1 /* crypto/bn/bn_div.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
59 #define OPENSSL_FIPSAPI
62 #include <openssl/bn.h>
67 /* The old slow way */
69 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
80 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
87 { if (BN_copy(rem,m) == NULL) return(0); }
88 if (dv != NULL) BN_zero(dv);
94 if (dv == NULL) dv = BN_CTX_get(ctx);
95 if (rem == NULL) rem = BN_CTX_get(ctx);
96 if (D == NULL || dv == NULL || rem == NULL)
101 if (BN_copy(D,d) == NULL) goto end;
102 if (BN_copy(rem,m) == NULL) goto end;
104 /* The next 2 are needed so we can do a dv->d[0]|=1 later
105 * since BN_lshift1 will only work once there is a value :-) */
107 if(bn_wexpand(dv,1) == NULL) goto end;
110 if (!BN_lshift(D,D,nm-nd)) goto end;
111 for (i=nm-nd; i>=0; i--)
113 if (!BN_lshift1(dv,dv)) goto end;
114 if (BN_ucmp(rem,D) >= 0)
117 if (!BN_usub(rem,rem,D)) goto end;
119 /* CAN IMPROVE (and have now :=) */
120 if (!BN_rshift1(D,D)) goto end;
122 rem->neg=BN_is_zero(rem)?0:m->neg;
123 dv->neg=m->neg^d->neg;
132 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
133 && !defined(PEDANTIC) && !defined(BN_DIV3W)
134 # if defined(__GNUC__) && __GNUC__>=2
135 # if defined(__i386) || defined (__i386__)
137 * There were two reasons for implementing this template:
138 * - GNU C generates a call to a function (__udivdi3 to be exact)
139 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
140 * understand why...);
141 * - divl doesn't only calculate quotient, but also leaves
142 * remainder in %edx which we can definitely use here:-)
144 * <appro@fy.chalmers.se>
147 # define bn_div_words(n0,n1,d0) \
150 : "=a"(q), "=d"(rem) \
151 : "a"(n1), "d"(n0), "g"(d0) \
155 # define REMAINDER_IS_ALREADY_CALCULATED
156 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
158 * Same story here, but it's 128-bit by 64-bit division. Wow!
159 * <appro@fy.chalmers.se>
162 # define bn_div_words(n0,n1,d0) \
165 : "=a"(q), "=d"(rem) \
166 : "a"(n1), "d"(n0), "g"(d0) \
170 # define REMAINDER_IS_ALREADY_CALCULATED
171 # endif /* __<cpu> */
172 # endif /* __GNUC__ */
173 #endif /* OPENSSL_NO_ASM */
176 /* BN_div[_no_branch] computes dv := num / divisor, rounding towards
177 * zero, and sets up rm such that dv*divisor + rm = num holds.
179 * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
180 * rm->neg == num->neg (unless the remainder is zero)
181 * If 'dv' or 'rm' is NULL, the respective value is not returned.
