xref: /freebsd/crypto/openssl/crypto/bn/bn_div.c (revision aa0a1e58)
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 	if(bn_wexpand(dv,1) == NULL) goto end;
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);
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 	/* Invalid zero-padding would have particularly bad consequences
191 	 * in the case of 'num', so don't just rely on bn_check_top() for this one
192 	 * (bn_check_top() works only for BN_DEBUG builds) */
193 	if (num->top > 0 && num->d[num->top - 1] == 0)
194 		{
195 		BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
196 		return 0;
197 		}
198 
199 	bn_check_top(num);
200 
201 	if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
202 		{
203 		return BN_div_no_branch(dv, rm, num, divisor, ctx);
204 		}
205 
206 	bn_check_top(dv);
207 	bn_check_top(rm);
208 	/* bn_check_top(num); */ /* 'num' has been checked already */
209 	bn_check_top(divisor);
210 
211 	if (BN_is_zero(divisor))
212 		{
213 		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
214 		return(0);
215 		}
216 
217 	if (BN_ucmp(num,divisor) < 0)
218 		{
219 		if (rm != NULL)
220 			{ if (BN_copy(rm,num) == NULL) return(0); }
221 		if (dv != NULL) BN_zero(dv);
222 		return(1);
223 		}
224 
225 	BN_CTX_start(ctx);
226 	tmp=BN_CTX_get(ctx);
227 	snum=BN_CTX_get(ctx);
228 	sdiv=BN_CTX_get(ctx);
229 	if (dv == NULL)
230 		res=BN_CTX_get(ctx);
231 	else	res=dv;
232 	if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
233 		goto err;
234 
235 	/* First we normalise the numbers */
236 	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
237 	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
238 	sdiv->neg=0;
239 	norm_shift+=BN_BITS2;
240 	if (!(BN_lshift(snum,num,norm_shift))) goto err;
241 	snum->neg=0;
242 	div_n=sdiv->top;
243 	num_n=snum->top;
244 	loop=num_n-div_n;
245 	/* Lets setup a 'window' into snum
246 	 * This is the part that corresponds to the current
247 	 * 'area' being divided */
248 	wnum.neg   = 0;
249 	wnum.d     = &(snum->d[loop]);
250 	wnum.top   = div_n;
251 	/* only needed when BN_ucmp messes up the values between top and max */
252 	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
253 
254 	/* Get the top 2 words of sdiv */
255 	/* div_n=sdiv->top; */
256 	d0=sdiv->d[div_n-1];
257 	d1=(div_n == 1)?0:sdiv->d[div_n-2];
258 
259 	/* pointer to the 'top' of snum */
260 	wnump= &(snum->d[num_n-1]);
261 
262 	/* Setup to 'res' */
263 	res->neg= (num->neg^divisor->neg);
264 	if (!bn_wexpand(res,(loop+1))) goto err;
265 	res->top=loop;
266 	resp= &(res->d[loop-1]);
267 
268 	/* space for temp */
269 	if (!bn_wexpand(tmp,(div_n+1))) goto err;
270 
271 	if (BN_ucmp(&wnum,sdiv) >= 0)
272 		{
273 		/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
274 		 * bn_pollute) the const bignum arguments =>
275 		 * clean the values between top and max again */
276 		bn_clear_top2max(&wnum);
277 		bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
278 		*resp=1;
279 		}
280 	else
281 		res->top--;
282 	/* if res->top == 0 then clear the neg value otherwise decrease
283 	 * the resp pointer */
284 	if (res->top == 0)
285 		res->neg = 0;
286 	else
287 		resp--;
288 
289 	for (i=0; i<loop-1; i++, wnump--, resp--)
290 		{
291 		BN_ULONG q,l0;
292 		/* the first part of the loop uses the top two words of
293 		 * snum and sdiv to calculate a BN_ULONG q such that
294 		 * | wnum - sdiv * q | < sdiv */
295 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
296 		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
297 		q=bn_div_3_words(wnump,d1,d0);
298 #else
299 		BN_ULONG n0,n1,rem=0;
300 
301 		n0=wnump[0];
302 		n1=wnump[-1];
303 		if (n0 == d0)
304 			q=BN_MASK2;
305 		else 			/* n0 < d0 */
306 			{
307 #ifdef BN_LLONG
308 			BN_ULLONG t2;
309 
310 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
311 			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
312 #else
313 			q=bn_div_words(n0,n1,d0);
314 #ifdef BN_DEBUG_LEVITTE
315 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
316 X) -> 0x%08X\n",
317 				n0, n1, d0, q);
318 #endif
319 #endif
320 
321 #ifndef REMAINDER_IS_ALREADY_CALCULATED
322 			/*
323 			 * rem doesn't have to be BN_ULLONG. The least we
324 			 * know it's less that d0, isn't it?
