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      1 #!/usr/bin/env perl
      2 
      3 # ====================================================================
      4 # Written by Andy Polyakov <appro (at] 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 # ====================================================================
      9 
     10 # October 2005
     11 #
     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%:-)
     22 
     23 # December 2006
     24 #
     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...
     28 
     29 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
     30 push(@INC,"${dir}","${dir}../../perlasm");
     31 require "x86asm.pl";
     32 
     33 &asm_init($ARGV[0],$0);
     34 
     35 $sse2=0;
     36 for (@ARGV) { $sse2=1 if (/-DOPENSSL_IA32_SSE2/); }
     37 
     38 &external_label("OPENSSL_ia32cap_P") if ($sse2);
     39 
     40 &function_begin("bn_mul_mont");
     41 
     42 $i="edx";
     43 $j="ecx";
     44 $ap="esi";	$tp="esi";		# overlapping variables!!!
     45 $rp="edi";	$bp="edi";		# overlapping variables!!!
     46 $np="ebp";
     47 $num="ebx";
     48 
     49 $_num=&DWP(4*0,"esp");			# stack top layout
     50 $_rp=&DWP(4*1,"esp");
     51 $_ap=&DWP(4*2,"esp");
     52 $_bp=&DWP(4*3,"esp");
     53 $_np=&DWP(4*4,"esp");
     54 $_n0=&DWP(4*5,"esp");	$_n0q=&QWP(4*5,"esp");
     55 $_sp=&DWP(4*6,"esp");
     56 $_bpend=&DWP(4*7,"esp");
     57 $frame=32;				# size of above frame rounded up to 16n
     58 
     59 	&xor	("eax","eax");
     60 	&mov	("edi",&wparam(5));	# int num
     61 	&cmp	("edi",4);
     62 	&jl	(&label("just_leave"));
     63 
     64 	&lea	("esi",&wparam(0));	# put aside pointer to argument block
     65 	&lea	("edx",&wparam(1));	# load ap
     66 	&mov	("ebp","esp");		# saved stack pointer!
     67 	&add	("edi",2);		# extra two words on top of tp
     68 	&neg	("edi");
     69 	&lea	("esp",&DWP(-$frame,"esp","edi",4));	# alloca($frame+4*(num+2))
     70 	&neg	("edi");
     71 
     72 	# minimize cache contention by arraning 2K window between stack
     73 	# pointer and ap argument [np is also position sensitive vector,
     74 	# but it's assumed to be near ap, as it's allocated at ~same
     75 	# time].
     76 	&mov	("eax","esp");
     77 	&sub	("eax","edx");
     78 	&and	("eax",2047);
     79 	&sub	("esp","eax");		# this aligns sp and ap modulo 2048
     80 
     81 	&xor	("edx","esp");
     82 	&and	("edx",2048);
     83 	&xor	("edx",2048);
     84 	&sub	("esp","edx");		# this splits them apart modulo 4096
     85 
     86 	&and	("esp",-64);		# align to cache line
     87 
     88 	################################# load argument block...
     89 	&mov	("eax",&DWP(0*4,"esi"));# BN_ULONG *rp
     90 	&mov	("ebx",&DWP(1*4,"esi"));# const BN_ULONG *ap
     91 	&mov	("ecx",&DWP(2*4,"esi"));# const BN_ULONG *bp
     92 	&mov	("edx",&DWP(3*4,"esi"));# const BN_ULONG *np
     93 	&mov	("esi",&DWP(4*4,"esi"));# const BN_ULONG *n0
     94 	#&mov	("edi",&DWP(5*4,"esi"));# int num
     95 
     96 	&mov	("esi",&DWP(0,"esi"));	# pull n0[0]
     97 	&mov	($_rp,"eax");		# ... save a copy of argument block
     98 	&mov	($_ap,"ebx");
     99 	&mov	($_bp,"ecx");
    100 	&mov	($_np,"edx");
    101 	&mov	($_n0,"esi");
    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!
