arm_sin_f32.c

00001 /* ----------------------------------------------------------------------  
00002 * Copyright (C) 2010 ARM Limited. All rights reserved.  
00003 *  
00004 * $Date:        29. November 2010  
00005 * $Revision:    V1.0.3  
00006 *  
00007 * Project:      CMSIS DSP Library  
00008 * Title:        arm_sin_f32.c  
00009 *  
00010 * Description:  Fast sine calculation for floating-point values. 
00011 *  
00012 * Target Processor: Cortex-M4/Cortex-M3
00013 *  
00014 * Version 1.0.3 2010/11/29 
00015 *    Re-organized the CMSIS folders and updated documentation.  
00016 *   
00017 * Version 1.0.2 2010/11/11  
00018 *    Documentation updated.   
00019 *  
00020 * Version 1.0.1 2010/10/05   
00021 *    Production release and review comments incorporated.  
00022 *  
00023 * Version 1.0.0 2010/09/20   
00024 *    Production release and review comments incorporated.  
00025 * -------------------------------------------------------------------- */ 
00026  
00027 #include "arm_math.h" 
00028  
00029 /**  
00030  * @ingroup groupFastMath  
00031  */ 
00032  
00033 /**  
00034  * @defgroup sin Sine  
00035  *  
00036  * Computes the trigonometric sine function using a combination of table lookup 
00037  * and cubic interpolation.  There are separate functions for 
00038  * Q15, Q31, and floating-point data types. 
00039  * The input to the floating-point version is in radians while the 
00040  * fixed-point Q15 and Q31 have a scaled input with the range 
00041  * [0 1) mapping to [0 2*pi). 
00042  * 
00043  * The implementation is based on table lookup using 256 values together with cubic interpolation. 
00044  * The steps used are: 
00045  *  -# Calculation of the nearest integer table index 
00046  *  -# Fetch the four table values a, b, c, and d   
00047  *  -# Compute the fractional portion (fract) of the table index. 
00048  *  -# Calculation of wa, wb, wc, wd  
00049  *  -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code> 
00050  * 
00051  * where 
00052  * <pre>  
00053  *    a=Table[index-1];  
00054  *    b=Table[index+0];  
00055  *    c=Table[index+1];  
00056  *    d=Table[index+2];  
00057  * </pre> 
00058  * and 
00059  * <pre>  
00060  *    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;  
00061  *    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;  
00062  *    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;  
00063  *    wd=(1/6)*fract.^3 - (1/6)*fract;  
00064  * </pre>  
00065  */ 
00066  
00067 /**  
00068  * @addtogroup sin  
00069  * @{  
00070  */ 
00071  
00072  
00073 /** 
00074  * \par  
00075  * Example code for Generation of Floating-point Sin Table: 
00076  * tableSize = 256;  
00077  * <pre>for(n = -1; n < (tableSize + 1); n++)  
00078  * {  
00079  *  sinTable[n+1]=sin(2*pi*n/tableSize);  
00080  * }</pre>  
00081  * \par  
00082  * where pi value is  3.14159265358979  
00083  */ 
00084  
00085 static const float32_t sinTable [259] = { 
00086   -0.024541229009628296f, 0.000000000000000000f, 0.024541229009628296f, 
00087   0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f, 
00088   0.122410677373409270f, 0.146730467677116390f, 
00089   0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f, 
00090   0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f, 
00091   0.313681751489639280f, 0.336889863014221190f, 
00092   0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f, 
00093   0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f, 
00094   0.492898195981979370f, 0.514102756977081300f, 
00095   0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f, 
00096   0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f, 
00097   0.653172850608825680f, 0.671558976173400880f, 
00098   0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f, 
00099   0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f, 
00100   0.788346409797668460f, 0.803207516670227050f, 
00101   0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f, 
00102   0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f, 
00103   0.893224298954010010f, 0.903989315032958980f, 
00104   0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f, 
00105   0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f, 
00106   0.963776051998138430f, 0.970031261444091800f, 
00107   0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f, 
00108   0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f, 
00109   0.997290432453155520f, 0.998795449733734130f, 
00110   0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f, 
00111   0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f, 
00112   0.992479562759399410f, 0.989176511764526370f, 
00113   0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f, 
00114   0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f, 
00115   0.949528157711029050f, 0.941544055938720700f, 
00116   0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f, 
00117   0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f, 
00118   0.870086967945098880f, 0.857728600502014160f, 
00119   0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f, 
00120   0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f, 
00121   0.757208824157714840f, 0.740951120853424070f, 
00122   0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f, 
00123   0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f, 
00124   0.615231573581695560f, 0.595699310302734380f, 
00125   0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f, 
00126   0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f, 
00127   0.449611335992813110f, 0.427555084228515630f, 
00128   0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f, 
00129   0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f, 
00130   0.266712754964828490f, 0.242980182170867920f, 
00131   0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f, 
