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1 //=========================================================================== |
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2 // |
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3 // k_sin.c |
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4 // |
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5 // Part of the standard mathematical function library |
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6 // |
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7 //=========================================================================== |
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8 //####COPYRIGHTBEGIN#### |
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9 // |
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10 // ------------------------------------------- |
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11 // The contents of this file are subject to the Cygnus eCos Public License |
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12 // Version 1.0 (the "License"); you may not use this file except in |
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13 // compliance with the License. You may obtain a copy of the License at |
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14 // http://sourceware.cygnus.com/ecos |
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15 // |
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16 // Software distributed under the License is distributed on an "AS IS" |
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17 // basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the |
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18 // License for the specific language governing rights and limitations under |
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19 // the License. |
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20 // |
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21 // The Original Code is eCos - Embedded Cygnus Operating System, released |
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22 // September 30, 1998. |
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23 // |
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24 // The Initial Developer of the Original Code is Cygnus. Portions created |
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25 // by Cygnus are Copyright (C) 1998,1999 Cygnus Solutions. All Rights Reserved. |
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26 // ------------------------------------------- |
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27 // |
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28 //####COPYRIGHTEND#### |
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29 //=========================================================================== |
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30 //#####DESCRIPTIONBEGIN#### |
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31 // |
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32 // Author(s): jlarmour |
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33 // Contributors: jlarmour |
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34 // Date: 1998-02-13 |
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35 // Purpose: |
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36 // Description: |
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37 // Usage: |
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38 // |
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39 //####DESCRIPTIONEND#### |
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40 // |
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41 //=========================================================================== |
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42 |
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43 // CONFIGURATION |
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44 |
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45 #include <pkgconf/libm.h> // Configuration header |
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46 |
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47 // Include the Math library? |
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48 #ifdef CYGPKG_LIBM |
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49 |
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50 // Derived from code with the following copyright |
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51 |
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52 |
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53 /* @(#)k_sin.c 1.3 95/01/18 */ |
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54 /* |
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55 * ==================================================== |
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56 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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57 * |
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58 * Developed at SunSoft, a Sun Microsystems, Inc. business. |
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59 * Permission to use, copy, modify, and distribute this |
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60 * software is freely granted, provided that this notice |
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61 * is preserved. |
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62 * ==================================================== |
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63 */ |
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64 |
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65 /* __kernel_sin( x, y, iy) |
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66 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
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67 * Input x is assumed to be bounded by ~pi/4 in magnitude. |
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68 * Input y is the tail of x. |
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69 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). |
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70 * |
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71 * Algorithm |
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72 * 1. Since sin(-x) = -sin(x), we need only to consider positive x. |
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73 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. |
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74 * 3. sin(x) is approximated by a polynomial of degree 13 on |
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75 * [0,pi/4] |
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76 * 3 13 |
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77 * sin(x) ~ x + S1*x + ... + S6*x |
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78 * where |
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79 * |
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80 * |sin(x) 2 4 6 8 10 12 | -58 |
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81 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 |
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82 * | x | |
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83 * |
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84 * 4. sin(x+y) = sin(x) + sin'(x')*y |
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85 * ~ sin(x) + (1-x*x/2)*y |
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86 * For better accuracy, let |
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87 * 3 2 2 2 2 |
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88 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) |
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89 * then 3 2 |
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90 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) |
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91 */ |
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92 |
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93 #include "mathincl/fdlibm.h" |
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94 |
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95 static const double |
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96 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
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97 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ |
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98 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ |
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99 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ |
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100 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ |
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101 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ |
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102 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ |
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103 |
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104 double __kernel_sin(double x, double y, int iy) |
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105 { |
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106 double z,r,v; |
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107 int ix; |
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108 ix = CYG_LIBM_HI(x)&0x7fffffff; /* high word of x */ |
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109 if(ix<0x3e400000) /* |x| < 2**-27 */ |
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110 {if((int)x==0) return x;} /* generate inexact */ |
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111 z = x*x; |
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112 v = z*x; |
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113 r = S2+z*(S3+z*(S4+z*(S5+z*S6))); |
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114 if(iy==0) return x+v*(S1+z*r); |
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115 else return x-((z*(half*y-v*r)-y)-v*S1); |
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116 } |
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117 |
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118 #endif // ifdef CYGPKG_LIBM |
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119 |
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120 // EOF k_sin.c |
