libFDK/src/FDK_trigFcts.cpp

   1
   2 /* -----------------------------------------------------------------------------------------------------------
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  10 the MPEG Advanced Audio Coding ("AAC") encoding and decoding scheme for digital audio.
  11 This FDK AAC Codec software is intended to be used on a wide variety of Android devices.
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  73 5.    CONTACT INFORMATION
  74
  75 Fraunhofer Institute for Integrated Circuits IIS
  76 Attention: Audio and Multimedia Departments - FDK AAC LL
  77 Am Wolfsmantel 33
  78 91058 Erlangen, Germany
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  81 amm-info@iis.fraunhofer.de
  82 ----------------------------------------------------------------------------------------------------------- */
  83
  84 /***************************  Fraunhofer IIS FDK Tools  **********************
  85
  86    Author(s):   Haricharan Lakshman, Manuel Jander
  87    Description: Trigonometric functions fixed point fractional implementation.
  88
  89 ******************************************************************************/
  90
  91 #include "FDK_trigFcts.h"
  92
  93 #include "fixpoint_math.h"
  94
  95
  96
  97
  98 #define IMPROVE_ATAN2_ACCURACY  1  // 0 --> 59 dB SNR     1 --> 65 dB SNR
  99 #define MINSFTAB  7
 100 #define MAXSFTAB 25
 101
 102 #if IMPROVE_ATAN2_ACCURACY
 103 static const FIXP_DBL f_atan_expand_range[MAXSFTAB-(MINSFTAB-1)]  =
 104 {
 105   /*****************************************************************************
 106    *
 107    *  Table holds fixp_atan() output values which are outside of input range
 108    *  of fixp_atan() to improve SNR of fixp_atan2().
 109    *
 110    *  This Table might also be used in fixp_atan() [todo] so there a wider input
 111    *  range can be covered, too.
 112    *
 113    *  Matlab (generate table):
 114    *    for scl = 7:25            % MINSFTAB .. MAXSFTAB
 115    *      at=atan(0.5 *(2^scl));  % 0.5 because get in 'middle' area of current scale level 'scl'
 116    *      at/2                    % div at by ATO_SCALE
 117    *    end
 118    *
 119    *  Table divided by 2=ATO_SCALE  <--  SF=ATO_SF
 120    *****************************************************************************/
 121    FL2FXCONST_DBL(7.775862990872099e-001), FL2FXCONST_DBL(7.814919928673978e-001), FL2FXCONST_DBL(7.834450483314648e-001),
 122    FL2FXCONST_DBL(7.844216021392089e-001), FL2FXCONST_DBL(7.849098823026687e-001), FL2FXCONST_DBL(7.851540227918509e-001),
 123    FL2FXCONST_DBL(7.852760930873737e-001), FL2FXCONST_DBL(7.853371282415015e-001), FL2FXCONST_DBL(7.853676458193612e-001),
 124    FL2FXCONST_DBL(7.853829046083906e-001), FL2FXCONST_DBL(7.853905340029177e-001), FL2FXCONST_DBL(7.853943487001828e-001),
 125    FL2FXCONST_DBL(7.853962560488155e-001), FL2FXCONST_DBL(7.853972097231319e-001), FL2FXCONST_DBL(7.853976865602901e-001),
 126    FL2FXCONST_DBL(7.853979249788692e-001), FL2FXCONST_DBL(7.853980441881587e-001), FL2FXCONST_DBL(7.853981037928035e-001),
 127    FL2FXCONST_DBL(7.853981335951259e-001)
 128    //     pi/4 = 0.785398163397448 = pi/2/ATO_SCALE
 129 };
 130 #endif
 131
 132 FIXP_DBL fixp_atan2(FIXP_DBL y, FIXP_DBL x)
 133 {
 134     FIXP_DBL q;
 135     FIXP_DBL at;  // atan  out
 136     FIXP_DBL at2; // atan2 out
 137     FIXP_DBL ret = FL2FXCONST_DBL(-1.0f);
 138     INT sf,sfo,stf;
 139
 140     // --- division
 141
 142     if      (y > FL2FXCONST_DBL(0.0f))
 143     {
 144         if      (x > FL2FXCONST_DBL(0.0f)) {
 145                                            q =  fDivNormHighPrec( y, x, &sf); // both pos.
