tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FilteringFunctions/arm_conv_q31.c

   1 /* ----------------------------------------------------------------------
   2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
   3 *
   4 * $Date:        17. January 2013
   5 * $Revision:    V1.4.1
   6 *
   7 * Project:          CMSIS DSP Library
   8 * Title:                arm_conv_q31.c
   9 *
  10 * Description:  Convolution of Q31 sequences.
  11 *
  12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  13 *
  14 * Redistribution and use in source and binary forms, with or without
  15 * modification, are permitted provided that the following conditions
  16 * are met:
  17 *   - Redistributions of source code must retain the above copyright
  18 *     notice, this list of conditions and the following disclaimer.
  19 *   - Redistributions in binary form must reproduce the above copyright
  20 *     notice, this list of conditions and the following disclaimer in
  21 *     the documentation and/or other materials provided with the
  22 *     distribution.
  23 *   - Neither the name of ARM LIMITED nor the names of its contributors
  24 *     may be used to endorse or promote products derived from this
  25 *     software without specific prior written permission.
  26 *
  27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  38 * POSSIBILITY OF SUCH DAMAGE.
  39 * -------------------------------------------------------------------- */
  40
  41 #include "arm_math.h"
  42
  43 /**
  44  * @ingroup groupFilters
  45  */
  46
  47 /**
  48  * @addtogroup Conv
  49  * @{
  50  */
  51
  52 /**
  53  * @brief Convolution of Q31 sequences.
  54  * @param[in] *pSrcA points to the first input sequence.
  55  * @param[in] srcALen length of the first input sequence.
  56  * @param[in] *pSrcB points to the second input sequence.
  57  * @param[in] srcBLen length of the second input sequence.
  58  * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.
  59  * @return none.
  60  *
  61  * @details
  62  * <b>Scaling and Overflow Behavior:</b>
  63  *
  64  * \par
  65  * The function is implemented using an internal 64-bit accumulator.
  66  * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
  67  * There is no saturation on intermediate additions.
  68  * Thus, if the accumulator overflows it wraps around and distorts the result.
  69  * The input signals should be scaled down to avoid intermediate overflows.
  70  * Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,
  71  * as maximum of min(srcALen, srcBLen) number of additions are carried internally.
  72  * The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.
  73  *
  74  * \par
  75  * See <code>arm_conv_fast_q31()</code> for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.
  76  */
  77
  78 void arm_conv_q31(
  79   q31_t * pSrcA,
  80   uint32_t srcALen,
  81   q31_t * pSrcB,
  82   uint32_t srcBLen,
  83   q31_t * pDst)
  84 {
  85
  86
  87 #ifndef ARM_MATH_CM0_FAMILY
  88
  89   /* Run the below code for Cortex-M4 and Cortex-M3 */
  90
  91   q31_t *pIn1;                                   /* inputA pointer */
  92   q31_t *pIn2;                                   /* inputB pointer */
  93   q31_t *pOut = pDst;                            /* output pointer */
  94   q31_t *px;                                     /* Intermediate inputA pointer  */
  95   q31_t *py;                                     /* Intermediate inputB pointer  */
  96   q31_t *pSrc1, *pSrc2;                          /* Intermediate pointers */
  97   q63_t sum;                                     /* Accumulator */
  98   q63_t acc0, acc1, acc2;                        /* Accumulator */
  99   q31_t x0, x1, x2, c0;                          /* Temporary variables to hold state and coefficient values */
 100   uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3;     /* loop counter */
 101
 102   /* The algorithm implementation is based on the lengths of the inputs. */
 103   /* srcB is always made to slide across srcA. */
 104   /* So srcBLen is always considered as shorter or equal to srcALen */
 105   if(srcALen >= srcBLen)
 106   {
 107     /* Initialization of inputA pointer */
 108     pIn1 = pSrcA;
 109
 110     /* Initialization of inputB pointer */
 111     pIn2 = pSrcB;
 112   }
 113   else
 114   {
 115     /* Initialization of inputA pointer */
 116     pIn1 = (q31_t *) pSrcB;
 117
 118     /* Initialization of inputB pointer */
 119     pIn2 = (q31_t *) pSrcA;
 120
 121     /* srcBLen is always considered as shorter or equal to srcALen */
 122     j = srcBLen;
 123     srcBLen = srcALen;
 124     srcALen = j;
 125   }
 126
 127   /* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
 128   /* The function is internally
 129    * divided into three stages according to the number of multiplications that has to be
 130    * taken place between inputA samples and inputB samples. In the first stage of the
 131    * algorithm, the multiplications increase by one for every iteration.
 132    * In the second stage of the algorithm, srcBLen number of multiplications are done.
 133    * In the third stage of the algorithm, the multiplications decrease by one
 134    * for every iteration. */
 135
 136   /* The algorithm is implemented in three stages.
