GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libcrypto/bn/bn_mul.c Lines: 243 487 49.9 %
Date: 2017-11-07 Branches: 142 320 44.4 %

Line Branch Exec Source
1
/* $OpenBSD: bn_mul.c,v 1.20 2015/02/09 15:49:22 jsing Exp $ */
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 <assert.h>
65
#include <stdio.h>
66
#include <string.h>
67
68
#include <openssl/opensslconf.h>
69
70
#include "bn_lcl.h"
71
72
#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
73
/* Here follows specialised variants of bn_add_words() and
74
   bn_sub_words().  They have the property performing operations on
75
   arrays of different sizes.  The sizes of those arrays is expressed through
76
   cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
77
   which is the delta between the two lengths, calculated as len(a)-len(b).
78
   All lengths are the number of BN_ULONGs...  For the operations that require
79
   a result array as parameter, it must have the length cl+abs(dl).
80
   These functions should probably end up in bn_asm.c as soon as there are
81
   assembler counterparts for the systems that use assembler files.  */
82
83
BN_ULONG
84
bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
85
    int dl)
86
{
87
	BN_ULONG c, t;
88
89
	assert(cl >= 0);
90
1373580
	c = bn_sub_words(r, a, b, cl);
91
92
686790
	if (dl == 0)
93
661367
		return c;
94
95
25423
	r += cl;
96
25423
	a += cl;
97
25423
	b += cl;
98
99
25423
	if (dl < 0) {
100
#ifdef BN_COUNT
101
		fprintf(stderr,
102
		    "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n",
103
		    cl, dl, c);
104
#endif
105
196
		for (;;) {
106
220
			t = b[0];
107
220
			r[0] = (0 - t - c) & BN_MASK2;
108
220
			if (t != 0)
109
				c = 1;
110
220
			if (++dl >= 0)
111
				break;
112
113
220
			t = b[1];
114
220
			r[1] = (0 - t - c) & BN_MASK2;
115
220
			if (t != 0)
116
				c = 1;
117
220
			if (++dl >= 0)
118
				break;
119
120
220
			t = b[2];
121
220
			r[2] = (0 - t - c) & BN_MASK2;
122
220
			if (t != 0)
123
				c = 1;
124
220
			if (++dl >= 0)
125
				break;
126
127
196
			t = b[3];
128
196
			r[3] = (0 - t - c) & BN_MASK2;
129
196
			if (t != 0)
130
				c = 1;
131
196
			if (++dl >= 0)
132
				break;
133
134
196
			b += 4;
135
196
			r += 4;
136
		}
137
	} else {
138
		int save_dl = dl;
139
#ifdef BN_COUNT
140
		fprintf(stderr,
141
		    "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n",
142
		    cl, dl, c);
143
#endif
144
58584
		while (c) {
145
18215
			t = a[0];
146
18215
			r[0] = (t - c) & BN_MASK2;
147
18215
			if (t != 0)
148
18193
				c = 0;
149
18215
			if (--dl <= 0)
150
				break;
151
152
3898
			t = a[1];
153
3898
			r[1] = (t - c) & BN_MASK2;
154
3898
			if (t != 0)
155
3890
				c = 0;
156
3898
			if (--dl <= 0)
157
				break;
158
159
3898
			t = a[2];
160
3898
			r[2] = (t - c) & BN_MASK2;
161
3898
			if (t != 0)
162
3884
				c = 0;
163
3898
			if (--dl <= 0)
164
				break;
165
166
3898
			t = a[3];
167
3898
			r[3] = (t - c) & BN_MASK2;
168
3898
			if (t != 0)
169
3889
				c = 0;
170
3898
			if (--dl <= 0)
171
				break;
172
173
			save_dl = dl;
174
3893
			a += 4;
175
3893
			r += 4;
176
		}
177
25399
		if (dl > 0) {
178
#ifdef BN_COUNT
179
			fprintf(stderr,
180
			    "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n",
181
			    cl, dl);
182
#endif
183
11077
			if (save_dl > dl) {
184
				switch (save_dl - dl) {
185
				case 1:
186
					r[1] = a[1];
187
					if (--dl <= 0)
188
						break;
189
				case 2:
190
					r[2] = a[2];
191
					if (--dl <= 0)
192
						break;
193
				case 3:
194
					r[3] = a[3];
195
					if (--dl <= 0)
196
						break;
197
				}
198
				a += 4;
199
				r += 4;
200
			}
201
		}
202
25399
		if (dl > 0) {
203
#ifdef BN_COUNT
204
			fprintf(stderr,
205
			    "  bn_sub_part_words %d + %d (dl > 0, copy)\n",
