1/* mpih-div.c  -  MPI helper functions
2 * Copyright (C) 1994, 1996, 1998, 2000,
3 *               2001, 2002 Free Software Foundation, Inc.
4 *
5 * This file is part of Libgcrypt.
6 *
7 * Libgcrypt is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU Lesser General Public License as
9 * published by the Free Software Foundation; either version 2.1 of
10 * the License, or (at your option) any later version.
11 *
12 * Libgcrypt is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public
18 * License along with this program; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
20 *
21 * Note: This code is heavily based on the GNU MP Library.
22 *	 Actually it's the same code with only minor changes in the
23 *	 way the data is stored; this is to support the abstraction
24 *	 of an optional secure memory allocation which may be used
25 *	 to avoid revealing of sensitive data due to paging etc.
26 */
27
28#include <config.h>
29#include <stdio.h>
30#include <stdlib.h>
31#include "mpi-internal.h"
32#include "longlong.h"
33
34#ifndef UMUL_TIME
35#define UMUL_TIME 1
36#endif
37#ifndef UDIV_TIME
38#define UDIV_TIME UMUL_TIME
39#endif
40
41/* FIXME: We should be using invert_limb (or invert_normalized_limb)
42 * here (not udiv_qrnnd).
43 */
44
45mpi_limb_t
46_gcry_mpih_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
47				      mpi_limb_t divisor_limb)
48{
49    mpi_size_t i;
50    mpi_limb_t n1, n0, r;
51    int dummy;
52
53    /* Botch: Should this be handled at all?  Rely on callers?	*/
54    if( !dividend_size )
55	return 0;
56
57    /* If multiplication is much faster than division, and the
58     * dividend is large, pre-invert the divisor, and use
59     * only multiplications in the inner loop.
60     *
61     * This test should be read:
62     *	 Does it ever help to use udiv_qrnnd_preinv?
63     *	   && Does what we save compensate for the inversion overhead?
64     */
65    if( UDIV_TIME > (2 * UMUL_TIME + 6)
66	&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
67	int normalization_steps;
68
69	count_leading_zeros( normalization_steps, divisor_limb );
70	if( normalization_steps ) {
71	    mpi_limb_t divisor_limb_inverted;
72
73	    divisor_limb <<= normalization_steps;
74
75	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
76	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
77	     * most significant bit (with weight 2**N) implicit.
78	     *
79	     * Special case for DIVISOR_LIMB == 100...000.
80	     */
81	    if( !(divisor_limb << 1) )
82		divisor_limb_inverted = ~(mpi_limb_t)0;
83	    else
84		udiv_qrnnd(divisor_limb_inverted, dummy,
85			   -divisor_limb, 0, divisor_limb);
86
87	    n1 = dividend_ptr[dividend_size - 1];
88	    r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
89
90	    /* Possible optimization:
91	     * if (r == 0
92	     * && divisor_limb > ((n1 << normalization_steps)
93	     *		       | (dividend_ptr[dividend_size - 2] >> ...)))
94	     * ...one division less...
95	     */
96	    for( i = dividend_size - 2; i >= 0; i--) {
97		n0 = dividend_ptr[i];
98		UDIV_QRNND_PREINV(dummy, r, r,
99				   ((n1 << normalization_steps)
100			  | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
101			  divisor_limb, divisor_limb_inverted);
102		n1 = n0;
103	    }
104	    UDIV_QRNND_PREINV(dummy, r, r,
105			      n1 << normalization_steps,
106			      divisor_limb, divisor_limb_inverted);
107	    return r >> normalization_steps;
108	}
109	else {
110	    mpi_limb_t divisor_limb_inverted;
111
112	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
113	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
114	     * most significant bit (with weight 2**N) implicit.
115	     *
116	     * Special case for DIVISOR_LIMB == 100...000.
