1 /*- 2 * Copyright (c) 2017-2021 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 "math.h" 32 #include "math_private.h" 33 34 /* 35 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi. 36 */ 37 static const long double 38 pi_hi = 3.14159265358979322702026593105983920e+00L, 39 pi_lo = 1.14423774522196636802434264184180742e-17L; 40 41 static inline long double 42 __kernel_tanpil(long double x) 43 { 44 long double hi, lo, t; 45 46 if (x < 0.25) { 47 hi = (double)x; 48 lo = x - hi; 49 lo = lo * (pi_lo + pi_hi) + hi * pi_lo; 50 hi *= pi_hi; 51 _2sumF(hi, lo); 52 t = __kernel_tanl(hi, lo, -1); 53 } else if (x > 0.25) { 54 x = 0.5 - x; 55 hi = (double)x; 56 lo = x - hi; 57 lo = lo * (pi_lo + pi_hi) + hi * pi_lo; 58 hi *= pi_hi; 59 _2sumF(hi, lo); 60 t = - __kernel_tanl(hi, lo, 1); 61 } else 62 t = 1; 63 64 return (t); 65 } 66 67 volatile static const double vzero = 0; 68 69 long double 70 tanpil(long double x) 71 { 72 long double ax, hi, lo, xf, t; 73 uint32_t ix; 74 75 ax = fabsl(x); 76 77 if (ax < 1) { 78 if (ax < 0.5) { 79 if (ax < 0x1p-60) { 80 if (x == 0) 81 return (x); 82 hi = (double)x; 83 hi *= 0x1p113L; 84 lo = x * 0x1p113L - hi; 85 t = (pi_lo + pi_hi) * lo + pi_lo * lo + 86 pi_hi * hi; 87 return (t * 0x1p-113L); 88 } 89 t = __kernel_tanpil(ax); 90 } else if (ax == 0.5) 91 return ((ax - ax) / (ax - ax)); 92 else 93 t = -__kernel_tanpil(1 - ax); 94 return (x < 0 ? -t : t); 95 } 96 97 if (ix < 0x1p112) { 98 /* Split x = n + r with 0 <= r < 1. */ 99 xf = (ax + 0x1p112L) - 0x1p112L; /* Integer part */ 100 ax -= xf; /* Remainder */ 101 if (ax < 0) { 102 ax += 1; 103 xf -= 1; 104 } 105 106 if (ax < 0.5) 107 t = ax == 0 ? 0 : __kernel_tanpil(ax); 108 else if (ax == 0.5) 109 return ((ax - ax) / (ax - ax)); 110 else 111 t = -__kernel_tanpil(1 - ax); 112 return (x < 0 ? -t : t); 113 } 114 115 /* x = +-inf or nan. */ 116 if (isinf(x) || isnan(x)) 117 return (vzero / vzero); 118 119 /* 120 * |x| >= 0x1p112 is always an integer, so return +-0. 121 */ 122 return (copysignl(0, x)); 123 } 124