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Annotation of OpenXM_contrib/gmp/mpq/get_d.c, Revision 1.1.1.1

1.1       maekawa     1: /* double mpq_get_d (mpq_t src) -- Return the double approximation to SRC.
                      2:
                      3: Copyright (C) 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: #include "gmp.h"
                     23: #include "gmp-impl.h"
                     24: #include "longlong.h"
                     25:
                     26: /* Algorithm:
                     27:    1. Develop >= n bits of src.num / src.den, where n is the number of bits
                     28:       in a double.  This (partial) division will use all bits from the
                     29:       denominator.
                     30:    2. Use the remainder to determine how to round the result.
                     31:    3. Assign the integral result to a temporary double.
                     32:    4. Scale the temporary double, and return the result.
                     33:
                     34:    An alternative algorithm, that would be faster:
                     35:    0. Let n be somewhat larger than the number of significant bits in a double.
                     36:    1. Extract the most significant n bits of the denominator, and an equal
                     37:       number of bits from the numerator.
                     38:    2. Interpret the extracted numbers as integers, call them a and b
                     39:       respectively, and develop n bits of the fractions ((a + 1) / b) and
                     40:       (a / (b + 1)) using mpn_divrem.
                     41:    3. If the computed values are identical UP TO THE POSITION WE CARE ABOUT,
                     42:       we are done.  If they are different, repeat the algorithm from step 1,
                     43:       but first let n = n * 2.
                     44:    4. If we end up using all bits from the numerator and denominator, fall
                     45:       back to the first algorithm above.
                     46:    5. Just to make life harder, The computation of a + 1 and b + 1 above
                     47:       might give carry-out...  Needs special handling.  It might work to
                     48:       subtract 1 in both cases instead.
                     49: */
                     50:
                     51: double
                     52: #if __STDC__
                     53: mpq_get_d (const MP_RAT *src)
                     54: #else
                     55: mpq_get_d (src)
                     56:      const MP_RAT *src;
                     57: #endif
                     58: {
                     59:   mp_ptr np, dp;
                     60:   mp_ptr rp;
                     61:   mp_size_t nsize = src->_mp_num._mp_size;
                     62:   mp_size_t dsize = src->_mp_den._mp_size;
                     63:   mp_size_t qsize, rsize;
                     64:   mp_size_t sign_quotient = nsize ^ dsize;
                     65:   unsigned normalization_steps;
                     66:   mp_limb_t qlimb;
                     67: #define N_QLIMBS (1 + (sizeof (double) + BYTES_PER_MP_LIMB-1) / BYTES_PER_MP_LIMB)
                     68:   mp_limb_t qp[N_QLIMBS + 1];
                     69:   TMP_DECL (marker);
                     70:
                     71:   if (nsize == 0)
                     72:     return 0.0;
                     73:
                     74:   TMP_MARK (marker);
                     75:   nsize = ABS (nsize);
                     76:   dsize = ABS (dsize);
                     77:   np = src->_mp_num._mp_d;
                     78:   dp = src->_mp_den._mp_d;
                     79:
                     80:   rsize = dsize + N_QLIMBS;
                     81:   rp = (mp_ptr) TMP_ALLOC ((rsize + 1) * BYTES_PER_MP_LIMB);
                     82:
                     83:   count_leading_zeros (normalization_steps, dp[dsize - 1]);
                     84:
                     85:   /* Normalize the denominator, i.e. make its most significant bit set by
                     86:      shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
                     87:      numerator the same number of steps (to keep the quotient the same!).  */
                     88:   if (normalization_steps != 0)
                     89:     {
                     90:       mp_ptr tp;
                     91:       mp_limb_t nlimb;
                     92:
                     93:       /* Shift up the denominator setting the most significant bit of
                     94:         the most significant limb.  Use temporary storage not to clobber
                     95:         the original contents of the denominator.  */
                     96:       tp = (mp_ptr) TMP_ALLOC (dsize * BYTES_PER_MP_LIMB);
                     97:       mpn_lshift (tp, dp, dsize, normalization_steps);
                     98:       dp = tp;
                     99:
                    100:       if (rsize > nsize)
                    101:        {
                    102:          MPN_ZERO (rp, rsize - nsize);
                    103:          nlimb = mpn_lshift (rp + (rsize - nsize),
                    104:                              np, nsize, normalization_steps);
                    105:        }
                    106:       else
                    107:        {
                    108:          nlimb = mpn_lshift (rp, np + (nsize - rsize),
                    109:                              rsize, normalization_steps);
                    110:        }
                    111:       if (nlimb != 0)
                    112:        {
                    113:          rp[rsize] = nlimb;
                    114:          rsize++;
                    115:        }
                    116:     }
                    117:   else
                    118:     {
                    119:       if (rsize > nsize)
                    120:        {
                    121:          MPN_ZERO (rp, rsize - nsize);
                    122:          MPN_COPY (rp + (rsize - nsize), np, nsize);
                    123:        }
                    124:       else
                    125:        {
                    126:          MPN_COPY (rp, np + (nsize - rsize), rsize);
                    127:        }
                    128:     }
                    129:
                    130:   qlimb = mpn_divmod (qp, rp, rsize, dp, dsize);
                    131:   qsize = rsize - dsize;
                    132:   if (qlimb)
                    133:     {
                    134:       qp[qsize] = qlimb;
                    135:       qsize++;
                    136:     }
                    137:
                    138:   {
                    139:     double res;
                    140:     mp_size_t i;
                    141:
                    142:     res = qp[qsize - 1];
                    143:     for (i = qsize - 2; i >= 0; i--)
                    144:       res = res * MP_BASE_AS_DOUBLE + qp[i];
                    145:
                    146:     res = __gmp_scale2 (res, BITS_PER_MP_LIMB * (nsize - dsize - N_QLIMBS));
                    147:
                    148:     TMP_FREE (marker);
                    149:     return sign_quotient >= 0 ? res : -res;
                    150:   }
                    151: }