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 /* tan(x) 13 * Return tangent function of x. 14 * 15 * kernel function: 16 * __tan ... tangent function on [-pi/4,pi/4] 17 * __rem_pio2 ... argument reduction routine 18 * 19 * Method. 20 * Let S,C and T denote the sin, cos and tan respectively on 21 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 22 * in [-pi/4 , +pi/4], and let n = k mod 4. 23 * We have 24 * 25 * n sin(x) cos(x) tan(x) 26 * ---------------------------------------------------------- 27 * 0 S C T 28 * 1 C -S -1/T 29 * 2 -S -C T 30 * 3 -C S -1/T 31 * ---------------------------------------------------------- 32 * 33 * Special cases: 34 * Let trig be any of sin, cos, or tan. 35 * trig(+-INF) is NaN, with signals; 36 * trig(NaN) is that NaN; 37 * 38 * Accuracy: 39 * TRIG(x) returns trig(x) nearly rounded 40 */ 41 42 #include "libm.h" 43 44 double tan(double x) 45 { 46 double y[2]; 47 uint32_t ix; 48 unsigned n; 49 50 GET_HIGH_WORD(ix, x); 51 ix &= 0x7fffffff; 52 53 /* |x| ~< pi/4 */ 54 if (ix <= 0x3fe921fb) { 55 if (ix < 0x3e400000) { /* |x| < 2**-27 */ 56 /* raise inexact if x!=0 and underflow if subnormal */ 57 FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); 58 return x; 59 } 60 return __tan(x, 0.0, 0); 61 } 62 63 /* tan(Inf or NaN) is NaN */ 64 if (ix >= 0x7ff00000) 65 return x - x; 66 67 /* argument reduction */ 68 n = __rem_pio2(x, y); 69 return __tan(y[0], y[1], n&1); 70 } 71