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godot/thirdparty/openssl/crypto/bn/bn_div.c

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/* crypto/bn/bn_div.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
#include <stdio.h>
#include <openssl/bn.h>
#include "cryptlib.h"
#include "bn_lcl.h"
/* The old slow way */
#if 0
int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
BN_CTX *ctx)
{
int i, nm, nd;
int ret = 0;
BIGNUM *D;
bn_check_top(m);
bn_check_top(d);
if (BN_is_zero(d)) {
BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
return (0);
}
if (BN_ucmp(m, d) < 0) {
if (rem != NULL) {
if (BN_copy(rem, m) == NULL)
return (0);
}
if (dv != NULL)
BN_zero(dv);
return (1);
}
BN_CTX_start(ctx);
D = BN_CTX_get(ctx);
if (dv == NULL)
dv = BN_CTX_get(ctx);
if (rem == NULL)
rem = BN_CTX_get(ctx);
if (D == NULL || dv == NULL || rem == NULL)
goto end;
nd = BN_num_bits(d);
nm = BN_num_bits(m);
if (BN_copy(D, d) == NULL)
goto end;
if (BN_copy(rem, m) == NULL)
goto end;
/*
* The next 2 are needed so we can do a dv->d[0]|=1 later since
* BN_lshift1 will only work once there is a value :-)
*/
BN_zero(dv);
if (bn_wexpand(dv, 1) == NULL)
goto end;
dv->top = 1;
if (!BN_lshift(D, D, nm - nd))
goto end;
for (i = nm - nd; i >= 0; i--) {
if (!BN_lshift1(dv, dv))
goto end;
if (BN_ucmp(rem, D) >= 0) {
dv->d[0] |= 1;
if (!BN_usub(rem, rem, D))
goto end;
}
/* CAN IMPROVE (and have now :=) */
if (!BN_rshift1(D, D))
goto end;
}
rem->neg = BN_is_zero(rem) ? 0 : m->neg;
dv->neg = m->neg ^ d->neg;
ret = 1;
end:
BN_CTX_end(ctx);
return (ret);
}
#else
# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
&& !defined(PEDANTIC) && !defined(BN_DIV3W)
# if defined(__GNUC__) && __GNUC__>=2
# if defined(__i386) || defined (__i386__)
/*-
* There were two reasons for implementing this template:
* - GNU C generates a call to a function (__udivdi3 to be exact)
* in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
* understand why...);
* - divl doesn't only calculate quotient, but also leaves
* remainder in %edx which we can definitely use here:-)
*
* <appro@fy.chalmers.se>
*/
# undef bn_div_words
# define bn_div_words(n0,n1,d0) \
({ asm volatile ( \
"divl %4" \
: "=a"(q), "=d"(rem) \
: "a"(n1), "d"(n0), "r"(d0) \
: "cc"); \
q; \
})
# define REMAINDER_IS_ALREADY_CALCULATED
# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
/*
* Same story here, but it's 128-bit by 64-bit division. Wow!
* <appro@fy.chalmers.se>
*/
# undef bn_div_words
# define bn_div_words(n0,n1,d0) \
({ asm volatile ( \
"divq %4" \
: "=a"(q), "=d"(rem) \
: "a"(n1), "d"(n0), "r"(d0) \
: "cc"); \
q; \
})
# define REMAINDER_IS_ALREADY_CALCULATED
# endif /* __<cpu> */
# endif /* __GNUC__ */
# endif /* OPENSSL_NO_ASM */
/*-
* BN_div computes dv := num / divisor, rounding towards
* zero, and sets up rm such that dv*divisor + rm = num holds.
* Thus:
* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
* rm->neg == num->neg (unless the remainder is zero)
* If 'dv' or 'rm' is NULL, the respective value is not returned.
*/
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift, i, loop;
BIGNUM *tmp, wnum, *snum, *sdiv, *res;
BN_ULONG *resp, *wnump;
BN_ULONG d0, d1;
int num_n, div_n;
int no_branch = 0;
/*
* Invalid zero-padding would have particularly bad consequences so don't
* just rely on bn_check_top() here (bn_check_top() works only for
* BN_DEBUG builds)
*/
if ((num->top > 0 && num->d[num->top - 1] == 0) ||
(divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
return 0;
}
bn_check_top(num);
bn_check_top(divisor);
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
|| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
no_branch = 1;
}
bn_check_top(dv);
bn_check_top(rm);
/*- bn_check_top(num); *//*
* 'num' has been checked already
*/
/*- bn_check_top(divisor); *//*
* 'divisor' has been checked already
*/
if (BN_is_zero(divisor)) {
BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
return (0);
}
if (!no_branch && BN_ucmp(num, divisor) < 0) {
if (rm != NULL) {
if (BN_copy(rm, num) == NULL)
return (0);
}
if (dv != NULL)
BN_zero(dv);
return (1);
}
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
if (dv == NULL)
res = BN_CTX_get(ctx);
else
res = dv;
if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
goto err;
/* First we normalise the numbers */
norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
if (!(BN_lshift(sdiv, divisor, norm_shift)))
goto err;
sdiv->neg = 0;
norm_shift += BN_BITS2;
if (!(BN_lshift(snum, num, norm_shift)))
goto err;
snum->neg = 0;
if (no_branch) {
/*
* Since we don't know whether snum is larger than sdiv, we pad snum
* with enough zeroes without changing its value.
