get_d.c revision 1.1.1.5
1/* mpfr_get_d, mpfr_get_d_2exp -- convert a multiple precision floating-point 2 number to a machine double precision float 3 4Copyright 1999-2023 Free Software Foundation, Inc. 5Contributed by the AriC and Caramba projects, INRIA. 6 7This file is part of the GNU MPFR Library. 8 9The GNU MPFR Library is free software; you can redistribute it and/or modify 10it under the terms of the GNU Lesser General Public License as published by 11the Free Software Foundation; either version 3 of the License, or (at your 12option) any later version. 13 14The GNU MPFR Library is distributed in the hope that it will be useful, but 15WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 16or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 17License for more details. 18 19You should have received a copy of the GNU Lesser General Public License 20along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 21https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2251 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 23 24#include <float.h> 25 26#define MPFR_NEED_LONGLONG_H 27#include "mpfr-impl.h" 28 29#include "ieee_floats.h" 30 31/* Assumes IEEE-754 double precision; otherwise, only an approximated 32 result will be returned, without any guaranty (and special cases 33 such as NaN must be avoided if not supported). */ 34 35double 36mpfr_get_d (mpfr_srcptr src, mpfr_rnd_t rnd_mode) 37{ 38 double d; 39 int negative; 40 mpfr_exp_t e; 41 42 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src))) 43 { 44 if (MPFR_IS_NAN (src)) 45 { 46 /* we don't propagate the sign bit */ 47 return MPFR_DBL_NAN; 48 } 49 50 negative = MPFR_IS_NEG (src); 51 52 if (MPFR_IS_INF (src)) 53 return negative ? MPFR_DBL_INFM : MPFR_DBL_INFP; 54 55 MPFR_ASSERTD (MPFR_IS_ZERO(src)); 56 return negative ? DBL_NEG_ZERO : 0.0; 57 } 58 59 e = MPFR_GET_EXP (src); 60 negative = MPFR_IS_NEG (src); 61 62 if (MPFR_UNLIKELY(rnd_mode == MPFR_RNDA)) 63 rnd_mode = negative ? MPFR_RNDD : MPFR_RNDU; 64 65 /* the smallest normalized number is 2^(-1022)=0.1e-1021, and the smallest 66 subnormal is 2^(-1074)=0.1e-1073 */ 67 if (MPFR_UNLIKELY (e < -1073)) 68 { 69 /* Note: Avoid using a constant expression DBL_MIN * DBL_EPSILON 70 as this gives 0 instead of the correct result with gcc on some 71 Alpha machines. */ 72 d = negative ? 73 (rnd_mode == MPFR_RNDD || 74 (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp(src, -1, -1075) < 0) 75 ? -DBL_MIN : DBL_NEG_ZERO) : 76 (rnd_mode == MPFR_RNDU || 77 (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp(src, 1, -1075) > 0) 78 ? DBL_MIN : 0.0); 79 if (d != 0.0) /* we multiply DBL_MIN = 2^(-1022) by DBL_EPSILON = 2^(-52) 80 to get +-2^(-1074) */ 81 d *= DBL_EPSILON; 82 } 83 /* the largest normalized number is 2^1024*(1-2^(-53))=0.111...111e1024 */ 84 else if (MPFR_UNLIKELY (e > 1024)) 85 { 86 d = negative ? 87 (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDU ? 88 -DBL_MAX : MPFR_DBL_INFM) : 89 (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD ? 90 DBL_MAX : MPFR_DBL_INFP); 91 } 92 else 93 { 94 int nbits; 95 mp_limb_t tp[ MPFR_LIMBS_PER_DOUBLE ]; 96 int carry; 97 98 nbits = IEEE_DBL_MANT_DIG; /* 53 */ 99 if (MPFR_UNLIKELY (e < -1021)) 100 /*In the subnormal case, compute the exact number of significant bits*/ 101 { 102 nbits += 1021 + e; 103 MPFR_ASSERTD (1 <= nbits && nbits < IEEE_DBL_MANT_DIG); 104 } 105 carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative, 106 nbits, rnd_mode); 107 if (MPFR_UNLIKELY(carry)) 108 d = 1.0; 109 else 110 { 111#if MPFR_LIMBS_PER_DOUBLE == 1 112 d = (double) tp[0] / MP_BASE_AS_DOUBLE; 113#else 114 mp_size_t np, i; 115 MPFR_ASSERTD (nbits <= IEEE_DBL_MANT_DIG); 116 np = MPFR_PREC2LIMBS (nbits); 117 MPFR_ASSERTD ( np <= MPFR_LIMBS_PER_DOUBLE ); 118 /* The following computations are exact thanks to the previous 119 mpfr_round_raw. */ 120 d = (double) tp[0] / MP_BASE_AS_DOUBLE; 121 for (i = 1 ; i < np ; i++) 122 d = (d + tp[i]) / MP_BASE_AS_DOUBLE; 123 /* d is the mantissa (between 1/2 and 1) of the argument rounded 124 to 53 bits */ 125#endif 126 } 127 d = mpfr_scale2 (d, e); 128 if (negative) 129 d = -d; 130 } 131 132 return d; 133} 134 135#undef mpfr_get_d1 136double 137mpfr_get_d1 (mpfr_srcptr src) 138{ 139 return mpfr_get_d (src, __gmpfr_default_rounding_mode); 140} 141 142double 143mpfr_get_d_2exp (long *expptr, mpfr_srcptr src, mpfr_rnd_t rnd_mode) 144{ 145 double ret; 146 mpfr_exp_t exp; 147 mpfr_t tmp; 148 149 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src))) 150 { 151 int negative; 152 *expptr = 0; 153 if (MPFR_IS_NAN (src)) 154 { 155 /* we don't propagate the sign bit */ 156 return MPFR_DBL_NAN; 157 } 158 negative = MPFR_IS_NEG (src); 159 if (MPFR_IS_INF (src)) 160 return negative ? MPFR_DBL_INFM : MPFR_DBL_INFP; 161 MPFR_ASSERTD (MPFR_IS_ZERO(src)); 162 return negative ? DBL_NEG_ZERO : 0.0; 163 } 164 165 MPFR_ALIAS (tmp, src, MPFR_SIGN (src), 0); 166 ret = mpfr_get_d (tmp, rnd_mode); 167 168 exp = MPFR_GET_EXP (src); 169 170 /* rounding can give 1.0, adjust back to 0.5 <= abs(ret) < 1.0 */ 171 if (ret == 1.0) 172 { 173 ret = 0.5; 174 exp++; 175 } 176 else if (ret == -1.0) 177 { 178 ret = -0.5; 179 exp++; 180 } 181 182 MPFR_ASSERTN ((ret >= 0.5 && ret < 1.0) 183 || (ret <= -0.5 && ret > -1.0)); 184 MPFR_ASSERTN (exp >= LONG_MIN && exp <= LONG_MAX); 185 186 *expptr = exp; 187 return ret; 188} 189