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}","${dir}../../perlasm");
34 open STDOUT,">$output";
36 &asm_init($ARGV[0],$0);
39 for (@ARGV) { $sse2=1 if (/-DOPENSSL_IA32_SSE2/); }
41 &external_label("OPENSSL_ia32cap_P") if ($sse2);
43 &function_begin("bn_mul_mont");
47 $ap="esi"; $tp="esi"; # overlapping variables!!!
48 $rp="edi"; $bp="edi"; # overlapping variables!!!
52 $_num=&DWP(4*0,"esp"); # stack top layout
57 $_n0=&DWP(4*5,"esp"); $_n0q=&QWP(4*5,"esp");
59 $_bpend=&DWP(4*7,"esp");
60 $frame=32; # size of above frame rounded up to 16n
63 &mov ("edi",&wparam(5)); # int num
65 &jl (&label("just_leave"));
67 &lea ("esi",&wparam(0)); # put aside pointer to argument block
68 &lea ("edx",&wparam(1)); # load ap
69 &mov ("ebp","esp"); # saved stack pointer!
70 &add ("edi",2); # extra two words on top of tp
72 &lea ("esp",&DWP(-$frame,"esp","edi",4)); # alloca($frame+4*(num+2))
75 # minimize cache contention by arraning 2K window between stack
76 # pointer and ap argument [np is also position sensitive vector,
77 # but it's assumed to be near ap, as it's allocated at ~same
82 &sub ("esp","eax"); # this aligns sp and ap modulo 2048
87 &sub ("esp","edx"); # this splits them apart modulo 4096
89 &and ("esp",-64); # align to cache line
91 # Some OSes (Windows) insist on stack being "wired" to
92 # physical memory in strictly sequential manner, i.e. if stack
93 # allocation spans two pages, then reference to farmost one can
94 # be punishable by SEGV. But page walking can do good even on
95 # other OSes, because it guarantees that villain thread hits
96 # the guard page before it can make damage to innocent one...
100 &set_label("page_walk");
101 &mov ("edx",&DWP(0,"esp","eax"));
104 &jnc (&label("page_walk"));
106 ################################# load argument block...
107 &mov ("eax",&DWP(0*4,"esi"));# BN_ULONG *rp
108 &mov ("ebx",&DWP(1*4,"esi"));# const BN_ULONG *ap
109 &mov ("ecx",&DWP(2*4,"esi"));# const BN_ULONG *bp
110 &mov ("edx",&DWP(3*4,"esi"));# const BN_ULONG *np
111 &mov ("esi",&DWP(4*4,"esi"));# const BN_ULONG *n0
112 #&mov ("edi",&DWP(5*4,"esi"));# int num
114 &mov ("esi",&DWP(0,"esi")); # pull n0[0]
115 &mov ($_rp,"eax"); # ... save a copy of argument block
120 &lea ($num,&DWP(-3,"edi")); # num=num-1 to assist modulo-scheduling
121 #&mov ($_num,$num); # redundant as $num is not reused
122 &mov ($_sp,"ebp"); # saved stack pointer!
125 $acc0="mm0"; # mmx register bank layout
134 &picmeup("eax","OPENSSL_ia32cap_P");
135 &bt (&DWP(0,"eax"),26);
136 &jnc (&label("non_sse2"));
139 &movd ($mask,"eax"); # mask 32 lower bits
141 &mov ($ap,$_ap); # load input pointers
148 &movd ($mul0,&DWP(0,$bp)); # bp[0]
149 &movd ($mul1,&DWP(0,$ap)); # ap[0]
150 &movd ($car1,&DWP(0,$np)); # np[0]
152 &pmuludq($mul1,$mul0); # ap[0]*bp[0]
154 &movq ($acc0,$mul1); # I wish movd worked for
155 &pand ($acc0,$mask); # inter-register transfers
157 &pmuludq($mul1,$_n0q); # *=n0
