3 # ====================================================================
4 # Written by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
5 # project. The module is, however, dual licensed under OpenSSL and
6 # CRYPTOGAMS licenses depending on where you obtain it. For further
7 # details see http://www.openssl.org/~appro/cryptogams/.
8 # ====================================================================
12 # This is a "teaser" code, as it can be improved in several ways...
13 # First of all non-SSE2 path should be implemented (yes, for now it
14 # performs Montgomery multiplication/convolution only on SSE2-capable
15 # CPUs such as P4, others fall down to original code). Then inner loop
16 # can be unrolled and modulo-scheduled to improve ILP and possibly
17 # moved to 128-bit XMM register bank (though it would require input
18 # rearrangement and/or increase bus bandwidth utilization). Dedicated
19 # squaring procedure should give further performance improvement...
20 # Yet, for being draft, the code improves rsa512 *sign* benchmark by
21 # 110%(!), rsa1024 one - by 70% and rsa4096 - by 20%:-)
25 # Modulo-scheduling SSE2 loops results in further 15-20% improvement.
26 # Integer-only code [being equipped with dedicated squaring procedure]
27 # gives ~40% on rsa512 sign benchmark...
29 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
30 push(@INC,"${dir}","${dir}../../perlasm");
33 &asm_init($ARGV[0],$0);
36 for (@ARGV) { $sse2=1 if (/-DOPENSSL_IA32_SSE2/); }
38 &external_label("OPENSSL_ia32cap_P") if ($sse2);
40 &function_begin("bn_mul_mont");
44 $ap="esi"; $tp="esi"; # overlapping variables!!!
45 $rp="edi"; $bp="edi"; # overlapping variables!!!
49 $_num=&DWP(4*0,"esp"); # stack top layout
54 $_n0=&DWP(4*5,"esp"); $_n0q=&QWP(4*5,"esp");
56 $_bpend=&DWP(4*7,"esp");
57 $frame=32; # size of above frame rounded up to 16n
60 &mov ("edi",&wparam(5)); # int num
62 &jl (&label("just_leave"));
64 &lea ("esi",&wparam(0)); # put aside pointer to argument block
65 &lea ("edx",&wparam(1)); # load ap
66 &mov ("ebp","esp"); # saved stack pointer!
67 &add ("edi",2); # extra two words on top of tp
69 &lea ("esp",&DWP(-$frame,"esp","edi",4)); # alloca($frame+4*(num+2))
72 # minimize cache contention by arraning 2K window between stack
73 # pointer and ap argument [np is also position sensitive vector,
74 # but it's assumed to be near ap, as it's allocated at ~same
79 &sub ("esp","eax"); # this aligns sp and ap modulo 2048
84 &sub ("esp","edx"); # this splits them apart modulo 4096
86 &and ("esp",-64); # align to cache line
88 ################################# load argument block...
89 &mov ("eax",&DWP(0*4,"esi"));# BN_ULONG *rp
90 &mov ("ebx",&DWP(1*4,"esi"));# const BN_ULONG *ap
91 &mov ("ecx",&DWP(2*4,"esi"));# const BN_ULONG *bp
92 &mov ("edx",&DWP(3*4,"esi"));# const BN_ULONG *np
93 &mov ("esi",&DWP(4*4,"esi"));# const BN_ULONG *n0
94 #&mov ("edi",&DWP(5*4,"esi"));# int num
96 &mov ("esi",&DWP(0,"esi")); # pull n0[0]
97 &mov ($_rp,"eax"); # ... save a copy of argument block
102 &lea ($num,&DWP(-3,"edi")); # num=num-1 to assist modulo-scheduling
103 #&mov ($_num,$num); # redundant as $num is not reused
104 &mov ($_sp,"ebp"); # saved stack pointer!
