newlib/libm/ld80/k_sinl.c

   1 /* From: @(#)k_sin.c 1.3 95/01/18 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
   6  *
   7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14 #include <sys/cdefs.h>
  15 __FBSDID("$FreeBSD$");
  16
  17 /*
  18  * ld80 version of k_sin.c.  See ../src/k_sin.c for most comments.
  19  */
  20 #include <math.h>
  21 #include "../ld/math_private.h"
  22
  23 static const double
  24 half =  0.5;
  25
  26 /*
  27  * Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22]
  28  * |sin(x)/x - s(x)| < 2**-72.1
  29  *
  30  * See ../ld80/k_cosl.c for more details about the polynomial.
  31  */
  32 #if defined(__amd64__) || defined(__i386__)
  33 /* Long double constants are slow on these arches, and broken on i386. */
  34 static const volatile double
  35 S1hi = -0.16666666666666666,            /* -0x15555555555555.0p-55 */
  36 S1lo = -9.2563760475949941e-18;         /* -0x15580000000000.0p-109 */
  37 #define S1      ((long double)S1hi + S1lo)
  38 #else
  39 static const long double
  40 S1 = -0.166666666666666666671L;         /* -0xaaaaaaaaaaaaaaab.0p-66 */
  41 #endif
  42
  43 static const double
  44 S2 =  0.0083333333333333332,            /*  0x11111111111111.0p-59 */
  45 S3 = -0.00019841269841269427,           /* -0x1a01a01a019f81.0p-65 */
  46 S4 =  0.0000027557319223597490,         /*  0x171de3a55560f7.0p-71 */
  47 S5 = -0.000000025052108218074604,       /* -0x1ae64564f16cad.0p-78 */
  48 S6 =  1.6059006598854211e-10,           /*  0x161242b90243b5.0p-85 */
  49 S7 = -7.6429779983024564e-13,           /* -0x1ae42ebd1b2e00.0p-93 */
  50 S8 =  2.6174587166648325e-15;           /*  0x179372ea0b3f64.0p-101 */
  51
  52 long double
  53 __kernel_sinl(long double x, long double y, int iy)
  54 {
  55         long double z,r,v;
  56
  57         z       =  x*x;
  58         v       =  z*x;
  59         r       =  S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8)))));
  60         if(iy==0) return x+v*(S1+z*r);
  61         else      return x-((z*(half*y-v*r)-y)-v*S1);
  62 }