3 # Implemented as a Perl wrapper as we want to support several different
4 # architectures with single file. We pick up the target based on the
5 # file name we are asked to generate.
7 # It should be noted though that this perl code is nothing like
8 # <openssl>/crypto/perlasm/x86*. In this case perl is used pretty much
9 # as pre-processor to cover for platform differences in name decoration,
10 # linker tables, 32-/64-bit instruction sets...
12 # As you might know there're several PowerPC ABI in use. Most notably
13 # Linux and AIX use different 32-bit ABIs. Good news are that these ABIs
14 # are similar enough to implement leaf(!) functions, which would be ABI
15 # neutral. And that's what you find here: ABI neutral leaf functions.
16 # In case you wonder what that is...
20 # MEASUREMENTS WITH cc ON a 200 MhZ PowerPC 604e.
22 # The following is the performance of 32-bit compiler
25 # OpenSSL 0.9.6c 21 dec 2001
26 # built on: Tue Jun 11 11:06:51 EDT 2002
27 # options:bn(64,32) ...
28 #compiler: cc -DTHREADS -DAIX -DB_ENDIAN -DBN_LLONG -O3
29 # sign verify sign/s verify/s
30 #rsa 512 bits 0.0098s 0.0009s 102.0 1170.6
31 #rsa 1024 bits 0.0507s 0.0026s 19.7 387.5
32 #rsa 2048 bits 0.3036s 0.0085s 3.3 117.1
33 #rsa 4096 bits 2.0040s 0.0299s 0.5 33.4
34 #dsa 512 bits 0.0087s 0.0106s 114.3 94.5
35 #dsa 1024 bits 0.0256s 0.0313s 39.0 32.0
37 # Same bechmark with this assembler code:
39 #rsa 512 bits 0.0056s 0.0005s 178.6 2049.2
40 #rsa 1024 bits 0.0283s 0.0015s 35.3 674.1
41 #rsa 2048 bits 0.1744s 0.0050s 5.7 201.2
42 #rsa 4096 bits 1.1644s 0.0179s 0.9 55.7
43 #dsa 512 bits 0.0052s 0.0062s 191.6 162.0
44 #dsa 1024 bits 0.0149s 0.0180s 67.0 55.5
46 # Number of operations increases by at almost 75%
48 # Here are performance numbers for 64-bit compiler
51 # OpenSSL 0.9.6g [engine] 9 Aug 2002
52 # built on: Fri Apr 18 16:59:20 EDT 2003
53 # options:bn(64,64) ...
54 # compiler: cc -DTHREADS -D_REENTRANT -q64 -DB_ENDIAN -O3
55 # sign verify sign/s verify/s
56 #rsa 512 bits 0.0028s 0.0003s 357.1 3844.4
57 #rsa 1024 bits 0.0148s 0.0008s 67.5 1239.7
58 #rsa 2048 bits 0.0963s 0.0028s 10.4 353.0
59 #rsa 4096 bits 0.6538s 0.0102s 1.5 98.1
60 #dsa 512 bits 0.0026s 0.0032s 382.5 313.7
61 #dsa 1024 bits 0.0081s 0.0099s 122.8 100.6
63 # Same benchmark with this assembler code:
65 #rsa 512 bits 0.0020s 0.0002s 510.4 6273.7
66 #rsa 1024 bits 0.0088s 0.0005s 114.1 2128.3
67 #rsa 2048 bits 0.0540s 0.0016s 18.5 622.5
68 #rsa 4096 bits 0.3700s 0.0058s 2.7 171.0
69 #dsa 512 bits 0.0016s 0.0020s 610.7 507.1
70 #dsa 1024 bits 0.0047s 0.0058s 212.5 173.2
72 # Again, performance increases by at about 75%
74 # Mac OS X, Apple G5 1.8GHz (Note this is 32 bit code)
75 # OpenSSL 0.9.7c 30 Sep 2003
79 #rsa 512 bits 0.0011s 0.0001s 906.1 11012.5
80 #rsa 1024 bits 0.0060s 0.0003s 166.6 3363.1
81 #rsa 2048 bits 0.0370s 0.0010s 27.1 982.4
82 #rsa 4096 bits 0.2426s 0.0036s 4.1 280.4
83 #dsa 512 bits 0.0010s 0.0012s 1038.1 841.5
84 #dsa 1024 bits 0.0030s 0.0037s 329.6 269.7
85 #dsa 2048 bits 0.0101s 0.0127s 98.9 78.6
87 # Same benchmark with this assembler code:
89 #rsa 512 bits 0.0007s 0.0001s 1416.2 16645.9
90 #rsa 1024 bits 0.0036s 0.0002s 274.4 5380.6
91 #rsa 2048 bits 0.0222s 0.0006s 45.1 1589.5
92 #rsa 4096 bits 0.1469s 0.0022s 6.8 449.6
93 #dsa 512 bits 0.0006s 0.0007s 1664.2 1376.2
94 #dsa 1024 bits 0.0018s 0.0023s 545.0 442.2
95 #dsa 2048 bits 0.0061s 0.0075s 163.5 132.8
97 # Performance increase of ~60%
99 # If you have comments or suggestions to improve code send
100 # me a note at schari@us.ibm.com
105 if ($flavour =~ /32/) {
111 $LDU= "lwzu"; # load and update
113 $STU= "stwu"; # store and update
114 $UMULL= "mullw"; # unsigned multiply low
115 $UMULH= "mulhwu"; # unsigned multiply high
116 $UDIV= "divwu"; # unsigned divide
117 $UCMPI= "cmplwi"; # unsigned compare with immediate
118 $UCMP= "cmplw"; # unsigned compare
119 $CNTLZ= "cntlzw"; # count leading zeros
120 $SHL= "slw"; # shift left
121 $SHR= "srw"; # unsigned shift right
122 $SHRI= "srwi"; # unsigned shift right by immediate
123 $SHLI= "slwi"; # shift left by immediate
124 $CLRU= "clrlwi"; # clear upper bits
125 $INSR= "insrwi"; # insert right
126 $ROTL= "rotlwi"; # rotate left by immediate
127 $TR= "tw"; # conditional trap
128 } elsif ($flavour =~ /64/) {
133 # same as above, but 64-bit mnemonics...
