2 #if !(defined(__GNUC__) && __GNUC__>=2)
3 # include "../bn_asm.c" /* kind of dirty hack for Sun Studio */
6 * x86_64 BIGNUM accelerator version 0.1, December 2002.
8 * Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
11 * Rights for redistribution and usage in source and binary forms are
12 * granted according to the OpenSSL license. Warranty of any kind is
15 * Q. Version 0.1? It doesn't sound like Andy, he used to assign real
16 * versions, like 1.0...
17 * A. Well, that's because this code is basically a quick-n-dirty
18 * proof-of-concept hack. As you can see it's implemented with
19 * inline assembler, which means that you're bound to GCC and that
20 * there might be enough room for further improvement.
22 * Q. Why inline assembler?
23 * A. x86_64 features own ABI which I'm not familiar with. This is
24 * why I decided to let the compiler take care of subroutine
25 * prologue/epilogue as well as register allocation. For reference.
26 * Win64 implements different ABI for AMD64, different from Linux.
28 * Q. How much faster does it get?
29 * A. 'apps/openssl speed rsa dsa' output with no-asm:
31 * sign verify sign/s verify/s
32 * rsa 512 bits 0.0006s 0.0001s 1683.8 18456.2
33 * rsa 1024 bits 0.0028s 0.0002s 356.0 6407.0
34 * rsa 2048 bits 0.0172s 0.0005s 58.0 1957.8
35 * rsa 4096 bits 0.1155s 0.0018s 8.7 555.6
36 * sign verify sign/s verify/s
37 * dsa 512 bits 0.0005s 0.0006s 2100.8 1768.3
38 * dsa 1024 bits 0.0014s 0.0018s 692.3 559.2
39 * dsa 2048 bits 0.0049s 0.0061s 204.7 165.0
41 * 'apps/openssl speed rsa dsa' output with this module:
43 * sign verify sign/s verify/s
44 * rsa 512 bits 0.0004s 0.0000s 2767.1 33297.9
45 * rsa 1024 bits 0.0012s 0.0001s 867.4 14674.7
46 * rsa 2048 bits 0.0061s 0.0002s 164.0 5270.0
47 * rsa 4096 bits 0.0384s 0.0006s 26.1 1650.8
48 * sign verify sign/s verify/s
49 * dsa 512 bits 0.0002s 0.0003s 4442.2 3786.3
50 * dsa 1024 bits 0.0005s 0.0007s 1835.1 1497.4
51 * dsa 2048 bits 0.0016s 0.0020s 620.4 504.6
53 * For the reference. IA-32 assembler implementation performs
54 * very much like 64-bit code compiled with no-asm on the same
58 #if defined(_WIN64) || !defined(__LP64__)
59 #define BN_ULONG unsigned long long
61 #define BN_ULONG unsigned long
68 * "m"(a), "+m"(r) is the way to favor DirectPath ยต-code;
69 * "g"(0) let the compiler to decide where does it
70 * want to keep the value of zero;
72 #define mul_add(r,a,word,carry) do { \
73 register BN_ULONG high,low; \
75 : "=a"(low),"=d"(high) \
78 asm ("addq %2,%0; adcq %3,%1" \
79 : "+r"(carry),"+d"(high)\
82 asm ("addq %2,%0; adcq %3,%1" \
83 : "+m"(r),"+d"(high) \
89 #define mul(r,a,word,carry) do { \
90 register BN_ULONG high,low; \
92 : "=a"(low),"=d"(high) \
95 asm ("addq %2,%0; adcq %3,%1" \
96 : "+r"(carry),"+d"(high)\
99 (r)=carry, carry=high; \
