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d02b48c6 | 1 | /* crypto/bn/bn_div.c */ |
58964a49 | 2 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
d02b48c6 RE |
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> | |
84c15db5 | 60 | #include <openssl/bn.h> |
d02b48c6 RE |
61 | #include "cryptlib.h" |
62 | #include "bn_lcl.h" | |
63 | ||
78a0c1f1 | 64 | |
d02b48c6 | 65 | /* The old slow way */ |
4a6222d7 | 66 | #if 0 |
0bde1089 UM |
67 | int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, |
68 | BN_CTX *ctx) | |
d02b48c6 RE |
69 | { |
70 | int i,nm,nd; | |
9b141126 | 71 | int ret = 0; |
d02b48c6 RE |
72 | BIGNUM *D; |
73 | ||
dfeab068 RE |
74 | bn_check_top(m); |
75 | bn_check_top(d); | |
d02b48c6 RE |
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 | ||
9b141126 UM |
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; | |
d02b48c6 RE |
96 | |
97 | nd=BN_num_bits(d); | |
98 | nm=BN_num_bits(m); | |
9b141126 UM |
99 | if (BN_copy(D,d) == NULL) goto end; |
100 | if (BN_copy(rem,m) == NULL) goto end; | |
d02b48c6 RE |
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); | |
dfeab068 | 105 | bn_wexpand(dv,1); |
d02b48c6 RE |
106 | dv->top=1; |
107 | ||
9b141126 | 108 | if (!BN_lshift(D,D,nm-nd)) goto end; |
d02b48c6 RE |
109 | for (i=nm-nd; i>=0; i--) |
110 | { | |
9b141126 | 111 | if (!BN_lshift1(dv,dv)) goto end; |
d02b48c6 RE |
112 | if (BN_ucmp(rem,D) >= 0) |
113 | { | |
114 | dv->d[0]|=1; | |
9b141126 | 115 | if (!BN_usub(rem,rem,D)) goto end; |
d02b48c6 RE |
116 | } |
117 | /* CAN IMPROVE (and have now :=) */ | |
9b141126 | 118 | if (!BN_rshift1(D,D)) goto end; |
d02b48c6 RE |
119 | } |
120 | rem->neg=BN_is_zero(rem)?0:m->neg; | |
121 | dv->neg=m->neg^d->neg; | |
9b141126 UM |
122 | ret = 1; |
123 | end: | |
124 | BN_CTX_end(ctx); | |
125 | return(ret); | |
d02b48c6 RE |
126 | } |
127 | ||
128 | #else | |
129 | ||
cf1b7d96 RL |
130 | #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \ |
131 | && !defined(PEDANTIC) && !defined(BN_DIV3W) | |
4a6222d7 | 132 | # if defined(__GNUC__) && __GNUC__>=2 |
5dd955dc | 133 | # if defined(__i386) || defined (__i386__) |
4a6222d7 UM |
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 | |
2f98abbc AP |
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 | |
4a6222d7 UM |
167 | # endif /* __<cpu> */ |
168 | # endif /* __GNUC__ */ | |
cf1b7d96 | 169 | #endif /* OPENSSL_NO_ASM */ |
4a6222d7 | 170 | |
78a0c1f1 BM |
171 | |
172 | /* BN_div computes dv := num / divisor, rounding towards zero, and sets up | |
173 | * 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 | */ | |
84c15db5 BL |
179 | int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, |
180 | BN_CTX *ctx) | |
d02b48c6 | 181 | { |
9e989810 | 182 | int norm_shift,i,loop; |
d02b48c6 RE |
183 | BIGNUM *tmp,wnum,*snum,*sdiv,*res; |
184 | BN_ULONG *resp,*wnump; | |
185 | BN_ULONG d0,d1; | |
186 | int num_n,div_n; | |
187 | ||
bd31fb21 BM |
188 | if (BN_get_flags(num, BN_FLG_CONSTTIME) != 0) |
189 | { | |
