| Rich Felker | 0b44a03 | 2011-02-12 00:22:29 -0500 | [diff] [blame] | 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 <math.h> |
| 44 | #include "math_private.h" |
| 45 | |
| 46 | double |
| 47 | tan(double x) |
| 48 | { |
| 49 | double y[2],z=0.0; |
| 50 | int32_t n, ix; |
| 51 | |
| 52 | /* High word of x. */ |
| 53 | GET_HIGH_WORD(ix,x); |
| 54 | |
| 55 | /* |x| ~< pi/4 */ |
| 56 | ix &= 0x7fffffff; |
| 57 | if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); |
| 58 | |
| 59 | /* tan(Inf or NaN) is NaN */ |
| 60 | else if (ix>=0x7ff00000) return x-x; /* NaN */ |
| 61 | |
| 62 | /* argument reduction needed */ |
| 63 | else { |
| 64 | n = __ieee754_rem_pio2(x,y); |
| 65 | return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even |
| 66 | -1 -- n odd */ |
| 67 | } |
| 68 | } |