    105 
    107 if($sse2) {
    108 $acc0="mm0";	# mmx register bank layout
    109 $acc1="mm1";
    110 $car0="mm2";
    111 $car1="mm3";
    112 $mul0="mm4";
    113 $mul1="mm5";
    114 $temp="mm6";
    115 $mask="mm7";
    116 
    117 	&picmeup("eax","OPENSSL_ia32cap_P");
    118 	&bt	(&DWP(0,"eax"),26);
    119 	&jnc	(&label("non_sse2"));
    120 
    121 	&mov	("eax",-1);
    122 	&movd	($mask,"eax");		# mask 32 lower bits
    123 
    124 	&mov	($ap,$_ap);		# load input pointers
    125 	&mov	($bp,$_bp);
    126 	&mov	($np,$_np);
    127 
    128 	&xor	($i,$i);		# i=0
    129 	&xor	($j,$j);		# j=0
    130 
    131 	&movd	($mul0,&DWP(0,$bp));		# bp[0]
    132 	&movd	($mul1,&DWP(0,$ap));		# ap[0]
    133 	&movd	($car1,&DWP(0,$np));		# np[0]
    134 
    135 	&pmuludq($mul1,$mul0);			# ap[0]*bp[0]
    136 	&movq	($car0,$mul1);
    137 	&movq	($acc0,$mul1);			# I wish movd worked for
    138 	&pand	($acc0,$mask);			# inter-register transfers
    139 
    140 	&pmuludq($mul1,$_n0q);			# *=n0
    141 
    142 	&pmuludq($car1,$mul1);			# "t[0]"*np[0]*n0
    143 	&paddq	($car1,$acc0);
    144 
    145 	&movd	($acc1,&DWP(4,$np));		# np[1]
    146 	&movd	($acc0,&DWP(4,$ap));		# ap[1]
    147 
    148 	&psrlq	($car0,32);
    149 	&psrlq	($car1,32);
    150 
    151 	&inc	($j);				# j++
    152 &set_label("1st",16);
    153 	&pmuludq($acc0,$mul0);			# ap[j]*bp[0]
    154 	&pmuludq($acc1,$mul1);			# np[j]*m1
    155 	&paddq	($car0,$acc0);			# +=c0
    156 	&paddq	($car1,$acc1);			# +=c1
    157 
    158 	&movq	($acc0,$car0);
    159 	&pand	($acc0,$mask);
    160 	&movd	($acc1,&DWP(4,$np,$j,4));	# np[j+1]
    161 	&paddq	($car1,$acc0);			# +=ap[j]*bp[0];
    162 	&movd	($acc0,&DWP(4,$ap,$j,4));	# ap[j+1]
    163 	&psrlq	($car0,32);
    164 	&movd	(&DWP($frame-4,"esp",$j,4),$car1);	# tp[j-1]=
    165 	&psrlq	($car1,32);
    166 
    167 	&lea	($j,&DWP(1,$j));
    168 	&cmp	($j,$num);
    169 	&jl	(&label("1st"));
    170 
    171 	&pmuludq($acc0,$mul0);			# ap[num-1]*bp[0]
    172 	&pmuludq($acc1,$mul1);			# np[num-1]*m1
    173 	&paddq	($car0,$acc0);			# +=c0
    174 	&paddq	($car1,$acc1);			# +=c1
    175 
    176 	&movq	($acc0,$car0);
    177 	&pand	($acc0,$mask);
    178 	&paddq	($car1,$acc0);			# +=ap[num-1]*bp[0];
    179 	&movd	(&DWP($frame-4,"esp",$j,4),$car1);	# tp[num-2]=
    180 
    181 	&psrlq	($car0,32);
    182 	&psrlq	($car1,32);
    183 
    184 	&paddq	($car1,$car0);
    185 	&movq	(&QWP($frame,"esp",$num,4),$car1);	# tp[num].tp[num-1]
    186 
    188 	&inc	($i);				# i++
    189 &set_label("outer");
    190 	&xor	($j,$j);			# j=0
    191 
    192 	&movd	($mul0,&DWP(0,$bp,$i,4));	# bp[i]
    193 	&movd	($mul1,&DWP(0,$ap));		# ap[0]
    194 	&movd	($temp,&DWP($frame,"esp"));	# tp[0]
    195 	&movd	($car1,&DWP(0,$np));		# np[0]
    196 	&pmuludq($mul1,$mul0);			# ap[0]*bp[i]
