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63640cb7 | 1 | /* Single-precision floating point 2^x. |
0ecb606c | 2 | Copyright (C) 1997,1998,2000,2001,2005,2006 Free Software Foundation, Inc. |
63640cb7 UD |
3 | This file is part of the GNU C Library. |
4 | Contributed by Geoffrey Keating <geoffk@ozemail.com.au> | |
5 | ||
6 | The GNU C Library is free software; you can redistribute it and/or | |
41bdb6e2 AJ |
7 | modify it under the terms of the GNU Lesser General Public |
8 | License as published by the Free Software Foundation; either | |
9 | version 2.1 of the License, or (at your option) any later version. | |
63640cb7 UD |
10 | |
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 | |
41bdb6e2 | 14 | Lesser General Public License for more details. |
63640cb7 | 15 | |
41bdb6e2 AJ |
16 | You should have received a copy of the GNU Lesser General Public |
17 | License along with the GNU C Library; if not, write to the Free | |
18 | Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA | |
19 | 02111-1307 USA. */ | |
63640cb7 UD |
20 | |
21 | /* The basic design here is from | |
22 | Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical | |
23 | Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., | |
24 | 17 (1), March 1991, pp. 26-45. | |
25 | It has been slightly modified to compute 2^x instead of e^x, and for | |
26 | single-precision. | |
27 | */ | |
28 | #ifndef _GNU_SOURCE | |
29 | # define _GNU_SOURCE | |
30 | #endif | |
31 | #include <stdlib.h> | |
32 | #include <float.h> | |
33 | #include <ieee754.h> | |
34 | #include <math.h> | |
35 | #include <fenv.h> | |
36 | #include <inttypes.h> | |
37 | #include <math_private.h> | |
38 | ||
39 | #include "t_exp2f.h" | |
40 | ||
41 | static const volatile float TWOM100 = 7.88860905e-31; | |
42 | static const volatile float TWO127 = 1.7014118346e+38; | |
43 | ||
44 | float | |
45 | __ieee754_exp2f (float x) | |
46 | { | |
47 | static const float himark = (float) FLT_MAX_EXP; | |
601d2942 | 48 | static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1); |
63640cb7 UD |
49 | |
50 | /* Check for usual case. */ | |
601d2942 | 51 | if (isless (x, himark) && isgreaterequal (x, lomark)) |
63640cb7 UD |
52 | { |
53 | static const float THREEp14 = 49152.0; | |
54 | int tval, unsafe; | |
55 | float rx, x22, result; | |
56 | union ieee754_float ex2_u, scale_u; | |
57 | fenv_t oldenv; | |
58 | ||
59 | feholdexcept (&oldenv); | |
60 | #ifdef FE_TONEAREST | |
61 | /* If we don't have this, it's too bad. */ | |
62 | fesetround (FE_TONEAREST); | |
63 | #endif | |
64 | ||
65 | /* 1. Argument reduction. | |
66 | Choose integers ex, -128 <= t < 128, and some real | |
67 | -1/512 <= x1 <= 1/512 so that | |
68 | x = ex + t/512 + x1. | |
69 | ||
70 | First, calculate rx = ex + t/256. */ | |
71 | rx = x + THREEp14; | |
72 | rx -= THREEp14; | |
73 | x -= rx; /* Compute x=x1. */ | |
74 | /* Compute tval = (ex*256 + t)+128. | |
75 | Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; and | |
76 | /-round-to-nearest not the usual c integer /]. */ | |
77 | tval = (int) (rx * 256.0f + 128.0f); | |
78 | ||
79 | /* 2. Adjust for accurate table entry. | |
80 | Find e so that | |
81 | x = ex + t/256 + e + x2 | |
82 | where -7e-4 < e < 7e-4, and | |
83 | (float)(2^(t/256+e)) | |
84 | is accurate to one part in 2^-64. */ | |
85 | ||
86 | /* 'tval & 255' is the same as 'tval%256' except that it's always | |
87 | positive. | |
88 | Compute x = x2. */ | |
89 | x -= __exp2f_deltatable[tval & 255]; | |
90 | ||
91 | /* 3. Compute ex2 = 2^(t/255+e+ex). */ | |
92 | ex2_u.f = __exp2f_atable[tval & 255]; | |
93 | tval >>= 8; | |
94 | unsafe = abs(tval) >= -FLT_MIN_EXP - 1; | |
95 | ex2_u.ieee.exponent += tval >> unsafe; | |
96 | scale_u.f = 1.0; | |
97 | scale_u.ieee.exponent += tval - (tval >> unsafe); | |
98 | ||
99 | /* 4. Approximate 2^x2 - 1, using a second-degree polynomial, | |
100 | with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14] | |
101 | less than 1.3e-10. */ | |
102 | ||
103 | x22 = (.24022656679f * x + .69314736128f) * ex2_u.f; | |
104 | ||
105 | /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ | |
106 | fesetenv (&oldenv); | |
107 | ||
108 | result = x22 * x + ex2_u.f; | |
109 | ||
110 | if (!unsafe) | |
111 | return result; | |
112 | else | |
113 | return result * scale_u.f; | |
114 | } | |
115 | /* Exceptional cases: */ | |
116 | else if (isless (x, himark)) | |
117 | { | |
118 | if (__isinff (x)) | |
119 | /* e^-inf == 0, with no error. */ | |
120 | return 0; | |
121 | else | |
122 | /* Underflow */ | |
123 | return TWOM100 * TWOM100; | |
124 | } | |
125 | else | |
126 | /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ | |
127 | return TWO127*x; | |
128 | } |