1*1424dfb3Schristos /* Split a double into fraction and mantissa.
2*1424dfb3Schristos Copyright (C) 2007-2020 Free Software Foundation, Inc.
3*1424dfb3Schristos
4*1424dfb3Schristos This program is free software: you can redistribute it and/or modify
5*1424dfb3Schristos it under the terms of the GNU General Public License as published by
6*1424dfb3Schristos the Free Software Foundation; either version 3 of the License, or
7*1424dfb3Schristos (at your option) any later version.
8*1424dfb3Schristos
9*1424dfb3Schristos This program is distributed in the hope that it will be useful,
10*1424dfb3Schristos but WITHOUT ANY WARRANTY; without even the implied warranty of
11*1424dfb3Schristos MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12*1424dfb3Schristos GNU General Public License for more details.
13*1424dfb3Schristos
14*1424dfb3Schristos You should have received a copy of the GNU General Public License
15*1424dfb3Schristos along with this program. If not, see <https://www.gnu.org/licenses/>. */
16*1424dfb3Schristos
17*1424dfb3Schristos /* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and
18*1424dfb3Schristos Bruno Haible <bruno@clisp.org>, 2007. */
19*1424dfb3Schristos
20*1424dfb3Schristos #if ! defined USE_LONG_DOUBLE
21*1424dfb3Schristos # include <config.h>
22*1424dfb3Schristos #endif
23*1424dfb3Schristos
24*1424dfb3Schristos /* Specification. */
25*1424dfb3Schristos #include <math.h>
26*1424dfb3Schristos
27*1424dfb3Schristos #include <float.h>
28*1424dfb3Schristos #ifdef USE_LONG_DOUBLE
29*1424dfb3Schristos # include "isnanl-nolibm.h"
30*1424dfb3Schristos # include "fpucw.h"
31*1424dfb3Schristos #else
32*1424dfb3Schristos # include "isnand-nolibm.h"
33*1424dfb3Schristos #endif
34*1424dfb3Schristos
35*1424dfb3Schristos /* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater
36*1424dfb3Schristos than 2, or not even a power of 2, some rounding errors can occur, so that
37*1424dfb3Schristos then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0. */
38*1424dfb3Schristos
39*1424dfb3Schristos #ifdef USE_LONG_DOUBLE
40*1424dfb3Schristos # define FUNC frexpl
41*1424dfb3Schristos # define DOUBLE long double
42*1424dfb3Schristos # define ISNAN isnanl
43*1424dfb3Schristos # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING
44*1424dfb3Schristos # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()
45*1424dfb3Schristos # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()
46*1424dfb3Schristos # define L_(literal) literal##L
47*1424dfb3Schristos #else
48*1424dfb3Schristos # define FUNC frexp
49*1424dfb3Schristos # define DOUBLE double
50*1424dfb3Schristos # define ISNAN isnand
51*1424dfb3Schristos # define DECL_ROUNDING
52*1424dfb3Schristos # define BEGIN_ROUNDING()
53*1424dfb3Schristos # define END_ROUNDING()
54*1424dfb3Schristos # define L_(literal) literal
55*1424dfb3Schristos #endif
56*1424dfb3Schristos
57*1424dfb3Schristos DOUBLE
FUNC(DOUBLE x,int * expptr)58*1424dfb3Schristos FUNC (DOUBLE x, int *expptr)
59*1424dfb3Schristos {
60*1424dfb3Schristos int sign;
61*1424dfb3Schristos int exponent;
62*1424dfb3Schristos DECL_ROUNDING
63*1424dfb3Schristos
64*1424dfb3Schristos /* Test for NaN, infinity, and zero. */
65*1424dfb3Schristos if (ISNAN (x) || x + x == x)
66*1424dfb3Schristos {
67*1424dfb3Schristos *expptr = 0;
68*1424dfb3Schristos return x;
69*1424dfb3Schristos }
70*1424dfb3Schristos
71*1424dfb3Schristos sign = 0;
72*1424dfb3Schristos if (x < 0)
73*1424dfb3Schristos {
74*1424dfb3Schristos x = - x;
75*1424dfb3Schristos sign = -1;
76*1424dfb3Schristos }
77*1424dfb3Schristos
