1 /* Split a double into fraction and mantissa. 2 Copyright (C) 2007-2012 Free Software Foundation, Inc. 3 4 This program is free software: you can redistribute it and/or modify 5 it under the terms of the GNU General Public License as published by 6 the Free Software Foundation; either version 3 of the License, or 7 (at your option) any later version. 8 9 This program is distributed in the hope that it will be useful, 10 but WITHOUT ANY WARRANTY; without even the implied warranty of 11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 GNU General Public License for more details. 13 14 You should have received a copy of the GNU General Public License 15 along with this program. If not, see <http://www.gnu.org/licenses/>. */ 16 17 /* Written by Paolo Bonzini <bonzini (at) gnu.org>, 2003, and 18 Bruno Haible <bruno (at) clisp.org>, 2007. */ 19 20 #if ! defined USE_LONG_DOUBLE 21 # include <config.h> 22 #endif 23 24 /* Specification. */ 25 #include <math.h> 26 27 #include <float.h> 28 #ifdef USE_LONG_DOUBLE 29 # include "isnanl-nolibm.h" 30 # include "fpucw.h" 31 #else 32 # include "isnand-nolibm.h" 33 #endif 34 35 /* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater 36 than 2, or not even a power of 2, some rounding errors can occur, so that 37 then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0. */ 38 39 #ifdef USE_LONG_DOUBLE 40 # define FUNC frexpl 41 # define DOUBLE long double 42 # define ISNAN isnanl 43 # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING 44 # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING () 45 # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING () 46 # define L_(literal) literal##L 47 #else 48 # define FUNC frexp 49 # define DOUBLE double 50 # define ISNAN isnand 51 # define DECL_ROUNDING 52 # define BEGIN_ROUNDING() 53 # define END_ROUNDING() 54 # define L_(literal) literal 55 #endif 56 57 DOUBLE 58 FUNC (DOUBLE x, int *expptr) 59 { 60 int sign; 61 int exponent; 62 DECL_ROUNDING 63 64 /* Test for NaN, infinity, and zero. */ 65 if (ISNAN (x) || x + x == x) 66 { 67 *expptr = 0; 68 return x; 69 } 70 71 sign = 0; 72 if (x < 0) 73 { 74 x = - x; 75 sign = -1; 76 } 77 78 BEGIN_ROUNDING (); 79 80 { 81 /* Since the exponent is an 'int', it fits in 64 bits. Therefore the 82 loops are executed no more than 64 times. */ 83 DOUBLE pow2[64]; /* pow2[i] = 2^2^i */ 84 DOUBLE powh[64]; /* powh[i] = 2^-2^i */ 85 int i; 86 87 exponent = 0; 88 if (x >= L_(1.0)) 89 { 90 /* A positive exponent. */ 91 DOUBLE pow2_i; /* = pow2[i] */ 92 DOUBLE powh_i; /* = powh[i] */ 93 94 /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 95 x * 2^exponent = argument, x >= 1.0. */ 96 for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 97 ; 98 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 99 { 100 if (x >= pow2_i) 101 { 102 exponent += (1 << i); 103 x *= powh_i; 104 } 105 else 106 break; 107 108 pow2[i] = pow2_i; 109 powh[i] = powh_i; 110 } 111 /* Avoid making x too small, as it could become a denormalized 112 number and thus lose precision. */ 113 while (i > 0 && x < pow2[i - 1]) 114 { 115 i--; 116 powh_i = powh[i]; 117 } 118 exponent += (1 << i); 119 x *= powh_i; 120 /* Here 2^-2^i <= x < 1.0. */ 121 } 122 else 123 { 124 /* A negative or zero exponent. */ 125 DOUBLE pow2_i; /* = pow2[i] */ 126 DOUBLE powh_i; /* = powh[i] */ 127 128 /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 129 x * 2^exponent = argument, x < 1.0. */ 130 for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 131 ; 132 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 133 { 134 if (x < powh_i) 135 { 136 exponent -= (1 << i); 137 x *= pow2_i; 138 } 139 else 140 break; 141 142 pow2[i] = pow2_i; 143 powh[i] = powh_i; 144 } 145 /* Here 2^-2^i <= x < 1.0. */ 146 } 147 148 /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */ 149 while (i > 0) 150 { 151 i--; 152 if (x < powh[i]) 153 { 154 exponent -= (1 << i); 155 x *= pow2[i]; 156 } 157 } 158 /* Here 0.5 <= x < 1.0. */ 159 } 160 161 if (sign < 0) 162 x = - x; 163 164 END_ROUNDING (); 165 166 *expptr = exponent; 167 return x; 168 } 169
