1 /* $OpenBSD: s_tanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */ 2 /*- 3 * Copyright (c) 2007 Steven G. Kargl 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice unmodified, this list of conditions, and the following 11 * disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 26 */ 27 28 /* 29 * Compute tan(x) for x where x is reduced to y = x - k * pi / 2. 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 <sys/types.h> 36 #include <machine/ieee.h> 37 #include <float.h> 38 #include <math.h> 39 40 #include "math_private.h" 41 42 #if LDBL_MANT_DIG == 64 43 #define NX 3 44 #define PREC 2 45 #elif LDBL_MANT_DIG == 113 46 #define NX 5 47 #define PREC 3 48 #else 49 #error "Unsupported long double format" 50 #endif 51 52 static const long double two24 = 1.67772160000000000000e+07L; 53 54 long double 55 tanl(long double x) 56 { 57 union { 58 long double e; 59 struct ieee_ext bits; 60 } z; 61 int i, e0, s; 62 double xd[NX], yd[PREC]; 63 long double hi, lo; 64 65 z.e = x; 66 s = z.bits.ext_sign; 67 z.bits.ext_sign = 0; 68 69 /* If x = +-0 or x is subnormal, then tan(x) = x. */ 70 if (z.bits.ext_exp == 0) 71 return (x); 72 73 /* If x = NaN or Inf, then tan(x) = NaN. */ 74 if (z.bits.ext_exp == 32767) 75 return ((x - x) / (x - x)); 76 77 /* Optimize the case where x is already within range. */ 78 if (z.e < M_PI_4) { 79 hi = __kernel_tanl(z.e, 0, 0); 80 return (s ? -hi : hi); 81 } 82 83 /* Split z.e into a 24-bit representation. */ 84 e0 = ilogbl(z.e) - 23; 85 z.e = scalbnl(z.e, -e0); 86 for (i = 0; i < NX; i++) { 87 xd[i] = (double)((int32_t)z.e); 88 z.e = (z.e - xd[i]) * two24; 89 } 90 91 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ 92 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); 93 94 #if PREC == 2 95 hi = (long double)yd[0] + yd[1]; 96 lo = yd[1] - (hi - yd[0]); 97 #else /* PREC == 3 */ 98 long double t; 99 t = (long double)yd[2] + yd[1]; 100 hi = t + yd[0]; 101 lo = yd[0] - (hi - t); 102 #endif 103 104 switch (e0 & 3) { 105 case 0: 106 case 2: 107 hi = __kernel_tanl(hi, lo, 0); 108 break; 109 case 1: 110 case 3: 111 hi = __kernel_tanl(hi, lo, 1); 112 break; 113 } 114 115 return (s ? -hi : hi); 116 } 117