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 <sys/cdefs.h> 28 __FBSDID("$FreeBSD$"); 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 #ifdef __i386__ 38 #include <ieeefp.h> 39 #endif 40 41 #include "math.h" 42 #include "math_private.h" 43 #if LDBL_MANT_DIG == 64 44 #include "../ld80/e_rem_pio2l.h" 45 #elif LDBL_MANT_DIG == 113 46 #include "../ld128/e_rem_pio2l.h" 47 #else 48 #error "Unsupported long double format" 49 #endif 50 51 long double 52 tanl(long double x) 53 { 54 union IEEEl2bits z; 55 int e0, s; 56 long double y[2]; 57 long double hi, lo; 58 59 z.e = x; 60 s = z.bits.sign; 61 z.bits.sign = 0; 62 63 /* If x = +-0 or x is subnormal, then tan(x) = x. */ 64 if (z.bits.exp == 0) 65 return (x); 66 67 /* If x = NaN or Inf, then tan(x) = NaN. */ 68 if (z.bits.exp == 32767) 69 return ((x - x) / (x - x)); 70 71 ENTERI(); 72 73 /* Optimize the case where x is already within range. */ 74 if (z.e < M_PI_4) { 75 hi = __kernel_tanl(z.e, 0, 0); 76 RETURNI(s ? -hi : hi); 77 } 78 79 e0 = __ieee754_rem_pio2l(x, y); 80 hi = y[0]; 81 lo = y[1]; 82 83 switch (e0 & 3) { 84 case 0: 85 case 2: 86 hi = __kernel_tanl(hi, lo, 0); 87 break; 88 case 1: 89 case 3: 90 hi = __kernel_tanl(hi, lo, 1); 91 break; 92 } 93 94 RETURNI(hi); 95 } 96