Update.
[glibc.git] / sysdeps / libm-ieee754 / e_expf.c
blobe8a9c9d8747fc959030dc91bbcd81d2421f282ef
1 /* Single-precision floating point e^x.
2 Copyright (C) 1997, 1998 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Library General Public License as
8 published by the Free Software Foundation; either version 2 of the
9 License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Library General Public License for more details.
16 You should have received a copy of the GNU Library General Public
17 License along with the GNU C Library; see the file COPYING.LIB. If not,
18 write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
19 Boston, MA 02111-1307, USA. */
21 /* How this works:
23 The input value, x, is written as
25 x = n * ln(2) + t/512 + delta[t] + x;
27 where:
28 - n is an integer, 127 >= n >= -150;
29 - t is an integer, 177 >= t >= -177
30 - delta is based on a table entry, delta[t] < 2^-28
31 - x is whatever is left, |x| < 2^-10
33 Then e^x is approximated as
35 e^x = 2^n ( e^(t/512 + delta[t])
36 + ( e^(t/512 + delta[t])
37 * ( p(x + delta[t] + n * ln(2)) - delta ) ) )
39 where
40 - p(x) is a polynomial approximating e(x)-1;
41 - e^(t/512 + delta[t]) is obtained from a table.
43 The table used is the same one as for the double precision version;
44 since we have the table, we might as well use it.
46 It turns out to be faster to do calculations in double precision than
47 to perform an 'accurate table method' expf, because of the range reduction
48 overhead (compare exp2f).
50 #ifndef _GNU_SOURCE
51 #define _GNU_SOURCE
52 #endif
53 #include <float.h>
54 #include <ieee754.h>
55 #include <math.h>
56 #include <fenv.h>
57 #include <inttypes.h>
58 #include <math_private.h>
60 extern const float __exp_deltatable[178];
61 extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
63 static const volatile float TWOM100 = 7.88860905e-31;
64 static const volatile float TWO127 = 1.7014118346e+38;
66 float
67 __ieee754_expf (float x)
69 static const float himark = 88.72283935546875;
70 static const float lomark = -103.972084045410;
71 /* Check for usual case. */
72 if (isless (x, himark) && isgreater (x, lomark))
74 static const float THREEp42 = 13194139533312.0;
75 static const float THREEp22 = 12582912.0;
76 /* 1/ln(2). */
77 #undef M_1_LN2
78 static const float M_1_LN2 = 1.44269502163f;
79 /* ln(2) */
80 #undef M_LN2
81 static const double M_LN2 = .6931471805599452862;
83 int tval;
84 double x22, t, result, dx;
85 float n, delta;
86 union ieee754_double ex2_u;
87 fenv_t oldenv;
89 feholdexcept (&oldenv);
90 #ifdef FE_TONEAREST
91 fesetround (FE_TONEAREST);
92 #endif
94 /* Calculate n. */
95 n = x * M_1_LN2 + THREEp22;
96 n -= THREEp22;
97 dx = x - n*M_LN2;
99 /* Calculate t/512. */
100 t = dx + THREEp42;
101 t -= THREEp42;
102 dx -= t;
104 /* Compute tval = t. */
105 tval = (int) (t * 512.0);
107 if (t >= 0)
108 delta = - __exp_deltatable[tval];
109 else
110 delta = __exp_deltatable[-tval];
112 /* Compute ex2 = 2^n e^(t/512+delta[t]). */
113 ex2_u.d = __exp_atable[tval+177];
114 ex2_u.ieee.exponent += (int) n;
116 /* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
117 with maximum error in [-2^-10-2^-28,2^-10+2^-28]
118 less than 5e-11. */
119 x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
121 /* Return result. */
122 fesetenv (&oldenv);
124 result = x22 * ex2_u.d + ex2_u.d;
125 return (float) result;
127 /* Exceptional cases: */
128 else if (isless (x, himark))
130 if (__isinff (x))
131 /* e^-inf == 0, with no error. */
132 return 0;
133 else
134 /* Underflow */
135 return TWOM100 * TWOM100;
137 else
138 /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
139 return TWO127*x;