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
67 int 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 #undef bn_div_words
145 # define bn_div_words(n0,n1,d0) \
146 ({ asm volatile ( \
147 "divl %4" \
148 : "=a"(q), "=d"(rem) \
149 : "a"(n1), "d"(n0), "g"(d0) \
150 : "cc"); \
151 q; \
152 })
153 # define REMAINDER_IS_ALREADY_CALCULATED
154 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
155 /*
156 * Same story here, but it's 128-bit by 64-bit division. Wow!
157 * <appro@fy.chalmers.se>
158 */
159 # undef bn_div_words
160 # define bn_div_words(n0,n1,d0) \
161 ({ asm volatile ( \
162 "divq %4" \
163 : "=a"(q), "=d"(rem) \
164 : "a"(n1), "d"(n0), "g"(d0) \
165 : "cc"); \
166 q; \
167 })
168 # define REMAINDER_IS_ALREADY_CALCULATED
169 # endif /* __<cpu> */
170 # endif /* __GNUC__ */
171 #endif /* OPENSSL_NO_ASM */
172
173
174 /* BN_div computes dv := num / divisor, rounding towards
175 * zero, and sets up rm such that dv*divisor + rm = num holds.
176 * Thus:
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.
180 */
181 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
182 BN_CTX *ctx)
183 {
184 int norm_shift,i,loop;
185 BIGNUM *tmp,wnum,*snum,*sdiv,*res;
186 BN_ULONG *resp,*wnump;
187 BN_ULONG d0,d1;
188 int num_n,div_n;
189 int no_branch=0;
190
191 /* Invalid zero-padding would have particularly bad consequences
192 * in the case of 'num', so don't just rely on bn_check_top() for this one
193 * (bn_check_top() works only for BN_DEBUG builds) */
194 if (num->top > 0 && num->d[num->top - 1] == 0)
195 {
196 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
197 return 0;
198 }
199
200 bn_check_top(num);
201
202 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
203 {
204 no_branch=1;
205 }
206
207 bn_check_top(dv);
208 bn_check_top(rm);
209 /* bn_check_top(num); */ /* 'num' has been checked already */
210 bn_check_top(divisor);
211
212 if (BN_is_zero(divisor))
213 {
214 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
215 return(0);
216 }
217
218 if (!no_branch && BN_ucmp(num,divisor) < 0)
219 {
220 if (rm != NULL)
221 { if (BN_copy(rm,num) == NULL) return(0); }
222 if (dv != NULL) BN_zero(dv);
223 return(1);
224 }
225
226 BN_CTX_start(ctx);
227 tmp=BN_CTX_get(ctx);
228 snum=BN_CTX_get(ctx);
229 sdiv=BN_CTX_get(ctx);
230 if (dv == NULL)
231 res=BN_CTX_get(ctx);
232 else res=dv;
233 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
234 goto err;
235
236 /* First we normalise the numbers */
237 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
238 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
239 sdiv->neg=0;
240 norm_shift+=BN_BITS2;
241 if (!(BN_lshift(snum,num,norm_shift))) goto err;
242 snum->neg=0;
243
244 if (no_branch)
245 {
246 /* Since we don't know whether snum is larger than sdiv,
247 * we pad snum with enough zeroes without changing its
248 * value.
249 */
250 if (snum->top <= sdiv->top+1)
251 {
252 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
253 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
254 snum->top = sdiv->top + 2;
255 }
256 else
257 {
258 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
259 snum->d[snum->top] = 0;
260 snum->top ++;
261 }
262 }
263
264 div_n=sdiv->top;
265 num_n=snum->top;
266 loop=num_n-div_n;
267 /* Lets setup a 'window' into snum
268 * This is the part that corresponds to the current
269 * 'area' being divided */
270 wnum.neg = 0;
271 wnum.d = &(snum->d[loop]);
272 wnum.top = div_n;
273 /* only needed when BN_ucmp messes up the values between top and max */
274 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
275
276 /* Get the top 2 words of sdiv */
277 /* div_n=sdiv->top; */
278 d0=sdiv->d[div_n-1];
279 d1=(div_n == 1)?0:sdiv->d[div_n-2];
280
281 /* pointer to the 'top' of snum */
282 wnump= &(snum->d[num_n-1]);
283
284 /* Setup to 'res' */
285 res->neg= (num->neg^divisor->neg);
286 if (!bn_wexpand(res,(loop+1))) goto err;
287 res->top=loop-no_branch;
288 resp= &(res->d[loop-1]);