107 $acc0="mm0"; # mmx register bank layout
116 &picmeup("eax","OPENSSL_ia32cap_P");
117 &bt (&DWP(0,"eax"),26);
118 &jnc (&label("non_sse2"));
121 &movd ($mask,"eax"); # mask 32 lower bits
123 &mov ($ap,$_ap); # load input pointers
130 &movd ($mul0,&DWP(0,$bp)); # bp[0]
131 &movd ($mul1,&DWP(0,$ap)); # ap[0]
132 &movd ($car1,&DWP(0,$np)); # np[0]
134 &pmuludq($mul1,$mul0); # ap[0]*bp[0]
136 &movq ($acc0,$mul1); # I wish movd worked for
137 &pand ($acc0,$mask); # inter-register transfers
139 &pmuludq($mul1,$_n0q); # *=n0
141 &pmuludq($car1,$mul1); # "t[0]"*np[0]*n0
142 &paddq ($car1,$acc0);
144 &movd ($acc1,&DWP(4,$np)); # np[1]
145 &movd ($acc0,&DWP(4,$ap)); # ap[1]
151 &set_label("1st",16);
152 &pmuludq($acc0,$mul0); # ap[j]*bp[0]
153 &pmuludq($acc1,$mul1); # np[j]*m1
154 &paddq ($car0,$acc0); # +=c0
155 &paddq ($car1,$acc1); # +=c1
159 &movd ($acc1,&DWP(4,$np,$j,4)); # np[j+1]
160 &paddq ($car1,$acc0); # +=ap[j]*bp[0];
161 &movd ($acc0,&DWP(4,$ap,$j,4)); # ap[j+1]
163 &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[j-1]=
166 &lea ($j,&DWP(1,$j));
170 &pmuludq($acc0,$mul0); # ap[num-1]*bp[0]
171 &pmuludq($acc1,$mul1); # np[num-1]*m1
172 &paddq ($car0,$acc0); # +=c0
173 &paddq ($car1,$acc1); # +=c1
177 &paddq ($car1,$acc0); # +=ap[num-1]*bp[0];
178 &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[num-2]=
183 &paddq ($car1,$car0);
184 &movq (&QWP($frame,"esp",$num,4),$car1); # tp[num].tp[num-1]
190 &movd ($mul0,&DWP(0,$bp,$i,4)); # bp[i]
191 &movd ($mul1,&DWP(0,$ap)); # ap[0]
192 &movd ($temp,&DWP($frame,"esp")); # tp[0]
193 &movd ($car1,&DWP(0,$np)); # np[0]
194 &pmuludq($mul1,$mul0); # ap[0]*bp[i]
196 &paddq ($mul1,$temp); # +=tp[0]
201 &pmuludq($mul1,$_n0q); # *=n0
203 &pmuludq($car1,$mul1);
204 &paddq ($car1,$acc0);
206 &movd ($temp,&DWP($frame+4,"esp")); # tp[1]
207 &movd ($acc1,&DWP(4,$np)); # np[1]
208 &movd ($acc0,&DWP(4,$ap)); # ap[1]
212 &paddq ($car0,$temp); # +=tp[1]
217 &pmuludq($acc0,$mul0); # ap[j]*bp[i]
218 &pmuludq($acc1,$mul1); # np[j]*m1
219 &paddq ($car0,$acc0); # +=c0
220 &paddq ($car1,$acc1); # +=c1
223 &movd ($temp,&DWP($frame+4,"esp",$j,4));# tp[j+1]
225 &movd ($acc1,&DWP(4,$np,$j,4)); # np[j+1]
226 &paddq ($car1,$acc0); # +=ap[j]*bp[i]+tp[j]
227 &movd ($acc0,&DWP(4,$ap,$j,4)); # ap[j+1]
229 &movd (&DWP($frame-4,"esp",$j,4),$car1);# tp[j-1]=
231 &paddq ($car0,$temp); # +=tp[j+1]
234 &lea ($j,&DWP(1,$j)); # j++
235 &jnz (&label("inner"));
238 &pmuludq($acc0,$mul0); # ap[num-1]*bp[i]
239 &pmuludq($acc1,$mul1); # np[num-1]*m1
240 &paddq ($car0,$acc0); # +=c0
241 &paddq ($car1,$acc1); # +=c1
245 &paddq ($car1,$acc0); # +=ap[num-1]*bp[i]+tp[num-1]
246 &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[num-2]=
250 &movd ($temp,&DWP($frame+4,"esp",$num,4)); # += tp[num]
251 &paddq ($car1,$car0);
252 &paddq ($car1,$temp);
253 &movq (&QWP($frame,"esp",$num,4),$car1); # tp[num].tp[num-1]
255 &lea ($i,&DWP(1,$i)); # i++
257 &jle (&label("outer"));
259 &emms (); # done with mmx bank
260 &jmp (&label("common_tail"));
262 &set_label("non_sse2",16);
267 &xor ("eax","eax"); # signal "not fast enough [yet]"
268 &jmp (&label("just_leave"));
269 # While the below code provides competitive performance for
270 # all key lengthes on modern Intel cores, it's still more
271 # than 10% slower for 4096-bit key elsewhere:-( "Competitive"
272 # means compared to the original integer-only assembler.
273 # 512-bit RSA sign is better by ~40%, but that's about all
274 # one can say about all CPUs...
