1/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13use core::f64;
14
15const O_THRESHOLD: f64 = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
16const LN2_HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
17const LN2_LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
18const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
19/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
20const Q1: f64 = -3.33333333333331316428e-02; /* BFA11111 111110F4 */
21const Q2: f64 = 1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */
22const Q3: f64 = -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */
23const Q4: f64 = 4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */
24const Q5: f64 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
25
26/// Exponential, base *e*, of x-1 (f64)
27///
28/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
29/// to the power `x` minus 1 (where *e* is the base of the natural
30/// system of logarithms, approximately 2.71828).
31/// The result is accurate even for small values of `x`,
32/// where using `exp(x)-1` would lose many significant digits.
33#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
34pub fn expm1(mut x: f64) -> f64 {
35 let hi: f64;
36 let lo: f64;
37 let k: i32;
38 let c: f64;
39 let mut t: f64;
40 let mut y: f64;
41
42 let mut ui = x.to_bits();
43 let hx = ((ui >> 32) & 0x7fffffff) as u32;
44 let sign = (ui >> 63) as i32;
45
46 /* filter out huge and non-finite argument */
47 if hx >= 0x4043687A {
48 /* if |x|>=56*ln2 */
49 if x.is_nan() {
50 return x;
51 }
52 if sign != 0 {
53 return -1.0;
54 }
55 if x > O_THRESHOLD {
56 x *= f64::from_bits(0x7fe0000000000000);
57 return x;
58 }
59 }
60
61 /* argument reduction */
62 if hx > 0x3fd62e42 {
63 /* if |x| > 0.5 ln2 */
64 if hx < 0x3FF0A2B2 {
65 /* and |x| < 1.5 ln2 */
66 if sign == 0 {
67 hi = x - LN2_HI;
68 lo = LN2_LO;
69 k = 1;
70 } else {
71 hi = x + LN2_HI;
72 lo = -LN2_LO;
73 k = -1;
74 }
75 } else {
76 k = (INVLN2 * x + if sign != 0 { -0.5 } else { 0.5 }) as i32;
77 t = k as f64;
78 hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
79 lo = t * LN2_LO;
80 }
81 x = hi - lo;
82 c = (hi - x) - lo;
83 } else if hx < 0x3c900000 {
84 /* |x| < 2**-54, return x */
85 if hx < 0x00100000 {
86 force_eval!(x);
87 }
88 return x;
89 } else {
90 c = 0.0;
91 k = 0;
92 }
93
94 /* x is now in primary range */
95 let hfx = 0.5 * x;
96 let hxs = x * hfx;
97 let r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
98 t = 3.0 - r1 * hfx;
99 let mut e = hxs * ((r1 - t) / (6.0 - x * t));
100 if k == 0 {
101 /* c is 0 */
102 return x - (x * e - hxs);
103 }
104 e = x * (e - c) - c;
105 e -= hxs;
106 /* exp(x) ~ 2^k (x_reduced - e + 1) */
107 if k == -1 {
108 return 0.5 * (x - e) - 0.5;
109 }
110 if k == 1 {
111 if x < -0.25 {
112 return -2.0 * (e - (x + 0.5));
113 }
114 return 1.0 + 2.0 * (x - e);
115 }
116 ui = ((0x3ff + k) as u64) << 52; /* 2^k */
117 let twopk = f64::from_bits(ui);
118 if !(0..=56).contains(&k) {
119 /* suffice to return exp(x)-1 */
120 y = x - e + 1.0;
121 if k == 1024 {
122 y = y * 2.0 * f64::from_bits(0x7fe0000000000000);
123 } else {
124 y = y * twopk;
125 }
126 return y - 1.0;
127 }
128 ui = ((0x3ff - k) as u64) << 52; /* 2^-k */
129 let uf = f64::from_bits(ui);
130 if k < 20 {
131 y = (x - e + (1.0 - uf)) * twopk;
132 } else {
133 y = (x - (e + uf) + 1.0) * twopk;
134 }
135 y
136}
137
138#[cfg(test)]
139mod tests {
140 #[test]
141 fn sanity_check() {
142 assert_eq!(super::expm1(1.1), 2.0041660239464334);
143 }
144}
145