1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 3 * 4 * Copyright (c) 2007 Steven G. Kargl 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice unmodified, this list of conditions, and the following 12 * disclaimer. 13 * 2. Redistributions in binary form must reproduce the above copyright 14 * notice, this list of conditions and the following disclaimer in the 15 * documentation and/or other materials provided with the distribution. 16 * 17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 */ 28 29 #include <sys/cdefs.h> 30 __FBSDID("$FreeBSD$"); 31 32 /* 33 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows 34 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million 35 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%). 36 */ 37 38 #include <float.h> 39 #ifdef __i386__ 40 #include <ieeefp.h> 41 #endif 42 43 #include "math.h" 44 #include "math_private.h" 45 #if LDBL_MANT_DIG == 64 46 #include "../ld80/e_rem_pio2l.h" 47 #elif LDBL_MANT_DIG == 113 48 #include "../ld128/e_rem_pio2l.h" 49 #else 50 #error "Unsupported long double format" 51 #endif 52 53 long double 54 tanl(long double x) 55 { 56 union IEEEl2bits z; 57 int e0, s; 58 long double y[2]; 59 long double hi, lo; 60 61 z.e = x; 62 s = z.bits.sign; 63 z.bits.sign = 0; 64 65 /* If x = +-0 or x is subnormal, then tan(x) = x. */ 66 if (z.bits.exp == 0) 67 return (x); 68 69 /* If x = NaN or Inf, then tan(x) = NaN. */ 70 if (z.bits.exp == 32767) 71 return ((x - x) / (x - x)); 72 73 ENTERI(); 74 75 /* Optimize the case where x is already within range. */ 76 if (z.e < M_PI_4) { 77 hi = __kernel_tanl(z.e, 0, 0); 78 RETURNI(s ? -hi : hi); 79 } 80 81 e0 = __ieee754_rem_pio2l(x, y); 82 hi = y[0]; 83 lo = y[1]; 84 85 switch (e0 & 3) { 86 case 0: 87 case 2: 88 hi = __kernel_tanl(hi, lo, 0); 89 break; 90 case 1: 91 case 3: 92 hi = __kernel_tanl(hi, lo, 1); 93 break; 94 } 95 96 RETURNI(hi); 97 } 98