190 | return BN_div_no_branch(dv, rm, num, divisor, ctx); | |
191 | } | |
192 | ||
8215e7a9 NL |
193 | bn_check_top(dv); |
194 | bn_check_top(rm); | |
dfeab068 RE |
195 | bn_check_top(num); |
196 | bn_check_top(divisor); | |
197 | ||
58964a49 | 198 | if (BN_is_zero(divisor)) |
d02b48c6 RE |
199 | { |
200 | BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); | |
201 | return(0); | |
202 | } | |
203 | ||
204 | if (BN_ucmp(num,divisor) < 0) | |
205 | { | |
206 | if (rm != NULL) | |
207 | { if (BN_copy(rm,num) == NULL) return(0); } | |
208 | if (dv != NULL) BN_zero(dv); | |
209 | return(1); | |
210 | } | |
211 | ||
9b141126 UM |
212 | BN_CTX_start(ctx); |
213 | tmp=BN_CTX_get(ctx); | |
9b141126 UM |
214 | snum=BN_CTX_get(ctx); |
215 | sdiv=BN_CTX_get(ctx); | |
d02b48c6 | 216 | if (dv == NULL) |
9b141126 | 217 | res=BN_CTX_get(ctx); |
d02b48c6 | 218 | else res=dv; |
7f7b8d68 | 219 | if (sdiv == NULL || res == NULL) goto err; |
d02b48c6 RE |
220 | |
221 | /* First we normalise the numbers */ | |
222 | norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); | |
9cdf87f1 | 223 | if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; |
d02b48c6 RE |
224 | sdiv->neg=0; |
225 | norm_shift+=BN_BITS2; | |
9cdf87f1 | 226 | if (!(BN_lshift(snum,num,norm_shift))) goto err; |
d02b48c6 RE |
227 | snum->neg=0; |
228 | div_n=sdiv->top; | |
229 | num_n=snum->top; | |
230 | loop=num_n-div_n; | |
d02b48c6 RE |
231 | /* Lets setup a 'window' into snum |
232 | * This is the part that corresponds to the current | |
233 | * 'area' being divided */ | |
9e989810 GT |
234 | wnum.neg = 0; |
235 | wnum.d = &(snum->d[loop]); | |
236 | wnum.top = div_n; | |
9e989810 GT |
237 | /* only needed when BN_ucmp messes up the values between top and max */ |
238 | wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ | |
d02b48c6 RE |
239 | |
240 | /* Get the top 2 words of sdiv */ | |
5c0c2280 | 241 | /* div_n=sdiv->top; */ |
d02b48c6 RE |
242 | d0=sdiv->d[div_n-1]; |
243 | d1=(div_n == 1)?0:sdiv->d[div_n-2]; | |
244 | ||
245 | /* pointer to the 'top' of snum */ | |
246 | wnump= &(snum->d[num_n-1]); | |
247 | ||
248 | /* Setup to 'res' */ | |
249 | res->neg= (num->neg^divisor->neg); | |
58964a49 | 250 | if (!bn_wexpand(res,(loop+1))) goto err; |
dfeab068 | 251 | res->top=loop; |
d02b48c6 RE |
252 | resp= &(res->d[loop-1]); |
253 | ||
254 | /* space for temp */ | |
58964a49 | 255 | if (!bn_wexpand(tmp,(div_n+1))) goto err; |
d02b48c6 RE |
256 | |
257 | if (BN_ucmp(&wnum,sdiv) >= 0) | |
258 | { | |
9e989810 GT |
259 | /* If BN_DEBUG_RAND is defined BN_ucmp changes (via |
260 | * bn_pollute) the const bignum arguments => | |
261 | * clean the values between top and max again */ | |
262 | bn_clear_top2max(&wnum); | |
9e989810 | 263 | bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n); |
d02b48c6 | 264 | *resp=1; |
d02b48c6 RE |
265 | } |
266 | else | |
267 | res->top--; | |
9e989810 GT |
268 | /* if res->top == 0 then clear the neg value otherwise decrease |
269 | * the resp pointer */ | |
80d89e6a BM |
