1 /* crypto/bn/bn_asm.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58
59 #ifndef BN_DEBUG
60 # undef NDEBUG /* avoid conflicting definitions */
61 # define NDEBUG
62 #endif
63
64 #include <stdio.h>
65 #include <assert.h>
66 #include "cryptlib.h"
67 #include "bn_lcl.h"
68
69 #if defined(BN_LLONG) || defined(BN_UMULT_HIGH)
70
bn_mul_add_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)71 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
72 BN_ULONG w)
73 {
74 BN_ULONG c1 = 0;
75
76 assert(num >= 0);
77 if (num <= 0)
78 return (c1);
79
80 # ifndef OPENSSL_SMALL_FOOTPRINT
81 while (num & ~3) {
82 mul_add(rp[0], ap[0], w, c1);
83 mul_add(rp[1], ap[1], w, c1);
84 mul_add(rp[2], ap[2], w, c1);
85 mul_add(rp[3], ap[3], w, c1);
86 ap += 4;
87 rp += 4;
88 num -= 4;
89 }
90 # endif
91 while (num) {
92 mul_add(rp[0], ap[0], w, c1);
93 ap++;
94 rp++;
95 num--;
96 }
97
98 return (c1);
99 }
100
bn_mul_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)101 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
102 {
103 BN_ULONG c1 = 0;
104
105 assert(num >= 0);
106 if (num <= 0)
107 return (c1);
108
109 # ifndef OPENSSL_SMALL_FOOTPRINT
110 while (num & ~3) {
111 mul(rp[0], ap[0], w, c1);
112 mul(rp[1], ap[1], w, c1);
113 mul(rp[2], ap[2], w, c1);
114 mul(rp[3], ap[3], w, c1);
115 ap += 4;
116 rp += 4;
117 num -= 4;
118 }
119 # endif
120 while (num) {
121 mul(rp[0], ap[0], w, c1);
122 ap++;
123 rp++;
124 num--;
125 }
126 return (c1);
127 }
128
bn_sqr_words(BN_ULONG * r,const BN_ULONG * a,int n)129 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
130 {
131 assert(n >= 0);
132 if (n <= 0)
133 return;
134
135 # ifndef OPENSSL_SMALL_FOOTPRINT
136 while (n & ~3) {
137 sqr(r[0], r[1], a[0]);
138 sqr(r[2], r[3], a[1]);
139 sqr(r[4], r[5], a[2]);
140 sqr(r[6], r[7], a[3]);
141 a += 4;
142 r += 8;
143 n -= 4;
144 }
145 # endif
146 while (n) {
147 sqr(r[0], r[1], a[0]);
148 a++;
149 r += 2;
150 n--;
151 }
152 }
153
154 #else /* !(defined(BN_LLONG) ||
155 * defined(BN_UMULT_HIGH)) */
156
bn_mul_add_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)157 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
158 BN_ULONG w)
159 {
160 BN_ULONG c = 0;
161 BN_ULONG bl, bh;
162
163 assert(num >= 0);
164 if (num <= 0)
165 return ((BN_ULONG)0);
166
167 bl = LBITS(w);
168 bh = HBITS(w);
169
170 # ifndef OPENSSL_SMALL_FOOTPRINT
171 while (num & ~3) {
172 mul_add(rp[0], ap[0], bl, bh, c);
173 mul_add(rp[1], ap[1], bl, bh, c);
174 mul_add(rp[2], ap[2], bl, bh, c);
175 mul_add(rp[3], ap[3], bl, bh, c);
176 ap += 4;
177 rp += 4;
178 num -= 4;
179 }
180 # endif
181 while (num) {
182 mul_add(rp[0], ap[0], bl, bh, c);
183 ap++;
184 rp++;
185 num--;
186 }
187 return (c);
188 }
189
bn_mul_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)190 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
191 {
192 BN_ULONG carry = 0;
193 BN_ULONG bl, bh;
194
195 assert(num >= 0);
196 if (num <= 0)
197 return ((BN_ULONG)0);
198
199 bl = LBITS(w);
200 bh = HBITS(w);
201
202 # ifndef OPENSSL_SMALL_FOOTPRINT
203 while (num & ~3) {
204 mul(rp[0], ap[0], bl, bh, carry);
205 mul(rp[1], ap[1], bl, bh, carry);
206 mul(rp[2], ap[2], bl, bh, carry);
207 mul(rp[3], ap[3], bl, bh, carry);
208 ap += 4;
209 rp += 4;
210 num -= 4;
211 }
212 # endif
213 while (num) {
