1 /* mpfr_get_flt -- convert a mpfr_t to a machine single precision float 2 3 Copyright 2009-2020 Free Software Foundation, Inc. 4 Contributed by the AriC and Caramba 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 https://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 /* FIXME: The code below assumes the IEEE-754 binary32 format 53 with subnormal support. Fix it by converting to double, then 54 to float, and in case of binary radix (for which we want 55 correct rounding), handle double-rounding issues somewhere 56 in the code? */ 57 58 /* the smallest positive normal float number is 2^(-126) = 0.5*2^(-125), 59 and the smallest positive subnormal number is 2^(-149) = 0.5*2^(-148) */ 60 if (MPFR_UNLIKELY (e < -148)) 61 { 62 /* |src| < 2^(-149), i.e., |src| is smaller than the smallest positive 63 subnormal number. 64 In round-to-nearest mode, 2^(-150) is rounded to zero. 65 */ 66 d = negative ? 67 (rnd_mode == MPFR_RNDD || 68 (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, -1, -150) < 0) 69 ? -FLT_MIN : FLT_NEG_ZERO) : 70 (rnd_mode == MPFR_RNDU || 71 (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, 1, -150) > 0) 72 ? FLT_MIN : 0.0); 73 if (d != 0.0) /* we multiply FLT_MIN = 2^(-126) by FLT_EPSILON = 2^(-23) 74 to get +-2^(-149) */ 75 d *= FLT_EPSILON; 76 } 77 /* the largest normal number is 2^128*(1-2^(-24)) = 0.111...111e128 */ 78 else if (MPFR_UNLIKELY (e > 128)) 79 { 80 d = negative ? 81 (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDU ? 82 -FLT_MAX : MPFR_FLT_INFM) : 83 (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD ? 84 FLT_MAX : MPFR_FLT_INFP); 85 } 86 else /* -148 <= e <= 127 */ 87 { 88 int nbits; 89 mp_limb_t tp[MPFR_LIMBS_PER_FLT]; 90 int carry; 91 double dd; 92 93 nbits = IEEE_FLT_MANT_DIG; /* 24 */ 94 if (MPFR_UNLIKELY (e < -125)) 95 /*In the subnormal case, compute the exact number of significant bits*/ 96 { 97 nbits += 125 + e; 98 MPFR_ASSERTD (1 <= nbits && nbits < 24); 99 } 100 carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative, 101 nbits, rnd_mode); 102 /* we perform the reconstruction using the 'double' type here, 103 knowing the result is exactly representable as 'float' */ 104 if (MPFR_UNLIKELY(carry)) 105 dd = 1.0; 106 else 107 { 108 #if MPFR_LIMBS_PER_FLT == 1 109 dd = (double) tp[0] / MP_BASE_AS_DOUBLE; 110 #else 111 mp_size_t np, i; 112 np = MPFR_PREC2LIMBS (nbits); 113 MPFR_ASSERTD(np <= MPFR_LIMBS_PER_FLT); 114 /* The following computations are exact thanks to the previous 115 mpfr_round_raw. */ 116 dd = (double) tp[0] / MP_BASE_AS_DOUBLE; 117 for (i = 1 ; i < np ; i++) 118 dd = (dd + tp[i]) / MP_BASE_AS_DOUBLE; 119 /* dd is the mantissa (between 1/2 and 1) of the argument rounded 120 to 24 bits */ 121 #endif 122 } 123 dd = mpfr_scale2 (dd, e); 124 if (negative) 125 dd = -dd; 126 127 /* convert (exactly) to float */ 128 d = (float) dd; 129 } 130 131 return d; 132 } 133 134