library/compiler-builtins/libm/src/math/atanf.rs

/* 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(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 }
}