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 #[inline]
34 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
expf(mut x: f32) -> f3235 pub fn expf(mut x: f32) -> f32 {
36 let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
37 let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126 /*original 0x1p-149f ??????????? */
38 let mut hx = x.to_bits();
39 let sign = (hx >> 31) as i32; /* sign bit of x */
40 let signb: bool = sign != 0;
41 hx &= 0x7fffffff; /* high word of |x| */
42
43 /* special cases */
44 if hx >= 0x42aeac50 {
45 /* if |x| >= -87.33655f or NaN */
46 if hx > 0x7f800000 {
47 /* NaN */
48 return x;
49 }
50 if (hx >= 0x42b17218) && (!signb) {
51 /* x >= 88.722839f */
52 /* overflow */
53 x *= x1p127;
54 return x;
55 }
56 if signb {
57 /* underflow */
58 force_eval!(-x1p_126 / x);
59 if hx >= 0x42cff1b5 {
60 /* x <= -103.972084f */
61 return 0.;
62 }
63 }
64 }
65
66 /* argument reduction */
67 let k: i32;
68 let hi: f32;
69 let lo: f32;
70 if hx > 0x3eb17218 {
71 /* if |x| > 0.5 ln2 */
72 if hx > 0x3f851592 {
73 /* if |x| > 1.5 ln2 */
74 k = (INV_LN2 * x + HALF[sign as usize]) as i32;
75 } else {
76 k = 1 - sign - sign;
77 }
78 let kf = k as f32;
79 hi = x - kf * LN2_HI; /* k*ln2hi is exact here */
80 lo = kf * LN2_LO;
81 x = hi - lo;
82 } else if hx > 0x39000000 {
83 /* |x| > 2**-14 */
84 k = 0;
85 hi = x;
86 lo = 0.;
87 } else {
88 /* raise inexact */
89 force_eval!(x1p127 + x);
90 return 1. + x;
91 }
92
93 /* x is now in primary range */
94 let xx = x * x;
95 let c = x - xx * (P1 + xx * P2);
96 let y = 1. + (x * c / (2. - c) - lo + hi);
97 if k == 0 {
98 y
99 } else {
100 scalbnf(y, k)
101 }
102 }
103