135 $LDU= "ldu"; # load and update
137 $STU= "stdu"; # store and update
138 $UMULL= "mulld"; # unsigned multiply low
139 $UMULH= "mulhdu"; # unsigned multiply high
140 $UDIV= "divdu"; # unsigned divide
141 $UCMPI= "cmpldi"; # unsigned compare with immediate
142 $UCMP= "cmpld"; # unsigned compare
143 $CNTLZ= "cntlzd"; # count leading zeros
144 $SHL= "sld"; # shift left
145 $SHR= "srd"; # unsigned shift right
146 $SHRI= "srdi"; # unsigned shift right by immediate
147 $SHLI= "sldi"; # shift left by immediate
148 $CLRU= "clrldi"; # clear upper bits
149 $INSR= "insrdi"; # insert right
150 $ROTL= "rotldi"; # rotate left by immediate
151 $TR= "td"; # conditional trap
152 } else { die "nonsense $flavour"; }
154 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
155 ( $xlate="${dir}ppc-xlate.pl" and -f $xlate ) or
156 ( $xlate="${dir}../../perlasm/ppc-xlate.pl" and -f $xlate) or
157 die "can't locate ppc-xlate.pl";
159 open STDOUT,"| $^X $xlate $flavour ".shift || die "can't call $xlate: $!";
162 #--------------------------------------------------------------------
169 # Created by: Suresh Chari
170 # IBM Thomas J. Watson Research Library
174 # Description: Optimized assembly routines for OpenSSL crypto
175 # on the 32 bitPowerPC platform.
180 # 2. Fixed bn_add,bn_sub and bn_div_words, added comments,
181 # cleaned up code. Also made a single version which can
182 # be used for both the AIX and Linux compilers. See NOTE
184 # 12/05/03 Suresh Chari
185 # (with lots of help from) Andy Polyakov
187 # 1. Initial version 10/20/02 Suresh Chari
190 # The following file works for the xlc,cc
193 # NOTE: To get the file to link correctly with the gcc compiler
194 # you have to change the names of the routines and remove
195 # the first .(dot) character. This should automatically
196 # be done in the build process.
198 # Hand optimized assembly code for the following routines
211 # NOTE: It is possible to optimize this code more for
212 # specific PowerPC or Power architectures. On the Northstar
213 # architecture the optimizations in this file do
214 # NOT provide much improvement.
216 # If you have comments or suggestions to improve code send
217 # me a note at schari\@us.ibm.com
219 #--------------------------------------------------------------------------
221 # Defines to be used in the assembly code.
223 #.set r0,0 # we use it as storage for value of 0
224 #.set SP,1 # preserved
225 #.set RTOC,2 # preserved
226 #.set r3,3 # 1st argument/return value
227 #.set r4,4 # 2nd argument/volatile register
228 #.set r5,5 # 3rd argument/volatile register
236 #.set r13,13 # not used, nor any other "below" it...
238 # Declare function names to be global
239 # NOTE: For gcc these names MUST be changed to remove
240 # the first . i.e. for example change ".bn_sqr_comba4"
241 # to "bn_sqr_comba4". This should be automatically done
244 .globl .bn_sqr_comba4
245 .globl .bn_sqr_comba8
246 .globl .bn_mul_comba4
247 .globl .bn_mul_comba8
253 .globl .bn_mul_add_words
260 # NOTE: The following label name should be changed to
261 # "bn_sqr_comba4" i.e. remove the first dot
262 # for the gcc compiler. This should be automatically
269 # Optimized version of bn_sqr_comba4.
271 # void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a)
275 # Freely use registers r5,r6,r7,r8,r9,r10,r11 as follows:
277 # r5,r6 are the two BN_ULONGs being multiplied.
278 # r7,r8 are the results of the 32x32 giving 64 bit multiply.
279 # r9,r10, r11 are the equivalents of c1,c2, c3.
280 # Here's the assembly
283 xor r0,r0,r0 # set r0 = 0. Used in the addze
286 #sqr_add_c(a,0,c1,c2,c3)
289 $UMULH r10,r5,r5 #in first iteration. No need
290 #to add since c1=c2=c3=0.
291 # Note c3(r11) is NOT set to 0
294 $ST r9,`0*$BNSZ`(r3) # r[0]=c1;
295 # sqr_add_c2(a,1,0,c2,c3,c1);
300 addc r7,r7,r7 # compute (r7,r8)=2*(r7,r8)
302 addze r9,r0 # catch carry if any.
303 # r9= r0(=0) and carry
305 addc r10,r7,r10 # now add to temp result.