214 mul(rp[0], ap[0], bl, bh, carry);
215 ap++;
216 rp++;
217 num--;
218 }
219 return (carry);
220 }
221
bn_sqr_words(BN_ULONG * r,const BN_ULONG * a,int n)222 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
223 {
224 assert(n >= 0);
225 if (n <= 0)
226 return;
227
228 # ifndef OPENSSL_SMALL_FOOTPRINT
229 while (n & ~3) {
230 sqr64(r[0], r[1], a[0]);
231 sqr64(r[2], r[3], a[1]);
232 sqr64(r[4], r[5], a[2]);
233 sqr64(r[6], r[7], a[3]);
234 a += 4;
235 r += 8;
236 n -= 4;
237 }
238 # endif
239 while (n) {
240 sqr64(r[0], r[1], a[0]);
241 a++;
242 r += 2;
243 n--;
244 }
245 }
246
247 #endif /* !(defined(BN_LLONG) ||
248 * defined(BN_UMULT_HIGH)) */
249
250 #if defined(BN_LLONG) && defined(BN_DIV2W)
251
bn_div_words(BN_ULONG h,BN_ULONG l,BN_ULONG d)252 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
253 {
254 return ((BN_ULONG)(((((BN_ULLONG) h) << BN_BITS2) | l) / (BN_ULLONG) d));
255 }
256
257 #else
258
259 /* Divide h,l by d and return the result. */
260 /* I need to test this some more :-( */
bn_div_words(BN_ULONG h,BN_ULONG l,BN_ULONG d)261 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
262 {
263 BN_ULONG dh, dl, q, ret = 0, th, tl, t;
264 int i, count = 2;
265
266 if (d == 0)
267 return (BN_MASK2);
268
269 i = BN_num_bits_word(d);
270 assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));
271
272 i = BN_BITS2 - i;
273 if (h >= d)
274 h -= d;
275
276 if (i) {
277 d <<= i;
278 h = (h << i) | (l >> (BN_BITS2 - i));
279 l <<= i;
280 }
281 dh = (d & BN_MASK2h) >> BN_BITS4;
282 dl = (d & BN_MASK2l);
283 for (;;) {
284 if ((h >> BN_BITS4) == dh)
285 q = BN_MASK2l;
286 else
287 q = h / dh;
288
289 th = q * dh;
290 tl = dl * q;
291 for (;;) {
292 t = h - th;
293 if ((t & BN_MASK2h) ||
294 ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4))))
295 break;
296 q--;
297 th -= dh;
298 tl -= dl;
299 }
300 t = (tl >> BN_BITS4);
301 tl = (tl << BN_BITS4) & BN_MASK2h;
302 th += t;
303
304 if (l < tl)
305 th++;
306 l -= tl;
307 if (h < th) {
308 h += d;
309 q--;
310 }
311 h -= th;
312
313 if (--count == 0)
314 break;
315
316 ret = q << BN_BITS4;
317 h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2;
318 l = (l & BN_MASK2l) << BN_BITS4;
319 }
320 ret |= q;
321 return (ret);
322 }
323 #endif /* !defined(BN_LLONG) && defined(BN_DIV2W) */
324
325 #ifdef BN_LLONG
bn_add_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int n)326 BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
327 int n)
328 {
329 BN_ULLONG ll = 0;
330
331 assert(n >= 0);
332 if (n <= 0)
333 return ((BN_ULONG)0);
334
335 # ifndef OPENSSL_SMALL_FOOTPRINT
336 while (n & ~3) {
337 ll += (BN_ULLONG) a[0] + b[0];
338 r[0] = (BN_ULONG)ll & BN_MASK2;
339 ll >>= BN_BITS2;
340 ll += (BN_ULLONG) a[1] + b[1];
341 r[1] = (BN_ULONG)ll & BN_MASK2;
342 ll >>= BN_BITS2;
343 ll += (BN_ULLONG) a[2] + b[2];
344 r[2] = (BN_ULONG)ll & BN_MASK2;
345 ll >>= BN_BITS2;
346 ll += (BN_ULLONG) a[3] + b[3];
347 r[3] = (BN_ULONG)ll & BN_MASK2;
348 ll >>= BN_BITS2;
349 a += 4;
350 b += 4;
351 r += 4;
352 n -= 4;
353 }
354 # endif
355 while (n) {
356 ll += (BN_ULLONG) a[0] + b[0];
357 r[0] = (BN_ULONG)ll & BN_MASK2;
358 ll >>= BN_BITS2;
359 a++;
360 b++;
361 r++;
362 n--;
363 }
364 return ((BN_ULONG)ll);
365 }
366 #else /* !BN_LLONG */
