arm_correlate_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_correlate_q31.c  
00009 *  
00010 * Description:  Q31 Correlation.  
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 * Version 0.0.7  2010/06/10   
00027 *    Misra-C changes done  
00028 *  
00029 * -------------------------------------------------------------------- */ 
00030  
00031 #include "arm_math.h" 
00032  
00033 /**  
00034  * @ingroup groupFilters  
00035  */ 
00036  
00037 /**  
00038  * @addtogroup Corr  
00039  * @{  
00040  */ 
00041  
00042 /**  
00043  * @brief Correlate Q31 sequences  
00044  * @param[in] *pSrcA points to the first input sequence.  
00045  * @param[in] srcALen length of the first input sequence.  
00046  * @param[in] *pSrcB points to the second input sequence.  
00047  * @param[in] srcBLen length of the second input sequence.  
00048  * @param[out] *pDst points to the location where the output result is written.  Length 2 * max(srcALen, srcBLen) - 1.  
00049  * @return none.  
00050  *  
00051  * @details  
00052  * <b>Scaling and Overflow Behavior:</b>  
00053  *  
00054  * \par  
00055  * The function is implemented using an internal 64-bit accumulator.  
00056  * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.  
00057  * There is no saturation on intermediate additions.  
00058  * Thus, if the accumulator overflows it wraps around and distorts the result.  
00059  * The input signals should be scaled down to avoid intermediate overflows.  
00060  * Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a  
00061  * maximum of min(srcALen, srcBLen) number of additions is carried internally.  
00062  * The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.  
00063  *  
00064  * \par  
00065  * See <code>arm_correlate_fast_q31()</code> for a faster but less precise implementation of this function.  
00066  */ 
00067  
00068 void arm_correlate_q31( 
00069   q31_t * pSrcA, 
00070   uint32_t srcALen, 
00071   q31_t * pSrcB, 
00072   uint32_t srcBLen, 
00073   q31_t * pDst) 
00074 { 
00075   q31_t *pIn1;                                   /* inputA pointer               */ 
00076   q31_t *pIn2;                                   /* inputB pointer               */ 
00077   q31_t *pOut = pDst;                            /* output pointer               */ 
00078   q31_t *px;                                     /* Intermediate inputA pointer  */ 
00079   q31_t *py;                                     /* Intermediate inputB pointer  */ 
00080   q31_t *pSrc1;                                  /* Intermediate pointers        */ 
00081   q63_t sum, acc0, acc1, acc2, acc3;             /* Accumulators                  */ 
00082   q31_t x0, x1, x2, x3, c0;                      /* temporary variables for holding input and coefficient values */ 
00083   uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3;  /* loop counter                 */ 
00084   int32_t inc = 1;                               /* Destination address modifier */ 
00085  
00086  
00087   /* The algorithm implementation is based on the lengths of the inputs. */ 
00088   /* srcB is always made to slide across srcA. */ 
00089   /* So srcBLen is always considered as shorter or equal to srcALen */ 
00090   /* But CORR(x, y) is reverse of CORR(y, x) */ 
00091   /* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */ 
00092   /* and the destination pointer modifier, inc is set to -1 */ 
00093   /* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */ 
00094   /* But to improve the performance,  
00095    * we include zeroes in the output instead of zero padding either of the the inputs*/ 
00096   /* If srcALen > srcBLen,  
00097    * (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */ 
00098   /* If srcALen < srcBLen,  
00099    * (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */ 
00100   if(srcALen >= srcBLen) 
00101   { 
00102     /* Initialization of inputA pointer */ 
00103     pIn1 = (pSrcA); 
00104  
00105     /* Initialization of inputB pointer */ 
00106     pIn2 = (pSrcB); 
00107  
00108     /* Number of output samples is calculated */ 
00109     outBlockSize = (2u * srcALen) - 1u; 
00110  
00111     /* When srcALen > srcBLen, zero padding is done to srcB  
00112      * to make their lengths equal.  