 137      The loop counters of each stage is initiated here. */
 138   blockSize1 = srcBLen - 1u;
 139   blockSize2 = srcALen - (srcBLen - 1u);
 140   blockSize3 = blockSize1;
 141
 142   /* --------------------------
 143    * Initializations of stage1
 144    * -------------------------*/
 145
 146   /* sum = x[0] * y[0]
 147    * sum = x[0] * y[1] + x[1] * y[0]
 148    * ....
 149    * sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
 150    */
 151
 152   /* In this stage the MAC operations are increased by 1 for every iteration.
 153      The count variable holds the number of MAC operations performed */
 154   count = 1u;
 155
 156   /* Working pointer of inputA */
 157   px = pIn1;
 158
 159   /* Working pointer of inputB */
 160   py = pIn2;
 161
 162
 163   /* ------------------------
 164    * Stage1 process
 165    * ----------------------*/
 166
 167   /* The first stage starts here */
 168   while(blockSize1 > 0u)
 169   {
 170     /* Accumulator is made zero for every iteration */
 171     sum = 0;
 172
 173     /* Apply loop unrolling and compute 4 MACs simultaneously. */
 174     k = count >> 2u;
 175
 176     /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.
 177      ** a second loop below computes MACs for the remaining 1 to 3 samples. */
 178     while(k > 0u)
 179     {
 180       /* x[0] * y[srcBLen - 1] */
 181       sum += (q63_t) * px++ * (*py--);
 182       /* x[1] * y[srcBLen - 2] */
 183       sum += (q63_t) * px++ * (*py--);
 184       /* x[2] * y[srcBLen - 3] */
 185       sum += (q63_t) * px++ * (*py--);
 186       /* x[3] * y[srcBLen - 4] */
 187       sum += (q63_t) * px++ * (*py--);
 188
 189       /* Decrement the loop counter */
 190       k--;
 191     }
 192
 193     /* If the count is not a multiple of 4, compute any remaining MACs here.
 194      ** No loop unrolling is used. */
 195     k = count % 0x4u;
 196
 197     while(k > 0u)
 198     {
 199       /* Perform the multiply-accumulate */
 200       sum += (q63_t) * px++ * (*py--);
 201
 202       /* Decrement the loop counter */
 203       k--;
 204     }
 205
 206     /* Store the result in the accumulator in the destination buffer. */
 207     *pOut++ = (q31_t) (sum >> 31);
 208
 209     /* Update the inputA and inputB pointers for next MAC calculation */
 210     py = pIn2 + count;
 211     px = pIn1;
 212
 213     /* Increment the MAC count */
 214     count++;
 215
 216     /* Decrement the loop counter */
 217     blockSize1--;
 218   }
 219
 220   /* --------------------------
 221    * Initializations of stage2
 222    * ------------------------*/
 223
 224   /* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
 225    * sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
 226    * ....
 227    * sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
 228    */
 229
 230   /* Working pointer of inputA */
 231   px = pIn1;
 232
 233   /* Working pointer of inputB */
 234   pSrc2 = pIn2 + (srcBLen - 1u);
 235   py = pSrc2;
 236
 237   /* count is index by which the pointer pIn1 to be incremented */
 238   count = 0u;
 239
 240   /* -------------------
 241    * Stage2 process
 242    * ------------------*/
 243
 244   /* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
 245    * So, to loop unroll over blockSize2,
 246    * srcBLen should be greater than or equal to 4 */
 247   if(srcBLen >= 4u)
 248   {
 249     /* Loop unroll by 3 */
 250     blkCnt = blockSize2 / 3;
 251
 252     while(blkCnt > 0u)
 253     {
 254       /* Set all accumulators to zero */
 255       acc0 = 0;
 256       acc1 = 0;
 257       acc2 = 0;
 258
 259       /* read x[0], x[1], x[2] samples */
 260       x0 = *(px++);
 261       x1 = *(px++);
 262
 263       /* Apply loop unrolling and compute 3 MACs simultaneously. */
 264       k = srcBLen / 3;
 265
 266       /* First part of the processing with loop unrolling.  Compute 3 MACs at a time.
