arm_sin_q15.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_q15.c  
00009 *  
00010 * Description:  Fast sine calculation for Q15 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  * @addtogroup sin  
00035  * @{  
00036  */ 
00037  
00038  
00039 /**  
00040  * \par  
00041  * Example code for Generation of Q15 Sin Table: 
00042  * \par  
00043  * <pre>tableSize = 256;  
00044  * for(n = -1; n < (tableSize + 1); n++)  
00045  * {  
00046  *  sinTable[n+1]=sin(2*pi*n/tableSize);  
00047  * } </pre>  
00048  * where pi value is  3.14159265358979  
00049  * \par  
00050  * Convert Floating point to Q15(Fixed point):  
00051  *  (sinTable[i] * pow(2, 15))  
00052  * \par  
00053  * rounding to nearest integer is done  
00054  *  sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);  
00055  */ 
00056  
00057  
00058 static const q15_t sinTableQ15 [259] = { 
00059   0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8, 
00060   0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f, 
00061   0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce, 
00062   0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6, 
00063   0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0, 
00064   0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6, 
00065   0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a, 
00066   0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9, 
00067   0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d, 
00068   0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885, 
00069   0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca, 
00070   0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7, 
00071   0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40, 
00072   0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba, 
00073   0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a, 
00074   0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648, 
00075   0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38, 
00076   0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1, 
00077   0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32, 
00078   0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a, 
00079   0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930, 
00080   0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a, 
00081   0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6, 
00082   0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027, 
00083   0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163, 
00084   0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b, 
00085   0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236, 
00086   0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129, 
00087   0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0, 
00088   0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946, 
00089   0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6, 
00090   0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8, 
00091   0xfcdc, 0x0, 0x324 
00092 }; 
00093  
00094  
00095 /** 
00096  * @brief Fast approximation to the trigonometric sine function for Q15 data. 
00097  * @param[in] x Scaled input value in radians. 
00098  * @return  sin(x). 
00099  * 
00100  * The Q15 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi). 
00101  */ 
00102  
00103 q15_t arm_sin_q15( 
00104   q15_t x) 
00105 { 
00106   q31_t sinVal;                                  /* Temporary variables output */ 
00107   q15_t *tablePtr;                               /* Pointer to table */ 
00108   q15_t fract, in, in2;                          /* Temporary variables for input, output */ 
00109   q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */ 
00110   q15_t a, b, c, d;                              /* Four nearest output values */ 
00111   q15_t fractCube, fractSquare;                  /* Temporary values for fractional value */ 
00112   q15_t oneBy6 = 0x1555;                         /* Fixed point value of 1/6 */ 
00113   q15_t tableSpacing = TABLE_SPACING_Q15;        /* Table spacing */ 
00114   int32_t index;                                 /* Index variable */ 
00115  
00116   in = x; 
00117  
00118   /* Calculate the nearest index */ 
00119   index = (int32_t) in / tableSpacing; 
00120  
00121   /* Calculate the nearest value of input */ 
00122   in2 = (q15_t) ((index) * tableSpacing); 
00123  
00124   /* Calculation of fractional value */ 
00125   fract = (in - in2) << 8; 
00126  
00127   /* fractSquare = fract * fract */ 
00128   fractSquare = (q15_t) ((fract * fract) >> 15); 
00129  
00130   /* fractCube = fract * fract * fract */ 
00131   fractCube = (q15_t) ((fractSquare * fract) >> 15); 
00132  
00133   /* Initialise table pointer */ 
00134   tablePtr = (q15_t *) & sinTableQ15 [index]; 
00135  
00136   /* Cubic interpolation process */ 
00137   /* Calculation of wa */ 
00138   /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */ 
00139   wa = (q31_t) oneBy6 *fractCube; 
00140   wa += (q31_t) 0x2AAA * fract; 
00141   wa = -(wa >> 15); 
00142   wa += ((q31_t) fractSquare >> 1u); 
00143  
00144   /* Read first nearest value of output from the sin table */ 
00145   a = *tablePtr++; 
00146  
00147   /* sinVal = a * wa */ 
00148   sinVal = a * wa; 
00149  
00150   /* Calculation of wb */ 
00151   wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) - 
00152        (((q31_t) fract >> 1u) - 0x7FFF); 
00153  
00154   /* Read second nearest value of output from the sin table */ 
00155   b = *tablePtr++; 
00156  
00157   /*      sinVal += b*wb */ 
00158   sinVal += b * wb; 
00159  
00160  
00161   /* Calculation of wc */ 
00162   wc = -(q31_t) fractCube + fractSquare; 
00163   wc = (wc >> 1u) + fract; 
00164  
00165   /* Read third nearest value of output from the sin table */ 
00166   c = *tablePtr++; 
00167  
00168   /*      sinVal += c*wc */ 
00169   sinVal += c * wc; 
00170  
00171   /* Calculation of wd */ 
00172   /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ 
00173   fractCube = fractCube - fract; 
00174   wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15)); 
00175  
00176   /* Read fourth nearest value of output from the sin table */ 
00177   d = *tablePtr++; 
00178  
00179   /* sinVal += d*wd; */ 
00180   sinVal += d * wd; 
00181  
00182   /* Return the output value in 1.15(q15) format */ 
00183   return ((q15_t) (sinVal >> 15u)); 
00184  
00185 } 
00186  
00187 /**  
00188  * @} end of sin group  
00189  */