bn_add_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int n)367 BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
368 int n)
369 {
370 BN_ULONG c, l, t;
371
372 assert(n >= 0);
373 if (n <= 0)
374 return ((BN_ULONG)0);
375
376 c = 0;
377 # ifndef OPENSSL_SMALL_FOOTPRINT
378 while (n & ~3) {
379 t = a[0];
380 t = (t + c) & BN_MASK2;
381 c = (t < c);
382 l = (t + b[0]) & BN_MASK2;
383 c += (l < t);
384 r[0] = l;
385 t = a[1];
386 t = (t + c) & BN_MASK2;
387 c = (t < c);
388 l = (t + b[1]) & BN_MASK2;
389 c += (l < t);
390 r[1] = l;
391 t = a[2];
392 t = (t + c) & BN_MASK2;
393 c = (t < c);
394 l = (t + b[2]) & BN_MASK2;
395 c += (l < t);
396 r[2] = l;
397 t = a[3];
398 t = (t + c) & BN_MASK2;
399 c = (t < c);
400 l = (t + b[3]) & BN_MASK2;
401 c += (l < t);
402 r[3] = l;
403 a += 4;
404 b += 4;
405 r += 4;
406 n -= 4;
407 }
408 # endif
409 while (n) {
410 t = a[0];
411 t = (t + c) & BN_MASK2;
412 c = (t < c);
413 l = (t + b[0]) & BN_MASK2;
414 c += (l < t);
415 r[0] = l;
416 a++;
417 b++;
418 r++;
419 n--;
420 }
421 return ((BN_ULONG)c);
422 }
423 #endif /* !BN_LLONG */
424
bn_sub_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int n)425 BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
426 int n)
427 {
428 BN_ULONG t1, t2;
429 int c = 0;
430
431 assert(n >= 0);
432 if (n <= 0)
433 return ((BN_ULONG)0);
434
435 #ifndef OPENSSL_SMALL_FOOTPRINT
436 while (n & ~3) {
437 t1 = a[0];
438 t2 = b[0];
439 r[0] = (t1 - t2 - c) & BN_MASK2;
440 if (t1 != t2)
441 c = (t1 < t2);
442 t1 = a[1];
443 t2 = b[1];
444 r[1] = (t1 - t2 - c) & BN_MASK2;
445 if (t1 != t2)
446 c = (t1 < t2);
447 t1 = a[2];
448 t2 = b[2];
449 r[2] = (t1 - t2 - c) & BN_MASK2;
450 if (t1 != t2)
451 c = (t1 < t2);
452 t1 = a[3];
453 t2 = b[3];
454 r[3] = (t1 - t2 - c) & BN_MASK2;
455 if (t1 != t2)
456 c = (t1 < t2);
457 a += 4;
458 b += 4;
459 r += 4;
460 n -= 4;
461 }
462 #endif
463 while (n) {
464 t1 = a[0];
465 t2 = b[0];
466 r[0] = (t1 - t2 - c) & BN_MASK2;
467 if (t1 != t2)
468 c = (t1 < t2);
469 a++;
470 b++;
471 r++;
472 n--;
473 }
474 return (c);
475 }
476
477 #if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT)
478
479 # undef bn_mul_comba8
480 # undef bn_mul_comba4
481 # undef bn_sqr_comba8
482 # undef bn_sqr_comba4
483
484 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
485 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
486 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
487 /*
488 * sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number
489 * c=(c2,c1,c0)
490 */
491
492 /*
493 * Keep in mind that carrying into high part of multiplication result
494 * can not overflow, because it cannot be all-ones.
495 */
496 # ifdef BN_LLONG
497 # define mul_add_c(a,b,c0,c1,c2) \
498 t=(BN_ULLONG)a*b; \
499 t1=(BN_ULONG)Lw(t); \
500 t2=(BN_ULONG)Hw(t); \
501 c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
502 c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;
503
504 # define mul_add_c2(a,b,c0,c1,c2) \
505 t=(BN_ULLONG)a*b; \
506 tt=(t+t)&BN_MASK; \
507 if (tt < t) c2++; \
508 t1=(BN_ULONG)Lw(tt); \
509 t2=(BN_ULONG)Hw(tt); \
510 c0=(c0+t1)&BN_MASK2; \
511 if ((c0 < t1) && (((++t2)&BN_MASK2) == 0)) c2++; \
512 c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;
513
514 # define sqr_add_c(a,i,c0,c1,c2) \
515 t=(BN_ULLONG)a[i]*a[i]; \