270 | if (res->top == 0) |
271 | res->neg = 0; | |
bd31fb21 BM |
272 | else |
273 | resp--; | |
274 | ||
275 | for (i=0; i<loop-1; i++, wnump--, resp--) | |
276 | { | |
277 | BN_ULONG q,l0; | |
278 | /* the first part of the loop uses the top two words of | |
279 | * snum and sdiv to calculate a BN_ULONG q such that | |
280 | * | wnum - sdiv * q | < sdiv */ | |
281 | #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) | |
282 | BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); | |
283 | q=bn_div_3_words(wnump,d1,d0); | |
284 | #else | |
285 | BN_ULONG n0,n1,rem=0; | |
286 | ||
287 | n0=wnump[0]; | |
288 | n1=wnump[-1]; | |
289 | if (n0 == d0) | |
290 | q=BN_MASK2; | |
291 | else /* n0 < d0 */ | |
292 | { | |
293 | #ifdef BN_LLONG | |
294 | BN_ULLONG t2; | |
295 | ||
296 | #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) | |
297 | q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); | |
298 | #else | |
299 | q=bn_div_words(n0,n1,d0); | |
300 | #ifdef BN_DEBUG_LEVITTE | |
301 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ | |
302 | X) -> 0x%08X\n", | |
303 | n0, n1, d0, q); | |
304 | #endif | |
305 | #endif | |
306 | ||
307 | #ifndef REMAINDER_IS_ALREADY_CALCULATED | |
308 | /* | |
309 | * rem doesn't have to be BN_ULLONG. The least we | |
310 | * know it's less that d0, isn't it? | |
311 | */ | |
312 | rem=(n1-q*d0)&BN_MASK2; | |
313 | #endif | |
314 | t2=(BN_ULLONG)d1*q; | |
315 | ||
316 | for (;;) | |
317 | { | |
318 | if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) | |
319 | break; | |
320 | q--; | |
321 | rem += d0; | |
322 | if (rem < d0) break; /* don't let rem overflow */ | |
323 | t2 -= d1; | |
324 | } | |
325 | #else /* !BN_LLONG */ | |
326 | BN_ULONG t2l,t2h,ql,qh; | |
327 | ||
328 | q=bn_div_words(n0,n1,d0); | |
329 | #ifdef BN_DEBUG_LEVITTE | |
330 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ | |
331 | X) -> 0x%08X\n", | |
332 | n0, n1, d0, q); | |
333 | #endif | |
334 | #ifndef REMAINDER_IS_ALREADY_CALCULATED | |
335 | rem=(n1-q*d0)&BN_MASK2; | |
336 | #endif | |
337 | ||
338 | #if defined(BN_UMULT_LOHI) | |
339 | BN_UMULT_LOHI(t2l,t2h,d1,q); | |
340 | #elif defined(BN_UMULT_HIGH) | |
341 | t2l = d1 * q; | |
342 | t2h = BN_UMULT_HIGH(d1,q); | |
343 | #else | |
344 | t2l=LBITS(d1); t2h=HBITS(d1); | |
345 | ql =LBITS(q); qh =HBITS(q); | |
346 | mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ | |
347 | #endif | |
348 | ||
349 | for (;;) | |
350 | { | |
351 | if ((t2h < rem) || | |
352 | ((t2h == rem) && (t2l <= wnump[-2]))) | |
353 | break; | |
354 | q--; | |
355 | rem += d0; | |
356 | if (rem < d0) break; /* don't let rem overflow */ | |
357 | if (t2l < d1) t2h--; t2l -= d1; | |
358 | } | |
359 | #endif /* !BN_LLONG */ | |
360 | } | |
361 | #endif /* !BN_DIV3W */ | |
362 | ||
363 | l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); | |
364 | tmp->d[div_n]=l0; | |
365 | wnum.d--; | |
366 | /* ingore top values of the bignums just sub the two | |
367 | * BN_ULONG arrays with bn_sub_words */ | |
