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 //__FBSDID("$FreeBSD: src/lib/msun/src/s_tanl.c,v 1.3 2011/05/30 19:41:28 kargl Exp $");
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
36 #if LDBL_MANT_DIG == 64
37 #include "../ld80/e_rem_pio2l.h"
38 #elif LDBL_MANT_DIG == 113
39 #include "../ld128/e_rem_pio2l.h"
40 #else
41 #error "Unsupported long double format"
42 #endif
43
44 long double
tanl(long double x)45 tanl(long double x)
46 {
47 union IEEEl2bits z;
48 int e0, s;
49 long double y[2];
50 long double hi, lo;
51
52 z.e = x;
53 s = z.bits.sign;
54 z.bits.sign = 0;
55
56 /* If x = +-0 or x is subnormal, then tan(x) = x. */
57 if (z.bits.exp == 0)
58 return (x);
59
60 /* If x = NaN or Inf, then tan(x) = NaN. */
61 if (z.bits.exp == 32767)
62 return __math_invalidl(x);
63
64 /* Optimize the case where x is already within range. */
65 if (z.e < _M_PI_4L) {
66 hi = __kernel_tanl(z.e, 0, 0);
67 return (s ? -hi : hi);
68 }
69
70 e0 = __ieee754_rem_pio2l(x, y);
71 hi = y[0];
72 lo = y[1];
73
74 switch (e0 & 3) {
75 case 0:
76 case 2:
77 hi = __kernel_tanl(hi, lo, 0);
78 break;
79 case 1:
80 case 3:
81 hi = __kernel_tanl(hi, lo, 1);
82 break;
83 }
84
85 return (hi);
86 }
87
