1 2 /* @(#)s_tan.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* ieee_tan(x) 15 * Return tangent function of x. 16 * 17 * kernel function: 18 * __kernel_tan ... tangent function on [-pi/4,pi/4] 19 * __ieee754_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 ieee_sin(x) ieee_cos(x) ieee_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 */ 43 44 #include "fdlibm.h" 45 46 #ifdef __STDC__ ieee_tan(double x)47 double ieee_tan(double x) 48 #else 49 double ieee_tan(x) 50 double x; 51 #endif 52 { 53 double y[2],z=0.0; 54 int n, ix; 55 56 /* High word of x. */ 57 ix = __HI(x); 58 59 /* |x| ~< pi/4 */ 60 ix &= 0x7fffffff; 61 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); 62 63 /* ieee_tan(Inf or NaN) is NaN */ 64 else if (ix>=0x7ff00000) return x-x; /* NaN */ 65 66 /* argument reduction needed */ 67 else { 68 n = __ieee754_rem_pio2(x,y); 69 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 70 -1 -- n odd */ 71 } 72 } 73