206
			    cl, dl);
207
#endif
208
32178
			for (;;) {
209
43255
				r[0] = a[0];
210
43255
				if (--dl <= 0)
211
					break;
212
37790
				r[1] = a[1];
213
37790
				if (--dl <= 0)
214
					break;
215
36756
				r[2] = a[2];
216
36756
				if (--dl <= 0)
217
					break;
218
35822
				r[3] = a[3];
219
35822
				if (--dl <= 0)
220
					break;
221
222
32178
				a += 4;
223
32178
				r += 4;
224
			}
225
		}
226
	}
227
25423
	return c;
228
686790
}
229
#endif
230
231
BN_ULONG
232
bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
233
    int dl)
234
{
235
	BN_ULONG c, l, t;
236
237
	assert(cl >= 0);
238
	c = bn_add_words(r, a, b, cl);
239
240
	if (dl == 0)
241
		return c;
242
243
	r += cl;
244
	a += cl;
245
	b += cl;
246
247
	if (dl < 0) {
248
		int save_dl = dl;
249
#ifdef BN_COUNT
250
		fprintf(stderr,
251
		    "  bn_add_part_words %d + %d (dl < 0, c = %d)\n",
252
		    cl, dl, c);
253
#endif
254
		while (c) {
255
			l = (c + b[0]) & BN_MASK2;
256
			c = (l < c);
257
			r[0] = l;
258
			if (++dl >= 0)
259
				break;
260
261
			l = (c + b[1]) & BN_MASK2;
262
			c = (l < c);
263
			r[1] = l;
264
			if (++dl >= 0)
265
				break;
266
267
			l = (c + b[2]) & BN_MASK2;
268
			c = (l < c);
269
			r[2] = l;
270
			if (++dl >= 0)
271
				break;
272
273
			l = (c + b[3]) & BN_MASK2;
274
			c = (l < c);
275
			r[3] = l;
276
			if (++dl >= 0)
277
				break;
278
279
			save_dl = dl;
280
			b += 4;
281
			r += 4;
282
		}
283
		if (dl < 0) {
284
#ifdef BN_COUNT
285
			fprintf(stderr,
286
			    "  bn_add_part_words %d + %d (dl < 0, c == 0)\n",
287
			    cl, dl);
288
#endif
289
			if (save_dl < dl) {
290
				switch (dl - save_dl) {
291
				case 1:
292
					r[1] = b[1];
293
					if (++dl >= 0)
294
						break;
295
				case 2:
296
					r[2] = b[2];
297
					if (++dl >= 0)
298
						break;
299
				case 3:
300
					r[3] = b[3];
301
					if (++dl >= 0)
302
						break;
303
				}
304
				b += 4;
305
				r += 4;
306
			}
307
		}
308
		if (dl < 0) {
309
#ifdef BN_COUNT
310
			fprintf(stderr,
311
			    "  bn_add_part_words %d + %d (dl < 0, copy)\n",
312
			    cl, dl);
313
#endif
314
			for (;;) {
315
				r[0] = b[0];
316
				if (++dl >= 0)
317
					break;
318
				r[1] = b[1];
319
				if (++dl >= 0)
320
					break;
321
				r[2] = b[2];
322
				if (++dl >= 0)
323
					break;
324
				r[3] = b[3];
325
				if (++dl >= 0)
326
					break;
327
328
				b += 4;
329
				r += 4;
330
			}
331
		}
332
	} else {
333
		int save_dl = dl;
334
#ifdef BN_COUNT
335
		fprintf(stderr,
336
		    "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
337
#endif
338
		while (c) {
339
			t = (a[0] + c) & BN_MASK2;
340
			c = (t < c);
341
			r[0] = t;
342
			if (--dl <= 0)
343
				break;
344
345
			t = (a[1] + c) & BN_MASK2;
346
			c = (t < c);
347
			r[1] = t;
348
			if (--dl <= 0)
349
				break;
350
351
			t = (a[2] + c) & BN_MASK2;
352
			c = (t < c);
353
			r[2] = t;
354
			if (--dl <= 0)
355
				break;
356
357
			t = (a[3] + c) & BN_MASK2;
358
			c = (t < c);
359
			r[3] = t;
360
			if (--dl <= 0)
361
				break;
362
363
			save_dl = dl;
364
			a += 4;
365
			r += 4;
366
		}
367
#ifdef BN_COUNT
368
		fprintf(stderr,
369
		    "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
370
#endif
371
		if (dl > 0) {
372
			if (save_dl > dl) {
373
				switch (save_dl - dl) {
374
				case 1:
375
					r[1] = a[1];
376
					if (--dl <= 0)
377
						break;
378
				case 2:
379
					r[2] = a[2];
380
					if (--dl <= 0)
381
						break;
382
				case 3:
383
					r[3] = a[3];
384
					if (--dl <= 0)
385
						break;
386
				}
387
				a += 4;
388
				r += 4;
389
			}
390
		}
391
		if (dl > 0) {
392
#ifdef BN_COUNT
393
			fprintf(stderr,
394
			    "  bn_add_part_words %d + %d (dl > 0, copy)\n",
395
			    cl, dl);
396
#endif
397
