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 #ifdef __i386__
32 #include <ieeefp.h>
33 #endif
34 #include <stdint.h>
35
36 #include "fpmath.h"
37 #include "math.h"
38 #include "math_private.h"
39
40 static const double
41 pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
42 pi_lo = -2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
43
44 static inline long double
__kernel_tanpil(long double x)45 __kernel_tanpil(long double x)
46 {
47 long double hi, lo, t;
48
49 if (x < 0.25) {
50 hi = (float)x;
51 lo = x - hi;
52 lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
53 hi *= pi_hi;
54 _2sumF(hi, lo);
55 t = __kernel_tanl(hi, lo, -1);
56 } else if (x > 0.25) {
57 x = 0.5 - x;
58 hi = (float)x;
59 lo = x - hi;
60 lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
61 hi *= pi_hi;
62 _2sumF(hi, lo);
63 t = - __kernel_tanl(hi, lo, 1);
64 } else
65 t = 1;
66
67 return (t);
68 }
69
70 volatile static const double vzero = 0;
71
72 long double
tanpil(long double x)73 tanpil(long double x)
74 {
75 long double ax, hi, lo, odd, t;
76 uint64_t lx, m;
77 uint32_t j0;
78 uint16_t hx, ix;
79
80 EXTRACT_LDBL80_WORDS(hx, lx, x);
81 ix = hx & 0x7fff;
82 INSERT_LDBL80_WORDS(ax, ix, lx);
83
84 ENTERI();
85
86 if (ix < 0x3fff) { /* |x| < 1 */
87 if (ix < 0x3ffe) { /* |x| < 0.5 */
88 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
89 if (x == 0)
90 RETURNI(x);
91 INSERT_LDBL80_WORDS(hi, hx,
92 lx & 0xffffffff00000000ull);
93 hi *= 0x1p63L;
94 lo = x * 0x1p63L - hi;
95 t = (pi_lo + pi_hi) * lo + pi_lo * hi +
96 pi_hi * hi;
97 RETURNI(t * 0x1p-63L);
98 }
99 t = __kernel_tanpil(ax);
100 } else if (ax == 0.5)
101 t = 1 / vzero;
102 else
103 t = -__kernel_tanpil(1 - ax);
104 RETURNI((hx & 0x8000) ? -t : t);
105 }
106
107 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
108 FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */
109 odd = (uint64_t)x & 1 ? -1 : 1;
110 ax -= x;
111 EXTRACT_LDBL80_WORDS(ix, lx, ax);
112
113 if (ix < 0x3ffe) /* |x| < 0.5 */
114 t = ix == 0 ? copysignl(0, odd) : __kernel_tanpil(ax);
115 else if (ax == 0.5L)
116 t = odd / vzero;
117 else
118 t = -__kernel_tanpil(1 - ax);
119 RETURNI((hx & 0x8000) ? -t : t);
120 }
121
122 /* x = +-inf or nan. */
123 if (ix >= 0x7fff)
124 RETURNI(vzero / vzero);
125
126 /*
127 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
128 * or odd integer to set t = +0 or -0.
129 * For |x| >= 0x1p64, it is always an even integer, so t = 0.
130 */
131 t = ix >= 0x403f ? 0 : (copysignl(0, (lx & 1) ? -1 : 1));
132 RETURNI((hx & 0x8000) ? -t : t);
133 }
134