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 __FBSDID("$FreeBSD$"); 15 16 /* tan(x) 17 * Return tangent function of x. 18 * 19 * kernel function: 20 * __kernel_tan ... tangent function on [-pi/4,pi/4] 21 * __ieee754_rem_pio2 ... argument reduction routine 22 * 23 * Method. 24 * Let S,C and T denote the sin, cos and tan respectively on 25 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 26 * in [-pi/4 , +pi/4], and let n = k mod 4. 27 * We have 28 * 29 * n sin(x) cos(x) tan(x) 30 * ---------------------------------------------------------- 31 * 0 S C T 32 * 1 C -S -1/T 33 * 2 -S -C T 34 * 3 -C S -1/T 35 * ---------------------------------------------------------- 36 * 37 * Special cases: 38 * Let trig be any of sin, cos, or tan. 39 * trig(+-INF) is NaN, with signals; 40 * trig(NaN) is that NaN; 41 * 42 * Accuracy: 43 * TRIG(x) returns trig(x) nearly rounded 44 */ 45 46 #include <float.h> 47 48 #include "math.h" 49 #define INLINE_REM_PIO2 50 #include "math_private.h" 51 #include "e_rem_pio2.c" 52 53 double 54 tan(double x) 55 { 56 double y[2],z=0.0; 57 int32_t n, ix; 58 59 /* High word of x. */ 60 GET_HIGH_WORD(ix,x); 61 62 /* |x| ~< pi/4 */ 63 ix &= 0x7fffffff; 64 if(ix <= 0x3fe921fb) { 65 if(ix<0x3e400000) /* x < 2**-27 */ 66 if((int)x==0) return x; /* generate inexact */ 67 return __kernel_tan(x,z,1); 68 } 69 70 /* tan(Inf or NaN) is NaN */ 71 else if (ix>=0x7ff00000) return x-x; /* NaN */ 72 73 /* argument reduction needed */ 74 else { 75 n = __ieee754_rem_pio2(x,y); 76 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 77 -1 -- n odd */ 78 } 79 } 80 81 #if (LDBL_MANT_DIG == 53) 82 __weak_reference(tan, tanl); 83 #endif 84