276 $inp="esi"; # integer path uses these registers differently
281 &lea ($carry,&DWP(1,$num));
285 &and ($carry,1); # see if num is even
286 &sub ("edx",$word); # see if ap==bp
287 &lea ("eax",&DWP(4,$word,$num,4)); # &bp[num]
289 &mov ($word,&DWP(0,$word)); # bp[0]
290 &jz (&label("bn_sqr_mont"));
291 &mov ($_bpend,"eax");
292 &mov ("eax",&DWP(0,$inp));
295 &set_label("mull",16);
297 &mul ($word); # ap[j]*bp[0]
299 &lea ($j,&DWP(1,$j));
301 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j+1]
303 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
304 &jl (&label("mull"));
307 &mul ($word); # ap[num-1]*bp[0]
312 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
314 &mov (&DWP($frame,"esp",$num,4),"eax"); # tp[num-1]=
316 &mov (&DWP($frame+4,"esp",$num,4),"edx"); # tp[num]=
317 &mov (&DWP($frame+8,"esp",$num,4),$j); # tp[num+1]=
319 &mov ("eax",&DWP(0,$inp)); # np[0]
320 &mul ($word); # np[0]*m
321 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
322 &mov ("eax",&DWP(4,$inp)); # np[1]
326 &jmp (&label("2ndmadd"));
328 &set_label("1stmadd",16);
330 &mul ($word); # ap[j]*bp[i]
331 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
332 &lea ($j,&DWP(1,$j));
335 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j+1]
338 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
339 &jl (&label("1stmadd"));
342 &mul ($word); # ap[num-1]*bp[i]
343 &add ("eax",&DWP($frame,"esp",$num,4)); # +=tp[num-1]
349 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
352 &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num]
353 &mov (&DWP($frame,"esp",$num,4),$carry); # tp[num-1]=
355 &mov ("eax",&DWP(0,$inp)); # np[0]
356 &mov (&DWP($frame+4,"esp",$num,4),"edx"); # tp[num]=
357 &mov (&DWP($frame+8,"esp",$num,4),$j); # tp[num+1]=
359 &mul ($word); # np[0]*m
360 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
361 &mov ("eax",&DWP(4,$inp)); # np[1]
365 &set_label("2ndmadd",16);
367 &mul ($word); # np[j]*m
368 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
369 &lea ($j,&DWP(1,$j));
372 &mov ("eax",&DWP(0,$inp,$j,4)); # np[j+1]
375 &mov (&DWP($frame-8,"esp",$j,4),$carry); # tp[j-1]=
376 &jl (&label("2ndmadd"));
379 &mul ($word); # np[j]*m
380 &add ($carry,&DWP($frame,"esp",$num,4)); # +=tp[num-1]
384 &mov (&DWP($frame-4,"esp",$num,4),$carry); # tp[num-2]=
387 &mov ($j,$_bp); # &bp[i]
388 &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num]
389 &adc ("eax",&DWP($frame+8,"esp",$num,4)); # +=tp[num+1]
390 &lea ($j,&DWP(4,$j));
391 &mov (&DWP($frame,"esp",$num,4),"edx"); # tp[num-1]=
393 &mov (&DWP($frame+4,"esp",$num,4),"eax"); # tp[num]=
394 &je (&label("common_tail"));
396 &mov ($word,&DWP(0,$j)); # bp[i+1]
398 &mov ($_bp,$j); # &bp[++i]
401 &mov ("eax",&DWP(0,$inp));
402 &jmp (&label("1stmadd"));
404 &set_label("bn_sqr_mont",16);
407 &mov ($_bp,$j); # i=0
409 &mov ("eax",$word); # ap[0]
410 &mul ($word); # ap[0]*ap[0]
411 &mov (&DWP($frame,"esp"),"eax"); # tp[0]=
416 &set_label("sqr",16);
417 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j]
419 &mul ($word); # ap[j]*ap[0]
421 &lea ($j,&DWP(1,$j));
423 &lea ($carry,&DWP(0,$sbit,"eax",2));
427 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
430 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[num-1]
432 &mul ($word); # ap[num-1]*ap[0]
437 &lea ($carry,&DWP(0,$sbit,"eax",2));
438 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
440 &mov (&DWP($frame,"esp",$j,4),$carry); # tp[num-1]=