    197 
    198 	&paddq	($mul1,$temp);			# +=tp[0]
    199 	&movq	($acc0,$mul1);
    200 	&movq	($car0,$mul1);
    201 	&pand	($acc0,$mask);
    202 
    203 	&pmuludq($mul1,$_n0q);			# *=n0
    204 
    205 	&pmuludq($car1,$mul1);
    206 	&paddq	($car1,$acc0);
    207 
    208 	&movd	($temp,&DWP($frame+4,"esp"));	# tp[1]
    209 	&movd	($acc1,&DWP(4,$np));		# np[1]
    210 	&movd	($acc0,&DWP(4,$ap));		# ap[1]
    211 
    212 	&psrlq	($car0,32);
    213 	&psrlq	($car1,32);
    214 	&paddq	($car0,$temp);			# +=tp[1]
    215 
    216 	&inc	($j);				# j++
    217 	&dec	($num);
    218 &set_label("inner");
    219 	&pmuludq($acc0,$mul0);			# ap[j]*bp[i]
    220 	&pmuludq($acc1,$mul1);			# np[j]*m1
    221 	&paddq	($car0,$acc0);			# +=c0
    222 	&paddq	($car1,$acc1);			# +=c1
    223 
    224 	&movq	($acc0,$car0);
    225 	&movd	($temp,&DWP($frame+4,"esp",$j,4));# tp[j+1]
    226 	&pand	($acc0,$mask);
    227 	&movd	($acc1,&DWP(4,$np,$j,4));	# np[j+1]
    228 	&paddq	($car1,$acc0);			# +=ap[j]*bp[i]+tp[j]
    229 	&movd	($acc0,&DWP(4,$ap,$j,4));	# ap[j+1]
    230 	&psrlq	($car0,32);
    231 	&movd	(&DWP($frame-4,"esp",$j,4),$car1);# tp[j-1]=
    232 	&psrlq	($car1,32);
    233 	&paddq	($car0,$temp);			# +=tp[j+1]
    234 
    235 	&dec	($num);
    236 	&lea	($j,&DWP(1,$j));		# j++
    237 	&jnz	(&label("inner"));
    238 
    239 	&mov	($num,$j);
    240 	&pmuludq($acc0,$mul0);			# ap[num-1]*bp[i]
    241 	&pmuludq($acc1,$mul1);			# np[num-1]*m1
    242 	&paddq	($car0,$acc0);			# +=c0
    243 	&paddq	($car1,$acc1);			# +=c1
    244 
    245 	&movq	($acc0,$car0);
    246 	&pand	($acc0,$mask);
    247 	&paddq	($car1,$acc0);			# +=ap[num-1]*bp[i]+tp[num-1]
    248 	&movd	(&DWP($frame-4,"esp",$j,4),$car1);	# tp[num-2]=
    249 	&psrlq	($car0,32);
    250 	&psrlq	($car1,32);
    251 
    252 	&movd	($temp,&DWP($frame+4,"esp",$num,4));	# += tp[num]
    253 	&paddq	($car1,$car0);
    254 	&paddq	($car1,$temp);
    255 	&movq	(&QWP($frame,"esp",$num,4),$car1);	# tp[num].tp[num-1]
    256 
    257 	&lea	($i,&DWP(1,$i));		# i++
    258 	&cmp	($i,$num);
    259 	&jle	(&label("outer"));
    260 
    261 	&emms	();				# done with mmx bank
    262 	&jmp	(&label("common_tail"));
    263 
    264 &set_label("non_sse2",16);
    265 }
    266 
    268 if (0) {
    269 	&mov	("esp",$_sp);
    270 	&xor	("eax","eax");	# signal "not fast enough [yet]"
    271 	&jmp	(&label("just_leave"));
    272 	# While the below code provides competitive performance for
    273 	# all key lengthes on modern Intel cores, it's still more
    274 	# than 10% slower for 4096-bit key elsewhere:-( "Competitive"
    275 	# means compared to the original integer-only assembler.
    276 	# 512-bit RSA sign is better by ~40%, but that's about all
    277 	# one can say about all CPUs...
