libm/math/
expm1f.rs

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1/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.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
16const O_THRESHOLD: f32 = 8.8721679688e+01; /* 0x42b17180 */
17const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
18const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
19const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */
20/*
21 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
22 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
23 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
24 */
25const Q1: f32 = -3.3333212137e-2; /* -0x888868.0p-28 */
26const Q2: f32 = 1.5807170421e-3; /*  0xcf3010.0p-33 */
27
28/// Exponential, base *e*, of x-1 (f32)
29///
30/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
31/// to the power `x` minus 1 (where *e* is the base of the natural
32/// system of logarithms, approximately 2.71828).
33/// The result is accurate even for small values of `x`,
34/// where using `exp(x)-1` would lose many significant digits.
35#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
36pub fn expm1f(mut x: f32) -> f32 {
37    let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
38
39    let mut hx = x.to_bits();
40    let sign = (hx >> 31) != 0;
41    hx &= 0x7fffffff;
42
43    /* filter out huge and non-finite argument */
44    if hx >= 0x4195b844 {
45        /* if |x|>=27*ln2 */
46        if hx > 0x7f800000 {
47            /* NaN */
48            return x;
49        }
50        if sign {
51            return -1.;
52        }
53        if x > O_THRESHOLD {
54            x *= x1p127;
55            return x;
56        }
57    }
58
59    let k: i32;
60    let hi: f32;
61    let lo: f32;
62    let mut c = 0f32;
63    /* argument reduction */
64    if hx > 0x3eb17218 {
65        /* if  |x| > 0.5 ln2 */
66        if hx < 0x3F851592 {
67            /* and |x| < 1.5 ln2 */
68            if !sign {
69                hi = x - LN2_HI;
70                lo = LN2_LO;
71                k = 1;
72            } else {
73                hi = x + LN2_HI;
74                lo = -LN2_LO;
75                k = -1;
76            }
77        } else {
78            k = (INV_LN2 * x + (if sign { -0.5 } else { 0.5 })) as i32;
79            let t = k as f32;
80            hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
81            lo = t * LN2_LO;
82        }
83        x = hi - lo;
84        c = (hi - x) - lo;
85    } else if hx < 0x33000000 {
86        /* when |x|<2**-25, return x */
87        if hx < 0x00800000 {
88            force_eval!(x * x);
89        }
90        return x;
91    } else {
92        k = 0;
93    }
94
95    /* x is now in primary range */
96    let hfx = 0.5 * x;
97    let hxs = x * hfx;
98    let r1 = 1. + hxs * (Q1 + hxs * Q2);
99    let t = 3. - r1 * hfx;
100    let mut e = hxs * ((r1 - t) / (6. - x * t));
101    if k == 0 {
102        /* c is 0 */
103        return x - (x * e - hxs);
104    }
105    e = x * (e - c) - c;
106    e -= hxs;
107    /* exp(x) ~ 2^k (x_reduced - e + 1) */
108    if k == -1 {
109        return 0.5 * (x - e) - 0.5;
110    }
111    if k == 1 {
112        if x < -0.25 {
113            return -2. * (e - (x + 0.5));
114        }
115        return 1. + 2. * (x - e);
116    }
117    let twopk = f32::from_bits(((0x7f + k) << 23) as u32); /* 2^k */
118    if (k < 0) || (k > 56) {
119        /* suffice to return exp(x)-1 */
120        let mut y = x - e + 1.;
121        if k == 128 {
122            y = y * 2. * x1p127;
123        } else {
124            y = y * twopk;
125        }
126        return y - 1.;
127    }
128    let uf = f32::from_bits(((0x7f - k) << 23) as u32); /* 2^-k */
129    if k < 23 { (x - e + (1. - uf)) * twopk } else { (x - (e + uf) + 1.) * twopk }
130}
libm/math/expm1f.rs

libm/math/
expm1f.rs