			for (;;) {
398
				r[0] = a[0];
399
				if (--dl <= 0)
400
					break;
401
				r[1] = a[1];
402
				if (--dl <= 0)
403
					break;
404
				r[2] = a[2];
405
				if (--dl <= 0)
406
					break;
407
				r[3] = a[3];
408
				if (--dl <= 0)
409
					break;
410
411
				a += 4;
412
				r += 4;
413
			}
414
		}
415
	}
416
	return c;
417
}
418
419
#ifdef BN_RECURSION
420
/* Karatsuba recursive multiplication algorithm
421
 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
422
423
/* r is 2*n2 words in size,
424
 * a and b are both n2 words in size.
425
 * n2 must be a power of 2.
426
 * We multiply and return the result.
427
 * t must be 2*n2 words in size
428
 * We calculate
429
 * a[0]*b[0]
430
 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
431
 * a[1]*b[1]
432
 */
433
/* dnX may not be positive, but n2/2+dnX has to be */
434
void
435
bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna,
436
    int dnb, BN_ULONG *t)
437
{
438
715200
	int n = n2 / 2, c1, c2;
439
357600
	int tna = n + dna, tnb = n + dnb;
440
	unsigned int neg, zero;
441
	BN_ULONG ln, lo, *p;
442
443
# ifdef BN_COUNT
444
	fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
445
# endif
446
# ifdef BN_MUL_COMBA
447
#  if 0
448
	if (n2 == 4) {
449
		bn_mul_comba4(r, a, b);
450
		return;
451
	}
452
#  endif
453
	/* Only call bn_mul_comba 8 if n2 == 8 and the
454
	 * two arrays are complete [steve]
455
	 */
456
357600
	if (n2 == 8 && dna == 0 && dnb == 0) {
457
12186
		bn_mul_comba8(r, a, b);
458
12186
		return;
459
	}
460
# endif /* BN_MUL_COMBA */
461
	/* Else do normal multiply */
462
345414
	if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
463
7017
		bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
464
7017
		if ((dna + dnb) < 0)
465
14034
			memset(&r[2*n2 + dna + dnb], 0,
466
7017
			    sizeof(BN_ULONG) * -(dna + dnb));
467
7017
		return;
468
	}
469
	/* r=(a[0]-a[1])*(b[1]-b[0]) */
470
676794
	c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
471
676794
	c2 = bn_cmp_part_words(&(b[n]), b,tnb, tnb - n);
472
	zero = neg = 0;
473


676794
	switch (c1 * 3 + c2) {
474
	case -4:
475
61969
		bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
476
61969
		bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
477
61969
		break;
478
	case -3:
479
		zero = 1;
480
		break;
481
	case -2:
482
63633
		bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
483
63633
		bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
484
		neg = 1;
485
63633
		break;
486
	case -1:
487
	case 0:
488
	case 1:
489
		zero = 1;
490
108
		break;
491
	case 2:
492
123104
		bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
493
123104
		bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
494
		neg = 1;
495
123104
		break;
496
	case 3:
497
		zero = 1;
498
		break;
499
	case 4:
500
89583
		bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
501
89583
		bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
502
89583
		break;
503
	}
504
505
# ifdef BN_MUL_COMBA
506
338397
	if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
507
					       extra args to do this well */
508
	{
509
		if (!zero)
510
			bn_mul_comba4(&(t[n2]), t, &(t[n]));
511
		else
512
			memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
513
514
		bn_mul_comba4(r, a, b);
515
		bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
516
338397
	} else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
517
						    take extra args to do this
518
						    well */
519
	{
520
254010
		if (!zero)
521
253938
			bn_mul_comba8(&(t[n2]), t, &(t[n]));
522
		else
523
72
			memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
524
525
254010
		bn_mul_comba8(r, a, b);
526
254010
		bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
527
254010
	} else
528
