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1 /* crypto/bn/bn_div.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
60 #include <openssl/bn.h>
65 /* The old slow way */
67 int BN_div(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
, const BIGNUM
*d
,
78 BNerr(BN_F_BN_DIV
,BN_R_DIV_BY_ZERO
);
85 { if (BN_copy(rem
,m
) == NULL
) return(0); }
86 if (dv
!= NULL
) BN_zero(dv
);
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
)
99 if (BN_copy(D
,d
) == NULL
) goto end
;
100 if (BN_copy(rem
,m
) == NULL
) goto end
;
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 :-) */
108 if (!BN_lshift(D
,D
,nm
-nd
)) goto end
;
109 for (i
=nm
-nd
; i
>=0; i
--)
111 if (!BN_lshift1(dv
,dv
)) goto end
;
112 if (BN_ucmp(rem
,D
) >= 0)
115 if (!BN_usub(rem
,rem
,D
)) goto end
;
117 /* CAN IMPROVE (and have now :=) */
118 if (!BN_rshift1(D
,D
)) goto end
;
120 rem
->neg
=BN_is_zero(rem
)?0:m
->neg
;
121 dv
->neg
=m
->neg
^d
->neg
;
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__)
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:-)
142 * <appro@fy.chalmers.se>
144 # define bn_div_words(n0,n1,d0) \
147 : "=a"(q), "=d"(rem) \
148 : "a"(n1), "d"(n0), "g"(d0) \
152 # define REMAINDER_IS_ALREADY_CALCULATED
153 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
155 * Same story here, but it's 128-bit by 64-bit division. Wow!
156 * <appro@fy.chalmers.se>
158 # define bn_div_words(n0,n1,d0) \
161 : "=a"(q), "=d"(rem) \
162 : "a"(n1), "d"(n0), "g"(d0) \
166 # define REMAINDER_IS_ALREADY_CALCULATED
167 # endif /* __<cpu> */
168 # endif /* __GNUC__ */
169 #endif /* OPENSSL_NO_ASM */
172 /* BN_div computes dv := num / divisor, rounding towards zero, and sets up
173 * rm such that dv*divisor + rm = num holds.
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.
179 int BN_div(BIGNUM
*dv
, BIGNUM
*rm
, const BIGNUM
*num
, const BIGNUM
*divisor
,
182 int norm_shift
,i
,j
,loop
;
183 BIGNUM
*tmp
,wnum
,*snum
,*sdiv
,*res
;
184 BN_ULONG
*resp
,*wnump
;
189 bn_check_top(divisor
);
191 if (BN_is_zero(divisor
))
193 BNerr(BN_F_BN_DIV
,BN_R_DIV_BY_ZERO
);
197 if (BN_ucmp(num
,divisor
) < 0)
200 { if (BN_copy(rm
,num
) == NULL
) return(0); }
201 if (dv
!= NULL
) BN_zero(dv
);
207 snum
=BN_CTX_get(ctx
);
208 sdiv
=BN_CTX_get(ctx
);
212 if (sdiv
== NULL
|| res
== NULL
) goto err
;
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
;
219 norm_shift
+=BN_BITS2
;
220 if (!(BN_lshift(snum
,num
,norm_shift
))) goto err
;
226 /* Lets setup a 'window' into snum
227 * This is the part that corresponds to the current
228 * 'area' being divided */
230 wnum
.flags
= BN_FLG_STATIC_DATA
; /* prevent accidental "expands" */
231 wnum
.d
= &(snum
->d
[loop
]);
233 wnum
.dmax
= snum
->dmax
- loop
; /* so we don't step out of bounds */
235 /* Get the top 2 words of sdiv */
238 d1
=(div_n
== 1)?0:sdiv
->d
[div_n
-2];
240 /* pointer to the 'top' of snum */
241 wnump
= &(snum
->d
[num_n
-1]);
244 res
->neg
= (num
->neg
^divisor
->neg
);
245 if (!bn_wexpand(res
,(loop
+1))) goto err
;
247 resp
= &(res
->d
[loop
-1]);
250 if (!bn_wexpand(tmp
,(div_n
+1))) goto err
;
253 if (BN_ucmp(&wnum
,sdiv
) >= 0)
255 if (!BN_usub(&wnum
,&wnum
,sdiv
)) goto err
;
257 res
->d
[res
->top
-1]=1;
265 for (i
=0; i
<loop
-1; i
++)
268 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
269 BN_ULONG
bn_div_3_words(BN_ULONG
*,BN_ULONG
,BN_ULONG
);
270 q
=bn_div_3_words(wnump
,d1
,d0
);
272 BN_ULONG n0
,n1
,rem
=0;
283 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
284 q
=(BN_ULONG
)(((((BN_ULLONG
)n0
)<<BN_BITS2
)|n1
)/d0
);
286 q
=bn_div_words(n0
,n1
,d0
);
287 #ifdef BN_DEBUG_LEVITTE
288 fprintf(stderr
,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
294 #ifndef REMAINDER_IS_ALREADY_CALCULATED
296 * rem doesn't have to be BN_ULLONG. The least we
297 * know it's less that d0, isn't it?
299 rem
=(n1
-q
*d0
)&BN_MASK2
;
305 if (t2
<= ((((BN_ULLONG
)rem
)<<BN_BITS2
)|wnump
[-2]))
309 if (rem
< d0
) break; /* don't let rem overflow */
312 #else /* !BN_LLONG */
313 BN_ULONG t2l
,t2h
,ql
,qh
;
315 q
=bn_div_words(n0
,n1
,d0
);
316 #ifdef BN_DEBUG_LEVITTE
317 fprintf(stderr
,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
321 #ifndef REMAINDER_IS_ALREADY_CALCULATED
322 rem
=(n1
-q
*d0
)&BN_MASK2
;
325 #if defined(BN_UMULT_LOHI)
326 BN_UMULT_LOHI(t2l
,t2h
,d1
,q
);
327 #elif defined(BN_UMULT_HIGH)
329 t2h
= BN_UMULT_HIGH(d1
,q
);
331 t2l
=LBITS(d1
); t2h
=HBITS(d1
);
332 ql
=LBITS(q
); qh
=HBITS(q
);
333 mul64(t2l
,t2h
,ql
,qh
); /* t2=(BN_ULLONG)d1*q; */
339 ((t2h
== rem
) && (t2l
<= wnump
[-2])))
343 if (rem
< d0
) break; /* don't let rem overflow */
344 if (t2l
< d1
) t2h
--; t2l
-= d1
;
346 #endif /* !BN_LLONG */
348 #endif /* !BN_DIV3W */
350 l0
=bn_mul_words(tmp
->d
,sdiv
->d
,div_n
,q
);
351 wnum
.d
--; wnum
.top
++; wnum
.dmax
++;
353 /* XXX: Couldn't we replace this with;
357 for (j
=div_n
+1; j
>0; j
--)
358 if (tmp
->d
[j
-1]) break;
363 if (!BN_sub(&wnum
,&wnum
,tmp
)) goto err
;
365 snum
->top
=snum
->top
+wnum
.top
-j
;
371 if (!BN_add(&wnum
,&wnum
,sdiv
)) goto err
;
372 snum
->top
+=wnum
.top
-j
;
379 /* Keep a copy of the neg flag in num because if rm==num
380 * BN_rshift() will overwrite it.
384 BN_rshift(rm
,snum
,norm_shift
);