// origin: FreeBSD /usr/src/lib/msun/src/s_tan.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.
// ====================================================

use super::{k_tan, rem_pio2};

// tan(x)
// Return tangent function of x.
//
// kernel function:
//      k_tan           ... tangent function on [-pi/4,pi/4]
//      rem_pio2        ... argument reduction routine
//
// Method.
//      Let S,C and T denote the sin, cos and tan respectively on
//      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
//      in [-pi/4 , +pi/4], and let n = k mod 4.
//      We have
//
//          n        sin(x)      cos(x)        tan(x)
//     ----------------------------------------------------------
//          0          S           C             T
//          1          C          -S            -1/T
//          2         -S          -C             T
//          3         -C           S            -1/T
//     ----------------------------------------------------------
//
// Special cases:
//      Let trig be any of sin, cos, or tan.
//      trig(+-INF)  is NaN, with signals;
//      trig(NaN)    is that NaN;
//
// Accuracy:
//      TRIG(x) returns trig(x) nearly rounded
#[inline]
pub fn tan(x: f64) -> f64 {
    let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120

    let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
    /* |x| ~< pi/4 */
    if ix <= 0x3fe921fb {
        if ix < 0x3e400000 {
            /* |x| < 2**-27 */
            /* raise inexact if x!=0 and underflow if subnormal */
            force_eval!(if ix < 0x00100000 {
                x / x1p120 as f64
            } else {
                x + x1p120 as f64
            });
            return x;
        }
        return k_tan(x, 0.0, 0);
    }

    /* tan(Inf or NaN) is NaN */
    if ix >= 0x7ff00000 {
        return x - x;
    }

    /* argument reduction */
    let (n, y0, y1) = rem_pio2(x);
    k_tan(y0, y1, n & 1)
}