# endif /* BN_MUL_COMBA */
529
	{
530
84387
		p = &(t[n2 * 2]);
531
84387
		if (!zero)
532
84351
			bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
533
		else
534
36
			memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
535
84387
		bn_mul_recursive(r, a, b, n, 0, 0, p);
536
84387
		bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
537
	}
538
539
	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
540
	 * r[10] holds (a[0]*b[0])
541
	 * r[32] holds (b[1]*b[1])
542
	 */
543
544
338397
	c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
545
546
338397
	if (neg) /* if t[32] is negative */
547
	{
548
186737
		c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
549
186737
	} else {
550
		/* Might have a carry */
551
151660
		c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
552
	}
553
554
	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
555
	 * r[10] holds (a[0]*b[0])
556
	 * r[32] holds (b[1]*b[1])
557
	 * c1 holds the carry bits
558
	 */
559
338397
	c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
560
338397
	if (c1) {
561
157322
		p = &(r[n + n2]);
562
157322
		lo= *p;
563
157322
		ln = (lo + c1) & BN_MASK2;
564
157322
		*p = ln;
565
566
		/* The overflow will stop before we over write
567
		 * words we should not overwrite */
568
157322
		if (ln < (BN_ULONG)c1) {
569
			do {
570
				p++;
571
				lo= *p;
572
				ln = (lo + 1) & BN_MASK2;
573
				*p = ln;
574
			} while (ln == 0);
575
		}
576
	}
577
695997
}
578
579
/* n+tn is the word length
580
 * t needs to be n*4 is size, as does r */
581
/* tnX may not be negative but less than n */
582
void
583
bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna,
584
    int tnb, BN_ULONG *t)
585
{
586
10212
	int i, j, n2 = n * 2;
587
	int c1, c2, neg;
588
	BN_ULONG ln, lo, *p;
589
590
# ifdef BN_COUNT
591
	fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
592
	    n, tna, n, tnb);
593
# endif
594
5106
	if (n < 8) {
595
		bn_mul_normal(r, a, n + tna, b, n + tnb);
596
		return;
597
	}
598
599
	/* r=(a[0]-a[1])*(b[1]-b[0]) */
600
10212
	c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
601
10212
	c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
602
	neg = 0;
603


10212
	switch (c1 * 3 + c2) {
604
	case -4:
605
		bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
606
		bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
607
		break;
608
	case -3:
609
		/* break; */
610
	case -2:
611
12
		bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
612
12
		bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
613
		neg = 1;
614
12
		break;
615
	case -1:
616
	case 0:
617
	case 1:
618
		/* break; */
619
	case 2:
620
5094
		bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
621
5094
		bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
622
		neg = 1;
623
5094
		break;
624
	case 3:
625
		/* break; */
626
	case 4:
627
		bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
628
		bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
629
		break;
630
	}
631
		/* The zero case isn't yet implemented here. The speedup
632
		   would probably be negligible. */
633
# if 0
634
	if (n == 4) {
635
		bn_mul_comba4(&(t[n2]), t, &(t[n]));
636
		bn_mul_comba4(r, a, b);
637
		bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
638
		memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2));
639
	} else
640
# endif
641
5106
		if (n == 8) {
642
214
		bn_mul_comba8(&(t[n2]), t, &(t[n]));
643
214
		bn_mul_comba8(r, a, b);
644
214
		bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
645
428
		memset(&(r[n2 + tna + tnb]), 0,
646
214
		    sizeof(BN_ULONG) * (n2 - tna - tnb));
647
214
	} else {
648
4892
		p = &(t[n2*2]);
649
4892
		bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
650
4892