102 #define sqr(r0,r1,a) \
104 : "=a"(r0),"=d"(r1) \
108 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
112 if (num <= 0) return(c1);
116 mul_add(rp[0],ap[0],w,c1);
117 mul_add(rp[1],ap[1],w,c1);
118 mul_add(rp[2],ap[2],w,c1);
119 mul_add(rp[3],ap[3],w,c1);
120 ap+=4; rp+=4; num-=4;
124 mul_add(rp[0],ap[0],w,c1); if (--num==0) return c1;
125 mul_add(rp[1],ap[1],w,c1); if (--num==0) return c1;
126 mul_add(rp[2],ap[2],w,c1); return c1;
132 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
136 if (num <= 0) return(c1);
140 mul(rp[0],ap[0],w,c1);
141 mul(rp[1],ap[1],w,c1);
142 mul(rp[2],ap[2],w,c1);
143 mul(rp[3],ap[3],w,c1);
144 ap+=4; rp+=4; num-=4;
148 mul(rp[0],ap[0],w,c1); if (--num == 0) return c1;
149 mul(rp[1],ap[1],w,c1); if (--num == 0) return c1;
150 mul(rp[2],ap[2],w,c1);
155 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
169 sqr(r[0],r[1],a[0]); if (--n == 0) return;
170 sqr(r[2],r[3],a[1]); if (--n == 0) return;
175 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
176 { BN_ULONG ret,waste;
179 : "=a"(ret),"=d"(waste)
180 : "a"(l),"d"(h),"g"(d)
186 BN_ULONG bn_add_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
190 if (n <= 0) return 0;
193 " subq %0,%0 \n" /* clear carry */
196 "1: movq (%4,%2,8),%0 \n"
197 " adcq (%5,%2,8),%0 \n"
198 " movq %0,(%3,%2,8) \n"
202 : "=&r"(ret),"+c"(n),"+r"(i)
203 : "r"(rp),"r"(ap),"r"(bp)
211 BN_ULONG bn_sub_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
215 if (n <= 0) return 0;
218 " subq %0,%0 \n" /* clear borrow */
221 "1: movq (%4,%2,8),%0 \n"
222 " sbbq (%5,%2,8),%0 \n"
223 " movq %0,(%3,%2,8) \n"
227 : "=&r"(ret),"+c"(n),"+r"(i)
228 : "r"(rp),"r"(ap),"r"(bp)
235 /* Simics 1.4<7 has buggy sbbq:-( */
236 #define BN_MASK2 0xffffffffffffffffL
237 BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
242 if (n <= 0) return((BN_ULONG)0);
247 r[0]=(t1-t2-c)&BN_MASK2;
248 if (t1 != t2) c=(t1 < t2);
252 r[1]=(t1-t2-c)&BN_MASK2;
253 if (t1 != t2) c=(t1 < t2);
257 r[2]=(t1-t2-c)&BN_MASK2;
258 if (t1 != t2) c=(t1 < t2);
262 r[3]=(t1-t2-c)&BN_MASK2;
263 if (t1 != t2) c=(t1 < t2);
274 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
275 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
276 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
277 /* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */
280 * Keep in mind that carrying into high part of multiplication result
281 * can not overflow, because it cannot be all-ones.
284 /* original macros are kept for reference purposes */
285 #define mul_add_c(a,b,c0,c1,c2) do { \
286 BN_ULONG ta = (a), tb = (b); \
288 BN_UMULT_LOHI(lo,hi,ta,tb); \
289 c0 += lo; hi += (c0<lo)?1:0; \
290 c1 += hi; c2 += (c1<hi)?1:0; \
293 #define mul_add_c2(a,b,c0,c1,c2) do { \
294 BN_ULONG ta = (a), tb = (b); \
295 BN_ULONG lo, hi, tt; \
