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1 /* crypto/bn/bn_div.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 #include <stdio.h>
60 #include <openssl/bn.h>
61 #include "cryptlib.h"
62 #include "bn_lcl.h"
63 
64 
65 /* The old slow way */
66 #if 0
67 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
68 	   BN_CTX *ctx)
69 	{
70 	int i,nm,nd;
71 	int ret = 0;
72 	BIGNUM *D;
73 
74 	bn_check_top(m);
75 	bn_check_top(d);
76 	if (BN_is_zero(d))
77 		{
78 		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
79 		return(0);
80 		}
81 
82 	if (BN_ucmp(m,d) < 0)
83 		{
84 		if (rem != NULL)
85 			{ if (BN_copy(rem,m) == NULL) return(0); }
86 		if (dv != NULL) BN_zero(dv);
87 		return(1);
88 		}
89 
90 	BN_CTX_start(ctx);
91 	D = BN_CTX_get(ctx);
92 	if (dv == NULL) dv = BN_CTX_get(ctx);
93 	if (rem == NULL) rem = BN_CTX_get(ctx);
94 	if (D == NULL || dv == NULL || rem == NULL)
95 		goto end;
96 
97 	nd=BN_num_bits(d);
98 	nm=BN_num_bits(m);
99 	if (BN_copy(D,d) == NULL) goto end;
100 	if (BN_copy(rem,m) == NULL) goto end;
101 
102 	/* The next 2 are needed so we can do a dv->d[0]|=1 later
103 	 * since BN_lshift1 will only work once there is a value :-) */
104 	BN_zero(dv);
105 	bn_wexpand(dv,1);
106 	dv->top=1;
107 
108 	if (!BN_lshift(D,D,nm-nd)) goto end;
109 	for (i=nm-nd; i>=0; i--)
110 		{
111 		if (!BN_lshift1(dv,dv)) goto end;
112 		if (BN_ucmp(rem,D) >= 0)
113 			{
114 			dv->d[0]|=1;
115 			if (!BN_usub(rem,rem,D)) goto end;
116 			}
117 /* CAN IMPROVE (and have now :=) */
118 		if (!BN_rshift1(D,D)) goto end;
119 		}
120 	rem->neg=BN_is_zero(rem)?0:m->neg;
121 	dv->neg=m->neg^d->neg;
122 	ret = 1;
123  end:
124 	BN_CTX_end(ctx);
125 	return(ret);
126 	}
127 
128 #else
129 
130 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
131     && !defined(PEDANTIC) && !defined(BN_DIV3W)
132 # if defined(__GNUC__) && __GNUC__>=2
133 #  if defined(__i386) || defined (__i386__)
134    /*
135     * There were two reasons for implementing this template:
136     * - GNU C generates a call to a function (__udivdi3 to be exact)
137     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
138     *   understand why...);
139     * - divl doesn't only calculate quotient, but also leaves
140     *   remainder in %edx which we can definitely use here:-)
141     *
142     *					<appro@fy.chalmers.se>
143     */
144 #  define bn_div_words(n0,n1,d0)		\
145 	({  asm volatile (			\
146 		"divl	%4"			\
147 		: "=a"(q), "=d"(rem)		\
148 		: "a"(n1), "d"(n0), "g"(d0)	\
149 		: "cc");			\
150 	    q;					\
151 	})
152 #  define REMAINDER_IS_ALREADY_CALCULATED
153 #  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
154    /*
155     * Same story here, but it's 128-bit by 64-bit division. Wow!
156     *					<appro@fy.chalmers.se>
157     */
158 #  define bn_div_words(n0,n1,d0)		\
159 	({  asm volatile (			\
160 		"divq	%4"			\
161 		: "=a"(q), "=d"(rem)		\
162 		: "a"(n1), "d"(n0), "g"(d0)	\
163 		: "cc");			\
164 	    q;					\
165 	})
166 #  define REMAINDER_IS_ALREADY_CALCULATED
167 #  endif /* __<cpu> */
168 # endif /* __GNUC__ */
169 #endif /* OPENSSL_NO_ASM */
170 
171 
172 /* BN_div[_no_branch] computes  dv := num / divisor,  rounding towards
173  * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
174  * Thus:
175  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
176  *     rm->neg == num->neg                 (unless the remainder is zero)
177  * If 'dv' or 'rm' is NULL, the respective value is not returned.
