1 /*-
2 * Copyright (c) 2017,2023 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
29 /*
30 * See ../src/s_tanpi.c for implementation details.
31 */
32
33 #include "namespace.h"
34 __weak_alias(tanpif, _tanpif)
35 #define INLINE_KERNEL_TANDF
36
37 #include "math.h"
38 #include "math_private.h"
39 #include "k_tandf.c"
40
41 static const float
42 pi_hi = 3.14160156e+00F, /* 0x40491000 */
43 pi_lo = -8.90890988e-06F; /* 0xb715777a */
44
45 static inline float
__kernel_tanpif(float x)46 __kernel_tanpif(float x)
47 {
48 float t;
49
50 if (x < 0.25F)
51 t = __kernel_tandf(M_PI * x, 1);
52 else if (x > 0.25F)
53 t = -__kernel_tandf(M_PI * (0.5 - x), -1);
54 else
55 t = 1;
56
57 return (t);
58 }
59
60 static volatile const float vzero = 0;
61
62 float
tanpif(float x)63 tanpif(float x)
64 {
65 float ax, hi, lo, odd, t;
66 uint32_t hx, ix, jj0;
67
68 GET_FLOAT_WORD(hx, x);
69 ix = hx & 0x7fffffff;
70 SET_FLOAT_WORD(ax, ix);
71
72 if (ix < 0x3f800000) { /* |x| < 1 */
73 if (ix < 0x3f000000) { /* |x| < 0.5 */
74 if (ix < 0x38800000) { /* |x| < 0x1p-14 */
75 if (ix == 0)
76 return (x);
77 SET_FLOAT_WORD(hi, hx & 0xffff0000);
78 hi *= 0x1p23F;
79 lo = x * 0x1p23F - hi;
80 t = (pi_lo + pi_hi) * lo + pi_lo * hi +
81 pi_hi * hi;
82 return (t * 0x1p-23F);
83 }
84 t = __kernel_tanpif(ax);
85 } else if (ix == 0x3f000000)
86 t = 1 / vzero;
87 else
88 t = - __kernel_tanpif(1 - ax);
89 return ((hx & 0x80000000) ? -t : t);
90 }
91
92 if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */
93 FFLOORF(x, jj0, ix); /* Integer part of ax. */
94 odd = (uint32_t)x & 1 ? -1 : 1;
95 ax -= x;
96 GET_FLOAT_WORD(ix, ax);
97
98 if (ix < 0x3f000000) /* |x| < 0.5 */
99 t = ix == 0 ? copysignf(0, odd) : __kernel_tanpif(ax);
100 else if (ix == 0x3f000000)
101 t = odd / vzero;
102 else
103 t = - __kernel_tanpif(1 - ax);
104 return ((hx & 0x80000000) ? -t : t);
105 }
106
107 /* x = +-inf or nan. */
108 if (ix >= 0x7f800000)
109 return (vzero / vzero);
110
111 /*
112 * For 0x1p23 <= |x| < 0x1p24 need to determine if x is an even
113 * or odd integer to set t = +0 or -0.
114 * For |x| >= 0x1p24, it is always an even integer, so t = 0.
115 */
116 t = ix >= 0x4b800000 ? 0 : (copysignf(0, (ix & 1) ? -1 : 1));
117 return ((hx & 0x80000000) ? -t : t);
118 }
119