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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
67int 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 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 */
179int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
180 BN_CTX *ctx)
181 {
182 int norm_shift,i,loop;
183 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
184 BN_ULONG *resp,*wnump;
185 BN_ULONG d0,d1;
186 int num_n,div_n;
187 int no_branch=0;
188
189 /* Invalid zero-padding would have particularly bad consequences
190 * in the case of 'num', so don't just rely on bn_check_top() for this one
191 * (bn_check_top() works only for BN_DEBUG builds) */
192 if (num->top > 0 && num->d[num->top - 1] == 0)
193 {
194 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
195 return 0;
196 }
197
198 bn_check_top(num);
199
200 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
201 {
202 no_branch=1;
203 }
204
205 bn_check_top(dv);
206 bn_check_top(rm);
207 /* bn_check_top(num); */ /* 'num' has been checked already */
208 bn_check_top(divisor);
209
210 if (BN_is_zero(divisor))
211 {
212 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
213 return(0);
214 }
215
216 if (!no_branch && BN_ucmp(num,divisor) < 0)
217 {
218 if (rm != NULL)
219 { if (BN_copy(rm,num) == NULL) return(0); }
220 if (dv != NULL) BN_zero(dv);
221 return(1);
222 }
223
224 BN_CTX_start(ctx);
225 tmp=BN_CTX_get(ctx);
226 snum=BN_CTX_get(ctx);
227 sdiv=BN_CTX_get(ctx);
228 if (dv == NULL)
229 res=BN_CTX_get(ctx);
230 else res=dv;
231 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
232 goto err;
233
234 /* First we normalise the numbers */
235 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
236 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
237 sdiv->neg=0;
238 norm_shift+=BN_BITS2;
239 if (!(BN_lshift(snum,num,norm_shift))) goto err;
240 snum->neg=0;
241
242 if (no_branch)
243 {
244 /* Since we don't know whether snum is larger than sdiv,
245 * we pad snum with enough zeroes without changing its
246 * value.
247 */
248 if (snum->top <= sdiv->top+1)
249 {
250 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
251 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
252 snum->top = sdiv->top + 2;
253 }
254 else
255 {
256 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
257 snum->d[snum->top] = 0;
258 snum->top ++;
259 }
260 }
261
262 div_n=sdiv->top;
263 num_n=snum->top;
264 loop=num_n-div_n;
265 /* Lets setup a 'window' into snum
266 * This is the part that corresponds to the current
267 * 'area' being divided */
268 wnum.neg = 0;
269 wnum.d = &(snum->d[loop]);
270 wnum.top = div_n;
271 /* only needed when BN_ucmp messes up the values between top and max */
272 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
273
274 /* Get the top 2 words of sdiv */
275 /* div_n=sdiv->top; */
276 d0=sdiv->d[div_n-1];
277 d1=(div_n == 1)?0:sdiv->d[div_n-2];
278
279 /* pointer to the 'top' of snum */
280 wnump= &(snum->d[num_n-1]);
281
282 /* Setup to 'res' */
283 res->neg= (num->neg^divisor->neg);
284 if (!bn_wexpand(res,(loop+1))) goto err;
285 res->top=loop-no_branch;
286 resp= &(res->d[loop-1]);
287
288 /* space for temp */
289 if (!bn_wexpand(tmp,(div_n+1))) goto err;
290
291 if (!no_branch)
292 {
293 if (BN_ucmp(&wnum,sdiv) >= 0)
294 {
295 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
296 * bn_pollute) the const bignum arguments =>
297 * clean the values between top and max again */
298 bn_clear_top2max(&wnum);
299 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
300 *resp=1;
301 }
302 else
303 res->top--;
304 }
305
306 /* if res->top == 0 then clear the neg value otherwise decrease
307 * the resp pointer */
308 if (res->top == 0)
309 res->neg = 0;
310 else
311 resp--;
312
313 for (i=0; i<loop-1; i++, wnump--, resp--)
314 {
315 BN_ULONG q,l0;
316 /* the first part of the loop uses the top two words of
317 * snum and sdiv to calculate a BN_ULONG q such that
318 * | wnum - sdiv * q | < sdiv */
319#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
320 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
321 q=bn_div_3_words(wnump,d1,d0);
322#else
323 BN_ULONG n0,n1,rem=0;
324
325 n0=wnump[0];
326 n1=wnump[-1];
327 if (n0 == d0)
328 q=BN_MASK2;
329 else /* n0 < d0 */
330 {
331#ifdef BN_LLONG
332 BN_ULLONG t2;
333
334#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
335 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
336#else
337 q=bn_div_words(n0,n1,d0);
338#ifdef BN_DEBUG_LEVITTE
339 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
340X) -> 0x%08X\n",
341 n0, n1, d0, q);
342#endif
343#endif
344
345#ifndef REMAINDER_IS_ALREADY_CALCULATED
346 /*
347 * rem doesn't have to be BN_ULLONG. The least we
348 * know it's less that d0, isn't it?
