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

//

// ====================================================

// Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.

//

// Permission to use, copy, modify, and distribute this

// software is freely granted, provided that this notice

// is preserved.

// ====================================================

// kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854

// Input x is assumed to be bounded by ~pi/4 in magnitude.

// Input y is the tail of x.

// Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned.

//

// Algorithm

//      1. Since tan(-x) = -tan(x), we need only to consider positive x.

//      2. Callers must return tan(-0) = -0 without calling here since our

//         odd polynomial is not evaluated in a way that preserves -0.

//         Callers may do the optimization tan(x) ~ x for tiny x.

//      3. tan(x) is approximated by a odd polynomial of degree 27 on

//         [0,0.67434]

//                               3             27

//              tan(x) ~ x + T1*x + ... + T13*x

//         where

//

//              |tan(x)         2     4            26   |     -59.2

//              |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2

//              |  x                                    |

//

//         Note: tan(x+y) = tan(x) + tan'(x)*y

//                        ~ tan(x) + (1+x*x)*y

//         Therefore, for better accuracy in computing tan(x+y), let

//                   3      2      2       2       2

//              r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))

//         then

//                                  3    2

//              tan(x+y) = x + (T1*x + (x *(r+y)+y))

//

//      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then

//              tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))

//                     = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))

static T: [f64; 13] = [

    3.33333333333334091986e-01,  /* 3FD55555, 55555563 */

    1.33333333333201242699e-01,  /* 3FC11111, 1110FE7A */

    5.39682539762260521377e-02,  /* 3FABA1BA, 1BB341FE */

    2.18694882948595424599e-02,  /* 3F9664F4, 8406D637 */

    8.86323982359930005737e-03,  /* 3F8226E3, E96E8493 */

    3.59207910759131235356e-03,  /* 3F6D6D22, C9560328 */

    1.45620945432529025516e-03,  /* 3F57DBC8, FEE08315 */

    5.88041240820264096874e-04,  /* 3F4344D8, F2F26501 */

    2.46463134818469906812e-04,  /* 3F3026F7, 1A8D1068 */

    7.81794442939557092300e-05,  /* 3F147E88, A03792A6 */

    7.14072491382608190305e-05,  /* 3F12B80F, 32F0A7E9 */

    -1.85586374855275456654e-05, /* BEF375CB, DB605373 */

    2.59073051863633712884e-05,  /* 3EFB2A70, 74BF7AD4 */

];

const PIO4: f64 = 7.85398163397448278999e-01; /* 3FE921FB, 54442D18 */

const PIO4_LO: f64 = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */

#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]

pub(crate) fn k_tan(mut x: f64, mut y: f64, odd: i32) -> f64 {

    let hx = (f64::to_bits(x) >> 32) as u32;

    let big = (hx & 0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */

    if big {

        let sign = hx >> 31;

        if sign != 0 {

            x = -x;

            y = -y;

        }

        x = (PIO4 - x) + (PIO4_LO - y);

        y = 0.0;

    }

    let z = x * x;

    let w = z * z;

    /*

     * Break x^5*(T[1]+x^2*T[2]+...) into

     * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +

     * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))

     */

    let r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + w * T[11]))));

    let v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + w * T[12])))));

    let s = z * x;

    let r = y + z * (s * (r + v) + y) + s * T[0];

    let w = x + r;

    if big {

        let sign = hx >> 31;

        let s = 1.0 - 2.0 * odd as f64;

        let v = s - 2.0 * (x + (r - w * w / (w + s)));

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

    }

    if odd == 0 {

        return w;

    }

    /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */

    let w0 = zero_low_word(w);

    let v = r - (w0 - x); /* w0+v = r+x */

    let a = -1.0 / w;

    let a0 = zero_low_word(a);

    a0 + a * (1.0 + a0 * w0 + a0 * v)

}

fn zero_low_word(x: f64) -> f64 {

    f64::from_bits(f64::to_bits(x) & 0xFFFF_FFFF_0000_0000)

}