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 /* tan(x) 14 * Return tangent function of x. 15 * 16 * kernel function: 17 * __kernel_tan ... tangent function on [-pi/4,pi/4] 18 * __ieee754_rem_pio2 ... argument reduction routine 19 * 20 * Method. 21 * Let S,C and T denote the sin, cos and tan respectively on 22 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 23 * in [-pi/4 , +pi/4], and let n = k mod 4. 24 * We have 25 * 26 * n sin(x) cos(x) tan(x) 27 * ---------------------------------------------------------- 28 * 0 S C T 29 * 1 C -S -1/T 30 * 2 -S -C T 31 * 3 -C S -1/T 32 * ---------------------------------------------------------- 33 * 34 * Special cases: 35 * Let trig be any of sin, cos, or tan. 36 * trig(+-INF) is NaN, with signals; 37 * trig(NaN) is that NaN; 38 * 39 * Accuracy: 40 * TRIG(x) returns trig(x) nearly rounded 41 */ 42 43 #include <float.h> 44 #include <math.h> 45 46 #include "math_private.h" 47 48 double 49 tan(double x) 50 { 51 double y[2],z=0.0; 52 int32_t n, ix; 53 54 /* High word of x. */ 55 GET_HIGH_WORD(ix,x); 56 57 /* |x| ~< pi/4 */ 58 ix &= 0x7fffffff; 59 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); 60 61 /* tan(Inf or NaN) is NaN */ 62 else if (ix>=0x7ff00000) return x-x; /* NaN */ 63 64 /* argument reduction needed */ 65 else { 66 n = __ieee754_rem_pio2(x,y); 67 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 68 -1 -- n odd */ 69 } 70 } 71 72 #if LDBL_MANT_DIG == DBL_MANT_DIG 73 __strong_alias(tanl, tan); 74 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 75