1 /* Split a double into fraction and mantissa, for hexadecimal printf. 2 Copyright (C) 2007, 2009-2012 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 #if ! defined USE_LONG_DOUBLE 18 # include <config.h> 19 #endif 20 21 /* Specification. */ 22 #ifdef USE_LONG_DOUBLE 23 # include "printf-frexpl.h" 24 #else 25 # include "printf-frexp.h" 26 #endif 27 28 #include <float.h> 29 #include <math.h> 30 #ifdef USE_LONG_DOUBLE 31 # include "fpucw.h" 32 #endif 33 34 /* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater 35 than 2, or not even a power of 2, some rounding errors can occur, so that 36 then the returned mantissa is only guaranteed to be <= 2.0, not < 2.0. */ 37 38 #ifdef USE_LONG_DOUBLE 39 # define FUNC printf_frexpl 40 # define DOUBLE long double 41 # define MIN_EXP LDBL_MIN_EXP 42 # if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC 43 # define USE_FREXP_LDEXP 44 # define FREXP frexpl 45 # define LDEXP ldexpl 46 # endif 47 # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING 48 # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING () 49 # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING () 50 # define L_(literal) literal##L 51 #else 52 # define FUNC printf_frexp 53 # define DOUBLE double 54 # define MIN_EXP DBL_MIN_EXP 55 # if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC 56 # define USE_FREXP_LDEXP 57 # define FREXP frexp 58 # define LDEXP ldexp 59 # endif 60 # define DECL_ROUNDING 61 # define BEGIN_ROUNDING() 62 # define END_ROUNDING() 63 # define L_(literal) literal 64 #endif 65 66 DOUBLE 67 FUNC (DOUBLE x, int *expptr) 68 { 69 int exponent; 70 DECL_ROUNDING 71 72 BEGIN_ROUNDING (); 73 74 #ifdef USE_FREXP_LDEXP 75 /* frexp and ldexp are usually faster than the loop below. */ 76 x = FREXP (x, &exponent); 77 78 x = x + x; 79 exponent -= 1; 80 81 if (exponent < MIN_EXP - 1) 82 { 83 x = LDEXP (x, exponent - (MIN_EXP - 1)); 84 exponent = MIN_EXP - 1; 85 } 86 #else 87 { 88 /* Since the exponent is an 'int', it fits in 64 bits. Therefore the 89 loops are executed no more than 64 times. */ 90 DOUBLE pow2[64]; /* pow2[i] = 2^2^i */ 91 DOUBLE powh[64]; /* powh[i] = 2^-2^i */ 92 int i; 93 94 exponent = 0; 95 if (x >= L_(1.0)) 96 { 97 /* A nonnegative exponent. */ 98 { 99 DOUBLE pow2_i; /* = pow2[i] */ 100 DOUBLE powh_i; /* = powh[i] */ 101 102 /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 103 x * 2^exponent = argument, x >= 1.0. */ 104 for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 105 ; 106 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 107 { 108 if (x >= pow2_i) 109 { 110 exponent += (1 << i); 111 x *= powh_i; 112 } 113 else 114 break; 115 116 pow2[i] = pow2_i; 117 powh[i] = powh_i; 118 } 119 } 120 /* Here 1.0 <= x < 2^2^i. */ 121 } 122 else 123 { 124 /* A negative exponent. */ 125 { 126 DOUBLE pow2_i; /* = pow2[i] */ 127 DOUBLE powh_i; /* = powh[i] */ 128 129 /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 130 x * 2^exponent = argument, x < 1.0, exponent >= MIN_EXP - 1. */ 131 for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 132 ; 133 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 134 { 135 if (exponent - (1 << i) < MIN_EXP - 1) 136 break; 137 138 exponent -= (1 << i); 139 x *= pow2_i; 140 if (x >= L_(1.0)) 141 break; 142 143 pow2[i] = pow2_i; 144 powh[i] = powh_i; 145 } 146 } 147 /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent, 148 or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 149 150 if (x < L_(1.0)) 151 /* Invariants: x * 2^exponent = argument, x < 1.0 and 152 exponent - 2^i < MIN_EXP - 1 <= exponent. */ 153 while (i > 0) 154 { 155 i--; 156 if (exponent - (1 << i) >= MIN_EXP - 1) 157 { 158 exponent -= (1 << i); 159 x *= pow2[i]; 160 if (x >= L_(1.0)) 161 break; 162 } 163 } 164 165 /* Here either x < 1.0 and exponent = MIN_EXP - 1, 166 or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 167 } 168 169 /* Invariants: x * 2^exponent = argument, and 170 either x < 1.0 and exponent = MIN_EXP - 1, 171 or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 172 while (i > 0) 173 { 174 i--; 175 if (x >= pow2[i]) 176 { 177 exponent += (1 << i); 178 x *= powh[i]; 179 } 180 } 181 /* Here either x < 1.0 and exponent = MIN_EXP - 1, 182 or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1. */ 183 } 184 #endif 185 186 END_ROUNDING (); 187 188 *expptr = exponent; 189 return x; 190 } 191
