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
28 /*
29 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
30 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
31 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
32 */
33
34
35 #if LDBL_MANT_DIG == 64
36 #include "../ld80/e_rem_pio2l.h"
37 #elif LDBL_MANT_DIG == 113
38 #include "../ld128/e_rem_pio2l.h"
39 #else
40 #error "Unsupported long double format"
41 #endif
42
43 long double
tanl(long double x)44 tanl(long double x)
45 {
46 union IEEEl2bits z;
47 int e0, s;
48 long double y[2];
49 long double hi, lo;
50
51 z.e = x;
52 s = z.bits.sign;
53 z.bits.sign = 0;
54
55 /* If x = +-0 or x is subnormal, then tan(x) = x. */
56 if (z.bits.exp == 0)
57 return (x);
58
59 /* If x = NaN or Inf, then tan(x) = NaN. */
60 if (z.bits.exp == 32767)
61 return __math_invalidl(x);
62
63 /* Optimize the case where x is already within range. */
64 if (z.e < _M_PI_4L) {
65 hi = __kernel_tanl(z.e, 0, 0);
66 return (s ? -hi : hi);
67 }
68
69 e0 = __ieee754_rem_pio2l(x, y);
70 hi = y[0];
71 lo = y[1];
72
73 switch (e0 & 3) {
74 case 0:
75 case 2:
76 hi = __kernel_tanl(hi, lo, 0);
77 break;
78 case 1:
79 case 3:
80 hi = __kernel_tanl(hi, lo, 1);
81 break;
82 }
83
84 return (hi);
85 }
86
