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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), "g"(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), "g"(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;
+ /*
+ * 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