xref: /freebsd/lib/msun/src/s_tanl.c (revision 6472ac3d8a86336899b6cfb789a4cd9897e3fab5)
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 
38 #include "math.h"
39 #include "math_private.h"
40 #if LDBL_MANT_DIG == 64
41 #include "../ld80/e_rem_pio2l.h"
42 #elif LDBL_MANT_DIG == 113
43 #include "../ld128/e_rem_pio2l.h"
44 #else
45 #error "Unsupported long double format"
46 #endif
47 
48 long double
49 tanl(long double x)
50 {
51 	union IEEEl2bits z;
52 	int e0, s;
53 	long double y[2];
54 	long double hi, lo;
55 
56 	z.e = x;
57 	s = z.bits.sign;
58 	z.bits.sign = 0;
59 
60 	/* If x = +-0 or x is subnormal, then tan(x) = x. */
61 	if (z.bits.exp == 0)
62 		return (x);
63 
64 	/* If x = NaN or Inf, then tan(x) = NaN. */
65 	if (z.bits.exp == 32767)
66 		return ((x - x) / (x - x));
67 
68 	/* Optimize the case where x is already within range. */
69 	if (z.e < M_PI_4) {
70 		hi = __kernel_tanl(z.e, 0, 0);
71 		return (s ? -hi : hi);
72 	}
73 
74 	e0 = __ieee754_rem_pio2l(x, y);
75 	hi = y[0];
76 	lo = y[1];
77 
78 	switch (e0 & 3) {
79 	case 0:
80 	case 2:
81 	    hi = __kernel_tanl(hi, lo, 0);
82 	    break;
83 	case 1:
84 	case 3:
85 	    hi = __kernel_tanl(hi, lo, 1);
86 	    break;
87 	}
88 
89 	return (hi);
90 }
91