1 /* $OpenBSD: s_sinl.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 sin(x) for x where x is reduced to y = x - k * pi / 2. 30 */ 31 32 #include <sys/types.h> 33 #include <machine/ieee.h> 34 #include <float.h> 35 #include <math.h> 36 37 #include "math_private.h" 38 39 #if LDBL_MANT_DIG == 64 40 #define NX 3 41 #define PREC 2 42 #elif LDBL_MANT_DIG == 113 43 #define NX 5 44 #define PREC 3 45 #else 46 #error "Unsupported long double format" 47 #endif 48 49 static const long double two24 = 1.67772160000000000000e+07L; 50 51 long double 52 sinl(long double x) 53 { 54 union { 55 long double e; 56 struct ieee_ext bits; 57 } z; 58 int i, e0, s; 59 double xd[NX], yd[PREC]; 60 long double hi, lo; 61 62 z.e = x; 63 s = z.bits.ext_sign; 64 z.bits.ext_sign = 0; 65 66 /* If x = +-0 or x is a subnormal number, then sin(x) = x */ 67 if (z.bits.ext_exp == 0) 68 return (x); 69 70 /* If x = NaN or Inf, then sin(x) = NaN. */ 71 if (z.bits.ext_exp == 32767) 72 return ((x - x) / (x - x)); 73 74 /* Optimize the case where x is already within range. */ 75 if (z.e < M_PI_4) { 76 hi = __kernel_sinl(z.e, 0, 0); 77 return (s ? -hi : hi); 78 } 79 80 /* Split z.e into a 24-bit representation. */ 81 e0 = ilogbl(z.e) - 23; 82 z.e = scalbnl(z.e, -e0); 83 for (i = 0; i < NX; i++) { 84 xd[i] = (double)((int32_t)z.e); 85 z.e = (z.e - xd[i]) * two24; 86 } 87 88 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ 89 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); 90 91 #if PREC == 2 92 hi = (long double)yd[0] + yd[1]; 93 lo = yd[1] - (hi - yd[0]); 94 #else /* PREC == 3 */ 95 long double t; 96 t = (long double)yd[2] + yd[1]; 97 hi = t + yd[0]; 98 lo = yd[0] - (hi - t); 99 #endif 100 101 switch (e0 & 3) { 102 case 0: 103 hi = __kernel_sinl(hi, lo, 1); 104 break; 105 case 1: 106 hi = __kernel_cosl(hi, lo); 107 break; 108 case 2: 109 hi = - __kernel_sinl(hi, lo, 1); 110 break; 111 case 3: 112 hi = - __kernel_cosl(hi, lo); 113 break; 114 } 115 116 return (s ? -hi : hi); 117 } 118