00113      * Instead, (outBlockSize - (srcALen + srcBLen - 1))  
00114      * number of output samples are made zero */ 
00115     j = outBlockSize - (srcALen + (srcBLen - 1u)); 
00116  
00117     while(j > 0u) 
00118     { 
00119       /* Zero is stored in the destination buffer */ 
00120       *pOut++ = 0; 
00121  
00122       /* Decrement the loop counter */ 
00123       j--; 
00124     } 
00125  
00126   } 
00127   else 
00128   { 
00129     /* Initialization of inputA pointer */ 
00130     pIn1 = (pSrcB); 
00131  
00132     /* Initialization of inputB pointer */ 
00133     pIn2 = (pSrcA); 
00134  
00135     /* srcBLen is always considered as shorter or equal to srcALen */ 
00136     j = srcBLen; 
00137     srcBLen = srcALen; 
00138     srcALen = j; 
00139  
00140     /* CORR(x, y) = Reverse order(CORR(y, x)) */ 
00141     /* Hence set the destination pointer to point to the last output sample */ 
00142     pOut = pDst + ((srcALen + srcBLen) - 2u); 
00143  
00144     /* Destination address modifier is set to -1 */ 
00145     inc = -1; 
00146  
00147   } 
00148  
00149   /* The function is internally  
00150    * divided into three parts according to the number of multiplications that has to be  
00151    * taken place between inputA samples and inputB samples. In the first part of the  
00152    * algorithm, the multiplications increase by one for every iteration.  
00153    * In the second part of the algorithm, srcBLen number of multiplications are done.  
00154    * In the third part of the algorithm, the multiplications decrease by one  
00155    * for every iteration.*/ 
00156   /* The algorithm is implemented in three stages.  
00157    * The loop counters of each stage is initiated here. */ 
00158   blockSize1 = srcBLen - 1u; 
00159   blockSize2 = srcALen - (srcBLen - 1u); 
00160   blockSize3 = blockSize1; 
00161  
00162   /* --------------------------  
00163    * Initializations of stage1  
00164    * -------------------------*/ 
00165  
00166   /* sum = x[0] * y[srcBlen - 1]  
00167    * sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]  
00168    * ....  
00169    * sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]  
00170    */ 
00171  
00172   /* In this stage the MAC operations are increased by 1 for every iteration.  
00173      The count variable holds the number of MAC operations performed */ 
00174   count = 1u; 
00175  
00176   /* Working pointer of inputA */ 
00177   px = pIn1; 
00178  
00179   /* Working pointer of inputB */ 
00180   pSrc1 = pIn2 + (srcBLen - 1u); 
00181   py = pSrc1; 
00182  
00183   /* ------------------------  
00184    * Stage1 process  
00185    * ----------------------*/ 
00186  
00187   /* The first stage starts here */ 
00188   while(blockSize1 > 0u) 
00189   { 
00190     /* Accumulator is made zero for every iteration */ 
00191     sum = 0; 
00192  
00193     /* Apply loop unrolling and compute 4 MACs simultaneously. */ 
00194     k = count >> 2; 
00195  
00196     /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.  
00197      ** a second loop below computes MACs for the remaining 1 to 3 samples. */ 
00198     while(k > 0u) 
00199     { 
00200       /* x[0] * y[srcBLen - 4] */ 
00201       sum += (q63_t) * px++ * (*py++); 
00202       /* x[1] * y[srcBLen - 3] */ 
00203       sum += (q63_t) * px++ * (*py++); 
00204       /* x[2] * y[srcBLen - 2] */ 
00205       sum += (q63_t) * px++ * (*py++); 
00206       /* x[3] * y[srcBLen - 1] */ 
00207       sum += (q63_t) * px++ * (*py++); 
00208  
00209       /* Decrement the loop counter */ 
00210       k--; 
00211     } 
00212  
00213     /* If the count is not a multiple of 4, compute any remaining MACs here.  
00214      ** No loop unrolling is used. */ 
00215     k = count % 0x4u; 
00216  
00217     while(k > 0u) 
00218     { 
00219       /* Perform the multiply-accumulates */ 
00220       /* x[0] * y[srcBLen - 1] */ 
00221       sum += (q63_t) * px++ * (*py++); 
00222  
00223       /* Decrement the loop counter */ 
00224       k--; 
00225     } 
00226  
00227     /* Store the result in the accumulator in the destination buffer. */ 
00228     *pOut = (q31_t) (sum >> 31); 
00229     /* Destination pointer is updated according to the address modifier, inc */ 
00230     pOut += inc; 
00231  
00232     /* Update the inputA and inputB pointers for next MAC calculation */ 
00233     py = pSrc1 - count; 
00234     px = pIn1; 
00235  
00236     /* Increment the MAC count */ 
00237     count++; 
00238  
00239     /* Decrement the loop counter */ 
00240     blockSize1--; 
00241   } 
00242  
00243   /* --------------------------  
00244    * Initializations of stage2  
00245    * ------------------------*/ 
00246  
00247   /* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]  
00248    * sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]  
00249    * ....  