    278 } else {
    279 $inp="esi";	# integer path uses these registers differently
    280 $word="edi";
    281 $carry="ebp";
    282 
    283 	&mov	($inp,$_ap);
    284 	&lea	($carry,&DWP(1,$num));
    285 	&mov	($word,$_bp);
    286 	&xor	($j,$j);				# j=0
    287 	&mov	("edx",$inp);
    288 	&and	($carry,1);				# see if num is even
    289 	&sub	("edx",$word);				# see if ap==bp
    290 	&lea	("eax",&DWP(4,$word,$num,4));		# &bp[num]
    291 	&or	($carry,"edx");
    292 	&mov	($word,&DWP(0,$word));			# bp[0]
    293 	&jz	(&label("bn_sqr_mont"));
    294 	&mov	($_bpend,"eax");
    295 	&mov	("eax",&DWP(0,$inp));
    296 	&xor	("edx","edx");
    297 
    298 &set_label("mull",16);
    299 	&mov	($carry,"edx");
    300 	&mul	($word);				# ap[j]*bp[0]
    301 	&add	($carry,"eax");
    302 	&lea	($j,&DWP(1,$j));
    303 	&adc	("edx",0);
    304 	&mov	("eax",&DWP(0,$inp,$j,4));		# ap[j+1]
    305 	&cmp	($j,$num);
    306 	&mov	(&DWP($frame-4,"esp",$j,4),$carry);	# tp[j]=
    307 	&jl	(&label("mull"));
    308 
    309 	&mov	($carry,"edx");
    310 	&mul	($word);				# ap[num-1]*bp[0]
    311 	 &mov	($word,$_n0);
    312 	&add	("eax",$carry);
    313 	 &mov	($inp,$_np);
    314 	&adc	("edx",0);
    315 	 &imul	($word,&DWP($frame,"esp"));		# n0*tp[0]
    316 
    317 	&mov	(&DWP($frame,"esp",$num,4),"eax");	# tp[num-1]=
    318 	&xor	($j,$j);
    319 	&mov	(&DWP($frame+4,"esp",$num,4),"edx");	# tp[num]=
    320 	&mov	(&DWP($frame+8,"esp",$num,4),$j);	# tp[num+1]=
    321 
    322 	&mov	("eax",&DWP(0,$inp));			# np[0]
    323 	&mul	($word);				# np[0]*m
    324 	&add	("eax",&DWP($frame,"esp"));		# +=tp[0]
    325 	&mov	("eax",&DWP(4,$inp));			# np[1]
    326 	&adc	("edx",0);
    327 	&inc	($j);
    328 
    329 	&jmp	(&label("2ndmadd"));
    330 
    333 &set_label("1stmadd",16);
    334 	&mov	($carry,"edx");
    335 	&mul	($word);				# ap[j]*bp[i]
    336 	&add	($carry,&DWP($frame,"esp",$j,4));	# +=tp[j]
    337 	&lea	($j,&DWP(1,$j));
    338 	&adc	("edx",0);
    339 	&add	($carry,"eax");
    340 	&mov	("eax",&DWP(0,$inp,$j,4));		# ap[j+1]
    341 	&adc	("edx",0);
    342 	&cmp	($j,$num);
    343 	&mov	(&DWP($frame-4,"esp",$j,4),$carry);	# tp[j]=
    344 	&jl	(&label("1stmadd"));
    345 
    346 	&mov	($carry,"edx");
    347 	&mul	($word);				# ap[num-1]*bp[i]
    348 	&add	("eax",&DWP($frame,"esp",$num,4));	# +=tp[num-1]
    349 	 &mov	($word,$_n0);
    350 	&adc	("edx",0);
    351 	 &mov	($inp,$_np);
    352 	&add	($carry,"eax");
    353 	&adc	("edx",0);
    354 	 &imul	($word,&DWP($frame,"esp"));		# n0*tp[0]
    355 
    356 	&xor	($j,$j);
    357 	&add	("edx",&DWP($frame+4,"esp",$num,4));	# carry+=tp[num]
    358 	&mov	(&DWP($frame,"esp",$num,4),$carry);	# tp[num-1]=
    359 	&adc	($j,0);
    360 	 &mov	("eax",&DWP(0,$inp));			# np[0]