178  */
179 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
180         const BIGNUM *divisor, BN_CTX *ctx);
BN_div(BIGNUM * dv,BIGNUM * rm,const BIGNUM * num,const BIGNUM * divisor,BN_CTX * ctx)181 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
182 	   BN_CTX *ctx)
183 	{
184 	int norm_shift,i,loop;
185 	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
186 	BN_ULONG *resp,*wnump;
187 	BN_ULONG d0,d1;
188 	int num_n,div_n;
189 
190 	if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
191 		{
192 		return BN_div_no_branch(dv, rm, num, divisor, ctx);
193 		}
194 
195 	bn_check_top(dv);
196 	bn_check_top(rm);
197 	bn_check_top(num);
198 	bn_check_top(divisor);
199 
200 	if (BN_is_zero(divisor))
201 		{
202 		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
203 		return(0);
204 		}
205 
206 	if (BN_ucmp(num,divisor) < 0)
207 		{
208 		if (rm != NULL)
209 			{ if (BN_copy(rm,num) == NULL) return(0); }
210 		if (dv != NULL) BN_zero(dv);
211 		return(1);
212 		}
213 
214 	BN_CTX_start(ctx);
215 	tmp=BN_CTX_get(ctx);
216 	snum=BN_CTX_get(ctx);
217 	sdiv=BN_CTX_get(ctx);
218 	if (dv == NULL)
219 		res=BN_CTX_get(ctx);
220 	else	res=dv;
221 	if (sdiv == NULL || res == NULL) goto err;
222 
223 	/* First we normalise the numbers */
224 	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
225 	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
226 	sdiv->neg=0;
227 	norm_shift+=BN_BITS2;
228 	if (!(BN_lshift(snum,num,norm_shift))) goto err;
229 	snum->neg=0;
230 	div_n=sdiv->top;
231 	num_n=snum->top;
232 	loop=num_n-div_n;
233 	/* Lets setup a 'window' into snum
234 	 * This is the part that corresponds to the current
235 	 * 'area' being divided */
236 	wnum.neg   = 0;
237 	wnum.d     = &(snum->d[loop]);
238 	wnum.top   = div_n;
239 	/* only needed when BN_ucmp messes up the values between top and max */
240 	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
241 
242 	/* Get the top 2 words of sdiv */
243 	/* div_n=sdiv->top; */
244 	d0=sdiv->d[div_n-1];
245 	d1=(div_n == 1)?0:sdiv->d[div_n-2];
246 
247 	/* pointer to the 'top' of snum */
248 	wnump= &(snum->d[num_n-1]);
249 
250 	/* Setup to 'res' */
251 	res->neg= (num->neg^divisor->neg);
252 	if (!bn_wexpand(res,(loop+1))) goto err;
253 	res->top=loop;
254 	resp= &(res->d[loop-1]);
255 
256 	/* space for temp */
257 	if (!bn_wexpand(tmp,(div_n+1))) goto err;
258 
259 	if (BN_ucmp(&wnum,sdiv) >= 0)
260 		{
261 		/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
262 		 * bn_pollute) the const bignum arguments =>
263 		 * clean the values between top and max again */
264 		bn_clear_top2max(&wnum);
265 		bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
266 		*resp=1;
267 		}
268 	else
269 		res->top--;
270 	/* if res->top == 0 then clear the neg value otherwise decrease
271 	 * the resp pointer */
272 	if (res->top == 0)
273 		res->neg = 0;
274 	else
275 		resp--;
276 
277 	for (i=0; i<loop-1; i++, wnump--, resp--)
278 		{
279 		BN_ULONG q,l0;
280 		/* the first part of the loop uses the top two words of
281 		 * snum and sdiv to calculate a BN_ULONG q such that
282 		 * | wnum - sdiv * q | < sdiv */
283 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
284 		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
285 		q=bn_div_3_words(wnump,d1,d0);
286 #else
287 		BN_ULONG n0,n1,rem=0;
288 
289 		n0=wnump[0];
290 		n1=wnump[-1];
291 		if (n0 == d0)
292 			q=BN_MASK2;
293 		else 			/* n0 < d0 */
294 			{
295 #ifdef BN_LLONG
296 			BN_ULLONG t2;
297 
298 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
299 			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
300 #else
301 			q=bn_div_words(n0,n1,d0);
302 #ifdef BN_DEBUG_LEVITTE
303 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
304 X) -> 0x%08X\n",
305 				n0, n1, d0, q);
306 #endif
307 #endif
308 
309 #ifndef REMAINDER_IS_ALREADY_CALCULATED
310 			/*
311 			 * rem doesn't have to be BN_ULLONG. The least we
312 			 * know it's less that d0, isn't it?
