drivers/generic_math.h

   1 /*
   2    generic implementation of sin(x) and cos(x) functions.
   3    Specially for Linux.
   4    Licence: GPL
   5    Copyright (C) 2002 Nick Kurshev
   6 */
   7
   8 #ifndef GENERIC_MATH_H
   9 #define GENERIC_MATH_H
  10
  11 typedef struct _gen_sincos
  12 {
  13   double x;
  14   double sinx;
  15   double cosx;
  16 }gen_sincos_t;
  17
  18 static gen_sincos_t g_sincos[201] = {
  19 { -3.141600e+00, 7.346410e-06, -1.000000e-00 },
  20 { -3.110184e+00, -3.140349e-02, -9.995068e-01 },
  21 { -3.078768e+00, -6.278333e-02, -9.980272e-01 },
  22 { -3.047352e+00, -9.410122e-02, -9.955626e-01 },
  23 { -3.015936e+00, -1.253262e-01, -9.921156e-01 },
  24 { -2.984520e+00, -1.564276e-01, -9.876894e-01 },
  25 { -2.953104e+00, -1.873745e-01, -9.822885e-01 },
  26 { -2.921688e+00, -2.181366e-01, -9.759183e-01 },
  27 { -2.890272e+00, -2.486833e-01, -9.685848e-01 },
  28 { -2.858856e+00, -2.789847e-01, -9.602956e-01 },
  29 { -2.827440e+00, -3.090107e-01, -9.510586e-01 },
  30 { -2.796024e+00, -3.387318e-01, -9.408830e-01 },
  31 { -2.764608e+00, -3.681185e-01, -9.297789e-01 },
  32 { -2.733192e+00, -3.971420e-01, -9.177572e-01 },
  33 { -2.701776e+00, -4.257736e-01, -9.048297e-01 },
  34 { -2.670360e+00, -4.539849e-01, -8.910094e-01 },
  35 { -2.638944e+00, -4.817483e-01, -8.763097e-01 },
  36 { -2.607528e+00, -5.090362e-01, -8.607451e-01 },
  37 { -2.576112e+00, -5.358217e-01, -8.443312e-01 },
  38 { -2.544696e+00, -5.620785e-01, -8.270839e-01 },
  39 { -2.513280e+00, -5.877805e-01, -8.090204e-01 },
  40 { -2.481864e+00, -6.129025e-01, -7.901586e-01 },
  41 { -2.450448e+00, -6.374196e-01, -7.705169e-01 },
  42 { -2.419032e+00, -6.613076e-01, -7.501148e-01 },
  43 { -2.387616e+00, -6.845430e-01, -7.289724e-01 },
  44 { -2.356200e+00, -7.071029e-01, -7.071107e-01 },
  45 { -2.324784e+00, -7.289649e-01, -6.845511e-01 },
  46 { -2.293368e+00, -7.501075e-01, -6.613159e-01 },
  47 { -2.261952e+00, -7.705099e-01, -6.374281e-01 },
  48 { -2.230536e+00, -7.901518e-01, -6.129112e-01 },
  49 { -2.199120e+00, -8.090140e-01, -5.877894e-01 },
  50 { -2.167704e+00, -8.270777e-01, -5.620876e-01 },
  51 { -2.136288e+00, -8.443252e-01, -5.358310e-01 },
  52 { -2.104872e+00, -8.607395e-01, -5.090457e-01 },
  53 { -2.073456e+00, -8.763043e-01, -4.817579e-01 },
  54 { -2.042040e+00, -8.910044e-01, -4.539948e-01 },
  55 { -2.010624e+00, -9.048251e-01, -4.257835e-01 },
  56 { -1.979208e+00, -9.177528e-01, -3.971521e-01 },
  57 { -1.947792e+00, -9.297748e-01, -3.681288e-01 },
  58 { -1.916376e+00, -9.408793e-01, -3.387421e-01 },
  59 { -1.884960e+00, -9.510552e-01, -3.090212e-01 },
  60 { -1.853544e+00, -9.602925e-01, -2.789953e-01 },
  61 { -1.822128e+00, -9.685821e-01, -2.486940e-01 },
  62 { -1.790712e+00, -9.759158e-01, -2.181473e-01 },
  63 { -1.759296e+00, -9.822865e-01, -1.873854e-01 },
  64 { -1.727880e+00, -9.876877e-01, -1.564385e-01 },
  65 { -1.696464e+00, -9.921142e-01, -1.253372e-01 },
  66 { -1.665048e+00, -9.955616e-01, -9.411219e-02 },