306 addze r11,r8 # r8 added to r11 which is 0
309 $ST r10,`1*$BNSZ`(r3) #r[1]=c2;
310 #sqr_add_c(a,1,c3,c1,c2)
316 #sqr_add_c2(a,2,0,c3,c1,c2)
328 $ST r11,`2*$BNSZ`(r3) #r[2]=c3
329 #sqr_add_c2(a,3,0,c1,c2,c3);
340 #sqr_add_c2(a,2,1,c1,c2,c3);
352 $ST r9,`3*$BNSZ`(r3) #r[3]=c1
353 #sqr_add_c(a,2,c2,c3,c1);
359 #sqr_add_c2(a,3,1,c2,c3,c1);
370 $ST r10,`4*$BNSZ`(r3) #r[4]=c2
371 #sqr_add_c2(a,3,2,c3,c1,c2);
382 $ST r11,`5*$BNSZ`(r3) #r[5] = c3
383 #sqr_add_c(a,3,c1,c2,c3);
389 $ST r9,`6*$BNSZ`(r3) #r[6]=c1
390 $ST r10,`7*$BNSZ`(r3) #r[7]=c2
395 # NOTE: The following label name should be changed to
396 # "bn_sqr_comba8" i.e. remove the first dot
397 # for the gcc compiler. This should be automatically
404 # This is an optimized version of the bn_sqr_comba8 routine.
405 # Tightly uses the adde instruction
408 # void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a)
412 # Freely use registers r5,r6,r7,r8,r9,r10,r11 as follows:
414 # r5,r6 are the two BN_ULONGs being multiplied.
415 # r7,r8 are the results of the 32x32 giving 64 bit multiply.
416 # r9,r10, r11 are the equivalents of c1,c2, c3.
418 # Possible optimization of loading all 8 longs of a into registers
419 # doesnt provide any speedup
422 xor r0,r0,r0 #set r0 = 0.Used in addze
425 #sqr_add_c(a,0,c1,c2,c3);
427 $UMULL r9,r5,r5 #1st iteration: no carries.
429 $ST r9,`0*$BNSZ`(r3) # r[0]=c1;
430 #sqr_add_c2(a,1,0,c2,c3,c1);
435 addc r10,r7,r10 #add the two register number
436 adde r11,r8,r0 # (r8,r7) to the three register
437 addze r9,r0 # number (r9,r11,r10).NOTE:r0=0
439 addc r10,r7,r10 #add the two register number
440 adde r11,r8,r11 # (r8,r7) to the three register
441 addze r9,r9 # number (r9,r11,r10).
443 $ST r10,`1*$BNSZ`(r3) # r[1]=c2
445 #sqr_add_c(a,1,c3,c1,c2);
451 #sqr_add_c2(a,2,0,c3,c1,c2);
464 $ST r11,`2*$BNSZ`(r3) #r[2]=c3
465 #sqr_add_c2(a,3,0,c1,c2,c3);
466 $LD r6,`3*$BNSZ`(r4) #r6 = a[3]. r5 is already a[0].
477 #sqr_add_c2(a,2,1,c1,c2,c3);
491 $ST r9,`3*$BNSZ`(r3) #r[3]=c1;
492 #sqr_add_c(a,2,c2,c3,c1);
499 #sqr_add_c2(a,3,1,c2,c3,c1);
511 #sqr_add_c2(a,4,0,c2,c3,c1);
524 $ST r10,`4*$BNSZ`(r3) #r[4]=c2;
525 #sqr_add_c2(a,5,0,c3,c1,c2);
537 #sqr_add_c2(a,4,1,c3,c1,c2);
550 #sqr_add_c2(a,3,2,c3,c1,c2);
563 $ST r11,`5*$BNSZ`(r3) #r[5]=c3;
564 #sqr_add_c(a,3,c1,c2,c3);
570 #sqr_add_c2(a,4,2,c1,c2,c3);
582 #sqr_add_c2(a,5,1,c1,c2,c3);
595 #sqr_add_c2(a,6,0,c1,c2,c3);
606 $ST r9,`6*$BNSZ`(r3) #r[6]=c1;
607 #sqr_add_c2(a,7,0,c2,c3,c1);
618 #sqr_add_c2(a,6,1,c2,c3,c1);
630 #sqr_add_c2(a,5,2,c2,c3,c1);
641 #sqr_add_c2(a,4,3,c2,c3,c1);
653 $ST r10,`7*$BNSZ`(r3) #r[7]=c2;
654 #sqr_add_c(a,4,c3,c1,c2);
660 #sqr_add_c2(a,5,3,c3,c1,c2);
670 #sqr_add_c2(a,6,2,c3,c1,c2);
682 #sqr_add_c2(a,7,1,c3,c1,c2);
693 $ST r11,`8*$BNSZ`(r3) #r[8]=c3;
694 #sqr_add_c2(a,7,2,c1,c2,c3);
705 #sqr_add_c2(a,6,3,c1,c2,c3);
716 #sqr_add_c2(a,5,4,c1,c2,c3);
727 $ST r9,`9*$BNSZ`(r3) #r[9]=c1;
728 #sqr_add_c(a,5,c2,c3,c1);
734 #sqr_add_c2(a,6,4,c2,c3,c1);
744 #sqr_add_c2(a,7,3,c2,c3,c1);
755 $ST r10,`10*$BNSZ`(r3) #r[10]=c2;
756 #sqr_add_c2(a,7,4,c3,c1,c2);
766 #sqr_add_c2(a,6,5,c3,c1,c2);
777 $ST r11,`11*$BNSZ`(r3) #r[11]=c3;
778 #sqr_add_c(a,6,c1,c2,c3);
784 #sqr_add_c2(a,7,5,c1,c2,c3)
794 $ST r9,`12*$BNSZ`(r3) #r[12]=c1;
796 #sqr_add_c2(a,7,6,c2,c3,c1)
806 $ST r10,`13*$BNSZ`(r3) #r[13]=c2;
807 #sqr_add_c(a,7,c3,c1,c2);
812 $ST r11,`14*$BNSZ`(r3) #r[14]=c3;
813 $ST r9, `15*$BNSZ`(r3) #r[15]=c1;
821 # NOTE: The following label name should be changed to
822 # "bn_mul_comba4" i.e. remove the first dot
823 # for the gcc compiler. This should be automatically
830 # This is an optimized version of the bn_mul_comba4 routine.
