| /* 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. |
| * ==================================================== |
| */ |
| /* tan(x) |
| * Return tangent function of x. |
| * |
| * kernel function: |
| * __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 |
| */ |
| |
| #include "libm.h" |
| |
| double tan(double x) |
| { |
| double y[2]; |
| uint32_t ix; |
| unsigned n; |
| |
| GET_HIGH_WORD(ix, x); |
| ix &= 0x7fffffff; |
| |
| /* |x| ~< pi/4 */ |
| if (ix <= 0x3fe921fb) { |
| if (ix < 0x3e400000) { /* |x| < 2**-27 */ |
| /* raise inexact if x!=0 and underflow if subnormal */ |
| FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); |
| return x; |
| } |
| return __tan(x, 0.0, 0); |
| } |
| |
| /* tan(Inf or NaN) is NaN */ |
| if (ix >= 0x7ff00000) |
| return x - x; |
| |
| /* argument reduction */ |
| n = __rem_pio2(x, y); |
| return __tan(y[0], y[1], n&1); |
| } |