00250    * sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]  
00251    */ 
00252  
00253   /* Working pointer of inputA */ 
00254   px = pIn1; 
00255  
00256   /* Working pointer of inputB */ 
00257   py = pIn2; 
00258  
00259   /* count is index by which the pointer pIn1 to be incremented */ 
00260   count = 1u; 
00261  
00262   /* -------------------  
00263    * Stage2 process  
00264    * ------------------*/ 
00265  
00266   /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.  
00267    * So, to loop unroll over blockSize2,  
00268    * srcBLen should be greater than or equal to 4 */ 
00269   if(srcBLen >= 4u) 
00270   { 
00271     /* Loop unroll over blockSize2, by 4 */ 
00272     blkCnt = blockSize2 >> 2u; 
00273  
00274     while(blkCnt > 0u) 
00275     { 
00276       /* Set all accumulators to zero */ 
00277       acc0 = 0; 
00278       acc1 = 0; 
00279       acc2 = 0; 
00280       acc3 = 0; 
00281  
00282       /* read x[0], x[1], x[2] samples */ 
00283       x0 = *(px++); 
00284       x1 = *(px++); 
00285       x2 = *(px++); 
00286  
00287       /* Apply loop unrolling and compute 4 MACs simultaneously. */ 
00288       k = srcBLen >> 2u; 
00289  
00290       /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.  
00291        ** a second loop below computes MACs for the remaining 1 to 3 samples. */ 
00292       do 
00293       { 
00294         /* Read y[0] sample */ 
00295         c0 = *(py++); 
00296  
00297         /* Read x[3] sample */ 
00298         x3 = *(px++); 
00299  
00300         /* Perform the multiply-accumulate */ 
00301         /* acc0 +=  x[0] * y[0] */ 
00302         acc0 += ((q63_t) x0 * c0); 
00303         /* acc1 +=  x[1] * y[0] */ 
00304         acc1 += ((q63_t) x1 * c0); 
00305         /* acc2 +=  x[2] * y[0] */ 
00306         acc2 += ((q63_t) x2 * c0); 
00307         /* acc3 +=  x[3] * y[0] */ 
00308         acc3 += ((q63_t) x3 * c0); 
00309  
00310         /* Read y[1] sample */ 
00311         c0 = *(py++); 
00312  
00313         /* Read x[4] sample */ 
00314         x0 = *(px++); 
00315  
00316         /* Perform the multiply-accumulates */ 
00317         /* acc0 +=  x[1] * y[1] */ 
00318         acc0 += ((q63_t) x1 * c0); 
00319         /* acc1 +=  x[2] * y[1] */ 
00320         acc1 += ((q63_t) x2 * c0); 
00321         /* acc2 +=  x[3] * y[1] */ 
00322         acc2 += ((q63_t) x3 * c0); 
00323         /* acc3 +=  x[4] * y[1] */ 
00324         acc3 += ((q63_t) x0 * c0); 
00325         /* Read y[2] sample */ 
00326         c0 = *(py++); 
00327  
00328         /* Read x[5] sample */ 
00329         x1 = *(px++); 
00330  
00331         /* Perform the multiply-accumulates */ 
00332         /* acc0 +=  x[2] * y[2] */ 
00333         acc0 += ((q63_t) x2 * c0); 
00334         /* acc1 +=  x[3] * y[2] */ 
00335         acc1 += ((q63_t) x3 * c0); 
00336         /* acc2 +=  x[4] * y[2] */ 
00337         acc2 += ((q63_t) x0 * c0); 
00338         /* acc3 +=  x[5] * y[2] */ 
00339         acc3 += ((q63_t) x1 * c0); 
00340  
00341         /* Read y[3] sample */ 
00342         c0 = *(py++); 
00343  
00344         /* Read x[6] sample */ 
00345         x2 = *(px++); 
00346  
00347         /* Perform the multiply-accumulates */ 
00348         /* acc0 +=  x[3] * y[3] */ 
00349         acc0 += ((q63_t) x3 * c0); 
00350         /* acc1 +=  x[4] * y[3] */ 
00351         acc1 += ((q63_t) x0 * c0); 
00352         /* acc2 +=  x[5] * y[3] */ 
00353         acc2 += ((q63_t) x1 * c0); 
00354         /* acc3 +=  x[6] * y[3] */ 
00355         acc3 += ((q63_t) x2 * c0); 
00356  
00357  
00358       } while(--k); 
00359  
00360       /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.  
