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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */ |
| 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 /* tan(x) |
| 13 * Return tangent function of x. |
| 14 * |
| 15 * kernel function: |
| 16 * __tan ... tangent function on [-pi/4,pi/4] |
| 17 * __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 "libm.h" |
| 43 |
| 44 double tan(double x) |
| 45 { |
| 46 double y[2]; |
| 47 uint32_t ix; |
| 48 unsigned n; |
| 49 |
| 50 GET_HIGH_WORD(ix, x); |
| 51 ix &= 0x7fffffff; |
| 52 |
| 53 /* |x| ~< pi/4 */ |
| 54 if (ix <= 0x3fe921fb) { |
| 55 if (ix < 0x3e400000) { /* |x| < 2**-27 */ |
| 56 /* raise inexact if x!=0 and underflow if subnormal */ |
| 57 FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); |
| 58 return x; |
| 59 } |
| 60 return __tan(x, 0.0, 0); |
| 61 } |
| 62 |
| 63 /* tan(Inf or NaN) is NaN */ |
| 64 if (ix >= 0x7ff00000) |
| 65 return x - x; |
| 66 |
| 67 /* argument reduction */ |
| 68 n = __rem_pio2(x, y); |
| 69 return __tan(y[0], y[1], n&1); |
| 70 } |
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