    361 	&mov	(&DWP($frame+4,"esp",$num,4),"edx");	# tp[num]=
    362 	&mov	(&DWP($frame+8,"esp",$num,4),$j);	# tp[num+1]=
    363 
    364 	&mul	($word);				# np[0]*m
    365 	&add	("eax",&DWP($frame,"esp"));		# +=tp[0]
    366 	&mov	("eax",&DWP(4,$inp));			# np[1]
    367 	&adc	("edx",0);
    368 	&mov	($j,1);
    369 
    371 &set_label("2ndmadd",16);
    372 	&mov	($carry,"edx");
    373 	&mul	($word);				# np[j]*m
    374 	&add	($carry,&DWP($frame,"esp",$j,4));	# +=tp[j]
    375 	&lea	($j,&DWP(1,$j));
    376 	&adc	("edx",0);
    377 	&add	($carry,"eax");
    378 	&mov	("eax",&DWP(0,$inp,$j,4));		# np[j+1]
    379 	&adc	("edx",0);
    380 	&cmp	($j,$num);
    381 	&mov	(&DWP($frame-8,"esp",$j,4),$carry);	# tp[j-1]=
    382 	&jl	(&label("2ndmadd"));
    383 
    384 	&mov	($carry,"edx");
    385 	&mul	($word);				# np[j]*m
    386 	&add	($carry,&DWP($frame,"esp",$num,4));	# +=tp[num-1]
    387 	&adc	("edx",0);
    388 	&add	($carry,"eax");
    389 	&adc	("edx",0);
    390 	&mov	(&DWP($frame-4,"esp",$num,4),$carry);	# tp[num-2]=
    391 
    392 	&xor	("eax","eax");
    393 	 &mov	($j,$_bp);				# &bp[i]
    394 	&add	("edx",&DWP($frame+4,"esp",$num,4));	# carry+=tp[num]
    395 	&adc	("eax",&DWP($frame+8,"esp",$num,4));	# +=tp[num+1]
    396 	 &lea	($j,&DWP(4,$j));
    397 	&mov	(&DWP($frame,"esp",$num,4),"edx");	# tp[num-1]=
    398 	 &cmp	($j,$_bpend);
    399 	&mov	(&DWP($frame+4,"esp",$num,4),"eax");	# tp[num]=
    400 	&je	(&label("common_tail"));
    401 
    402 	&mov	($word,&DWP(0,$j));			# bp[i+1]
    403 	&mov	($inp,$_ap);
    404 	&mov	($_bp,$j);				# &bp[++i]
    405 	&xor	($j,$j);
    406 	&xor	("edx","edx");
    407 	&mov	("eax",&DWP(0,$inp));
    408 	&jmp	(&label("1stmadd"));
    409 
    411 &set_label("bn_sqr_mont",16);
    412 $sbit=$num;
    413 	&mov	($_num,$num);
    414 	&mov	($_bp,$j);				# i=0
    415 
    416 	&mov	("eax",$word);				# ap[0]
    417 	&mul	($word);				# ap[0]*ap[0]
    418 	&mov	(&DWP($frame,"esp"),"eax");		# tp[0]=
    419 	&mov	($sbit,"edx");
    420 	&shr	("edx",1);
    421 	&and	($sbit,1);
    422 	&inc	($j);
    423 &set_label("sqr",16);
    424 	&mov	("eax",&DWP(0,$inp,$j,4));		# ap[j]
    425 	&mov	($carry,"edx");
    426 	&mul	($word);				# ap[j]*ap[0]
    427 	&add	("eax",$carry);
    428 	&lea	($j,&DWP(1,$j));
    429 	&adc	("edx",0);
    430 	&lea	($carry,&DWP(0,$sbit,"eax",2));
    431 	&shr	("eax",31);
    432 	&cmp	($j,$_num);
    433 	&mov	($sbit,"eax");
    434 	&mov	(&DWP($frame-4,"esp",$j,4),$carry);	# tp[j]=
    435 	&jl	(&label("sqr"));
    436 
    437 	&mov	("eax",&DWP(0,$inp,$j,4));		# ap[num-1]
    438 	&mov	($carry,"edx");
    439 	&mul	($word);				# ap[num-1]*ap[0]
    440 	&add	("eax",$carry);
    441 	 &mov	($word,$_n0);
    442 	&adc	("edx",0);
    443 	 &mov	($inp,$_np);