		bn_mul_recursive(r, a, b, n, 0, 0, p);
651
4892
		i = n / 2;
652
		/* If there is only a bottom half to the number,
653
		 * just do it */
654
4892
		if (tna > tnb)
655
1242
			j = tna - i;
656
		else
657
3650
			j = tnb - i;
658
4892
		if (j == 0) {
659
6168
			bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
660
3084
			    i, tna - i, tnb - i, p);
661
6168
			memset(&(r[n2 + i * 2]), 0,
662
3084
			    sizeof(BN_ULONG) * (n2 - i * 2));
663
3084
		}
664
1808
		else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
665
		{
666
250
			bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
667
250
			    i, tna - i, tnb - i, p);
668
500
			memset(&(r[n2 + tna + tnb]), 0,
669
250
			    sizeof(BN_ULONG) * (n2 - tna - tnb));
670
250
		}
671
		else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
672
		{
673
1558
			memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
674
3116
			if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
675
1558
			    tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
676
1546
				bn_mul_normal(&(r[n2]), &(a[n]), tna,
677
				    &(b[n]), tnb);
678
1546
			} else {
679
				for (;;) {
680
14
					i /= 2;
681
					/* these simplified conditions work
682
					 * exclusively because difference
683
					 * between tna and tnb is 1 or 0 */
684

16
					if (i < tna || i < tnb) {
685
12
						bn_mul_part_recursive(&(r[n2]),
686
						    &(a[n]), &(b[n]), i,
687
12
						    tna - i, tnb - i, p);
688
12
						break;
689

4
					} else if (i == tna || i == tnb) {
690
						bn_mul_recursive(&(r[n2]),
691
						    &(a[n]), &(b[n]), i,
692
						    tna - i, tnb - i, p);
693
						break;
694
					}
695
				}
696
			}
697
		}
698
	}
699
700
	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
701
	 * r[10] holds (a[0]*b[0])
702
	 * r[32] holds (b[1]*b[1])
703
	 */
704
705
5106
	c1 = (int)(bn_add_words(t, r,&(r[n2]), n2));
706
707
5106
	if (neg) /* if t[32] is negative */
708
	{
709
5106
		c1 -= (int)(bn_sub_words(&(t[n2]), t,&(t[n2]), n2));
710
5106
	} else {
711
		/* Might have a carry */
712
		c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
713
	}
714
715
	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
716
	 * r[10] holds (a[0]*b[0])
717
	 * r[32] holds (b[1]*b[1])
718
	 * c1 holds the carry bits
719
	 */
720
5106
	c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
721
5106
	if (c1) {
722
		p = &(r[n + n2]);
723
		lo= *p;
724
		ln = (lo + c1)&BN_MASK2;
725
		*p = ln;
726
727
		/* The overflow will stop before we over write
728
		 * words we should not overwrite */
729
		if (ln < (BN_ULONG)c1) {
730
			do {
731
				p++;
732
				lo= *p;
733
				ln = (lo + 1) & BN_MASK2;
734
				*p = ln;
735
			} while (ln == 0);
736
		}
737
	}
738
10212
}
739
740
/* a and b must be the same size, which is n2.
741
 * r needs to be n2 words and t needs to be n2*2
742
 */
743
void
744
bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, BN_ULONG *t)
745
{
746
	int n = n2 / 2;
747
748
# ifdef BN_COUNT
749
	fprintf(stderr, " bn_mul_low_recursive %d * %d\n",n2,n2);
750
# endif
751
752
	bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
753
	if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
754
		bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
755
		bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
756
		bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
757
		bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
758
	} else {
759
		bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
760
		bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
761
		bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
762
		bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
763
	}
764
}
765
766
/* a and b must be the same size, which is n2.
