arm_var_q31.c

00001 /* ----------------------------------------------------------------------    
00002 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.    
00003 *    
00004 * $Date:        17. January 2013
00005 * $Revision:    V1.4.1  
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/Cortex-M0
00013 *  
00014 * Redistribution and use in source and binary forms, with or without 
00015 * modification, are permitted provided that the following conditions
00016 * are met:
00017 *   - Redistributions of source code must retain the above copyright
00018 *     notice, this list of conditions and the following disclaimer.
00019 *   - Redistributions in binary form must reproduce the above copyright
00020 *     notice, this list of conditions and the following disclaimer in
00021 *     the documentation and/or other materials provided with the 
00022 *     distribution.
00023 *   - Neither the name of ARM LIMITED nor the names of its contributors
00024 *     may be used to endorse or promote products derived from this
00025 *     software without specific prior written permission.
00026 *
00027 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
00028 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
00029 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
00030 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
00031 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
00032 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
00033 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
00034 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
00035 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
00036 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
00037 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
00038 * POSSIBILITY OF SUCH DAMAGE.   
00039 * -------------------------------------------------------------------- */
00040 
00041 #include "arm_math.h"
00042 
00043 /**        
00044  * @ingroup groupStats        
00045  */
00046 
00047 /**        
00048  * @addtogroup variance        
00049  * @{        
00050  */
00051 
00052 /**        
00053  * @brief Variance of the elements of a Q31 vector.        
00054  * @param[in]       *pSrc points to the input vector        
00055  * @param[in]       blockSize length of the input vector        
00056  * @param[out]      *pResult variance value returned here        
00057  * @return none.        
00058  *        
00059  * @details        
00060  * <b>Scaling and Overflow Behavior:</b>        
00061  *        
00062  *\par        
00063  * The function is implemented using an internal 64-bit accumulator.        
00064  * The input is represented in 1.31 format, and intermediate multiplication        
00065  * yields a 2.62 format.        
00066  * The accumulator maintains full precision of the intermediate multiplication results,         
00067  * but provides only a single guard bit.        
00068  * There is no saturation on intermediate additions.        
00069  * If the accumulator overflows it wraps around and distorts the result.        
00070  * In order to avoid overflows completely the input signal must be scaled down by         
00071  * log2(blockSize) bits, as a total of blockSize additions are performed internally.         
00072  * Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.        
00073  *        
00074  */
00075 
00076 
00077 void arm_var_q31(
00078   q31_t * pSrc,
00079   uint32_t blockSize,
00080   q63_t * pResult)
00081 {
00082   q63_t sum = 0, sumSquare = 0;                  /* Accumulator */
00083   q31_t meanOfSquares, squareOfMean;             /* square of mean and mean of square */
00084   q31_t mean;                                    /* mean */
00085   q31_t in;                                      /* input value */
00086   q31_t t;                                       /* Temporary variable */
00087   uint32_t blkCnt;                               /* loop counter */
00088 
00089 #ifndef ARM_MATH_CM0_FAMILY
00090 
00091   /* Run the below code for Cortex-M4 and Cortex-M3 */
00092   q63_t sumSquare1 = 0;                          /* Accumulator */
00093   q31_t in1, in2, in3, in4;                      /* Temporary input variables */
00094 
00095   /*loop Unrolling */
00096   blkCnt = blockSize >> 2u;
00097 
00098   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
00099    ** a second loop below computes the remaining 1 to 3 samples. */
00100   while(blkCnt > 0u)
00101   {
00102     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
00103     /* Compute Sum of squares of the input samples        
00104      * and then store the result in a temporary variable, sum. */
00105     /* read input samples from source buffer */
00106     in1 = pSrc[0];
00107     in2 = pSrc[1];
00108 
00109     /* calculate sum of inputs */
00110     sum += in1;
00111     /* calculate sum of squares */
00112     sumSquare += ((q63_t) (in1) * (in1));
00113     in3 = pSrc[2];
00114     sum += in2;
00115     sumSquare1 += ((q63_t) (in2) * (in2));
00116     in4 = pSrc[3];
00117     sum += in3;
00118     sumSquare += ((q63_t) (in3) * (in3));
00119     sum += in4;
00120     sumSquare1 += ((q63_t) (in4) * (in4));
00121 
00122     /* update input pointer to process next samples */
00123     pSrc += 4u;
00124 
00125     /* Decrement the loop counter */
00126     blkCnt--;
00127   }
00128 
00129   /* add two accumulators */
00130   sumSquare = sumSquare + sumSquare1;
00131 
00132   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
00133    ** No loop unrolling is used. */
00134   blkCnt = blockSize % 0x4u;
00135 
00136 #else
00137 
00138   /* Run the below code for Cortex-M0 */
00139   blkCnt = blockSize;
00140 
00141 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
00142 
00143   while(blkCnt > 0u)
00144   {
00145     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
00146     /* Compute Sum of squares of the input samples        
00147      * and then store the result in a temporary variable, sum. */
00148     in = *pSrc++;
00149     sumSquare += ((q63_t) (in) * (in));
00150     sum += in;
00151 
00152     /* Decrement the loop counter */
00153     blkCnt--;
00154   }
00155 
00156   t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
00157 
00158   /* Compute Mean of squares of the input samples        
00159    * and then store the result in a temporary variable, meanOfSquares. */
00160   sumSquare = (sumSquare >> 31);
00161   meanOfSquares = (q31_t) ((sumSquare * t) >> 30);
00162 
00163   /* Compute mean of all input values */
00164   t = (q31_t) ((1.0f / (blockSize * (blockSize - 1u))) * 2147483648.0f);
00165   mean = (q31_t) (sum);
00166 
00167   /* Compute square of mean */
00168   squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31);
00169   squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31);
00170 
00171   /* Compute variance and then store the result to the destination */
00172   *pResult = (q63_t) meanOfSquares - squareOfMean;
00173 
00174 }
00175 
00176 /**        
00177  * @} end of variance group        
00178  */