Annotation of OpenXM_contrib/gmp/mpn/generic/divrem.c, Revision 1.1
1.1 ! maekawa 1: /* mpn_divrem -- Divide natural numbers, producing both remainder and
! 2: quotient.
! 3:
! 4: Copyright (C) 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
! 5:
! 6: This file is part of the GNU MP Library.
! 7:
! 8: The GNU MP Library is free software; you can redistribute it and/or modify
! 9: it under the terms of the GNU Library General Public License as published by
! 10: the Free Software Foundation; either version 2 of the License, or (at your
! 11: option) any later version.
! 12:
! 13: The GNU MP Library is distributed in the hope that it will be useful, but
! 14: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
! 15: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
! 16: License for more details.
! 17:
! 18: You should have received a copy of the GNU Library General Public License
! 19: along with the GNU MP Library; see the file COPYING.LIB. If not, write to
! 20: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
! 21: MA 02111-1307, USA. */
! 22:
! 23: #include "gmp.h"
! 24: #include "gmp-impl.h"
! 25: #include "longlong.h"
! 26:
! 27: /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
! 28: the NSIZE-DSIZE least significant quotient limbs at QP
! 29: and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
! 30: non-zero, generate that many fraction bits and append them after the
! 31: other quotient limbs.
! 32: Return the most significant limb of the quotient, this is always 0 or 1.
! 33:
! 34: Preconditions:
! 35: 0. NSIZE >= DSIZE.
! 36: 1. The most significant bit of the divisor must be set.
! 37: 2. QP must either not overlap with the input operands at all, or
! 38: QP + DSIZE >= NP must hold true. (This means that it's
! 39: possible to put the quotient in the high part of NUM, right after the
! 40: remainder in NUM.
! 41: 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */
! 42:
! 43: mp_limb_t
! 44: #if __STDC__
! 45: mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs,
! 46: mp_ptr np, mp_size_t nsize,
! 47: mp_srcptr dp, mp_size_t dsize)
! 48: #else
! 49: mpn_divrem (qp, qextra_limbs, np, nsize, dp, dsize)
! 50: mp_ptr qp;
! 51: mp_size_t qextra_limbs;
! 52: mp_ptr np;
! 53: mp_size_t nsize;
! 54: mp_srcptr dp;
! 55: mp_size_t dsize;
! 56: #endif
! 57: {
! 58: mp_limb_t most_significant_q_limb = 0;
! 59:
! 60: switch (dsize)
! 61: {
! 62: case 0:
! 63: /* We are asked to divide by zero, so go ahead and do it! (To make
! 64: the compiler not remove this statement, return the value.) */
! 65: return 1 / dsize;
! 66:
! 67: case 1:
! 68: {
! 69: mp_size_t i;
! 70: mp_limb_t n1;
! 71: mp_limb_t d;
! 72:
! 73: d = dp[0];
! 74: n1 = np[nsize - 1];
! 75:
! 76: if (n1 >= d)
! 77: {
! 78: n1 -= d;
! 79: most_significant_q_limb = 1;
! 80: }
! 81:
! 82: qp += qextra_limbs;
! 83: for (i = nsize - 2; i >= 0; i--)
! 84: udiv_qrnnd (qp[i], n1, n1, np[i], d);
! 85: qp -= qextra_limbs;
! 86:
! 87: for (i = qextra_limbs - 1; i >= 0; i--)
! 88: udiv_qrnnd (qp[i], n1, n1, 0, d);
! 89:
! 90: np[0] = n1;
! 91: }
! 92: break;
! 93:
! 94: case 2:
! 95: {
! 96: mp_size_t i;
! 97: mp_limb_t n1, n0, n2;
! 98: mp_limb_t d1, d0;
! 99:
! 100: np += nsize - 2;
! 101: d1 = dp[1];
