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>
160 # define bn_div_words(n0,n1,d0) \
163 : "=a"(q), "=d"(rem) \
164 : "a"(n1), "d"(n0), "g"(d0) \
168 # define REMAINDER_IS_ALREADY_CALCULATED
169 # endif /* __<cpu> */
170 # endif /* __GNUC__ */
171 #endif /* OPENSSL_NO_ASM */
174 /* BN_div[_no_branch] computes dv := num / divisor, rounding towards
175 * zero, and sets up rm such that dv*divisor + rm = num holds.
177 * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
178 * rm->neg == num->neg (unless the remainder is zero)
179 * If 'dv' or 'rm' is NULL, the respective value is not returned.
181 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
182 const BIGNUM *divisor, BN_CTX *ctx);
183 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
186 int norm_shift,i,loop;
187 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
188 BN_ULONG *resp,*wnump;
192 /* Invalid zero-padding would have particularly bad consequences
193 * in the case of 'num', so don't just rely on bn_check_top() for this one
194 * (bn_check_top() works only for BN_DEBUG builds) */
195 if (num->top > 0 && num->d[num->top - 1] == 0)
197 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
203 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
205 return BN_div_no_branch(dv, rm, num, divisor, ctx);
210 /* bn_check_top(num); */ /* 'num' has been checked already */
211 bn_check_top(divisor);
213 if (BN_is_zero(divisor))
215 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
219 if (BN_ucmp(num,divisor) < 0)
222 { if (BN_copy(rm,num) == NULL) return(0); }
223 if (dv != NULL) BN_zero(dv);
229 snum=BN_CTX_get(ctx);
230 sdiv=BN_CTX_get(ctx);
234 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
237 /* First we normalise the numbers */
238 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
239 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
241 norm_shift+=BN_BITS2;
242 if (!(BN_lshift(snum,num,norm_shift))) goto err;
247 /* Lets setup a 'window' into snum
248 * This is the part that corresponds to the current
249 * 'area' being divided */
251 wnum.d = &(snum->d[loop]);
253 /* only needed when BN_ucmp messes up the values between top and max */
254 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
256 /* Get the top 2 words of sdiv */
257 /* div_n=sdiv->top; */
259 d1=(div_n == 1)?0:sdiv->d[div_n-2];
261 /* pointer to the 'top' of snum */
262 wnump= &(snum->d[num_n-1]);
265 res->neg= (num->neg^divisor->neg);
266 if (!bn_wexpand(res,(loop+1))) goto err;
268 resp= &(res->d[loop-1]);
271 if (!bn_wexpand(tmp,(div_n+1))) goto err;
273 if (BN_ucmp(&wnum,sdiv) >= 0)
275 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
276 * bn_pollute) the const bignum arguments =>
277 * clean the values between top and max again */
278 bn_clear_top2max(&wnum);
279 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
284 /* if res->top == 0 then clear the neg value otherwise decrease
285 * the resp pointer */
291 for (i=0; i<loop-1; i++, wnump--, resp--)
294 /* the first part of the loop uses the top two words of
295 * snum and sdiv to calculate a BN_ULONG q such that
296 * | wnum - sdiv * q | < sdiv */
297 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
298 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
299 q=bn_div_3_words(wnump,d1,d0);
301 BN_ULONG n0,n1,rem=0;
312 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
313 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
315 q=bn_div_words(n0,n1,d0);
316 #ifdef BN_DEBUG_LEVITTE
317 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
323 #ifndef REMAINDER_IS_ALREADY_CALCULATED
325 * rem doesn't have to be BN_ULLONG. The least we
326 * know it's less that d0, isn't it?
328 rem=(n1-q*d0)&BN_MASK2;
334 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
338 if (rem < d0) break; /* don't let rem overflow */
341 #else /* !BN_LLONG */
344 q=bn_div_words(n0,n1,d0);
345 #ifdef BN_DEBUG_LEVITTE
346 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
350 #ifndef REMAINDER_IS_ALREADY_CALCULATED
351 rem=(n1-q*d0)&BN_MASK2;
354 #if defined(BN_UMULT_LOHI)
355 BN_UMULT_LOHI(t2l,t2h,d1,q);
356 #elif defined(BN_UMULT_HIGH)
358 t2h = BN_UMULT_HIGH(d1,q);
362 t2l=LBITS(d1); t2h=HBITS(d1);
363 ql =LBITS(q); qh =HBITS(q);
364 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
371 ((t2h == rem) && (t2l <= wnump[-2])))
375 if (rem < d0) break; /* don't let rem overflow */
376 if (t2l < d1) t2h--; t2l -= d1;
378 #endif /* !BN_LLONG */
380 #endif /* !BN_DIV3W */
382 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
385 /* ingore top values of the bignums just sub the two
386 * BN_ULONG arrays with bn_sub_words */
387 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
389 /* Note: As we have considered only the leading
390 * two BN_ULONGs in the calculation of q, sdiv * q
391 * might be greater than wnum (but then (q-1) * sdiv
392 * is less or equal than wnum)
395 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
396 /* we can't have an overflow here (assuming
397 * that q != 0, but if q == 0 then tmp is
401 /* store part of the result */
404 bn_correct_top(snum);
407 /* Keep a copy of the neg flag in num because if rm==num
408 * BN_rshift() will overwrite it.