516 t1=(BN_ULONG)Lw(t); \
517 t2=(BN_ULONG)Hw(t); \
518 c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
519 c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;
520
521 # define sqr_add_c2(a,i,j,c0,c1,c2) \
522 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
523
524 # elif defined(BN_UMULT_LOHI)
525
526 # define mul_add_c(a,b,c0,c1,c2) { \
527 BN_ULONG ta=(a),tb=(b); \
528 BN_UMULT_LOHI(t1,t2,ta,tb); \
529 c0 += t1; t2 += (c0<t1)?1:0; \
530 c1 += t2; c2 += (c1<t2)?1:0; \
531 }
532
533 # define mul_add_c2(a,b,c0,c1,c2) { \
534 BN_ULONG ta=(a),tb=(b),t0; \
535 BN_UMULT_LOHI(t0,t1,ta,tb); \
536 c0 += t0; t2 = t1+((c0<t0)?1:0);\
537 c1 += t2; c2 += (c1<t2)?1:0; \
538 c0 += t0; t1 += (c0<t0)?1:0; \
539 c1 += t1; c2 += (c1<t1)?1:0; \
540 }
541
542 # define sqr_add_c(a,i,c0,c1,c2) { \
543 BN_ULONG ta=(a)[i]; \
544 BN_UMULT_LOHI(t1,t2,ta,ta); \
545 c0 += t1; t2 += (c0<t1)?1:0; \
546 c1 += t2; c2 += (c1<t2)?1:0; \
547 }
548
549 # define sqr_add_c2(a,i,j,c0,c1,c2) \
550 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
551
552 # elif defined(BN_UMULT_HIGH)
553
554 # define mul_add_c(a,b,c0,c1,c2) { \
555 BN_ULONG ta=(a),tb=(b); \
556 t1 = ta * tb; \
557 t2 = BN_UMULT_HIGH(ta,tb); \
558 c0 += t1; t2 += (c0<t1)?1:0; \
559 c1 += t2; c2 += (c1<t2)?1:0; \
560 }
561
562 # define mul_add_c2(a,b,c0,c1,c2) { \
563 BN_ULONG ta=(a),tb=(b),t0; \
564 t1 = BN_UMULT_HIGH(ta,tb); \
565 t0 = ta * tb; \
566 c0 += t0; t2 = t1+((c0<t0)?1:0);\
567 c1 += t2; c2 += (c1<t2)?1:0; \
568 c0 += t0; t1 += (c0<t0)?1:0; \
569 c1 += t1; c2 += (c1<t1)?1:0; \
570 }
571
572 # define sqr_add_c(a,i,c0,c1,c2) { \
573 BN_ULONG ta=(a)[i]; \
574 t1 = ta * ta; \
575 t2 = BN_UMULT_HIGH(ta,ta); \
576 c0 += t1; t2 += (c0<t1)?1:0; \
577 c1 += t2; c2 += (c1<t2)?1:0; \
578 }
579
580 # define sqr_add_c2(a,i,j,c0,c1,c2) \
581 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
582
583 # else /* !BN_LLONG */
584 # define mul_add_c(a,b,c0,c1,c2) \
585 t1=LBITS(a); t2=HBITS(a); \
586 bl=LBITS(b); bh=HBITS(b); \
587 mul64(t1,t2,bl,bh); \
588 c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
589 c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;
590
591 # define mul_add_c2(a,b,c0,c1,c2) \
592 t1=LBITS(a); t2=HBITS(a); \
593 bl=LBITS(b); bh=HBITS(b); \
594 mul64(t1,t2,bl,bh); \
595 if (t2 & BN_TBIT) c2++; \
596 t2=(t2+t2)&BN_MASK2; \
597 if (t1 & BN_TBIT) t2++; \
598 t1=(t1+t1)&BN_MASK2; \
599 c0=(c0+t1)&BN_MASK2; \
600 if ((c0 < t1) && (((++t2)&BN_MASK2) == 0)) c2++; \
601 c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;
602
603 # define sqr_add_c(a,i,c0,c1,c2) \
604 sqr64(t1,t2,(a)[i]); \
605 c0=(c0+t1)&BN_MASK2; if ((c0) < t1) t2++; \
606 c1=(c1+t2)&BN_MASK2; if ((c1) < t2) c2++;
607
608 # define sqr_add_c2(a,i,j,c0,c1,c2) \
609 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
610 # endif /* !BN_LLONG */
611
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)612 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
613 {
614 # ifdef BN_LLONG
615 BN_ULLONG t;
616 # else
617 BN_ULONG bl, bh;
618 # endif
619 BN_ULONG t1, t2;
620 BN_ULONG c1, c2, c3;
621
622 c1 = 0;
623 c2 = 0;
624 c3 = 0;
625 mul_add_c(a[0], b[0], c1, c2, c3);
626 r[0] = c1;
627 c1 = 0;
628 mul_add_c(a[0], b[1], c2, c3, c1);
629 mul_add_c(a[1], b[0], c2, c3, c1);