159 &pmuludq($car1,$mul1); # "t[0]"*np[0]*n0
160 &paddq ($car1,$acc0);
162 &movd ($acc1,&DWP(4,$np)); # np[1]
163 &movd ($acc0,&DWP(4,$ap)); # ap[1]
169 &set_label("1st",16);
170 &pmuludq($acc0,$mul0); # ap[j]*bp[0]
171 &pmuludq($acc1,$mul1); # np[j]*m1
172 &paddq ($car0,$acc0); # +=c0
173 &paddq ($car1,$acc1); # +=c1
177 &movd ($acc1,&DWP(4,$np,$j,4)); # np[j+1]
178 &paddq ($car1,$acc0); # +=ap[j]*bp[0];
179 &movd ($acc0,&DWP(4,$ap,$j,4)); # ap[j+1]
181 &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[j-1]=
184 &lea ($j,&DWP(1,$j));
188 &pmuludq($acc0,$mul0); # ap[num-1]*bp[0]
189 &pmuludq($acc1,$mul1); # np[num-1]*m1
190 &paddq ($car0,$acc0); # +=c0
191 &paddq ($car1,$acc1); # +=c1
195 &paddq ($car1,$acc0); # +=ap[num-1]*bp[0];
196 &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[num-2]=
201 &paddq ($car1,$car0);
202 &movq (&QWP($frame,"esp",$num,4),$car1); # tp[num].tp[num-1]
208 &movd ($mul0,&DWP(0,$bp,$i,4)); # bp[i]
209 &movd ($mul1,&DWP(0,$ap)); # ap[0]
210 &movd ($temp,&DWP($frame,"esp")); # tp[0]
211 &movd ($car1,&DWP(0,$np)); # np[0]
212 &pmuludq($mul1,$mul0); # ap[0]*bp[i]
214 &paddq ($mul1,$temp); # +=tp[0]
219 &pmuludq($mul1,$_n0q); # *=n0
221 &pmuludq($car1,$mul1);
222 &paddq ($car1,$acc0);
224 &movd ($temp,&DWP($frame+4,"esp")); # tp[1]
225 &movd ($acc1,&DWP(4,$np)); # np[1]
226 &movd ($acc0,&DWP(4,$ap)); # ap[1]
230 &paddq ($car0,$temp); # +=tp[1]
235 &pmuludq($acc0,$mul0); # ap[j]*bp[i]
236 &pmuludq($acc1,$mul1); # np[j]*m1
237 &paddq ($car0,$acc0); # +=c0
238 &paddq ($car1,$acc1); # +=c1
241 &movd ($temp,&DWP($frame+4,"esp",$j,4));# tp[j+1]
243 &movd ($acc1,&DWP(4,$np,$j,4)); # np[j+1]
244 &paddq ($car1,$acc0); # +=ap[j]*bp[i]+tp[j]
245 &movd ($acc0,&DWP(4,$ap,$j,4)); # ap[j+1]
247 &movd (&DWP($frame-4,"esp",$j,4),$car1);# tp[j-1]=
249 &paddq ($car0,$temp); # +=tp[j+1]
252 &lea ($j,&DWP(1,$j)); # j++
253 &jnz (&label("inner"));
256 &pmuludq($acc0,$mul0); # ap[num-1]*bp[i]
257 &pmuludq($acc1,$mul1); # np[num-1]*m1
258 &paddq ($car0,$acc0); # +=c0
259 &paddq ($car1,$acc1); # +=c1
263 &paddq ($car1,$acc0); # +=ap[num-1]*bp[i]+tp[num-1]
264 &movd (&DWP($frame-4,"esp",$j,4),$car1); # tp[num-2]=
268 &movd ($temp,&DWP($frame+4,"esp",$num,4)); # += tp[num]
269 &paddq ($car1,$car0);
270 &paddq ($car1,$temp);
271 &movq (&QWP($frame,"esp",$num,4),$car1); # tp[num].tp[num-1]
273 &lea ($i,&DWP(1,$i)); # i++
275 &jle (&label("outer"));
277 &emms (); # done with mmx bank
278 &jmp (&label("common_tail"));
280 &set_label("non_sse2",16);
285 &xor ("eax","eax"); # signal "not fast enough [yet]"
286 &jmp (&label("just_leave"));
287 # While the below code provides competitive performance for
288 # all key lengthes on modern Intel cores, it's still more
289 # than 10% slower for 4096-bit key elsewhere:-( "Competitive"
290 # means compared to the original integer-only assembler.
291 # 512-bit RSA sign is better by ~40%, but that's about all
292 # one can say about all CPUs...