00132   0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f, 
00133   0.073564566671848297f, 0.049067676067352295f, 
00134   0.024541229009628296f, 0.000000000000000122f, -0.024541229009628296f, 
00135   -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f, 
00136   -0.122410677373409270f, -0.146730467677116390f, 
00137   -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f, 
00138   -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f, 
00139   -0.313681751489639280f, -0.336889863014221190f, 
00140   -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f, 
00141   -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f, 
00142   -0.492898195981979370f, -0.514102756977081300f, 
00143   -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f, 
00144   -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f, 
00145   -0.653172850608825680f, -0.671558976173400880f, 
00146   -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f, 
00147   -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f, 
00148   -0.788346409797668460f, -0.803207516670227050f, 
00149   -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f, 
00150   -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f, 
00151   -0.893224298954010010f, -0.903989315032958980f, 
00152   -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f, 
00153   -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f, 
00154   -0.963776051998138430f, -0.970031261444091800f, 
00155   -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f, 
00156   -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f, 
00157   -0.997290432453155520f, -0.998795449733734130f, 
00158   -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f, 
00159   -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f, 
00160   -0.992479562759399410f, -0.989176511764526370f, 
00161   -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f, 
00162   -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f, 
00163   -0.949528157711029050f, -0.941544055938720700f, 
00164   -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f, 
00165   -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f, 
00166   -0.870086967945098880f, -0.857728600502014160f, 
00167   -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f, 
00168   -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f, 
00169   -0.757208824157714840f, -0.740951120853424070f, 
00170   -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f, 
00171   -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f, 
00172   -0.615231573581695560f, -0.595699310302734380f, 
00173   -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f, 
00174   -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f, 
00175   -0.449611335992813110f, -0.427555084228515630f, 
00176   -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f, 
00177   -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f, 
00178   -0.266712754964828490f, -0.242980182170867920f, 
00179   -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f, 
00180   -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f, 
00181   -0.073564566671848297f, -0.049067676067352295f, 
00182   -0.024541229009628296f, -0.000000000000000245f, 0.024541229009628296f 
00183 }; 
00184  
00185  
00186 /** 
00187  * @brief  Fast approximation to the trigonometric sine function for floating-point data. 
00188  * @param[in] x input value in radians. 
00189  * @return  sin(x). 
00190  */ 
00191  
00192 float32_t arm_sin_f32( 
00193   float32_t x) 
00194 { 
00195   float32_t sinVal, fract, in;                   /* Temporary variables for input, output */ 
00196   uint32_t index;                                /* Index variables */ 
00197   uint32_t tableSize = (uint32_t) TABLE_SIZE;    /* Initialise tablesize */ 
00198   float32_t wa, wb, wc, wd;                      /* Cubic interpolation coefficients */ 
00199   float32_t a, b, c, d;                          /* Four nearest output values */ 
00200   float32_t *tablePtr;                           /* Pointer to table */ 
00201   int32_t n; 
00202  
00203   /* input x is in radians */ 
00204   /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */ 
00205   in = x * 0.159154943092f; 
00206  
00207   /* Calculation of floor value of input */ 
00208   n = (int32_t) in; 
00209  
00210   /* Make negative values towards -infinity */ 
00211   if(x < 0.0f) 
00212   { 
00213     n = n - 1; 
00214   } 
00215  
00216   /* Map input value to [0 1] */ 
00217   in = in - (float32_t) n; 
00218  
00219   /* Calculation of index of the table */ 
00220   index = (uint32_t) (tableSize * in); 
00221  
00222   /* fractional value calculation */ 
00223   fract = ((float32_t) tableSize * in) - (float32_t) index; 
00224  
00225   /* Initialise table pointer */ 
00226   tablePtr = (float32_t *) & sinTable [index]; 
00227  
00228   /* Read four nearest values of output value from the sin table */ 
00229   a = *tablePtr++; 
00230   b = *tablePtr++; 
00231   c = *tablePtr++; 
00232   d = *tablePtr++; 
00233  
00234   /* Cubic interpolation process */ 
00235   wa = -(((0.166666667f) * (fract * (fract * fract))) + 
00236         ((0.3333333333333f) * fract)) + ((0.5f) * (fract * fract)); 
00237   wb = (((0.5f) * (fract * (fract * fract))) - 
00238        ((fract * fract) + ((0.5f) * fract))) + 1.0f; 
00239   wc = (-((0.5f) * (fract * (fract * fract))) +  
00240        ((0.5f) * (fract * fract))) + fract; 
00241   wd = ((0.166666667f) * (fract * (fract * fract))) -  
00242        ((0.166666667f) * fract); 
00243  
00244   /* Calculate sin value */ 
00245   sinVal = ((a * wa) + (b * wb)) + ((c * wc) + (d * wd)); 
00246  
00247   /* Return the output value */ 
00248   return (sinVal); 
00249  
00250 } 
00251  
00252 /**  
00253  * @} end of sin group  
00254  */