summaryrefslogtreecommitdiffabout
path: root/pwmanager/libcrypt/mpi/mpih-div.c
blob: e41e205e1d1edeb8d9c95a6f8d389c442ec851fa (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
/* mpih-div.c  -  MPI helper functions
 * Copyright (C) 1994, 1996, 1998, 2000,
 *               2001, 2002 Free Software Foundation, Inc.
 *
 * This file is part of Libgcrypt.
 *
 * Libgcrypt is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as
 * published by the Free Software Foundation; either version 2.1 of
 * the License, or (at your option) any later version.
 *
 * Libgcrypt is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
 *
 * Note: This code is heavily based on the GNU MP Library.
 *	 Actually it's the same code with only minor changes in the
 *	 way the data is stored; this is to support the abstraction
 *	 of an optional secure memory allocation which may be used
 *	 to avoid revealing of sensitive data due to paging etc.
 */

#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include "mpi-internal.h"
#include "longlong.h"

#ifndef UMUL_TIME
#define UMUL_TIME 1
#endif
#ifndef UDIV_TIME
#define UDIV_TIME UMUL_TIME
#endif

/* FIXME: We should be using invert_limb (or invert_normalized_limb)
 * here (not udiv_qrnnd).
 */

mpi_limb_t
_gcry_mpih_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
				      mpi_limb_t divisor_limb)
{
    mpi_size_t i;
    mpi_limb_t n1, n0, r;
    int dummy;

    /* Botch: Should this be handled at all?  Rely on callers?	*/
    if( !dividend_size )
	return 0;

    /* If multiplication is much faster than division, and the
     * dividend is large, pre-invert the divisor, and use
     * only multiplications in the inner loop.
     *
     * This test should be read:
     *	 Does it ever help to use udiv_qrnnd_preinv?
     *	   && Does what we save compensate for the inversion overhead?
     */
    if( UDIV_TIME > (2 * UMUL_TIME + 6)
	&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
	int normalization_steps;

	count_leading_zeros( normalization_steps, divisor_limb );
	if( normalization_steps ) {
	    mpi_limb_t divisor_limb_inverted;

	    divisor_limb <<= normalization_steps;

	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
	     * most significant bit (with weight 2**N) implicit.
	     *
	     * Special case for DIVISOR_LIMB == 100...000.
	     */
	    if( !(divisor_limb << 1) )
		divisor_limb_inverted = ~(mpi_limb_t)0;
	    else
		udiv_qrnnd(divisor_limb_inverted, dummy,
			   -divisor_limb, 0, divisor_limb);

	    n1 = dividend_ptr[dividend_size - 1];
	    r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

	    /* Possible optimization:
	     * if (r == 0
	     * && divisor_limb > ((n1 << normalization_steps)
	     *		       | (dividend_ptr[dividend_size - 2] >> ...)))
	     * ...one division less...
	     */
	    for( i = dividend_size - 2; i >= 0; i--) {
		n0 = dividend_ptr[i];
		UDIV_QRNND_PREINV(dummy, r, r,
				   ((n1 << normalization_steps)
			  | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
			  divisor_limb, divisor_limb_inverted);
		n1 = n0;
	    }
	    UDIV_QRNND_PREINV(dummy, r, r,
			      n1 << normalization_steps,
			      divisor_limb, divisor_limb_inverted);
	    return r >> normalization_steps;
	}
	else {
	    mpi_limb_t divisor_limb_inverted;

	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
	     * most significant bit (with weight 2**N) implicit.
	     *
	     * Special case for DIVISOR_LIMB == 100...000.
	     */
	    if( !(divisor_limb << 1) )
		divisor_limb_inverted = ~(mpi_limb_t)0;
	    else
		udiv_qrnnd(divisor_limb_inverted, dummy,
			    -divisor_limb, 0, divisor_limb);

	    i = dividend_size - 1;
	    r = dividend_ptr[i];

	    if( r >= divisor_limb )
		r = 0;
	    else
		i--;

	    for( ; i >= 0; i--) {
		n0 = dividend_ptr[i];
		UDIV_QRNND_PREINV(dummy, r, r,
				  n0, divisor_limb, divisor_limb_inverted);
	    }
	    return r;
	}
    }
    else {
	if( UDIV_NEEDS_NORMALIZATION ) {
	    int normalization_steps;

	    count_leading_zeros(normalization_steps, divisor_limb);
	    if( normalization_steps ) {
		divisor_limb <<= normalization_steps;

		n1 = dividend_ptr[dividend_size - 1];
		r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

