1 /* derived from /netlib/fdlibm */ 2 3 /* @(#)s_tan.c 1.3 95/01/18 */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15 /* tan(x) 16 * Return tangent function of x. 17 * 18 * kernel function: 19 * __kernel_tan ... tangent function on [-pi/4,pi/4] 20 * __ieee754_rem_pio2 ... argument reduction routine 21 * 22 * Method. 23 * Let S,C and T denote the sin, cos and tan respectively on 24 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 25 * in [-pi/4 , +pi/4], and let n = k mod 4. 26 * We have 27 * 28 * n sin(x) cos(x) tan(x) 29 * ---------------------------------------------------------- 30 * 0 S C T 31 * 1 C -S -1/T 32 * 2 -S -C T 33 * 3 -C S -1/T 34 * ---------------------------------------------------------- 35 * 36 * Special cases: 37 * Let trig be any of sin, cos, or tan. 38 * trig(+-INF) is NaN, with signals; 39 * trig(NaN) is that NaN; 40 * 41 * Accuracy: 42 * TRIG(x) returns trig(x) nearly rounded 43 */ 44 45 #include "fdlibm.h" 46 47 double tan(double x) 48 { 49 double y[2],z=0.0; 50 int n, ix; 51 52 /* High word of x. */ 53 ix = __HI(x); 54 55 /* |x| ~< pi/4 */ 56 ix &= 0x7fffffff; 57 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); 58 59 /* tan(Inf or NaN) is NaN */ 60 else if (ix>=0x7ff00000) return x-x; /* NaN */ 61 62 /* argument reduction needed */ 63 else { 64 n = __ieee754_rem_pio2(x,y); 65 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 66 -1 -- n odd */ 67 } 68 } 69