-# 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
-# endif /* __<cpu> */
-# endif /* __GNUC__ */
-#endif /* NO_ASM */
- BN_ULONG n0,n1,rem=0;
-
- n0=wnump[0];
- n1=wnump[-1];
- if (n0 == d0)
- {
- q=BN_MASK2;
-#ifdef REMAINDER_IS_ALREADY_CALCULATED /* in this case it isn't */
- rem=(n1-q*d0)&BN_MASK2;
-#endif
- }
- else /* n0 < d0 */
-#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);
-#endif
- {
-#ifdef BN_LLONG
- BN_ULLONG t2;
-
-#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_ULONG t2l,t2h,ql,qh;
-
-#ifndef REMAINDER_IS_ALREADY_CALCULATED
- /*
- * It's more than enough with the only multiplication.
- * See the comment above in BN_LLONG section...
- */
- rem=(n1-q*d0)&BN_MASK2;
-#endif
-#ifdef BN_UMULT_HIGH
- t2l = d1 * q;
- t2h = BN_UMULT_HIGH(d1,q);
-#else
- 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
- }
-#endif /* !BN_DIV3W */
- l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
- wnum.d--; wnum.top++;
- tmp->d[div_n]=l0;
- for (j=div_n+1; j>0; j--)
- if (tmp->d[j-1]) break;
- tmp->top=j;
-
- j=wnum.top;
- BN_sub(&wnum,&wnum,tmp);
-
- snum->top=snum->top+wnum.top-j;
-
- if (wnum.neg)
- {
- q--;
- j=wnum.top;
- BN_add(&wnum,&wnum,sdiv);
- snum->top+=wnum.top-j;
- }
- *(resp--)=q;
- wnump--;
- }
- if (rm != NULL)
- {
- BN_rshift(rm,snum,norm_shift);
- rm->neg=num->neg;
- }
- BN_CTX_end(ctx);
- return(1);
-err:
- BN_CX_end(ctx);
- return(0);
- }
-
-#endif
-
-/* rem != m */
-int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
- {
-#if 0 /* The old slow way */
- int i,nm,nd;
- BIGNUM *dv;
-
- if (BN_ucmp(m,d) < 0)
- return((BN_copy(rem,m) == NULL)?0:1);
-
- BN_CTX_start(ctx);
- dv=BN_CTX_get(ctx);
-
- if (!BN_copy(rem,m)) goto err;
-
- nm=BN_num_bits(rem);
- nd=BN_num_bits(d);
- if (!BN_lshift(dv,d,nm-nd)) goto err;
- for (i=nm-nd; i>=0; i--)
- {
- if (BN_cmp(rem,dv) >= 0)
- {
- if (!BN_sub(rem,rem,dv)) goto err;
- }
- if (!BN_rshift1(dv,dv)) goto err;
- }
- BN_CTX_end(ctx);
- return(1);
+# 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;
+ /*
+ * 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' */
+ if (!bn_wexpand(res, (loop + 1)))
+ goto err;
+ res->neg = (num->neg ^ divisor->neg);
+ 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--;
+ }
+
+ /* Increase the resp pointer so that we never create an invalid pointer. */
+ resp++;
+
+ /*
+ * 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--) {
+ 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);
+# 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);
+# 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--;
+ *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);