294 $inp="esi"; # integer path uses these registers differently
299 &lea ($carry,&DWP(1,$num));
303 &and ($carry,1); # see if num is even
304 &sub ("edx",$word); # see if ap==bp
305 &lea ("eax",&DWP(4,$word,$num,4)); # &bp[num]
307 &mov ($word,&DWP(0,$word)); # bp[0]
308 &jz (&label("bn_sqr_mont"));
309 &mov ($_bpend,"eax");
310 &mov ("eax",&DWP(0,$inp));
313 &set_label("mull",16);
315 &mul ($word); # ap[j]*bp[0]
317 &lea ($j,&DWP(1,$j));
319 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j+1]
321 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
322 &jl (&label("mull"));
325 &mul ($word); # ap[num-1]*bp[0]
330 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
332 &mov (&DWP($frame,"esp",$num,4),"eax"); # tp[num-1]=
334 &mov (&DWP($frame+4,"esp",$num,4),"edx"); # tp[num]=
335 &mov (&DWP($frame+8,"esp",$num,4),$j); # tp[num+1]=
337 &mov ("eax",&DWP(0,$inp)); # np[0]
338 &mul ($word); # np[0]*m
339 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
340 &mov ("eax",&DWP(4,$inp)); # np[1]
344 &jmp (&label("2ndmadd"));
346 &set_label("1stmadd",16);
348 &mul ($word); # ap[j]*bp[i]
349 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
350 &lea ($j,&DWP(1,$j));
353 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j+1]
356 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
357 &jl (&label("1stmadd"));
360 &mul ($word); # ap[num-1]*bp[i]
361 &add ("eax",&DWP($frame,"esp",$num,4)); # +=tp[num-1]
367 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
370 &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num]
371 &mov (&DWP($frame,"esp",$num,4),$carry); # tp[num-1]=
373 &mov ("eax",&DWP(0,$inp)); # np[0]
374 &mov (&DWP($frame+4,"esp",$num,4),"edx"); # tp[num]=
375 &mov (&DWP($frame+8,"esp",$num,4),$j); # tp[num+1]=
377 &mul ($word); # np[0]*m
378 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
379 &mov ("eax",&DWP(4,$inp)); # np[1]
383 &set_label("2ndmadd",16);
385 &mul ($word); # np[j]*m
386 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
387 &lea ($j,&DWP(1,$j));
390 &mov ("eax",&DWP(0,$inp,$j,4)); # np[j+1]
393 &mov (&DWP($frame-8,"esp",$j,4),$carry); # tp[j-1]=
394 &jl (&label("2ndmadd"));
397 &mul ($word); # np[j]*m
398 &add ($carry,&DWP($frame,"esp",$num,4)); # +=tp[num-1]
402 &mov (&DWP($frame-4,"esp",$num,4),$carry); # tp[num-2]=
405 &mov ($j,$_bp); # &bp[i]
406 &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num]
407 &adc ("eax",&DWP($frame+8,"esp",$num,4)); # +=tp[num+1]
408 &lea ($j,&DWP(4,$j));
409 &mov (&DWP($frame,"esp",$num,4),"edx"); # tp[num-1]=
411 &mov (&DWP($frame+4,"esp",$num,4),"eax"); # tp[num]=
412 &je (&label("common_tail"));
414 &mov ($word,&DWP(0,$j)); # bp[i+1]
416 &mov ($_bp,$j); # &bp[++i]
419 &mov ("eax",&DWP(0,$inp));
420 &jmp (&label("1stmadd"));
422 &set_label("bn_sqr_mont",16);
425 &mov ($_bp,$j); # i=0
427 &mov ("eax",$word); # ap[0]
428 &mul ($word); # ap[0]*ap[0]
429 &mov (&DWP($frame,"esp"),"eax"); # tp[0]=
434 &set_label("sqr",16);
435 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j]
437 &mul ($word); # ap[j]*ap[0]
439 &lea ($j,&DWP(1,$j));
441 &lea ($carry,&DWP(0,$sbit,"eax",2));
445 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
448 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[num-1]
450 &mul ($word); # ap[num-1]*ap[0]
455 &lea ($carry,&DWP(0,$sbit,"eax",2));
456 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