183 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
184 const BIGNUM *divisor, BN_CTX *ctx);
185 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
188 int norm_shift,i,loop;
189 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
190 BN_ULONG *resp,*wnump;
194 /* Invalid zero-padding would have particularly bad consequences
195 * in the case of 'num', so don't just rely on bn_check_top() for this one
196 * (bn_check_top() works only for BN_DEBUG builds) */
197 if (num->top > 0 && num->d[num->top - 1] == 0)
199 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
205 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
207 return BN_div_no_branch(dv, rm, num, divisor, ctx);
212 /* bn_check_top(num); */ /* 'num' has been checked already */
213 bn_check_top(divisor);
215 if (BN_is_zero(divisor))
217 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
221 if (BN_ucmp(num,divisor) < 0)
224 { if (BN_copy(rm,num) == NULL) return(0); }
225 if (dv != NULL) BN_zero(dv);
231 snum=BN_CTX_get(ctx);
232 sdiv=BN_CTX_get(ctx);
236 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
239 /* First we normalise the numbers */
240 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
241 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
243 norm_shift+=BN_BITS2;
244 if (!(BN_lshift(snum,num,norm_shift))) goto err;
249 /* Lets setup a 'window' into snum
250 * This is the part that corresponds to the current
251 * 'area' being divided */
253 wnum.d = &(snum->d[loop]);
255 /* only needed when BN_ucmp messes up the values between top and max */
256 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
258 /* Get the top 2 words of sdiv */
259 /* div_n=sdiv->top; */
261 d1=(div_n == 1)?0:sdiv->d[div_n-2];
263 /* pointer to the 'top' of snum */
264 wnump= &(snum->d[num_n-1]);
267 res->neg= (num->neg^divisor->neg);
268 if (!bn_wexpand(res,(loop+1))) goto err;
270 resp= &(res->d[loop-1]);
273 if (!bn_wexpand(tmp,(div_n+1))) goto err;
275 if (BN_ucmp(&wnum,sdiv) >= 0)
277 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
278 * bn_pollute) the const bignum arguments =>
279 * clean the values between top and max again */
280 bn_clear_top2max(&wnum);
281 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
286 /* if res->top == 0 then clear the neg value otherwise decrease
287 * the resp pointer */
293 for (i=0; i<loop-1; i++, wnump--, resp--)
296 /* the first part of the loop uses the top two words of
297 * snum and sdiv to calculate a BN_ULONG q such that
298 * | wnum - sdiv * q | < sdiv */
299 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
300 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
301 q=bn_div_3_words(wnump,d1,d0);
303 BN_ULONG n0,n1,rem=0;
314 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
315 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
317 q=bn_div_words(n0,n1,d0);
318 #ifdef BN_DEBUG_LEVITTE
319 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
325 #ifndef REMAINDER_IS_ALREADY_CALCULATED
327 * rem doesn't have to be BN_ULLONG. The least we
328 * know it's less that d0, isn't it?
330 rem=(n1-q*d0)&BN_MASK2;
336 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
340 if (rem < d0) break; /* don't let rem overflow */
343 #else /* !BN_LLONG */
346 q=bn_div_words(n0,n1,d0);
347 #ifdef BN_DEBUG_LEVITTE
348 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
352 #ifndef REMAINDER_IS_ALREADY_CALCULATED
353 rem=(n1-q*d0)&BN_MASK2;
356 #if defined(BN_UMULT_LOHI)
357 BN_UMULT_LOHI(t2l,t2h,d1,q);
358 #elif defined(BN_UMULT_HIGH)
360 t2h = BN_UMULT_HIGH(d1,q);
364 t2l=LBITS(d1); t2h=HBITS(d1);
365 ql =LBITS(q); qh =HBITS(q);
366 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
373 ((t2h == rem) && (t2l <= wnump[-2])))
377 if (rem < d0) break; /* don't let rem overflow */
378 if (t2l < d1) t2h--; t2l -= d1;
380 #endif /* !BN_LLONG */
382 #endif /* !BN_DIV3W */
384 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
387 /* ingore top values of the bignums just sub the two
388 * BN_ULONG arrays with bn_sub_words */
389 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
391 /* Note: As we have considered only the leading
392 * two BN_ULONGs in the calculation of q, sdiv * q
393 * might be greater than wnum (but then (q-1) * sdiv
394 * is less or equal than wnum)
397 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
398 /* we can't have an overflow here (assuming
399 * that q != 0, but if q == 0 then tmp is
403 /* store part of the result */
406 bn_correct_top(snum);
409 /* Keep a copy of the neg flag in num because if rm==num
410 * BN_rshift() will overwrite it.
413 BN_rshift(rm,snum,norm_shift);
427 /* BN_div_no_branch is a special version of BN_div. It does not contain
428 * branches that may leak sensitive information.
