_mont code |
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# base and compiler generated code with in-lined umull and even umlal |
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# instructions. The latter means that this code didn't really have an |
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# "advantage" of utilizing some "secret" instruction. |
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# |
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# The code is interoperable with Thumb ISA and is rather compact, less |
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# than 1/2KB. Windows CE port would be trivial, as it's exclusively |
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# about decorations, ABI and instruction syntax are identical. |
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while (($output=shift) && ($output!~/^\w[\w\-]*\.\w+$/)) {} |
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open STDOUT,">$output"; |
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$num="r0"; # starts as num argument, but holds &tp[num-1] |
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$ap="r1"; |
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$bp="r2"; $bi="r2"; $rp="r2"; |
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$np="r3"; |
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$tp="r4"; |
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$aj="r5"; |
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$nj="r6"; |
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$tj="r7"; |
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$n0="r8"; |
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########### # r9 is reserved by ELF as platform specific, e.g. TLS pointer |
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$alo="r10"; # sl, gcc uses it to keep @GOT |
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$ahi="r11"; # fp |
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$nlo="r12"; # ip |
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########### # r13 is stack pointer |
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$nhi="r14"; # lr |
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########### # r15 is program counter |
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#### argument block layout relative to &tp[num-1], a.k.a. $num |
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$_rp="$num,#12*4"; |
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# ap permanently resides in r1 |
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$_bp="$num,#13*4"; |
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# np permanently resides in r3 |
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$_n0="$num,#14*4"; |
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$_num="$num,#15*4"; $_bpend=$_num; |
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$code=<<___; |
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.text |
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.global bn_mul_mont |
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.type bn_mul_mont,%function |
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.align 2 |
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bn_mul_mont: |
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stmdb sp!,{r0,r2} @ sp points at argument block |
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ldr $num,[sp,#3*4] @ load num |
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cmp $num,#2 |
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movlt r0,#0 |
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addlt sp,sp,#2*4 |
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blt .Labrt |
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stmdb sp!,{r4-r12,lr} @ save 10 registers |
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mov $num,$num,lsl#2 @ rescale $num for byte count |
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sub sp,sp,$num @ alloca(4*num) |
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sub sp,sp,#4 @ +extra dword |
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sub $num,$num,#4 @ "num=num-1" |
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add $tp,$bp,$num @ &bp[num-1] |
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add $num,sp,$num @ $num to point at &tp[num-1] |
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ldr $n0,[$_n0] @ &n0 |
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ldr $bi,[$bp] @ bp[0] |
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ldr $aj,[$ap],#4 @ ap[0],ap++ |
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ldr $nj,[$np],#4 @ np[0],np++ |
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ldr $n0,[$n0] @ *n0 |
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str $tp,[$_bpend] @ save &bp[num] |
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umull $alo,$ahi,$aj,$bi @ ap[0]*bp[0] |
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str $n0,[$_n0] @ save n0 value |
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mul $n0,$alo,$n0 @ "tp[0]"*n0 |
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mov $nlo,#0 |
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umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"t[0]" |
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mov $tp,sp |
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.L1st: |
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ldr $aj,[$ap],#4 @ ap[j],ap++ |
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mov $alo,$ahi |
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ldr $nj,[$np],#4 @ np[j],np++ |
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mov $ahi,#0 |
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umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[0] |
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mov $nhi,#0 |
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umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0 |
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adds $nlo,$nlo,$alo |
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str $nlo,[$tp],#4 @ tp[j-1]=,tp++ |
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adc $nlo,$nhi,#0 |
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cmp $tp,$num |
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bne .L1st |
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adds $nlo,$nlo,$ahi |
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ldr $tp,[$_bp] @ restore bp |
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mov $nhi,#0 |
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ldr $n0,[$_n0] @ restore n0 |
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adc $nhi,$nhi,#0 |
