1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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 #include <sys/cdefs.h>
30 __FBSDID("$FreeBSD$");
31
32 /*
33 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
34 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
35 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
36 */
37
38 #include <float.h>
39 #ifdef __i386__
40 #include <ieeefp.h>
41 #endif
42
43 #include "math.h"
44 #include "math_private.h"
45 #if LDBL_MANT_DIG == 64
46 #include "../ld80/e_rem_pio2l.h"
47 #elif LDBL_MANT_DIG == 113
48 #include "../ld128/e_rem_pio2l.h"
49 #else
50 #error "Unsupported long double format"
51 #endif
52
53 long double
tanl(long double x)54 tanl(long double x)
55 {
56 union IEEEl2bits z;
57 int e0, s;
58 long double y[2];
59 long double hi, lo;
60
61 z.e = x;
62 s = z.bits.sign;
63 z.bits.sign = 0;
64
65 /* If x = +-0 or x is subnormal, then tan(x) = x. */
66 if (z.bits.exp == 0)
67 return (x);
68
69 /* If x = NaN or Inf, then tan(x) = NaN. */
70 if (z.bits.exp == 32767)
71 return ((x - x) / (x - x));
72
73 ENTERI();
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 RETURNI(s ? -hi : hi);
79 }
80
81 e0 = __ieee754_rem_pio2l(x, y);
82 hi = y[0];
83 lo = y[1];
84
85 switch (e0 & 3) {
86 case 0:
87 case 2:
88 hi = __kernel_tanl(hi, lo, 0);
89 break;
90 case 1:
91 case 3:
92 hi = __kernel_tanl(hi, lo, 1);
93 break;
94 }
95
96 RETURNI(hi);
97 }
98