libm/math/
atanf.rs

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1/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.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
16use super::fabsf;
17
18const ATAN_HI: [f32; 4] = [
19    4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
20    7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
21    9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
22    1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
23];
24
25const ATAN_LO: [f32; 4] = [
26    5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
27    3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
28    3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
29    7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
30];
31
32const A_T: [f32; 5] =
33    [3.3333328366e-01, -1.9999158382e-01, 1.4253635705e-01, -1.0648017377e-01, 6.1687607318e-02];
34
35/// Arctangent (f32)
36///
37/// Computes the inverse tangent (arc tangent) of the input value.
38/// Returns a value in radians, in the range of -pi/2 to pi/2.
39#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
40pub fn atanf(mut x: f32) -> f32 {
41    let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
42
43    let z: f32;
44
45    let mut ix = x.to_bits();
46    let sign = (ix >> 31) != 0;
47    ix &= 0x7fffffff;
48
49    if ix >= 0x4c800000 {
50        /* if |x| >= 2**26 */
51        if x.is_nan() {
52            return x;
53        }
54        z = i!(ATAN_HI, 3) + x1p_120;
55        return if sign { -z } else { z };
56    }
57    let id = if ix < 0x3ee00000 {
58        /* |x| < 0.4375 */
59        if ix < 0x39800000 {
60            /* |x| < 2**-12 */
61            if ix < 0x00800000 {
62                /* raise underflow for subnormal x */
63                force_eval!(x * x);
64            }
65            return x;
66        }
67        -1
68    } else {
69        x = fabsf(x);
70        if ix < 0x3f980000 {
71            /* |x| < 1.1875 */
72            if ix < 0x3f300000 {
73                /*  7/16 <= |x| < 11/16 */
74                x = (2. * x - 1.) / (2. + x);
75                0
76            } else {
77                /* 11/16 <= |x| < 19/16 */
78                x = (x - 1.) / (x + 1.);
79                1
80            }
81        } else if ix < 0x401c0000 {
82            /* |x| < 2.4375 */
83            x = (x - 1.5) / (1. + 1.5 * x);
84            2
85        } else {
86            /* 2.4375 <= |x| < 2**26 */
87            x = -1. / x;
88            3
89        }
90    };
91    /* end of argument reduction */
92    z = x * x;
93    let w = z * z;
94    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
95    let s1 = z * (i!(A_T, 0) + w * (i!(A_T, 2) + w * i!(A_T, 4)));
96    let s2 = w * (i!(A_T, 1) + w * i!(A_T, 3));
97    if id < 0 {
98        return x - x * (s1 + s2);
99    }
100    let id = id as usize;
101    let z = i!(ATAN_HI, id) - ((x * (s1 + s2) - i!(ATAN_LO, id)) - x);
102    if sign { -z } else { z }
103}
libm/math/atanf.rs

libm/math/
atanf.rs