630 r[1] = c2;
631 c2 = 0;
632 mul_add_c(a[2], b[0], c3, c1, c2);
633 mul_add_c(a[1], b[1], c3, c1, c2);
634 mul_add_c(a[0], b[2], c3, c1, c2);
635 r[2] = c3;
636 c3 = 0;
637 mul_add_c(a[0], b[3], c1, c2, c3);
638 mul_add_c(a[1], b[2], c1, c2, c3);
639 mul_add_c(a[2], b[1], c1, c2, c3);
640 mul_add_c(a[3], b[0], c1, c2, c3);
641 r[3] = c1;
642 c1 = 0;
643 mul_add_c(a[4], b[0], c2, c3, c1);
644 mul_add_c(a[3], b[1], c2, c3, c1);
645 mul_add_c(a[2], b[2], c2, c3, c1);
646 mul_add_c(a[1], b[3], c2, c3, c1);
647 mul_add_c(a[0], b[4], c2, c3, c1);
648 r[4] = c2;
649 c2 = 0;
650 mul_add_c(a[0], b[5], c3, c1, c2);
651 mul_add_c(a[1], b[4], c3, c1, c2);
652 mul_add_c(a[2], b[3], c3, c1, c2);
653 mul_add_c(a[3], b[2], c3, c1, c2);
654 mul_add_c(a[4], b[1], c3, c1, c2);
655 mul_add_c(a[5], b[0], c3, c1, c2);
656 r[5] = c3;
657 c3 = 0;
658 mul_add_c(a[6], b[0], c1, c2, c3);
659 mul_add_c(a[5], b[1], c1, c2, c3);
660 mul_add_c(a[4], b[2], c1, c2, c3);
661 mul_add_c(a[3], b[3], c1, c2, c3);
662 mul_add_c(a[2], b[4], c1, c2, c3);
663 mul_add_c(a[1], b[5], c1, c2, c3);
664 mul_add_c(a[0], b[6], c1, c2, c3);
665 r[6] = c1;
666 c1 = 0;
667 mul_add_c(a[0], b[7], c2, c3, c1);
668 mul_add_c(a[1], b[6], c2, c3, c1);
669 mul_add_c(a[2], b[5], c2, c3, c1);
670 mul_add_c(a[3], b[4], c2, c3, c1);
671 mul_add_c(a[4], b[3], c2, c3, c1);
672 mul_add_c(a[5], b[2], c2, c3, c1);
673 mul_add_c(a[6], b[1], c2, c3, c1);
674 mul_add_c(a[7], b[0], c2, c3, c1);
675 r[7] = c2;
676 c2 = 0;
677 mul_add_c(a[7], b[1], c3, c1, c2);
678 mul_add_c(a[6], b[2], c3, c1, c2);
679 mul_add_c(a[5], b[3], c3, c1, c2);
680 mul_add_c(a[4], b[4], c3, c1, c2);
681 mul_add_c(a[3], b[5], c3, c1, c2);
682 mul_add_c(a[2], b[6], c3, c1, c2);
683 mul_add_c(a[1], b[7], c3, c1, c2);
684 r[8] = c3;
685 c3 = 0;
686 mul_add_c(a[2], b[7], c1, c2, c3);
687 mul_add_c(a[3], b[6], c1, c2, c3);
688 mul_add_c(a[4], b[5], c1, c2, c3);
689 mul_add_c(a[5], b[4], c1, c2, c3);
690 mul_add_c(a[6], b[3], c1, c2, c3);
691 mul_add_c(a[7], b[2], c1, c2, c3);
692 r[9] = c1;
693 c1 = 0;
694 mul_add_c(a[7], b[3], c2, c3, c1);
695 mul_add_c(a[6], b[4], c2, c3, c1);
696 mul_add_c(a[5], b[5], c2, c3, c1);
697 mul_add_c(a[4], b[6], c2, c3, c1);
698 mul_add_c(a[3], b[7], c2, c3, c1);
699 r[10] = c2;
700 c2 = 0;
701 mul_add_c(a[4], b[7], c3, c1, c2);
702 mul_add_c(a[5], b[6], c3, c1, c2);
703 mul_add_c(a[6], b[5], c3, c1, c2);
704 mul_add_c(a[7], b[4], c3, c1, c2);
705 r[11] = c3;
706 c3 = 0;
707 mul_add_c(a[7], b[5], c1, c2, c3);
708 mul_add_c(a[6], b[6], c1, c2, c3);
709 mul_add_c(a[5], b[7], c1, c2, c3);
710 r[12] = c1;
711 c1 = 0;
712 mul_add_c(a[6], b[7], c2, c3, c1);
713 mul_add_c(a[7], b[6], c2, c3, c1);
714 r[13] = c2;
715 c2 = 0;
716 mul_add_c(a[7], b[7], c3, c1, c2);
717 r[14] = c3;
718 r[15] = c1;
719 }
720
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)721 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
722 {
723 # ifdef BN_LLONG
724 BN_ULLONG t;
725 # else
726 BN_ULONG bl, bh;
727 # endif
728 BN_ULONG t1, t2;
729 BN_ULONG c1, c2, c3;
730
731 c1 = 0;
732 c2 = 0;
733 c3 = 0;
734 mul_add_c(a[0], b[0], c1, c2, c3);
735 r[0] = c1;
736 c1 = 0;
737 mul_add_c(a[0], b[1], c2, c3, c1);
738 mul_add_c(a[1], b[0], c2, c3, c1);
739 r[1] = c2;
740 c2 = 0;
741 mul_add_c(a[2], b[0], c3, c1, c2);
