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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 | ||
64 | /* The old slow way */ | |
4a6222d7 | 65 | #if 0 |
0bde1089 UM |
66 | int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, |
67 | BN_CTX *ctx) | |
d02b48c6 RE |
68 | { |
69 | int i,nm,nd; | |
9b141126 | 70 | int ret = 0; |
d02b48c6 RE |
71 | BIGNUM *D; |
72 | ||
dfeab068 RE |
73 | bn_check_top(m); |
74 | bn_check_top(d); | |
d02b48c6 RE |
75 | if (BN_is_zero(d)) |
76 | { | |
77 | BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); | |
78 | return(0); | |
79 | } | |
80 | ||
81 | if (BN_ucmp(m,d) < 0) | |
82 | { | |
83 | if (rem != NULL) | |
84 | { if (BN_copy(rem,m) == NULL) return(0); } | |
85 | if (dv != NULL) BN_zero(dv); | |
86 | return(1); | |
87 | } | |
88 | ||
9b141126 UM |
89 | BN_CTX_start(ctx); |
90 | D = BN_CTX_get(ctx); | |
91 | if (dv == NULL) dv = BN_CTX_get(ctx); | |
92 | if (rem == NULL) rem = BN_CTX_get(ctx); | |
93 | if (D == NULL || dv == NULL || rem == NULL) | |
94 | goto end; | |
d02b48c6 RE |
95 | |
96 | nd=BN_num_bits(d); | |
97 | nm=BN_num_bits(m); | |
9b141126 UM |
98 | if (BN_copy(D,d) == NULL) goto end; |
99 | if (BN_copy(rem,m) == NULL) goto end; | |
d02b48c6 RE |
100 | |
101 | /* The next 2 are needed so we can do a dv->d[0]|=1 later | |
102 | * since BN_lshift1 will only work once there is a value :-) */ | |
103 | BN_zero(dv); | |
dfeab068 | 104 | bn_wexpand(dv,1); |
d02b48c6 RE |
105 | dv->top=1; |
106 | ||
9b141126 | 107 | if (!BN_lshift(D,D,nm-nd)) goto end; |
d02b48c6 RE |
108 | for (i=nm-nd; i>=0; i--) |
109 | { | |
9b141126 | 110 | if (!BN_lshift1(dv,dv)) goto end; |
d02b48c6 RE |
111 | if (BN_ucmp(rem,D) >= 0) |
112 | { | |
113 | dv->d[0]|=1; | |
9b141126 | 114 | if (!BN_usub(rem,rem,D)) goto end; |
d02b48c6 RE |
115 | } |
116 | /* CAN IMPROVE (and have now :=) */ | |
9b141126 | 117 | if (!BN_rshift1(D,D)) goto end; |
d02b48c6 RE |
118 | } |
119 | rem->neg=BN_is_zero(rem)?0:m->neg; | |
120 | dv->neg=m->neg^d->neg; | |
9b141126 UM |
121 | ret = 1; |
122 | end: | |
123 | BN_CTX_end(ctx); | |
124 | return(ret); | |
d02b48c6 RE |
125 | } |
126 | ||
127 | #else | |
128 | ||
4a6222d7 UM |
129 | #if !defined(NO_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W) |
130 | # if defined(__GNUC__) && __GNUC__>=2 | |
131 | # if defined(__i386) | |
132 | /* | |
133 | * There were two reasons for implementing this template: | |
134 | * - GNU C generates a call to a function (__udivdi3 to be exact) | |
135 | * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to | |
136 | * understand why...); | |
137 | * - divl doesn't only calculate quotient, but also leaves | |
138 | * remainder in %edx which we can definitely use here:-) | |
139 | * | |
140 | * <appro@fy.chalmers.se> | |
141 | */ | |
142 | # define bn_div_words(n0,n1,d0) \ | |
143 | ({ asm volatile ( \ | |
144 | "divl %4" \ | |
145 | : "=a"(q), "=d"(rem) \ | |
146 | : "a"(n1), "d"(n0), "g"(d0) \ | |
147 | : "cc"); \ | |
148 | q; \ | |
149 | }) | |
150 | # define REMAINDER_IS_ALREADY_CALCULATED | |
151 | # endif /* __<cpu> */ | |
152 | # endif /* __GNUC__ */ | |
153 | #endif /* NO_ASM */ | |
154 | ||
84c15db5 BL |
155 | int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, |
156 | BN_CTX *ctx) | |
d02b48c6 RE |
157 | { |
158 | int norm_shift,i,j,loop; | |
159 | BIGNUM *tmp,wnum,*snum,*sdiv,*res; | |
160 | BN_ULONG *resp,*wnump; | |
