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// origin: FreeBSD /usr/src/lib/msun/src/s_sin.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_cos, k_sin, rem_pio2};
// sin(x)
// Return sine function of x.
//
// kernel function:
// k_sin ... sine function on [-pi/4,pi/4]
// k_cos ... cose 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
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn sin(x: f64) -> f64 {
let x1p120 = f64::from_bits(0x4770000000000000); // 0x1p120f === 2 ^ 120
/* High word of x. */
let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
/* |x| ~< pi/4 */
if ix <= 0x3fe921fb {
if ix < 0x3e500000 {
/* |x| < 2**-26 */
/* raise inexact if x != 0 and underflow if subnormal*/
if ix < 0x00100000 {
force_eval!(x / x1p120);
} else {
force_eval!(x + x1p120);
}
return x;
}
return k_sin(x, 0.0, 0);
}
/* sin(Inf or NaN) is NaN */
if ix >= 0x7ff00000 {
return x - x;
}
/* argument reduction needed */
let (n, y0, y1) = rem_pio2(x);
match n & 3 {
0 => k_sin(y0, y1, 1),
1 => k_cos(y0, y1),
2 => -k_sin(y0, y1, 1),
_ => -k_cos(y0, y1),
}
}
#[test]
fn test_near_pi() {
let x = f64::from_bits(0x400921fb000FD5DD); // 3.141592026217707
let sx = f64::from_bits(0x3ea50d15ced1a4a2); // 6.273720864039205e-7
let result = sin(x);
#[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
let result = force_eval!(result);
assert_eq!(result, sx);
}