/* double mpq_get_d (mpq_t src) -- Return the double approximation to SRC. Copyright (C) 1995, 1996 Free Software Foundation, Inc. This file is part of the GNU MP Library. The GNU MP Library is free software; you can redistribute it and/or modify it under the terms of the GNU Library General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. The GNU MP Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more details. You should have received a copy of the GNU Library General Public License along with the GNU MP Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include "gmp.h" #include "gmp-impl.h" #include "longlong.h" /* Algorithm: 1. Develop >= n bits of src.num / src.den, where n is the number of bits in a double. This (partial) division will use all bits from the denominator. 2. Use the remainder to determine how to round the result. 3. Assign the integral result to a temporary double. 4. Scale the temporary double, and return the result. An alternative algorithm, that would be faster: 0. Let n be somewhat larger than the number of significant bits in a double. 1. Extract the most significant n bits of the denominator, and an equal number of bits from the numerator. 2. Interpret the extracted numbers as integers, call them a and b respectively, and develop n bits of the fractions ((a + 1) / b) and (a / (b + 1)) using mpn_divrem. 3. If the computed values are identical UP TO THE POSITION WE CARE ABOUT, we are done. If they are different, repeat the algorithm from step 1, but first let n = n * 2. 4. If we end up using all bits from the numerator and denominator, fall back to the first algorithm above. 5. Just to make life harder, The computation of a + 1 and b + 1 above might give carry-out... Needs special handling. It might work to subtract 1 in both cases instead. */ double #if __STDC__ mpq_get_d (const MP_RAT *src) #else mpq_get_d (src) const MP_RAT *src; #endif { mp_ptr np, dp; mp_ptr rp; mp_size_t nsize = src->_mp_num._mp_size; mp_size_t dsize = src->_mp_den._mp_size; mp_size_t qsize, rsize; mp_size_t sign_quotient = nsize ^ dsize; unsigned normalization_steps; mp_limb_t qlimb; #define N_QLIMBS (1 + (sizeof (double) + BYTES_PER_MP_LIMB-1) / BYTES_PER_MP_LIMB) mp_limb_t qp[N_QLIMBS + 1]; TMP_DECL (marker); if (nsize == 0) return 0.0; TMP_MARK (marker); nsize = ABS (nsize); dsize = ABS (dsize); np = src->_mp_num._mp_d; dp = src->_mp_den._mp_d; rsize = dsize + N_QLIMBS; rp = (mp_ptr) TMP_ALLOC ((rsize + 1) * BYTES_PER_MP_LIMB); count_leading_zeros (normalization_steps, dp[dsize - 1]); /* Normalize the denominator, i.e. make its most significant bit set by shifting it NORMALIZATION_STEPS bits to the left. Also shift the numerator the same number of steps (to keep the quotient the same!). */ if (normalization_steps != 0) { mp_ptr tp; mp_limb_t nlimb; /* Shift up the denominator setting the most significant bit of the most significant limb. Use temporary storage not to clobber the original contents of the denominator. */ tp = (mp_ptr) TMP_ALLOC (dsize * BYTES_PER_MP_LIMB); mpn_lshift (tp, dp, dsize, normalization_steps); dp = tp; if (rsize > nsize) { MPN_ZERO (rp, rsize - nsize); nlimb = mpn_lshift (rp + (rsize - nsize), np, nsize, normalization_steps); } else { nlimb = mpn_lshift (rp, np + (nsize - rsize), rsize, normalization_steps); } if (nlimb != 0) { rp[rsize] = nlimb; rsize++; } } else { if (rsize > nsize) { MPN_ZERO (rp, rsize - nsize); MPN_COPY (rp + (rsize - nsize), np, nsize); } else { MPN_COPY (rp, np + (nsize - rsize), rsize); } } qlimb = mpn_divmod (qp, rp, rsize, dp, dsize); qsize = rsize - dsize; if (qlimb) { qp[qsize] = qlimb; qsize++; } { double res; mp_size_t i; res = qp[qsize - 1]; for (i = qsize - 2; i >= 0; i--) res = res * MP_BASE_AS_DOUBLE + qp[i]; res = __gmp_scale2 (res, BITS_PER_MP_LIMB * (nsize - dsize - N_QLIMBS)); TMP_FREE (marker); return sign_quotient >= 0 ? res : -res; } }