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[] = "$FreeBSD: src/lib/msun/src/s_tan.c,v 1.10 2005/11/02 14:01:45 bde 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 #include "math_private.h" 49 50 double 51 tan(double x) 52 { 53 double y[2],z=0.0; 54 int32_t n, ix; 55 56 /* High word of x. */ 57 GET_HIGH_WORD(ix,x); 58 59 /* |x| ~< pi/4 */ 60 ix &= 0x7fffffff; 61 if(ix <= 0x3fe921fb) { 62 if(ix<0x3e300000) /* x < 2**-28 */ 63 if((int)x==0) return x; /* generate inexact */ 64 return __kernel_tan(x,z,1); 65 } 66 67 /* tan(Inf or NaN) is NaN */ 68 else if (ix>=0x7ff00000) return x-x; /* NaN */ 69 70 /* argument reduction needed */ 71 else { 72 n = __ieee754_rem_pio2(x,y); 73 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 74 -1 -- n odd */ 75 } 76 } 77