742 mul_add_c(a[1], b[1], c3, c1, c2);
743 mul_add_c(a[0], b[2], c3, c1, c2);
744 r[2] = c3;
745 c3 = 0;
746 mul_add_c(a[0], b[3], c1, c2, c3);
747 mul_add_c(a[1], b[2], c1, c2, c3);
748 mul_add_c(a[2], b[1], c1, c2, c3);
749 mul_add_c(a[3], b[0], c1, c2, c3);
750 r[3] = c1;
751 c1 = 0;
752 mul_add_c(a[3], b[1], c2, c3, c1);
753 mul_add_c(a[2], b[2], c2, c3, c1);
754 mul_add_c(a[1], b[3], c2, c3, c1);
755 r[4] = c2;
756 c2 = 0;
757 mul_add_c(a[2], b[3], c3, c1, c2);
758 mul_add_c(a[3], b[2], c3, c1, c2);
759 r[5] = c3;
760 c3 = 0;
761 mul_add_c(a[3], b[3], c1, c2, c3);
762 r[6] = c1;
763 r[7] = c2;
764 }
765
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)766 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
767 {
768 # ifdef BN_LLONG
769 BN_ULLONG t, tt;
770 # else
771 BN_ULONG bl, bh;
772 # endif
773 BN_ULONG t1, t2;
774 BN_ULONG c1, c2, c3;
775
776 c1 = 0;
777 c2 = 0;
778 c3 = 0;
779 sqr_add_c(a, 0, c1, c2, c3);
780 r[0] = c1;
781 c1 = 0;
782 sqr_add_c2(a, 1, 0, c2, c3, c1);
783 r[1] = c2;
784 c2 = 0;
785 sqr_add_c(a, 1, c3, c1, c2);
786 sqr_add_c2(a, 2, 0, c3, c1, c2);
787 r[2] = c3;
788 c3 = 0;
789 sqr_add_c2(a, 3, 0, c1, c2, c3);
790 sqr_add_c2(a, 2, 1, c1, c2, c3);
791 r[3] = c1;
792 c1 = 0;
793 sqr_add_c(a, 2, c2, c3, c1);
794 sqr_add_c2(a, 3, 1, c2, c3, c1);
795 sqr_add_c2(a, 4, 0, c2, c3, c1);
796 r[4] = c2;
797 c2 = 0;
798 sqr_add_c2(a, 5, 0, c3, c1, c2);
799 sqr_add_c2(a, 4, 1, c3, c1, c2);
800 sqr_add_c2(a, 3, 2, c3, c1, c2);
801 r[5] = c3;
802 c3 = 0;
803 sqr_add_c(a, 3, c1, c2, c3);
804 sqr_add_c2(a, 4, 2, c1, c2, c3);
805 sqr_add_c2(a, 5, 1, c1, c2, c3);
806 sqr_add_c2(a, 6, 0, c1, c2, c3);
807 r[6] = c1;
808 c1 = 0;
809 sqr_add_c2(a, 7, 0, c2, c3, c1);
810 sqr_add_c2(a, 6, 1, c2, c3, c1);
811 sqr_add_c2(a, 5, 2, c2, c3, c1);
812 sqr_add_c2(a, 4, 3, c2, c3, c1);
813 r[7] = c2;
814 c2 = 0;
815 sqr_add_c(a, 4, c3, c1, c2);
816 sqr_add_c2(a, 5, 3, c3, c1, c2);
817 sqr_add_c2(a, 6, 2, c3, c1, c2);
818 sqr_add_c2(a, 7, 1, c3, c1, c2);
819 r[8] = c3;
820 c3 = 0;
821 sqr_add_c2(a, 7, 2, c1, c2, c3);
822 sqr_add_c2(a, 6, 3, c1, c2, c3);
823 sqr_add_c2(a, 5, 4, c1, c2, c3);
824 r[9] = c1;
825 c1 = 0;
826 sqr_add_c(a, 5, c2, c3, c1);
827 sqr_add_c2(a, 6, 4, c2, c3, c1);
828 sqr_add_c2(a, 7, 3, c2, c3, c1);
829 r[10] = c2;
830 c2 = 0;
831 sqr_add_c2(a, 7, 4, c3, c1, c2);
832 sqr_add_c2(a, 6, 5, c3, c1, c2);
833 r[11] = c3;
834 c3 = 0;
835 sqr_add_c(a, 6, c1, c2, c3);
836 sqr_add_c2(a, 7, 5, c1, c2, c3);
837 r[12] = c1;
838 c1 = 0;
839 sqr_add_c2(a, 7, 6, c2, c3, c1);
840 r[13] = c2;
841 c2 = 0;
842 sqr_add_c(a, 7, c3, c1, c2);
843 r[14] = c3;
844 r[15] = c1;
845 }
846
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)847 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
848 {
849 # ifdef BN_LLONG
850 BN_ULLONG t, tt;
851 # else
852 BN_ULONG bl, bh;
853 # endif
854 BN_ULONG t1, t2;
855 BN_ULONG c1, c2, c3;
856
857 c1 = 0;
858 c2 = 0;
859 c3 = 0;
860 sqr_add_c(a, 0, c1, c2, c3);
861 r[0] = c1;
862 c1 = 0;
863 sqr_add_c2(a, 1, 0, c2, c3, c1);
864 r[1] = c2;
865 c2 = 0;
866 sqr_add_c(a, 1, c3, c1, c2);
867 sqr_add_c2(a, 2, 0, c3, c1, c2);
868 r[2] = c3;
869 c3 = 0;
870 sqr_add_c2(a, 3, 0, c1, c2, c3);
871 sqr_add_c2(a, 2, 1, c1, c2, c3);
872 r[3] = c1;
873 c1 = 0;
874 sqr_add_c(a, 2, c2, c3, c1);
