1 /* $OpenBSD: s_sinl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */
2 /*-
3 * Copyright (c) 2007 Steven G. Kargl
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice unmodified, this list of conditions, and the following
11 * disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 */
27
28 /*
29 * Compute sin(x) for x where x is reduced to y = x - k * pi / 2.
30 */
31
32 #include <sys/types.h>
33 #include <machine/ieee.h>
34 #include <float.h>
35 #include <math.h>
36
37 #include "math_private.h"
38
39 #if LDBL_MANT_DIG == 64
40 #define NX 3
41 #define PREC 2
42 #elif LDBL_MANT_DIG == 113
43 #define NX 5
44 #define PREC 3
45 #else
46 #error "Unsupported long double format"
47 #endif
48
49 static const long double two24 = 1.67772160000000000000e+07L;
50
51 long double
sinl(long double x)52 sinl(long double x)
53 {
54 union {
55 long double e;
56 struct ieee_ext bits;
57 } z;
58 int i, e0, s;
59 double xd[NX], yd[PREC];
60 long double hi, lo;
61
62 z.e = x;
63 s = z.bits.ext_sign;
64 z.bits.ext_sign = 0;
65
66 /* If x = +-0 or x is a subnormal number, then sin(x) = x */
67 if (z.bits.ext_exp == 0)
68 return (x);
69
70 /* If x = NaN or Inf, then sin(x) = NaN. */
71 if (z.bits.ext_exp == 32767)
72 return ((x - x) / (x - x));
73
74 /* Optimize the case where x is already within range. */
75 if (z.e < M_PI_4) {
76 hi = __kernel_sinl(z.e, 0, 0);
77 return (s ? -hi : hi);
78 }
79
80 /* Split z.e into a 24-bit representation. */
81 e0 = ilogbl(z.e) - 23;
82 z.e = scalbnl(z.e, -e0);
83 for (i = 0; i < NX; i++) {
84 xd[i] = (double)((int32_t)z.e);
85 z.e = (z.e - xd[i]) * two24;
86 }
87
88 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */
89 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC);
90
91 #if PREC == 2
92 hi = (long double)yd[0] + yd[1];
93 lo = yd[1] - (hi - yd[0]);
94 #else /* PREC == 3 */
95 long double t;
96 t = (long double)yd[2] + yd[1];
97 hi = t + yd[0];
98 lo = yd[0] - (hi - t);
99 #endif
100
101 switch (e0 & 3) {
102 case 0:
103 hi = __kernel_sinl(hi, lo, 1);
104 break;
105 case 1:
106 hi = __kernel_cosl(hi, lo);
107 break;
108 case 2:
109 hi = - __kernel_sinl(hi, lo, 1);
110 break;
111 case 3:
112 hi = - __kernel_cosl(hi, lo);
113 break;
114 }
115
116 return (s ? -hi : hi);
117 }
118