00361        ** No loop unrolling is used. */ 
00362       k = srcBLen % 0x4u; 
00363  
00364       while(k > 0u) 
00365       { 
00366         /* Read y[4] sample */ 
00367         c0 = *(py++); 
00368  
00369         /* Read x[7] sample */ 
00370         x3 = *(px++); 
00371  
00372         /* Perform the multiply-accumulates */ 
00373         /* acc0 +=  x[4] * y[4] */ 
00374         acc0 += ((q63_t) x0 * c0); 
00375         /* acc1 +=  x[5] * y[4] */ 
00376         acc1 += ((q63_t) x1 * c0); 
00377         /* acc2 +=  x[6] * y[4] */ 
00378         acc2 += ((q63_t) x2 * c0); 
00379         /* acc3 +=  x[7] * y[4] */ 
00380         acc3 += ((q63_t) x3 * c0); 
00381  
00382         /* Reuse the present samples for the next MAC */ 
00383         x0 = x1; 
00384         x1 = x2; 
00385         x2 = x3; 
00386  
00387         /* Decrement the loop counter */ 
00388         k--; 
00389       } 
00390  
00391       /* Store the result in the accumulator in the destination buffer. */ 
00392       *pOut = (q31_t) (acc0 >> 31); 
00393       /* Destination pointer is updated according to the address modifier, inc */ 
00394       pOut += inc; 
00395  
00396       *pOut = (q31_t) (acc1 >> 31); 
00397       pOut += inc; 
00398  
00399       *pOut = (q31_t) (acc2 >> 31); 
00400       pOut += inc; 
00401  
00402       *pOut = (q31_t) (acc3 >> 31); 
00403       pOut += inc; 
00404  
00405       /* Update the inputA and inputB pointers for next MAC calculation */ 
00406       px = pIn1 + (count * 4u); 
00407       py = pIn2; 
00408  
00409       /* Increment the pointer pIn1 index, count by 1 */ 
00410       count++; 
00411  
00412       /* Decrement the loop counter */ 
00413       blkCnt--; 
00414     } 
00415  
00416     /* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.  
00417      ** No loop unrolling is used. */ 
00418     blkCnt = blockSize2 % 0x4u; 
00419  
00420     while(blkCnt > 0u) 
00421     { 
00422       /* Accumulator is made zero for every iteration */ 
00423       sum = 0; 
00424  
00425       /* Apply loop unrolling and compute 4 MACs simultaneously. */ 
00426       k = srcBLen >> 2u; 
00427  
00428       /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.  
00429        ** a second loop below computes MACs for the remaining 1 to 3 samples. */ 
00430       while(k > 0u) 
00431       { 
00432         /* Perform the multiply-accumulates */ 
00433         sum += (q63_t) * px++ * (*py++); 
00434         sum += (q63_t) * px++ * (*py++); 
00435         sum += (q63_t) * px++ * (*py++); 
00436         sum += (q63_t) * px++ * (*py++); 
00437  
00438         /* Decrement the loop counter */ 
00439         k--; 
00440       } 
00441  
00442       /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.  