117	     */
118	    if( !(divisor_limb << 1) )
119		divisor_limb_inverted = ~(mpi_limb_t)0;
120	    else
121		udiv_qrnnd(divisor_limb_inverted, dummy,
122			    -divisor_limb, 0, divisor_limb);
123
124	    i = dividend_size - 1;
125	    r = dividend_ptr[i];
126
127	    if( r >= divisor_limb )
128		r = 0;
129	    else
130		i--;
131
132	    for( ; i >= 0; i--) {
133		n0 = dividend_ptr[i];
134		UDIV_QRNND_PREINV(dummy, r, r,
135				  n0, divisor_limb, divisor_limb_inverted);
136	    }
137	    return r;
138	}
139    }
140    else {
141	if( UDIV_NEEDS_NORMALIZATION ) {
142	    int normalization_steps;
143
144	    count_leading_zeros(normalization_steps, divisor_limb);
145	    if( normalization_steps ) {
146		divisor_limb <<= normalization_steps;
147
148		n1 = dividend_ptr[dividend_size - 1];
149		r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
150
151		/* Possible optimization:
152		 * if (r == 0
153		 * && divisor_limb > ((n1 << normalization_steps)
154		 *		   | (dividend_ptr[dividend_size - 2] >> ...)))
155		 * ...one division less...
156		 */
157		for(i = dividend_size - 2; i >= 0; i--) {
158		    n0 = dividend_ptr[i];
159		    udiv_qrnnd (dummy, r, r,
160				((n1 << normalization_steps)
161			 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
162			 divisor_limb);
163		    n1 = n0;
164		}
165		udiv_qrnnd (dummy, r, r,
166			    n1 << normalization_steps,
167			    divisor_limb);
168		return r >> normalization_steps;
169	    }
170	}
171	/* No normalization needed, either because udiv_qrnnd doesn't require
172	 * it, or because DIVISOR_LIMB is already normalized.  */
173	i = dividend_size - 1;
174	r = dividend_ptr[i];
175
176	if(r >= divisor_limb)
177	    r = 0;
178	else
179	    i--;
180
181	for(; i >= 0; i--) {
182	    n0 = dividend_ptr[i];
183	    udiv_qrnnd (dummy, r, r, n0, divisor_limb);
184	}
185	return r;
186    }
187}
188
189/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
190 * the NSIZE-DSIZE least significant quotient limbs at QP
191 * and the DSIZE long remainder at NP.	If QEXTRA_LIMBS is
192 * non-zero, generate that many fraction bits and append them after the
193 * other quotient limbs.
194 * Return the most significant limb of the quotient, this is always 0 or 1.
195 *
196 * Preconditions:
197 * 0. NSIZE >= DSIZE.
198 * 1. The most significant bit of the divisor must be set.
199 * 2. QP must either not overlap with the input operands at all, or
200 *    QP + DSIZE >= NP must hold true.	(This means that it's
201 *    possible to put the quotient in the high part of NUM, right after the
202 *    remainder in NUM.
203 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
204 */
205
206mpi_limb_t
207_gcry_mpih_divrem( mpi_ptr_t qp, mpi_size_t qextra_limbs,
208                      mpi_ptr_t np, mpi_size_t nsize,
209                      mpi_ptr_t dp, mpi_size_t dsize)
210{
211    mpi_limb_t most_significant_q_limb = 0;
212
213    switch(dsize) {
214      case 0:
215	/* We are asked to divide by zero, so go ahead and do it!  (To make
216	   the compiler not remove this statement, return the value.)  */
217	return 1 / dsize;
218
219      case 1:
220	{
221	    mpi_size_t i;
222	    mpi_limb_t n1;
223	    mpi_limb_t d;
224
225	    d = dp[0];
226	    n1 = np[nsize - 1];
227
228	    if( n1 >= d ) {
229		n1 -= d;
230		most_significant_q_limb = 1;
231	    }
232
233	    qp += qextra_limbs;
234	    for( i = nsize - 2; i >= 0; i--)
235		udiv_qrnnd( qp[i], n1, n1, np[i], d );
236	    qp -= qextra_limbs;
237
238	    for( i = qextra_limbs - 1; i >= 0; i-- )
239		udiv_qrnnd (qp[i], n1, n1, 0, d);
240
241	    np[0] = n1;
242	}
243	break;
244
245      case 2:
246	{
247	    mpi_size_t i;
248	    mpi_limb_t n1, n0, n2;
249	    mpi_limb_t d1, d0;
250
251	    np += nsize - 2;
252	    d1 = dp[1];
253	    d0 = dp[0];
254	    n1 = np[1];
255	    n0 = np[0];
256
257	    if( n1 >= d1 && (n1 > d1 || n0 >= d0) ) {