832 # void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
836 # r6, r7 are the 2 BN_ULONGs being multiplied.
837 # r8, r9 are the results of the 32x32 giving 64 multiply.
838 # r10, r11, r12 are the equivalents of c1, c2, and c3.
840 xor r0,r0,r0 #r0=0. Used in addze below.
841 #mul_add_c(a[0],b[0],c1,c2,c3);
846 $ST r10,`0*$BNSZ`(r3) #r[0]=c1
847 #mul_add_c(a[0],b[1],c2,c3,c1);
854 #mul_add_c(a[1],b[0],c2,c3,c1);
855 $LD r6, `1*$BNSZ`(r4)
856 $LD r7, `0*$BNSZ`(r5)
862 $ST r11,`1*$BNSZ`(r3) #r[1]=c2
863 #mul_add_c(a[2],b[0],c3,c1,c2);
870 #mul_add_c(a[1],b[1],c3,c1,c2);
878 #mul_add_c(a[0],b[2],c3,c1,c2);
886 $ST r12,`2*$BNSZ`(r3) #r[2]=c3
887 #mul_add_c(a[0],b[3],c1,c2,c3);
894 #mul_add_c(a[1],b[2],c1,c2,c3);
902 #mul_add_c(a[2],b[1],c1,c2,c3);
910 #mul_add_c(a[3],b[0],c1,c2,c3);
918 $ST r10,`3*$BNSZ`(r3) #r[3]=c1
919 #mul_add_c(a[3],b[1],c2,c3,c1);
926 #mul_add_c(a[2],b[2],c2,c3,c1);
934 #mul_add_c(a[1],b[3],c2,c3,c1);
942 $ST r11,`4*$BNSZ`(r3) #r[4]=c2
943 #mul_add_c(a[2],b[3],c3,c1,c2);
950 #mul_add_c(a[3],b[2],c3,c1,c2);
958 $ST r12,`5*$BNSZ`(r3) #r[5]=c3
959 #mul_add_c(a[3],b[3],c1,c2,c3);
966 $ST r10,`6*$BNSZ`(r3) #r[6]=c1
967 $ST r11,`7*$BNSZ`(r3) #r[7]=c2
972 # NOTE: The following label name should be changed to
973 # "bn_mul_comba8" i.e. remove the first dot
974 # for the gcc compiler. This should be automatically
981 # Optimized version of the bn_mul_comba8 routine.
983 # void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
987 # r6, r7 are the 2 BN_ULONGs being multiplied.
988 # r8, r9 are the results of the 32x32 giving 64 multiply.
989 # r10, r11, r12 are the equivalents of c1, c2, and c3.
991 xor r0,r0,r0 #r0=0. Used in addze below.
993 #mul_add_c(a[0],b[0],c1,c2,c3);
994 $LD r6,`0*$BNSZ`(r4) #a[0]
995 $LD r7,`0*$BNSZ`(r5) #b[0]
998 $ST r10,`0*$BNSZ`(r3) #r[0]=c1;
999 #mul_add_c(a[0],b[1],c2,c3,c1);
1000 $LD r7,`1*$BNSZ`(r5)
1004 addze r12,r9 # since we didnt set r12 to zero before.
1006 #mul_add_c(a[1],b[0],c2,c3,c1);
1007 $LD r6,`1*$BNSZ`(r4)
1008 $LD r7,`0*$BNSZ`(r5)
1014 $ST r11,`1*$BNSZ`(r3) #r[1]=c2;
1015 #mul_add_c(a[2],b[0],c3,c1,c2);
1016 $LD r6,`2*$BNSZ`(r4)
1022 #mul_add_c(a[1],b[1],c3,c1,c2);
1023 $LD r6,`1*$BNSZ`(r4)
1024 $LD r7,`1*$BNSZ`(r5)
1030 #mul_add_c(a[0],b[2],c3,c1,c2);
1031 $LD r6,`0*$BNSZ`(r4)
1032 $LD r7,`2*$BNSZ`(r5)
1038 $ST r12,`2*$BNSZ`(r3) #r[2]=c3;
1039 #mul_add_c(a[0],b[3],c1,c2,c3);
1040 $LD r7,`3*$BNSZ`(r5)
1046 #mul_add_c(a[1],b[2],c1,c2,c3);
1047 $LD r6,`1*$BNSZ`(r4)
1048 $LD r7,`2*$BNSZ`(r5)
1055 #mul_add_c(a[2],b[1],c1,c2,c3);
1056 $LD r6,`2*$BNSZ`(r4)
1057 $LD r7,`1*$BNSZ`(r5)
1063 #mul_add_c(a[3],b[0],c1,c2,c3);
1064 $LD r6,`3*$BNSZ`(r4)
1065 $LD r7,`0*$BNSZ`(r5)
1071 $ST r10,`3*$BNSZ`(r3) #r[3]=c1;
1072 #mul_add_c(a[4],b[0],c2,c3,c1);
1073 $LD r6,`4*$BNSZ`(r4)
1079 #mul_add_c(a[3],b[1],c2,c3,c1);
