1/*	$OpenBSD: s_tanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $	*/
2/*-
3 * Copyright (c) 2007 Steven G. Kargl
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice unmodified, this list of conditions, and the following
11 *    disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in the
14 *    documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 */
27
28/*
29 * Compute tan(x) for x where x is reduced to y = x - k * pi / 2.
30 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
31 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
32 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
33 */
34
35#include <sys/types.h>
36#include <machine/ieee.h>
37#include <float.h>
38#include <math.h>
39
40#include "math_private.h"
41
42#if LDBL_MANT_DIG == 64
43#define	NX	3
44#define	PREC	2
45#elif LDBL_MANT_DIG == 113
46#define	NX	5
47#define	PREC	3
48#else
49#error "Unsupported long double format"
50#endif
51
52static const long double two24 = 1.67772160000000000000e+07L;
53
54long double
55tanl(long double x)
56{
57	union {
58		long double e;
59		struct ieee_ext bits;
60	} z;
61	int i, e0, s;
62	double xd[NX], yd[PREC];
63	long double hi, lo;
64
65	z.e = x;
66	s = z.bits.ext_sign;
67	z.bits.ext_sign = 0;
68
69	/* If x = +-0 or x is subnormal, then tan(x) = x. */
70	if (z.bits.ext_exp == 0)
71		return (x);
72
73	/* If x = NaN or Inf, then tan(x) = NaN. */
74	if (z.bits.ext_exp == 32767)
75		return ((x - x) / (x - x));
76
77	/* Optimize the case where x is already within range. */
78	if (z.e < M_PI_4) {
79		hi = __kernel_tanl(z.e, 0, 0);
80		return (s ? -hi : hi);
81	}
82
83	/* Split z.e into a 24-bit representation. */
84	e0 = ilogbl(z.e) - 23;
85	z.e = scalbnl(z.e, -e0);
86	for (i = 0; i < NX; i++) {
87		xd[i] = (double)((int32_t)z.e);
88		z.e = (z.e - xd[i]) * two24;
89	}
90
91	/* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */
92	e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC);
93
94#if PREC == 2
95	hi = (long double)yd[0] + yd[1];
96	lo = yd[1] - (hi - yd[0]);
97#else /* PREC == 3 */
98	long double t;
99	t = (long double)yd[2] + yd[1];
100	hi = t + yd[0];
101	lo = yd[0] - (hi - t);
102#endif
103
104	switch (e0 & 3) {
105	case 0:
106	case 2:
107	    hi = __kernel_tanl(hi, lo, 0);
108	    break;
109	case 1:
110	case 3:
111	    hi = __kernel_tanl(hi, lo, 1);
112	    break;
113	}
114
115	return (s ? -hi : hi);
116}
117