#!/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/. # ==================================================================== # October 2005 # # This is a "teaser" code, as it can be improved in several ways... # First of all non-SSE2 path should be implemented (yes, for now it # performs Montgomery multiplication/convolution only on SSE2-capable # CPUs such as P4, others fall down to original code). Then inner loop # can be unrolled and modulo-scheduled to improve ILP and possibly # moved to 128-bit XMM register bank (though it would require input # rearrangement and/or increase bus bandwidth utilization). Dedicated # squaring procedure should give further performance improvement... # Yet, for being draft, the code improves rsa512 *sign* benchmark by # 110%(!), rsa1024 one - by 70% and rsa4096 - by 20%:-) # December 2006 # # Modulo-scheduling SSE2 loops results in further 15-20% improvement. # Integer-only code [being equipped with dedicated squaring procedure] # gives ~40% on rsa512 sign benchmark... $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; push(@INC,"${dir}","${dir}../../perlasm"); require "x86asm.pl"; &asm_init($ARGV[0],$0); $sse2=0; for (@ARGV) { $sse2=1 if (/-DOPENSSL_IA32_SSE2/); } &external_label("OPENSSL_ia32cap_P") if ($sse2); &function_begin("bn_mul_mont"); $i="edx"; $j="ecx"; $ap="esi"; $tp="esi"; # overlapping variables!!! $rp="edi"; $bp="edi"; # overlapping variables!!! $np="ebp"; $num="ebx"; $_num=&DWP(4*0,"esp"); # stack top layout $_rp=&DWP(4*1,"esp"); $_ap=&DWP(4*2,"esp"); $_bp=&DWP(4*3,"esp"); $_np=&DWP(4*4,"esp"); $_n0=&DWP(4*5,"esp"); $_n0q=&QWP(4*5,"esp"); $_sp=&DWP(4*6,"esp"); $_bpend=&DWP(4*7,"esp"); $frame=32; # size of above frame rounded up to 16n &xor ("eax","eax"); &mov ("edi",&wparam(5)); # int num &cmp ("edi",4); &jl (&label("just_leave")); &lea ("esi",&wparam(0)); # put aside pointer to argument block &lea ("edx",&wparam(1)); # load ap &mov ("ebp","esp"); # saved stack pointer! &add ("edi",2); # extra two words on top of tp &neg ("edi"); &lea ("esp",&DWP(-$frame,"esp","edi",4)); # alloca($frame+4*(num+2)) &neg ("edi"); # minimize cache contention by arraning 2K window between stack # pointer and ap argument [np is also position sensitive vector, # but it's assumed to be near ap, as it's allocated at ~same # time]. &mov ("eax","esp"); &sub ("eax","edx"); &and ("eax",2047); &sub ("esp","eax"); # this aligns sp and ap modulo 2048 &xor ("edx","esp"); &and ("edx",2048); &xor ("edx",2048); &sub ("esp","edx"); # this splits them apart modulo 4096 &and ("esp",-64); # align to cache line ################################# load argument block... &mov ("eax",&DWP(0*4,"esi"));# BN_ULONG *rp &mov ("ebx",&DWP(1*4,"esi"));# const BN_ULONG *ap &mov ("ecx",&DWP(2*4,"esi"));# const BN_ULONG *bp &mov ("edx",&DWP(3*4,"esi"));# const BN_ULONG *np &mov ("esi",&DWP(4*4,"esi"));# const BN_ULONG *n0 #&mov ("edi",&DWP(5*4,"esi"));# int num &mov ("esi",&DWP(0,"esi")); # pull n0[0] &mov ($_rp,"eax"); # ... save a copy of argument block &mov ($_ap,"ebx"); &mov ($_bp,"ecx"); &mov ($_np,"edx"); &mov ($_n0,"esi"); &lea ($num,&DWP(-3,"edi")); # num=num-1 to assist modulo-scheduling #&mov ($_num,$num); # redundant as $num is not reused &mov ($_sp,"ebp"); # saved stack pointer! if($sse2) { $acc0="mm0"; # mmx register bank layout $acc1="mm1"; $car0="mm2"; $car1="mm3"; $mul0="mm4"; $mul1="mm5"; $temp="mm6"; $mask="mm7"; &picmeup("eax","OPENSSL_ia32cap_P"); &bt (&DWP(0,"eax"),26); &jnc (&label("non_sse2")); &mov ("eax",-1); &movd ($mask,"eax"); # mask 32 lower bits &mov ($ap,$_ap); # load input pointers &mov ($bp,$_bp); &mov ($np,$_np); &xor ($i,$i); # i=0 &xor ($j,$j); # j=0 &movd ($mul0,&DWP(0,$bp)); # bp[0] &movd ($mul1,&DWP(0,$ap)); # ap[0] &movd ($car1,&DWP(0,$np)); # np[0] &pmuludq($mul1,$mul0); # ap[0]*bp[0] &movq ($car0,$mul1); &movq ($acc0,$mul1); # I wish movd worked for &pand ($acc0,$mask); # inter-register transfers &pmuludq($mul1,$_n0q); # *=n0 &pmuludq($car1,$mul1); # "t[0]"*np[0]*n0 &paddq ($car1,$acc0); &movd ($acc1,&DWP(4,$np)); # np[1] &movd ($acc0,&DWP(4,$ap)); # ap[1] &psrlq ($car0,32); &psrlq ($car1,32); &inc ($j); # j++ &set_label("1st",16); &pmuludq($acc0,$mul0); # ap[j]*bp[0] &pmuludq($acc1,$mul1); # np[j]*m1 &paddq ($car0,$acc0); # +=c0 &paddq ($car1,$acc1); # +=c1 &movq ($acc0,$car0); &pand ($acc0,$mask); &movd ($acc1,&DWP(4,$np,$j,4)); # np[j+1] &paddq ($car1,$acc0); # +=ap[j]*bp[0]; &movd ($acc0,&DWP(4,$ap,$j,4)); # ap[j+1] &psrlq ($car0,32); &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[j-1]= &psrlq ($car1,32); &lea ($j,&DWP(1,$j)); &cmp ($j,$num); &jl (&label("1st")); &pmuludq($acc0,$mul0); # ap[num-1]*bp[0] &pmuludq($acc1,$mul1); # np[num-1]*m1 &paddq ($car0,$acc0); # +=c0 &paddq ($car1,$acc1); # +=c1 &movq ($acc0,$car0); &pand ($acc0,$mask); &paddq ($car1,$acc0); # +=ap[num-1]*bp[0]; &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[num-2]= &psrlq ($car0,32); &psrlq ($car1,32); &paddq ($car1,$car0); &movq (&QWP($frame,"esp",$num,4),$car1); # tp[num].tp[num-1] &inc ($i); # i++ &set_label("outer"); &xor ($j,$j); # j=0 &movd ($mul0,&DWP(0,$bp,$i,4)); # bp[i] &movd ($mul1,&DWP(0,$ap)); # ap[0] &movd ($temp,&DWP($frame,"esp")); # tp[0] &movd ($car1,&DWP(0,$np)); # np[0] &pmuludq($mul1,$mul0); # ap[0]*bp[i] &paddq ($mul1,$temp); # +=tp[0] &movq ($acc0,$mul1); &movq ($car0,$mul1); &pand ($acc0,$mask); &pmuludq($mul1,$_n0q); # *=n0 &pmuludq($car1,$mul1); &paddq ($car1,$acc0); &movd ($temp,&DWP($frame+4,"esp")); # tp[1] &movd ($acc1,&DWP(4,$np)); # np[1] &movd ($acc0,&DWP(4,$ap)); # ap[1] &psrlq ($car0,32); &psrlq ($car1,32); &paddq ($car0,$temp); # +=tp[1] &inc ($j); # j++ &dec ($num); &set_label("inner"); &pmuludq($acc0,$mul0); # ap[j]*bp[i] &pmuludq($acc1,$mul1); # np[j]*m1 &paddq ($car0,$acc0); # +=c0 &paddq ($car1,$acc1); # +=c1 &movq ($acc0,$car0); &movd ($temp,&DWP($frame+4,"esp",$j,4));# tp[j+1] &pand ($acc0,$mask); &movd ($acc1,&DWP(4,$np,$j,4)); # np[j+1] &paddq ($car1,$acc0); # +=ap[j]*bp[i]+tp[j] &movd ($acc0,&DWP(4,$ap,$j,4)); # ap[j+1] &psrlq ($car0,32); &movd (&DWP($frame-4,"esp",$j,4),$car1);# tp[j-1]= &psrlq ($car1,32); &paddq ($car0,$temp); # +=tp[j+1] &dec ($num); &lea ($j,&DWP(1,$j)); # j++ &jnz (&label("inner")); &mov ($num,$j); &pmuludq($acc0,$mul0); # ap[num-1]*bp[i] &pmuludq($acc1,$mul1); # np[num-1]*m1 &paddq ($car0,$acc0); # +=c0 &paddq ($car1,$acc1); # +=c1 &movq ($acc0,$car0); &pand ($acc0,$mask); &paddq ($car1,$acc0); # +=ap[num-1]*bp[i]+tp[num-1] &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[num-2]= &psrlq ($car0,32); &psrlq ($car1,32); &movd ($temp,&DWP($frame+4,"esp",$num,4)); # += tp[num] &paddq ($car1,$car0); &paddq ($car1,$temp); &movq (&QWP($frame,"esp",$num,4),$car1); # tp[num].tp[num-1] &lea ($i,&DWP(1,$i)); # i++ &cmp ($i,$num); &jle (&label("outer")); &emms (); # done with mmx bank &jmp (&label("common_tail")); &set_label("non_sse2",16); } if (0) { &mov ("esp",$_sp); &xor ("eax","eax"); # signal "not fast enough [yet]" &jmp (&label("just_leave")); # While the below code provides competitive performance for # all key lengthes on modern Intel cores, it's still more # than 10% slower for 4096-bit key elsewhere:-( "Competitive" # means compared to the original integer-only assembler. # 512-bit RSA sign is better by ~40%, but that's about all # one can say about all CPUs... } else { $inp="esi"; # integer path uses these registers differently $word="edi"; $carry="ebp"; &mov ($inp,$_ap); &lea ($carry,&DWP(1,$num)); &mov ($word,$_bp); &xor ($j,$j); # j=0 &mov ("edx",$inp); &and ($carry,1); # see if num is even &sub ("edx",$word); # see if ap==bp &lea ("eax",&DWP(4,$word,$num,4)); # &bp[num] &or ($carry,"edx"); &mov ($word,&DWP(0,$word)); # bp[0] &jz (&label("bn_sqr_mont")); &mov ($_bpend,"eax"); &mov ("eax",&DWP(0,$inp)); &xor ("edx","edx"); &set_label("mull",16); &mov ($carry,"edx"); &mul ($word); # ap[j]*bp[0] &add ($carry,"eax"); &lea ($j,&DWP(1,$j)); &adc ("edx",0); &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j+1] &cmp ($j,$num); &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]= &jl (&label("mull")); &mov ($carry,"edx"); &mul ($word); # ap[num-1]*bp[0] &mov ($word,$_n0); &add ("eax",$carry); &mov ($inp,$_np); &adc ("edx",0); &imul ($word,&DWP($frame,"esp")); # n0*tp[0] &mov (&DWP($frame,"esp",$num,4),"eax"); # tp[num-1]= &xor ($j,$j); &mov (&DWP($frame+4,"esp",$num,4),"edx"); # tp[num]= &mov (&DWP($frame+8,"esp",$num,4),$j); # tp[num+1]= &mov ("eax",&DWP(0,$inp)); # np[0] &mul ($word); # np[0]*m &add ("eax",&DWP($frame,"esp")); # +=tp[0] &mov ("eax",&DWP(4,$inp)); # np[1] &adc ("edx",0); &inc ($j); &jmp (&label("2ndmadd")); &set_label("1stmadd",16); &mov ($carry,"edx"); &mul ($word); # ap[j]*bp[i] &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j] &lea ($j,&DWP(1,$j)); &adc ("edx",0); &add ($carry,"eax"); &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j+1] &adc ("edx",0); &cmp ($j,$num); &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]= &jl (&label("1stmadd")); &mov ($carry,"edx"); &mul ($word); # ap[num-1]*bp[i] &add ("eax",&DWP($frame,"esp",$num,4)); # +=tp[num-1] &mov ($word,$_n0); &adc ("edx",0); &mov ($inp,$_np); &add ($carry,"eax"); &adc ("edx",0); &imul ($word,&DWP($frame,"esp")); # n0*tp[0] &xor ($j,$j); &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num] &mov (&DWP($frame,"esp",$num,4),$carry); # tp[num-1]= &adc ($j,0); &mov ("eax",&DWP(0,$inp)); # np[0] &mov (&DWP($frame+4,"esp",$num,4),"edx"); # tp[num]= &mov (&DWP($frame+8,"esp",$num,4),$j); # tp[num+1]= &mul ($word); # np[0]*m &add ("eax",&DWP($frame,"esp")); # +=tp[0] &mov ("eax",&DWP(4,$inp)); # np[1] &adc ("edx",0); &mov ($j,1); &set_label("2ndmadd",16); &mov ($carry,"edx"); &mul ($word); # np[j]*m &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j] &lea ($j,&DWP(1,$j)); &adc ("edx",0); &add ($carry,"eax"); &mov ("eax",&DWP(0,$inp,$j,4)); # np[j+1] &adc ("edx",0); &cmp ($j,$num); &mov (&DWP($frame-8,"esp",$j,4),$carry); # tp[j-1]= &jl (&label("2ndmadd")); &mov ($carry,"edx"); &mul ($word); # np[j]*m &add ($carry,&DWP($frame,"esp",$num,4)); # +=tp[num-1] &adc ("edx",0); &add ($carry,"eax"); &adc ("edx",0); &mov (&DWP($frame-4,"esp",$num,4),$carry); # tp[num-2]= &xor ("eax","eax"); &mov ($j,$_bp); # &bp[i] &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num] &adc ("eax",&DWP($frame+8,"esp",$num,4)); # +=tp[num+1] &lea ($j,&DWP(4,$j)); &mov (&DWP($frame,"esp",$num,4),"edx"); # tp[num-1]= &cmp ($j,$_bpend); &mov (&DWP($frame+4,"esp",$num,4),"eax"); # tp[num]= &je (&label("common_tail")); &mov ($word,&DWP(0,$j)); # bp[i+1] &mov ($inp,$_ap); &mov ($_bp,$j); # &bp[++i] &xor ($j,$j); &xor ("edx","edx"); &mov ("eax",&DWP(0,$inp)); &jmp (&label("1stmadd")); &set_label("bn_sqr_mont",16); $sbit=$num; &mov ($_num,$num); &mov ($_bp,$j); # i=0 &mov ("eax",$word); # ap[0] &mul ($word); # ap[0]*ap[0] &mov (&DWP($frame,"esp"),"eax"); # tp[0]= &mov ($sbit,"edx"); &shr ("edx",1); &and ($sbit,1); &inc ($j); &set_label("sqr",16); &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j] &mov ($carry,"edx"); &mul ($word); # ap[j]*ap[0] &add ("eax",$carry); &lea ($j,&DWP(1,$j)); &adc ("edx",0); &lea ($carry,&DWP(0,$sbit,"eax",2)); &shr ("eax",31); &cmp ($j,$_num); &mov ($sbit,"eax"); &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]= &jl (&label("sqr")); &mov ("eax",&DWP(0,$inp,$j,4)); # ap[num-1] &mov ($carry,"edx"); &mul ($word); # ap[num-1]*ap[0] &add ("eax",$carry); &mov ($word,$_n0); &adc ("edx",0); &mov ($inp,$_np); &lea ($carry,&DWP(0,$sbit,"eax",2)); &imul ($word,&DWP($frame,"esp")); # n0*tp[0] &shr ("eax",31); &mov (&DWP($frame,"esp",$j,4),$carry); # tp[num-1]= &lea ($carry,&DWP(0,"eax","edx",2)); &mov ("eax",&DWP(0,$inp)); # np[0] &shr ("edx",31); &mov (&DWP($frame+4,"esp",$j,4),$carry); # tp[num]= &mov (&DWP($frame+8,"esp",$j,4),"edx"); # tp[num+1]= &mul ($word); # np[0]*m &add ("eax",&DWP($frame,"esp")); # +=tp[0] &mov ($num,$j); &adc ("edx",0); &mov ("eax",&DWP(4,$inp)); # np[1] &mov ($j,1); &set_label("3rdmadd",16); &mov ($carry,"edx"); &mul ($word); # np[j]*m &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j] &adc ("edx",0); &add ($carry,"eax"); &mov ("eax",&DWP(4,$inp,$j,4)); # np[j+1] &adc ("edx",0); &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j-1]= &mov ($carry,"edx"); &mul ($word); # np[j+1]*m &add ($carry,&DWP($frame+4,"esp",$j,4)); # +=tp[j+1] &lea ($j,&DWP(2,$j)); &adc ("edx",0); &add ($carry,"eax"); &mov ("eax",&DWP(0,$inp,$j,4)); # np[j+2] &adc ("edx",0); &cmp ($j,$num); &mov (&DWP($frame-8,"esp",$j,4),$carry); # tp[j]= &jl (&label("3rdmadd")); &mov ($carry,"edx"); &mul ($word); # np[j]*m &add ($carry,&DWP($frame,"esp",$num,4)); # +=tp[num-1] &adc ("edx",0); &add ($carry,"eax"); &adc ("edx",0); &mov (&DWP($frame-4,"esp",$num,4),$carry); # tp[num-2]= &mov ($j,$_bp); # i &xor ("eax","eax"); &mov ($inp,$_ap); &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num] &adc ("eax",&DWP($frame+8,"esp",$num,4)); # +=tp[num+1] &mov (&DWP($frame,"esp",$num,4),"edx"); # tp[num-1]= &cmp ($j,$num); &mov (&DWP($frame+4,"esp",$num,4),"eax"); # tp[num]= &je (&label("common_tail")); &mov ($word,&DWP(4,$inp,$j,4)); # ap[i] &lea ($j,&DWP(1,$j)); &mov ("eax",$word); &mov ($_bp,$j); # ++i &mul ($word); # ap[i]*ap[i] &add ("eax",&DWP($frame,"esp",$j,4)); # +=tp[i] &adc ("edx",0); &mov (&DWP($frame,"esp",$j,4),"eax"); # tp[i]= &xor ($carry,$carry); &cmp ($j,$num); &lea ($j,&DWP(1,$j)); &je (&label("sqrlast")); &mov ($sbit,"edx"); # zaps $num &shr ("edx",1); &and ($sbit,1); &set_label("sqradd",16); &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j] &mov ($carry,"edx"); &mul ($word); # ap[j]*ap[i] &add ("eax",$carry); &lea ($carry,&DWP(0,"eax","eax")); &adc ("edx",0); &shr ("eax",31); &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j] &lea ($j,&DWP(1,$j)); &adc ("eax",0); &add ($carry,$sbit); &adc ("eax",0); &cmp ($j,$_num); &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]= &mov ($sbit,"eax"); &jle (&label("sqradd")); &mov ($carry,"edx"); &lea ("edx",&DWP(0,$sbit,"edx",2)); &shr ($carry,31); &set_label("sqrlast"); &mov ($word,$_n0); &mov ($inp,$_np); &imul ($word,&DWP($frame,"esp")); # n0*tp[0] &add ("edx",&DWP($frame,"esp",$j,4)); # +=tp[num] &mov ("eax",&DWP(0,$inp)); # np[0] &adc ($carry,0); &mov (&DWP($frame,"esp",$j,4),"edx"); # tp[num]= &mov (&DWP($frame+4,"esp",$j,4),$carry); # tp[num+1]= &mul ($word); # np[0]*m &add ("eax",&DWP($frame,"esp")); # +=tp[0] &lea ($num,&DWP(-1,$j)); &adc ("edx",0); &mov ($j,1); &mov ("eax",&DWP(4,$inp)); # np[1] &jmp (&label("3rdmadd")); } &set_label("common_tail",16); &mov ($np,$_np); # load modulus pointer &mov ($rp,$_rp); # load result pointer &lea ($tp,&DWP($frame,"esp")); # [$ap and $bp are zapped] &mov ("eax",&DWP(0,$tp)); # tp[0] &mov ($j,$num); # j=num-1 &xor ($i,$i); # i=0 and clear CF! &set_label("sub",16); &sbb ("eax",&DWP(0,$np,$i,4)); &mov (&DWP(0,$rp,$i,4),"eax"); # rp[i]=tp[i]-np[i] &dec ($j); # doesn't affect CF! &mov ("eax",&DWP(4,$tp,$i,4)); # tp[i+1] &lea ($i,&DWP(1,$i)); # i++ &jge (&label("sub")); &sbb ("eax",0); # handle upmost overflow bit &and ($tp,"eax"); ¬ ("eax"); &mov ($np,$rp); &and ($np,"eax"); &or ($tp,$np); # tp=carry?tp:rp &set_label("copy",16); # copy or in-place refresh &mov ("eax",&DWP(0,$tp,$num,4)); &mov (&DWP(0,$rp,$num,4),"eax"); # rp[i]=tp[i] &mov (&DWP($frame,"esp",$num,4),$j); # zap temporary vector &dec ($num); &jge (&label("copy")); &mov ("esp",$_sp); # pull saved stack pointer &mov ("eax",1); &set_label("just_leave"); &function_end("bn_mul_mont"); &asciz("Montgomery Multiplication for x86, CRYPTOGAMS by <appro\@openssl.org>"); &asm_finish();