arm_var_q31.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_var_q31.c  
00009 *  
00010 * Description:  Variance of an array of Q31 type.  
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 groupStats  
00031  */ 
00032  
00033 /**  
00034  * @addtogroup variance  
00035  * @{  
00036  */ 
00037  
00038 /**  
00039  * @brief Variance of the elements of a Q31 vector.  
00040  * @param[in]       *pSrc points to the input vector  
00041  * @param[in]       blockSize length of the input vector  
00042  * @param[out]      *pResult variance value returned here  
00043  * @return none.  
00044  *  
00045  * @details  
00046  * <b>Scaling and Overflow Behavior:</b>  
00047  *  
00048  *\par  
00049  * The function is implemented using an internal 64-bit accumulator.  
00050  * The input is represented in 1.31 format, and intermediate multiplication  
00051  * yields a 2.62 format.  
00052  * The accumulator maintains full precision of the intermediate multiplication results,   
00053  * but provides only a single guard bit.  
00054  * There is no saturation on intermediate additions.  
00055  * If the accumulator overflows it wraps around and distorts the result.  
00056  * In order to avoid overflows completely the input signal must be scaled down by   
00057  * log2(blockSize) bits, as a total of blockSize additions are performed internally.   
00058  * Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.  
00059  *  
00060  */ 
00061  
00062  
00063 void arm_var_q31( 
00064   q31_t * pSrc, 
00065   uint32_t blockSize, 
00066   q63_t * pResult) 
00067 { 
00068   q63_t sum = 0;                                 /* Accumulator */ 
00069   q31_t meanOfSquares, squareOfMean;             /* Mean of square and square of mean */ 
00070   q31_t mean;                                    /* Mean */ 
00071   q31_t in;                                      /* Input variable */ 
00072   q31_t t;                                       /* Temporary variable */ 
00073   uint32_t blkCnt;                               /* loop counter */ 
00074   q31_t *pIn;                                    /* Temporary pointer */ 
00075  
00076   pIn = pSrc; 
00077  
00078   /*loop Unrolling */ 
00079   blkCnt = blockSize >> 2u; 
00080  
00081   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
00082    ** a second loop below computes the remaining 1 to 3 samples. */ 
00083   while(blkCnt > 0u) 
00084   { 
00085     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */ 
00086     /* Compute Sum of squares of the input samples  
00087      * and then store the result in a temporary variable, sum. */ 
00088     in = *pSrc++; 
00089     sum += ((q63_t) (in) * (in)); 
00090     in = *pSrc++; 
00091     sum += ((q63_t) (in) * (in)); 
00092     in = *pSrc++; 
00093     sum += ((q63_t) (in) * (in)); 
00094     in = *pSrc++; 
00095     sum += ((q63_t) (in) * (in)); 
00096  
00097     /* Decrement the loop counter */ 
00098     blkCnt--; 
00099   } 
00100  
00101   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
00102    ** No loop unrolling is used. */ 
00103   blkCnt = blockSize % 0x4u; 
00104  
00105   while(blkCnt > 0u) 
00106   { 
00107     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */ 
00108     /* Compute Sum of squares of the input samples  
00109      * and then store the result in a temporary variable, sum. */ 
00110     in = *pSrc++; 
00111     sum += ((q63_t) (in) * (in)); 
00112  
00113     /* Decrement the loop counter */ 
00114     blkCnt--; 
00115   } 
00116  
00117   /* Compute Mean of squares of the input samples  
00118    * and then store the result in a temporary variable, meanOfSquares. */ 
00119   t = (q31_t) ((1.0 / (blockSize - 1)) * 1073741824LL); 
00120   sum = (sum >> 31); 
00121   meanOfSquares = (q31_t) ((sum * t) >> 30); 
00122  
00123   /* Reset the accumulator */ 
00124   sum = 0; 
00125  
00126   /*loop Unrolling */ 
00127   blkCnt = blockSize >> 2u; 
00128  
00129   /* Reset the input working pointer */ 
00130   pSrc = pIn; 
00131  
00132   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
00133    ** a second loop below computes the remaining 1 to 3 samples. */ 
00134   while(blkCnt > 0u) 
00135   { 
00136     /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */ 
00137     /* Compute sum of all input values and then store the result in a temporary variable, sum. */ 
00138     sum += *pSrc++; 
00139     sum += *pSrc++; 
00140     sum += *pSrc++; 
00141     sum += *pSrc++; 
00142  
00143     /* Decrement the loop counter */ 
00144     blkCnt--; 
00145   } 
00146  
00147   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
00148    ** No loop unrolling is used. */ 
00149   blkCnt = blockSize % 0x4u; 
00150  
00151   while(blkCnt > 0u) 
00152   { 
00153     /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */ 
00154     /* Compute sum of all input values and then store the result in a temporary variable, sum. */ 
00155     sum += *pSrc++; 
00156  
00157     /* Decrement the loop counter */ 
00158     blkCnt--; 
00159   } 
00160  
00161   /* Compute mean of all input values */ 
00162   t = (q31_t) ((1.0 / (blockSize * (blockSize - 1u))) * 2147483648LL); 
00163   mean = (q31_t) (sum); 
00164  
00165   /* Compute square of mean */ 
00166   squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31); 
00167   squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31); 
00168  
00169   /* Compute variance and then store the result to the destination */ 
00170   *pResult = (q63_t) meanOfSquares - squareOfMean; 
00171  
00172 } 
00173  
00174 /**  
00175  * @} end of variance group  
00176  */