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("$FreeBSD$");
29
30 /*
31 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
32 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
33 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
34 */
35
36 #include <float.h>
37 #ifdef __i386__
38 #include <ieeefp.h>
39 #endif
40
41 #include "math.h"
42 #include "math_private.h"
43 #if LDBL_MANT_DIG == 64
44 #include "../ld80/e_rem_pio2l.h"
45 #elif LDBL_MANT_DIG == 113
46 #include "../ld128/e_rem_pio2l.h"
47 #else
48 #error "Unsupported long double format"
49 #endif
50
51 long double
tanl(long double x)52 tanl(long double x)
53 {
54 union IEEEl2bits z;
55 int e0, s;
56 long double y[2];
57 long double hi, lo;
58
59 z.e = x;
60 s = z.bits.sign;
61 z.bits.sign = 0;
62
63 /* If x = +-0 or x is subnormal, then tan(x) = x. */
64 if (z.bits.exp == 0)
65 return (x);
66
67 /* If x = NaN or Inf, then tan(x) = NaN. */
68 if (z.bits.exp == 32767)
69 return ((x - x) / (x - x));
70
71 ENTERI();
72
73 /* Optimize the case where x is already within range. */
74 if (z.e < M_PI_4) {
75 hi = __kernel_tanl(z.e, 0, 0);
76 RETURNI(s ? -hi : hi);
77 }
78
79 e0 = __ieee754_rem_pio2l(x, y);
80 hi = y[0];
81 lo = y[1];
82
83 switch (e0 & 3) {
84 case 0:
85 case 2:
86 hi = __kernel_tanl(hi, lo, 0);
87 break;
88 case 1:
89 case 3:
90 hi = __kernel_tanl(hi, lo, 1);
91 break;
92 }
93
94 RETURNI(hi);
95 }
96