258		sub_ddmmss (n1, n0, n1, n0, d1, d0);
259		most_significant_q_limb = 1;
260	    }
261
262	    for( i = qextra_limbs + nsize - 2 - 1; i >= 0; i-- ) {
263		mpi_limb_t q;
264		mpi_limb_t r;
265
266		if( i >= qextra_limbs )
267		    np--;
268		else
269		    np[0] = 0;
270
271		if( n1 == d1 ) {
272		    /* Q should be either 111..111 or 111..110.  Need special
273		     * treatment of this rare case as normal division would
274		     * give overflow.  */
275		    q = ~(mpi_limb_t)0;
276
277		    r = n0 + d1;
278		    if( r < d1 ) {   /* Carry in the addition? */
279			add_ssaaaa( n1, n0, r - d0, np[0], 0, d0 );
280			qp[i] = q;
281			continue;
282		    }
283		    n1 = d0 - (d0 != 0?1:0);
284		    n0 = -d0;
285		}
286		else {
287		    udiv_qrnnd (q, r, n1, n0, d1);
288		    umul_ppmm (n1, n0, d0, q);
289		}
290
291		n2 = np[0];
292	      q_test:
293		if( n1 > r || (n1 == r && n0 > n2) ) {
294		    /* The estimated Q was too large.  */
295		    q--;
296		    sub_ddmmss (n1, n0, n1, n0, 0, d0);
297		    r += d1;
298		    if( r >= d1 )    /* If not carry, test Q again.  */
299			goto q_test;
300		}
301
302		qp[i] = q;
303		sub_ddmmss (n1, n0, r, n2, n1, n0);
304	    }
305	    np[1] = n1;
306	    np[0] = n0;
307	}
308	break;
309
310      default:
311	{
312	    mpi_size_t i;
313	    mpi_limb_t dX, d1, n0;
314
315	    np += nsize - dsize;
316	    dX = dp[dsize - 1];
317	    d1 = dp[dsize - 2];
318	    n0 = np[dsize - 1];
319
320	    if( n0 >= dX ) {
321		if(n0 > dX || _gcry_mpih_cmp(np, dp, dsize - 1) >= 0 ) {
322		    _gcry_mpih_sub_n(np, np, dp, dsize);
323		    n0 = np[dsize - 1];
324		    most_significant_q_limb = 1;
325		}
326	    }
327
328	    for( i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
329		mpi_limb_t q;
330		mpi_limb_t n1, n2;
331		mpi_limb_t cy_limb;
332
333		if( i >= qextra_limbs ) {
334		    np--;
335		    n2 = np[dsize];
336		}
337		else {
338		    n2 = np[dsize - 1];
339		    MPN_COPY_DECR (np + 1, np, dsize - 1);
340		    np[0] = 0;
341		}
342
343		if( n0 == dX ) {
344		    /* This might over-estimate q, but it's probably not worth
345		     * the extra code here to find out.  */
346		    q = ~(mpi_limb_t)0;
347		}
348		else {
349		    mpi_limb_t r;
350
351		    udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
352		    umul_ppmm(n1, n0, d1, q);
353
354		    while( n1 > r || (n1 == r && n0 > np[dsize - 2])) {
355			q--;
356			r += dX;
357			if( r < dX ) /* I.e. "carry in previous addition?" */
358			    break;
359			n1 -= n0 < d1;
360			n0 -= d1;
361		    }
362		}
363
364		/* Possible optimization: We already have (q * n0) and (1 * n1)
365		 * after the calculation of q.	Taking advantage of that, we
366		 * could make this loop make two iterations less.  */
367		cy_limb = _gcry_mpih_submul_1(np, dp, dsize, q);
368
369		if( n2 != cy_limb ) {
370		    _gcry_mpih_add_n(np, np, dp, dsize);
371		    q--;
372		}
373
374		qp[i] = q;
375		n0 = np[dsize - 1];
376	    }
377	}
378    }
379
380    return most_significant_q_limb;
381}
382
383
384/****************
385 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
386 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
387 * Return the single-limb remainder.
388 * There are no constraints on the value of the divisor.
389 *
390 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
391 */
392
393mpi_limb_t
394_gcry_mpih_divmod_1( mpi_ptr_t quot_ptr,
395                        mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
396                        mpi_limb_t divisor_limb)
397{
398    mpi_size_t i;
399    mpi_limb_t n1, n0, r;
400    int dummy;
401
402    if( !dividend_size )
403	return 0;
404
405    /* If multiplication is much faster than division, and the
406     * dividend is large, pre-invert the divisor, and use
407     * only multiplications in the inner loop.
408     *
409     * This test should be read:
410     * Does it ever help to use udiv_qrnnd_preinv?
