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