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
16use super::scalbnf;
17
18const HALF: [f32; 2] = [0.5, -0.5];
19const LN2_HI: f32 = 6.9314575195e-01; /* 0x3f317200 */
20const LN2_LO: f32 = 1.4286067653e-06; /* 0x35bfbe8e */
21const 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 */
26const P1: f32 = 1.6666625440e-1; /* 0xaaaa8f.0p-26 */
27const 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)]
34pub 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 { y } else { scalbnf(y, k) }
97}
98