411     * && Does what we save compensate for the inversion overhead?
412     */
413    if( UDIV_TIME > (2 * UMUL_TIME + 6)
414	&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
415	int normalization_steps;
416
417	count_leading_zeros( normalization_steps, divisor_limb );
418	if( normalization_steps ) {
419	    mpi_limb_t divisor_limb_inverted;
420
421	    divisor_limb <<= normalization_steps;
422
423	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
424	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
425	     * most significant bit (with weight 2**N) implicit.
426	     */
427	    /* Special case for DIVISOR_LIMB == 100...000.  */
428	    if( !(divisor_limb << 1) )
429		divisor_limb_inverted = ~(mpi_limb_t)0;
430	    else
431		udiv_qrnnd(divisor_limb_inverted, dummy,
432			   -divisor_limb, 0, divisor_limb);
433
434	    n1 = dividend_ptr[dividend_size - 1];
435	    r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
436
437	    /* Possible optimization:
438	     * if (r == 0
439	     * && divisor_limb > ((n1 << normalization_steps)
440	     *		       | (dividend_ptr[dividend_size - 2] >> ...)))
441	     * ...one division less...
442	     */
443	    for( i = dividend_size - 2; i >= 0; i--) {
444		n0 = dividend_ptr[i];
445		UDIV_QRNND_PREINV( quot_ptr[i + 1], r, r,
446				   ((n1 << normalization_steps)
447			 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
448			      divisor_limb, divisor_limb_inverted);
449		n1 = n0;
450	    }
451	    UDIV_QRNND_PREINV( quot_ptr[0], r, r,
452			       n1 << normalization_steps,
453			       divisor_limb, divisor_limb_inverted);
454	    return r >> normalization_steps;
455	}
456	else {
457	    mpi_limb_t divisor_limb_inverted;
458
459	    /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
460	     * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
461	     * most significant bit (with weight 2**N) implicit.
462	     */
463	    /* Special case for DIVISOR_LIMB == 100...000.  */
464	    if( !(divisor_limb << 1) )
465		divisor_limb_inverted = ~(mpi_limb_t) 0;
466	    else
467		udiv_qrnnd(divisor_limb_inverted, dummy,
468			   -divisor_limb, 0, divisor_limb);
469
470	    i = dividend_size - 1;
471	    r = dividend_ptr[i];
472
473	    if( r >= divisor_limb )
474		r = 0;
475	    else
476		quot_ptr[i--] = 0;
477
478	    for( ; i >= 0; i-- ) {
479		n0 = dividend_ptr[i];
480		UDIV_QRNND_PREINV( quot_ptr[i], r, r,
481				   n0, divisor_limb, divisor_limb_inverted);
482	    }
483	    return r;
484	}
485    }
486    else {
487	if(UDIV_NEEDS_NORMALIZATION) {
488	    int normalization_steps;
489
490	    count_leading_zeros (normalization_steps, divisor_limb);
491	    if( normalization_steps ) {
492		divisor_limb <<= normalization_steps;
493
494		n1 = dividend_ptr[dividend_size - 1];
495		r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
496
497		/* Possible optimization:
498		 * if (r == 0
499		 * && divisor_limb > ((n1 << normalization_steps)
500		 *		   | (dividend_ptr[dividend_size - 2] >> ...)))
501		 * ...one division less...
502		 */
503		for( i = dividend_size - 2; i >= 0; i--) {
504		    n0 = dividend_ptr[i];
505		    udiv_qrnnd (quot_ptr[i + 1], r, r,
506			     ((n1 << normalization_steps)
507			 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
508				divisor_limb);
509		    n1 = n0;
510		}
511		udiv_qrnnd (quot_ptr[0], r, r,
512			    n1 << normalization_steps,
513			    divisor_limb);
514		return r >> normalization_steps;
515	    }
516	}
517	/* No normalization needed, either because udiv_qrnnd doesn't require
518	 * it, or because DIVISOR_LIMB is already normalized.  */
519	i = dividend_size - 1;
520	r = dividend_ptr[i];
521
522	if(r >= divisor_limb)
523	    r = 0;
524	else
525	    quot_ptr[i--] = 0;
526
527	for(; i >= 0; i--) {
528	    n0 = dividend_ptr[i];
529	    udiv_qrnnd( quot_ptr[i], r, r, n0, divisor_limb );
530	}
531	return r;
532    }
533}
534