 146         }
 147         else if (x < FL2FXCONST_DBL(0.0f)) {
 148                                            q = -fDivNormHighPrec( y,-x, &sf); // x neg.
 149         }
 150         else {//(x ==FL2FXCONST_DBL(0.0f))
 151                                            q =  FL2FXCONST_DBL(+1.0f);  // y/x = pos/zero = +Inf
 152                                            sf = 0;
 153         }
 154     }
 155     else if (y < FL2FXCONST_DBL(0.0f))
 156     {
 157         if      (x > FL2FXCONST_DBL(0.0f)) {
 158                                            q = -fDivNormHighPrec(-y, x, &sf); // y neg.
 159         }
 160         else if (x < FL2FXCONST_DBL(0.0f)) {
 161                                            q =  fDivNormHighPrec(-y,-x, &sf); // both neg.
 162         }
 163         else {//(x ==FL2FXCONST_DBL(0.0f))
 164                                            q =  FL2FXCONST_DBL(-1.0f);  // y/x = neg/zero = -Inf
 165                                            sf = 0;
 166         }
 167     }
 168     else { // (y ==FL2FXCONST_DBL(0.0f))
 169         q = FL2FXCONST_DBL(0.0f);
 170         sf = 0;
 171     }
 172     sfo = sf;
 173
 174     // --- atan()
 175
 176     if  ( sfo > ATI_SF ) {
 177         // --- could not calc fixp_atan() here bec of input data out of range
 178         //     ==> therefore give back boundary values
 179
 180         #if IMPROVE_ATAN2_ACCURACY
 181         if (sfo > MAXSFTAB) sfo = MAXSFTAB;
 182         #endif
 183
 184         if      (  q > FL2FXCONST_DBL(0.0f) ) {
 185            #if IMPROVE_ATAN2_ACCURACY
 186             at = +f_atan_expand_range[sfo-ATI_SF-1];
 187            #else
 188             at = FL2FXCONST_DBL( +M_PI/2 / ATO_SCALE);
 189            #endif
 190         }
 191         else if (  q < FL2FXCONST_DBL(0.0f) ) {
 192            #if IMPROVE_ATAN2_ACCURACY
 193             at = -f_atan_expand_range[sfo-ATI_SF-1];
 194            #else
 195             at = FL2FXCONST_DBL( -M_PI/2 / ATO_SCALE);
 196            #endif
 197         }
 198         else {  // q== FL2FXCONST_DBL(0.0f)
 199             at = FL2FXCONST_DBL( 0.0f );
 200         }
 201     }else{
 202         // --- calc of fixp_atan() is possible; input data within range
 203         //     ==> set q on fixed scale level as desired from fixp_atan()
 204         stf = sfo - ATI_SF;
 205         if (stf > 0)  q = q << (INT)fMin( stf,DFRACT_BITS-1);
 206         else          q = q >> (INT)fMin(-stf,DFRACT_BITS-1);
 207         at = fixp_atan(q);  // ATO_SF
 208     }
 209
 210     // --- atan2()
 211
 212     at2 = at >> (AT2O_SF - ATO_SF); // now AT2O_SF for atan2
 213     if      (  x > FL2FXCONST_DBL(0.0f) ) {
 214         ret = at2;
 215     }
 216     else if (  x < FL2FXCONST_DBL(0.0f) ) {
 217         if (  y >= FL2FXCONST_DBL(0.0f) ) {
 218             ret = at2 + FL2FXCONST_DBL( M_PI / AT2O_SCALE);
 219         } else {
 220             ret = at2 - FL2FXCONST_DBL( M_PI / AT2O_SCALE);
 221         }
 222     }
 223     else {
 224         // x == 0
 225         if      ( y >  FL2FXCONST_DBL(0.0f) ) {
 226             ret = FL2FXCONST_DBL( +M_PI/2 / AT2O_SCALE);
