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 /*
28 * See ../src/s_tanpi.c for implementation details.
29 */
30
31 #define INLINE_KERNEL_TANDF
32
33 #include "math.h"
34 #include "math_private.h"
35 #include "k_tanf.c"
36
37 static const float
38 pi_hi = 3.14160156e+00F, /* 0x40491000 */
39 pi_lo = -8.90890988e-06F; /* 0xb715777a */
40
41 static inline float
__kernel_tanpif(float x)42 __kernel_tanpif(float x)
43 {
44 float t;
45
46 if (x < 0.25F)
47 t = __kernel_tandf(M_PI * x, 1);
48 else if (x > 0.25F)
49 t = -__kernel_tandf(M_PI * (0.5 - x), -1);
50 else
51 t = 1;
52
53 return (t);
54 }
55
56 volatile static const float vzero = 0;
57
58 float
tanpif(float x)59 tanpif(float x)
60 {
61 float ax, hi, lo, odd, t;
62 uint32_t hx, ix, j0;
63
64 GET_FLOAT_WORD(hx, x);
65 ix = hx & 0x7fffffff;
66 SET_FLOAT_WORD(ax, ix);
67
68 if (ix < 0x3f800000) { /* |x| < 1 */
69 if (ix < 0x3f000000) { /* |x| < 0.5 */
70 if (ix < 0x38800000) { /* |x| < 0x1p-14 */
71 if (ix == 0)
72 return (x);
73 SET_FLOAT_WORD(hi, hx & 0xffff0000);
74 hi *= 0x1p23F;
75 lo = x * 0x1p23F - hi;
76 t = (pi_lo + pi_hi) * lo + pi_lo * hi +
77 pi_hi * hi;
78 return (t * 0x1p-23F);
79 }
80 t = __kernel_tanpif(ax);
81 } else if (ix == 0x3f000000)
82 t = 1 / vzero;
83 else
84 t = - __kernel_tanpif(1 - ax);
85 return ((hx & 0x80000000) ? -t : t);
86 }
87
88 if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */
89 FFLOORF(x, j0, ix); /* Integer part of ax. */
90 odd = (uint32_t)x & 1 ? -1 : 1;
91 ax -= x;
92 GET_FLOAT_WORD(ix, ax);
93
94 if (ix < 0x3f000000) /* |x| < 0.5 */
95 t = ix == 0 ? copysignf(0, odd) : __kernel_tanpif(ax);
96 else if (ix == 0x3f000000)
97 t = odd / vzero;
98 else
99 t = - __kernel_tanpif(1 - ax);
100 return ((hx & 0x80000000) ? -t : t);
101 }
102
103 /* x = +-inf or nan. */
104 if (ix >= 0x7f800000)
105 return (vzero / vzero);
106
107 /*
108 * For 0x1p23 <= |x| < 0x1p24 need to determine if x is an even
109 * or odd integer to set t = +0 or -0.
110 * For |x| >= 0x1p24, it is always an even integer, so t = 0.
111 */
112 t = ix >= 0x4b800000 ? 0 : (copysignf(0, (ix & 1) ? -1 : 1));
113 return ((hx & 0x80000000) ? -t : t);
114 }
115