  67 { -1.633632e+00, -9.980265e-01, -6.279433e-02 },
  68 { -1.602216e+00, -9.995064e-01, -3.141450e-02 },
  69 { -1.570800e+00, -1.000000e-00, -3.673205e-06 },
  70 { -1.539384e+00, -9.995067e-01, 3.140716e-02 },
  71 { -1.507968e+00, -9.980269e-01, 6.278700e-02 },
  72 { -1.476552e+00, -9.955623e-01, 9.410488e-02 },
  73 { -1.445136e+00, -9.921151e-01, 1.253299e-01 },
  74 { -1.413720e+00, -9.876889e-01, 1.564312e-01 },
  75 { -1.382304e+00, -9.822879e-01, 1.873781e-01 },
  76 { -1.350888e+00, -9.759175e-01, 2.181402e-01 },
  77 { -1.319472e+00, -9.685839e-01, 2.486869e-01 },
  78 { -1.288056e+00, -9.602945e-01, 2.789882e-01 },
  79 { -1.256640e+00, -9.510574e-01, 3.090142e-01 },
  80 { -1.225224e+00, -9.408817e-01, 3.387352e-01 },
  81 { -1.193808e+00, -9.297775e-01, 3.681220e-01 },
  82 { -1.162392e+00, -9.177557e-01, 3.971454e-01 },
  83 { -1.130976e+00, -9.048282e-01, 4.257769e-01 },
  84 { -1.099560e+00, -8.910077e-01, 4.539882e-01 },
  85 { -1.068144e+00, -8.763079e-01, 4.817515e-01 },
  86 { -1.036728e+00, -8.607433e-01, 5.090393e-01 },
  87 { -1.005312e+00, -8.443292e-01, 5.358248e-01 },
  88 { -9.738960e-01, -8.270819e-01, 5.620815e-01 },
  89 { -9.424800e-01, -8.090183e-01, 5.877835e-01 },
  90 { -9.110640e-01, -7.901563e-01, 6.129054e-01 },
  91 { -8.796480e-01, -7.705146e-01, 6.374224e-01 },
  92 { -8.482320e-01, -7.501124e-01, 6.613104e-01 },
  93 { -8.168160e-01, -7.289699e-01, 6.845457e-01 },
  94 { -7.854000e-01, -7.071081e-01, 7.071055e-01 },
  95 { -7.539840e-01, -6.845484e-01, 7.289674e-01 },
  96 { -7.225680e-01, -6.613131e-01, 7.501100e-01 },
  97 { -6.911520e-01, -6.374252e-01, 7.705122e-01 },
  98 { -6.597360e-01, -6.129083e-01, 7.901541e-01 },
  99 { -6.283200e-01, -5.877864e-01, 8.090161e-01 },
 100 { -5.969040e-01, -5.620845e-01, 8.270798e-01 },
 101 { -5.654880e-01, -5.358279e-01, 8.443272e-01 },
 102 { -5.340720e-01, -5.090425e-01, 8.607414e-01 },
 103 { -5.026560e-01, -4.817547e-01, 8.763061e-01 },
 104 { -4.712400e-01, -4.539915e-01, 8.910060e-01 },
 105 { -4.398240e-01, -4.257802e-01, 9.048266e-01 },
 106 { -4.084080e-01, -3.971488e-01, 9.177542e-01 },
 107 { -3.769920e-01, -3.681254e-01, 9.297762e-01 },
 108 { -3.455760e-01, -3.387387e-01, 9.408805e-01 },
 109 { -3.141600e-01, -3.090177e-01, 9.510563e-01 },
 110 { -2.827440e-01, -2.789917e-01, 9.602935e-01 },
 111 { -2.513280e-01, -2.486905e-01, 9.685830e-01 },
 112 { -2.199120e-01, -2.181437e-01, 9.759166e-01 },
 113 { -1.884960e-01, -1.873817e-01, 9.822872e-01 },
 114 { -1.570800e-01, -1.564348e-01, 9.876883e-01 },
 115 { -1.256640e-01, -1.253335e-01, 9.921147e-01 },
 116 { -9.424800e-02, -9.410853e-02, 9.955619e-01 },
 117 { -6.283200e-02, -6.279067e-02, 9.980267e-01 },
 118 { -3.141600e-02, -3.141083e-02, 9.995066e-01 },
 119 { 0.000000e+00, 0.000000e+00, 1.000000e+00 },
 120 { 3.141600e-02, 3.141083e-02, 9.995066e-01 },
 121 { 6.283200e-02, 6.279067e-02, 9.980267e-01 },
 122 { 9.424800e-02, 9.410853e-02, 9.955619e-01 },
 123 { 1.256640e-01, 1.253335e-01, 9.921147e-01 },
