lookup_tables.h

//#define N 5000   // number of calls to make during test
#define NS 1024   // number of entries in sin table
#define MAXI 32768  // max integer value in table
#define I2F (1./MAXI) // conversion from integer to float

#ifndef _swap_int16_t
#define _swap_int16_t(a, b) { int16_t t = a; a = b; b = t; }
#endif


int i ;
long startTime, endTime ;
float dt ;
float d = 0.0 ;  // argument to sin function, degrees
float s ;  // result of sin function

// sin table
// values for first quadrant, other quadrants calculated by symetry
const uint16_t sintab[NS] = {
  0,
  50,100,150,201,251,
  301,351,402,452,502,
  552,603,653,703,753,
  804,854,904,954,1005,
  1055,1105,1155,1206,1256,
  1306,1356,1407,1457,1507,
  1557,1607,1658,1708,1758,
  1808,1858,1909,1959,2009,
  2059,2109,2159,2210,2260,
  2310,2360,2410,2460,2510,
  2560,2611,2661,2711,2761,
  2811,2861,2911,2961,3011,
  3061,3111,3161,3211,3261,
  3311,3361,3411,3461,3511,
  3561,3611,3661,3711,3761,
  3811,3861,3911,3961,4011,
  4061,4110,4160,4210,4260,
  4310,4360,4409,4459,4509,
  4559,4609,4658,4708,4758,
  4808,4857,4907,4957,5006,
  5056,5106,5155,5205,5255,
  5304,5354,5403,5453,5503,
  5552,5602,5651,5701,5750,
  5800,5849,5898,5948,5997,
  6047,6096,6146,6195,6244,
  6294,6343,6392,6442,6491,
  6540,6589,6639,6688,6737,
  6786,6835,6884,6934,6983,
  7032,7081,7130,7179,7228,
  7277,7326,7375,7424,7473,
  7522,7571,7620,7669,7717,
  7766,7815,7864,7913,7961,
  8010,8059,8108,8156,8205,
  8254,8302,8351,8400,8448,
  8497,8545,8594,8642,8691,
  8739,8788,8836,8884,8933,
  8981,9029,9078,9126,9174,
  9223,9271,9319,9367,9415,
  9463,9512,9560,9608,9656,
  9704,9752,9800,9848,9896,
  9944,9991,10039,10087,10135,
  10183,10230,10278,10326,10374,
  10421,10469,10517,10564,10612,
  10659,10707,10754,10802,10849,
  10897,10944,10991,11039,11086,
  11133,11181,11228,11275,11322,
  11369,11416,11464,11511,11558,
  11605,11652,11699,11746,11793,
  11839,11886,11933,11980,12027,
  12073,12120,12167,12213,12260,
  12307,12353,12400,12446,12493,
  12539,12586,12632,12678,12725,
  12771,12817,12864,12910,12956,
  13002,13048,13094,13140,13186,
  13232,13278,13324,13370,13416,
  13462,13508,13554,13599,13645,
  13691,13736,13782,13828,13873,
  13919,13964,14010,14055,14100,
  14146,14191,14236,14282,14327,
  14372,14417,14462,14507,14552,
  14598,14642,14687,14732,14777,
  14822,14867,14912,14956,15001,
  15046,15090,15135,15180,15224,
  15269,15313,15357,15402,15446,
  15491,15535,15579,15623,15667,
  15712,15756,15800,15844,15888,
  15932,15976,16019,16063,16107,
  16151,16195,16238,16282,16325,
  16369,16413,16456,16499,16543,
  16586,16630,16673,16716,16759,
  16802,16846,16889,16932,16975,
  17018,17061,17104,17146,17189,
  17232,17275,17317,17360,17403,
  17445,17488,17530,17573,17615,
  17658,17700,17742,17784,17827,
  17869,17911,17953,17995,18037,
  18079,18121,18163,18204,18246,
  18288,18330,18371,18413,18454,
  18496,18537,18579,18620,18662,
  18703,18744,18785,18826,18868,
  18909,18950,18991,19032,19073,
  19113,19154,19195,19236,19276,
  19317,19358,19398,19439,19479,
  19519,19560,19600,19640,19681,
  19721,19761,19801,19841,19881,
  19921,19961,20001,20040,20080,
  20120,20159,20199,20239,20278,
  20318,20357,20396,20436,20475,
  20514,20553,20592,20631,20671,
  20709,20748,20787,20826,20865,
  20904,20942,20981,21020,21058,
  21097,21135,21173,21212,21250,
  21288,21326,21365,21403,21441,
  21479,21517,21555,21592,21630,
  21668,21706,21743,21781,21818,
  21856,21893,21931,21968,22005,
  22042,22080,22117,22154,22191,