 227         }
 228         else if ( y <  FL2FXCONST_DBL(0.0f) ) {
 229             ret = FL2FXCONST_DBL( -M_PI/2 / AT2O_SCALE);
 230         }
 231         else if ( y == FL2FXCONST_DBL(0.0f) ) {
 232             ret = FL2FXCONST_DBL(0.0f);
 233         }
 234     }
 235     return ret;
 236 }
 237
 238
 239 FIXP_DBL fixp_atan(FIXP_DBL x)
 240 {
 241     INT sign;
 242     FIXP_DBL result, temp;
 243
 244     // SNR of fixp_atan() = 56 dB
 245     FIXP_DBL ONEBY3P56  = (FIXP_DBL)0x26800000; // 1.0/3.56 in q31
 246     FIXP_DBL P281       = (FIXP_DBL)0x00013000; // 0.281 in q18
 247     FIXP_DBL ONEP571    = (FIXP_DBL)0x6487ef00; // 1.571 in q30
 248
 249     if (x < FIXP_DBL(0)) {
 250       sign = 1;
 251       x = - x ;
 252     } else {
 253       sign = 0;
 254     }
 255
 256     /* calc of arctan */
 257     if(x < ( Q(Q_ATANINP)-FL2FXCONST_DBL(0.00395)) )
 258     {
 259         INT res_e;
 260
 261         temp = fPow2(x);            // q25 * q25 - (DFRACT_BITS-1) = q19
 262         temp = fMult(temp, ONEBY3P56);      // q19 * q31 - (DFRACT_BITS-1) = q19
 263         temp = temp + Q(19);                // q19 + q19 = q19
 264         result = fDivNorm(x, temp, &res_e);
 265         result = scaleValue(result, (Q_ATANOUT-Q_ATANINP+19-DFRACT_BITS+1) + res_e  );
 266     }
 267     else if( x < FL2FXCONST_DBL(1.28/64.0) )
 268     {
 269         FIXP_DBL delta_fix;
 270         FIXP_DBL PI_BY_4 = FL2FXCONST_DBL(3.1415926/4.0) >> 1; /* pi/4 in q30 */
 271
 272         delta_fix = (x - FL2FXCONST_DBL(1.0/64.0)) << 5; /* q30 */
 273         result = PI_BY_4 + (delta_fix >> 1) - (fPow2Div2(delta_fix));
 274     }
 275     else
 276     {
 277         INT res_e;
 278
 279         temp = fPow2Div2(x);        // q25 * q25 - (DFRACT_BITS-1) - 1 = q18
 280         temp = temp + P281;                 // q18 + q18 = q18
 281         result = fDivNorm(x, temp, &res_e);
 282         result = scaleValue(result, (Q_ATANOUT-Q_ATANINP+18-DFRACT_BITS+1) + res_e );
 283         result = ONEP571 - result;          // q30 + q30 = q30
 284     }
 285     if (sign) {
 286       result = -result;
 287     }
 288
 289     return(result);
 290 }
 291
 292
 293
 294 #include "FDK_tools_rom.h"
 295
 296 FIXP_DBL fixp_cos(FIXP_DBL x, int scale)
 297 {
 298     FIXP_DBL residual, error, sine, cosine;
 299
 300     residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
 301     error = fMult(sine, residual);
 302
 303     return cosine - error;
 304 }
 305
 306 FIXP_DBL fixp_sin(FIXP_DBL x, int scale)
 307 {
 308     FIXP_DBL residual, error, sine, cosine;
 309
 310     residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
 311     error = fMult(cosine, residual);
 312
 313     return sine + error;
 314 }
 315
 316 void fixp_cos_sin (FIXP_DBL x, int scale, FIXP_DBL *cos, FIXP_DBL *sin)
 317 {
 318     FIXP_DBL residual, error0, error1, sine, cosine;
 319
 320     residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
 321     error0 = fMult(sine, residual);
 322     error1 = fMult(cosine, residual);
 323     *cos  = cosine - error0;
 324     *sin  = sine + error1;
 325 }
 326
 327
 328
 329
 330