430 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
431 const BIGNUM *divisor, BN_CTX *ctx)
433 int norm_shift,i,loop;
434 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
435 BN_ULONG *resp,*wnump;
441 /* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
442 bn_check_top(divisor);
444 if (BN_is_zero(divisor))
446 BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
452 snum=BN_CTX_get(ctx);
453 sdiv=BN_CTX_get(ctx);
457 if (sdiv == NULL || res == NULL) goto err;
459 /* First we normalise the numbers */
460 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
461 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
463 norm_shift+=BN_BITS2;
464 if (!(BN_lshift(snum,num,norm_shift))) goto err;
467 /* Since we don't know whether snum is larger than sdiv,
468 * we pad snum with enough zeroes without changing its
471 if (snum->top <= sdiv->top+1)
473 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
474 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
475 snum->top = sdiv->top + 2;
479 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
480 snum->d[snum->top] = 0;
487 /* Lets setup a 'window' into snum
488 * This is the part that corresponds to the current
489 * 'area' being divided */
491 wnum.d = &(snum->d[loop]);
493 /* only needed when BN_ucmp messes up the values between top and max */
494 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
496 /* Get the top 2 words of sdiv */
497 /* div_n=sdiv->top; */
499 d1=(div_n == 1)?0:sdiv->d[div_n-2];
501 /* pointer to the 'top' of snum */
502 wnump= &(snum->d[num_n-1]);
505 res->neg= (num->neg^divisor->neg);
506 if (!bn_wexpand(res,(loop+1))) goto err;
508 resp= &(res->d[loop-1]);
511 if (!bn_wexpand(tmp,(div_n+1))) goto err;
513 /* if res->top == 0 then clear the neg value otherwise decrease
514 * the resp pointer */
520 for (i=0; i<loop-1; i++, wnump--, resp--)
523 /* the first part of the loop uses the top two words of
524 * snum and sdiv to calculate a BN_ULONG q such that
525 * | wnum - sdiv * q | < sdiv */
526 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
527 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
528 q=bn_div_3_words(wnump,d1,d0);
530 BN_ULONG n0,n1,rem=0;
541 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
542 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
544 q=bn_div_words(n0,n1,d0);
545 #ifdef BN_DEBUG_LEVITTE
546 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
552 #ifndef REMAINDER_IS_ALREADY_CALCULATED
554 * rem doesn't have to be BN_ULLONG. The least we
555 * know it's less that d0, isn't it?
557 rem=(n1-q*d0)&BN_MASK2;
563 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
567 if (rem < d0) break; /* don't let rem overflow */
570 #else /* !BN_LLONG */
573 q=bn_div_words(n0,n1,d0);
574 #ifdef BN_DEBUG_LEVITTE
575 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
579 #ifndef REMAINDER_IS_ALREADY_CALCULATED
580 rem=(n1-q*d0)&BN_MASK2;
583 #if defined(BN_UMULT_LOHI)
584 BN_UMULT_LOHI(t2l,t2h,d1,q);
585 #elif defined(BN_UMULT_HIGH)
587 t2h = BN_UMULT_HIGH(d1,q);
591 t2l=LBITS(d1); t2h=HBITS(d1);
592 ql =LBITS(q); qh =HBITS(q);
593 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
600 ((t2h == rem) && (t2l <= wnump[-2])))
604 if (rem < d0) break; /* don't let rem overflow */
605 if (t2l < d1) t2h--; t2l -= d1;
607 #endif /* !BN_LLONG */
609 #endif /* !BN_DIV3W */
611 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
614 /* ingore top values of the bignums just sub the two
615 * BN_ULONG arrays with bn_sub_words */
616 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
618 /* Note: As we have considered only the leading
619 * two BN_ULONGs in the calculation of q, sdiv * q
620 * might be greater than wnum (but then (q-1) * sdiv
621 * is less or equal than wnum)
624 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
625 /* we can't have an overflow here (assuming
626 * that q != 0, but if q == 0 then tmp is
630 /* store part of the result */
633 bn_correct_top(snum);
636 /* Keep a copy of the neg flag in num because if rm==num
637 * BN_rshift() will overwrite it.
640 BN_rshift(rm,snum,norm_shift);