arm_std_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_std_q31.c    
00009 *    
00010 * Description:  Standard deviation 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 STD    
00049  * @{    
00050  */
00051 
00052 
00053 /**    
00054  * @brief Standard deviation of the elements of a Q31 vector.    
00055  * @param[in]       *pSrc points to the input vector    
00056  * @param[in]       blockSize length of the input vector    
00057  * @param[out]      *pResult standard deviation value returned here    
00058  * @return none.    
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_std_q31(
00078   q31_t * pSrc,
00079   uint32_t blockSize,
00080   q31_t * pResult)
00081 {
00082   q63_t sum = 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   q63_t sumOfSquares = 0;                        /* Accumulator */
00089 
00090 #ifndef ARM_MATH_CM0_FAMILY
00091 
00092   /* Run the below code for Cortex-M4 and Cortex-M3 */
00093 
00094   /*loop Unrolling */
00095   blkCnt = blockSize >> 2u;
00096 
00097   /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
00098    ** a second loop below computes the remaining 1 to 3 samples. */
00099   while(blkCnt > 0u)
00100   {
00101     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1])  */
00102     /* Compute Sum of squares of the input samples    
00103      * and then store the result in a temporary variable, sum. */
00104     in = *pSrc++;
00105     sum += in;
00106     sumOfSquares += ((q63_t) (in) * (in));
00107     in = *pSrc++;
00108     sum += in;
00109     sumOfSquares += ((q63_t) (in) * (in));
00110     in = *pSrc++;
00111     sum += in;
00112     sumOfSquares += ((q63_t) (in) * (in));
00113     in = *pSrc++;
00114     sum += in;
00115     sumOfSquares += ((q63_t) (in) * (in));
00116 
00117     /* Decrement the loop counter */
00118     blkCnt--;
00119   }
00120 
00121   /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
00122    ** No loop unrolling is used. */
00123   blkCnt = blockSize % 0x4u;
00124 
00125   while(blkCnt > 0u)
00126   {
00127     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
00128     /* Compute Sum of squares of the input samples    
00129      * and then store the result in a temporary variable, sum. */
00130     in = *pSrc++;
00131     sum += in;
00132     sumOfSquares += ((q63_t) (in) * (in));
00133 
00134     /* Decrement the loop counter */
00135     blkCnt--;
00136   }
00137 
00138   t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
00139 
00140   /* Compute Mean of squares of the input samples    
00141    * and then store the result in a temporary variable, meanOfSquares. */
00142   sumOfSquares = (sumOfSquares >> 31);
00143   meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);
00144 
00145 #else
00146 
00147   /* Run the below code for Cortex-M0 */
00148 
00149   /* Loop over blockSize number of values */
00150   blkCnt = blockSize;
00151 
00152   while(blkCnt > 0u)
00153   {
00154     /* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
00155     /* Compute Sum of squares of the input samples     
00156      * and then store the result in a temporary variable, sumOfSquares. */
00157     in = *pSrc++;
00158     sumOfSquares += ((q63_t) (in) * (in));
00159 
00160     /* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
00161     /* Compute sum of all input values and then store the result in a temporary variable, sum. */
00162     sum += in;
00163 
00164     /* Decrement the loop counter */
00165     blkCnt--;
00166   }
00167 
00168   /* Compute Mean of squares of the input samples     
00169    * and then store the result in a temporary variable, meanOfSquares. */
00170   t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
00171   sumOfSquares = (sumOfSquares >> 31);
00172   meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);
00173 
00174 #endif /* #ifndef ARM_MATH_CM0_FAMILY */
00175 
00176   /* Compute mean of all input values */
00177   t = (q31_t) ((1.0f / (blockSize * (blockSize - 1u))) * 2147483648.0f);
00178   mean = (q31_t) (sum);
00179 
00180   /* Compute square of mean */
00181   squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31);
00182   squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31);
00183 
00184 
00185   /* Compute standard deviation and then store the result to the destination */
00186   arm_sqrt_q31(meanOfSquares - squareOfMean, pResult);
00187 
00188 }
00189 
00190 /**    
00191  * @} end of STD group    
00192  */