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[uclibc-ng.git] / libm / s_tan.c
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1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 * ====================================================
12 /* tan(x)
13 * Return tangent function of x.
15 * kernel function:
16 * __kernel_tan ... tangent function on [-pi/4,pi/4]
17 * __ieee754_rem_pio2 ... argument reduction routine
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
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 * ----------------------------------------------------------
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;
38 * Accuracy:
39 * TRIG(x) returns trig(x) nearly rounded
42 #include "math.h"
43 #include "math_private.h"
45 double tan(double x)
47 double y[2],z=0.0;
48 int32_t n, ix;
50 /* High word of x. */
51 GET_HIGH_WORD(ix,x);
53 /* |x| ~< pi/4 */
54 ix &= 0x7fffffff;
55 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
57 /* tan(Inf or NaN) is NaN */
58 else if (ix>=0x7ff00000) return x-x; /* NaN */
60 /* argument reduction needed */
61 else {
62 n = __ieee754_rem_pio2(x,y);
63 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
64 -1 -- n odd */
67 libm_hidden_def(tan)