vendor/compiler_builtins/libm/src/math/tan.rs

   1 // origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */
   2 //
   3 // ====================================================
   4 // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5 //
   6 // Developed at SunPro, a Sun Microsystems, Inc. business.
   7 // Permission to use, copy, modify, and distribute this
   8 // software is freely granted, provided that this notice
   9 // is preserved.
  10 // ====================================================
  11
  12 use super::{k_tan, rem_pio2};
  13
  14 // tan(x)
  15 // Return tangent function of x.
  16 //
  17 // kernel function:
  18 //      k_tan           ... tangent function on [-pi/4,pi/4]
  19 //      rem_pio2        ... argument reduction routine
  20 //
  21 // Method.
  22 //      Let S,C and T denote the sin, cos and tan respectively on
  23 //      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  24 //      in [-pi/4 , +pi/4], and let n = k mod 4.
  25 //      We have
  26 //
  27 //          n        sin(x)      cos(x)        tan(x)
  28 //     ----------------------------------------------------------
  29 //          0          S           C             T
  30 //          1          C          -S            -1/T
  31 //          2         -S          -C             T
  32 //          3         -C           S            -1/T
  33 //     ----------------------------------------------------------
  34 //
  35 // Special cases:
  36 //      Let trig be any of sin, cos, or tan.
  37 //      trig(+-INF)  is NaN, with signals;
  38 //      trig(NaN)    is that NaN;
  39 //
  40 // Accuracy:
  41 //      TRIG(x) returns trig(x) nearly rounded
  42 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
  43 pub fn tan(x: f64) -> f64 {
  44     let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
  45
  46     let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
  47     /* |x| ~< pi/4 */
  48     if ix <= 0x3fe921fb {
  49         if ix < 0x3e400000 {
  50             /* |x| < 2**-27 */
  51             /* raise inexact if x!=0 and underflow if subnormal */
  52             force_eval!(if ix < 0x00100000 {
  53                 x / x1p120 as f64
  54             } else {
  55                 x + x1p120 as f64
  56             });
  57             return x;
  58         }
  59         return k_tan(x, 0.0, 0);
  60     }
  61
  62     /* tan(Inf or NaN) is NaN */
  63     if ix >= 0x7ff00000 {
  64         return x - x;
  65     }
  66
  67     /* argument reduction */
  68     let (n, y0, y1) = rem_pio2(x);
  69     k_tan(y0, y1, n & 1)
  70 }