 124 { 1.570800e-01, 1.564348e-01, 9.876883e-01 },
 125 { 1.884960e-01, 1.873817e-01, 9.822872e-01 },
 126 { 2.199120e-01, 2.181437e-01, 9.759166e-01 },
 127 { 2.513280e-01, 2.486905e-01, 9.685830e-01 },
 128 { 2.827440e-01, 2.789917e-01, 9.602935e-01 },
 129 { 3.141600e-01, 3.090177e-01, 9.510563e-01 },
 130 { 3.455760e-01, 3.387387e-01, 9.408805e-01 },
 131 { 3.769920e-01, 3.681254e-01, 9.297762e-01 },
 132 { 4.084080e-01, 3.971488e-01, 9.177542e-01 },
 133 { 4.398240e-01, 4.257802e-01, 9.048266e-01 },
 134 { 4.712400e-01, 4.539915e-01, 8.910060e-01 },
 135 { 5.026560e-01, 4.817547e-01, 8.763061e-01 },
 136 { 5.340720e-01, 5.090425e-01, 8.607414e-01 },
 137 { 5.654880e-01, 5.358279e-01, 8.443272e-01 },
 138 { 5.969040e-01, 5.620845e-01, 8.270798e-01 },
 139 { 6.283200e-01, 5.877864e-01, 8.090161e-01 },
 140 { 6.597360e-01, 6.129083e-01, 7.901541e-01 },
 141 { 6.911520e-01, 6.374252e-01, 7.705122e-01 },
 142 { 7.225680e-01, 6.613131e-01, 7.501100e-01 },
 143 { 7.539840e-01, 6.845484e-01, 7.289674e-01 },
 144 { 7.854000e-01, 7.071081e-01, 7.071055e-01 },
 145 { 8.168160e-01, 7.289699e-01, 6.845457e-01 },
 146 { 8.482320e-01, 7.501124e-01, 6.613104e-01 },
 147 { 8.796480e-01, 7.705146e-01, 6.374224e-01 },
 148 { 9.110640e-01, 7.901563e-01, 6.129054e-01 },
 149 { 9.424800e-01, 8.090183e-01, 5.877835e-01 },
 150 { 9.738960e-01, 8.270819e-01, 5.620815e-01 },
 151 { 1.005312e+00, 8.443292e-01, 5.358248e-01 },
 152 { 1.036728e+00, 8.607433e-01, 5.090393e-01 },
 153 { 1.068144e+00, 8.763079e-01, 4.817515e-01 },
 154 { 1.099560e+00, 8.910077e-01, 4.539882e-01 },
 155 { 1.130976e+00, 9.048282e-01, 4.257769e-01 },
 156 { 1.162392e+00, 9.177557e-01, 3.971454e-01 },
 157 { 1.193808e+00, 9.297775e-01, 3.681220e-01 },
 158 { 1.225224e+00, 9.408817e-01, 3.387352e-01 },
 159 { 1.256640e+00, 9.510574e-01, 3.090142e-01 },
 160 { 1.288056e+00, 9.602945e-01, 2.789882e-01 },
 161 { 1.319472e+00, 9.685839e-01, 2.486869e-01 },
 162 { 1.350888e+00, 9.759175e-01, 2.181402e-01 },
 163 { 1.382304e+00, 9.822879e-01, 1.873781e-01 },
 164 { 1.413720e+00, 9.876889e-01, 1.564312e-01 },
 165 { 1.445136e+00, 9.921151e-01, 1.253299e-01 },
 166 { 1.476552e+00, 9.955623e-01, 9.410488e-02 },
 167 { 1.507968e+00, 9.980269e-01, 6.278700e-02 },
 168 { 1.539384e+00, 9.995067e-01, 3.140716e-02 },
 169 { 1.570800e+00, 1.000000e-00, -3.673205e-06 },
 170 { 1.602216e+00, 9.995064e-01, -3.141450e-02 },
 171 { 1.633632e+00, 9.980265e-01, -6.279433e-02 },
 172 { 1.665048e+00, 9.955616e-01, -9.411219e-02 },
 173 { 1.696464e+00, 9.921142e-01, -1.253372e-01 },
 174 { 1.727880e+00, 9.876877e-01, -1.564385e-01 },
 175 { 1.759296e+00, 9.822865e-01, -1.873854e-01 },
 176 { 1.790712e+00, 9.759158e-01, -2.181473e-01 },
 177 { 1.822128e+00, 9.685821e-01, -2.486940e-01 },
 178 { 1.853544e+00, 9.602925e-01, -2.789953e-01 },
 179 { 1.884960e+00, 9.510552e-01, -3.090212e-01 },
 180 { 1.916376e+00, 9.408793e-01, -3.387421e-01 },
 181 { 1.947792e+00, 9.297748e-01, -3.681288e-01 },
 182 { 1.979208e+00, 9.177528e-01, -3.971521e-01 },