		/* Possible optimization:
		 * if (r == 0
		 * && divisor_limb > ((n1 << normalization_steps)
		 *		   | (dividend_ptr[dividend_size - 2] >> ...)))
		 * ...one division less...
		 */
		for(i = dividend_size - 2; i >= 0; i--) {
		    n0 = dividend_ptr[i];
		    udiv_qrnnd (dummy, r, r,
				((n1 << normalization_steps)
			 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
			 divisor_limb);
		    n1 = n0;
		}
		udiv_qrnnd (dummy, r, r,
			    n1 << normalization_steps,
			    divisor_limb);
		return r >> normalization_steps;
	    }
	}
	/* No normalization needed, either because udiv_qrnnd doesn't require
	 * it, or because DIVISOR_LIMB is already normalized.  */
	i = dividend_size - 1;
	r = dividend_ptr[i];

	if(r >= divisor_limb)
	    r = 0;
	else
	    i--;

	for(; i >= 0; i--) {
	    n0 = dividend_ptr[i];
	    udiv_qrnnd (dummy, r, r, n0, divisor_limb);
	}
	return r;
    }
}

/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
 * the NSIZE-DSIZE least significant quotient limbs at QP
 * and the DSIZE long remainder at NP.	If QEXTRA_LIMBS is
 * non-zero, generate that many fraction bits and append them after the
 * other quotient limbs.
 * Return the most significant limb of the quotient, this is always 0 or 1.
 *
 * Preconditions:
 * 0. NSIZE >= DSIZE.
 * 1. The most significant bit of the divisor must be set.
 * 2. QP must either not overlap with the input operands at all, or
 *    QP + DSIZE >= NP must hold true.	(This means that it's
 *    possible to put the quotient in the high part of NUM, right after the
 *    remainder in NUM.
 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
 */

mpi_limb_t
_gcry_mpih_divrem( mpi_ptr_t qp, mpi_size_t qextra_limbs,
                      mpi_ptr_t np, mpi_size_t nsize,
                      mpi_ptr_t dp, mpi_size_t dsize)
{
    mpi_limb_t most_significant_q_limb = 0;

    switch(dsize) {
      case 0:
	/* We are asked to divide by zero, so go ahead and do it!  (To make
	   the compiler not remove this statement, return the value.)  */
	return 1 / dsize;

      case 1:
	{
	    mpi_size_t i;
	    mpi_limb_t n1;
	    mpi_limb_t d;

	    d = dp[0];
	    n1 = np[nsize - 1];

	    if( n1 >= d ) {
		n1 -= d;
		most_significant_q_limb = 1;
	    }

	    qp += qextra_limbs;
	    for( i = nsize - 2; i >= 0; i--)
		udiv_qrnnd( qp[i], n1, n1, np[i], d );
	    qp -= qextra_limbs;

	    for( i = qextra_limbs - 1; i >= 0; i-- )
		udiv_qrnnd (qp[i], n1, n1, 0, d);

	    np[0] = n1;
	}
	break;

      case 2:
	{
	    mpi_size_t i;
	    mpi_limb_t n1, n0, n2;
	    mpi_limb_t d1, d0;

	    np += nsize - 2;
	    d1 = dp[1];
	    d0 = dp[0];
	    n1 = np[1];
	    n0 = np[0];

	    if( n1 >= d1 && (n1 > d1 || n0 >= d0) ) {
		sub_ddmmss (n1, n0, n1, n0, d1, d0);
		most_significant_q_limb = 1;
	    }

