libm/math/
exp2f.rs

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(assert_no_panic, no_panic::no_panic)]
77pub fn exp2f(mut x: f32) -> f32 {
78    select_implementation! {
79        name: x87_exp2f,
80        use_arch_required: x86_no_sse,
81        args: x,
82    }
83
84    let redux = f32::from_bits(0x4b400000) / TBLSIZE as f32;
85    let p1 = f32::from_bits(0x3f317218);
86    let p2 = f32::from_bits(0x3e75fdf0);
87    let p3 = f32::from_bits(0x3d6359a4);
88    let p4 = f32::from_bits(0x3c1d964e);
89
90    // double_t t, r, z;
91    // uint32_t ix, i0, k;
92
93    let x1p127 = f32::from_bits(0x7f000000);
94
95    /* Filter out exceptional cases. */
96    let ui = f32::to_bits(x);
97    let ix = ui & 0x7fffffff;
98    if ix > 0x42fc0000 {
99        /* |x| > 126 */
100        if ix > 0x7f800000 {
101            /* NaN */
102            return x;
103        }
104        if (0x43000000..0x80000000).contains(&ui) {
105            /* x >= 128 */
106            x *= x1p127;
107            return x;
108        }
109        if ui >= 0x80000000 {
110            /* x < -126 */
111            if ui >= 0xc3160000 || (ui & 0x0000ffff != 0) {
112                unsafe { ::core::ptr::read_volatile(&(f32::from_bits(0x80000001) / x)) };force_eval!(f32::from_bits(0x80000001) / x);
113            }
114            if ui >= 0xc3160000 {
115                /* x <= -150 */
116                return 0.0;
117            }
118        }
119    } else if ix <= 0x33000000 {
120        /* |x| <= 0x1p-25 */
121        return 1.0 + x;
122    }
123
124    /* Reduce x, computing z, i0, and k. */
125    let ui = f32::to_bits(x + redux);
126    let mut i0 = ui;
127    i0 += TBLSIZE as u32 / 2;
128    let k = i0 / TBLSIZE as u32;
129    let ukf = f64::from_bits(((0x3ff + k) as u64) << 52);
130    i0 &= TBLSIZE as u32 - 1;
131    let mut uf = f32::from_bits(ui);
132    uf -= redux;
133    let z: f64 = (x - uf) as f64;
134    /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
135    let r: f64 = f64::from_bits(*EXP2FT.get(i0 as usize).unwrap()i!(EXP2FT, i0 as usize));
136    let t: f64 = r * z;
137    let r: f64 = r + t * (p1 as f64 + z * p2 as f64) + t * (z * z) * (p3 as f64 + z * p4 as f64);
138
139    /* Scale by 2**k */
140    (r * ukf) as f32
141}
libm/math/exp2f.rs

libm/math/
exp2f.rs