313 			 */
314 			rem=(n1-q*d0)&BN_MASK2;
315 #endif
316 			t2=(BN_ULLONG)d1*q;
317 
318 			for (;;)
319 				{
320 				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
321 					break;
322 				q--;
323 				rem += d0;
324 				if (rem < d0) break; /* don't let rem overflow */
325 				t2 -= d1;
326 				}
327 #else /* !BN_LLONG */
328 			BN_ULONG t2l,t2h,ql,qh;
329 
330 			q=bn_div_words(n0,n1,d0);
331 #ifdef BN_DEBUG_LEVITTE
332 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
333 X) -> 0x%08X\n",
334 				n0, n1, d0, q);
335 #endif
336 #ifndef REMAINDER_IS_ALREADY_CALCULATED
337 			rem=(n1-q*d0)&BN_MASK2;
338 #endif
339 
340 #if defined(BN_UMULT_LOHI)
341 			BN_UMULT_LOHI(t2l,t2h,d1,q);
342 #elif defined(BN_UMULT_HIGH)
343 			t2l = d1 * q;
344 			t2h = BN_UMULT_HIGH(d1,q);
345 #else
346 			t2l=LBITS(d1); t2h=HBITS(d1);
347 			ql =LBITS(q);  qh =HBITS(q);
348 			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
349 #endif
350 
351 			for (;;)
352 				{
353 				if ((t2h < rem) ||
354 					((t2h == rem) && (t2l <= wnump[-2])))
355 					break;
356 				q--;
357 				rem += d0;
358 				if (rem < d0) break; /* don't let rem overflow */
359 				if (t2l < d1) t2h--; t2l -= d1;
360 				}
361 #endif /* !BN_LLONG */
362 			}
363 #endif /* !BN_DIV3W */
364 
365 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
366 		tmp->d[div_n]=l0;
367 		wnum.d--;
368 		/* ingore top values of the bignums just sub the two
369 		 * BN_ULONG arrays with bn_sub_words */
370 		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
371 			{
372 			/* Note: As we have considered only the leading
373 			 * two BN_ULONGs in the calculation of q, sdiv * q
374 			 * might be greater than wnum (but then (q-1) * sdiv
375 			 * is less or equal than wnum)
376 			 */
377 			q--;
378 			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
379 				/* we can't have an overflow here (assuming
380 				 * that q != 0, but if q == 0 then tmp is
381 				 * zero anyway) */
382 				(*wnump)++;
383 			}
384 		/* store part of the result */
385 		*resp = q;
386 		}
387 	bn_correct_top(snum);
388 	if (rm != NULL)
389 		{
390 		/* Keep a copy of the neg flag in num because if rm==num
391 		 * BN_rshift() will overwrite it.
