1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2007 Steven G. Kargl
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice unmodified, this list of conditions, and the following
12 * disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 * notice, this list of conditions and the following disclaimer in the
15 * documentation and/or other materials provided with the distribution.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27 */
28
29 /*
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 <float.h>
36 #ifdef __i386__
37 #include <ieeefp.h>
38 #endif
39
40 #include "math.h"
41 #include "math_private.h"
42 #if LDBL_MANT_DIG == 64
43 #include "../ld80/e_rem_pio2l.h"
44 #elif LDBL_MANT_DIG == 113
45 #include "../ld128/e_rem_pio2l.h"
46 #else
47 #error "Unsupported long double format"
48 #endif
49
50 long double
tanl(long double x)51 tanl(long double x)
52 {
53 union IEEEl2bits z;
54 int e0, s;
55 long double y[2];
56 long double hi, lo;
57
58 z.e = x;
59 s = z.bits.sign;
60 z.bits.sign = 0;
61
62 /* If x = +-0 or x is subnormal, then tan(x) = x. */
63 if (z.bits.exp == 0)
64 return (x);
65
66 /* If x = NaN or Inf, then tan(x) = NaN. */
67 if (z.bits.exp == 32767)
68 return ((x - x) / (x - x));
69
70 ENTERI();
71
72 /* Optimize the case where x is already within range. */
73 if (z.e < M_PI_4) {
74 hi = __kernel_tanl(z.e, 0, 0);
75 RETURNI(s ? -hi : hi);
76 }
77
78 e0 = __ieee754_rem_pio2l(x, y);
79 hi = y[0];
80 lo = y[1];
81
82 switch (e0 & 3) {
83 case 0:
84 case 2:
85 hi = __kernel_tanl(hi, lo, 0);
86 break;
87 case 1:
88 case 3:
89 hi = __kernel_tanl(hi, lo, 1);
90 break;
91 }
92
93 RETURNI(hi);
94 }
95