289
290 /* space for temp */
291 if (!bn_wexpand(tmp,(div_n+1))) goto err;
292
293 if (!no_branch)
294 {
295 if (BN_ucmp(&wnum,sdiv) >= 0)
296 {
297 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
298 * bn_pollute) the const bignum arguments =>
299 * clean the values between top and max again */
300 bn_clear_top2max(&wnum);
301 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
302 *resp=1;
303 }
304 else
305 res->top--;
306 }
307
308 /* if res->top == 0 then clear the neg value otherwise decrease
309 * the resp pointer */
310 if (res->top == 0)
311 res->neg = 0;
312 else
313 resp--;
314
315 for (i=0; i<loop-1; i++, wnump--, resp--)
316 {
317 BN_ULONG q,l0;
318 /* the first part of the loop uses the top two words of
319 * snum and sdiv to calculate a BN_ULONG q such that
320 * | wnum - sdiv * q | < sdiv */
321 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
322 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
323 q=bn_div_3_words(wnump,d1,d0);
324 #else
325 BN_ULONG n0,n1,rem=0;
326
327 n0=wnump[0];
328 n1=wnump[-1];
329 if (n0 == d0)
330 q=BN_MASK2;
331 else /* n0 < d0 */
332 {
333 #ifdef BN_LLONG
334 BN_ULLONG t2;
335
336 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
337 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
338 #else
339 q=bn_div_words(n0,n1,d0);
340 #ifdef BN_DEBUG_LEVITTE
341 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
342 X) -> 0x%08X\n",
343 n0, n1, d0, q);
344 #endif
345 #endif
346
347 #ifndef REMAINDER_IS_ALREADY_CALCULATED
348 /*
349 * rem doesn't have to be BN_ULLONG. The least we
350 * know it's less that d0, isn't it?
351 */
352 rem=(n1-q*d0)&BN_MASK2;
353 #endif
354 t2=(BN_ULLONG)d1*q;
355
356 for (;;)
357 {
358 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
359 break;
360 q--;
361 rem += d0;
362 if (rem < d0) break; /* don't let rem overflow */
363 t2 -= d1;
364 }
365 #else /* !BN_LLONG */
366 BN_ULONG t2l,t2h;
367
368 q=bn_div_words(n0,n1,d0);
369 #ifdef BN_DEBUG_LEVITTE
370 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
371 X) -> 0x%08X\n",
372 n0, n1, d0, q);
373 #endif
374 #ifndef REMAINDER_IS_ALREADY_CALCULATED
375 rem=(n1-q*d0)&BN_MASK2;
376 #endif
377
378 #if defined(BN_UMULT_LOHI)
379 BN_UMULT_LOHI(t2l,t2h,d1,q);
380 #elif defined(BN_UMULT_HIGH)
381 t2l = d1 * q;
382 t2h = BN_UMULT_HIGH(d1,q);
383 #else
384 {
385 BN_ULONG ql, qh;
386 t2l=LBITS(d1); t2h=HBITS(d1);
387 ql =LBITS(q); qh =HBITS(q);
388 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
389 }
390 #endif
391
392 for (;;)
393 {
394 if ((t2h < rem) ||
395 ((t2h == rem) && (t2l <= wnump[-2])))
396 break;
397 q--;
398 rem += d0;
399 if (rem < d0) break; /* don't let rem overflow */
400 if (t2l < d1) t2h--; t2l -= d1;
401 }
402 #endif /* !BN_LLONG */
403 }
404 #endif /* !BN_DIV3W */
405
406 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
407 tmp->d[div_n]=l0;
408 wnum.d--;
409 /* ingore top values of the bignums just sub the two
410 * BN_ULONG arrays with bn_sub_words */
411 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
412 {
413 /* Note: As we have considered only the leading
414 * two BN_ULONGs in the calculation of q, sdiv * q
415 * might be greater than wnum (but then (q-1) * sdiv
416 * is less or equal than wnum)
417 */
418 q--;
419 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
420 /* we can't have an overflow here (assuming
421 * that q != 0, but if q == 0 then tmp is
422 * zero anyway) */
423 (*wnump)++;
424 }
425 /* store part of the result */
426 *resp = q;
427 }
428 bn_correct_top(snum);
429 if (rm != NULL)
430 {
431 /* Keep a copy of the neg flag in num because if rm==num
432 * BN_rshift() will overwrite it.
433 */
434 int neg = num->neg;
435 BN_rshift(rm,snum,norm_shift);
436 if (!BN_is_zero(rm))
437 rm->neg = neg;
438 bn_check_top(rm);
439 }
440 if (no_branch) bn_correct_top(res);
441 BN_CTX_end(ctx);
442 return(1);
443 err:
444 bn_check_top(rm);
445 BN_CTX_end(ctx);
446 return(0);
447 }
448 #endif