1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */ |
2 | /* |
3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
4 | */ |
5 | /* |
6 | * ==================================================== |
7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
8 | * |
9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
10 | * Permission to use, copy, modify, and distribute this |
11 | * software is freely granted, provided that this notice |
12 | * is preserved. |
13 | * ==================================================== |
14 | */ |
15 | |
16 | use super::scalbnf; |
17 | |
18 | const HALF: [f32; 2] = [0.5, -0.5]; |
19 | const LN2_HI: f32 = 6.9314575195e-01; /* 0x3f317200 */ |
20 | const LN2_LO: f32 = 1.4286067653e-06; /* 0x35bfbe8e */ |
21 | const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */ |
22 | /* |
23 | * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: |
24 | * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 |
25 | */ |
26 | const P1: f32 = 1.6666625440e-1; /* 0xaaaa8f.0p-26 */ |
27 | const P2: f32 = -2.7667332906e-3; /* -0xb55215.0p-32 */ |
28 | |
29 | /// Exponential, base *e* (f32) |
30 | /// |
31 | /// Calculate the exponential of `x`, that is, *e* raised to the power `x` |
32 | /// (where *e* is the base of the natural system of logarithms, approximately 2.71828). |
33 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
34 | pub fn expf(mut x: f32) -> f32 { |
35 | let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127 |
36 | let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126 /*original 0x1p-149f ??????????? */ |
37 | let mut hx = x.to_bits(); |
38 | let sign = (hx >> 31) as i32; /* sign bit of x */ |
39 | let signb: bool = sign != 0; |
40 | hx &= 0x7fffffff; /* high word of |x| */ |
41 | |
42 | /* special cases */ |
43 | if hx >= 0x42aeac50 { |
44 | /* if |x| >= -87.33655f or NaN */ |
45 | if hx > 0x7f800000 { |
46 | /* NaN */ |
47 | return x; |
48 | } |
49 | if (hx >= 0x42b17218) && (!signb) { |
50 | /* x >= 88.722839f */ |
51 | /* overflow */ |
52 | x *= x1p127; |
53 | return x; |
54 | } |
55 | if signb { |
56 | /* underflow */ |
57 | force_eval!(-x1p_126 / x); |
58 | if hx >= 0x42cff1b5 { |
59 | /* x <= -103.972084f */ |
60 | return 0.; |
61 | } |
62 | } |
63 | } |
64 | |
65 | /* argument reduction */ |
66 | let k: i32; |
67 | let hi: f32; |
68 | let lo: f32; |
69 | if hx > 0x3eb17218 { |
70 | /* if |x| > 0.5 ln2 */ |
71 | if hx > 0x3f851592 { |
72 | /* if |x| > 1.5 ln2 */ |
73 | k = (INV_LN2 * x + i!(HALF, sign as usize)) as i32; |
74 | } else { |
75 | k = 1 - sign - sign; |
76 | } |
77 | let kf = k as f32; |
78 | hi = x - kf * LN2_HI; /* k*ln2hi is exact here */ |
79 | lo = kf * LN2_LO; |
80 | x = hi - lo; |
81 | } else if hx > 0x39000000 { |
82 | /* |x| > 2**-14 */ |
83 | k = 0; |
84 | hi = x; |
85 | lo = 0.; |
86 | } else { |
87 | /* raise inexact */ |
88 | force_eval!(x1p127 + x); |
89 | return 1. + x; |
90 | } |
91 | |
92 | /* x is now in primary range */ |
93 | let xx = x * x; |
94 | let c = x - xx * (P1 + xx * P2); |
95 | let y = 1. + (x * c / (2. - c) - lo + hi); |
96 | if k == 0 { |
97 | y |
98 | } else { |
99 | scalbnf(y, k) |
100 | } |
101 | } |
102 | |