349 */
350 rem=(n1-q*d0)&BN_MASK2;
351#endif
352 t2=(BN_ULLONG)d1*q;
353
354 for (;;)
355 {
356 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
357 break;
358 q--;
359 rem += d0;
360 if (rem < d0) break; /* don't let rem overflow */
361 t2 -= d1;
362 }
363#else /* !BN_LLONG */
364 BN_ULONG t2l,t2h;
365
366 q=bn_div_words(n0,n1,d0);
367#ifdef BN_DEBUG_LEVITTE
368 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
369X) -> 0x%08X\n",
370 n0, n1, d0, q);
371#endif
372#ifndef REMAINDER_IS_ALREADY_CALCULATED
373 rem=(n1-q*d0)&BN_MASK2;
374#endif
375
376#if defined(BN_UMULT_LOHI)
377 BN_UMULT_LOHI(t2l,t2h,d1,q);
378#elif defined(BN_UMULT_HIGH)
379 t2l = d1 * q;
380 t2h = BN_UMULT_HIGH(d1,q);
381#else
382 {
383 BN_ULONG ql, qh;
384 t2l=LBITS(d1); t2h=HBITS(d1);
385 ql =LBITS(q); qh =HBITS(q);
386 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
387 }
388#endif
389
390 for (;;)
391 {
392 if ((t2h < rem) ||
393 ((t2h == rem) && (t2l <= wnump[-2])))
394 break;
395 q--;
396 rem += d0;
397 if (rem < d0) break; /* don't let rem overflow */
398 if (t2l < d1) t2h--; t2l -= d1;
399 }
400#endif /* !BN_LLONG */
401 }
402#endif /* !BN_DIV3W */
403
404 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
405 tmp->d[div_n]=l0;
406 wnum.d--;
407 /* ingore top values of the bignums just sub the two
408 * BN_ULONG arrays with bn_sub_words */
409 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
410 {
411 /* Note: As we have considered only the leading
412 * two BN_ULONGs in the calculation of q, sdiv * q
413 * might be greater than wnum (but then (q-1) * sdiv
414 * is less or equal than wnum)
415 */
416 q--;
417 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
418 /* we can't have an overflow here (assuming
419 * that q != 0, but if q == 0 then tmp is
420 * zero anyway) */
421 (*wnump)++;
422 }
423 /* store part of the result */
424 *resp = q;
425 }
426 bn_correct_top(snum);
427 if (rm != NULL)
428 {
429 /* Keep a copy of the neg flag in num because if rm==num
430 * BN_rshift() will overwrite it.
431 */
432 int neg = num->neg;
433 BN_rshift(rm,snum,norm_shift);
434 if (!BN_is_zero(rm))
435 rm->neg = neg;
436 bn_check_top(rm);
437 }
438 if (no_branch) bn_correct_top(res);
439 BN_CTX_end(ctx);
440 return(1);
441err:
442 bn_check_top(rm);
443 BN_CTX_end(ctx);
444 return(0);
445 }
446#endif
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