  22228,22265,22301,22338,22375,
  22412,22448,22485,22521,22558,
  22594,22631,22667,22703,22740,
  22776,22812,22848,22884,22920,
  22956,22992,23027,23063,23099,
  23134,23170,23205,23241,23276,
  23312,23347,23382,23417,23453,
  23488,23523,23558,23593,23627,
  23662,23697,23732,23766,23801,
  23835,23870,23904,23939,23973,
  24007,24041,24075,24109,24144,
  24177,24211,24245,24279,24313,
  24346,24380,24414,24447,24480,
  24514,24547,24580,24614,24647,
  24680,24713,24746,24779,24812,
  24845,24877,24910,24943,24975,
  25008,25040,25073,25105,25137,
  25169,25201,25234,25266,25298,
  25330,25361,25393,25425,25457,
  25488,25520,25551,25583,25614,
  25645,25677,25708,25739,25770,
  25801,25832,25863,25894,25925,
  25955,25986,26016,26047,26077,
  26108,26138,26169,26199,26229,
  26259,26289,26319,26349,26379,
  26409,26438,26468,26498,26527,
  26557,26586,26615,26645,26674,
  26703,26732,26761,26790,26819,
  26848,26877,26905,26934,26963,
  26991,27020,27048,27076,27105,
  27133,27161,27189,27217,27245,
  27273,27301,27329,27356,27384,
  27411,27439,27466,27494,27521,
  27548,27576,27603,27630,27657,
  27684,27711,27737,27764,27791,
  27817,27844,27870,27897,27923,
  27949,27976,28002,28028,28054,
  28080,28106,28131,28157,28183,
  28208,28234,28259,28285,28310,
  28335,28361,28386,28411,28436,
  28461,28486,28511,28535,28560,
  28585,28609,28634,28658,28682,
  28707,28731,28755,28779,28803,
  28827,28851,28875,28898,28922,
  28946,28969,28993,29016,29039,
  29062,29086,29109,29132,29155,
  29178,29201,29223,29246,29269,
  29291,29314,29336,29359,29381,
  29403,29425,29447,29469,29491,
  29513,29535,29557,29578,29600,
  29621,29643,29664,29686,29707,
  29728,29749,29770,29791,29812,
  29833,29854,29874,29895,29915,
  29936,29956,29977,29997,30017,
  30037,30057,30077,30097,30117,
  30137,30156,30176,30196,30215,
  30235,30254,30273,30292,30312,
  30331,30350,30368,30387,30406,
  30425,30443,30462,30480,30499,
  30517,30535,30554,30572,30590,
  30608,30626,30644,30661,30679,
  30697,30714,30732,30749,30766,
  30784,30801,30818,30835,30852,
  30869,30886,30902,30919,30936,
  30952,30969,30985,31001,31018,
  31034,31050,31066,31082,31098,
  31114,31129,31145,31161,31176,
  31192,31207,31222,31237,31253,
  31268,31283,31298,31312,31327,
  31342,31357,31371,31386,31400,
  31414,31429,31443,31457,31471,
  31485,31499,31513,31526,31540,
  31554,31567,31581,31594,31607,
  31620,31634,31647,31660,31673,
  31685,31698,31711,31723,31736,
  31749,31761,31773,31785,31798,
  31810,31822,31834,31846,31857,
  31869,31881,31892,31904,31915,
  31927,31938,31949,31960,31971,
  31982,31993,32004,32015,32025,
  32036,32047,32057,32067,32078,
  32088,32098,32108,32118,32128,
  32138,32148,32157,32167,32176,
  32186,32195,32205,32214,32223,
  32232,32241,32250,32259,32268,
  32276,32285,32294,32302,32311,
  32319,32327,32335,32343,32351,
  32359,32367,32375,32383,32390,
  32398,32405,32413,32420,32427,
  32435,32442,32449,32456,32463,
  32469,32476,32483,32489,32496,
  32502,32509,32515,32521,32527,
  32533,32539,32545,32551,32557,
  32562,32568,32573,32579,32584,
  32589,32595,32600,32605,32610,
  32615,32619,32624,32629,32633,
  32638,32642,32647,32651,32655,
  32659,32663,32667,32671,32675,
  32679,32682,32686,32689,32693,
  32696,32700,32703,32706,32709,
  32712,32715,32718,32720,32723,
  32726,32728,32730,32733,32735,
  32737,32739,32741,32743,32745,
  32747,32749,32750,32752,32754,
  32755,32756,32758,32759,32760,
  32761,32762,32763,32764,32764,
  32765,32766,32766,32767,32767,
  32767,32767,32767
} ;