1080 $LD r6,`3*$BNSZ`(r4)
1081 $LD r7,`1*$BNSZ`(r5)
1087 #mul_add_c(a[2],b[2],c2,c3,c1);
1088 $LD r6,`2*$BNSZ`(r4)
1089 $LD r7,`2*$BNSZ`(r5)
1095 #mul_add_c(a[1],b[3],c2,c3,c1);
1096 $LD r6,`1*$BNSZ`(r4)
1097 $LD r7,`3*$BNSZ`(r5)
1103 #mul_add_c(a[0],b[4],c2,c3,c1);
1104 $LD r6,`0*$BNSZ`(r4)
1105 $LD r7,`4*$BNSZ`(r5)
1111 $ST r11,`4*$BNSZ`(r3) #r[4]=c2;
1112 #mul_add_c(a[0],b[5],c3,c1,c2);
1113 $LD r7,`5*$BNSZ`(r5)
1119 #mul_add_c(a[1],b[4],c3,c1,c2);
1120 $LD r6,`1*$BNSZ`(r4)
1121 $LD r7,`4*$BNSZ`(r5)
1127 #mul_add_c(a[2],b[3],c3,c1,c2);
1128 $LD r6,`2*$BNSZ`(r4)
1129 $LD r7,`3*$BNSZ`(r5)
1135 #mul_add_c(a[3],b[2],c3,c1,c2);
1136 $LD r6,`3*$BNSZ`(r4)
1137 $LD r7,`2*$BNSZ`(r5)
1143 #mul_add_c(a[4],b[1],c3,c1,c2);
1144 $LD r6,`4*$BNSZ`(r4)
1145 $LD r7,`1*$BNSZ`(r5)
1151 #mul_add_c(a[5],b[0],c3,c1,c2);
1152 $LD r6,`5*$BNSZ`(r4)
1153 $LD r7,`0*$BNSZ`(r5)
1159 $ST r12,`5*$BNSZ`(r3) #r[5]=c3;
1160 #mul_add_c(a[6],b[0],c1,c2,c3);
1161 $LD r6,`6*$BNSZ`(r4)
1167 #mul_add_c(a[5],b[1],c1,c2,c3);
1168 $LD r6,`5*$BNSZ`(r4)
1169 $LD r7,`1*$BNSZ`(r5)
1175 #mul_add_c(a[4],b[2],c1,c2,c3);
1176 $LD r6,`4*$BNSZ`(r4)
1177 $LD r7,`2*$BNSZ`(r5)
1183 #mul_add_c(a[3],b[3],c1,c2,c3);
1184 $LD r6,`3*$BNSZ`(r4)
1185 $LD r7,`3*$BNSZ`(r5)
1191 #mul_add_c(a[2],b[4],c1,c2,c3);
1192 $LD r6,`2*$BNSZ`(r4)
1193 $LD r7,`4*$BNSZ`(r5)
1199 #mul_add_c(a[1],b[5],c1,c2,c3);
1200 $LD r6,`1*$BNSZ`(r4)
1201 $LD r7,`5*$BNSZ`(r5)
1207 #mul_add_c(a[0],b[6],c1,c2,c3);
1208 $LD r6,`0*$BNSZ`(r4)
1209 $LD r7,`6*$BNSZ`(r5)
1215 $ST r10,`6*$BNSZ`(r3) #r[6]=c1;
1216 #mul_add_c(a[0],b[7],c2,c3,c1);
1217 $LD r7,`7*$BNSZ`(r5)
1223 #mul_add_c(a[1],b[6],c2,c3,c1);
1224 $LD r6,`1*$BNSZ`(r4)
1225 $LD r7,`6*$BNSZ`(r5)
1231 #mul_add_c(a[2],b[5],c2,c3,c1);
1232 $LD r6,`2*$BNSZ`(r4)
1233 $LD r7,`5*$BNSZ`(r5)
1239 #mul_add_c(a[3],b[4],c2,c3,c1);
1240 $LD r6,`3*$BNSZ`(r4)
1241 $LD r7,`4*$BNSZ`(r5)
1247 #mul_add_c(a[4],b[3],c2,c3,c1);
1248 $LD r6,`4*$BNSZ`(r4)
1249 $LD r7,`3*$BNSZ`(r5)
1255 #mul_add_c(a[5],b[2],c2,c3,c1);
1256 $LD r6,`5*$BNSZ`(r4)
1257 $LD r7,`2*$BNSZ`(r5)
1263 #mul_add_c(a[6],b[1],c2,c3,c1);
1264 $LD r6,`6*$BNSZ`(r4)
1265 $LD r7,`1*$BNSZ`(r5)
1271 #mul_add_c(a[7],b[0],c2,c3,c1);
1272 $LD r6,`7*$BNSZ`(r4)
1273 $LD r7,`0*$BNSZ`(r5)
1279 $ST r11,`7*$BNSZ`(r3) #r[7]=c2;
1280 #mul_add_c(a[7],b[1],c3,c1,c2);
1281 $LD r7,`1*$BNSZ`(r5)
1287 #mul_add_c(a[6],b[2],c3,c1,c2);
1288 $LD r6,`6*$BNSZ`(r4)
1289 $LD r7,`2*$BNSZ`(r5)
1295 #mul_add_c(a[5],b[3],c3,c1,c2);
1296 $LD r6,`5*$BNSZ`(r4)
1297 $LD r7,`3*$BNSZ`(r5)
1303 #mul_add_c(a[4],b[4],c3,c1,c2);
1304 $LD r6,`4*$BNSZ`(r4)
1305 $LD r7,`4*$BNSZ`(r5)
1311 #mul_add_c(a[3],b[5],c3,c1,c2);
1312 $LD r6,`3*$BNSZ`(r4)
1313 $LD r7,`5*$BNSZ`(r5)
1319 #mul_add_c(a[2],b[6],c3,c1,c2);
1320 $LD r6,`2*$BNSZ`(r4)
1321 $LD r7,`6*$BNSZ`(r5)
1327 #mul_add_c(a[1],b[7],c3,c1,c2);