00443        ** No loop unrolling is used. */ 
00444       k = srcBLen % 0x4u; 
00445  
00446       while(k > 0u) 
00447       { 
00448         /* Perform the multiply-accumulate */ 
00449         sum += (q63_t) * px++ * (*py++); 
00450  
00451         /* Decrement the loop counter */ 
00452         k--; 
00453       } 
00454  
00455       /* Store the result in the accumulator in the destination buffer. */ 
00456       *pOut = (q31_t) (sum >> 31); 
00457       /* Destination pointer is updated according to the address modifier, inc */ 
00458       pOut += inc; 
00459  
00460       /* Update the inputA and inputB pointers for next MAC calculation */ 
00461       px = pIn1 + count; 
00462       py = pIn2; 
00463  
00464       /* Increment the MAC count */ 
00465       count++; 
00466  
00467       /* Decrement the loop counter */ 
00468       blkCnt--; 
00469     } 
00470   } 
00471   else 
00472   { 
00473     /* If the srcBLen is not a multiple of 4,  
00474      * the blockSize2 loop cannot be unrolled by 4 */ 
00475     blkCnt = blockSize2; 
00476  
00477     while(blkCnt > 0u) 
00478     { 
00479       /* Accumulator is made zero for every iteration */ 
00480       sum = 0; 
00481  
00482       /* Loop over srcBLen */ 
00483       k = srcBLen; 
00484  
00485       while(k > 0u) 
00486       { 
00487         /* Perform the multiply-accumulate */ 
00488         sum += (q63_t) * px++ * (*py++); 
00489  
00490         /* Decrement the loop counter */ 
00491         k--; 
00492       } 
00493  
00494       /* Store the result in the accumulator in the destination buffer. */ 
00495       *pOut = (q31_t) (sum >> 31); 
00496       /* Destination pointer is updated according to the address modifier, inc */ 
00497       pOut += inc; 
00498  
00499       /* Update the inputA and inputB pointers for next MAC calculation */ 
00500       px = pIn1 + count; 
00501       py = pIn2; 
00502  
00503       /* Increment the MAC count */ 
00504       count++; 
00505  
00506       /* Decrement the loop counter */ 
00507       blkCnt--; 
00508     } 
00509   } 
00510  
00511   /* --------------------------  
00512    * Initializations of stage3  
00513    * -------------------------*/ 
00514  
00515   /* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]  
00516    * sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]  
00517    * ....  
00518    * sum +=  x[srcALen-2] * y[0] + x[srcALen-1] * y[1]  
00519    * sum +=  x[srcALen-1] * y[0]  
00520    */ 
00521  
00522   /* In this stage the MAC operations are decreased by 1 for every iteration.  
00523      The count variable holds the number of MAC operations performed */ 
00524   count = srcBLen - 1u; 
00525  
00526   /* Working pointer of inputA */ 
00527   pSrc1 = pIn1 + (srcALen - (srcBLen - 1u)); 
00528   px = pSrc1; 
00529  
00530   /* Working pointer of inputB */ 
00531   py = pIn2; 
00532  
00533   /* -------------------  
00534    * Stage3 process  
00535    * ------------------*/ 
00536  
00537   while(blockSize3 > 0u) 
00538   { 
00539     /* Accumulator is made zero for every iteration */ 
00540     sum = 0; 
00541  
00542     /* Apply loop unrolling and compute 4 MACs simultaneously. */ 
00543     k = count >> 2u; 
00544  
00545     /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.  
00546      ** a second loop below computes MACs for the remaining 1 to 3 samples. */ 
00547     while(k > 0u) 
00548     { 
00549       /* Perform the multiply-accumulates */ 
00550       /* sum += x[srcALen - srcBLen + 4] * y[3] */ 
00551       sum += (q63_t) * px++ * (*py++); 
00552       /* sum += x[srcALen - srcBLen + 3] * y[2] */ 
00553       sum += (q63_t) * px++ * (*py++); 
00554       /* sum += x[srcALen - srcBLen + 2] * y[1] */ 
00555       sum += (q63_t) * px++ * (*py++); 
00556       /* sum += x[srcALen - srcBLen + 1] * y[0] */ 
00557       sum += (q63_t) * px++ * (*py++); 
00558  
00559       /* Decrement the loop counter */ 
00560       k--; 
00561     } 
00562  
00563     /* If the count is not a multiple of 4, compute any remaining MACs here.  
00564      ** No loop unrolling is used. */ 
00565     k = count % 0x4u; 
00566  
00567     while(k > 0u) 
00568     { 
00569       /* Perform the multiply-accumulates */ 
00570       sum += (q63_t) * px++ * (*py++); 
00571  
00572       /* Decrement the loop counter */ 
00573       k--; 
00574     } 
00575  
00576     /* Store the result in the accumulator in the destination buffer. */ 
00577     *pOut = (q31_t) (sum >> 31); 
00578     /* Destination pointer is updated according to the address modifier, inc */ 
00579     pOut += inc; 
00580  
00581     /* Update the inputA and inputB pointers for next MAC calculation */ 
00582     px = ++pSrc1; 
00583     py = pIn2; 
00584  
00585     /* Decrement the MAC count */ 
00586     count--; 
00587  
00588     /* Decrement the loop counter */ 
00589     blockSize3--; 
00590   } 
00591  
00592 } 
00593  
00594 /**  
00595  * @} end of Corr group  
00596  */