1 /* @(#)s_tan.c 5.1 93/09/24 */ 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 13 #ifndef lint 14 static char rcsid[] = "$Id: s_tan.c,v 1.3 1994/02/18 02:27:01 jtc Exp $"; 15 #endif 16 17 /* tan(x) 18 * Return tangent function of x. 19 * 20 * kernel function: 21 * __kernel_tan ... tangent function on [-pi/4,pi/4] 22 * __ieee754_rem_pio2 ... argument reduction routine 23 * 24 * Method. 25 * Let S,C and T denote the sin, cos and tan respectively on 26 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 27 * in [-pi/4 , +pi/4], and let n = k mod 4. 28 * We have 29 * 30 * n sin(x) cos(x) tan(x) 31 * ---------------------------------------------------------- 32 * 0 S C T 33 * 1 C -S -1/T 34 * 2 -S -C T 35 * 3 -C S -1/T 36 * ---------------------------------------------------------- 37 * 38 * Special cases: 39 * Let trig be any of sin, cos, or tan. 40 * trig(+-INF) is NaN, with signals; 41 * trig(NaN) is that NaN; 42 * 43 * Accuracy: 44 * TRIG(x) returns trig(x) nearly rounded 45 */ 46 47 #include <math.h> 48 49 #ifdef __STDC__ 50 static const double one=1.0; 51 #else 52 static double one=1.0; 53 #endif 54 55 #ifdef __STDC__ 56 double tan(double x) 57 #else 58 double tan(x) 59 double x; 60 #endif 61 { 62 double y[2],z=0.0; 63 int n, ix; 64 65 /* High word of x. */ 66 ix = *( (((*(int*)&one)>>29)^1) + (int*)&x); 67 68 /* |x| ~< pi/4 */ 69 ix &= 0x7fffffff; 70 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); 71 72 /* tan(Inf or NaN) is NaN */ 73 else if (ix>=0x7ff00000) return x-x; /* NaN */ 74 75 /* argument reduction needed */ 76 else { 77 n = __ieee754_rem_pio2(x,y); 78 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 79 -1 -- n odd */ 80 } 81 } 82