392 		 */
393 		int neg = num->neg;
394 		BN_rshift(rm,snum,norm_shift);
395 		if (!BN_is_zero(rm))
396 			rm->neg = neg;
397 		bn_check_top(rm);
398 		}
399 	BN_CTX_end(ctx);
400 	return(1);
401 err:
402 	bn_check_top(rm);
403 	BN_CTX_end(ctx);
404 	return(0);
405 	}
406 
407 
408 /* BN_div_no_branch is a special version of BN_div. It does not contain
409  * branches that may leak sensitive information.
410  */
BN_div_no_branch(BIGNUM * dv,BIGNUM * rm,const BIGNUM * num,const BIGNUM * divisor,BN_CTX * ctx)411 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
412 	const BIGNUM *divisor, BN_CTX *ctx)
413 	{
414 	int norm_shift,i,loop;
415 	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
416 	BN_ULONG *resp,*wnump;
417 	BN_ULONG d0,d1;
418 	int num_n,div_n;
419 
420 	bn_check_top(dv);
421 	bn_check_top(rm);
422 	bn_check_top(num);
423 	bn_check_top(divisor);
424 
425 	if (BN_is_zero(divisor))
426 		{
427 		BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
428 		return(0);
429 		}
430 
431 	BN_CTX_start(ctx);
432 	tmp=BN_CTX_get(ctx);
433 	snum=BN_CTX_get(ctx);
434 	sdiv=BN_CTX_get(ctx);
435 	if (dv == NULL)
436 		res=BN_CTX_get(ctx);
437 	else	res=dv;
438 	if (sdiv == NULL || res == NULL) goto err;
439 
440 	/* First we normalise the numbers */
441 	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
442 	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
443 	sdiv->neg=0;
444 	norm_shift+=BN_BITS2;
445 	if (!(BN_lshift(snum,num,norm_shift))) goto err;
446 	snum->neg=0;
447 
448 	/* Since we don't know whether snum is larger than sdiv,
449 	 * we pad snum with enough zeroes without changing its
450 	 * value.
451 	 */
452 	if (snum->top <= sdiv->top+1)
453 		{
454 		if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
455 		for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
456 		snum->top = sdiv->top + 2;
457 		}
458 	else
459 		{
460 		if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
461 		snum->d[snum->top] = 0;
462 		snum->top ++;
463 		}
464 
465 	div_n=sdiv->top;
466 	num_n=snum->top;
467 	loop=num_n-div_n;
468 	/* Lets setup a 'window' into snum
469 	 * This is the part that corresponds to the current
470 	 * 'area' being divided */
471 	wnum.neg   = 0;
472 	wnum.d     = &(snum->d[loop]);
473 	wnum.top   = div_n;
474 	/* only needed when BN_ucmp messes up the values between top and max */
475 	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
476 
477 	/* Get the top 2 words of sdiv */
478 	/* div_n=sdiv->top; */
479 	d0=sdiv->d[div_n-1];
480 	d1=(div_n == 1)?0:sdiv->d[div_n-2];
481 
482 	/* pointer to the 'top' of snum */
483 	wnump= &(snum->d[num_n-1]);
484 
485 	/* Setup to 'res' */
486 	res->neg= (num->neg^divisor->neg);
487 	if (!bn_wexpand(res,(loop+1))) goto err;
488 	res->top=loop-1;
489 	resp= &(res->d[loop-1]);
490 
491 	/* space for temp */
492 	if (!bn_wexpand(tmp,(div_n+1))) goto err;
493 
494 	/* if res->top == 0 then clear the neg value otherwise decrease
495 	 * the resp pointer */
496 	if (res->top == 0)
497 		res->neg = 0;
498 	else
499 		resp--;
500 
501 	for (i=0; i<loop-1; i++, wnump--, resp--)
502 		{
503 		BN_ULONG q,l0;
504 		/* the first part of the loop uses the top two words of
505 		 * snum and sdiv to calculate a BN_ULONG q such that
506 		 * | wnum - sdiv * q | < sdiv */
507 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
508 		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
509 		q=bn_div_3_words(wnump,d1,d0);
510 #else
511 		BN_ULONG n0,n1,rem=0;
512 
513 		n0=wnump[0];
514 		n1=wnump[-1];
515 		if (n0 == d0)
516 			q=BN_MASK2;
517 		else 			/* n0 < d0 */
518 			{
519 #ifdef BN_LLONG
520 			BN_ULLONG t2;
521 
522 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
523 			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
524 #else
525 			q=bn_div_words(n0,n1,d0);
526 #ifdef BN_DEBUG_LEVITTE
527 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
528 X) -> 0x%08X\n",
529 				n0, n1, d0, q);
530 #endif
531 #endif
532 
533 #ifndef REMAINDER_IS_ALREADY_CALCULATED
534 			/*
535 			 * rem doesn't have to be BN_ULLONG. The least we
536 			 * know it's less that d0, isn't it?