442 &lea ($carry,&DWP(0,"eax","edx",2));
443 &mov ("eax",&DWP(0,$inp)); # np[0]
445 &mov (&DWP($frame+4,"esp",$j,4),$carry); # tp[num]=
446 &mov (&DWP($frame+8,"esp",$j,4),"edx"); # tp[num+1]=
448 &mul ($word); # np[0]*m
449 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
452 &mov ("eax",&DWP(4,$inp)); # np[1]
455 &set_label("3rdmadd",16);
457 &mul ($word); # np[j]*m
458 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
461 &mov ("eax",&DWP(4,$inp,$j,4)); # np[j+1]
463 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j-1]=
466 &mul ($word); # np[j+1]*m
467 &add ($carry,&DWP($frame+4,"esp",$j,4)); # +=tp[j+1]
468 &lea ($j,&DWP(2,$j));
471 &mov ("eax",&DWP(0,$inp,$j,4)); # np[j+2]
474 &mov (&DWP($frame-8,"esp",$j,4),$carry); # tp[j]=
475 &jl (&label("3rdmadd"));
478 &mul ($word); # np[j]*m
479 &add ($carry,&DWP($frame,"esp",$num,4)); # +=tp[num-1]
483 &mov (&DWP($frame-4,"esp",$num,4),$carry); # tp[num-2]=
488 &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num]
489 &adc ("eax",&DWP($frame+8,"esp",$num,4)); # +=tp[num+1]
490 &mov (&DWP($frame,"esp",$num,4),"edx"); # tp[num-1]=
492 &mov (&DWP($frame+4,"esp",$num,4),"eax"); # tp[num]=
493 &je (&label("common_tail"));
495 &mov ($word,&DWP(4,$inp,$j,4)); # ap[i]
496 &lea ($j,&DWP(1,$j));
498 &mov ($_bp,$j); # ++i
499 &mul ($word); # ap[i]*ap[i]
500 &add ("eax",&DWP($frame,"esp",$j,4)); # +=tp[i]
502 &mov (&DWP($frame,"esp",$j,4),"eax"); # tp[i]=
503 &xor ($carry,$carry);
505 &lea ($j,&DWP(1,$j));
506 &je (&label("sqrlast"));
508 &mov ($sbit,"edx"); # zaps $num
511 &set_label("sqradd",16);
512 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j]
514 &mul ($word); # ap[j]*ap[i]
516 &lea ($carry,&DWP(0,"eax","eax"));
519 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
520 &lea ($j,&DWP(1,$j));
525 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
527 &jle (&label("sqradd"));
530 &lea ("edx",&DWP(0,$sbit,"edx",2));
532 &set_label("sqrlast");
535 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
537 &add ("edx",&DWP($frame,"esp",$j,4)); # +=tp[num]
538 &mov ("eax",&DWP(0,$inp)); # np[0]
540 &mov (&DWP($frame,"esp",$j,4),"edx"); # tp[num]=
541 &mov (&DWP($frame+4,"esp",$j,4),$carry); # tp[num+1]=
543 &mul ($word); # np[0]*m
544 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
545 &lea ($num,&DWP(-1,$j));
548 &mov ("eax",&DWP(4,$inp)); # np[1]
550 &jmp (&label("3rdmadd"));
553 &set_label("common_tail",16);
554 &mov ($np,$_np); # load modulus pointer
555 &mov ($rp,$_rp); # load result pointer
556 &lea ($tp,&DWP($frame,"esp")); # [$ap and $bp are zapped]
558 &mov ("eax",&DWP(0,$tp)); # tp[0]
559 &mov ($j,$num); # j=num-1
560 &xor ($i,$i); # i=0 and clear CF!
562 &set_label("sub",16);
563 &sbb ("eax",&DWP(0,$np,$i,4));
564 &mov (&DWP(0,$rp,$i,4),"eax"); # rp[i]=tp[i]-np[i]
565 &dec ($j); # doesn't affect CF!
566 &mov ("eax",&DWP(4,$tp,$i,4)); # tp[i+1]
567 &lea ($i,&DWP(1,$i)); # i++
568 &jge (&label("sub"));
570 &sbb ("eax",0); # handle upmost overflow bit
575 &or ($tp,$np); # tp=carry?tp:rp
577 &set_label("copy",16); # copy or in-place refresh
578 &mov ("eax",&DWP(0,$tp,$num,4));
579 &mov (&DWP(0,$rp,$num,4),"eax"); # rp[i]=tp[i]
580 &mov (&DWP($frame,"esp",$num,4),$j); # zap temporary vector
582 &jge (&label("copy"));
584 &mov ("esp",$_sp); # pull saved stack pointer
586 &set_label("just_leave");
587 &function_end("bn_mul_mont");
589 &asciz("Montgomery Multiplication for x86, CRYPTOGAMS by <appro\@openssl.org>");