1 /* Split a double into fraction and mantissa, for hexadecimal printf.
2 Copyright (C) 2007, 2009-2011 Free Software Foundation, Inc.
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.
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.
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/>. */
20 #ifdef USE_LONG_DOUBLE
21 # include "printf-frexpl.h"
23 # include "printf-frexp.h"
28 #ifdef USE_LONG_DOUBLE
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. */
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
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
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
58 # define DECL_ROUNDING
59 # define BEGIN_ROUNDING()
60 # define END_ROUNDING()
61 # define L_(literal) literal
65 FUNC (DOUBLE x, int *expptr)
72 #ifdef USE_FREXP_LDEXP
73 /* frexp and ldexp are usually faster than the loop below. */
74 x = FREXP (x, &exponent);
79 if (exponent < MIN_EXP - 1)
81 x = LDEXP (x, exponent - (MIN_EXP - 1));
82 exponent = MIN_EXP - 1;
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 */
95 /* A nonnegative exponent. */
97 DOUBLE pow2_i; /* = pow2[i] */
98 DOUBLE powh_i; /* = powh[i] */
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);
104 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
108 exponent += (1 << i);
118 /* Here 1.0 <= x < 2^2^i. */
122 /* A negative exponent. */
124 DOUBLE pow2_i; /* = pow2[i] */
125 DOUBLE powh_i; /* = powh[i] */
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);
131 i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
133 if (exponent - (1 << i) < MIN_EXP - 1)
136 exponent -= (1 << i);
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. */
149 /* Invariants: x * 2^exponent = argument, x < 1.0 and
150 exponent - 2^i < MIN_EXP - 1 <= exponent. */
154 if (exponent - (1 << i) >= MIN_EXP - 1)
156 exponent -= (1 << i);
163 /* Here either x < 1.0 and exponent = MIN_EXP - 1,
164 or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */
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. */
175 exponent += (1 << i);
179 /* Here either x < 1.0 and exponent = MIN_EXP - 1,
180 or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1. */