1 /*- 2 * Copyright (c) 2007 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 #include "cdefs-compat.h" 28 //__FBSDID("$FreeBSD: src/lib/msun/src/s_tanl.c,v 1.3 2011/05/30 19:41:28 kargl Exp $"); 29 30 /* 31 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows 32 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million 33 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%). 34 */ 35 36 #include <float.h> 37 #include <openlibm_math.h> 38 39 #include "math_private.h" 40 #if LDBL_MANT_DIG == 64 41 #include "../ld80/e_rem_pio2l.h" 42 #elif LDBL_MANT_DIG == 113 43 #include "../ld128/e_rem_pio2l.h" 44 #else 45 #error "Unsupported long double format" 46 #endif 47 48 DLLEXPORT long double 49 tanl(long double x) 50 { 51 union IEEEl2bits z; 52 int e0, s; 53 long double y[2]; 54 long double hi, lo; 55 56 z.e = x; 57 s = z.bits.sign; 58 z.bits.sign = 0; 59 60 /* If x = +-0 or x is subnormal, then tan(x) = x. */ 61 if (z.bits.exp == 0) 62 return (x); 63 64 /* If x = NaN or Inf, then tan(x) = NaN. */ 65 if (z.bits.exp == 32767) 66 return ((x - x) / (x - x)); 67 68 /* Optimize the case where x is already within range. */ 69 if (z.e < M_PI_4) { 70 hi = __kernel_tanl(z.e, 0, 0); 71 return (s ? -hi : hi); 72 } 73 74 e0 = __ieee754_rem_pio2l(x, y); 75 hi = y[0]; 76 lo = y[1]; 77 78 switch (e0 & 3) { 79 case 0: 80 case 2: 81 hi = __kernel_tanl(hi, lo, 0); 82 break; 83 case 1: 84 case 3: 85 hi = __kernel_tanl(hi, lo, 1); 86 break; 87 } 88 89 return (hi); 90 } 91