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/* mpn_divrem -- Divide natural numbers, producing both remainder and
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quotient.
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Copyright (C) 1993-2018 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, see
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<http://www.gnu.org/licenses/>. */
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#include <gmp.h>
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#include "gmp-impl.h"
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#include "longlong.h"
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/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
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the NSIZE-DSIZE least significant quotient limbs at QP
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and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
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non-zero, generate that many fraction bits and append them after the
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other quotient limbs.
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Return the most significant limb of the quotient, this is always 0 or 1.
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Preconditions:
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0. NSIZE >= DSIZE.
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1. The most significant bit of the divisor must be set.
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2. QP must either not overlap with the input operands at all, or
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QP + DSIZE >= NP must hold true. (This means that it's
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possible to put the quotient in the high part of NUM, right after the
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remainder in NUM.
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3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */
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mp_limb_t
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mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs,
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mp_ptr np, mp_size_t nsize,
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mp_srcptr dp, mp_size_t dsize)
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{
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mp_limb_t most_significant_q_limb = 0;
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switch (dsize)
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{
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case 0:
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/* We are asked to divide by zero, so go ahead and do it! (To make
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the compiler not remove this statement, return the value.) */
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return 1 / dsize;
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case 1:
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{
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mp_size_t i;
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mp_limb_t n1;
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mp_limb_t d;
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d = dp[0];
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n1 = np[nsize - 1];
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if (n1 >= d)
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{
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n1 -= d;
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most_significant_q_limb = 1;
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}
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qp += qextra_limbs;
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for (i = nsize - 2; i >= 0; i--)
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udiv_qrnnd (qp[i], n1, n1, np[i], d);
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qp -= qextra_limbs;
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for (i = qextra_limbs - 1; i >= 0; i--)
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udiv_qrnnd (qp[i], n1, n1, 0, d);
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np[0] = n1;
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}
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break;
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case 2:
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{
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mp_size_t i;
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mp_limb_t n1, n0, n2;
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mp_limb_t d1, d0;
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np += nsize - 2;
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d1 = dp[1];
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d0 = dp[0];
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n1 = np[1];
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n0 = np[0];
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if (n1 >= d1 && (n1 > d1 || n0 >= d0))
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{
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sub_ddmmss (n1, n0, n1, n0, d1, d0);
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most_significant_q_limb = 1;
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}
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for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--)
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{
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mp_limb_t q;
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mp_limb_t r;
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if (i >= qextra_limbs)
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np--;
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else
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np[0] = 0;
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if (n1 == d1)
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{
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/* Q should be either 111..111 or 111..110. Need special
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treatment of this rare case as normal division would
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give overflow. */
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q = ~(mp_limb_t) 0;
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r = n0 + d1;
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if (r < d1) /* Carry in the addition? */
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{
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add_ssaaaa (n1, n0, r - d0, np[0], 0, d0);
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qp[i] = q;
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continue;
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}
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n1 = d0 - (d0 != 0);
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n0 = -d0;
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}
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else
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{
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udiv_qrnnd (q, r, n1, n0, d1);
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umul_ppmm (n1, n0, d0, q);
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}
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n2 = np[0];
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q_test:
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if (n1 > r || (n1 == r && n0 > n2))
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{
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/* The estimated Q was too large. */
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q--;
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sub_ddmmss (n1, n0, n1, n0, 0, d0);
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r += d1;
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if (r >= d1) /* If not carry, test Q again. */
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goto q_test;
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}
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qp[i] = q;
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sub_ddmmss (n1, n0, r, n2, n1, n0);
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}
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np[1] = n1;
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np[0] = n0;
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}
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break;
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default:
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{
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mp_size_t i;
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mp_limb_t dX, d1, n0;
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np += nsize - dsize;
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dX = dp[dsize - 1];
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d1 = dp[dsize - 2];
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n0 = np[dsize - 1];
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if (n0 >= dX)
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{
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if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0)
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{
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mpn_sub_n (np, np, dp, dsize);
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n0 = np[dsize - 1];
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most_significant_q_limb = 1;
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}
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}
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for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--)
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{
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mp_limb_t q;
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mp_limb_t n1, n2;
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mp_limb_t cy_limb;
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if (i >= qextra_limbs)
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{
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np--;
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n2 = np[dsize];
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}
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else
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{
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n2 = np[dsize - 1];
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MPN_COPY_DECR (np + 1, np, dsize);
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np[0] = 0;
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}
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if (n0 == dX)
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/* This might over-estimate q, but it's probably not worth
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the extra code here to find out. */
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q = ~(mp_limb_t) 0;
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else
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{
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mp_limb_t r;
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udiv_qrnnd (q, r, n0, np[dsize - 1], dX);
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umul_ppmm (n1, n0, d1, q);
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while (n1 > r || (n1 == r && n0 > np[dsize - 2]))
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{
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q--;
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r += dX;
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if (r < dX) /* I.e. "carry in previous addition?" */
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break;
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n1 -= n0 < d1;
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n0 -= d1;
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}
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}
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/* Possible optimization: We already have (q * n0) and (1 * n1)
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after the calculation of q. Taking advantage of that, we
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could make this loop make two iterations less. */
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cy_limb = mpn_submul_1 (np, dp, dsize, q);
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if (n2 != cy_limb)
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{
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mpn_add_n (np, np, dp, dsize);
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q--;
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}
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qp[i] = q;
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n0 = np[dsize - 1];
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}
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}
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}
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return most_significant_q_limb;
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}
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