411 BN_rshift(rm,snum,norm_shift);
425 /* BN_div_no_branch is a special version of BN_div. It does not contain
426 * branches that may leak sensitive information.
428 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
429 const BIGNUM *divisor, BN_CTX *ctx)
431 int norm_shift,i,loop;
432 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
433 BN_ULONG *resp,*wnump;
439 /* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
440 bn_check_top(divisor);
442 if (BN_is_zero(divisor))
444 BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
450 snum=BN_CTX_get(ctx);
451 sdiv=BN_CTX_get(ctx);
455 if (sdiv == NULL || res == NULL) goto err;
457 /* First we normalise the numbers */
458 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
459 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
461 norm_shift+=BN_BITS2;
462 if (!(BN_lshift(snum,num,norm_shift))) goto err;
465 /* Since we don't know whether snum is larger than sdiv,
466 * we pad snum with enough zeroes without changing its
469 if (snum->top <= sdiv->top+1)
471 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
472 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
473 snum->top = sdiv->top + 2;
477 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
478 snum->d[snum->top] = 0;
485 /* Lets setup a 'window' into snum
486 * This is the part that corresponds to the current
487 * 'area' being divided */
489 wnum.d = &(snum->d[loop]);
491 /* only needed when BN_ucmp messes up the values between top and max */
492 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
494 /* Get the top 2 words of sdiv */
495 /* div_n=sdiv->top; */
497 d1=(div_n == 1)?0:sdiv->d[div_n-2];
499 /* pointer to the 'top' of snum */
500 wnump= &(snum->d[num_n-1]);
503 res->neg= (num->neg^divisor->neg);
504 if (!bn_wexpand(res,(loop+1))) goto err;
506 resp= &(res->d[loop-1]);
509 if (!bn_wexpand(tmp,(div_n+1))) goto err;
511 /* if res->top == 0 then clear the neg value otherwise decrease
512 * the resp pointer */
518 for (i=0; i<loop-1; i++, wnump--, resp--)
521 /* the first part of the loop uses the top two words of
522 * snum and sdiv to calculate a BN_ULONG q such that
523 * | wnum - sdiv * q | < sdiv */
524 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
525 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
526 q=bn_div_3_words(wnump,d1,d0);
528 BN_ULONG n0,n1,rem=0;
539 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
540 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
542 q=bn_div_words(n0,n1,d0);
543 #ifdef BN_DEBUG_LEVITTE
544 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
550 #ifndef REMAINDER_IS_ALREADY_CALCULATED
552 * rem doesn't have to be BN_ULLONG. The least we
553 * know it's less that d0, isn't it?
555 rem=(n1-q*d0)&BN_MASK2;
561 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
565 if (rem < d0) break; /* don't let rem overflow */
568 #else /* !BN_LLONG */
571 q=bn_div_words(n0,n1,d0);
572 #ifdef BN_DEBUG_LEVITTE
573 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
577 #ifndef REMAINDER_IS_ALREADY_CALCULATED
578 rem=(n1-q*d0)&BN_MASK2;
581 #if defined(BN_UMULT_LOHI)
582 BN_UMULT_LOHI(t2l,t2h,d1,q);
583 #elif defined(BN_UMULT_HIGH)
585 t2h = BN_UMULT_HIGH(d1,q);
589 t2l=LBITS(d1); t2h=HBITS(d1);
590 ql =LBITS(q); qh =HBITS(q);
591 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
598 ((t2h == rem) && (t2l <= wnump[-2])))
602 if (rem < d0) break; /* don't let rem overflow */
603 if (t2l < d1) t2h--; t2l -= d1;
605 #endif /* !BN_LLONG */
607 #endif /* !BN_DIV3W */
609 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
612 /* ingore top values of the bignums just sub the two
613 * BN_ULONG arrays with bn_sub_words */
614 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
616 /* Note: As we have considered only the leading
617 * two BN_ULONGs in the calculation of q, sdiv * q
618 * might be greater than wnum (but then (q-1) * sdiv
619 * is less or equal than wnum)
622 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
623 /* we can't have an overflow here (assuming
624 * that q != 0, but if q == 0 then tmp is
628 /* store part of the result */
631 bn_correct_top(snum);
634 /* Keep a copy of the neg flag in num because if rm==num
635 * BN_rshift() will overwrite it.
638 BN_rshift(rm,snum,norm_shift);