 267        ** a second loop below computes MACs for the remaining 1 to 2 samples. */
 268       do
 269       {
 270         /* Read y[srcBLen - 1] sample */
 271         c0 = *(py);
 272
 273         /* Read x[3] sample */
 274         x2 = *(px);
 275
 276         /* Perform the multiply-accumulates */
 277         /* acc0 +=  x[0] * y[srcBLen - 1] */
 278         acc0 += ((q63_t) x0 * c0);
 279         /* acc1 +=  x[1] * y[srcBLen - 1] */
 280         acc1 += ((q63_t) x1 * c0);
 281         /* acc2 +=  x[2] * y[srcBLen - 1] */
 282         acc2 += ((q63_t) x2 * c0);
 283
 284         /* Read y[srcBLen - 2] sample */
 285         c0 = *(py - 1u);
 286
 287         /* Read x[4] sample */
 288         x0 = *(px + 1u);
 289
 290         /* Perform the multiply-accumulate */
 291         /* acc0 +=  x[1] * y[srcBLen - 2] */
 292         acc0 += ((q63_t) x1 * c0);
 293         /* acc1 +=  x[2] * y[srcBLen - 2] */
 294         acc1 += ((q63_t) x2 * c0);
 295         /* acc2 +=  x[3] * y[srcBLen - 2] */
 296         acc2 += ((q63_t) x0 * c0);
 297
 298         /* Read y[srcBLen - 3] sample */
 299         c0 = *(py - 2u);
 300
 301         /* Read x[5] sample */
 302         x1 = *(px + 2u);
 303
 304         /* Perform the multiply-accumulates */
 305         /* acc0 +=  x[2] * y[srcBLen - 3] */
 306         acc0 += ((q63_t) x2 * c0);
 307         /* acc1 +=  x[3] * y[srcBLen - 2] */
 308         acc1 += ((q63_t) x0 * c0);
 309         /* acc2 +=  x[4] * y[srcBLen - 2] */
 310         acc2 += ((q63_t) x1 * c0);
 311
 312         /* update scratch pointers */
 313         px += 3u;
 314         py -= 3u;
 315
 316       } while(--k);
 317
 318       /* If the srcBLen is not a multiple of 3, compute any remaining MACs here.
 319        ** No loop unrolling is used. */
 320       k = srcBLen - (3 * (srcBLen / 3));
 321
 322       while(k > 0u)
 323       {
 324         /* Read y[srcBLen - 5] sample */
 325         c0 = *(py--);
 326
 327         /* Read x[7] sample */
 328         x2 = *(px++);
 329
 330         /* Perform the multiply-accumulates */
 331         /* acc0 +=  x[4] * y[srcBLen - 5] */
 332         acc0 += ((q63_t) x0 * c0);
 333         /* acc1 +=  x[5] * y[srcBLen - 5] */
 334         acc1 += ((q63_t) x1 * c0);
 335         /* acc2 +=  x[6] * y[srcBLen - 5] */
 336         acc2 += ((q63_t) x2 * c0);
 337
 338         /* Reuse the present samples for the next MAC */
 339         x0 = x1;
 340         x1 = x2;
 341
 342         /* Decrement the loop counter */
 343         k--;
 344       }
 345
 346       /* Store the results in the accumulators in the destination buffer. */
 347       *pOut++ = (q31_t) (acc0 >> 31);
 348       *pOut++ = (q31_t) (acc1 >> 31);
 349       *pOut++ = (q31_t) (acc2 >> 31);
 350
 351       /* Increment the pointer pIn1 index, count by 3 */
 352       count += 3u;
 353
 354       /* Update the inputA and inputB pointers for next MAC calculation */
 355       px = pIn1 + count;
 356       py = pSrc2;
 357
 358       /* Decrement the loop counter */
 359       blkCnt--;
 360     }
 361
 362     /* If the blockSize2 is not a multiple of 3, compute any remaining output samples here.
 363      ** No loop unrolling is used. */
 364     blkCnt = blockSize2 - 3 * (blockSize2 / 3);
 365
 366     while(blkCnt > 0u)
 367     {
 368       /* Accumulator is made zero for every iteration */
 369       sum = 0;
 370
 371       /* Apply loop unrolling and compute 4 MACs simultaneously. */
 372       k = srcBLen >> 2u;
 373
 374       /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.
