1*05a0b428SJohn Marino /* @(#)s_tan.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* tan(x)
14*05a0b428SJohn Marino * Return tangent function of x.
15*05a0b428SJohn Marino *
16*05a0b428SJohn Marino * kernel function:
17*05a0b428SJohn Marino * __kernel_tan ... tangent function on [-pi/4,pi/4]
18*05a0b428SJohn Marino * __ieee754_rem_pio2 ... argument reduction routine
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Method.
21*05a0b428SJohn Marino * Let S,C and T denote the sin, cos and tan respectively on
22*05a0b428SJohn Marino * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23*05a0b428SJohn Marino * in [-pi/4 , +pi/4], and let n = k mod 4.
24*05a0b428SJohn Marino * We have
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * n sin(x) cos(x) tan(x)
27*05a0b428SJohn Marino * ----------------------------------------------------------
28*05a0b428SJohn Marino * 0 S C T
29*05a0b428SJohn Marino * 1 C -S -1/T
30*05a0b428SJohn Marino * 2 -S -C T
31*05a0b428SJohn Marino * 3 -C S -1/T
32*05a0b428SJohn Marino * ----------------------------------------------------------
33*05a0b428SJohn Marino *
34*05a0b428SJohn Marino * Special cases:
35*05a0b428SJohn Marino * Let trig be any of sin, cos, or tan.
36*05a0b428SJohn Marino * trig(+-INF) is NaN, with signals;
37*05a0b428SJohn Marino * trig(NaN) is that NaN;
38*05a0b428SJohn Marino *
39*05a0b428SJohn Marino * Accuracy:
40*05a0b428SJohn Marino * TRIG(x) returns trig(x) nearly rounded
41*05a0b428SJohn Marino */
42*05a0b428SJohn Marino
43*05a0b428SJohn Marino #include <float.h>
44*05a0b428SJohn Marino #include <math.h>
45*05a0b428SJohn Marino
46*05a0b428SJohn Marino #include "math_private.h"
47*05a0b428SJohn Marino
48*05a0b428SJohn Marino double
tan(double x)49*05a0b428SJohn Marino tan(double x)
50*05a0b428SJohn Marino {
51*05a0b428SJohn Marino double y[2],z=0.0;
52*05a0b428SJohn Marino int32_t n, ix;
53*05a0b428SJohn Marino
54*05a0b428SJohn Marino /* High word of x. */
55*05a0b428SJohn Marino GET_HIGH_WORD(ix,x);
56*05a0b428SJohn Marino
57*05a0b428SJohn Marino /* |x| ~< pi/4 */
58*05a0b428SJohn Marino ix &= 0x7fffffff;
59*05a0b428SJohn Marino if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
60*05a0b428SJohn Marino
61*05a0b428SJohn Marino /* tan(Inf or NaN) is NaN */
62*05a0b428SJohn Marino else if (ix>=0x7ff00000) return x-x; /* NaN */
63*05a0b428SJohn Marino
64*05a0b428SJohn Marino /* argument reduction needed */
65*05a0b428SJohn Marino else {
66*05a0b428SJohn Marino n = __ieee754_rem_pio2(x,y);
67*05a0b428SJohn Marino return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
68*05a0b428SJohn Marino -1 -- n odd */
69*05a0b428SJohn Marino }
70*05a0b428SJohn Marino }
71*05a0b428SJohn Marino
72*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
73*05a0b428SJohn Marino __strong_alias(tanl, tan);
74*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
75