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str $nlo,[$num] @ tp[num-1]= |
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str $nhi,[$num,#4] @ tp[num]= |
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.Louter: |
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sub $tj,$num,sp @ "original" $num-1 value |
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sub $ap,$ap,$tj @ "rewind" ap to &ap[1] |
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ldr $bi,[$tp,#4]! @ *(++bp) |
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sub $np,$np,$tj @ "rewind" np to &np[1] |
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ldr $aj,[$ap,#-4] @ ap[0] |
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ldr $alo,[sp] @ tp[0] |
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ldr $nj,[$np,#-4] @ np[0] |
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ldr $tj,[sp,#4] @ tp[1] |
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mov $ahi,#0 |
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umlal $alo,$ahi,$aj,$bi @ ap[0]*bp[i]+tp[0] |
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str $tp,[$_bp] @ save bp |
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mul $n0,$alo,$n0 |
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mov $nlo,#0 |
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umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"tp[0]" |
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mov $tp,sp |
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.Linner: |
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ldr $aj,[$ap],#4 @ ap[j],ap++ |
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adds $alo,$ahi,$tj @ +=tp[j] |
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ldr $nj,[$np],#4 @ np[j],np++ |
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mov $ahi,#0 |
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umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[i] |
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mov $nhi,#0 |
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umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0 |
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adc $ahi,$ahi,#0 |
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ldr $tj,[$tp,#8] @ tp[j+1] |
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adds $nlo,$nlo,$alo |
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str $nlo,[$tp],#4 @ tp[j-1]=,tp++ |
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adc $nlo,$nhi,#0 |
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cmp $tp,$num |
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bne .Linner |
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adds $nlo,$nlo,$ahi |
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mov $nhi,#0 |
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ldr $tp,[$_bp] @ restore bp |
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adc $nhi,$nhi,#0 |
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ldr $n0,[$_n0] @ restore n0 |
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adds $nlo,$nlo,$tj |
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ldr $tj,[$_bpend] @ restore &bp[num] |
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adc $nhi,$nhi,#0 |
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str $nlo,[$num] @ tp[num-1]= |
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str $nhi,[$num,#4] @ tp[num]= |
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cmp $tp,$tj |
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bne .Louter |
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ldr $rp,[$_rp] @ pull rp |
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add $num,$num,#4 @ $num to point at &tp[num] |
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sub $aj,$num,sp @ "original" num value |
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mov $tp,sp @ "rewind" $tp |
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mov $ap,$tp @ "borrow" $ap |
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sub $np,$np,$aj @ "rewind" $np to &np[0] |
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subs $tj,$tj,$tj @ "clear" carry flag |
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.Lsub: ldr $tj,[$tp],#4 |
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ldr $nj,[$np],#4 |
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sbcs $tj,$tj,$nj @ tp[j]-np[j] |
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str $tj,[$rp],#4 @ rp[j]= |
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teq $tp,$num @ preserve carry |
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bne .Lsub |
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sbcs $nhi,$nhi,#0 @ upmost carry |
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mov $tp,sp @ "rewind" $tp |
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sub $rp,$rp,$aj @ "rewind" $rp |
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and $ap,$tp,$nhi |
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bic $np,$rp,$nhi |
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orr $ap,$ap,$np @ ap=borrow?tp:rp |
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.Lcopy: ldr $tj,[$ap],#4 @ copy or in-place refresh |
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str sp,[$tp],#4 @ zap tp |
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str $tj,[$rp],#4 |
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cmp $tp,$num |
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bne .Lcopy |
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add sp,$num,#4 @ skip over tp[num+1] |
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ldmia sp!,{r4-r12,lr} @ restore registers |
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add sp,sp,#2*4 @ skip over {r0,r2} |
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mov r0,#1 |
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.Labrt: tst lr,#1 |
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moveq pc,lr @ be binary compatible with V4, yet |
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bx lr @ interoperable with Thumb ISA:-) |
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.size bn_mul_mont,.-bn_mul_mont |
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.asciz "Montgomery multiplication for ARMv4, CRYPTOGAMS by <appro\@openssl.org>" |
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.align 2 |
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___ |
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$code =~ s/\bbx\s+lr\b/.word\t0xe12fff1e/gm; # make it possible to compile with -march=armv4 |
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print $code; |
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close STDOUT;
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