1176360Sdas/*- 2176360Sdas * Copyright (c) 2007 Steven G. Kargl 3176360Sdas * All rights reserved. 4176360Sdas * 5176360Sdas * Redistribution and use in source and binary forms, with or without 6176360Sdas * modification, are permitted provided that the following conditions 7176360Sdas * are met: 8176360Sdas * 1. Redistributions of source code must retain the above copyright 9176360Sdas * notice unmodified, this list of conditions, and the following 10176360Sdas * disclaimer. 11176360Sdas * 2. Redistributions in binary form must reproduce the above copyright 12176360Sdas * notice, this list of conditions and the following disclaimer in the 13176360Sdas * documentation and/or other materials provided with the distribution. 14176360Sdas * 15176360Sdas * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 16176360Sdas * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 17176360Sdas * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 18176360Sdas * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 19176360Sdas * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 20176360Sdas * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21176360Sdas * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22176360Sdas * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23176360Sdas * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24176360Sdas * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25176360Sdas */ 26176360Sdas 27176360Sdas#include <sys/cdefs.h> 28176360Sdas__FBSDID("$FreeBSD$"); 29176360Sdas 30176360Sdas/* 31176360Sdas * Limited testing on pseudorandom numbers drawn within [0:4e8] shows 32176360Sdas * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million 33176360Sdas * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%). 34176360Sdas */ 35176360Sdas 36176360Sdas#include <float.h> 37240828Skargl#ifdef __i386__ 38240828Skargl#include <ieeefp.h> 39240828Skargl#endif 40176360Sdas 41176360Sdas#include "math.h" 42176360Sdas#include "math_private.h" 43176360Sdas#if LDBL_MANT_DIG == 64 44221234Skargl#include "../ld80/e_rem_pio2l.h" 45176360Sdas#elif LDBL_MANT_DIG == 113 46221234Skargl#include "../ld128/e_rem_pio2l.h" 47176360Sdas#else 48176360Sdas#error "Unsupported long double format" 49176360Sdas#endif 50176360Sdas 51176360Sdaslong double 52176360Sdastanl(long double x) 53176360Sdas{ 54176360Sdas union IEEEl2bits z; 55221234Skargl int e0, s; 56221234Skargl long double y[2]; 57176360Sdas long double hi, lo; 58176360Sdas 59176360Sdas z.e = x; 60176360Sdas s = z.bits.sign; 61176360Sdas z.bits.sign = 0; 62176360Sdas 63176360Sdas /* If x = +-0 or x is subnormal, then tan(x) = x. */ 64176360Sdas if (z.bits.exp == 0) 65176360Sdas return (x); 66176360Sdas 67176360Sdas /* If x = NaN or Inf, then tan(x) = NaN. */ 68176360Sdas if (z.bits.exp == 32767) 69176360Sdas return ((x - x) / (x - x)); 70176360Sdas 71240828Skargl ENTERI(); 72240828Skargl 73176360Sdas /* Optimize the case where x is already within range. */ 74176360Sdas if (z.e < M_PI_4) { 75176360Sdas hi = __kernel_tanl(z.e, 0, 0); 76240828Skargl RETURNI(s ? -hi : hi); 77176360Sdas } 78176360Sdas 79221234Skargl e0 = __ieee754_rem_pio2l(x, y); 80221234Skargl hi = y[0]; 81221234Skargl lo = y[1]; 82176360Sdas 83176360Sdas switch (e0 & 3) { 84176360Sdas case 0: 85176360Sdas case 2: 86176360Sdas hi = __kernel_tanl(hi, lo, 0); 87176360Sdas break; 88176360Sdas case 1: 89176360Sdas case 3: 90176360Sdas hi = __kernel_tanl(hi, lo, 1); 91176360Sdas break; 92176360Sdas } 93176360Sdas 94240828Skargl RETURNI(hi); 95176360Sdas} 96