trig_const/
atan.rs

1/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.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/* atan(x)
13 * Method
14 *   1. Reduce x to positive by atan(x) = -atan(-x).
15 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
16 *      is further reduced to one of the following intervals and the
17 *      arctangent of t is evaluated by the corresponding formula:
18 *
19 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
20 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
21 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
22 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
23 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
24 *
25 * Constants:
26 * The hexadecimal values are the intended ones for the following
27 * constants. The decimal values may be used, provided that the
28 * compiler will convert from decimal to binary accurately enough
29 * to produce the hexadecimal values shown.
30 */
31
32use crate::fabs;
33
34const ATANHI: [f64; 4] = [
35    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
36    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
37    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
38    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
39];
40
41const ATANLO: [f64; 4] = [
42    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
43    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
44    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
45    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
46];
47
48const AT: [f64; 11] = [
49    3.33333333333329318027e-01,  /* 0x3FD55555, 0x5555550D */
50    -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
51    1.42857142725034663711e-01,  /* 0x3FC24924, 0x920083FF */
52    -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
53    9.09088713343650656196e-02,  /* 0x3FB745CD, 0xC54C206E */
54    -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
55    6.66107313738753120669e-02,  /* 0x3FB10D66, 0xA0D03D51 */
56    -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
57    4.97687799461593236017e-02,  /* 0x3FA97B4B, 0x24760DEB */
58    -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
59    1.62858201153657823623e-02,  /* 0x3F90AD3A, 0xE322DA11 */
60];
61
62/// Arctangent
63///
64/// ```
65/// # use trig_const::atan;
66/// # use core::f64::consts::PI;
67/// const ATAN_1: f64 = atan(1.0);
68/// assert_eq!(ATAN_1, PI / 4.0);
69/// ```
70pub const fn atan(x: f64) -> f64 {
71    let mut x = x;
72    let mut ix = (x.to_bits() >> 32) as u32;
73    let sign = ix >> 31;
74    ix &= 0x7fff_ffff;
75    if ix >= 0x4410_0000 {
76        if x.is_nan() {
77            return x;
78        }
79
80        let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f
81        return if sign != 0 { -z } else { z };
82    }
83
84    let id = if ix < 0x3fdc_0000 {
85        /* |x| < 0.4375 */
86        if ix < 0x3e40_0000 {
87            /* |x| < 2^-27 */
88
89            return x;
90        }
91
92        -1
93    } else {
94        x = fabs(x);
95        if ix < 0x3ff30000 {
96            /* |x| < 1.1875 */
97            if ix < 0x3fe60000 {
98                /* 7/16 <= |x| < 11/16 */
99                x = (2. * x - 1.) / (2. + x);
100                0
101            } else {
102                /* 11/16 <= |x| < 19/16 */
103                x = (x - 1.) / (x + 1.);
104                1
105            }
106        } else if ix < 0x40038000 {
107            /* |x| < 2.4375 */
108            x = (x - 1.5) / (1. + 1.5 * x);
109            2
110        } else {
111            /* 2.4375 <= |x| < 2^66 */
112            x = -1. / x;
113            3
114        }
115    };
116
117    let z = x * x;
118    let w = z * z;
119    /* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */
120    let s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));
121    let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));
122
123    if id < 0 {
124        return x - x * (s1 + s2);
125    }
126
127    let z = ATANHI[id as usize] - (x * (s1 + s2) - ATANLO[id as usize] - x);
128
129    if sign != 0 {
130        -z
131    } else {
132        z
133    }
134}
trig_const/atan.rs

trig_const/
atan.rs