368 | if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1)) | |
369 | { | |
370 | /* Note: As we have considered only the leading | |
371 | * two BN_ULONGs in the calculation of q, sdiv * q | |
372 | * might be greater than wnum (but then (q-1) * sdiv | |
373 | * is less or equal than wnum) | |
374 | */ | |
375 | q--; | |
376 | if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) | |
377 | /* we can't have an overflow here (assuming | |
378 | * that q != 0, but if q == 0 then tmp is | |
379 | * zero anyway) */ | |
380 | (*wnump)++; | |
381 | } | |
382 | /* store part of the result */ | |
383 | *resp = q; | |
384 | } | |
385 | bn_correct_top(snum); | |
386 | if (rm != NULL) | |
387 | { | |
388 | /* Keep a copy of the neg flag in num because if rm==num | |
389 | * BN_rshift() will overwrite it. | |
390 | */ | |
391 | int neg = num->neg; | |
392 | BN_rshift(rm,snum,norm_shift); | |
393 | if (!BN_is_zero(rm)) | |
394 | rm->neg = neg; | |
395 | bn_check_top(rm); | |
396 | } | |
397 | BN_CTX_end(ctx); | |
398 | return(1); | |
399 | err: | |
400 | bn_check_top(rm); | |
401 | BN_CTX_end(ctx); | |
402 | return(0); | |
403 | } | |
404 | ||
405 | ||
406 | /* BN_div_no_branch is a special version of BN_div. It does not contain | |
407 | * branches that may leak sensitive information. | |
408 | */ | |
409 | int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, | |
410 | const BIGNUM *divisor, BN_CTX *ctx) | |
411 | { | |
412 | int norm_shift,i,loop; | |
413 | BIGNUM *tmp,wnum,*snum,*sdiv,*res; | |
414 | BN_ULONG *resp,*wnump; | |
415 | BN_ULONG d0,d1; | |
416 | int num_n,div_n; | |
417 | ||
418 | bn_check_top(dv); | |
419 | bn_check_top(rm); | |
420 | bn_check_top(num); | |
421 | bn_check_top(divisor); | |
422 | ||
423 | if (BN_is_zero(divisor)) | |
424 | { | |
425 | BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); | |
426 | return(0); | |
427 | } | |
428 | ||
429 | BN_CTX_start(ctx); | |
430 | tmp=BN_CTX_get(ctx); | |
431 | snum=BN_CTX_get(ctx); | |
432 | sdiv=BN_CTX_get(ctx); | |
433 | if (dv == NULL) | |
434 | res=BN_CTX_get(ctx); | |
435 | else res=dv; | |
436 | if (sdiv == NULL || res == NULL) goto err; | |
437 | ||
438 | /* First we normalise the numbers */ | |
439 | norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); | |
440 | if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; | |
441 | sdiv->neg=0; | |
442 | norm_shift+=BN_BITS2; | |
443 | if (!(BN_lshift(snum,num,norm_shift))) goto err; | |
444 | snum->neg=0; | |
445 | ||
446 | /* Since we don't know whether snum is larger than sdiv, | |
447 | * we pad snum with enough zeroes without changing its | |
448 | * value. | |
449 | */ | |
450 | if (snum->top <= sdiv->top+1) | |
451 | { | |
452 | if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err; | |
453 | for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0; | |
454 | snum->top = sdiv->top + 2; | |
455 | } | |
456 | else | |
457 | { | |
458 | if (bn_wexpand(snum, snum->top + 1) == NULL) goto err; | |
459 | snum->d[snum->top] = 0; | |
