xref: /freebsd/crypto/openssl/crypto/bn/bn_div.c (revision daf1cffce2e07931f27c6c6998652e90df6ba87e)
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 /* The old slow way */
65 #if 0
66 int BN_div(BIGNUM *dv, BIGNUM *rem, BIGNUM *m, BIGNUM *d, BN_CTX *ctx)
67 	{
68 	int i,nm,nd;
69 	BIGNUM *D;
70 
71 	bn_check_top(m);
72 	bn_check_top(d);
73 	if (BN_is_zero(d))
74 		{
75 		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
76 		return(0);
77 		}
78 
79 	if (BN_ucmp(m,d) < 0)
80 		{
81 		if (rem != NULL)
82 			{ if (BN_copy(rem,m) == NULL) return(0); }
83 		if (dv != NULL) BN_zero(dv);
84 		return(1);
85 		}
86 
87 	D= &(ctx->bn[ctx->tos]);
88 	if (dv == NULL) dv= &(ctx->bn[ctx->tos+1]);
89 	if (rem == NULL) rem= &(ctx->bn[ctx->tos+2]);
90 
91 	nd=BN_num_bits(d);
92 	nm=BN_num_bits(m);
93 	if (BN_copy(D,d) == NULL) return(0);
94 	if (BN_copy(rem,m) == NULL) return(0);
95 
96 	/* The next 2 are needed so we can do a dv->d[0]|=1 later
97 	 * since BN_lshift1 will only work once there is a value :-) */
98 	BN_zero(dv);
99 	bn_wexpand(dv,1);
100 	dv->top=1;
101 
102 	if (!BN_lshift(D,D,nm-nd)) return(0);
103 	for (i=nm-nd; i>=0; i--)
104 		{
105 		if (!BN_lshift1(dv,dv)) return(0);
106 		if (BN_ucmp(rem,D) >= 0)
107 			{
108 			dv->d[0]|=1;
109 			if (!BN_usub(rem,rem,D)) return(0);
110 			}
111 /* CAN IMPROVE (and have now :=) */
112 		if (!BN_rshift1(D,D)) return(0);
113 		}
114 	rem->neg=BN_is_zero(rem)?0:m->neg;
115 	dv->neg=m->neg^d->neg;
116 	return(1);
117 	}
118 
119 #else
120 
121 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
122 	   BN_CTX *ctx)
123 	{
124 	int norm_shift,i,j,loop;
125 	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
126 	BN_ULONG *resp,*wnump;
127 	BN_ULONG d0,d1;
128 	int num_n,div_n;
129 
130 	bn_check_top(num);
131 	bn_check_top(divisor);
132 
133 	if (BN_is_zero(divisor))
134 		{
135 		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
136 		return(0);
137 		}
138 
139 	if (BN_ucmp(num,divisor) < 0)
140 		{
141 		if (rm != NULL)
142 			{ if (BN_copy(rm,num) == NULL) return(0); }
143 		if (dv != NULL) BN_zero(dv);
144 		return(1);
145 		}
146 
147 	tmp= &(ctx->bn[ctx->tos]);
148 	tmp->neg=0;
149 	snum= &(ctx->bn[ctx->tos+1]);
150 	sdiv= &(ctx->bn[ctx->tos+2]);
151 	if (dv == NULL)
152 		res= &(ctx->bn[ctx->tos+3]);
153 	else	res=dv;
154 
155 	/* First we normalise the numbers */
156 	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
157 	BN_lshift(sdiv,divisor,norm_shift);
158 	sdiv->neg=0;
159 	norm_shift+=BN_BITS2;
160 	BN_lshift(snum,num,norm_shift);
161 	snum->neg=0;
162 	div_n=sdiv->top;
163 	num_n=snum->top;
164 	loop=num_n-div_n;
165 
166 	/* Lets setup a 'window' into snum
167 	 * This is the part that corresponds to the current
168 	 * 'area' being divided */
169 	BN_init(&wnum);
170 	wnum.d=	 &(snum->d[loop]);
171 	wnum.top= div_n;
172 	wnum.max= snum->max+1; /* a bit of a lie */
173 
174 	/* Get the top 2 words of sdiv */
175 	/* i=sdiv->top; */
176 	d0=sdiv->d[div_n-1];
177 	d1=(div_n == 1)?0:sdiv->d[div_n-2];
178 
179 	/* pointer to the 'top' of snum */
180 	wnump= &(snum->d[num_n-1]);
181 
182 	/* Setup to 'res' */
183 	res->neg= (num->neg^divisor->neg);
184 	if (!bn_wexpand(res,(loop+1))) goto err;
185 	res->top=loop;
186 	resp= &(res->d[loop-1]);
187 
188 	/* space for temp */
189 	if (!bn_wexpand(tmp,(div_n+1))) goto err;
190 
191 	if (BN_ucmp(&wnum,sdiv) >= 0)
192 		{
193 		if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
194 		*resp=1;
195 		res->d[res->top-1]=1;
196 		}
197 	else
198 		res->top--;
199 	resp--;
200 
201 	for (i=0; i<loop-1; i++)
202 		{
203 		BN_ULONG q,l0;
204 #ifdef BN_DIV3W
205 		q=bn_div_3_words(wnump,d0,d1);
206 #else
207 
