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 38 #include "math.h" 39 #define INLINE_REM_PIO2L 40 #include "math_private.h" 41 #if LDBL_MANT_DIG == 64 42 #include "../ld80/e_rem_pio2l.h" 43 #elif LDBL_MANT_DIG == 113 44 #include "../ld128/e_rem_pio2l.h" 45 #else 46 #error "Unsupported long double format" 47 #endif 48 49 long double 50 tanl(long double x) 51 { 52 union IEEEl2bits z; 53 int e0, s; 54 long double y[2]; 55 long double hi, lo; 56 57 z.e = x; 58 s = z.bits.sign; 59 z.bits.sign = 0; 60 61 /* If x = +-0 or x is subnormal, then tan(x) = x. */ 62 if (z.bits.exp == 0) 63 return (x); 64 65 /* If x = NaN or Inf, then tan(x) = NaN. */ 66 if (z.bits.exp == 32767) 67 return ((x - x) / (x - x)); 68 69 /* Optimize the case where x is already within range. */ 70 if (z.e < M_PI_4) { 71 hi = __kernel_tanl(z.e, 0, 0); 72 return (s ? -hi : hi); 73 } 74 75 e0 = __ieee754_rem_pio2l(x, y); 76 hi = y[0]; 77 lo = y[1]; 78 79 switch (e0 & 3) { 80 case 0: 81 case 2: 82 hi = __kernel_tanl(hi, lo, 0); 83 break; 84 case 1: 85 case 3: 86 hi = __kernel_tanl(hi, lo, 1); 87 break; 88 } 89 90 return (hi); 91 } 92