460 | snum->top ++; | |
461 | } | |
462 | ||
463 | div_n=sdiv->top; | |
464 | num_n=snum->top; | |
465 | loop=num_n-div_n; | |
466 | /* Lets setup a 'window' into snum | |
467 | * This is the part that corresponds to the current | |
468 | * 'area' being divided */ | |
469 | wnum.neg = 0; | |
470 | wnum.d = &(snum->d[loop]); | |
471 | wnum.top = div_n; | |
472 | /* only needed when BN_ucmp messes up the values between top and max */ | |
473 | wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ | |
474 | ||
475 | /* Get the top 2 words of sdiv */ | |
476 | /* div_n=sdiv->top; */ | |
477 | d0=sdiv->d[div_n-1]; | |
478 | d1=(div_n == 1)?0:sdiv->d[div_n-2]; | |
479 | ||
480 | /* pointer to the 'top' of snum */ | |
481 | wnump= &(snum->d[num_n-1]); | |
482 | ||
483 | /* Setup to 'res' */ | |
484 | res->neg= (num->neg^divisor->neg); | |
485 | if (!bn_wexpand(res,(loop+1))) goto err; | |
486 | res->top=loop-1; | |
487 | resp= &(res->d[loop-1]); | |
488 | ||
489 | /* space for temp */ | |
490 | if (!bn_wexpand(tmp,(div_n+1))) goto err; | |
491 | ||
492 | /* if res->top == 0 then clear the neg value otherwise decrease | |
493 | * the resp pointer */ | |
494 | if (res->top == 0) | |
495 | res->neg = 0; | |
9e989810 GT |
496 | else |
497 | resp--; | |
d02b48c6 | 498 | |
9e989810 | 499 | for (i=0; i<loop-1; i++, wnump--, resp--) |
d02b48c6 | 500 | { |
0dd25e36 | 501 | BN_ULONG q,l0; |
9e989810 GT |
502 | /* the first part of the loop uses the top two words of |
503 | * snum and sdiv to calculate a BN_ULONG q such that | |
504 | * | wnum - sdiv * q | < sdiv */ | |
cf1b7d96 | 505 | #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) |
500230ee | 506 | BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); |
0bbd0352 | 507 | q=bn_div_3_words(wnump,d1,d0); |
0dd25e36 | 508 | #else |
4c22909e | 509 | BN_ULONG n0,n1,rem=0; |
d02b48c6 | 510 | |
d02b48c6 RE |
511 | n0=wnump[0]; |
512 | n1=wnump[-1]; | |
513 | if (n0 == d0) | |
514 | q=BN_MASK2; | |
4a6222d7 UM |
515 | else /* n0 < d0 */ |
516 | { | |
517 | #ifdef BN_LLONG | |
518 | BN_ULLONG t2; | |
519 | ||
4c22909e | 520 | #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
8e1589ec | 521 | q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); |
0dd25e36 | 522 | #else |
dfeab068 | 523 | q=bn_div_words(n0,n1,d0); |
3c801fa4 RL |
524 | #ifdef BN_DEBUG_LEVITTE |
525 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ | |
526 | X) -> 0x%08X\n", | |
527 | n0, n1, d0, q); | |
528 | #endif | |
0dd25e36 | 529 | #endif |
0dd25e36 | 530 | |
fe7cd164 | 531 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
4a6222d7 UM |
532 | /* |
533 | * rem doesn't have to be BN_ULLONG. The least we | |
534 | * know it's less that d0, isn't it? | |
535 | */ | |
536 | rem=(n1-q*d0)&BN_MASK2; | |
4c22909e | 537 | #endif |
4a6222d7 UM |
538 | t2=(BN_ULLONG)d1*q; |
539 | ||
540 | for (;;) | |
541 | { | |
542 | if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) | |
543 | break; | |
544 | q--; | |
545 | rem += d0; | |
