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 * Compute tan(x) for x where x is reduced to y = x - k * pi / 2. 32 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows 33 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million 34 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%). 35 */ 36 37 #include <float.h> 38 39 #include "math.h" 40 #include "math_private.h" 41 #include "fpmath.h" 42 43 #if LDBL_MANT_DIG == 64 44 #define NX 3 45 #define PREC 2 46 #elif LDBL_MANT_DIG == 113 47 #define NX 5 48 #define PREC 3 49 #else 50 #error "Unsupported long double format" 51 #endif 52 53 static const long double two24 = 1.67772160000000000000e+07L; 54 55 long double 56 tanl(long double x) 57 { 58 union IEEEl2bits z; 59 int i, e0, s; 60 double xd[NX], yd[PREC]; 61 long double hi, lo; 62 63 z.e = x; 64 s = z.bits.sign; 65 z.bits.sign = 0; 66 67 /* If x = +-0 or x is subnormal, then tan(x) = x. */ 68 if (z.bits.exp == 0) 69 return (x); 70 71 /* If x = NaN or Inf, then tan(x) = NaN. */ 72 if (z.bits.exp == 32767) 73 return ((x - x) / (x - x)); 74 75 /* Optimize the case where x is already within range. */ 76 if (z.e < M_PI_4) { 77 hi = __kernel_tanl(z.e, 0, 0); 78 return (s ? -hi : hi); 79 } 80 81 /* Split z.e into a 24-bit representation. */ 82 e0 = ilogbl(z.e) - 23; 83 z.e = scalbnl(z.e, -e0); 84 for (i = 0; i < NX; i++) { 85 xd[i] = (double)((int32_t)z.e); 86 z.e = (z.e - xd[i]) * two24; 87 } 88 89 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ 90 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); 91 92 #if PREC == 2 93 hi = (long double)yd[0] + yd[1]; 94 lo = yd[1] - (hi - yd[0]); 95 #else /* PREC == 3 */ 96 long double t; 97 t = (long double)yd[2] + yd[1]; 98 hi = t + yd[0]; 99 lo = yd[0] - (hi - t); 100 #endif 101 102 switch (e0 & 3) { 103 case 0: 104 case 2: 105 hi = __kernel_tanl(hi, lo, 0); 106 break; 107 case 1: 108 case 3: 109 hi = __kernel_tanl(hi, lo, 1); 110 break; 111 } 112 113 return (s ? -hi : hi); 114 } 115