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+/* __mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) --
+ Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
+ Return the single-limb remainder.
+ There are no constraints on the value of the divisor.
+
+ QUOT_PTR and DIVIDEND_PTR might point to the same limb.
+
+Copyright (C) 1991, 1993, 1994, Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Library General Public License as published by
+the Free Software Foundation; either version 2 of the License, or (at your
+option) any later version.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
+License for more details.
+
+You should have received a copy of the GNU Library General Public License
+along with the GNU MP Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+#ifndef UMUL_TIME
+#define UMUL_TIME 1
+#endif
+
+#ifndef UDIV_TIME
+#define UDIV_TIME UMUL_TIME
+#endif
+
+/* FIXME: We should be using invert_limb (or invert_normalized_limb)
+ here (not udiv_qrnnd). */
+
+mp_limb
+#if __STDC__
+__mpn_mod_1 (mp_srcptr dividend_ptr, mp_size_t dividend_size,
+ mp_limb divisor_limb)
+#else
+__mpn_mod_1 (dividend_ptr, dividend_size, divisor_limb)
+ mp_srcptr dividend_ptr;
+ mp_size_t dividend_size;
+ mp_limb divisor_limb;
+#endif
+{
+ mp_size_t i;
+ mp_limb n1, n0, r;
+ int dummy;
+
+ /* Botch: Should this be handled at all? Rely on callers? */
+ if (dividend_size == 0)
+ return 0;
+
+ /* If multiplication is much faster than division, and the
+ dividend is large, pre-invert the divisor, and use
+ only multiplications in the inner loop. */
+
+ /* This test should be read:
+ Does it ever help to use udiv_qrnnd_preinv?
+ && Does what we save compensate for the inversion overhead? */
+ if (UDIV_TIME > (2 * UMUL_TIME + 6)
+ && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
+ {
+ int normalization_steps;
+
+ count_leading_zeros (normalization_steps, divisor_limb);
+ if (normalization_steps != 0)
+ {
+ mp_limb divisor_limb_inverted;
+
+ divisor_limb <<= normalization_steps;
+
+ /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
+ result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
+ most significant bit (with weight 2**N) implicit. */
+
+ /* Special case for DIVISOR_LIMB == 100...000. */
+ if (divisor_limb << 1 == 0)
+ divisor_limb_inverted = ~(mp_limb) 0;
+ else
+ udiv_qrnnd (divisor_limb_inverted, dummy,
+ -divisor_limb, 0, divisor_limb);
+
+ n1 = dividend_ptr[dividend_size - 1];
+ r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
+
+ /* Possible optimization:
+ if (r == 0
+ && divisor_limb > ((n1 << normalization_steps)
+ | (dividend_ptr[dividend_size - 2] >> ...)))
+ ...one division less... */
+
+ for (i = dividend_size - 2; i >= 0; i--)
+ {
+ n0 = dividend_ptr[i];
+ udiv_qrnnd_preinv (dummy, r, r,
+ ((n1 << normalization_steps)
+ | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
+ divisor_limb, divisor_limb_inverted);
+ n1 = n0;
+ }
+ udiv_qrnnd_preinv (dummy, r, r,
+ n1 << normalization_steps,
+ divisor_limb, divisor_limb_inverted);
+ return r >> normalization_steps;
+ }
+ else
+ {
+ mp_limb divisor_limb_inverted;
+
+ /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
+ result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
+ most significant bit (with weight 2**N) implicit. */
+
+ /* Special case for DIVISOR_LIMB == 100...000. */
+ if (divisor_limb << 1 == 0)
+ divisor_limb_inverted = ~(mp_limb) 0;
+ else
+ udiv_qrnnd (divisor_limb_inverted, dummy,
+ -divisor_limb, 0, divisor_limb);
+
+ i = dividend_size - 1;
+ r = dividend_ptr[i];
+
+ if (r >= divisor_limb)
+ r = 0;
+ else
+ i--;
+
+ for (; i >= 0; i--)
+ {
+ n0 = dividend_ptr[i];
+ udiv_qrnnd_preinv (dummy, r, r,
+ n0, divisor_limb, divisor_limb_inverted);
+ }
+ return r;
+ }
+ }
+ else
+ {
+ if (UDIV_NEEDS_NORMALIZATION)
+ {
+ int normalization_steps;
+
+ count_leading_zeros (normalization_steps, divisor_limb);
+ if (normalization_steps != 0)
+ {
+ divisor_limb <<= normalization_steps;
+
+ n1 = dividend_ptr[dividend_size - 1];
+ r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
+
+ /* Possible optimization:
+ if (r == 0
+ && divisor_limb > ((n1 << normalization_steps)
+ | (dividend_ptr[dividend_size - 2] >> ...)))
+ ...one division less... */
+
+ for (i = dividend_size - 2; i >= 0; i--)
+ {
+ n0 = dividend_ptr[i];
+ udiv_qrnnd (dummy, r, r,
+ ((n1 << normalization_steps)
+ | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
+ divisor_limb);
+ n1 = n0;
+ }
+ udiv_qrnnd (dummy, r, r,
+ n1 << normalization_steps,
+ divisor_limb);
+ return r >> normalization_steps;
+ }
+ }
+ /* No normalization needed, either because udiv_qrnnd doesn't require
+ it, or because DIVISOR_LIMB is already normalized. */
+
+ i = dividend_size - 1;
+ r = dividend_ptr[i];
+
+ if (r >= divisor_limb)
+ r = 0;
+ else
+ i--;
+
+ for (; i >= 0; i--)
+ {
+ n0 = dividend_ptr[i];
+ udiv_qrnnd (dummy, r, r, n0, divisor_limb);
+ }
+ return r;
+ }
+}