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 sin(x) for x where x is reduced to y = x - k * pi / 2. 32 */ 33 34 #include <float.h> 35 36 #include "math.h" 37 #include "math_private.h" 38 #include "fpmath.h" 39 40 #if LDBL_MANT_DIG == 64 41 #define NX 3 42 #define PREC 2 43 #elif LDBL_MANT_DIG == 113 44 #define NX 5 45 #define PREC 3 46 #else 47 #error "Unsupported long double format" 48 #endif 49 50 static const long double two24 = 1.67772160000000000000e+07L; 51 52 long double 53 sinl(long double x) 54 { 55 union IEEEl2bits z; 56 int i, e0, s; 57 double xd[NX], yd[PREC]; 58 long double hi, lo; 59 60 z.e = x; 61 s = z.bits.sign; 62 z.bits.sign = 0; 63 64 /* If x = +-0 or x is a subnormal number, then sin(x) = x */ 65 if (z.bits.exp == 0) 66 return (x); 67 68 /* If x = NaN or Inf, then sin(x) = NaN. */ 69 if (z.bits.exp == 32767) 70 return ((x - x) / (x - x)); 71 72 /* Optimize the case where x is already within range. */ 73 if (z.e < M_PI_4) { 74 hi = __kernel_sinl(z.e, 0, 0); 75 return (s ? -hi : hi); 76 } 77 78 /* Split z.e into a 24-bit representation. */ 79 e0 = ilogbl(z.e) - 23; 80 z.e = scalbnl(z.e, -e0); 81 for (i = 0; i < NX; i++) { 82 xd[i] = (double)((int32_t)z.e); 83 z.e = (z.e - xd[i]) * two24; 84 } 85 86 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ 87 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); 88 89 #if PREC == 2 90 hi = (long double)yd[0] + yd[1]; 91 lo = yd[1] - (hi - yd[0]); 92 #else /* PREC == 3 */ 93 long double t; 94 t = (long double)yd[2] + yd[1]; 95 hi = t + yd[0]; 96 lo = yd[0] - (hi - t); 97 #endif 98 99 switch (e0 & 3) { 100 case 0: 101 hi = __kernel_sinl(hi, lo, 1); 102 break; 103 case 1: 104 hi = __kernel_cosl(hi, lo); 105 break; 106 case 2: 107 hi = - __kernel_sinl(hi, lo, 1); 108 break; 109 case 3: 110 hi = - __kernel_cosl(hi, lo); 111 break; 112 } 113 114 return (s ? -hi : hi); 115 } 116