    444 	&lea	($carry,&DWP(0,$sbit,"eax",2));
    445 	 &imul	($word,&DWP($frame,"esp"));		# n0*tp[0]
    446 	&shr	("eax",31);
    447 	&mov	(&DWP($frame,"esp",$j,4),$carry);	# tp[num-1]=
    448 
    449 	&lea	($carry,&DWP(0,"eax","edx",2));
    450 	 &mov	("eax",&DWP(0,$inp));			# np[0]
    451 	&shr	("edx",31);
    452 	&mov	(&DWP($frame+4,"esp",$j,4),$carry);	# tp[num]=
    453 	&mov	(&DWP($frame+8,"esp",$j,4),"edx");	# tp[num+1]=
    454 
    455 	&mul	($word);				# np[0]*m
    456 	&add	("eax",&DWP($frame,"esp"));		# +=tp[0]
    457 	&mov	($num,$j);
    458 	&adc	("edx",0);
    459 	&mov	("eax",&DWP(4,$inp));			# np[1]
    460 	&mov	($j,1);
    461 
    464 &set_label("3rdmadd",16);
    465 	&mov	($carry,"edx");
    466 	&mul	($word);				# np[j]*m
    467 	&add	($carry,&DWP($frame,"esp",$j,4));	# +=tp[j]
    468 	&adc	("edx",0);
    469 	&add	($carry,"eax");
    470 	&mov	("eax",&DWP(4,$inp,$j,4));		# np[j+1]
    471 	&adc	("edx",0);
    472 	&mov	(&DWP($frame-4,"esp",$j,4),$carry);	# tp[j-1]=
    473 
    474 	&mov	($carry,"edx");
    475 	&mul	($word);				# np[j+1]*m
    476 	&add	($carry,&DWP($frame+4,"esp",$j,4));	# +=tp[j+1]
    477 	&lea	($j,&DWP(2,$j));
    478 	&adc	("edx",0);
    479 	&add	($carry,"eax");
    480 	&mov	("eax",&DWP(0,$inp,$j,4));		# np[j+2]
    481 	&adc	("edx",0);
    482 	&cmp	($j,$num);
    483 	&mov	(&DWP($frame-8,"esp",$j,4),$carry);	# tp[j]=
    484 	&jl	(&label("3rdmadd"));
    485 
    486 	&mov	($carry,"edx");
    487 	&mul	($word);				# np[j]*m
    488 	&add	($carry,&DWP($frame,"esp",$num,4));	# +=tp[num-1]
    489 	&adc	("edx",0);
    490 	&add	($carry,"eax");
    491 	&adc	("edx",0);
    492 	&mov	(&DWP($frame-4,"esp",$num,4),$carry);	# tp[num-2]=
    493 
    494 	&mov	($j,$_bp);				# i
    495 	&xor	("eax","eax");
    496 	&mov	($inp,$_ap);
    497 	&add	("edx",&DWP($frame+4,"esp",$num,4));	# carry+=tp[num]
    498 	&adc	("eax",&DWP($frame+8,"esp",$num,4));	# +=tp[num+1]
    499 	&mov	(&DWP($frame,"esp",$num,4),"edx");	# tp[num-1]=
    500 	&cmp	($j,$num);
    501 	&mov	(&DWP($frame+4,"esp",$num,4),"eax");	# tp[num]=
    502 	&je	(&label("common_tail"));
    503 
    505 	&mov	($word,&DWP(4,$inp,$j,4));		# ap[i]
    506 	&lea	($j,&DWP(1,$j));
    507 	&mov	("eax",$word);
    508 	&mov	($_bp,$j);				# ++i
    509 	&mul	($word);				# ap[i]*ap[i]
    510 	&add	("eax",&DWP($frame,"esp",$j,4));	# +=tp[i]
    511 	&adc	("edx",0);
    512 	&mov	(&DWP($frame,"esp",$j,4),"eax");	# tp[i]=
    513 	&xor	($carry,$carry);
    514 	&cmp	($j,$num);
    515 	&lea	($j,&DWP(1,$j));
    516 	&je	(&label("sqrlast"));
    517 
    518 	&mov	($sbit,"edx");				# zaps $num
    519 	&shr	("edx",1);
    520 	&and	($sbit,1);
    521 &set_label("sqradd",16);
    522 	&mov	("eax",&DWP(0,$inp,$j,4));		# ap[j]
