1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 /* tan(x) 13 * Return tangent function of x. 14 * 15 * kernel function: 16 * __kernel_tan ... tangent function on [-pi/4,pi/4] 17 * __ieee754_rem_pio2 ... argument reduction routine 18 * 19 * Method. 20 * Let S,C and T denote the sin, cos and tan respectively on 21 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 22 * in [-pi/4 , +pi/4], and let n = k mod 4. 23 * We have 24 * 25 * n sin(x) cos(x) tan(x) 26 * ---------------------------------------------------------- 27 * 0 S C T 28 * 1 C -S -1/T 29 * 2 -S -C T 30 * 3 -C S -1/T 31 * ---------------------------------------------------------- 32 * 33 * Special cases: 34 * Let trig be any of sin, cos, or tan. 35 * trig(+-INF) is NaN, with signals; 36 * trig(NaN) is that NaN; 37 * 38 * Accuracy: 39 * TRIG(x) returns trig(x) nearly rounded 40 */ 41 42 #include <float.h> 43 44 #include "math.h" 45 #define INLINE_REM_PIO2 46 #include "math_private.h" 47 #include "e_rem_pio2.c" 48 49 double 50 tan(double x) 51 { 52 double y[2],z=0.0; 53 int32_t n, ix; 54 55 /* High word of x. */ 56 GET_HIGH_WORD(ix,x); 57 58 /* |x| ~< pi/4 */ 59 ix &= 0x7fffffff; 60 if(ix <= 0x3fe921fb) { 61 if(ix<0x3e400000) /* x < 2**-27 */ 62 if((int)x==0) return x; /* generate inexact */ 63 return __kernel_tan(x,z,1); 64 } 65 66 /* tan(Inf or NaN) is NaN */ 67 else if (ix>=0x7ff00000) return x-x; /* NaN */ 68 69 /* argument reduction needed */ 70 else { 71 n = __ieee754_rem_pio2(x,y); 72 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even 73 -1 -- n odd */ 74 } 75 } 76 77 #if (LDBL_MANT_DIG == 53) 78 __weak_reference(tan, tanl); 79 #endif 80