*/
if (snum->top <= sdiv->top + 1) {
if (bn_wexpand(snum, sdiv->top + 2) == NULL)
goto err;
for (i = snum->top; i < sdiv->top + 2; i++)
snum->d[i] = 0;
snum->top = sdiv->top + 2;
} else {
if (bn_wexpand(snum, snum->top + 1) == NULL)
goto err;
snum->d[snum->top] = 0;
snum->top++;
}
}
div_n = sdiv->top;
num_n = snum->top;
loop = num_n - div_n;
/*
* Lets setup a 'window' into snum This is the part that corresponds to
* the current 'area' being divided
*/
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
wnum.flags = BN_FLG_STATIC_DATA;
/*
* only needed when BN_ucmp messes up the values between top and max
*/
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0 = sdiv->d[div_n - 1];
d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
/* pointer to the 'top' of snum */
wnump = &(snum->d[num_n - 1]);
/* Setup to 'res' */
res->neg = (num->neg ^ divisor->neg);
if (!bn_wexpand(res, (loop + 1)))
goto err;
res->top = loop - no_branch;
resp = &(res->d[loop - 1]);
/* space for temp */
if (!bn_wexpand(tmp, (div_n + 1)))
goto err;
if (!no_branch) {
if (BN_ucmp(&wnum, sdiv) >= 0) {
/*
* If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
* the const bignum arguments => clean the values between top and
* max again
*/
bn_clear_top2max(&wnum);
bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
*resp = 1;
} else
res->top--;
}
/*
* if res->top == 0 then clear the neg value otherwise decrease the resp
* pointer
*/
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i = 0; i < loop - 1; i++, wnump--, resp--) {
BN_ULONG q, l0;
/*
* the first part of the loop uses the top two words of snum and sdiv
* to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
*/
# if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
q = bn_div_3_words(wnump, d1, d0);
# else
BN_ULONG n0, n1, rem = 0;
n0 = wnump[0];
n1 = wnump[-1];
if (n0 == d0)
q = BN_MASK2;
else { /* n0 < d0 */
# ifdef BN_LLONG
BN_ULLONG t2;
# if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
# else
q = bn_div_words(n0, n1, d0);
# ifdef BN_DEBUG_LEVITTE
fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n", n0, n1, d0, q);
# endif
# endif
# ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem = (n1 - q * d0) & BN_MASK2;
# endif
t2 = (BN_ULLONG) d1 *q;
for (;;) {
if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
t2 -= d1;
}
# else /* !BN_LLONG */
BN_ULONG t2l, t2h;
q = bn_div_words(n0, n1, d0);
# ifdef BN_DEBUG_LEVITTE
fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n", n0, n1, d0, q);
# endif
# ifndef REMAINDER_IS_ALREADY_CALCULATED
rem = (n1 - q * d0) & BN_MASK2;
# endif
# if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l, t2h, d1, q);
# elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1, q);
# else
{
BN_ULONG ql, qh;
t2l = LBITS(d1);
t2h = HBITS(d1);
ql = LBITS(q);
qh = HBITS(q);
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
}
# endif
for (;;) {
if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
if (t2l < d1)
t2h--;
t2l -= d1;
}
# endif /* !BN_LLONG */
}
# endif /* !BN_DIV3W */
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
tmp->d[div_n] = l0;
wnum.d--;
/*
* ingore top values of the bignums just sub the two BN_ULONG arrays
* with bn_sub_words
*/
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
/*
* Note: As we have considered only the leading two BN_ULONGs in
* the calculation of q, sdiv * q might be greater than wnum (but
* then (q-1) * sdiv is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
/*
* we can't have an overflow here (assuming that q != 0, but
* if q == 0 then tmp is zero anyway)
*/
(*wnump)++;
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL) {
/*
* Keep a copy of the neg flag in num because if rm==num BN_rshift()
* will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm, snum, norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
if (no_branch)
bn_correct_top(res);
BN_CTX_end(ctx);
return (1);
err:
bn_check_top(rm);
BN_CTX_end(ctx);
return (0);
}
#endif
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