	    for( i = qextra_limbs + nsize - 2 - 1; i >= 0; i-- ) {
		mpi_limb_t q;
		mpi_limb_t r;

		if( i >= qextra_limbs )
		    np--;
		else
		    np[0] = 0;

		if( n1 == d1 ) {
		    /* Q should be either 111..111 or 111..110.  Need special
		     * treatment of this rare case as normal division would
		     * give overflow.  */
		    q = ~(mpi_limb_t)0;

		    r = n0 + d1;
		    if( r < d1 ) {   /* Carry in the addition? */
			add_ssaaaa( n1, n0, r - d0, np[0], 0, d0 );
			qp[i] = q;
			continue;
		    }
		    n1 = d0 - (d0 != 0?1:0);
		    n0 = -d0;
		}
		else {
		    udiv_qrnnd (q, r, n1, n0, d1);
		    umul_ppmm (n1, n0, d0, q);
		}

		n2 = np[0];
	      q_test:
		if( n1 > r || (n1 == r && n0 > n2) ) {
		    /* The estimated Q was too large.  */
		    q--;
		    sub_ddmmss (n1, n0, n1, n0, 0, d0);
		    r += d1;
		    if( r >= d1 )    /* If not carry, test Q again.  */
			goto q_test;
		}

		qp[i] = q;
		sub_ddmmss (n1, n0, r, n2, n1, n0);
	    }
	    np[1] = n1;
	    np[0] = n0;
	}
	break;

      default:
	{
	    mpi_size_t i;
	    mpi_limb_t dX, d1, n0;

	    np += nsize - dsize;
	    dX = dp[dsize - 1];
	    d1 = dp[dsize - 2];
	    n0 = np[dsize - 1];

	    if( n0 >= dX ) {
		if(n0 > dX || _gcry_mpih_cmp(np, dp, dsize - 1) >= 0 ) {
		    _gcry_mpih_sub_n(np, np, dp, dsize);
		    n0 = np[dsize - 1];
		    most_significant_q_limb = 1;
		}
	    }

	    for( i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
		mpi_limb_t q;
		mpi_limb_t n1, n2;
		mpi_limb_t cy_limb;

		if( i >= qextra_limbs ) {
		    np--;
		    n2 = np[dsize];
		}
		else {
		    n2 = np[dsize - 1];
		    MPN_COPY_DECR (np + 1, np, dsize - 1);
		    np[0] = 0;
		}

		if( n0 == dX ) {
		    /* This might over-estimate q, but it's probably not worth
		     * the extra code here to find out.  */
		    q = ~(mpi_limb_t)0;
		}
		else {
		    mpi_limb_t r;

		    udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
		    umul_ppmm(n1, n0, d1, q);

		    while( n1 > r || (n1 == r && n0 > np[dsize - 2])) {
			q--;
			r += dX;
			if( r < dX ) /* I.e. "carry in previous addition?" */
			    break;
			n1 -= n0 < d1;
			n0 -= d1;
		    }
		}

		/* Possible optimization: We already have (q * n0) and (1 * n1)
		 * after the calculation of q.	Taking advantage of that, we
		 * could make this loop make two iterations less.  */
		cy_limb = _gcry_mpih_submul_1(np, dp, dsize, q);

		if( n2 != cy_limb ) {
		    _gcry_mpih_add_n(np, np, dp, dsize);
		    q--;
		}

		qp[i] = q;
		n0 = np[dsize - 1];
	    }
	}
    }

    return most_significant_q_limb;
}


/****************
 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
 * Return the single-limb remainder.
 * There are no constraints on the value of the divisor.
 *
 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
 */

mpi_limb_t
_gcry_mpih_divmod_1( mpi_ptr_t quot_ptr,
                        mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
                        mpi_limb_t divisor_limb)
{
    mpi_size_t i;
    mpi_limb_t n1, n0, r;
    int dummy;

    if( !dividend_size )
	return 0;

