Annotation of src/lib/libm/src/s_tan.c, Revision 1.10
1.1 jtc 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
1.9 simonb 8: * software is freely granted, provided that this notice
1.1 jtc 9: * is preserved.
10: * ====================================================
11: */
1.3 jtc 12:
1.8 lukem 13: #include <sys/cdefs.h>
1.6 jtc 14: #if defined(LIBM_SCCS) && !defined(lint)
1.10 ! wiz 15: __RCSID("$NetBSD: s_tan.c,v 1.9 1999/07/02 15:37:43 simonb Exp $");
1.3 jtc 16: #endif
1.1 jtc 17:
18: /* tan(x)
19: * Return tangent function of x.
20: *
21: * kernel function:
22: * __kernel_tan ... tangent function on [-pi/4,pi/4]
23: * __ieee754_rem_pio2 ... argument reduction routine
24: *
25: * Method.
1.9 simonb 26: * Let S,C and T denote the sin, cos and tan respectively on
27: * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
1.1 jtc 28: * in [-pi/4 , +pi/4], and let n = k mod 4.
29: * We have
30: *
31: * n sin(x) cos(x) tan(x)
32: * ----------------------------------------------------------
33: * 0 S C T
34: * 1 C -S -1/T
35: * 2 -S -C T
36: * 3 -C S -1/T
37: * ----------------------------------------------------------
38: *
39: * Special cases:
40: * Let trig be any of sin, cos, or tan.
41: * trig(+-INF) is NaN, with signals;
42: * trig(NaN) is that NaN;
43: *
44: * Accuracy:
1.9 simonb 45: * TRIG(x) returns trig(x) nearly rounded
1.1 jtc 46: */
47:
1.4 jtc 48: #include "math.h"
49: #include "math_private.h"
1.1 jtc 50:
1.10 ! wiz 51: double
! 52: tan(double x)
1.1 jtc 53: {
54: double y[2],z=0.0;
1.5 jtc 55: int32_t n, ix;
1.1 jtc 56:
57: /* High word of x. */
1.4 jtc 58: GET_HIGH_WORD(ix,x);
1.1 jtc 59:
60: /* |x| ~< pi/4 */
61: ix &= 0x7fffffff;
62: if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
63:
64: /* tan(Inf or NaN) is NaN */
65: else if (ix>=0x7ff00000) return x-x; /* NaN */
66:
67: /* argument reduction needed */
68: else {
69: n = __ieee754_rem_pio2(x,y);
70: return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
71: -1 -- n odd */
72: }
73: }
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