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Annotation of OpenXM_contrib/gmp/mpn/generic/divrem.c, Revision 1.1.1.1

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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