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.]
61 #include <openssl/bn.h>
66 /* The old slow way */
68 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
79 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
86 { if (BN_copy(rem,m) == NULL) return(0); }
87 if (dv != NULL) BN_zero(dv);
93 if (dv == NULL) dv = BN_CTX_get(ctx);
94 if (rem == NULL) rem = BN_CTX_get(ctx);
95 if (D == NULL || dv == NULL || rem == NULL)
100 if (BN_copy(D,d) == NULL) goto end;
101 if (BN_copy(rem,m) == NULL) goto end;
103 /* The next 2 are needed so we can do a dv->d[0]|=1 later
104 * since BN_lshift1 will only work once there is a value :-) */
106 if(bn_wexpand(dv,1) == NULL) goto end;
109 if (!BN_lshift(D,D,nm-nd)) goto end;
110 for (i=nm-nd; i>=0; i--)
112 if (!BN_lshift1(dv,dv)) goto end;
113 if (BN_ucmp(rem,D) >= 0)
116 if (!BN_usub(rem,rem,D)) goto end;
118 /* CAN IMPROVE (and have now :=) */
119 if (!BN_rshift1(D,D)) goto end;
121 rem->neg=BN_is_zero(rem)?0:m->neg;
122 dv->neg=m->neg^d->neg;
131 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
132 && !defined(PEDANTIC) && !defined(BN_DIV3W)
133 # if defined(__GNUC__) && __GNUC__>=2
134 # if defined(__i386) || defined (__i386__)
136 * There were two reasons for implementing this template:
137 * - GNU C generates a call to a function (__udivdi3 to be exact)
138 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
139 * understand why...);
140 * - divl doesn't only calculate quotient, but also leaves
141 * remainder in %edx which we can definitely use here:-)
143 * <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 */
176 * BN_div 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 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;
193 /* Invalid zero-padding would have particularly bad consequences
194 * so don't just rely on bn_check_top() here
195 * (bn_check_top() works only for BN_DEBUG builds) */
196 if ((num->top > 0 && num->d[num->top - 1] == 0) ||
197 (divisor->top > 0 && divisor->d[divisor->top - 1] == 0))
199 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
204 bn_check_top(divisor);
206 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
213 /* bn_check_top(num); */ /* 'num' has been checked already */
214 /* bn_check_top(divisor); */ /* 'divisor' has been checked already */
216 if (BN_is_zero(divisor))
218 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
222 if (!no_branch && BN_ucmp(num,divisor) < 0)
225 { if (BN_copy(rm,num) == NULL) return(0); }
226 if (dv != NULL) BN_zero(dv);
232 snum=BN_CTX_get(ctx);
233 sdiv=BN_CTX_get(ctx);
237 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
240 /* First we normalise the numbers */
241 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
242 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
244 norm_shift+=BN_BITS2;
245 if (!(BN_lshift(snum,num,norm_shift))) goto err;
250 /* Since we don't know whether snum is larger than sdiv,
251 * we pad snum with enough zeroes without changing its
254 if (snum->top <= sdiv->top+1)
256 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
257 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
258 snum->top = sdiv->top + 2;
262 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
263 snum->d[snum->top] = 0;
271 /* Lets setup a 'window' into snum
272 * This is the part that corresponds to the current
273 * 'area' being divided */
275 wnum.d = &(snum->d[loop]);
277 /* only needed when BN_ucmp messes up the values between top and max */
278 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
280 /* Get the top 2 words of sdiv */
281 /* div_n=sdiv->top; */
283 d1=(div_n == 1)?0:sdiv->d[div_n-2];
285 /* pointer to the 'top' of snum */
286 wnump= &(snum->d[num_n-1]);
289 res->neg= (num->neg^divisor->neg);
290 if (!bn_wexpand(res,(loop+1))) goto err;
291 res->top=loop-no_branch;
292 resp= &(res->d[loop-1]);
295 if (!bn_wexpand(tmp,(div_n+1))) goto err;
299 if (BN_ucmp(&wnum,sdiv) >= 0)
301 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
302 * bn_pollute) the const bignum arguments =>
303 * clean the values between top and max again */
304 bn_clear_top2max(&wnum);
305 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
312 /* if res->top == 0 then clear the neg value otherwise decrease
313 * the resp pointer */
319 for (i=0; i<loop-1; i++, wnump--, resp--)
322 /* the first part of the loop uses the top two words of
323 * snum and sdiv to calculate a BN_ULONG q such that
324 * | wnum - sdiv * q | < sdiv */
325 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
326 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
327 q=bn_div_3_words(wnump,d1,d0);
329 BN_ULONG n0,n1,rem=0;
340 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
341 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
343 q=bn_div_words(n0,n1,d0);
344 #ifdef BN_DEBUG_LEVITTE
345 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
351 #ifndef REMAINDER_IS_ALREADY_CALCULATED
353 * rem doesn't have to be BN_ULLONG. The least we
354 * know it's less that d0, isn't it?
356 rem=(n1-q*d0)&BN_MASK2;
362 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
366 if (rem < d0) break; /* don't let rem overflow */
369 #else /* !BN_LLONG */
372 q=bn_div_words(n0,n1,d0);
373 #ifdef BN_DEBUG_LEVITTE
374 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
378 #ifndef REMAINDER_IS_ALREADY_CALCULATED
379 rem=(n1-q*d0)&BN_MASK2;
382 #if defined(BN_UMULT_LOHI)
383 BN_UMULT_LOHI(t2l,t2h,d1,q);
384 #elif defined(BN_UMULT_HIGH)
386 t2h = BN_UMULT_HIGH(d1,q);
390 t2l=LBITS(d1); t2h=HBITS(d1);
391 ql =LBITS(q); qh =HBITS(q);
392 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
399 ((t2h == rem) && (t2l <= wnump[-2])))
403 if (rem < d0) break; /* don't let rem overflow */
404 if (t2l < d1) t2h--; t2l -= d1;
406 #endif /* !BN_LLONG */
408 #endif /* !BN_DIV3W */
410 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
413 /* ingore top values of the bignums just sub the two
414 * BN_ULONG arrays with bn_sub_words */
415 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
417 /* Note: As we have considered only the leading
418 * two BN_ULONGs in the calculation of q, sdiv * q
419 * might be greater than wnum (but then (q-1) * sdiv
420 * is less or equal than wnum)
423 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
424 /* we can't have an overflow here (assuming
425 * that q != 0, but if q == 0 then tmp is
429 /* store part of the result */
432 bn_correct_top(snum);
435 /* Keep a copy of the neg flag in num because if rm==num
436 * BN_rshift() will overwrite it.
439 BN_rshift(rm,snum,norm_shift);
444 if (no_branch) bn_correct_top(res);