296 BN_UMULT_LOHI(lo,hi,ta,tb); \
297 c0 += lo; tt = hi+((c0<lo)?1:0); \
298 c1 += tt; c2 += (c1<tt)?1:0; \
299 c0 += lo; hi += (c0<lo)?1:0; \
300 c1 += hi; c2 += (c1<hi)?1:0; \
303 #define sqr_add_c(a,i,c0,c1,c2) do { \
304 BN_ULONG ta = (a)[i]; \
306 BN_UMULT_LOHI(lo,hi,ta,ta); \
307 c0 += lo; hi += (c0<lo)?1:0; \
308 c1 += hi; c2 += (c1<hi)?1:0; \
311 #define mul_add_c(a,b,c0,c1,c2) do { \
314 : "=a"(t1),"=d"(t2) \
317 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
318 : "+r"(c0),"+r"(c1),"+r"(c2) \
319 : "r"(t1),"r"(t2),"g"(0) \
323 #define sqr_add_c(a,i,c0,c1,c2) do { \
326 : "=a"(t1),"=d"(t2) \
329 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
330 : "+r"(c0),"+r"(c1),"+r"(c2) \
331 : "r"(t1),"r"(t2),"g"(0) \
335 #define mul_add_c2(a,b,c0,c1,c2) do { \
338 : "=a"(t1),"=d"(t2) \
341 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
342 : "+r"(c0),"+r"(c1),"+r"(c2) \
343 : "r"(t1),"r"(t2),"g"(0) \
345 asm ("addq %3,%0; adcq %4,%1; adcq %5,%2" \
346 : "+r"(c0),"+r"(c1),"+r"(c2) \
347 : "r"(t1),"r"(t2),"g"(0) \
352 #define sqr_add_c2(a,i,j,c0,c1,c2) \
353 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
355 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
362 mul_add_c(a[0],b[0],c1,c2,c3);
365 mul_add_c(a[0],b[1],c2,c3,c1);
366 mul_add_c(a[1],b[0],c2,c3,c1);
369 mul_add_c(a[2],b[0],c3,c1,c2);
370 mul_add_c(a[1],b[1],c3,c1,c2);
371 mul_add_c(a[0],b[2],c3,c1,c2);
374 mul_add_c(a[0],b[3],c1,c2,c3);
375 mul_add_c(a[1],b[2],c1,c2,c3);
376 mul_add_c(a[2],b[1],c1,c2,c3);
377 mul_add_c(a[3],b[0],c1,c2,c3);
380 mul_add_c(a[4],b[0],c2,c3,c1);
381 mul_add_c(a[3],b[1],c2,c3,c1);
382 mul_add_c(a[2],b[2],c2,c3,c1);
383 mul_add_c(a[1],b[3],c2,c3,c1);
384 mul_add_c(a[0],b[4],c2,c3,c1);
387 mul_add_c(a[0],b[5],c3,c1,c2);
388 mul_add_c(a[1],b[4],c3,c1,c2);
389 mul_add_c(a[2],b[3],c3,c1,c2);
390 mul_add_c(a[3],b[2],c3,c1,c2);
391 mul_add_c(a[4],b[1],c3,c1,c2);
392 mul_add_c(a[5],b[0],c3,c1,c2);
395 mul_add_c(a[6],b[0],c1,c2,c3);
396 mul_add_c(a[5],b[1],c1,c2,c3);
397 mul_add_c(a[4],b[2],c1,c2,c3);
398 mul_add_c(a[3],b[3],c1,c2,c3);
399 mul_add_c(a[2],b[4],c1,c2,c3);
400 mul_add_c(a[1],b[5],c1,c2,c3);
401 mul_add_c(a[0],b[6],c1,c2,c3);
404 mul_add_c(a[0],b[7],c2,c3,c1);
405 mul_add_c(a[1],b[6],c2,c3,c1);
406 mul_add_c(a[2],b[5],c2,c3,c1);
407 mul_add_c(a[3],b[4],c2,c3,c1);
408 mul_add_c(a[4],b[3],c2,c3,c1);
409 mul_add_c(a[5],b[2],c2,c3,c1);
410 mul_add_c(a[6],b[1],c2,c3,c1);
411 mul_add_c(a[7],b[0],c2,c3,c1);
414 mul_add_c(a[7],b[1],c3,c1,c2);
415 mul_add_c(a[6],b[2],c3,c1,c2);
416 mul_add_c(a[5],b[3],c3,c1,c2);
417 mul_add_c(a[4],b[4],c3,c1,c2);
418 mul_add_c(a[3],b[5],c3,c1,c2);
419 mul_add_c(a[2],b[6],c3,c1,c2);
420 mul_add_c(a[1],b[7],c3,c1,c2);
423 mul_add_c(a[2],b[7],c1,c2,c3);
424 mul_add_c(a[3],b[6],c1,c2,c3);
425 mul_add_c(a[4],b[5],c1,c2,c3);