! 102: d0 = dp[0];
! 103: n1 = np[1];
! 104: n0 = np[0];
! 105:
! 106: if (n1 >= d1 && (n1 > d1 || n0 >= d0))
! 107: {
! 108: sub_ddmmss (n1, n0, n1, n0, d1, d0);
! 109: most_significant_q_limb = 1;
! 110: }
! 111:
! 112: for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--)
! 113: {
! 114: mp_limb_t q;
! 115: mp_limb_t r;
! 116:
! 117: if (i >= qextra_limbs)
! 118: np--;
! 119: else
! 120: np[0] = 0;
! 121:
! 122: if (n1 == d1)
! 123: {
! 124: /* Q should be either 111..111 or 111..110. Need special
! 125: treatment of this rare case as normal division would
! 126: give overflow. */
! 127: q = ~(mp_limb_t) 0;
! 128:
! 129: r = n0 + d1;
! 130: if (r < d1) /* Carry in the addition? */
! 131: {
! 132: add_ssaaaa (n1, n0, r - d0, np[0], 0, d0);
! 133: qp[i] = q;
! 134: continue;
! 135: }
! 136: n1 = d0 - (d0 != 0);
! 137: n0 = -d0;
! 138: }
! 139: else
! 140: {
! 141: udiv_qrnnd (q, r, n1, n0, d1);
! 142: umul_ppmm (n1, n0, d0, q);
! 143: }
! 144:
! 145: n2 = np[0];
! 146: q_test:
! 147: if (n1 > r || (n1 == r && n0 > n2))
! 148: {
! 149: /* The estimated Q was too large. */
! 150: q--;
! 151:
! 152: sub_ddmmss (n1, n0, n1, n0, 0, d0);
! 153: r += d1;
! 154: if (r >= d1) /* If not carry, test Q again. */
! 155: goto q_test;
! 156: }
! 157:
! 158: qp[i] = q;
! 159: sub_ddmmss (n1, n0, r, n2, n1, n0);
! 160: }
! 161: np[1] = n1;
! 162: np[0] = n0;
! 163: }
! 164: break;
! 165:
! 166: default:
! 167: {
! 168: mp_size_t i;
! 169: mp_limb_t dX, d1, n0;
! 170:
! 171: np += nsize - dsize;
! 172: dX = dp[dsize - 1];
! 173: d1 = dp[dsize - 2];
! 174: n0 = np[dsize - 1];
! 175:
! 176: if (n0 >= dX)
! 177: {
! 178: if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0)
! 179: {
! 180: mpn_sub_n (np, np, dp, dsize);
! 181: n0 = np[dsize - 1];
! 182: most_significant_q_limb = 1;
! 183: }
! 184: }
! 185:
! 186: for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--)
! 187: {
! 188: mp_limb_t q;
! 189: mp_limb_t n1, n2;
! 190: mp_limb_t cy_limb;
! 191:
! 192: if (i >= qextra_limbs)
! 193: {
! 194: np--;
! 195: n2 = np[dsize];
! 196: }
! 197: else
! 198: {
! 199: n2 = np[dsize - 1];
! 200: MPN_COPY_DECR (np + 1, np, dsize);
! 201: np[0] = 0;
! 202: }
! 203:
! 204: if (n0 == dX)
! 205: /* This might over-estimate q, but it's probably not worth
! 206: the extra code here to find out. */
! 207: q = ~(mp_limb_t) 0;
! 208: else
! 209: {
! 210: mp_limb_t r;
! 211:
! 212: udiv_qrnnd (q, r, n0, np[dsize - 1], dX);
! 213: umul_ppmm (n1, n0, d1, q);
! 214:
! 215: while (n1 > r || (n1 == r && n0 > np[dsize - 2]))
! 216: {
! 217: q--;
! 218: r += dX;
! 219: if (r < dX) /* I.e. "carry in previous addition?" */
! 220: break;
! 221: n1 -= n0 < d1;
! 222: n0 -= d1;
! 223: }
! 224: }
! 225:
! 226: /* Possible optimization: We already have (q * n0) and (1 * n1)
! 227: after the calculation of q. Taking advantage of that, we
! 228: could make this loop make two iterations less. */
! 229:
! 230: cy_limb = mpn_submul_1 (np, dp, dsize, q);
! 231:
! 232: if (n2 != cy_limb)
! 233: {
! 234: mpn_add_n (np, np, dp, dsize);
! 235: q--;
! 236: }
! 237:
! 238: qp[i] = q;
! 239: n0 = np[dsize - 1];
! 240: }
! 241: }
! 242: }
! 243:
! 244: return most_significant_q_limb;
! 245: }
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