trig-const 0.4.0

// origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.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.
// ====================================================
//
// Optimized by Bruce D. Evans. */
use super::rem_pio2_large::rem_pio2_large;

// #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
// #define EPS DBL_EPSILON
const EPS: f64 = 2.2204460492503131e-16;
// #elif FLT_EVAL_METHOD==2
// #define EPS LDBL_EPSILON
// #endif

// TODO: Support FLT_EVAL_METHOD?

const TO_INT: f64 = 1.5 / EPS;
/// 53 bits of 2/pi
const INV_PIO2: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
/// first 33 bits of pi/2
const PIO2_1: f64 = 1.57079632673412561417e+00; /* 0x3FF921FB, 0x54400000 */
/// pi/2 - PIO2_1
const PIO2_1T: f64 = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
/// second 33 bits of pi/2
const PIO2_2: f64 = 6.07710050630396597660e-11; /* 0x3DD0B461, 0x1A600000 */
/// pi/2 - (PIO2_1+PIO2_2)
const PIO2_2T: f64 = 2.02226624879595063154e-21; /* 0x3BA3198A, 0x2E037073 */
/// third 33 bits of pi/2
const PIO2_3: f64 = 2.02226624871116645580e-21; /* 0x3BA3198A, 0x2E000000 */
/// pi/2 - (PIO2_1+PIO2_2+PIO2_3)
const PIO2_3T: f64 = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */

// return the remainder of x rem pi/2 in y[0]+y[1]
// use rem_pio2_large() for large x
//
// caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
pub(crate) const fn rem_pio2(x: f64) -> (i32, f64, f64) {
    let x1p24 = f64::from_bits(0x4170000000000000);

    let sign = (f64::to_bits(x) >> 63) as i32;
    let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;

    const fn medium(x: f64, ix: u32) -> (i32, f64, f64) {
        /* rint(x/(pi/2)), Assume round-to-nearest. */
        let tmp = x * INV_PIO2 + TO_INT;
        // force rounding of tmp to it's storage format on x87 to avoid
        // excess precision issues.
        let f_n = tmp - TO_INT;
        let n = f_n as i32;
        let mut r = x - f_n * PIO2_1;
        let mut w = f_n * PIO2_1T; /* 1st round, good to 85 bits */
        let mut y0 = r - w;
        let ui = f64::to_bits(y0);
        let ey = (ui >> 52) as i32 & 0x7ff;
        let ex = (ix >> 20) as i32;
        if ex - ey > 16 {
            /* 2nd round, good to 118 bits */
            let t = r;
            w = f_n * PIO2_2;
            r = t - w;
            w = f_n * PIO2_2T - ((t - r) - w);
            y0 = r - w;
            let ey = (f64::to_bits(y0) >> 52) as i32 & 0x7ff;
            if ex - ey > 49 {
                /* 3rd round, good to 151 bits, covers all cases */
                let t = r;
                w = f_n * PIO2_3;
                r = t - w;
                w = f_n * PIO2_3T - ((t - r) - w);
                y0 = r - w;
            }
        }
        let y1 = (r - y0) - w;
        (n, y0, y1)
    }

    if ix <= 0x400f6a7a {
        /* |x| ~<= 5pi/4 */
        if (ix & 0xfffff) == 0x921fb {
            /* |x| ~= pi/2 or 2pi/2 */
            return medium(x, ix); /* cancellation -- use medium case */
        }
        if ix <= 0x4002d97c {
            /* |x| ~<= 3pi/4 */
            if sign == 0 {
                let z = x - PIO2_1; /* one round good to 85 bits */
                let y0 = z - PIO2_1T;
                let y1 = (z - y0) - PIO2_1T;
                return (1, y0, y1);
            } else {
                let z = x + PIO2_1;
                let y0 = z + PIO2_1T;
                let y1 = (z - y0) + PIO2_1T;
                return (-1, y0, y1);
            }
        } else if sign == 0 {
            let z = x - 2.0 * PIO2_1;
            let y0 = z - 2.0 * PIO2_1T;
            let y1 = (z - y0) - 2.0 * PIO2_1T;
            return (2, y0, y1);
        } else {
            let z = x + 2.0 * PIO2_1;
            let y0 = z + 2.0 * PIO2_1T;
            let y1 = (z - y0) + 2.0 * PIO2_1T;
            return (-2, y0, y1);
        }
    }
    if ix <= 0x401c463b {
        /* |x| ~<= 9pi/4 */
        if ix <= 0x4015fdbc {
            /* |x| ~<= 7pi/4 */
            if ix == 0x4012d97c {
                /* |x| ~= 3pi/2 */
                return medium(x, ix);
            }
            if sign == 0 {
                let z = x - 3.0 * PIO2_1;
                let y0 = z - 3.0 * PIO2_1T;
                let y1 = (z - y0) - 3.0 * PIO2_1T;
                return (3, y0, y1);
            } else {
                let z = x + 3.0 * PIO2_1;
                let y0 = z + 3.0 * PIO2_1T;
                let y1 = (z - y0) + 3.0 * PIO2_1T;
                return (-3, y0, y1);
            }
        } else {
            if ix == 0x401921fb {
                /* |x| ~= 4pi/2 */
                return medium(x, ix);
            }
            if sign == 0 {
                let z = x - 4.0 * PIO2_1;
                let y0 = z - 4.0 * PIO2_1T;
                let y1 = (z - y0) - 4.0 * PIO2_1T;
                return (4, y0, y1);
            } else {
                let z = x + 4.0 * PIO2_1;
                let y0 = z + 4.0 * PIO2_1T;
                let y1 = (z - y0) + 4.0 * PIO2_1T;
                return (-4, y0, y1);
            }
        }
    }
    if ix < 0x413921fb {
        /* |x| ~< 2^20*(pi/2), medium size */
        return medium(x, ix);
    }
    /*
     * all other (large) arguments
     */
    if ix >= 0x7ff00000 {
        /* x is inf or NaN */
        let y0 = 0.0;
        let y1 = y0;
        return (0, y0, y1);
    }
    /* set z = scalbn(|x|,-ilogb(x)+23) */
    let mut ui = f64::to_bits(x);
    ui &= (!1) >> 12;
    ui |= (0x3ff + 23) << 52;
    let mut z = f64::from_bits(ui);
    let mut tx = [0.0; 3];

    let mut i = 0;
    while i < 2 {
        tx[i] = z as i32 as f64;
        z = (z - tx[i]) * x1p24;
        i += 1;
    }
    tx[2] = z;
    /* skip zero terms, first term is non-zero */
    let mut i = 2;
    while i != 0 && tx[i] == 0.0 {
        i -= 1;
    }
    let mut ty = [0.0; 3];
    let s: &[f64] = match i {
        0 => &[tx[0]],
        1 => &[tx[0], tx[1]],
        2 => &[tx[0], tx[1], tx[2]],
        _ => unreachable!(),
    };
    let n = rem_pio2_large(s, &mut ty, ((ix as i32) >> 20) - (0x3ff + 23), 1);
    if sign != 0 {
        return (-n, -ty[0], -ty[1]);
    }
    (n, ty[0], ty[1])
}