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,
34 -1.9999158382e-01,
35 1.4253635705e-01,
36 -1.0648017377e-01,
37 6.1687607318e-02,
38];
39
40/// Arctangent (f32)
41///
42/// Computes the inverse tangent (arc tangent) of the input value.
43/// Returns a value in radians, in the range of -pi/2 to pi/2.
44#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
45pub fn atanf(mut x: f32) -> f32 {
46 let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
47
48 let z: f32;
49
50 let mut ix = x.to_bits();
51 let sign = (ix >> 31) != 0;
52 ix &= 0x7fffffff;
53
54 if ix >= 0x4c800000 {
55 /* if |x| >= 2**26 */
56 if x.is_nan() {
57 return x;
58 }
59 z = i!(ATAN_HI, 3) + x1p_120;
60 return if sign { -z } else { z };
61 }
62 let id = if ix < 0x3ee00000 {
63 /* |x| < 0.4375 */
64 if ix < 0x39800000 {
65 /* |x| < 2**-12 */
66 if ix < 0x00800000 {
67 /* raise underflow for subnormal x */
68 force_eval!(x * x);
69 }
70 return x;
71 }
72 -1
73 } else {
74 x = fabsf(x);
75 if ix < 0x3f980000 {
76 /* |x| < 1.1875 */
77 if ix < 0x3f300000 {
78 /* 7/16 <= |x| < 11/16 */
79 x = (2. * x - 1.) / (2. + x);
80 0
81 } else {
82 /* 11/16 <= |x| < 19/16 */
83 x = (x - 1.) / (x + 1.);
84 1
85 }
86 } else if ix < 0x401c0000 {
87 /* |x| < 2.4375 */
88 x = (x - 1.5) / (1. + 1.5 * x);
89 2
90 } else {
91 /* 2.4375 <= |x| < 2**26 */
92 x = -1. / x;
93 3
94 }
95 };
96 /* end of argument reduction */
97 z = x * x;
98 let w = z * z;
99 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
100 let s1 = z * (i!(A_T, 0) + w * (i!(A_T, 2) + w * i!(A_T, 4)));
101 let s2 = w * (i!(A_T, 1) + w * i!(A_T, 3));
102 if id < 0 {
103 return x - x * (s1 + s2);
104 }
105 let id = id as usize;
106 let z = i!(ATAN_HI, id) - ((x * (s1 + s2) - i!(ATAN_LO, id)) - x);
107 if sign { -z } else { z }
108}
109