546 | if (rem < d0) break; /* don't let rem overflow */ | |
547 | t2 -= d1; | |
548 | } | |
549 | #else /* !BN_LLONG */ | |
550 | BN_ULONG t2l,t2h,ql,qh; | |
0dd25e36 | 551 | |
4a6222d7 | 552 | q=bn_div_words(n0,n1,d0); |
3c801fa4 RL |
553 | #ifdef BN_DEBUG_LEVITTE |
554 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ | |
555 | X) -> 0x%08X\n", | |
556 | n0, n1, d0, q); | |
557 | #endif | |
fe7cd164 | 558 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
4a6222d7 | 559 | rem=(n1-q*d0)&BN_MASK2; |
4c22909e | 560 | #endif |
4a6222d7 | 561 | |
2f98abbc AP |
562 | #if defined(BN_UMULT_LOHI) |
563 | BN_UMULT_LOHI(t2l,t2h,d1,q); | |
564 | #elif defined(BN_UMULT_HIGH) | |
4a6222d7 UM |
565 | t2l = d1 * q; |
566 | t2h = BN_UMULT_HIGH(d1,q); | |
fb81ac5e | 567 | #else |
4a6222d7 UM |
568 | t2l=LBITS(d1); t2h=HBITS(d1); |
569 | ql =LBITS(q); qh =HBITS(q); | |
570 | mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ | |
fb81ac5e | 571 | #endif |
0dd25e36 | 572 | |
4a6222d7 UM |
573 | for (;;) |
574 | { | |
575 | if ((t2h < rem) || | |
576 | ((t2h == rem) && (t2l <= wnump[-2]))) | |
577 | break; | |
578 | q--; | |
579 | rem += d0; | |
580 | if (rem < d0) break; /* don't let rem overflow */ | |
581 | if (t2l < d1) t2h--; t2l -= d1; | |
582 | } | |
583 | #endif /* !BN_LLONG */ | |
d02b48c6 | 584 | } |
4c22909e | 585 | #endif /* !BN_DIV3W */ |
4a6222d7 | 586 | |
58964a49 | 587 | l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); |
d02b48c6 | 588 | tmp->d[div_n]=l0; |
9e989810 GT |
589 | wnum.d--; |
590 | /* ingore top values of the bignums just sub the two | |
591 | * BN_ULONG arrays with bn_sub_words */ | |
592 | if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1)) | |
d02b48c6 | 593 | { |
9e989810 GT |
594 | /* Note: As we have considered only the leading |
595 | * two BN_ULONGs in the calculation of q, sdiv * q | |
596 | * might be greater than wnum (but then (q-1) * sdiv | |
597 | * is less or equal than wnum) | |
598 | */ | |
d02b48c6 | 599 | q--; |
9e989810 GT |
600 | if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) |
601 | /* we can't have an overflow here (assuming | |
602 | * that q != 0, but if q == 0 then tmp is | |
603 | * zero anyway) */ | |
604 | (*wnump)++; | |
d02b48c6 | 605 | } |
9e989810 GT |
606 | /* store part of the result */ |
607 | *resp = q; | |
d02b48c6 | 608 | } |
a8aa764d | 609 | bn_correct_top(snum); |
d02b48c6 RE |
610 | if (rm != NULL) |
611 | { | |
3d2e469c DSH |
612 | /* Keep a copy of the neg flag in num because if rm==num |
613 | * BN_rshift() will overwrite it. | |
614 | */ | |
615 | int neg = num->neg; | |
d02b48c6 | 616 | BN_rshift(rm,snum,norm_shift); |
78a0c1f1 | 617 | if (!BN_is_zero(rm)) |
3d2e469c | 618 | rm->neg = neg; |
d870740c | 619 | bn_check_top(rm); |
d02b48c6 | 620 | } |
9b141126 | 621 | BN_CTX_end(ctx); |
d02b48c6 RE |
622 | return(1); |
623 | err: | |
8215e7a9 | 624 | bn_check_top(rm); |
4a6222d7 | 625 | BN_CTX_end(ctx); |
d02b48c6 RE |
626 | return(0); |
627 | } | |
628 | ||
629 | #endif |