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 #include "fpmath.h" 32 #include "math.h" 33 #include "math_private.h" 34 35 /* 36 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi. 37 */ 38 static const long double 39 pi_hi = 3.14159265358979322702026593105983920e+00L, 40 pi_lo = 1.14423774522196636802434264184180742e-17L; 41 42 static inline long double 43 __kernel_tanpil(long double x) 44 { 45 long double hi, lo, t; 46 47 if (x < 0.25) { 48 hi = (double)x; 49 lo = x - hi; 50 lo = lo * (pi_lo + pi_hi) + hi * pi_lo; 51 hi *= pi_hi; 52 _2sumF(hi, lo); 53 t = __kernel_tanl(hi, lo, -1); 54 } else if (x > 0.25) { 55 x = 0.5 - x; 56 hi = (double)x; 57 lo = x - hi; 58 lo = lo * (pi_lo + pi_hi) + hi * pi_lo; 59 hi *= pi_hi; 60 _2sumF(hi, lo); 61 t = - __kernel_tanl(hi, lo, 1); 62 } else 63 t = 1; 64 65 return (t); 66 } 67 68 volatile static const double vzero = 0; 69 70 long double 71 tanpil(long double x) 72 { 73 long double ai, ar, ax, hi, lo, t; 74 double odd; 75 76 ax = fabsl(x); 77 78 if (ax < 1) { 79 if (ax < 0.5) { 80 if (ax < 0x1p-60) { 81 if (x == 0) 82 return (x); 83 hi = (double)x; 84 hi *= 0x1p113L; 85 lo = x * 0x1p113L - hi; 86 t = (pi_lo + pi_hi) * lo + pi_lo * lo + 87 pi_hi * hi; 88 return (t * 0x1p-113L); 89 } 90 t = __kernel_tanpil(ax); 91 } else if (ax == 0.5) 92 t = 1 / vzero; 93 else 94 t = -__kernel_tanpil(1 - ax); 95 return (x < 0 ? -t : t); 96 } 97 98 if (ax < 0x1p112) { 99 /* Split ax = ai + ar with 0 <= ar < 1. */ 100 FFLOORL128(ax, ai, ar); 101 odd = fmodl(ai, 2.L) == 0 ? 1 : -1; 102 if (ar < 0.5) 103 t = ar == 0 ? copysign(0., odd) : __kernel_tanpil(ar); 104 else if (ar == 0.5) 105 t = odd / vzero; 106 else 107 t = -__kernel_tanpil(1 - ar); 108 return (x < 0 ? -t : t); 109 } 110 111 /* x = +-inf or nan. */ 112 if (isinf(x) || isnan(x)) 113 return (vzero / vzero); 114 115 /* 116 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even 117 * or odd integer to set t = +0 or -0. 118 * For |x| >= 0x1p113, it is always an even integer, so t = 0. 119 */ 120 t = fmodl(ax,2.L) == 0 ? 0 : copysign(0., -1.); 121 return (copysignl(t, x)); 122 } 123