float TWOPI = PI*2;
float HALFPI = PI*0.5;
float ITWOPI = 1./TWOPI;


float dosincos(float x, bool iscos) {
  int ix ;   // index into sin table
  int is ;   // value read from sin table
  int q ;    // quadrant number 0,1,2,3
  int j ;
  if(iscos) x += HALFPI;
  x *= ITWOPI;
  x -= (int)x ;
  if (x < 0)
    x += 1.0 ;   // x is now between 0 and 1, representing 0 to 360 degrees
  q = x * 4 ;   // get quadrant number
  ix = (int)(x*4*NS) % NS ;  // get index into table

  switch(q) {
    case 0:   // 0-90
      is = sintab[ix];
    break ;
    case 1:   // 90-180
      ix = NS - ix - 1 ;  // reflect
      is = sintab[ix];
    break ;
    case 2:   // 180-270
      is = -sintab[ix];  // negate
    break ;
    case 3:   // 270-360
      ix = NS - ix - 1;   // reflect
      is = -sintab[ix];   // negate
    break ;
  }
  return((float)is*I2F) ;
}

float romsin(float x) {
  return dosincos(x, false);
}
float romcos(float x) {
  return dosincos(x, true);
}



#define LOG_CACHE_SIZE 1024
static float logCache[LOG_CACHE_SIZE];
float precision = 8.90; // 512 / 115
bool romloginit = false;

float romlog( float in ) {
  int logindex = in*precision;
  if( logindex > LOG_CACHE_SIZE ) {
    //log_n("Out of cache size at offset %.8f", in);
    return log(in);
  }
  if(!romloginit) { 
    for( uint16_t i=0;i<LOG_CACHE_SIZE;i++) logCache[i] = -1.0;
    romloginit = true;
  }
  if( logCache[logindex]!=-1.0 ) return logCache[logindex];
  logCache[logindex] = log(in);
  return logCache[logindex];
}



#define SQR_CACHE_SIZE SIZE*8
static float sqrtCache[SQR_CACHE_SIZE];
float sqrtprecision = .08;
bool romsqrtinit = false;

float romsqrt( float in ) {
  int sqrtindex = in*sqrtprecision;
  if( sqrtindex > SQR_CACHE_SIZE ) {
    log_n("Out of cache size at offset %.8f", in);
    return sqrt(in);
  }
  if(!romsqrtinit) { 
    for( uint16_t i=0;i<SQR_CACHE_SIZE;i++) sqrtCache[i] = -1.0;
    romsqrtinit = true;
  }
  if( sqrtCache[sqrtindex]!=-1.0 ) return sqrtCache[sqrtindex];
  sqrtCache[sqrtindex] = sqrt(in);
  return sqrtCache[sqrtindex];
}

#define POW_CACHE_SIZE SIZE
static float powCache[POW_CACHE_SIZE];
float powprecision = 1;
bool rompowinit = false;
float rompow( float in ) {
  int powindex = abs(in*powprecision);
  if( powindex > POW_CACHE_SIZE ) {
    log_n("Out of cache size at offset %.8f", in);
    return in*in;
  }
  if(!rompowinit) { 
    for( uint16_t i=0;i<POW_CACHE_SIZE;i++) powCache[i] = -1.0;
    rompowinit = true;
  }
  if( powCache[powindex]!=-1.0 ) return powCache[powindex];
  powCache[powindex] = in*in;
  return powCache[powindex];
}