1328 $LD r6,`1*$BNSZ`(r4)
1329 $LD r7,`7*$BNSZ`(r5)
1335 $ST r12,`8*$BNSZ`(r3) #r[8]=c3;
1336 #mul_add_c(a[2],b[7],c1,c2,c3);
1337 $LD r6,`2*$BNSZ`(r4)
1343 #mul_add_c(a[3],b[6],c1,c2,c3);
1344 $LD r6,`3*$BNSZ`(r4)
1345 $LD r7,`6*$BNSZ`(r5)
1351 #mul_add_c(a[4],b[5],c1,c2,c3);
1352 $LD r6,`4*$BNSZ`(r4)
1353 $LD r7,`5*$BNSZ`(r5)
1359 #mul_add_c(a[5],b[4],c1,c2,c3);
1360 $LD r6,`5*$BNSZ`(r4)
1361 $LD r7,`4*$BNSZ`(r5)
1367 #mul_add_c(a[6],b[3],c1,c2,c3);
1368 $LD r6,`6*$BNSZ`(r4)
1369 $LD r7,`3*$BNSZ`(r5)
1375 #mul_add_c(a[7],b[2],c1,c2,c3);
1376 $LD r6,`7*$BNSZ`(r4)
1377 $LD r7,`2*$BNSZ`(r5)
1383 $ST r10,`9*$BNSZ`(r3) #r[9]=c1;
1384 #mul_add_c(a[7],b[3],c2,c3,c1);
1385 $LD r7,`3*$BNSZ`(r5)
1391 #mul_add_c(a[6],b[4],c2,c3,c1);
1392 $LD r6,`6*$BNSZ`(r4)
1393 $LD r7,`4*$BNSZ`(r5)
1399 #mul_add_c(a[5],b[5],c2,c3,c1);
1400 $LD r6,`5*$BNSZ`(r4)
1401 $LD r7,`5*$BNSZ`(r5)
1407 #mul_add_c(a[4],b[6],c2,c3,c1);
1408 $LD r6,`4*$BNSZ`(r4)
1409 $LD r7,`6*$BNSZ`(r5)
1415 #mul_add_c(a[3],b[7],c2,c3,c1);
1416 $LD r6,`3*$BNSZ`(r4)
1417 $LD r7,`7*$BNSZ`(r5)
1423 $ST r11,`10*$BNSZ`(r3) #r[10]=c2;
1424 #mul_add_c(a[4],b[7],c3,c1,c2);
1425 $LD r6,`4*$BNSZ`(r4)
1431 #mul_add_c(a[5],b[6],c3,c1,c2);
1432 $LD r6,`5*$BNSZ`(r4)
1433 $LD r7,`6*$BNSZ`(r5)
1439 #mul_add_c(a[6],b[5],c3,c1,c2);
1440 $LD r6,`6*$BNSZ`(r4)
1441 $LD r7,`5*$BNSZ`(r5)
1447 #mul_add_c(a[7],b[4],c3,c1,c2);
1448 $LD r6,`7*$BNSZ`(r4)
1449 $LD r7,`4*$BNSZ`(r5)
1455 $ST r12,`11*$BNSZ`(r3) #r[11]=c3;
1456 #mul_add_c(a[7],b[5],c1,c2,c3);
1457 $LD r7,`5*$BNSZ`(r5)
1463 #mul_add_c(a[6],b[6],c1,c2,c3);
1464 $LD r6,`6*$BNSZ`(r4)
1465 $LD r7,`6*$BNSZ`(r5)
1471 #mul_add_c(a[5],b[7],c1,c2,c3);
1472 $LD r6,`5*$BNSZ`(r4)
1473 $LD r7,`7*$BNSZ`(r5)
1479 $ST r10,`12*$BNSZ`(r3) #r[12]=c1;
1480 #mul_add_c(a[6],b[7],c2,c3,c1);
1481 $LD r6,`6*$BNSZ`(r4)
1487 #mul_add_c(a[7],b[6],c2,c3,c1);
1488 $LD r6,`7*$BNSZ`(r4)
1489 $LD r7,`6*$BNSZ`(r5)
1495 $ST r11,`13*$BNSZ`(r3) #r[13]=c2;
1496 #mul_add_c(a[7],b[7],c3,c1,c2);
1497 $LD r7,`7*$BNSZ`(r5)
1502 $ST r12,`14*$BNSZ`(r3) #r[14]=c3;
1503 $ST r10,`15*$BNSZ`(r3) #r[15]=c1;
1508 # NOTE: The following label name should be changed to
1509 # "bn_sub_words" i.e. remove the first dot
1510 # for the gcc compiler. This should be automatically
1517 # Handcoded version of bn_sub_words
1519 #BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1526 # Note: No loop unrolling done since this is not a performance
1529 xor r0,r0,r0 #set r0 = 0
1531 # check for r6 = 0 AND set carry bit.
1533 subfc. r7,r0,r6 # If r6 is 0 then result is 0.
1534 # if r6 > 0 then result !=0
1535 # In either case carry bit is set.
1536 beq Lppcasm_sub_adios
1541 Lppcasm_sub_mainloop:
1544 subfe r6,r8,r7 # r6 = r7+carry bit + onescomplement(r8)
1545 # if carry = 1 this is r7-r8. Else it
1546 # is r7-r8 -1 as we need.
