| // 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 | |
| /// The tangent of `x` (f64). | |
| /// | |
| /// `x` is specified in radians. | |
| #[cfg_attr(assert_no_panic, no_panic::no_panic)] | |
| 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) | |
| } |