 375        ** a second loop below computes MACs for the remaining 1 to 3 samples. */
 376       while(k > 0u)
 377       {
 378         /* Perform the multiply-accumulates */
 379         sum += (q63_t) * px++ * (*py--);
 380         sum += (q63_t) * px++ * (*py--);
 381         sum += (q63_t) * px++ * (*py--);
 382         sum += (q63_t) * px++ * (*py--);
 383
 384         /* Decrement the loop counter */
 385         k--;
 386       }
 387
 388       /* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
 389        ** No loop unrolling is used. */
 390       k = srcBLen % 0x4u;
 391
 392       while(k > 0u)
 393       {
 394         /* Perform the multiply-accumulate */
 395         sum += (q63_t) * px++ * (*py--);
 396
 397         /* Decrement the loop counter */
 398         k--;
 399       }
 400
 401       /* Store the result in the accumulator in the destination buffer. */
 402       *pOut++ = (q31_t) (sum >> 31);
 403
 404       /* Increment the MAC count */
 405       count++;
 406
 407       /* Update the inputA and inputB pointers for next MAC calculation */
 408       px = pIn1 + count;
 409       py = pSrc2;
 410
 411       /* Decrement the loop counter */
 412       blkCnt--;
 413     }
 414   }
 415   else
 416   {
 417     /* If the srcBLen is not a multiple of 4,
 418      * the blockSize2 loop cannot be unrolled by 4 */
 419     blkCnt = blockSize2;
 420
 421     while(blkCnt > 0u)
 422     {
 423       /* Accumulator is made zero for every iteration */
 424       sum = 0;
 425
 426       /* srcBLen number of MACS should be performed */
 427       k = srcBLen;
 428
 429       while(k > 0u)
 430       {
 431         /* Perform the multiply-accumulate */
 432         sum += (q63_t) * px++ * (*py--);
 433
 434         /* Decrement the loop counter */
 435         k--;
 436       }
 437
 438       /* Store the result in the accumulator in the destination buffer. */
 439       *pOut++ = (q31_t) (sum >> 31);
 440
 441       /* Increment the MAC count */
 442       count++;
 443
 444       /* Update the inputA and inputB pointers for next MAC calculation */
 445       px = pIn1 + count;
 446       py = pSrc2;
 447
 448       /* Decrement the loop counter */
 449       blkCnt--;
 450     }
 451   }
 452
 453
 454   /* --------------------------
 455    * Initializations of stage3
 456    * -------------------------*/
 457
 458   /* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
 459    * sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
 460    * ....
 461    * sum +=  x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
 462    * sum +=  x[srcALen-1] * y[srcBLen-1]
 463    */
 464
 465   /* In this stage the MAC operations are decreased by 1 for every iteration.
 466      The blockSize3 variable holds the number of MAC operations performed */
 467
 468   /* Working pointer of inputA */
 469   pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
 470   px = pSrc1;
 471
 472   /* Working pointer of inputB */
 473   pSrc2 = pIn2 + (srcBLen - 1u);
 474   py = pSrc2;
 475
 476   /* -------------------
 477    * Stage3 process
 478    * ------------------*/
 479
 480   while(blockSize3 > 0u)
 481   {
 482     /* Accumulator is made zero for every iteration */
 483     sum = 0;
 484
 485     /* Apply loop unrolling and compute 4 MACs simultaneously. */
 486     k = blockSize3 >> 2u;
 487
 488     /* First part of the processing with loop unrolling.  Compute 4 MACs at a time.
 489      ** a second loop below computes MACs for the remaining 1 to 3 samples. */
 490     while(k > 0u)
 491     {
 492       /* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
 493       sum += (q63_t) * px++ * (*py--);
 494       /* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
 495       sum += (q63_t) * px++ * (*py--);
 496       /* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
 497       sum += (q63_t) * px++ * (*py--);
 498       /* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
 499       sum += (q63_t) * px++ * (*py--);
 500
 501       /* Decrement the loop counter */
 502       k--;
 503     }
 504
 505     /* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.
 506      ** No loop unrolling is used. */
 507     k = blockSize3 % 0x4u;
 508
 509     while(k > 0u)
 510     {
 511       /* Perform the multiply-accumulate */
 512       sum += (q63_t) * px++ * (*py--);
 513
 514       /* Decrement the loop counter */
 515       k--;
 516     }
 517
 518     /* Store the result in the accumulator in the destination buffer. */
 519     *pOut++ = (q31_t) (sum >> 31);
 520
 521     /* Update the inputA and inputB pointers for next MAC calculation */
 522     px = ++pSrc1;
 523     py = pSrc2;
 524
 525     /* Decrement the loop counter */
 526     blockSize3--;
 527   }
 528
 529 #else
 530
 531   /* Run the below code for Cortex-M0 */
 532
 533   q31_t *pIn1 = pSrcA;                           /* input pointer */
 534   q31_t *pIn2 = pSrcB;                           /* coefficient pointer */
 535   q63_t sum;                                     /* Accumulator */
 536   uint32_t i, j;                                 /* loop counter */
 537
 538   /* Loop to calculate output of convolution for output length number of times */
 539   for (i = 0; i < (srcALen + srcBLen - 1); i++)
 540   {
 541     /* Initialize sum with zero to carry on MAC operations */
 542     sum = 0;
 543
 544     /* Loop to perform MAC operations according to convolution equation */
 545     for (j = 0; j <= i; j++)
 546     {
 547       /* Check the array limitations */
 548       if(((i - j) < srcBLen) && (j < srcALen))
 549       {
 550         /* z[i] += x[i-j] * y[j] */
 551         sum += ((q63_t) pIn1[j] * (pIn2[i - j]));
 552       }
 553     }
 554
 555     /* Store the output in the destination buffer */
 556     pDst[i] = (q31_t) (sum >> 31u);
 557   }
 558
 559 #endif /*     #ifndef ARM_MATH_CM0_FAMILY */
 560
 561 }
 562
 563 /**
 564  * @} end of Conv group
 565  */