1548 bdnz- Lppcasm_sub_mainloop
1550 subfze r3,r0 # if carry bit is set then r3 = 0 else -1
1551 andi. r3,r3,1 # keep only last bit.
1557 # NOTE: The following label name should be changed to
1558 # "bn_add_words" i.e. remove the first dot
1559 # for the gcc compiler. This should be automatically
1566 # Handcoded version of bn_add_words
1568 #BN_ULONG bn_add_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1575 # Note: No loop unrolling done since this is not a performance
1580 # check for r6 = 0. Is this needed?
1582 addic. r6,r6,0 #test r6 and clear carry bit.
1583 beq Lppcasm_add_adios
1588 Lppcasm_add_mainloop:
1593 bdnz- Lppcasm_add_mainloop
1595 addze r3,r0 #return carry bit.
1600 # NOTE: The following label name should be changed to
1601 # "bn_div_words" i.e. remove the first dot
1602 # for the gcc compiler. This should be automatically
1609 # This is a cleaned up version of code generated by
1610 # the AIX compiler. The only optimization is to use
1611 # the PPC instruction to count leading zeros instead
1612 # of call to num_bits_word. Since this was compiled
1613 # only at level -O2 we can possibly squeeze it more?
1619 $UCMPI 0,r5,0 # compare r5 and 0
1620 bne Lppcasm_div1 # proceed if d!=0
1621 li r3,-1 # d=0 return -1
1626 $CNTLZ. r7,r5 #r7 = num leading 0s in d.
1627 beq Lppcasm_div2 #proceed if no leading zeros
1628 subf r8,r7,r8 #r8 = BN_num_bits_word(d)
1629 $SHR. r9,r3,r8 #are there any bits above r8'th?
1630 $TR 16,r9,r0 #if there're, signal to dump core...
1632 $UCMP 0,r3,r5 #h>=d?
1633 blt Lppcasm_div3 #goto Lppcasm_div3 if not
1634 subf r3,r5,r3 #h-=d ;
1635 Lppcasm_div3: #r7 = BN_BITS2-i. so r7=i
1636 cmpi 0,0,r7,0 # is (i == 0)?
1638 $SHL r3,r3,r7 # h = (h<< i)
1639 $SHR r8,r4,r8 # r8 = (l >> BN_BITS2 -i)
1640 $SHL r5,r5,r7 # d<<=i
1641 or r3,r3,r8 # h = (h<<i)|(l>>(BN_BITS2-i))
1642 $SHL r4,r4,r7 # l <<=i
1644 $SHRI r9,r5,`$BITS/2` # r9 = dh
1645 # dl will be computed when needed
1646 # as it saves registers.
1648 mtctr r6 #counter will be in count.
1649 Lppcasm_divouterloop:
1650 $SHRI r8,r3,`$BITS/2` #r8 = (h>>BN_BITS4)
1651 $SHRI r11,r4,`$BITS/2` #r11= (l&BN_MASK2h)>>BN_BITS4
1652 # compute here for innerloop.
1653 $UCMP 0,r8,r9 # is (h>>BN_BITS4)==dh
1654 bne Lppcasm_div5 # goto Lppcasm_div5 if not
1657 $CLRU r8,r8,`$BITS/2` #q = BN_MASK2l
1660 $UDIV r8,r3,r9 #q = h/dh
1662 $UMULL r12,r9,r8 #th = q*dh
1663 $CLRU r10,r5,`$BITS/2` #r10=dl
1664 $UMULL r6,r8,r10 #tl = q*dl
1666 Lppcasm_divinnerloop:
1667 subf r10,r12,r3 #t = h -th
1668 $SHRI r7,r10,`$BITS/2` #r7= (t &BN_MASK2H), sort of...
1669 addic. r7,r7,0 #test if r7 == 0. used below.
1670 # now want to compute
1671 # r7 = (t<<BN_BITS4)|((l&BN_MASK2h)>>BN_BITS4)
1672 # the following 2 instructions do that
1673 $SHLI r7,r10,`$BITS/2` # r7 = (t<<BN_BITS4)
1674 or r7,r7,r11 # r7|=((l&BN_MASK2h)>>BN_BITS4)
1675 $UCMP cr1,r6,r7 # compare (tl <= r7)
1676 bne Lppcasm_divinnerexit
1677 ble cr1,Lppcasm_divinnerexit
1679 subf r12,r9,r12 #th -=dh
1680 $CLRU r10,r5,`$BITS/2` #r10=dl. t is no longer needed in loop.
1681 subf r6,r10,r6 #tl -=dl
1682 b Lppcasm_divinnerloop
1683 Lppcasm_divinnerexit:
1684 $SHRI r10,r6,`$BITS/2` #t=(tl>>BN_BITS4)
1685 $SHLI r11,r6,`$BITS/2` #tl=(tl<<BN_BITS4)&BN_MASK2h;
1686 $UCMP cr1,r4,r11 # compare l and tl
1687 add r12,r12,r10 # th+=t
1688 bge cr1,Lppcasm_div7 # if (l>=tl) goto Lppcasm_div7
1689 addi r12,r12,1 # th++
1691 subf r11,r11,r4 #r11=l-tl
1692 $UCMP cr1,r3,r12 #compare h and th
1693 bge cr1,Lppcasm_div8 #if (h>=th) goto Lppcasm_div8
1697 subf r12,r12,r3 #r12 = h-th
1698 $SHLI r4,r11,`$BITS/2` #l=(l&BN_MASK2l)<<BN_BITS4
1700 # h = ((h<<BN_BITS4)|(l>>BN_BITS4))&BN_MASK2
1701 # the following 2 instructions will do this.