875 sqr_add_c2(a, 3, 1, c2, c3, c1);
876 r[4] = c2;
877 c2 = 0;
878 sqr_add_c2(a, 3, 2, c3, c1, c2);
879 r[5] = c3;
880 c3 = 0;
881 sqr_add_c(a, 3, c1, c2, c3);
882 r[6] = c1;
883 r[7] = c2;
884 }
885
886 # ifdef OPENSSL_NO_ASM
887 # ifdef OPENSSL_BN_ASM_MONT
888 # include <alloca.h>
889 /*
890 * This is essentially reference implementation, which may or may not
891 * result in performance improvement. E.g. on IA-32 this routine was
892 * observed to give 40% faster rsa1024 private key operations and 10%
893 * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
894 * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
895 * reference implementation, one to be used as starting point for
896 * platform-specific assembler. Mentioned numbers apply to compiler
897 * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
898 * can vary not only from platform to platform, but even for compiler
899 * versions. Assembler vs. assembler improvement coefficients can
900 * [and are known to] differ and are to be documented elsewhere.
901 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0p,int num)902 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
903 const BN_ULONG *np, const BN_ULONG *n0p, int num)
904 {
905 BN_ULONG c0, c1, ml, *tp, n0;
906 # ifdef mul64
907 BN_ULONG mh;
908 # endif
909 volatile BN_ULONG *vp;
910 int i = 0, j;
911
912 # if 0 /* template for platform-specific
913 * implementation */
914 if (ap == bp)
915 return bn_sqr_mont(rp, ap, np, n0p, num);
916 # endif
917 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
918
919 n0 = *n0p;
920
921 c0 = 0;
922 ml = bp[0];
923 # ifdef mul64
924 mh = HBITS(ml);
925 ml = LBITS(ml);
926 for (j = 0; j < num; ++j)
927 mul(tp[j], ap[j], ml, mh, c0);
928 # else
929 for (j = 0; j < num; ++j)
930 mul(tp[j], ap[j], ml, c0);
931 # endif
932
933 tp[num] = c0;
934 tp[num + 1] = 0;
935 goto enter;
936
937 for (i = 0; i < num; i++) {
938 c0 = 0;
939 ml = bp[i];
940 # ifdef mul64
941 mh = HBITS(ml);
942 ml = LBITS(ml);
943 for (j = 0; j < num; ++j)
944 mul_add(tp[j], ap[j], ml, mh, c0);
945 # else
946 for (j = 0; j < num; ++j)
947 mul_add(tp[j], ap[j], ml, c0);
948 # endif
949 c1 = (tp[num] + c0) & BN_MASK2;
950 tp[num] = c1;
951 tp[num + 1] = (c1 < c0 ? 1 : 0);
952 enter:
953 c1 = tp[0];
954 ml = (c1 * n0) & BN_MASK2;
955 c0 = 0;
956 # ifdef mul64
957 mh = HBITS(ml);
958 ml = LBITS(ml);
959 mul_add(c1, np[0], ml, mh, c0);
960 # else
961 mul_add(c1, ml, np[0], c0);
962 # endif
963 for (j = 1; j < num; j++) {
964 c1 = tp[j];
965 # ifdef mul64
966 mul_add(c1, np[j], ml, mh, c0);
967 # else
968 mul_add(c1, ml, np[j], c0);
969 # endif
970 tp[j - 1] = c1 & BN_MASK2;
971 }
972 c1 = (tp[num] + c0) & BN_MASK2;
973 tp[num - 1] = c1;
974 tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0);
975 }
976
977 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
978 c0 = bn_sub_words(rp, tp, np, num);
979 if (tp[num] != 0 || c0 == 0) {
980 for (i = 0; i < num + 2; i++)
981 vp[i] = 0;
982 return 1;
983 }
984 }
985 for (i = 0; i < num; i++)
986 rp[i] = tp[i], vp[i] = 0;
987 vp[num] = 0;
988 vp[num + 1] = 0;
989 return 1;
990 }
991 # else
992 /*
993 * Return value of 0 indicates that multiplication/convolution was not
994 * performed to signal the caller to fall down to alternative/original
995 * code-path.