767
 * r needs to be n2 words and t needs to be n2*2
768
 * l is the low words of the output.
769
 * t needs to be n2*3
770
 */
771
void
772
bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
773
    BN_ULONG *t)
774
{
775
	int i, n;
776
	int c1, c2;
777
	int neg, oneg, zero;
778
	BN_ULONG ll, lc, *lp, *mp;
779
780
# ifdef BN_COUNT
781
	fprintf(stderr, " bn_mul_high %d * %d\n",n2,n2);
782
# endif
783
	n = n2 / 2;
784
785
	/* Calculate (al-ah)*(bh-bl) */
786
	neg = zero = 0;
787
	c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
788
	c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
789
	switch (c1 * 3 + c2) {
790
	case -4:
791
		bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
792
		bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
793
		break;
794
	case -3:
795
		zero = 1;
796
		break;
797
	case -2:
798
		bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
799
		bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
800
		neg = 1;
801
		break;
802
	case -1:
803
	case 0:
804
	case 1:
805
		zero = 1;
806
		break;
807
	case 2:
808
		bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
809
		bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
810
		neg = 1;
811
		break;
812
	case 3:
813
		zero = 1;
814
		break;
815
	case 4:
816
		bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
817
		bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
818
		break;
819
	}
820
821
	oneg = neg;
822
	/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
823
	/* r[10] = (a[1]*b[1]) */
824
# ifdef BN_MUL_COMBA
825
	if (n == 8) {
826
		bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
827
		bn_mul_comba8(r, &(a[n]), &(b[n]));
828
	} else
829
# endif
830
	{
831
		bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
832
		bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
833
	}
834
835
	/* s0 == low(al*bl)
836
	 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
837
	 * We know s0 and s1 so the only unknown is high(al*bl)
838
	 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
839
	 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
840
	 */
841
	if (l != NULL) {
842
		lp = &(t[n2 + n]);
843
		c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
844
	} else {
845
		c1 = 0;
846
		lp = &(r[0]);
847
	}
848
849
	if (neg)
850
		neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
851
	else {
852
		bn_add_words(&(t[n2]), lp, &(t[0]), n);
853
		neg = 0;
854
	}
855
856
	if (l != NULL) {
857
		bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
858
	} else {
859
		lp = &(t[n2 + n]);
860
		mp = &(t[n2]);
861
		for (i = 0; i < n; i++)
862
			lp[i] = ((~mp[i]) + 1) & BN_MASK2;
863
	}
864
865
	/* s[0] = low(al*bl)
866
	 * t[3] = high(al*bl)
867
	 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
868
	 * r[10] = (a[1]*b[1])
869
	 */
870
	/* R[10] = al*bl
871
	 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
872
	 * R[32] = ah*bh
873
	 */
874
	/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
875
	 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
876
	 * R[3]=r[1]+(carry/borrow)
877
	 */
878
	if (l != NULL) {
879
		lp = &(t[n2]);
880
		c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n));
881
	} else {
882
		lp = &(t[n2 + n]);
883
		c1 = 0;
884
	}
885
	c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n));
886
	if (oneg)
887
		c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n));
888
	else
889
		c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n));
890
891
	c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n));
892
	c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n));