325 			 */
326 			rem=(n1-q*d0)&BN_MASK2;
327 #endif
328 			t2=(BN_ULLONG)d1*q;
329 
330 			for (;;)
331 				{
332 				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
333 					break;
334 				q--;
335 				rem += d0;
336 				if (rem < d0) break; /* don't let rem overflow */
337 				t2 -= d1;
338 				}
339 #else /* !BN_LLONG */
340 			BN_ULONG t2l,t2h;
341 #if !defined(BN_UMULT_LOHI) && !defined(BN_UMULT_HIGH)
342 			BN_ULONG ql,qh;
343 #endif
344 
345 			q=bn_div_words(n0,n1,d0);
346 #ifdef BN_DEBUG_LEVITTE
347 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
348 X) -> 0x%08X\n",
349 				n0, n1, d0, q);
350 #endif
351 #ifndef REMAINDER_IS_ALREADY_CALCULATED
352 			rem=(n1-q*d0)&BN_MASK2;
353 #endif
354 
355 #if defined(BN_UMULT_LOHI)
356 			BN_UMULT_LOHI(t2l,t2h,d1,q);
357 #elif defined(BN_UMULT_HIGH)
358 			t2l = d1 * q;
359 			t2h = BN_UMULT_HIGH(d1,q);
360 #else
361 			t2l=LBITS(d1); t2h=HBITS(d1);
362 			ql =LBITS(q);  qh =HBITS(q);
363 			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
364 #endif
365 
366 			for (;;)
367 				{
368 				if ((t2h < rem) ||
369 					((t2h == rem) && (t2l <= wnump[-2])))
370 					break;
371 				q--;
372 				rem += d0;
373 				if (rem < d0) break; /* don't let rem overflow */
374 				if (t2l < d1) t2h--; t2l -= d1;
375 				}
376 #endif /* !BN_LLONG */
377 			}
378 #endif /* !BN_DIV3W */
379 
380 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
381 		tmp->d[div_n]=l0;
382 		wnum.d--;
383 		/* ingore top values of the bignums just sub the two
384 		 * BN_ULONG arrays with bn_sub_words */
385 		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
386 			{
387 			/* Note: As we have considered only the leading
388 			 * two BN_ULONGs in the calculation of q, sdiv * q
389 			 * might be greater than wnum (but then (q-1) * sdiv
390 			 * is less or equal than wnum)
391 			 */
392 			q--;
393 			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
394 				/* we can't have an overflow here (assuming
395 				 * that q != 0, but if q == 0 then tmp is
396 				 * zero anyway) */
397 				(*wnump)++;
398 			}
399 		/* store part of the result */
400 		*resp = q;
401 		}
402 	bn_correct_top(snum);
403 	if (rm != NULL)
404 		{
405 		/* Keep a copy of the neg flag in num because if rm==num
406 		 * BN_rshift() will overwrite it.
