/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */

/*

 * ====================================================

 * 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.

 * ====================================================

 */

/* atan(x)

 * Method

 *   1. Reduce x to positive by atan(x) = -atan(-x).

 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument

 *      is further reduced to one of the following intervals and the

 *      arctangent of t is evaluated by the corresponding formula:

 *

 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)

 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )

 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )

 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )

 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )

 *

 * Constants:

 * The hexadecimal values are the intended ones for the following

 * constants. The decimal values may be used, provided that the

 * compiler will convert from decimal to binary accurately enough

 * to produce the hexadecimal values shown.

 */

use core::f64;

use super::fabs;

const ATANHI: [f64; 4] = [

    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */

    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */

    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */

    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */

];

const ATANLO: [f64; 4] = [

    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */

    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */

    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */

    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */

];

const AT: [f64; 11] = [

    3.33333333333329318027e-01,  /* 0x3FD55555, 0x5555550D */

    -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */

    1.42857142725034663711e-01,  /* 0x3FC24924, 0x920083FF */

    -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */

    9.09088713343650656196e-02,  /* 0x3FB745CD, 0xC54C206E */

    -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */

    6.66107313738753120669e-02,  /* 0x3FB10D66, 0xA0D03D51 */

    -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */

    4.97687799461593236017e-02,  /* 0x3FA97B4B, 0x24760DEB */

    -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */

    1.62858201153657823623e-02,  /* 0x3F90AD3A, 0xE322DA11 */

];

/// Arctangent (f64)

///

/// 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 atan(x: f64) -> f64 {

    let mut x = x;

    let mut ix = (x.to_bits() >> 32) as u32;

    let sign = ix >> 31;

    ix &= 0x7fff_ffff;

    if ix >= 0x4410_0000 {

        if x.is_nan() {

            return x;

        }

        let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f

        return if sign != 0 { -z } else { z };

    }

    let id = if ix < 0x3fdc_0000 {

        /* |x| < 0.4375 */

        if ix < 0x3e40_0000 {

            /* |x| < 2^-27 */

            if ix < 0x0010_0000 {

                /* raise underflow for subnormal x */

                force_eval!(x as f32);

            }

            return x;

        }

        -1

    } else {

        x = fabs(x);

        if ix < 0x3ff30000 {

            /* |x| < 1.1875 */

            if ix < 0x3fe60000 {

                /* 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 < 0x40038000 {

            /* |x| < 2.4375 */

            x = (x - 1.5) / (1. + 1.5 * x);

            2

        } else {

            /* 2.4375 <= |x| < 2^66 */

            x = -1. / x;

            3

        }

    };

    let 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 * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));

    let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));

    if id < 0 {

        return x - x * (s1 + s2);

    }

    let z = i!(ATANHI, id as usize) - (x * (s1 + s2) - i!(ATANLO, id as usize) - x);

    if sign != 0 { -z } else { z }

}

#[cfg(test)]

mod tests {

    use core::f64;

    use super::atan;

    #[test]

    fn sanity_check() {

        for (input, answer) in [

            (3.0_f64.sqrt() / 3.0, f64::consts::FRAC_PI_6),

            (1.0, f64::consts::FRAC_PI_4),

            (3.0_f64.sqrt(), f64::consts::FRAC_PI_3),

            (-3.0_f64.sqrt() / 3.0, -f64::consts::FRAC_PI_6),

            (-1.0, -f64::consts::FRAC_PI_4),

            (-3.0_f64.sqrt(), -f64::consts::FRAC_PI_3),

        ]

        .iter()

        {

            assert!(

                (atan(*input) - answer) / answer < 1e-5,

                "\natan({:.4}/16) = {:.4}, actual: {}",

                input * 16.0,

                answer,

                atan(*input)

            );

        }

    }

    #[test]

    fn zero() {

        assert_eq!(atan(0.0), 0.0);

    }

    #[test]

    fn infinity() {

        assert_eq!(atan(f64::INFINITY), f64::consts::FRAC_PI_2);

    }

    #[test]

    fn minus_infinity() {

        assert_eq!(atan(f64::NEG_INFINITY), -f64::consts::FRAC_PI_2);

    }

    #[test]

    fn nan() {

        assert!(atan(f64::NAN).is_nan());

    }

}