    /* If multiplication is much faster than division, and the
     * dividend is large, pre-invert the divisor, and use
     * only multiplications in the inner loop.
     *
     * This test should be read:
     * Does it ever help to use udiv_qrnnd_preinv?
     * && Does what we save compensate for the inversion overhead?
     */
    if( UDIV_TIME > (2 * UMUL_TIME + 6)
	&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
	int normalization_steps;

	count_leading_zeros( normalization_steps, divisor_limb );
	if( normalization_steps ) {
	    mpi_limb_t divisor_limb_inverted;

	    divisor_limb <<= normalization_steps;

	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
	     * most significant bit (with weight 2**N) implicit.
	     */
	    /* Special case for DIVISOR_LIMB == 100...000.  */
	    if( !(divisor_limb << 1) )
		divisor_limb_inverted = ~(mpi_limb_t)0;
	    else
		udiv_qrnnd(divisor_limb_inverted, dummy,
			   -divisor_limb, 0, divisor_limb);

	    n1 = dividend_ptr[dividend_size - 1];
	    r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

	    /* Possible optimization:
	     * if (r == 0
	     * && divisor_limb > ((n1 << normalization_steps)
	     *		       | (dividend_ptr[dividend_size - 2] >> ...)))
	     * ...one division less...
	     */
	    for( i = dividend_size - 2; i >= 0; i--) {
		n0 = dividend_ptr[i];
		UDIV_QRNND_PREINV( quot_ptr[i + 1], r, r,
				   ((n1 << normalization_steps)
			 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
			      divisor_limb, divisor_limb_inverted);
		n1 = n0;
	    }
	    UDIV_QRNND_PREINV( quot_ptr[0], r, r,
			       n1 << normalization_steps,
			       divisor_limb, divisor_limb_inverted);
	    return r >> normalization_steps;
	}
	else {
	    mpi_limb_t divisor_limb_inverted;

	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
	     * most significant bit (with weight 2**N) implicit.
	     */
	    /* Special case for DIVISOR_LIMB == 100...000.  */
	    if( !(divisor_limb << 1) )
		divisor_limb_inverted = ~(mpi_limb_t) 0;
	    else
		udiv_qrnnd(divisor_limb_inverted, dummy,
			   -divisor_limb, 0, divisor_limb);

	    i = dividend_size - 1;
	    r = dividend_ptr[i];

	    if( r >= divisor_limb )
		r = 0;
	    else
		quot_ptr[i--] = 0;

	    for( ; i >= 0; i-- ) {
		n0 = dividend_ptr[i];
		UDIV_QRNND_PREINV( quot_ptr[i], r, r,
				   n0, divisor_limb, divisor_limb_inverted);
	    }
	    return r;
	}
    }
    else {
	if(UDIV_NEEDS_NORMALIZATION) {
	    int normalization_steps;

	    count_leading_zeros (normalization_steps, divisor_limb);
	    if( normalization_steps ) {
		divisor_limb <<= normalization_steps;

		n1 = dividend_ptr[dividend_size - 1];
		r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

		/* Possible optimization:
		 * if (r == 0
		 * && divisor_limb > ((n1 << normalization_steps)
		 *		   | (dividend_ptr[dividend_size - 2] >> ...)))
		 * ...one division less...
		 */
		for( i = dividend_size - 2; i >= 0; i--) {
		    n0 = dividend_ptr[i];
		    udiv_qrnnd (quot_ptr[i + 1], r, r,
			     ((n1 << normalization_steps)
			 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
				divisor_limb);
		    n1 = n0;
		}
		udiv_qrnnd (quot_ptr[0], r, r,
			    n1 << normalization_steps,
			    divisor_limb);
		return r >> normalization_steps;
	    }
	}
	/* No normalization needed, either because udiv_qrnnd doesn't require
	 * it, or because DIVISOR_LIMB is already normalized.  */
	i = dividend_size - 1;
	r = dividend_ptr[i];

	if(r >= divisor_limb)
	    r = 0;
	else
	    quot_ptr[i--] = 0;

	for(; i >= 0; i--) {
	    n0 = dividend_ptr[i];
	    udiv_qrnnd( quot_ptr[i], r, r, n0, divisor_limb );
	}
	return r;
    }
}