996 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0,int num)997 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
998 const BN_ULONG *np, const BN_ULONG *n0, int num)
999 {
1000 return 0;
1001 }
1002 # endif /* OPENSSL_BN_ASM_MONT */
1003 # endif
1004
1005 #else /* !BN_MUL_COMBA */
1006
1007 /* hmm... is it faster just to do a multiply? */
1008 # undef bn_sqr_comba4
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)1009 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
1010 {
1011 BN_ULONG t[8];
1012 bn_sqr_normal(r, a, 4, t);
1013 }
1014
1015 # undef bn_sqr_comba8
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)1016 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
1017 {
1018 BN_ULONG t[16];
1019 bn_sqr_normal(r, a, 8, t);
1020 }
1021
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)1022 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
1023 {
1024 r[4] = bn_mul_words(&(r[0]), a, 4, b[0]);
1025 r[5] = bn_mul_add_words(&(r[1]), a, 4, b[1]);
1026 r[6] = bn_mul_add_words(&(r[2]), a, 4, b[2]);
1027 r[7] = bn_mul_add_words(&(r[3]), a, 4, b[3]);
1028 }
1029
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)1030 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
1031 {
1032 r[8] = bn_mul_words(&(r[0]), a, 8, b[0]);
1033 r[9] = bn_mul_add_words(&(r[1]), a, 8, b[1]);
1034 r[10] = bn_mul_add_words(&(r[2]), a, 8, b[2]);
1035 r[11] = bn_mul_add_words(&(r[3]), a, 8, b[3]);
1036 r[12] = bn_mul_add_words(&(r[4]), a, 8, b[4]);
1037 r[13] = bn_mul_add_words(&(r[5]), a, 8, b[5]);
1038 r[14] = bn_mul_add_words(&(r[6]), a, 8, b[6]);
1039 r[15] = bn_mul_add_words(&(r[7]), a, 8, b[7]);
1040 }
1041
1042 # ifdef OPENSSL_NO_ASM
1043 # ifdef OPENSSL_BN_ASM_MONT
1044 # include <alloca.h>
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0p,int num)1045 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
1046 const BN_ULONG *np, const BN_ULONG *n0p, int num)
1047 {
1048 BN_ULONG c0, c1, *tp, n0 = *n0p;
1049 volatile BN_ULONG *vp;
1050 int i = 0, j;
1051
1052 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
1053
1054 for (i = 0; i <= num; i++)
1055 tp[i] = 0;
1056
1057 for (i = 0; i < num; i++) {
1058 c0 = bn_mul_add_words(tp, ap, num, bp[i]);
1059 c1 = (tp[num] + c0) & BN_MASK2;
1060 tp[num] = c1;
1061 tp[num + 1] = (c1 < c0 ? 1 : 0);
1062
1063 c0 = bn_mul_add_words(tp, np, num, tp[0] * n0);
1064 c1 = (tp[num] + c0) & BN_MASK2;
1065 tp[num] = c1;
1066 tp[num + 1] += (c1 < c0 ? 1 : 0);
1067 for (j = 0; j <= num; j++)
1068 tp[j] = tp[j + 1];
1069 }
1070
1071 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
1072 c0 = bn_sub_words(rp, tp, np, num);
1073 if (tp[num] != 0 || c0 == 0) {
1074 for (i = 0; i < num + 2; i++)
1075 vp[i] = 0;
1076 return 1;
1077 }
1078 }
1079 for (i = 0; i < num; i++)
1080 rp[i] = tp[i], vp[i] = 0;
1081 vp[num] = 0;
1082 vp[num + 1] = 0;
1083 return 1;
1084 }
1085 # else
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0,int num)1086 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
1087 const BN_ULONG *np, const BN_ULONG *n0, int num)
1088 {
1089 return 0;
1090 }
1091 # endif /* OPENSSL_BN_ASM_MONT */
1092 # endif
1093
1094 #endif /* !BN_MUL_COMBA */
1095