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/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
use super::fabsf;
const ATAN_HI: [f32; 4] = [
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
];
const ATAN_LO: [f32; 4] = [
5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
];
const A_T: [f32; 5] = [
3.3333328366e-01,
-1.9999158382e-01,
1.4253635705e-01,
-1.0648017377e-01,
6.1687607318e-02,
];
/// Arctangent (f32)
///
/// Computes the inverse tangent (arc tangent) of the input value.
/// Returns a value in radians, in the range of -pi/2 to pi/2.
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn atanf(mut x: f32) -> f32 {
let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
let z: f32;
let mut ix = x.to_bits();
let sign = (ix >> 31) != 0;
ix &= 0x7fffffff;
if ix >= 0x4c800000 {
/* if |x| >= 2**26 */
if x.is_nan() {
return x;
}
z = i!(ATAN_HI, 3) + x1p_120;
return if sign { -z } else { z };
}
let id = if ix < 0x3ee00000 {
/* |x| < 0.4375 */
if ix < 0x39800000 {
/* |x| < 2**-12 */
if ix < 0x00800000 {
/* raise underflow for subnormal x */
force_eval!(x * x);
}
return x;
}
-1
} else {
x = fabsf(x);
if ix < 0x3f980000 {
/* |x| < 1.1875 */
if ix < 0x3f300000 {
/* 7/16 <= |x| < 11/16 */
x = (2. * x - 1.) / (2. + x);
0
} else {
/* 11/16 <= |x| < 19/16 */
x = (x - 1.) / (x + 1.);
1
}
} else if ix < 0x401c0000 {
/* |x| < 2.4375 */
x = (x - 1.5) / (1. + 1.5 * x);
2
} else {
/* 2.4375 <= |x| < 2**26 */
x = -1. / x;
3
}
};
/* end of argument reduction */
z = x * x;
let w = z * z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
let s1 = z * (i!(A_T, 0) + w * (i!(A_T, 2) + w * i!(A_T, 4)));
let s2 = w * (i!(A_T, 1) + w * i!(A_T, 3));
if id < 0 {
return x - x * (s1 + s2);
}
let id = id as usize;
let z = i!(ATAN_HI, id) - ((x * (s1 + s2) - i!(ATAN_LO, id)) - x);
if sign {
-z
} else {
z
}
}
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