537 			 */
538 			rem=(n1-q*d0)&BN_MASK2;
539 #endif
540 			t2=(BN_ULLONG)d1*q;
541 
542 			for (;;)
543 				{
544 				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
545 					break;
546 				q--;
547 				rem += d0;
548 				if (rem < d0) break; /* don't let rem overflow */
549 				t2 -= d1;
550 				}
551 #else /* !BN_LLONG */
552 			BN_ULONG t2l,t2h,ql,qh;
553 
554 			q=bn_div_words(n0,n1,d0);
555 #ifdef BN_DEBUG_LEVITTE
556 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
557 X) -> 0x%08X\n",
558 				n0, n1, d0, q);
559 #endif
560 #ifndef REMAINDER_IS_ALREADY_CALCULATED
561 			rem=(n1-q*d0)&BN_MASK2;
562 #endif
563 
564 #if defined(BN_UMULT_LOHI)
565 			BN_UMULT_LOHI(t2l,t2h,d1,q);
566 #elif defined(BN_UMULT_HIGH)
567 			t2l = d1 * q;
568 			t2h = BN_UMULT_HIGH(d1,q);
569 #else
570 			t2l=LBITS(d1); t2h=HBITS(d1);
571 			ql =LBITS(q);  qh =HBITS(q);
572 			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
573 #endif
574 
575 			for (;;)
576 				{
577 				if ((t2h < rem) ||
578 					((t2h == rem) && (t2l <= wnump[-2])))
579 					break;
580 				q--;
581 				rem += d0;
582 				if (rem < d0) break; /* don't let rem overflow */
583 				if (t2l < d1) t2h--; t2l -= d1;
584 				}
585 #endif /* !BN_LLONG */
586 			}
587 #endif /* !BN_DIV3W */
588 
589 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
590 		tmp->d[div_n]=l0;
591 		wnum.d--;
592 		/* ingore top values of the bignums just sub the two
593 		 * BN_ULONG arrays with bn_sub_words */
594 		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
595 			{
596 			/* Note: As we have considered only the leading
597 			 * two BN_ULONGs in the calculation of q, sdiv * q
598 			 * might be greater than wnum (but then (q-1) * sdiv
599 			 * is less or equal than wnum)
600 			 */
601 			q--;
602 			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
603 				/* we can't have an overflow here (assuming
604 				 * that q != 0, but if q == 0 then tmp is
605 				 * zero anyway) */
606 				(*wnump)++;
607 			}
608 		/* store part of the result */
609 		*resp = q;
610 		}
611 	bn_correct_top(snum);
612 	if (rm != NULL)
613 		{
614 		/* Keep a copy of the neg flag in num because if rm==num
615 		 * BN_rshift() will overwrite it.
616 		 */
617 		int neg = num->neg;
618 		BN_rshift(rm,snum,norm_shift);
619 		if (!BN_is_zero(rm))
620 			rm->neg = neg;
621 		bn_check_top(rm);
622 		}
623 	bn_correct_top(res);
624 	BN_CTX_end(ctx);
625 	return(1);
626 err:
627 	bn_check_top(rm);
628 	BN_CTX_end(ctx);
629 	return(0);
630 	}
631 
632 #endif
633