78*1424dfb3Schristos BEGIN_ROUNDING ();
79*1424dfb3Schristos
80*1424dfb3Schristos {
81*1424dfb3Schristos /* Since the exponent is an 'int', it fits in 64 bits. Therefore the
82*1424dfb3Schristos loops are executed no more than 64 times. */
83*1424dfb3Schristos DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
84*1424dfb3Schristos DOUBLE powh[64]; /* powh[i] = 2^-2^i */
85*1424dfb3Schristos int i;
86*1424dfb3Schristos
87*1424dfb3Schristos exponent = 0;
88*1424dfb3Schristos if (x >= L_(1.0))
89*1424dfb3Schristos {
90*1424dfb3Schristos /* A positive exponent. */
91*1424dfb3Schristos DOUBLE pow2_i; /* = pow2[i] */
92*1424dfb3Schristos DOUBLE powh_i; /* = powh[i] */
93*1424dfb3Schristos
94*1424dfb3Schristos /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
95*1424dfb3Schristos x * 2^exponent = argument, x >= 1.0. */
96*1424dfb3Schristos for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
97*1424dfb3Schristos ;
98*1424dfb3Schristos i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
99*1424dfb3Schristos {
100*1424dfb3Schristos if (x >= pow2_i)
101*1424dfb3Schristos {
102*1424dfb3Schristos exponent += (1 << i);
103*1424dfb3Schristos x *= powh_i;
104*1424dfb3Schristos }
105*1424dfb3Schristos else
106*1424dfb3Schristos break;
107*1424dfb3Schristos
108*1424dfb3Schristos pow2[i] = pow2_i;
109*1424dfb3Schristos powh[i] = powh_i;
110*1424dfb3Schristos }
111*1424dfb3Schristos /* Avoid making x too small, as it could become a denormalized
112*1424dfb3Schristos number and thus lose precision. */
113*1424dfb3Schristos while (i > 0 && x < pow2[i - 1])
114*1424dfb3Schristos {
115*1424dfb3Schristos i--;
116*1424dfb3Schristos powh_i = powh[i];
117*1424dfb3Schristos }
118*1424dfb3Schristos exponent += (1 << i);
119*1424dfb3Schristos x *= powh_i;
120*1424dfb3Schristos /* Here 2^-2^i <= x < 1.0. */
121*1424dfb3Schristos }
122*1424dfb3Schristos else
123*1424dfb3Schristos {
124*1424dfb3Schristos /* A negative or zero exponent. */
125*1424dfb3Schristos DOUBLE pow2_i; /* = pow2[i] */
126*1424dfb3Schristos DOUBLE powh_i; /* = powh[i] */
127*1424dfb3Schristos
128*1424dfb3Schristos /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
129*1424dfb3Schristos x * 2^exponent = argument, x < 1.0. */
130*1424dfb3Schristos for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
131*1424dfb3Schristos ;
132*1424dfb3Schristos i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
133*1424dfb3Schristos {
134*1424dfb3Schristos if (x < powh_i)
135*1424dfb3Schristos {
136*1424dfb3Schristos exponent -= (1 << i);
137*1424dfb3Schristos x *= pow2_i;
138*1424dfb3Schristos }
139*1424dfb3Schristos else
140*1424dfb3Schristos break;
141*1424dfb3Schristos
142*1424dfb3Schristos pow2[i] = pow2_i;
143*1424dfb3Schristos powh[i] = powh_i;
144*1424dfb3Schristos }
145*1424dfb3Schristos /* Here 2^-2^i <= x < 1.0. */
146*1424dfb3Schristos }
147*1424dfb3Schristos
148*1424dfb3Schristos /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */
149*1424dfb3Schristos while (i > 0)
150*1424dfb3Schristos {
151*1424dfb3Schristos i--;
152*1424dfb3Schristos if (x < powh[i])
153*1424dfb3Schristos {
154*1424dfb3Schristos exponent -= (1 << i);
155*1424dfb3Schristos x *= pow2[i];
156*1424dfb3Schristos }
157*1424dfb3Schristos }
158*1424dfb3Schristos /* Here 0.5 <= x < 1.0. */
159*1424dfb3Schristos }
160*1424dfb3Schristos
161*1424dfb3Schristos if (sign < 0)
162*1424dfb3Schristos x = - x;
163*1424dfb3Schristos
164*1424dfb3Schristos END_ROUNDING ();
165*1424dfb3Schristos
166*1424dfb3Schristos *expptr = exponent;
167*1424dfb3Schristos return x;
168*1424dfb3Schristos }
169