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Annotation of OpenXM/src/kan96xx/gmp-2.0.2-ssh-2/mpn/generic/bdivmod.c, Revision 1.1.1.1

1.1       takayama    1: /* mpn/bdivmod.c: mpn_bdivmod for computing U/V mod 2^d.
                      2:
                      3: Copyright (C) 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
                      4:
                      5: This file is part of the GNU MP Library.
                      6:
                      7: The GNU MP Library is free software; you can redistribute it and/or modify
                      8: it under the terms of the GNU Library General Public License as published by
                      9: the Free Software Foundation; either version 2 of the License, or (at your
                     10: option) any later version.
                     11:
                     12: The GNU MP Library is distributed in the hope that it will be useful, but
                     13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
                     14: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public
                     15: License for more details.
                     16:
                     17: You should have received a copy of the GNU Library General Public License
                     18: along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
                     19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
                     20: MA 02111-1307, USA. */
                     21:
                     22: /* q_high = mpn_bdivmod (qp, up, usize, vp, vsize, d).
                     23:
                     24:    Puts the low d/BITS_PER_MP_LIMB limbs of Q = U / V mod 2^d at qp, and
                     25:    returns the high d%BITS_PER_MP_LIMB bits of Q as the result.
                     26:
                     27:    Also, U - Q * V mod 2^(usize*BITS_PER_MP_LIMB) is placed at up.  Since the
                     28:    low d/BITS_PER_MP_LIMB limbs of this difference are zero, the code allows
                     29:    the limb vectors at qp to overwrite the low limbs at up, provided qp <= up.
                     30:
                     31:    Preconditions:
                     32:    1.  V is odd.
                     33:    2.  usize * BITS_PER_MP_LIMB >= d.
                     34:    3.  If Q and U overlap, qp <= up.
                     35:
                     36:    Ken Weber (kweber@mat.ufrgs.br, kweber@mcs.kent.edu)
                     37:
                     38:    Funding for this work has been partially provided by Conselho Nacional
                     39:    de Desenvolvimento Cienti'fico e Tecnolo'gico (CNPq) do Brazil, Grant
                     40:    301314194-2, and was done while I was a visiting reseacher in the Instituto
                     41:    de Matema'tica at Universidade Federal do Rio Grande do Sul (UFRGS).
                     42:
                     43:    References:
                     44:        T. Jebelean, An algorithm for exact division, Journal of Symbolic
                     45:        Computation, v. 15, 1993, pp. 169-180.
                     46:
                     47:        K. Weber, The accelerated integer GCD algorithm, ACM Transactions on
                     48:        Mathematical Software, v. 21 (March), 1995, pp. 111-122.  */
                     49:
                     50: #include "gmp.h"
                     51: #include "gmp-impl.h"
                     52: #include "longlong.h"
                     53:
                     54: mp_limb_t
                     55: #if __STDC__
                     56: mpn_bdivmod (mp_ptr qp, mp_ptr up, mp_size_t usize,
                     57:             mp_srcptr vp, mp_size_t vsize, unsigned long int d)
                     58: #else
                     59: mpn_bdivmod (qp, up, usize, vp, vsize, d)
                     60:      mp_ptr qp;
                     61:      mp_ptr up;
                     62:      mp_size_t usize;
                     63:      mp_srcptr vp;
                     64:      mp_size_t vsize;
                     65:      unsigned long int d;
                     66: #endif
                     67: {
                     68:   /* Cache for v_inv is used to make mpn_accelgcd faster.  */
                     69:   static mp_limb_t previous_low_vlimb = 0;
                     70:   static mp_limb_t v_inv;              /* 1/V mod 2^BITS_PER_MP_LIMB.  */
                     71:
                     72:   if (vp[0] != previous_low_vlimb)     /* Cache miss; compute v_inv.  */
                     73:     {
                     74:       mp_limb_t v = previous_low_vlimb = vp[0];
                     75:       mp_limb_t make_zero = 1;
                     76:       mp_limb_t two_i = 1;
                     77:       v_inv = 0;
                     78:       do
                     79:        {
                     80:          while ((two_i & make_zero) == 0)
                     81:            two_i <<= 1, v <<= 1;
                     82:          v_inv += two_i;
                     83:          make_zero -= v;
                     84:        }
                     85:       while (make_zero);
                     86:     }
                     87:
                     88:   /* Need faster computation for some common cases in mpn_accelgcd.  */
                     89:   if (usize == 2 && vsize == 2 &&
                     90:       (d == BITS_PER_MP_LIMB || d == 2*BITS_PER_MP_LIMB))
                     91:     {
                     92:       mp_limb_t hi, lo;
                     93:       mp_limb_t q = up[0] * v_inv;
                     94:       umul_ppmm (hi, lo, q, vp[0]);
                     95:       up[0] = 0, up[1] -= hi + q*vp[1], qp[0] = q;
                     96:       if (d == 2*BITS_PER_MP_LIMB)
                     97:        q = up[1] * v_inv, up[1] = 0, qp[1] = q;
                     98:       return 0;
                     99:     }
                    100:
                    101:   /* Main loop.  */
                    102:   while (d >= BITS_PER_MP_LIMB)
                    103:     {
                    104:       mp_limb_t q = up[0] * v_inv;
                    105:       mp_limb_t b = mpn_submul_1 (up, vp, MIN (usize, vsize), q);
                    106:       if (usize > vsize)
                    107:        mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
                    108:       d -= BITS_PER_MP_LIMB;
                    109:       up += 1, usize -= 1;
                    110:       *qp++ = q;
                    111:     }
                    112:
                    113:   if (d)
                    114:     {
                    115:       mp_limb_t b;
                    116:       mp_limb_t q = (up[0] * v_inv) & (((mp_limb_t)1<<d) - 1);
                    117:       switch (q)
                    118:        {
                    119:          case 0:  return 0;
                    120:          case 1:  b = mpn_sub_n (up, up, vp, MIN (usize, vsize));   break;
                    121:          default: b = mpn_submul_1 (up, vp, MIN (usize, vsize), q); break;
                    122:        }
                    123:       if (usize > vsize)
                    124:        mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
                    125:       return q;
                    126:     }
                    127:
                    128:   return 0;
                    129: }