1702 $INSR r11,r12,`$BITS/2`,`$BITS/2` # r11 is the value we want rotated $BITS/2.
1703 $ROTL r3,r11,`$BITS/2` # rotate by $BITS/2 and store in r3
1704 bdz Lppcasm_div9 #if (count==0) break ;
1705 $SHLI r0,r8,`$BITS/2` #ret =q<<BN_BITS4
1706 b Lppcasm_divouterloop
1713 # NOTE: The following label name should be changed to
1714 # "bn_sqr_words" i.e. remove the first dot
1715 # for the gcc compiler. This should be automatically
1721 # Optimized version of bn_sqr_words
1723 # void bn_sqr_words(BN_ULONG *r, BN_ULONG *a, int n)
1732 # No unrolling done here. Not performance critical.
1734 addic. r5,r5,0 #test r5.
1735 beq Lppcasm_sqr_adios
1739 Lppcasm_sqr_mainloop:
1740 #sqr(r[0],r[1],a[0]);
1746 bdnz- Lppcasm_sqr_mainloop
1753 # NOTE: The following label name should be changed to
1754 # "bn_mul_words" i.e. remove the first dot
1755 # for the gcc compiler. This should be automatically
1762 # BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
1769 xor r12,r12,r12 # used for carry
1770 rlwinm. r7,r5,30,2,31 # num >> 2
1774 #mul(rp[0],ap[0],w,c1);
1775 $LD r8,`0*$BNSZ`(r4)
1779 #addze r10,r10 #carry is NOT ignored.
1780 #will be taken care of
1781 #in second spin below
1783 $ST r9,`0*$BNSZ`(r3)
1784 #mul(rp[1],ap[1],w,c1);
1785 $LD r8,`1*$BNSZ`(r4)
1790 $ST r11,`1*$BNSZ`(r3)
1791 #mul(rp[2],ap[2],w,c1);
1792 $LD r8,`2*$BNSZ`(r4)
1797 $ST r9,`2*$BNSZ`(r3)
1798 #mul_add(rp[3],ap[3],w,c1);
1799 $LD r8,`3*$BNSZ`(r4)
1803 addze r12,r12 #this spin we collect carry into
1805 $ST r11,`3*$BNSZ`(r3)
1807 addi r3,r3,`4*$BNSZ`
1808 addi r4,r4,`4*$BNSZ`
1809 bdnz- Lppcasm_mw_LOOP
1814 #mul(rp[0],ap[0],w,c1);
1815 $LD r8,`0*$BNSZ`(r4)
1820 $ST r9,`0*$BNSZ`(r3)
1828 #mul(rp[1],ap[1],w,c1);
1829 $LD r8,`1*$BNSZ`(r4)
1834 $ST r9,`1*$BNSZ`(r3)
1841 #mul_add(rp[2],ap[2],w,c1);
1842 $LD r8,`2*$BNSZ`(r4)
1847 $ST r9,`2*$BNSZ`(r3)
1856 # NOTE: The following label name should be changed to
1857 # "bn_mul_add_words" i.e. remove the first dot
1858 # for the gcc compiler. This should be automatically
1865 # BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
1872 # empirical evidence suggests that unrolled version performs best!!
1874 xor r0,r0,r0 #r0 = 0
1875 xor r12,r12,r12 #r12 = 0 . used for carry
1876 rlwinm. r7,r5,30,2,31 # num >> 2
1877 beq Lppcasm_maw_leftover # if (num < 4) go LPPCASM_maw_leftover
1879 Lppcasm_maw_mainloop:
1880 #mul_add(rp[0],ap[0],w,c1);
1881 $LD r8,`0*$BNSZ`(r4)
1882 $LD r11,`0*$BNSZ`(r3)
1885 addc r9,r9,r12 #r12 is carry.
1889 #the above instruction addze
1890 #is NOT needed. Carry will NOT
1891 #be ignored. It's not affected
1892 #by multiply and will be collected
1894 $ST r9,`0*$BNSZ`(r3)
1896 #mul_add(rp[1],ap[1],w,c1);
1897 $LD r8,`1*$BNSZ`(r4)
1898 $LD r9,`1*$BNSZ`(r3)
1901 adde r11,r11,r10 #r10 is carry.
1905 $ST r11,`1*$BNSZ`(r3)
1907 #mul_add(rp[2],ap[2],w,c1);
1908 $LD r8,`2*$BNSZ`(r4)
1910 $LD r11,`2*$BNSZ`(r3)
1916 $ST r9,`2*$BNSZ`(r3)
1918 #mul_add(rp[3],ap[3],w,c1);
1919 $LD r8,`3*$BNSZ`(r4)
1921 $LD r9,`3*$BNSZ`(r3)
1927 $ST r11,`3*$BNSZ`(r3)
1928 addi r3,r3,`4*$BNSZ`
1929 addi r4,r4,`4*$BNSZ`
1930 bdnz- Lppcasm_maw_mainloop
1932 Lppcasm_maw_leftover:
1934 beq Lppcasm_maw_adios
1937 #mul_add(rp[0],ap[0],w,c1);
1949 bdz Lppcasm_maw_adios
1950 #mul_add(rp[1],ap[1],w,c1);
1961 bdz Lppcasm_maw_adios
1962 #mul_add(rp[2],ap[2],w,c1);
1979 $data =~ s/\`([^\`]*)\`/eval $1/gem;