893
	if (oneg)
894
		c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n));
895
	else
896
		c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n));
897
898
	if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
899
	{
900
		i = 0;
901
		if (c1 > 0) {
902
			lc = c1;
903
			do {
904
				ll = (r[i] + lc) & BN_MASK2;
905
				r[i++] = ll;
906
				lc = (lc > ll);
907
			} while (lc);
908
		} else {
909
			lc = -c1;
910
			do {
911
				ll = r[i];
912
				r[i++] = (ll - lc) & BN_MASK2;
913
				lc = (lc > ll);
914
			} while (lc);
915
		}
916
	}
917
	if (c2 != 0) /* Add starting at r[1] */
918
	{
919
		i = n;
920
		if (c2 > 0) {
921
			lc = c2;
922
			do {
923
				ll = (r[i] + lc) & BN_MASK2;
924
				r[i++] = ll;
925
				lc = (lc > ll);
926
			} while (lc);
927
		} else {
928
			lc = -c2;
929
			do {
930
				ll = r[i];
931
				r[i++] = (ll - lc) & BN_MASK2;
932
				lc = (lc > ll);
933
			} while (lc);
934
		}
935
	}
936
}
937
#endif /* BN_RECURSION */
938
939
int
940
BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
941
{
942
	int ret = 0;
943
	int top, al, bl;
944
	BIGNUM *rr;
945
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
946
	int i;
947
#endif
948
#ifdef BN_RECURSION
949
	BIGNUM *t = NULL;
950
	int j = 0, k;
951
#endif
952
953
#ifdef BN_COUNT
954
	fprintf(stderr, "BN_mul %d * %d\n",a->top,b->top);
955
#endif
956
957
	bn_check_top(a);
958
	bn_check_top(b);
959
	bn_check_top(r);
960
961
15194552
	al = a->top;
962
7597276
	bl = b->top;
963
964
7597276
	if ((al == 0) || (bl == 0)) {
965
75820
		BN_zero(r);
966
75820
		return (1);
967
	}
968
7521456
	top = al + bl;
969
970
7521456
	BN_CTX_start(ctx);
971

14985730
	if ((r == a) || (r == b)) {
972
57278
		if ((rr = BN_CTX_get(ctx)) == NULL)
973
			goto err;
974
	} else
975
		rr = r;
976
7521456
	rr->neg = a->neg ^ b->neg;
977
978
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
979
7521456
	i = al - bl;
980
#endif
981
#ifdef BN_MUL_COMBA
982
15042912
	if (i == 0) {
983
# if 0
984
		if (al == 4) {
985
			if (bn_wexpand(rr, 8) == NULL)
986
				goto err;
987
			rr->top = 8;
988
			bn_mul_comba4(rr->d, a->d, b->d);
989
			goto end;
990
		}
991
# endif
992
7521456
		if (al == 8) {
993

2004549
			if (bn_wexpand(rr, 16) == NULL)
994
				goto err;
995
1002167
			rr->top = 16;
996
1002167
			bn_mul_comba8(rr->d, a->d, b->d);
997
1002167
			goto end;
998
		}
999
	}
1000
#endif /* BN_MUL_COMBA */
1001
#ifdef BN_RECURSION
1002
6519289
	if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
1003
99449
		if (i >= -1 && i <= 1) {
1004
			/* Find out the power of two lower or equal
1005
			   to the longest of the two numbers */
1006
96451
			if (i >= 0) {
1007
91660
				j = BN_num_bits_word((BN_ULONG)al);
1008
91660
			}
1009
96451
			if (i == -1) {
1010
4791
				j = BN_num_bits_word((BN_ULONG)bl);
1011
4791
			}
1012
96451
			j = 1 << (j - 1);
1013
			assert(j <= al || j <= bl);
1014
96451
			k = j + j;
1015
96451
			if ((t = BN_CTX_get(ctx)) == NULL)
1016
				goto err;
1017

188058
			if (al > j || bl > j) {
1018

10002
				if (bn_wexpand(t, k * 4) == NULL)
1019
					goto err;
1020

10004
				if (bn_wexpand(rr, k * 4) == NULL)
1021
					goto err;
1022
9688
				bn_mul_part_recursive(rr->d, a->d, b->d,
1023
4844
				    j, al - j, bl - j, t->d);
1024
4844
			}
1025
			else	/* al <= j || bl <= j */
1026
			{
1027

204774
				if (bn_wexpand(t, k * 2) == NULL)
1028
					goto err;
1029

206669
				if (bn_wexpand(rr, k * 2) == NULL)
1030
					goto err;
1031
183214
				bn_mul_recursive(rr->d, a->d, b->d,
1032
91607
				    j, al - j, bl - j, t->d);