458 &mov (&DWP($frame,"esp",$j,4),$carry); # tp[num-1]=
460 &lea ($carry,&DWP(0,"eax","edx",2));
461 &mov ("eax",&DWP(0,$inp)); # np[0]
463 &mov (&DWP($frame+4,"esp",$j,4),$carry); # tp[num]=
464 &mov (&DWP($frame+8,"esp",$j,4),"edx"); # tp[num+1]=
466 &mul ($word); # np[0]*m
467 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
470 &mov ("eax",&DWP(4,$inp)); # np[1]
473 &set_label("3rdmadd",16);
475 &mul ($word); # np[j]*m
476 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
479 &mov ("eax",&DWP(4,$inp,$j,4)); # np[j+1]
481 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j-1]=
484 &mul ($word); # np[j+1]*m
485 &add ($carry,&DWP($frame+4,"esp",$j,4)); # +=tp[j+1]
486 &lea ($j,&DWP(2,$j));
489 &mov ("eax",&DWP(0,$inp,$j,4)); # np[j+2]
492 &mov (&DWP($frame-8,"esp",$j,4),$carry); # tp[j]=
493 &jl (&label("3rdmadd"));
496 &mul ($word); # np[j]*m
497 &add ($carry,&DWP($frame,"esp",$num,4)); # +=tp[num-1]
501 &mov (&DWP($frame-4,"esp",$num,4),$carry); # tp[num-2]=
506 &add ("edx",&DWP($frame+4,"esp",$num,4)); # carry+=tp[num]
507 &adc ("eax",&DWP($frame+8,"esp",$num,4)); # +=tp[num+1]
508 &mov (&DWP($frame,"esp",$num,4),"edx"); # tp[num-1]=
510 &mov (&DWP($frame+4,"esp",$num,4),"eax"); # tp[num]=
511 &je (&label("common_tail"));
513 &mov ($word,&DWP(4,$inp,$j,4)); # ap[i]
514 &lea ($j,&DWP(1,$j));
516 &mov ($_bp,$j); # ++i
517 &mul ($word); # ap[i]*ap[i]
518 &add ("eax",&DWP($frame,"esp",$j,4)); # +=tp[i]
520 &mov (&DWP($frame,"esp",$j,4),"eax"); # tp[i]=
521 &xor ($carry,$carry);
523 &lea ($j,&DWP(1,$j));
524 &je (&label("sqrlast"));
526 &mov ($sbit,"edx"); # zaps $num
529 &set_label("sqradd",16);
530 &mov ("eax",&DWP(0,$inp,$j,4)); # ap[j]
532 &mul ($word); # ap[j]*ap[i]
534 &lea ($carry,&DWP(0,"eax","eax"));
537 &add ($carry,&DWP($frame,"esp",$j,4)); # +=tp[j]
538 &lea ($j,&DWP(1,$j));
543 &mov (&DWP($frame-4,"esp",$j,4),$carry); # tp[j]=
545 &jle (&label("sqradd"));
552 &set_label("sqrlast");
555 &imul ($word,&DWP($frame,"esp")); # n0*tp[0]
557 &add ("edx",&DWP($frame,"esp",$j,4)); # +=tp[num]
558 &mov ("eax",&DWP(0,$inp)); # np[0]
560 &mov (&DWP($frame,"esp",$j,4),"edx"); # tp[num]=
561 &mov (&DWP($frame+4,"esp",$j,4),$carry); # tp[num+1]=
563 &mul ($word); # np[0]*m
564 &add ("eax",&DWP($frame,"esp")); # +=tp[0]
565 &lea ($num,&DWP(-1,$j));
568 &mov ("eax",&DWP(4,$inp)); # np[1]
570 &jmp (&label("3rdmadd"));
573 &set_label("common_tail",16);
574 &mov ($np,$_np); # load modulus pointer
575 &mov ($rp,$_rp); # load result pointer
576 &lea ($tp,&DWP($frame,"esp")); # [$ap and $bp are zapped]
578 &mov ("eax",&DWP(0,$tp)); # tp[0]
579 &mov ($j,$num); # j=num-1
580 &xor ($i,$i); # i=0 and clear CF!
582 &set_label("sub",16);
583 &sbb ("eax",&DWP(0,$np,$i,4));
584 &mov (&DWP(0,$rp,$i,4),"eax"); # rp[i]=tp[i]-np[i]
585 &dec ($j); # doesn't affect CF!
586 &mov ("eax",&DWP(4,$tp,$i,4)); # tp[i+1]
587 &lea ($i,&DWP(1,$i)); # i++
588 &jge (&label("sub"));
590 &sbb ("eax",0); # handle upmost overflow bit
595 &or ($tp,$np); # tp=carry?tp:rp
597 &set_label("copy",16); # copy or in-place refresh
598 &mov ("eax",&DWP(0,$tp,$num,4));
599 &mov (&DWP(0,$rp,$num,4),"eax"); # rp[i]=tp[i]
600 &mov (&DWP($frame,"esp",$num,4),$j); # zap temporary vector
602 &jge (&label("copy"));
604 &mov ("esp",$_sp); # pull saved stack pointer
606 &set_label("just_leave");
607 &function_end("bn_mul_mont");
609 &asciz("Montgomery Multiplication for x86, CRYPTOGAMS by <appro\@openssl.org>");