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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 | |
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 o
ne | |
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 | |
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