208 #if !defined(NO_ASM) && !defined(PEDANTIC)
209 # if defined(__GNUC__) && __GNUC__>=2
210 #  if defined(__i386)
211    /*
212     * There were two reasons for implementing this template:
213     * - GNU C generates a call to a function (__udivdi3 to be exact)
214     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
215     *   understand why...);
216     * - divl doesn't only calculate quotient, but also leaves
217     *   remainder in %edx which we can definitely use here:-)
218     *
219     *					<appro@fy.chalmers.se>
220     */
221 #  define bn_div_words(n0,n1,d0)		\
222 	({  asm volatile (			\
223 		"divl	%4"			\
224 		: "=a"(q), "=d"(rem)		\
225 		: "a"(n1), "d"(n0), "g"(d0)	\
226 		: "cc");			\
227 	    q;					\
228 	})
229 #  define REMINDER_IS_ALREADY_CALCULATED
230 #  endif /* __<cpu> */
231 # endif /* __GNUC__ */
232 #endif /* NO_ASM */
233 		BN_ULONG n0,n1,rem=0;
234 
235 		n0=wnump[0];
236 		n1=wnump[-1];
237 		if (n0 == d0)
238 			q=BN_MASK2;
239 		else
240 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
241 			q=((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0;
242 #else
243 			q=bn_div_words(n0,n1,d0);
244 #endif
245 		{
246 #ifdef BN_LLONG
247 		BN_ULLONG t2;
248 
249 #ifndef REMINDER_IS_ALREADY_CALCULATED
250 		/*
251 		 * rem doesn't have to be BN_ULLONG. The least we
252 		 * know it's less that d0, isn't it?
253 		 */
254 		rem=(n1-q*d0)&BN_MASK2;
255 #endif
256 		t2=(BN_ULLONG)d1*q;
257 
258 		for (;;)
259 			{
260                         if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
261 				break;
262 			q--;
263 			rem += d0;
264 			if (rem < d0) break; /* don't let rem overflow */
265 			t2 -= d1;
266 			}
267 #else
268 		BN_ULONG t2l,t2h,ql,qh;
269 
270 #ifndef REMINDER_IS_ALREADY_CALCULATED
271 		/*
272 		 * It's more than enough with the only multiplication.
273 		 * See the comment above in BN_LLONG section...
274 		 */
275 		rem=(n1-q*d0)&BN_MASK2;
276 #endif
277 		t2l=LBITS(d1); t2h=HBITS(d1);
278 		ql =LBITS(q);  qh =HBITS(q);
279 		mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
280 
281 		for (;;)
282 			{
283 			if ((t2h < rem) ||
284 				((t2h == rem) && (t2l <= wnump[-2])))
285 				break;
286 			q--;
287 			rem += d0;
288 			if (rem < d0) break; /* don't let rem overflow */
289 			if (t2l < d1) t2h--; t2l -= d1;
290 			}
291 #endif
292 		}
293 #endif /* !BN_DIV3W */
294 		wnum.d--; wnum.top++;
295 		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
296 		tmp->d[div_n]=l0;
297 		for (j=div_n+1; j>0; j--)
298 			if (tmp->d[j-1]) break;
299 		tmp->top=j;
300 
301 		j=wnum.top;
302 		BN_sub(&wnum,&wnum,tmp);
303 
304 		snum->top=snum->top+wnum.top-j;
305 
306 		if (wnum.neg)
307 			{
308 			q--;
309 			j=wnum.top;
310 			BN_add(&wnum,&wnum,sdiv);
311 			snum->top+=wnum.top-j;
312 			}
313 		*(resp--)=q;
314 		wnump--;
315 		}
316 	if (rm != NULL)
317 		{
318 		BN_rshift(rm,snum,norm_shift);
319 		rm->neg=num->neg;
320 		}
321 	return(1);
322 err:
323 	return(0);
324 	}
325 
326 #endif
327 
328 /* rem != m */
329 int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
330 	{
331 #if 0 /* The old slow way */
332 	int i,nm,nd;
333 	BIGNUM *dv;
334 
335 	if (BN_ucmp(m,d) < 0)
336 		return((BN_copy(rem,m) == NULL)?0:1);
337 
338 	dv= &(ctx->bn[ctx->tos]);
339 
340 	if (!BN_copy(rem,m)) return(0);
341 
342 	nm=BN_num_bits(rem);
343 	nd=BN_num_bits(d);
344 	if (!BN_lshift(dv,d,nm-nd)) return(0);
345 	for (i=nm-nd; i>=0; i--)
346 		{
347 		if (BN_cmp(rem,dv) >= 0)
348 			{
349 			if (!BN_sub(rem,rem,dv)) return(0);
350 			}
351 		if (!BN_rshift1(dv,dv)) return(0);
352 		}
353 	return(1);
354 #else
355 	return(BN_div(NULL,rem,m,d,ctx));
356 #endif
357 	}
358 
359