1/* Split a double into fraction and mantissa, for hexadecimal printf. 2 Copyright (C) 2007, 2009, 2010 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 Lesser 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 Lesser General Public License for more details. 13 14 You should have received a copy of the GNU Lesser General Public License 15 along with this program. If not, see <http://www.gnu.org/licenses/>. */ 16 17#include <config.h> 18 19/* Specification. */ 20#ifdef USE_LONG_DOUBLE 21# include "printf-frexpl.h" 22#else 23# include "printf-frexp.h" 24#endif 25 26#include <float.h> 27#include <math.h> 28#ifdef USE_LONG_DOUBLE 29# include "fpucw.h" 30#endif 31 32/* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater 33 than 2, or not even a power of 2, some rounding errors can occur, so that 34 then the returned mantissa is only guaranteed to be <= 2.0, not < 2.0. */ 35 36#ifdef USE_LONG_DOUBLE 37# define FUNC printf_frexpl 38# define DOUBLE long double 39# define MIN_EXP LDBL_MIN_EXP 40# if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC 41# define USE_FREXP_LDEXP 42# define FREXP frexpl 43# define LDEXP ldexpl 44# endif 45# define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING 46# define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING () 47# define END_ROUNDING() END_LONG_DOUBLE_ROUNDING () 48# define L_(literal) literal##L 49#else 50# define FUNC printf_frexp 51# define DOUBLE double 52# define MIN_EXP DBL_MIN_EXP 53# if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC 54# define USE_FREXP_LDEXP 55# define FREXP frexp 56# define LDEXP ldexp 57# endif 58# define DECL_ROUNDING 59# define BEGIN_ROUNDING() 60# define END_ROUNDING() 61# define L_(literal) literal 62#endif 63 64DOUBLE 65FUNC (DOUBLE x, int *expptr) 66{ 67 int exponent; 68 DECL_ROUNDING 69 70 BEGIN_ROUNDING (); 71 72#ifdef USE_FREXP_LDEXP 73 /* frexp and ldexp are usually faster than the loop below. */ 74 x = FREXP (x, &exponent); 75 76 x = x + x; 77 exponent -= 1; 78 79 if (exponent < MIN_EXP - 1) 80 { 81 x = LDEXP (x, exponent - (MIN_EXP - 1)); 82 exponent = MIN_EXP - 1; 83 } 84#else 85 { 86 /* Since the exponent is an 'int', it fits in 64 bits. Therefore the 87 loops are executed no more than 64 times. */ 88 DOUBLE pow2[64]; /* pow2[i] = 2^2^i */ 89 DOUBLE powh[64]; /* powh[i] = 2^-2^i */ 90 int i; 91 92 exponent = 0; 93 if (x >= L_(1.0)) 94 { 95 /* A nonnegative exponent. */ 96 { 97 DOUBLE pow2_i; /* = pow2[i] */ 98 DOUBLE powh_i; /* = powh[i] */ 99 100 /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 101 x * 2^exponent = argument, x >= 1.0. */ 102 for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 103 ; 104 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 105 { 106 if (x >= pow2_i) 107 { 108 exponent += (1 << i); 109 x *= powh_i; 110 } 111 else 112 break; 113 114 pow2[i] = pow2_i; 115 powh[i] = powh_i; 116 } 117 } 118 /* Here 1.0 <= x < 2^2^i. */ 119 } 120 else 121 { 122 /* A negative exponent. */ 123 { 124 DOUBLE pow2_i; /* = pow2[i] */ 125 DOUBLE powh_i; /* = powh[i] */ 126 127 /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, 128 x * 2^exponent = argument, x < 1.0, exponent >= MIN_EXP - 1. */ 129 for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); 130 ; 131 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) 132 { 133 if (exponent - (1 << i) < MIN_EXP - 1) 134 break; 135 136 exponent -= (1 << i); 137 x *= pow2_i; 138 if (x >= L_(1.0)) 139 break; 140 141 pow2[i] = pow2_i; 142 powh[i] = powh_i; 143 } 144 } 145 /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent, 146 or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 147 148 if (x < L_(1.0)) 149 /* Invariants: x * 2^exponent = argument, x < 1.0 and 150 exponent - 2^i < MIN_EXP - 1 <= exponent. */ 151 while (i > 0) 152 { 153 i--; 154 if (exponent - (1 << i) >= MIN_EXP - 1) 155 { 156 exponent -= (1 << i); 157 x *= pow2[i]; 158 if (x >= L_(1.0)) 159 break; 160 } 161 } 162 163 /* Here either x < 1.0 and exponent = MIN_EXP - 1, 164 or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 165 } 166 167 /* Invariants: x * 2^exponent = argument, and 168 either x < 1.0 and exponent = MIN_EXP - 1, 169 or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */ 170 while (i > 0) 171 { 172 i--; 173 if (x >= pow2[i]) 174 { 175 exponent += (1 << i); 176 x *= powh[i]; 177 } 178 } 179 /* Here either x < 1.0 and exponent = MIN_EXP - 1, 180 or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1. */ 181 } 182#endif 183 184 END_ROUNDING (); 185 186 *expptr = exponent; 187 return x; 188} 189