 183 { 2.010624e+00, 9.048251e-01, -4.257835e-01 },
 184 { 2.042040e+00, 8.910044e-01, -4.539948e-01 },
 185 { 2.073456e+00, 8.763043e-01, -4.817579e-01 },
 186 { 2.104872e+00, 8.607395e-01, -5.090457e-01 },
 187 { 2.136288e+00, 8.443252e-01, -5.358310e-01 },
 188 { 2.167704e+00, 8.270777e-01, -5.620876e-01 },
 189 { 2.199120e+00, 8.090140e-01, -5.877894e-01 },
 190 { 2.230536e+00, 7.901518e-01, -6.129112e-01 },
 191 { 2.261952e+00, 7.705099e-01, -6.374281e-01 },
 192 { 2.293368e+00, 7.501075e-01, -6.613159e-01 },
 193 { 2.324784e+00, 7.289649e-01, -6.845511e-01 },
 194 { 2.356200e+00, 7.071029e-01, -7.071107e-01 },
 195 { 2.387616e+00, 6.845430e-01, -7.289724e-01 },
 196 { 2.419032e+00, 6.613076e-01, -7.501148e-01 },
 197 { 2.450448e+00, 6.374196e-01, -7.705169e-01 },
 198 { 2.481864e+00, 6.129025e-01, -7.901586e-01 },
 199 { 2.513280e+00, 5.877805e-01, -8.090204e-01 },
 200 { 2.544696e+00, 5.620785e-01, -8.270839e-01 },
 201 { 2.576112e+00, 5.358217e-01, -8.443312e-01 },
 202 { 2.607528e+00, 5.090362e-01, -8.607451e-01 },
 203 { 2.638944e+00, 4.817483e-01, -8.763097e-01 },
 204 { 2.670360e+00, 4.539849e-01, -8.910094e-01 },
 205 { 2.701776e+00, 4.257736e-01, -9.048297e-01 },
 206 { 2.733192e+00, 3.971420e-01, -9.177572e-01 },
 207 { 2.764608e+00, 3.681185e-01, -9.297789e-01 },
 208 { 2.796024e+00, 3.387318e-01, -9.408830e-01 },
 209 { 2.827440e+00, 3.090107e-01, -9.510586e-01 },
 210 { 2.858856e+00, 2.789847e-01, -9.602956e-01 },
 211 { 2.890272e+00, 2.486833e-01, -9.685848e-01 },
 212 { 2.921688e+00, 2.181366e-01, -9.759183e-01 },
 213 { 2.953104e+00, 1.873745e-01, -9.822885e-01 },
 214 { 2.984520e+00, 1.564276e-01, -9.876894e-01 },
 215 { 3.015936e+00, 1.253262e-01, -9.921156e-01 },
 216 { 3.047352e+00, 9.410122e-02, -9.955626e-01 },
 217 { 3.078768e+00, 6.278333e-02, -9.980272e-01 },
 218 { 3.110184e+00, 3.140349e-02, -9.995068e-01 },
 219 { 3.141600e+00, -7.346410e-06, -1.000000e-00 }
 220 };
 221
 222 # define M_PI           3.14159265358979323846  /* pi */
 223
 224 static double inline gen_sin(double x)
 225 {
 226   int i;
 227   if(x < 0) while(x < -M_PI) x+= M_PI;
 228   else      while(x > M_PI) x-= M_PI;
 229   for(i=0;i<sizeof(g_sincos)/sizeof(gen_sincos_t)-1;i++)
 230   {
 231     if(x>=g_sincos[i].x && x <= g_sincos[i+1].x)
 232     {
 233       return (g_sincos[i+1].sinx-g_sincos[i].sinx)*(x-g_sincos[i].x)/(g_sincos[i+1].x-g_sincos[i].x)+g_sincos[i].sinx;
 234     }
 235   }
 236   return x<0?1:-1;
 237 }
 238 #undef sin
 239 #define sin(x) gen_sin(x)
 240
 241 static double inline gen_cos(double x)
 242 {
 243   int i;
 244   if(x < 0) while(x < -M_PI) x+= M_PI;
 245   else      while(x > M_PI) x-= M_PI;
 246   for(i=0;i<sizeof(g_sincos)/sizeof(gen_sincos_t)-1;i++)
 247   {
 248     if(x>=g_sincos[i].x && x <= g_sincos[i+1].x)
 249     {
 250       return (g_sincos[i+1].cosx-g_sincos[i].cosx)*(x-g_sincos[i].x)/(g_sincos[i+1].x-g_sincos[i].x)+g_sincos[i].cosx;
 251     }
 252   }
 253   return x<0?1:-1;
 254 }
 255 #undef cos
 256 #define cos(x) gen_cos(x)
 257
 258 #endif