407 		 */
408 		int neg = num->neg;
409 		BN_rshift(rm,snum,norm_shift);
410 		if (!BN_is_zero(rm))
411 			rm->neg = neg;
412 		bn_check_top(rm);
413 		}
414 	BN_CTX_end(ctx);
415 	return(1);
416 err:
417 	bn_check_top(rm);
418 	BN_CTX_end(ctx);
419 	return(0);
420 	}
421 
422 
423 /* BN_div_no_branch is a special version of BN_div. It does not contain
424  * branches that may leak sensitive information.
425  */
426 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
427 	const BIGNUM *divisor, BN_CTX *ctx)
428 	{
429 	int norm_shift,i,loop;
430 	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
431 	BN_ULONG *resp,*wnump;
432 	BN_ULONG d0,d1;
433 	int num_n,div_n;
434 
435 	bn_check_top(dv);
436 	bn_check_top(rm);
437 	/* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
438 	bn_check_top(divisor);
439 
440 	if (BN_is_zero(divisor))
441 		{
442 		BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
443 		return(0);
444 		}
445 
446 	BN_CTX_start(ctx);
447 	tmp=BN_CTX_get(ctx);
448 	snum=BN_CTX_get(ctx);
449 	sdiv=BN_CTX_get(ctx);
450 	if (dv == NULL)
451 		res=BN_CTX_get(ctx);
452 	else	res=dv;
453 	if (sdiv == NULL || res == NULL) goto err;
454 
455 	/* First we normalise the numbers */
456 	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
457 	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
458 	sdiv->neg=0;
459 	norm_shift+=BN_BITS2;
460 	if (!(BN_lshift(snum,num,norm_shift))) goto err;
461 	snum->neg=0;
462 
463 	/* Since we don't know whether snum is larger than sdiv,
464 	 * we pad snum with enough zeroes without changing its
465 	 * value.
466 	 */
467 	if (snum->top <= sdiv->top+1)
468 		{
469 		if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
470 		for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
471 		snum->top = sdiv->top + 2;
472 		}
473 	else
474 		{
475 		if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
476 		snum->d[snum->top] = 0;
477 		snum->top ++;
478 		}
479 
480 	div_n=sdiv->top;
481 	num_n=snum->top;
482 	loop=num_n-div_n;
483 	/* Lets setup a 'window' into snum
484 	 * This is the part that corresponds to the current
485 	 * 'area' being divided */
486 	wnum.neg   = 0;
487 	wnum.d     = &(snum->d[loop]);
488 	wnum.top   = div_n;
489 	/* only needed when BN_ucmp messes up the values between top and max */
490 	wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
491 
492 	/* Get the top 2 words of sdiv */
493 	/* div_n=sdiv->top; */
494 	d0=sdiv->d[div_n-1];
495 	d1=(div_n == 1)?0:sdiv->d[div_n-2];
496 
497 	/* pointer to the 'top' of snum */
498 	wnump= &(snum->d[num_n-1]);
499 
500 	/* Setup to 'res' */
501 	res->neg= (num->neg^divisor->neg);
502 	if (!bn_wexpand(res,(loop+1))) goto err;
503 	res->top=loop-1;
504 	resp= &(res->d[loop-1]);
505 
506 	/* space for temp */
507 	if (!bn_wexpand(tmp,(div_n+1))) goto err;
508 
509 	/* if res->top == 0 then clear the neg value otherwise decrease
510 	 * the resp pointer */
511 	if (res->top == 0)
512 		res->neg = 0;
513 	else
514 		resp--;
515 
516 	for (i=0; i<loop-1; i++, wnump--, resp--)
517 		{
518 		BN_ULONG q,l0;
519 		/* the first part of the loop uses the top two words of
520 		 * snum and sdiv to calculate a BN_ULONG q such that
521 		 * | wnum - sdiv * q | < sdiv */
522 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
523 		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
524 		q=bn_div_3_words(wnump,d1,d0);
525 #else
526 		BN_ULONG n0,n1,rem=0;
527 
528 		n0=wnump[0];
529 		n1=wnump[-1];
530 		if (n0 == d0)
531 			q=BN_MASK2;
532 		else 			/* n0 < d0 */
533 			{
534 #ifdef BN_LLONG
535 			BN_ULLONG t2;
536 
537 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
538 			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
539 #else
540 			q=bn_div_words(n0,n1,d0);
541 #ifdef BN_DEBUG_LEVITTE
542 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
543 X) -> 0x%08X\n",
544 				n0, n1, d0, q);
545 #endif
546 #endif
547 
548 #ifndef REMAINDER_IS_ALREADY_CALCULATED
549 			/*
550 			 * rem doesn't have to be BN_ULLONG. The least we
551 			 * know it's less that d0, isn't it?