    523 	&mov	($carry,"edx");
    524 	&mul	($word);				# ap[j]*ap[i]
    525 	&add	("eax",$carry);
    526 	&lea	($carry,&DWP(0,"eax","eax"));
    527 	&adc	("edx",0);
    528 	&shr	("eax",31);
    529 	&add	($carry,&DWP($frame,"esp",$j,4));	# +=tp[j]
    530 	&lea	($j,&DWP(1,$j));
    531 	&adc	("eax",0);
    532 	&add	($carry,$sbit);
    533 	&adc	("eax",0);
    534 	&cmp	($j,$_num);
    535 	&mov	(&DWP($frame-4,"esp",$j,4),$carry);	# tp[j]=
    536 	&mov	($sbit,"eax");
    537 	&jle	(&label("sqradd"));
    538 
    539 	&mov	($carry,"edx");
    540 	&add	("edx","edx");
    541 	&shr	($carry,31);
    542 	&add	("edx",$sbit);
    543 	&adc	($carry,0);
    544 &set_label("sqrlast");
    545 	&mov	($word,$_n0);
    546 	&mov	($inp,$_np);
    547 	&imul	($word,&DWP($frame,"esp"));		# n0*tp[0]
    548 
    549 	&add	("edx",&DWP($frame,"esp",$j,4));	# +=tp[num]
    550 	&mov	("eax",&DWP(0,$inp));			# np[0]
    551 	&adc	($carry,0);
    552 	&mov	(&DWP($frame,"esp",$j,4),"edx");	# tp[num]=
    553 	&mov	(&DWP($frame+4,"esp",$j,4),$carry);	# tp[num+1]=
    554 
    555 	&mul	($word);				# np[0]*m
    556 	&add	("eax",&DWP($frame,"esp"));		# +=tp[0]
    557 	&lea	($num,&DWP(-1,$j));
    558 	&adc	("edx",0);
    559 	&mov	($j,1);
    560 	&mov	("eax",&DWP(4,$inp));			# np[1]
    561 
    562 	&jmp	(&label("3rdmadd"));
    563 }
    564 
    566 &set_label("common_tail",16);
    567 	&mov	($np,$_np);			# load modulus pointer
    568 	&mov	($rp,$_rp);			# load result pointer
    569 	&lea	($tp,&DWP($frame,"esp"));	# [$ap and $bp are zapped]
    570 
    571 	&mov	("eax",&DWP(0,$tp));		# tp[0]
    572 	&mov	($j,$num);			# j=num-1
    573 	&xor	($i,$i);			# i=0 and clear CF!
    574 
    575 &set_label("sub",16);
    576 	&sbb	("eax",&DWP(0,$np,$i,4));
    577 	&mov	(&DWP(0,$rp,$i,4),"eax");	# rp[i]=tp[i]-np[i]
    578 	&dec	($j);				# doesn't affect CF!
    579 	&mov	("eax",&DWP(4,$tp,$i,4));	# tp[i+1]
    580 	&lea	($i,&DWP(1,$i));		# i++
    581 	&jge	(&label("sub"));
    582 
    583 	&sbb	("eax",0);			# handle upmost overflow bit
    584 	&and	($tp,"eax");
    585 	&not	("eax");
    586 	&mov	($np,$rp);
    587 	&and	($np,"eax");
    588 	&or	($tp,$np);			# tp=carry?tp:rp
    589 
    590 &set_label("copy",16);				# copy or in-place refresh
    591 	&mov	("eax",&DWP(0,$tp,$num,4));
    592 	&mov	(&DWP(0,$rp,$num,4),"eax");	# rp[i]=tp[i]
    593 	&mov	(&DWP($frame,"esp",$num,4),$j);	# zap temporary vector
    594 	&dec	($num);
    595 	&jge	(&label("copy"));
    596 
    597 	&mov	("esp",$_sp);		# pull saved stack pointer
    598 	&mov	("eax",1);
    599 &set_label("just_leave");
    600 &function_end("bn_mul_mont");
    601 
    602 &asciz("Montgomery Multiplication for x86, CRYPTOGAMS by <appro\@openssl.org>");
    603 
    604 &asm_finish();
    605