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>
146 # define bn_div_words(n0,n1,d0) \
149 : "=a"(q), "=d"(rem) \
150 : "a"(n1), "d"(n0), "g"(d0) \
154 # define REMAINDER_IS_ALREADY_CALCULATED
155 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
157 * Same story here, but it's 128-bit by 64-bit division. Wow!
158 * <appro@fy.chalmers.se>
161 # define bn_div_words(n0,n1,d0) \
164 : "=a"(q), "=d"(rem) \
165 : "a"(n1), "d"(n0), "g"(d0) \
169 # define REMAINDER_IS_ALREADY_CALCULATED
170 # endif /* __<cpu> */
171 # endif /* __GNUC__ */
172 #endif /* OPENSSL_NO_ASM */
175 /* BN_div[_no_branch] computes dv := num / divisor, rounding towards
176 * zero, and sets up rm such that dv*divisor + rm = num holds.
178 * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
179 * rm->neg == num->neg (unless the remainder is zero)
180 * If 'dv' or 'rm' is NULL, the respective value is not returned.
182 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
183 const BIGNUM *divisor, BN_CTX *ctx);
184 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
187 int norm_shift,i,loop;
188 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
189 BN_ULONG *resp,*wnump;
193 /* Invalid zero-padding would have particularly bad consequences
194 * in the case of 'num', so don't just rely on bn_check_top() for this one
195 * (bn_check_top() works only for BN_DEBUG builds) */
196 if (num->top > 0 && num->d[num->top - 1] == 0)
198 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
204 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
206 return BN_div_no_branch(dv, rm, num, divisor, ctx);
211 /* bn_check_top(num); */ /* 'num' has been checked already */
212 bn_check_top(divisor);
214 if (BN_is_zero(divisor))
216 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
220 if (BN_ucmp(num,divisor) < 0)
223 { if (BN_copy(rm,num) == NULL) return(0); }
224 if (dv != NULL) BN_zero(dv);
230 snum=BN_CTX_get(ctx);
231 sdiv=BN_CTX_get(ctx);
235 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
238 /* First we normalise the numbers */
239 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
240 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
242 norm_shift+=BN_BITS2;
243 if (!(BN_lshift(snum,num,norm_shift))) goto err;
248 /* Lets setup a 'window' into snum
249 * This is the part that corresponds to the current
250 * 'area' being divided */
252 wnum.d = &(snum->d[loop]);
254 /* only needed when BN_ucmp messes up the values between top and max */
255 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
257 /* Get the top 2 words of sdiv */
258 /* div_n=sdiv->top; */
260 d1=(div_n == 1)?0:sdiv->d[div_n-2];
262 /* pointer to the 'top' of snum */
263 wnump= &(snum->d[num_n-1]);
266 res->neg= (num->neg^divisor->neg);
267 if (!bn_wexpand(res,(loop+1))) goto err;
269 resp= &(res->d[loop-1]);
272 if (!bn_wexpand(tmp,(div_n+1))) goto err;
274 if (BN_ucmp(&wnum,sdiv) >= 0)
276 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
277 * bn_pollute) the const bignum arguments =>
278 * clean the values between top and max again */
279 bn_clear_top2max(&wnum);
280 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
285 /* if res->top == 0 then clear the neg value otherwise decrease
286 * the resp pointer */
292 for (i=0; i<loop-1; i++, wnump--, resp--)
295 /* the first part of the loop uses the top two words of
296 * snum and sdiv to calculate a BN_ULONG q such that
297 * | wnum - sdiv * q | < sdiv */
298 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
299 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
300 q=bn_div_3_words(wnump,d1,d0);
302 BN_ULONG n0,n1,rem=0;
313 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
314 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
316 q=bn_div_words(n0,n1,d0);
317 #ifdef BN_DEBUG_LEVITTE
318 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
324 #ifndef REMAINDER_IS_ALREADY_CALCULATED
326 * rem doesn't have to be BN_ULLONG. The least we
327 * know it's less that d0, isn't it?
329 rem=(n1-q*d0)&BN_MASK2;
335 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
339 if (rem < d0) break; /* don't let rem overflow */
342 #else /* !BN_LLONG */
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\
351 #ifndef REMAINDER_IS_ALREADY_CALCULATED
352 rem=(n1-q*d0)&BN_MASK2;
355 #if defined(BN_UMULT_LOHI)
356 BN_UMULT_LOHI(t2l,t2h,d1,q);
357 #elif defined(BN_UMULT_HIGH)
359 t2h = BN_UMULT_HIGH(d1,q);
363 t2l=LBITS(d1); t2h=HBITS(d1);
364 ql =LBITS(q); qh =HBITS(q);
365 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
372 ((t2h == rem) && (t2l <= wnump[-2])))
376 if (rem < d0) break; /* don't let rem overflow */
377 if (t2l < d1) t2h--; t2l -= d1;
379 #endif /* !BN_LLONG */
381 #endif /* !BN_DIV3W */
383 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
386 /* ingore top values of the bignums just sub the two
387 * BN_ULONG arrays with bn_sub_words */
388 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
390 /* Note: As we have considered only the leading
391 * two BN_ULONGs in the calculation of q, sdiv * q
392 * might be greater than wnum (but then (q-1) * sdiv
393 * is less or equal than wnum)
396 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
397 /* we can't have an overflow here (assuming
398 * that q != 0, but if q == 0 then tmp is
402 /* store part of the result */
405 bn_correct_top(snum);
408 /* Keep a copy of the neg flag in num because if rm==num
409 * BN_rshift() will overwrite it.
