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 #include <sys/cdefs.h> 14 /* 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 sin(x) cos(x) 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 <float.h> 45 46 #include "math.h" 47 #define INLINE_REM_PIO2 48 #include "math_private.h" 49 #include "e_rem_pio2.c" 50 51 double 52 tan(double x) 53 { 54 double y[2],z=0.0; 55 int32_t n, ix; 56 57 /* High word of x. */ 58 GET_HIGH_WORD(ix,x); 59 60 /* |x| ~< pi/4 */ 61 ix &= 0x7fffffff; 62 if(ix <= 0x3fe921fb) { 63 if(ix<0x3e400000) /* x < 2**-27 */ 64 if((int)x==0) return x; /* generate inexact */ 65 return __kernel_tan(x,z,1); 66 } 67 68 /* tan(Inf or NaN) is NaN */ 69 else if (ix>=0x7ff00000) return x-x; /* NaN */ 70 71 /* argument reduction needed */ 72 else { 73 n = __ieee754_rem_pio2(x,y); 74 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 75 -1 -- n odd */ 76 } 77 } 78 79 #if (LDBL_MANT_DIG == 53) 80 __weak_reference(tan, tanl); 81 #endif 82