1*cfe182f3Schristos /*-
2*cfe182f3Schristos * Copyright (c) 2017-2023 Steven G. Kargl
3*cfe182f3Schristos * All rights reserved.
4*cfe182f3Schristos *
5*cfe182f3Schristos * Redistribution and use in source and binary forms, with or without
6*cfe182f3Schristos * modification, are permitted provided that the following conditions
7*cfe182f3Schristos * are met:
8*cfe182f3Schristos * 1. Redistributions of source code must retain the above copyright
9*cfe182f3Schristos * notice unmodified, this list of conditions, and the following
10*cfe182f3Schristos * disclaimer.
11*cfe182f3Schristos * 2. Redistributions in binary form must reproduce the above copyright
12*cfe182f3Schristos * notice, this list of conditions and the following disclaimer in the
13*cfe182f3Schristos * documentation and/or other materials provided with the distribution.
14*cfe182f3Schristos *
15*cfe182f3Schristos * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16*cfe182f3Schristos * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17*cfe182f3Schristos * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18*cfe182f3Schristos * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19*cfe182f3Schristos * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20*cfe182f3Schristos * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21*cfe182f3Schristos * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22*cfe182f3Schristos * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23*cfe182f3Schristos * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24*cfe182f3Schristos * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25*cfe182f3Schristos */
26*cfe182f3Schristos
27*cfe182f3Schristos /*
28*cfe182f3Schristos * See ../src/s_tanpi.c for implementation details.
29*cfe182f3Schristos */
30*cfe182f3Schristos
31*cfe182f3Schristos #include "math.h"
32*cfe182f3Schristos #include "math_private.h"
33*cfe182f3Schristos
34*cfe182f3Schristos /*
35*cfe182f3Schristos * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
36*cfe182f3Schristos */
37*cfe182f3Schristos static const long double
38*cfe182f3Schristos pi_hi = 3.14159265358979322702026593105983920e+00L,
39*cfe182f3Schristos pi_lo = 1.14423774522196636802434264184180742e-17L;
40*cfe182f3Schristos
41*cfe182f3Schristos static inline long double
__kernel_tanpil(long double x)42*cfe182f3Schristos __kernel_tanpil(long double x)
43*cfe182f3Schristos {
44*cfe182f3Schristos long double hi, lo, t;
45*cfe182f3Schristos
46*cfe182f3Schristos if (x < 0.25) {
47*cfe182f3Schristos hi = (double)x;
48*cfe182f3Schristos lo = x - hi;
49*cfe182f3Schristos lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
50*cfe182f3Schristos hi *= pi_hi;
51*cfe182f3Schristos _2sumF(hi, lo);
52*cfe182f3Schristos t = __kernel_tanl(hi, lo, -1);
53*cfe182f3Schristos } else if (x > 0.25) {
54*cfe182f3Schristos x = 0.5 - x;
55*cfe182f3Schristos hi = (double)x;
56*cfe182f3Schristos lo = x - hi;
57*cfe182f3Schristos lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
58*cfe182f3Schristos hi *= pi_hi;
59*cfe182f3Schristos _2sumF(hi, lo);
60*cfe182f3Schristos t = - __kernel_tanl(hi, lo, 1);
61*cfe182f3Schristos } else
62*cfe182f3Schristos t = 1;
63*cfe182f3Schristos
64*cfe182f3Schristos return (t);
65*cfe182f3Schristos }
66*cfe182f3Schristos
67*cfe182f3Schristos static volatile const double vzero = 0;
68*cfe182f3Schristos
69*cfe182f3Schristos long double
tanpil(long double x)70*cfe182f3Schristos tanpil(long double x)
71*cfe182f3Schristos {
72*cfe182f3Schristos long double ai, ar, ax, hi, lo, t;
73*cfe182f3Schristos double odd;
74*cfe182f3Schristos
75*cfe182f3Schristos ax = fabsl(x);
76*cfe182f3Schristos
77*cfe182f3Schristos if (ax < 1) {
78*cfe182f3Schristos if (ax < 0.5) {
79*cfe182f3Schristos if (ax < 0x1p-60) {
80*cfe182f3Schristos if (x == 0)
81*cfe182f3Schristos return (x);
82*cfe182f3Schristos hi = (double)x;
83*cfe182f3Schristos hi *= 0x1p113L;
84*cfe182f3Schristos lo = x * 0x1p113L - hi;
85*cfe182f3Schristos t = (pi_lo + pi_hi) * lo + pi_lo * lo +
86*cfe182f3Schristos pi_hi * hi;
87*cfe182f3Schristos return (t * 0x1p-113L);
88*cfe182f3Schristos }
89*cfe182f3Schristos t = __kernel_tanpil(ax);
90*cfe182f3Schristos } else if (ax == 0.5)
91*cfe182f3Schristos t = 1 / vzero;
92*cfe182f3Schristos else
93*cfe182f3Schristos t = -__kernel_tanpil(1 - ax);
94*cfe182f3Schristos return (x < 0 ? -t : t);
95*cfe182f3Schristos }
96*cfe182f3Schristos
97*cfe182f3Schristos if (ax < 0x1p112) {
98*cfe182f3Schristos /* Split ax = ai + ar with 0 <= ar < 1. */
99*cfe182f3Schristos FFLOORL128(ax, ai, ar);
100*cfe182f3Schristos odd = fmodl(ai, 2.L) == 0 ? 1 : -1;
101*cfe182f3Schristos if (ar < 0.5)
102*cfe182f3Schristos t = ar == 0 ? copysign(0., odd) : __kernel_tanpil(ar);
103*cfe182f3Schristos else if (ar == 0.5)
104*cfe182f3Schristos t = odd / vzero;
105*cfe182f3Schristos else
106*cfe182f3Schristos t = -__kernel_tanpil(1 - ar);
107*cfe182f3Schristos return (x < 0 ? -t : t);
108*cfe182f3Schristos }
109*cfe182f3Schristos
110*cfe182f3Schristos /* x = +-inf or nan. */
111*cfe182f3Schristos if (isinf(x) || isnan(x))
112*cfe182f3Schristos return (vzero / vzero);
113*cfe182f3Schristos
114*cfe182f3Schristos /*
115*cfe182f3Schristos * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
116*cfe182f3Schristos * or odd integer to set t = +0 or -0.
117*cfe182f3Schristos * For |x| >= 0x1p113, it is always an even integer, so t = 0.
118*cfe182f3Schristos */
119*cfe182f3Schristos t = fmodl(ax,2.L) == 0 ? 0 : copysign(0., -1.);
120*cfe182f3Schristos return (copysignl(t, x));
121*cfe182f3Schristos }
122