1// origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c
2//-
3// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
4// All rights reserved.
5//
6// Redistribution and use in source and binary forms, with or without
7// modification, are permitted provided that the following conditions
8// are met:
9// 1. Redistributions of source code must retain the above copyright
10// notice, this list of conditions and the following disclaimer.
11// 2. Redistributions in binary form must reproduce the above copyright
12// notice, this list of conditions and the following disclaimer in the
13// documentation and/or other materials provided with the distribution.
14//
15// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25// SUCH DAMAGE.
26
27const TBLSIZE: usize = 16;
28
29static EXP2FT: [u64; TBLSIZE] = [
30 0x3fe6a09e667f3bcd,
31 0x3fe7a11473eb0187,
32 0x3fe8ace5422aa0db,
33 0x3fe9c49182a3f090,
34 0x3feae89f995ad3ad,
35 0x3fec199bdd85529c,
36 0x3fed5818dcfba487,
37 0x3feea4afa2a490da,
38 0x3ff0000000000000,
39 0x3ff0b5586cf9890f,
40 0x3ff172b83c7d517b,
41 0x3ff2387a6e756238,
42 0x3ff306fe0a31b715,
43 0x3ff3dea64c123422,
44 0x3ff4bfdad5362a27,
45 0x3ff5ab07dd485429,
46];
47
48// exp2f(x): compute the base 2 exponential of x
49//
50// Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
51//
52// Method: (equally-spaced tables)
53//
54// Reduce x:
55// x = k + y, for integer k and |y| <= 1/2.
56// Thus we have exp2f(x) = 2**k * exp2(y).
57//
58// Reduce y:
59// y = i/TBLSIZE + z for integer i near y * TBLSIZE.
60// Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
61// with |z| <= 2**-(TBLSIZE+1).
62//
63// We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
64// degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
65// Using double precision for everything except the reduction makes
66// roundoff error insignificant and simplifies the scaling step.
67//
68// This method is due to Tang, but I do not use his suggested parameters:
69//
70// Tang, P. Table-driven Implementation of the Exponential Function
71// in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
72
73/// Exponential, base 2 (f32)
74///
75/// Calculate `2^x`, that is, 2 raised to the power `x`.
76#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
77pub fn exp2f(mut x: f32) -> f32 {
78 let redux = f32::from_bits(0x4b400000) / TBLSIZE as f32;
79 let p1 = f32::from_bits(0x3f317218);
80 let p2 = f32::from_bits(0x3e75fdf0);
81 let p3 = f32::from_bits(0x3d6359a4);
82 let p4 = f32::from_bits(0x3c1d964e);
83
84 // double_t t, r, z;
85 // uint32_t ix, i0, k;
86
87 let x1p127 = f32::from_bits(0x7f000000);
88
89 /* Filter out exceptional cases. */
90 let ui = f32::to_bits(x);
91 let ix = ui & 0x7fffffff;
92 if ix > 0x42fc0000 {
93 /* |x| > 126 */
94 if ix > 0x7f800000 {
95 /* NaN */
96 return x;
97 }
98 if (0x43000000..0x80000000).contains(&ui) {
99 /* x >= 128 */
100 x *= x1p127;
101 return x;
102 }
103 if ui >= 0x80000000 {
104 /* x < -126 */
105 if ui >= 0xc3160000 || (ui & 0x0000ffff != 0) {
106 force_eval!(f32::from_bits(0x80000001) / x);
107 }
108 if ui >= 0xc3160000 {
109 /* x <= -150 */
110 return 0.0;
111 }
112 }
113 } else if ix <= 0x33000000 {
114 /* |x| <= 0x1p-25 */
115 return 1.0 + x;
116 }
117
118 /* Reduce x, computing z, i0, and k. */
119 let ui = f32::to_bits(x + redux);
120 let mut i0 = ui;
121 i0 += TBLSIZE as u32 / 2;
122 let k = i0 / TBLSIZE as u32;
123 let ukf = f64::from_bits(((0x3ff + k) as u64) << 52);
124 i0 &= TBLSIZE as u32 - 1;
125 let mut uf = f32::from_bits(ui);
126 uf -= redux;
127 let z: f64 = (x - uf) as f64;
128 /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
129 let r: f64 = f64::from_bits(i!(EXP2FT, i0 as usize));
130 let t: f64 = r * z;
131 let r: f64 = r + t * (p1 as f64 + z * p2 as f64) + t * (z * z) * (p3 as f64 + z * p4 as f64);
132
133 /* Scale by 2**k */
134 (r * ukf) as f32
135}
136