1 | /* Single-precision floating point 2^x. |
2 | Copyright (C) 1997-2017 Free Software Foundation, Inc. |
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 |
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. |
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 |
14 | Lesser General Public License for more details. |
15 | |
16 | You should have received a copy of the GNU Lesser General Public |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ |
19 | |
20 | /* The basic design here is from |
21 | Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical |
22 | Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., |
23 | 17 (1), March 1991, pp. 26-45. |
24 | It has been slightly modified to compute 2^x instead of e^x, and for |
25 | single-precision. |
26 | */ |
27 | #ifndef _GNU_SOURCE |
28 | # define _GNU_SOURCE |
29 | #endif |
30 | #include <stdlib.h> |
31 | #include <float.h> |
32 | #include <ieee754.h> |
33 | #include <math.h> |
34 | #include <fenv.h> |
35 | #include <inttypes.h> |
36 | #include <math_private.h> |
37 | |
38 | #include "t_exp2f.h" |
39 | |
40 | static const float TWOM100 = 7.88860905e-31; |
41 | static const float TWO127 = 1.7014118346e+38; |
42 | |
43 | float |
44 | __ieee754_exp2f (float x) |
45 | { |
46 | static const float himark = (float) FLT_MAX_EXP; |
47 | static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1); |
48 | |
49 | /* Check for usual case. */ |
50 | if (isless (x, himark) && isgreaterequal (x, lomark)) |
51 | { |
52 | static const float THREEp14 = 49152.0; |
53 | int tval, unsafe; |
54 | float rx, x22, result; |
55 | union ieee754_float ex2_u, scale_u; |
56 | |
57 | if (fabsf (x) < FLT_EPSILON / 4.0f) |
58 | return 1.0f + x; |
59 | |
60 | { |
61 | SET_RESTORE_ROUND_NOEXF (FE_TONEAREST); |
62 | |
63 | /* 1. Argument reduction. |
64 | Choose integers ex, -128 <= t < 128, and some real |
65 | -1/512 <= x1 <= 1/512 so that |
66 | x = ex + t/512 + x1. |
67 | |
68 | First, calculate rx = ex + t/256. */ |
69 | rx = x + THREEp14; |
70 | rx -= THREEp14; |
71 | x -= rx; /* Compute x=x1. */ |
72 | /* Compute tval = (ex*256 + t)+128. |
73 | Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; |
74 | and /-round-to-nearest not the usual c integer /]. */ |
75 | tval = (int) (rx * 256.0f + 128.0f); |
76 | |
77 | /* 2. Adjust for accurate table entry. |
78 | Find e so that |
79 | x = ex + t/256 + e + x2 |
80 | where -7e-4 < e < 7e-4, and |
81 | (float)(2^(t/256+e)) |
82 | is accurate to one part in 2^-64. */ |
83 | |
84 | /* 'tval & 255' is the same as 'tval%256' except that it's always |
85 | positive. |
86 | Compute x = x2. */ |
87 | x -= __exp2f_deltatable[tval & 255]; |
88 | |
89 | /* 3. Compute ex2 = 2^(t/255+e+ex). */ |
90 | ex2_u.f = __exp2f_atable[tval & 255]; |
91 | tval >>= 8; |
92 | /* x2 is an integer multiple of 2^-30; avoid intermediate |
93 | underflow from the calculation of x22 * x. */ |
94 | unsafe = abs(tval) >= -FLT_MIN_EXP - 32; |
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 | |
106 | /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ |
107 | result = x22 * x + ex2_u.f; |
108 | |
109 | if (!unsafe) |
110 | return result; |
111 | else |
112 | { |
113 | result *= scale_u.f; |
114 | math_check_force_underflow_nonneg (result); |
115 | return result; |
116 | } |
117 | } |
118 | /* Exceptional cases: */ |
119 | else if (isless (x, himark)) |
120 | { |
121 | if (isinf (x)) |
122 | /* e^-inf == 0, with no error. */ |
123 | return 0; |
124 | else |
125 | /* Underflow */ |
126 | return TWOM100 * TWOM100; |
127 | } |
128 | else |
129 | /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ |
130 | return TWO127*x; |
131 | } |
132 | strong_alias (__ieee754_exp2f, __exp2f_finite) |
133 | |