1033
			}
1034
96451
			rr->top = top;
1035
96451
			goto end;
1036
		}
1037
#if 0
1038
		if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
1039
			BIGNUM *tmp_bn = (BIGNUM *)b;
1040
			if (bn_wexpand(tmp_bn, al) == NULL)
1041
				goto err;
1042
			tmp_bn->d[bl] = 0;
1043
			bl++;
1044
			i--;
1045
		} else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
1046
			BIGNUM *tmp_bn = (BIGNUM *)a;
1047
			if (bn_wexpand(tmp_bn, bl) == NULL)
1048
				goto err;
1049
			tmp_bn->d[al] = 0;
1050
			al++;
1051
			i++;
1052
		}
1053
		if (i == 0) {
1054
			/* symmetric and > 4 */
1055
			/* 16 or larger */
1056
			j = BN_num_bits_word((BN_ULONG)al);
1057
			j = 1 << (j - 1);
1058
			k = j + j;
1059
			if ((t = BN_CTX_get(ctx)) == NULL)
1060
				goto err;
1061
			if (al == j) /* exact multiple */
1062
			{
1063
				if (bn_wexpand(t, k * 2) == NULL)
1064
					goto err;
1065
				if (bn_wexpand(rr, k * 2) == NULL)
1066
					goto err;
1067
				bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
1068
			} else {
1069
				if (bn_wexpand(t, k * 4) == NULL)
1070
					goto err;
1071
				if (bn_wexpand(rr, k * 4) == NULL)
1072
					goto err;
1073
				bn_mul_part_recursive(rr->d, a->d, b->d,
1074
				    al - j, j, t->d);
1075
			}
1076
			rr->top = top;
1077
			goto end;
1078
		}
1079
#endif
1080
	}
1081
#endif /* BN_RECURSION */
1082

13291639
	if (bn_wexpand(rr, top) == NULL)
1083
		goto err;
1084
6422838
	rr->top = top;
1085
6422838
	bn_mul_normal(rr->d, a->d, al, b->d, bl);
1086
1087
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1088
end:
1089
#endif
1090

56474940
	bn_correct_top(rr);
1091
7521456
	if (r != rr)
1092
57278
		BN_copy(r, rr);
1093
7521456
	ret = 1;
1094
err:
1095
	bn_check_top(r);
1096
7521456
	BN_CTX_end(ctx);
1097
7521456
	return (ret);
1098
7597276
}
1099
1100
void
1101
bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1102
{
1103
	BN_ULONG *rr;
1104
1105
#ifdef BN_COUNT
1106
	fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
1107
#endif
1108
1109
12863230
	if (na < nb) {
1110
		int itmp;
1111
		BN_ULONG *ltmp;
1112
1113
		itmp = na;
1114
		na = nb;
1115
		nb = itmp;
1116
		ltmp = a;
1117
		a = b;
1118
		b = ltmp;
1119
1120
3633519
	}
1121
6431615
	rr = &(r[na]);
1122
6431615
	if (nb <= 0) {
1123
		(void)bn_mul_words(r, a, na, 0);
1124
		return;
1125
	} else
1126
6431615
		rr[0] = bn_mul_words(r, a, na, b[0]);
1127
1128
7382844
	for (;;) {
1129
7382844
		if (--nb <= 0)
1130
5925543
			return;
1131
1457301
		rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
1132
1457301
		if (--nb <= 0)
1133
18066
			return;
1134
1439235
		rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
1135
1439235
		if (--nb <= 0)
1136
83025
			return;
1137
1356210
		rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
1138
1356210
		if (--nb <= 0)
1139
404981
			return;
1140
951229
		rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
1141
		rr += 4;
1142
		r += 4;
1143
		b += 4;
1144
	}
1145
6431615
}
1146
1147
void
1148
bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1149
{
1150
#ifdef BN_COUNT
1151
	fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n);
1152
#endif
1153
	bn_mul_words(r, a, n, b[0]);
1154
1155
	for (;;) {
1156
		if (--n <= 0)
1157
			return;
1158
		bn_mul_add_words(&(r[1]), a, n, b[1]);
1159
		if (--n <= 0)
1160
			return;
1161
		bn_mul_add_words(&(r[2]), a, n, b[2]);
1162
		if (--n <= 0)
1163
			return;
1164
		bn_mul_add_words(&(r[3]), a, n, b[3]);
1165
		if (--n <= 0)
1166
			return;
1167
		bn_mul_add_words(&(r[4]), a, n, b[4]);
1168
		r += 4;
1169
		b += 4;
1170
	}
1171
}