426 mul_add_c(a[5],b[4],c1,c2,c3);
427 mul_add_c(a[6],b[3],c1,c2,c3);
428 mul_add_c(a[7],b[2],c1,c2,c3);
431 mul_add_c(a[7],b[3],c2,c3,c1);
432 mul_add_c(a[6],b[4],c2,c3,c1);
433 mul_add_c(a[5],b[5],c2,c3,c1);
434 mul_add_c(a[4],b[6],c2,c3,c1);
435 mul_add_c(a[3],b[7],c2,c3,c1);
438 mul_add_c(a[4],b[7],c3,c1,c2);
439 mul_add_c(a[5],b[6],c3,c1,c2);
440 mul_add_c(a[6],b[5],c3,c1,c2);
441 mul_add_c(a[7],b[4],c3,c1,c2);
444 mul_add_c(a[7],b[5],c1,c2,c3);
445 mul_add_c(a[6],b[6],c1,c2,c3);
446 mul_add_c(a[5],b[7],c1,c2,c3);
449 mul_add_c(a[6],b[7],c2,c3,c1);
450 mul_add_c(a[7],b[6],c2,c3,c1);
453 mul_add_c(a[7],b[7],c3,c1,c2);
458 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
465 mul_add_c(a[0],b[0],c1,c2,c3);
468 mul_add_c(a[0],b[1],c2,c3,c1);
469 mul_add_c(a[1],b[0],c2,c3,c1);
472 mul_add_c(a[2],b[0],c3,c1,c2);
473 mul_add_c(a[1],b[1],c3,c1,c2);
474 mul_add_c(a[0],b[2],c3,c1,c2);
477 mul_add_c(a[0],b[3],c1,c2,c3);
478 mul_add_c(a[1],b[2],c1,c2,c3);
479 mul_add_c(a[2],b[1],c1,c2,c3);
480 mul_add_c(a[3],b[0],c1,c2,c3);
483 mul_add_c(a[3],b[1],c2,c3,c1);
484 mul_add_c(a[2],b[2],c2,c3,c1);
485 mul_add_c(a[1],b[3],c2,c3,c1);
488 mul_add_c(a[2],b[3],c3,c1,c2);
489 mul_add_c(a[3],b[2],c3,c1,c2);
492 mul_add_c(a[3],b[3],c1,c2,c3);
497 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
504 sqr_add_c(a,0,c1,c2,c3);
507 sqr_add_c2(a,1,0,c2,c3,c1);
510 sqr_add_c(a,1,c3,c1,c2);
511 sqr_add_c2(a,2,0,c3,c1,c2);
514 sqr_add_c2(a,3,0,c1,c2,c3);
515 sqr_add_c2(a,2,1,c1,c2,c3);
518 sqr_add_c(a,2,c2,c3,c1);
519 sqr_add_c2(a,3,1,c2,c3,c1);
520 sqr_add_c2(a,4,0,c2,c3,c1);
523 sqr_add_c2(a,5,0,c3,c1,c2);
524 sqr_add_c2(a,4,1,c3,c1,c2);
525 sqr_add_c2(a,3,2,c3,c1,c2);
528 sqr_add_c(a,3,c1,c2,c3);
529 sqr_add_c2(a,4,2,c1,c2,c3);
530 sqr_add_c2(a,5,1,c1,c2,c3);
531 sqr_add_c2(a,6,0,c1,c2,c3);
534 sqr_add_c2(a,7,0,c2,c3,c1);
535 sqr_add_c2(a,6,1,c2,c3,c1);
536 sqr_add_c2(a,5,2,c2,c3,c1);
537 sqr_add_c2(a,4,3,c2,c3,c1);
540 sqr_add_c(a,4,c3,c1,c2);
541 sqr_add_c2(a,5,3,c3,c1,c2);
542 sqr_add_c2(a,6,2,c3,c1,c2);
543 sqr_add_c2(a,7,1,c3,c1,c2);
546 sqr_add_c2(a,7,2,c1,c2,c3);
547 sqr_add_c2(a,6,3,c1,c2,c3);
548 sqr_add_c2(a,5,4,c1,c2,c3);
551 sqr_add_c(a,5,c2,c3,c1);
552 sqr_add_c2(a,6,4,c2,c3,c1);
553 sqr_add_c2(a,7,3,c2,c3,c1);
556 sqr_add_c2(a,7,4,c3,c1,c2);
557 sqr_add_c2(a,6,5,c3,c1,c2);
560 sqr_add_c(a,6,c1,c2,c3);
561 sqr_add_c2(a,7,5,c1,c2,c3);
564 sqr_add_c2(a,7,6,c2,c3,c1);
567 sqr_add_c(a,7,c3,c1,c2);
572 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
579 sqr_add_c(a,0,c1,c2,c3);
582 sqr_add_c2(a,1,0,c2,c3,c1);
585 sqr_add_c(a,1,c3,c1,c2);
586 sqr_add_c2(a,2,0,c3,c1,c2);
589 sqr_add_c2(a,3,0,c1,c2,c3);
590 sqr_add_c2(a,2,1,c1,c2,c3);
593 sqr_add_c(a,2,c2,c3,c1);
594 sqr_add_c2(a,3,1,c2,c3,c1);
597 sqr_add_c2(a,3,2,c3,c1,c2);
600 sqr_add_c(a,3,c1,c2,c3);