s_tanl.c revision 176360 
1/*-
2 * Copyright (c) 2007 Steven G. Kargl
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 *    notice unmodified, this list of conditions, and the following
10 *    disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
28__FBSDID("$FreeBSD: head/lib/msun/src/s_tanl.c 176360 2008-02-17 07:33:12Z das $");
29
30/*
31 * Compute tan(x) for x where x is reduced to y = x - k * pi / 2.
32 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
33 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
34 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
35 */
36
37#include <float.h>
38
39#include "math.h"
40#include "math_private.h"
41#include "fpmath.h"
42
43#if LDBL_MANT_DIG == 64
44#define	NX	3
45#define	PREC	2
46#elif LDBL_MANT_DIG == 113
47#define	NX	5
48#define	PREC	3
49#else
50#error "Unsupported long double format"
51#endif
52
53static const long double two24 = 1.67772160000000000000e+07L;
54
55long double
56tanl(long double x)
57{
58	union IEEEl2bits z;
59	int i, e0, s;
60	double xd[NX], yd[PREC];
61	long double hi, lo;
62
63	z.e = x;
64	s = z.bits.sign;
65	z.bits.sign = 0;
66
67	/* If x = +-0 or x is subnormal, then tan(x) = x. */
68	if (z.bits.exp == 0)
69		return (x);
70
71	/* If x = NaN or Inf, then tan(x) = NaN. */
72	if (z.bits.exp == 32767)
73		return ((x - x) / (x - x));
74
75	/* Optimize the case where x is already within range. */
76	if (z.e < M_PI_4) {
77		hi = __kernel_tanl(z.e, 0, 0);
78		return (s ? -hi : hi);
79	}
80
81	/* Split z.e into a 24-bit representation. */
82	e0 = ilogbl(z.e) - 23;
83	z.e = scalbnl(z.e, -e0);
84	for (i = 0; i < NX; i++) {
85		xd[i] = (double)((int32_t)z.e);
86		z.e = (z.e - xd[i]) * two24;
87	}
88
89	/* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */
90	e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC);
91
92#if PREC == 2
93	hi = (long double)yd[0] + yd[1];
94	lo = yd[1] - (hi - yd[0]);
95#else /* PREC == 3 */
96	long double t;
97	t = (long double)yd[2] + yd[1];
98	hi = t + yd[0];
99	lo = yd[0] - (hi - t);
100#endif
101
102	switch (e0 & 3) {
103	case 0:
104	case 2:
105	    hi = __kernel_tanl(hi, lo, 0);
106	    break;
107	case 1:
108	case 3:
109	    hi = __kernel_tanl(hi, lo, 1);
110	    break;
111	}
112
113	return (s ? -hi : hi);
114}
115