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Annotation of OpenXM_contrib/gmp/mpf/set_q.c, Revision 1.1

1.1     ! maekawa     1: /* mpf_set_q (mpf_t rop, mpq_t op) -- Convert the rational op to the float rop.
        !             2:
        !             3: Copyright (C) 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: void
        !            52: #if __STDC__
        !            53: mpf_set_q (mpf_t r, mpq_srcptr q)
        !            54: #else
        !            55: mpf_set_q (r, q)
        !            56:      mpf_t r;
        !            57:      mpq_srcptr q;
        !            58: #endif
        !            59: {
        !            60:   mp_ptr np, dp;
        !            61:   mp_ptr rp;
        !            62:   mp_size_t nsize, dsize;
        !            63:   mp_size_t qsize, rsize;
        !            64:   mp_size_t sign_quotient;
        !            65:   unsigned normalization_steps;
        !            66:   mp_limb_t qlimb;
        !            67:   mp_ptr qp;
        !            68:   mp_size_t prec;
        !            69:   mp_exp_t exp;
        !            70:   TMP_DECL (marker);
        !            71:
        !            72:   nsize = SIZ (&q->_mp_num);
        !            73:   dsize = SIZ (&q->_mp_den);
        !            74:
        !            75:   if (nsize == 0)
        !            76:     {
        !            77:       SIZ (r) = 0;
        !            78:       EXP (r) = 0;
        !            79:       return;
        !            80:     }
        !            81:
        !            82:   prec = PREC (r) + 1;
        !            83:
        !            84:   TMP_MARK (marker);
        !            85:
        !            86:   qp = PTR (r);
        !            87:
        !            88:   sign_quotient = nsize ^ dsize;
        !            89:   nsize = ABS (nsize);
        !            90:   dsize = ABS (dsize);
        !            91:   np = PTR (&q->_mp_num);
        !            92:   dp = PTR (&q->_mp_den);
        !            93:
        !            94:   exp = nsize - dsize;
        !            95:
        !            96:   if (nsize > prec)
        !            97:     {
        !            98:       np += nsize - prec;
        !            99:       nsize = prec;
        !           100:     }
        !           101:   if (dsize > prec)
        !           102:     {
        !           103:       dp += dsize - prec;
        !           104:       dsize = prec;
        !           105:     }
        !           106:
        !           107:   rsize = MAX (nsize, dsize);
        !           108:   rp = (mp_ptr) TMP_ALLOC ((rsize + 1) * BYTES_PER_MP_LIMB);
        !           109:
        !           110:   count_leading_zeros (normalization_steps, dp[dsize - 1]);
        !           111:
        !           112:   /* Normalize the denominator, i.e. make its most significant bit set by
        !           113:      shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
        !           114:      numerator the same number of steps (to keep the quotient the same!).  */
        !           115:   if (normalization_steps != 0)
        !           116:     {
        !           117:       mp_ptr tp;
        !           118:       mp_limb_t nlimb;
        !           119:
        !           120:       /* Shift up the denominator setting the most significant bit of
        !           121:         the most significant limb.  Use temporary storage not to clobber
        !           122:         the original contents of the denominator.  */
        !           123:       tp = (mp_ptr) TMP_ALLOC (dsize * BYTES_PER_MP_LIMB);
        !           124:       mpn_lshift (tp, dp, dsize, normalization_steps);
        !           125:       dp = tp;
        !           126:
        !           127:       if (rsize != nsize)
        !           128:        {
        !           129:          MPN_ZERO (rp, rsize - nsize);
        !           130:          nlimb = mpn_lshift (rp + (rsize - nsize),
        !           131:                              np, nsize, normalization_steps);
        !           132:        }
        !           133:       else
        !           134:        {
        !           135:          nlimb = mpn_lshift (rp, np, nsize, normalization_steps);
        !           136:        }
        !           137:       if (nlimb != 0)
        !           138:        {
        !           139:          rp[rsize] = nlimb;
        !           140:          rsize++;
        !           141:          exp++;
        !           142:        }
        !           143:     }
        !           144:   else
        !           145:     {
        !           146:       if (rsize != nsize)
        !           147:        {
        !           148:          MPN_ZERO (rp, rsize - nsize);
        !           149:          MPN_COPY (rp + (rsize - nsize), np, nsize);
        !           150:        }
        !           151:       else
        !           152:        {
        !           153:          MPN_COPY (rp, np, rsize);
        !           154:        }
        !           155:     }
        !           156:
        !           157:   qlimb = mpn_divrem (qp, prec - 1 - (rsize - dsize), rp, rsize, dp, dsize);
        !           158:   qsize = prec - 1;
        !           159:   if (qlimb)
        !           160:     {
        !           161:       qp[qsize] = qlimb;
        !           162:       qsize++;
        !           163:       exp++;
        !           164:     }
        !           165:
        !           166:   EXP (r) = exp;
        !           167:   SIZ (r) = qsize;
        !           168:
        !           169:   TMP_FREE (marker);
        !           170: }