412 BN_rshift(rm,snum,norm_shift);
426 /* BN_div_no_branch is a special version of BN_div. It does not contain
427 * branches that may leak sensitive information.
429 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
430 const BIGNUM *divisor, BN_CTX *ctx)
432 int norm_shift,i,loop;
433 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
434 BN_ULONG *resp,*wnump;
440 /* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
441 bn_check_top(divisor);
443 if (BN_is_zero(divisor))
445 BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
451 snum=BN_CTX_get(ctx);
452 sdiv=BN_CTX_get(ctx);
456 if (sdiv == NULL || res == NULL) goto err;
458 /* First we normalise the numbers */
459 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
460 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
462 norm_shift+=BN_BITS2;
463 if (!(BN_lshift(snum,num,norm_shift))) goto err;
466 /* Since we don't know whether snum is larger than sdiv,
467 * we pad snum with enough zeroes without changing its
470 if (snum->top <= sdiv->top+1)
472 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
473 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
474 snum->top = sdiv->top + 2;
478 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
479 snum->d[snum->top] = 0;
486 /* Lets setup a 'window' into snum
487 * This is the part that corresponds to the current
488 * 'area' being divided */
490 wnum.d = &(snum->d[loop]);
492 /* only needed when BN_ucmp messes up the values between top and max */
493 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
495 /* Get the top 2 words of sdiv */
496 /* div_n=sdiv->top; */
498 d1=(div_n == 1)?0:sdiv->d[div_n-2];
500 /* pointer to the 'top' of snum */
501 wnump= &(snum->d[num_n-1]);
504 res->neg= (num->neg^divisor->neg);
505 if (!bn_wexpand(res,(loop+1))) goto err;
507 resp= &(res->d[loop-1]);
510 if (!bn_wexpand(tmp,(div_n+1))) goto err;
512 /* if res->top == 0 then clear the neg value otherwise decrease
513 * the resp pointer */
519 for (i=0; i<loop-1; i++, wnump--, resp--)
522 /* the first part of the loop uses the top two words of
523 * snum and sdiv to calculate a BN_ULONG q such that
524 * | wnum - sdiv * q | < sdiv */
525 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
526 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
527 q=bn_div_3_words(wnump,d1,d0);
529 BN_ULONG n0,n1,rem=0;
540 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
541 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
543 q=bn_div_words(n0,n1,d0);
544 #ifdef BN_DEBUG_LEVITTE
545 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
551 #ifndef REMAINDER_IS_ALREADY_CALCULATED
553 * rem doesn't have to be BN_ULLONG. The least we
554 * know it's less that d0, isn't it?
556 rem=(n1-q*d0)&BN_MASK2;
562 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
566 if (rem < d0) break; /* don't let rem overflow */
569 #else /* !BN_LLONG */
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\
578 #ifndef REMAINDER_IS_ALREADY_CALCULATED
579 rem=(n1-q*d0)&BN_MASK2;
582 #if defined(BN_UMULT_LOHI)
583 BN_UMULT_LOHI(t2l,t2h,d1,q);
584 #elif defined(BN_UMULT_HIGH)
586 t2h = BN_UMULT_HIGH(d1,q);
590 t2l=LBITS(d1); t2h=HBITS(d1);
591 ql =LBITS(q); qh =HBITS(q);
592 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
599 ((t2h == rem) && (t2l <= wnump[-2])))
603 if (rem < d0) break; /* don't let rem overflow */
604 if (t2l < d1) t2h--; t2l -= d1;
606 #endif /* !BN_LLONG */
608 #endif /* !BN_DIV3W */
610 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
613 /* ingore top values of the bignums just sub the two
614 * BN_ULONG arrays with bn_sub_words */
615 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
617 /* Note: As we have considered only the leading
618 * two BN_ULONGs in the calculation of q, sdiv * q
619 * might be greater than wnum (but then (q-1) * sdiv
620 * is less or equal than wnum)
623 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
624 /* we can't have an overflow here (assuming
625 * that q != 0, but if q == 0 then tmp is
629 /* store part of the result */
632 bn_correct_top(snum);
635 /* Keep a copy of the neg flag in num because if rm==num
636 * BN_rshift() will overwrite it.
639 BN_rshift(rm,snum,norm_shift);