161 | BN_ULONG d0,d1; | |
162 | int num_n,div_n; | |
163 | ||
dfeab068 RE |
164 | bn_check_top(num); |
165 | bn_check_top(divisor); | |
166 | ||
58964a49 | 167 | if (BN_is_zero(divisor)) |
d02b48c6 RE |
168 | { |
169 | BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); | |
170 | return(0); | |
171 | } | |
172 | ||
173 | if (BN_ucmp(num,divisor) < 0) | |
174 | { | |
175 | if (rm != NULL) | |
176 | { if (BN_copy(rm,num) == NULL) return(0); } | |
177 | if (dv != NULL) BN_zero(dv); | |
178 | return(1); | |
179 | } | |
180 | ||
9b141126 UM |
181 | BN_CTX_start(ctx); |
182 | tmp=BN_CTX_get(ctx); | |
d02b48c6 | 183 | tmp->neg=0; |
9b141126 UM |
184 | snum=BN_CTX_get(ctx); |
185 | sdiv=BN_CTX_get(ctx); | |
d02b48c6 | 186 | if (dv == NULL) |
9b141126 | 187 | res=BN_CTX_get(ctx); |
d02b48c6 | 188 | else res=dv; |
9b141126 | 189 | if (res == NULL) goto err; |
d02b48c6 RE |
190 | |
191 | /* First we normalise the numbers */ | |
192 | norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); | |
193 | BN_lshift(sdiv,divisor,norm_shift); | |
194 | sdiv->neg=0; | |
195 | norm_shift+=BN_BITS2; | |
196 | BN_lshift(snum,num,norm_shift); | |
197 | snum->neg=0; | |
198 | div_n=sdiv->top; | |
199 | num_n=snum->top; | |
200 | loop=num_n-div_n; | |
201 | ||
202 | /* Lets setup a 'window' into snum | |
203 | * This is the part that corresponds to the current | |
204 | * 'area' being divided */ | |
dfeab068 | 205 | BN_init(&wnum); |
d02b48c6 RE |
206 | wnum.d= &(snum->d[loop]); |
207 | wnum.top= div_n; | |
dfeab068 | 208 | wnum.max= snum->max+1; /* a bit of a lie */ |
d02b48c6 RE |
209 | |
210 | /* Get the top 2 words of sdiv */ | |
211 | /* i=sdiv->top; */ | |
212 | d0=sdiv->d[div_n-1]; | |
213 | d1=(div_n == 1)?0:sdiv->d[div_n-2]; | |
214 | ||
215 | /* pointer to the 'top' of snum */ | |
216 | wnump= &(snum->d[num_n-1]); | |
217 | ||
218 | /* Setup to 'res' */ | |
219 | res->neg= (num->neg^divisor->neg); | |
58964a49 | 220 | if (!bn_wexpand(res,(loop+1))) goto err; |
dfeab068 | 221 | res->top=loop; |
d02b48c6 RE |
222 | resp= &(res->d[loop-1]); |
223 | ||
224 | /* space for temp */ | |
58964a49 | 225 | if (!bn_wexpand(tmp,(div_n+1))) goto err; |
d02b48c6 RE |
226 | |
227 | if (BN_ucmp(&wnum,sdiv) >= 0) | |
228 | { | |
dfeab068 | 229 | if (!BN_usub(&wnum,&wnum,sdiv)) goto err; |
d02b48c6 RE |
230 | *resp=1; |
231 | res->d[res->top-1]=1; | |
232 | } | |
233 | else | |
234 | res->top--; | |
235 | resp--; | |
236 | ||
237 | for (i=0; i<loop-1; i++) | |
238 | { | |
0dd25e36 AP |
239 | BN_ULONG q,l0; |
240 | #ifdef BN_DIV3W | |
0bbd0352 | 241 | q=bn_div_3_words(wnump,d1,d0); |
0dd25e36 | 242 | #else |
4c22909e | 243 | BN_ULONG n0,n1,rem=0; |
d02b48c6 | 244 | |
d02b48c6 RE |
245 | n0=wnump[0]; |
246 | n1=wnump[-1]; | |
247 | if (n0 == d0) | |
248 | q=BN_MASK2; | |
4a6222d7 UM |
249 | else /* n0 < d0 */ |
250 | { | |
251 | #ifdef BN_LLONG | |
252 | BN_ULLONG t2; | |
253 | ||
4c22909e | 254 | #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
8e1589ec | 255 | q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); |
0dd25e36 | 256 | #else |
dfeab068 | 257 | q=bn_div_words(n0,n1,d0); |
0dd25e36 | 258 | #endif |
0dd25e36 | 259 | |
fe7cd164 | 260 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
4a6222d7 UM |
261 | /* |
262 | * rem doesn't have to be BN_ULLONG. The least we | |
263 | * know it's less that d0, isn't it? | |
264 | */ | |
