2 * Copyright (c) 2017, 2023 Steven G. Kargl
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
8 * 1. Redistributions of source code must retain the above copyright
9 * notice unmodified, this list of conditions, and the following
11 * 2. Redistributions in binary form must reproduce the above copyright
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13 * documentation and/or other materials provided with the distribution.
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17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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28 * See ../src/s_tanpi.c for implementation details.
38 #include "math_private.h"
41 pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
42 pi_lo = -2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
44 static inline long double
45 __kernel_tanpil(long double x)
47 long double hi, lo, t;
52 lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
55 t = __kernel_tanl(hi, lo, -1);
56 } else if (x > 0.25) {
60 lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
63 t = - __kernel_tanl(hi, lo, 1);
70 volatile static const double vzero = 0;
75 long double ax, hi, lo, odd, t;
80 EXTRACT_LDBL80_WORDS(hx, lx, x);
82 INSERT_LDBL80_WORDS(ax, ix, lx);
86 if (ix < 0x3fff) { /* |x| < 1 */
87 if (ix < 0x3ffe) { /* |x| < 0.5 */
88 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
91 INSERT_LDBL80_WORDS(hi, hx,
92 lx & 0xffffffff00000000ull);
94 lo = x * 0x1p63L - hi;
95 t = (pi_lo + pi_hi) * lo + pi_lo * hi +
97 RETURNI(t * 0x1p-63L);
99 t = __kernel_tanpil(ax);
100 } else if (ax == 0.5)
103 t = -__kernel_tanpil(1 - ax);
104 RETURNI((hx & 0x8000) ? -t : t);
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;
111 EXTRACT_LDBL80_WORDS(ix, lx, ax);
113 if (ix < 0x3ffe) /* |x| < 0.5 */
114 t = ix == 0 ? copysignl(0, odd) : __kernel_tanpil(ax);
118 t = -__kernel_tanpil(1 - ax);
119 RETURNI((hx & 0x8000) ? -t : t);
122 /* x = +-inf or nan. */
124 RETURNI(vzero / vzero);
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.
131 t = ix >= 0x403f ? 0 : (copysignl(0, (lx & 1) ? -1 : 1));
132 RETURNI((hx & 0x8000) ? -t : t);