1 /* mpfr_get_flt -- convert a mpfr_t to a machine single precision float 2 3 Copyright 2009, 2010, 2011 Free Software Foundation, Inc. 4 Contributed by the Arenaire and Caramel projects, INRIA. 5 6 This file is part of the GNU MPFR Library. 7 8 The GNU MPFR Library is free software; you can redistribute it and/or modify 9 it under the terms of the GNU Lesser General Public License as published by 10 the Free Software Foundation; either version 3 of the License, or (at your 11 option) any later version. 12 13 The GNU MPFR 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 Lesser General Public 16 License for more details. 17 18 You should have received a copy of the GNU Lesser General Public License 19 along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23 #include <float.h> /* for FLT_MIN */ 24 25 #define MPFR_NEED_LONGLONG_H 26 #include "mpfr-impl.h" 27 28 #include "ieee_floats.h" 29 30 #define FLT_NEG_ZERO ((float) DBL_NEG_ZERO) 31 #define MPFR_FLT_INFM ((float) MPFR_DBL_INFM) 32 #define MPFR_FLT_INFP ((float) MPFR_DBL_INFP) 33 34 float 35 mpfr_get_flt (mpfr_srcptr src, mpfr_rnd_t rnd_mode) 36 { 37 int negative; 38 mpfr_exp_t e; 39 float d; 40 41 /* in case of NaN, +Inf, -Inf, +0, -0, the conversion from double to float 42 is exact */ 43 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src))) 44 return (float) mpfr_get_d (src, rnd_mode); 45 46 e = MPFR_GET_EXP (src); 47 negative = MPFR_IS_NEG (src); 48 49 if (MPFR_UNLIKELY(rnd_mode == MPFR_RNDA)) 50 rnd_mode = negative ? MPFR_RNDD : MPFR_RNDU; 51 52 /* the smallest positive normal float number is 2^(-126) = 0.5*2^(-125), 53 and the smallest positive subnormal number is 2^(-149) = 0.5*2^(-148) */ 54 if (MPFR_UNLIKELY (e < -148)) 55 { 56 /* |src| < 2^(-149), i.e., |src| is smaller than the smallest positive 57 subnormal number. 58 In round-to-nearest mode, 2^(-150) is rounded to zero. 59 */ 60 d = negative ? 61 (rnd_mode == MPFR_RNDD || 62 (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, -1, -150) < 0) 63 ? -FLT_MIN : FLT_NEG_ZERO) : 64 (rnd_mode == MPFR_RNDU || 65 (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, 1, -150) > 0) 66 ? FLT_MIN : 0.0); 67 if (d != 0.0) /* we multiply FLT_MIN = 2^(-126) by FLT_EPSILON = 2^(-23) 68 to get +-2^(-149) */ 69 d *= FLT_EPSILON; 70 } 71 /* the largest normal number is 2^128*(1-2^(-24)) = 0.111...111e128 */ 72 else if (MPFR_UNLIKELY (e > 128)) 73 { 74 d = negative ? 75 (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDU ? 76 -FLT_MAX : MPFR_FLT_INFM) : 77 (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD ? 78 FLT_MAX : MPFR_FLT_INFP); 79 } 80 else /* -148 <= e <= 127 */ 81 { 82 int nbits; 83 mp_size_t np, i; 84 mp_limb_t tp[MPFR_LIMBS_PER_FLT]; 85 int carry; 86 double dd; 87 88 nbits = IEEE_FLT_MANT_DIG; /* 24 */ 89 if (MPFR_UNLIKELY (e < -125)) 90 /*In the subnormal case, compute the exact number of significant bits*/ 91 { 92 nbits += (125 + e); 93 MPFR_ASSERTD (nbits >= 1); 94 } 95 np = (nbits + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS; 96 MPFR_ASSERTD(np <= MPFR_LIMBS_PER_FLT); 97 carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative, 98 nbits, rnd_mode); 99 /* we perform the reconstruction using the 'double' type here, 100 knowing the result is exactly representable as 'float' */ 101 if (MPFR_UNLIKELY(carry)) 102 dd = 1.0; 103 else 104 { 105 /* The following computations are exact thanks to the previous 106 mpfr_round_raw. */ 107 dd = (double) tp[0] / MP_BASE_AS_DOUBLE; 108 for (i = 1 ; i < np ; i++) 109 dd = (dd + tp[i]) / MP_BASE_AS_DOUBLE; 110 /* dd is the mantissa (between 1/2 and 1) of the argument rounded 111 to 24 bits */ 112 } 113 dd = mpfr_scale2 (dd, e); 114 if (negative) 115 dd = -dd; 116 117 /* convert (exacly) to float */ 118 d = (float) dd; 119 } 120 121 return d; 122 } 123 124