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
67int 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	bn_wexpand(dv,1);
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#  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
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
167#  endif /* __<cpu> */
168# endif /* __GNUC__ */
169#endif /* OPENSSL_NO_ASM */
170
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 */
179int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
180	   BN_CTX *ctx)
181	{
182	int norm_shift,i,j,loop;
183	BIGNUM *tmp,wnum,*snum,*sdiv,*res;
184	BN_ULONG *resp,*wnump;
185	BN_ULONG d0,d1;
186	int num_n,div_n;
187
188	bn_check_top(num);
189	bn_check_top(divisor);
190
191	if (BN_is_zero(divisor))
192		{
193		BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
194		return(0);
195		}
196
197	if (BN_ucmp(num,divisor) < 0)
198		{
199		if (rm != NULL)
200			{ if (BN_copy(rm,num) == NULL) return(0); }
201		if (dv != NULL) BN_zero(dv);
202		return(1);
203		}
204
205	BN_CTX_start(ctx);
206	tmp=BN_CTX_get(ctx);
207	snum=BN_CTX_get(ctx);
208	sdiv=BN_CTX_get(ctx);
209	if (dv == NULL)
210		res=BN_CTX_get(ctx);
211	else	res=dv;
212	if (sdiv == NULL || res == NULL) goto err;
213	tmp->neg=0;
214
215	/* First we normalise the numbers */
216	norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
217	if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
218	sdiv->neg=0;
219	norm_shift+=BN_BITS2;
220	if (!(BN_lshift(snum,num,norm_shift))) goto err;
221	snum->neg=0;
222	div_n=sdiv->top;
223	num_n=snum->top;
224	loop=num_n-div_n;
225
226	/* Lets setup a 'window' into snum
227	 * This is the part that corresponds to the current
228	 * 'area' being divided */
229	BN_init(&wnum);
230	wnum.d=	 &(snum->d[loop]);
231	wnum.top= div_n;
232	wnum.dmax= snum->dmax+1; /* a bit of a lie */
233
234	/* Get the top 2 words of sdiv */
235	/* i=sdiv->top; */
236	d0=sdiv->d[div_n-1];
237	d1=(div_n == 1)?0:sdiv->d[div_n-2];
238
239	/* pointer to the 'top' of snum */
240	wnump= &(snum->d[num_n-1]);
241
242	/* Setup to 'res' */
243	res->neg= (num->neg^divisor->neg);
244	if (!bn_wexpand(res,(loop+1))) goto err;
245	res->top=loop;
246	resp= &(res->d[loop-1]);
247
248	/* space for temp */
249	if (!bn_wexpand(tmp,(div_n+1))) goto err;
250
251	if (BN_ucmp(&wnum,sdiv) >= 0)
252		{
253		if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
254		*resp=1;
255		res->d[res->top-1]=1;
256		}
257	else
258		res->top--;
259	if (res->top == 0)
260		res->neg = 0;
261	resp--;
262
263	for (i=0; i<loop-1; i++)
264		{
265		BN_ULONG q,l0;
266#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
267		BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
268		q=bn_div_3_words(wnump,d1,d0);
269#else
270		BN_ULONG n0,n1,rem=0;
271
272		n0=wnump[0];
273		n1=wnump[-1];
274		if (n0 == d0)
275			q=BN_MASK2;
276		else 			/* n0 < d0 */
277			{
278#ifdef BN_LLONG
279			BN_ULLONG t2;
280
281#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
282			q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
283#else
284			q=bn_div_words(n0,n1,d0);
285#ifdef BN_DEBUG_LEVITTE
286			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
287X) -> 0x%08X\n",
288				n0, n1, d0, q);
289#endif
290#endif
291
292#ifndef REMAINDER_IS_ALREADY_CALCULATED
293			/*
294			 * rem doesn't have to be BN_ULLONG. The least we
295			 * know it's less that d0, isn't it?
296			 */
297			rem=(n1-q*d0)&BN_MASK2;
298#endif
299			t2=(BN_ULLONG)d1*q;
300
301			for (;;)
302				{
303				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
304					break;
305				q--;
306				rem += d0;
307				if (rem < d0) break; /* don't let rem overflow */
308				t2 -= d1;
309				}
310#else /* !BN_LLONG */
311			BN_ULONG t2l,t2h,ql,qh;
312
313			q=bn_div_words(n0,n1,d0);
314#ifdef BN_DEBUG_LEVITTE
315			fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
316X) -> 0x%08X\n",
317				n0, n1, d0, q);
318#endif
319#ifndef REMAINDER_IS_ALREADY_CALCULATED
320			rem=(n1-q*d0)&BN_MASK2;
321#endif
322
323#if defined(BN_UMULT_LOHI)
324			BN_UMULT_LOHI(t2l,t2h,d1,q);
325#elif defined(BN_UMULT_HIGH)
326			t2l = d1 * q;
327			t2h = BN_UMULT_HIGH(d1,q);
328#else
329			t2l=LBITS(d1); t2h=HBITS(d1);
330			ql =LBITS(q);  qh =HBITS(q);
331			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
332#endif
333
334			for (;;)
335				{
336				if ((t2h < rem) ||
337					((t2h == rem) && (t2l <= wnump[-2])))
338					break;
339				q--;
340				rem += d0;
341				if (rem < d0) break; /* don't let rem overflow */
342				if (t2l < d1) t2h--; t2l -= d1;
343				}
344#endif /* !BN_LLONG */
345			}
346#endif /* !BN_DIV3W */
347
348		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
349		wnum.d--; wnum.top++;
350		tmp->d[div_n]=l0;
351		for (j=div_n+1; j>0; j--)
352			if (tmp->d[j-1]) break;
353		tmp->top=j;
354
355		j=wnum.top;
356		if (!BN_sub(&wnum,&wnum,tmp)) goto err;
357
358		snum->top=snum->top+wnum.top-j;
359
360		if (wnum.neg)
361			{
362			q--;
363			j=wnum.top;
364			if (!BN_add(&wnum,&wnum,sdiv)) goto err;
365			snum->top+=wnum.top-j;
366			}
367		*(resp--)=q;
368		wnump--;
369		}
370	if (rm != NULL)
371		{
372		/* Keep a copy of the neg flag in num because if rm==num
373		 * BN_rshift() will overwrite it.
374		 */
375		int neg = num->neg;
376		BN_rshift(rm,snum,norm_shift);
377		if (!BN_is_zero(rm))
378			rm->neg = neg;
379		}
380	BN_CTX_end(ctx);
381	return(1);
382err:
383	BN_CTX_end(ctx);
384	return(0);
385	}
386
387#endif
388