265 | rem=(n1-q*d0)&BN_MASK2; | |
4c22909e | 266 | #endif |
4a6222d7 UM |
267 | t2=(BN_ULLONG)d1*q; |
268 | ||
269 | for (;;) | |
270 | { | |
271 | if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) | |
272 | break; | |
273 | q--; | |
274 | rem += d0; | |
275 | if (rem < d0) break; /* don't let rem overflow */ | |
276 | t2 -= d1; | |
277 | } | |
278 | #else /* !BN_LLONG */ | |
279 | BN_ULONG t2l,t2h,ql,qh; | |
0dd25e36 | 280 | |
4a6222d7 | 281 | q=bn_div_words(n0,n1,d0); |
fe7cd164 | 282 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
4a6222d7 | 283 | rem=(n1-q*d0)&BN_MASK2; |
4c22909e | 284 | #endif |
4a6222d7 | 285 | |
fb81ac5e | 286 | #ifdef BN_UMULT_HIGH |
4a6222d7 UM |
287 | t2l = d1 * q; |
288 | t2h = BN_UMULT_HIGH(d1,q); | |
fb81ac5e | 289 | #else |
4a6222d7 UM |
290 | t2l=LBITS(d1); t2h=HBITS(d1); |
291 | ql =LBITS(q); qh =HBITS(q); | |
292 | mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ | |
fb81ac5e | 293 | #endif |
0dd25e36 | 294 | |
4a6222d7 UM |
295 | for (;;) |
296 | { | |
297 | if ((t2h < rem) || | |
298 | ((t2h == rem) && (t2l <= wnump[-2]))) | |
299 | break; | |
300 | q--; | |
301 | rem += d0; | |
302 | if (rem < d0) break; /* don't let rem overflow */ | |
303 | if (t2l < d1) t2h--; t2l -= d1; | |
304 | } | |
305 | #endif /* !BN_LLONG */ | |
d02b48c6 | 306 | } |
4c22909e | 307 | #endif /* !BN_DIV3W */ |
4a6222d7 | 308 | |
58964a49 | 309 | l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); |
0bbd0352 | 310 | wnum.d--; wnum.top++; |
d02b48c6 RE |
311 | tmp->d[div_n]=l0; |
312 | for (j=div_n+1; j>0; j--) | |
313 | if (tmp->d[j-1]) break; | |
314 | tmp->top=j; | |
315 | ||
316 | j=wnum.top; | |
317 | BN_sub(&wnum,&wnum,tmp); | |
318 | ||
319 | snum->top=snum->top+wnum.top-j; | |
320 | ||
321 | if (wnum.neg) | |
322 | { | |
323 | q--; | |
324 | j=wnum.top; | |
325 | BN_add(&wnum,&wnum,sdiv); | |
326 | snum->top+=wnum.top-j; | |
327 | } | |
328 | *(resp--)=q; | |
329 | wnump--; | |
330 | } | |
331 | if (rm != NULL) | |
332 | { | |
333 | BN_rshift(rm,snum,norm_shift); | |
334 | rm->neg=num->neg; | |
335 | } | |
9b141126 | 336 | BN_CTX_end(ctx); |
d02b48c6 RE |
337 | return(1); |
338 | err: | |
4a6222d7 | 339 | BN_CTX_end(ctx); |
d02b48c6 RE |
340 | return(0); |
341 | } | |
342 | ||
343 | #endif | |
dfeab068 RE |
344 | |
345 | /* rem != m */ | |
84c15db5 | 346 | int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) |
dfeab068 RE |
347 | { |
348 | #if 0 /* The old slow way */ | |
349 | int i,nm,nd; | |
350 | BIGNUM *dv; | |
351 | ||
352 | if (BN_ucmp(m,d) < 0) | |
353 | return((BN_copy(rem,m) == NULL)?0:1); | |
354 | ||
9b141126 UM |
355 | BN_CTX_start(ctx); |
356 | dv=BN_CTX_get(ctx); | |
dfeab068 | 357 | |
9b141126 | 358 | if (!BN_copy(rem,m)) goto err; |
dfeab068 RE |
359 | |
360 | nm=BN_num_bits(rem); | |
361 | nd=BN_num_bits(d); | |
9b141126 | 362 | if (!BN_lshift(dv,d,nm-nd)) goto err; |
dfeab068 RE |
363 | for (i=nm-nd; i>=0; i--) |
364 | { | |
365 | if (BN_cmp(rem,dv) >= 0) | |
366 | { | |
9b141126 | 367 | if (!BN_sub(rem,rem,dv)) goto err; |
dfeab068 | 368 | } |
9b141126 | 369 | if (!BN_rshift1(dv,dv)) goto err; |
dfeab068 | 370 | } |
9b141126 | 371 | BN_CTX_end(ctx); |
dfeab068 | 372 | return(1); |
9b141126 UM |
373 | err: |
374 | BN_CTX_end(ctx); | |
375 | return(0); | |
dfeab068 RE |
376 | #else |
377 | return(BN_div(NULL,rem,m,d,ctx)); | |
378 | #endif | |
379 | } | |
380 |