552 			 */
553 			rem=(n1-q*d0)&BN_MASK2;
554 #endif
555 			t2=(BN_ULLONG)d1*q;
556 
557 			for (;;)
558 				{
559 				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
560 					break;
561 				q--;
562 				rem += d0;
563 				if (rem < d0) break; /* don't let rem overflow */
564 				t2 -= d1;
565 				}
566 #else /* !BN_LLONG */
567 			BN_ULONG t2l,t2h;
568 #if !defined(BN_UMULT_LOHI) && !defined(BN_UMULT_HIGH)
569 			BN_ULONG ql,qh;
570 #endif
571 
572 			q=bn_div_words(n0,n1,d0);
573 #ifdef BN_DEBUG_LEVITTE
574 			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
575 X) -> 0x%08X\n",
576 				n0, n1, d0, q);
577 #endif
578 #ifndef REMAINDER_IS_ALREADY_CALCULATED
579 			rem=(n1-q*d0)&BN_MASK2;
580 #endif
581 
582 #if defined(BN_UMULT_LOHI)
583 			BN_UMULT_LOHI(t2l,t2h,d1,q);
584 #elif defined(BN_UMULT_HIGH)
585 			t2l = d1 * q;
586 			t2h = BN_UMULT_HIGH(d1,q);
587 #else
588 			t2l=LBITS(d1); t2h=HBITS(d1);
589 			ql =LBITS(q);  qh =HBITS(q);
590 			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
591 #endif
592 
593 			for (;;)
594 				{
595 				if ((t2h < rem) ||
596 					((t2h == rem) && (t2l <= wnump[-2])))
597 					break;
598 				q--;
599 				rem += d0;
600 				if (rem < d0) break; /* don't let rem overflow */
601 				if (t2l < d1) t2h--; t2l -= d1;
602 				}
603 #endif /* !BN_LLONG */
604 			}
605 #endif /* !BN_DIV3W */
606 
607 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
608 		tmp->d[div_n]=l0;
609 		wnum.d--;
610 		/* ingore top values of the bignums just sub the two
611 		 * BN_ULONG arrays with bn_sub_words */
612 		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
613 			{
614 			/* Note: As we have considered only the leading
615 			 * two BN_ULONGs in the calculation of q, sdiv * q
616 			 * might be greater than wnum (but then (q-1) * sdiv
617 			 * is less or equal than wnum)
618 			 */
619 			q--;
620 			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
621 				/* we can't have an overflow here (assuming
622 				 * that q != 0, but if q == 0 then tmp is
623 				 * zero anyway) */
624 				(*wnump)++;
625 			}
626 		/* store part of the result */
627 		*resp = q;
628 		}
629 	bn_correct_top(snum);
630 	if (rm != NULL)
631 		{
632 		/* Keep a copy of the neg flag in num because if rm==num
633 		 * BN_rshift() will overwrite it.
634 		 */
635 		int neg = num->neg;
636 		BN_rshift(rm,snum,norm_shift);
637 		if (!BN_is_zero(rm))
638 			rm->neg = neg;
639 		bn_check_top(rm);
640 		}
641 	bn_correct_top(res);
642 	BN_CTX_end(ctx);
643 	return(1);
644 err:
645 	bn_check_top(rm);
646 	BN_CTX_end(ctx);
647 	return(0);
648 	}
649 
650 #endif
651