1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 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 /* 30 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows 31 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million 32 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%). 33 */ 34 35 #include <float.h> 36 #ifdef __i386__ 37 #include <ieeefp.h> 38 #endif 39 40 #include "math.h" 41 #include "math_private.h" 42 #if LDBL_MANT_DIG == 64 43 #include "../ld80/e_rem_pio2l.h" 44 #elif LDBL_MANT_DIG == 113 45 #include "../ld128/e_rem_pio2l.h" 46 #else 47 #error "Unsupported long double format" 48 #endif 49 50 long double 51 tanl(long double x) 52 { 53 union IEEEl2bits z; 54 int e0, s; 55 long double y[2]; 56 long double hi, lo; 57 58 z.e = x; 59 s = z.bits.sign; 60 z.bits.sign = 0; 61 62 /* If x = +-0 or x is subnormal, then tan(x) = x. */ 63 if (z.bits.exp == 0) 64 return (x); 65 66 /* If x = NaN or Inf, then tan(x) = NaN. */ 67 if (z.bits.exp == 32767) 68 return ((x - x) / (x - x)); 69 70 ENTERI(); 71 72 /* Optimize the case where x is already within range. */ 73 if (z.e < M_PI_4) { 74 hi = __kernel_tanl(z.e, 0, 0); 75 RETURNI(s ? -hi : hi); 76 } 77 78 e0 = __ieee754_rem_pio2l(x, y); 79 hi = y[0]; 80 lo = y[1]; 81 82 switch (e0 & 3) { 83 case 0: 84 case 2: 85 hi = __kernel_tanl(hi, lo, 0); 86 break; 87 case 1: 88 case 3: 89 hi = __kernel_tanl(hi, lo, 1); 90 break; 91 } 92 93 RETURNI(hi); 94 } 95