arm_dct4_q31.c

/* ----------------------------------------------------------------------    
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
*    
* $Date:        19. March 2015 
* $Revision: 	V.1.4.5  
*    
* Project: 	    CMSIS DSP Library    
* Title:	    arm_dct4_q31.c    
*    
* Description:	Processing function of DCT4 & IDCT4 Q31.    
*    
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* Redistribution and use in source and binary forms, with or without 
* modification, are permitted provided that the following conditions
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*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the 
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* -------------------------------------------------------------------- */

#include "arm_math.h"

/**    
 * @addtogroup DCT4_IDCT4    
 * @{    
 */

/**    
 * @brief Processing function for the Q31 DCT4/IDCT4.   
 * @param[in]       *S             points to an instance of the Q31 DCT4 structure.   
 * @param[in]       *pState        points to state buffer.   
 * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
 * @return none.   
 * \par Input an output formats:    
 * Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process,    
 * as the conversion from DCT2 to DCT4 involves one subtraction.    
 * Internally inputs are downscaled in the RFFT process function to avoid overflows.    
 * Number of bits downscaled, depends on the size of the transform.    
 * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:     
 *    
 * \image html dct4FormatsQ31Table.gif    
 */

void arm_dct4_q31(
  const arm_dct4_instance_q31 * S,
  q31_t * pState,
  q31_t * pInlineBuffer)
{
  uint16_t i;                                    /* Loop counter */
  q31_t *weights = S->pTwiddle;                  /* Pointer to the Weights table */
  q31_t *cosFact = S->pCosFactor;                /* Pointer to the cos factors table */
  q31_t *pS1, *pS2, *pbuff;                      /* Temporary pointers for input buffer and pState buffer */
  q31_t in;                                      /* Temporary variable */


  /* DCT4 computation involves DCT2 (which is calculated using RFFT)    
   * along with some pre-processing and post-processing.    
   * Computational procedure is explained as follows:    
   * (a) Pre-processing involves multiplying input with cos factor,    
   *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))    
   *              where,    
   *                 r(n) -- output of preprocessing    
   *                 u(n) -- input to preprocessing(actual Source buffer)    
   * (b) Calculation of DCT2 using FFT is divided into three steps:    
   *                  Step1: Re-ordering of even and odd elements of input.    
   *                  Step2: Calculating FFT of the re-ordered input.    
   *                  Step3: Taking the real part of the product of FFT output and weights.    
   * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:    
   *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
   *                        where,    
   *                           Y4 -- DCT4 output,   Y2 -- DCT2 output    
   * (d) Multiplying the output with the normalizing factor sqrt(2/N).    
   */

        /*-------- Pre-processing ------------*/
  /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
  arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N);
  arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N);

  /* ----------------------------------------------------------------    
   * Step1: Re-ordering of even and odd elements as    
   *             pState[i] =  pInlineBuffer[2*i] and    
   *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2    
   ---------------------------------------------------------------------*/

  /* pS1 initialized to pState */
  pS1 = pState;

  /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
  pS2 = pState + (S->N - 1u);

  /* pbuff initialized to input buffer */
  pbuff = pInlineBuffer;

#ifndef ARM_MATH_CM0_FAMILY

  /* Run the below code for Cortex-M4 and Cortex-M3 */

  /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
  i = S->Nby2 >> 2u;

  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
   ** a second loop below computes the remaining 1 to 3 samples. */
  do
  {
    /* Re-ordering of even and odd elements */
    /* pState[i] =  pInlineBuffer[2*i] */
    *pS1++ = *pbuff++;
    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
    *pS2-- = *pbuff++;

    *pS1++ = *pbuff++;
    *pS2-- = *pbuff++;

    *pS1++ = *pbuff++;
    *pS2-- = *pbuff++;

    *pS1++ = *pbuff++;
    *pS2-- = *pbuff++;

    /* Decrement the loop counter */
    i--;
  } while(i > 0u);

  /* pbuff initialized to input buffer */
  pbuff = pInlineBuffer;

  /* pS1 initialized to pState */
  pS1 = pState;

  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
  i = S->N >> 2u;

  /* Processing with loop unrolling 4 times as N is always multiple of 4.    
   * Compute 4 outputs at a time */
  do
  {
    /* Writing the re-ordered output back to inplace input buffer */
    *pbuff++ = *pS1++;
    *pbuff++ = *pS1++;
    *pbuff++ = *pS1++;
    *pbuff++ = *pS1++;

    /* Decrement the loop counter */
    i--;
  } while(i > 0u);


  /* ---------------------------------------------------------    
   *     Step2: Calculate RFFT for N-point input    
   * ---------------------------------------------------------- */
  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
  arm_rfft_q31(S->pRfft, pInlineBuffer, pState);

  /*----------------------------------------------------------------------    
   *  Step3: Multiply the FFT output with the weights.    
   *----------------------------------------------------------------------*/
  arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);

  /* The output of complex multiplication is in 3.29 format.    
   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
  arm_shift_q31(pState, 2, pState, S->N * 2);

  /* ----------- Post-processing ---------- */
  /* DCT-IV can be obtained from DCT-II by the equation,    
   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
   *       Hence, Y4(0) = Y2(0)/2  */
  /* Getting only real part from the output and Converting to DCT-IV */

  /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
  i = (S->N - 1u) >> 2u;

  /* pbuff initialized to input buffer. */
  pbuff = pInlineBuffer;

  /* pS1 initialized to pState */
  pS1 = pState;

  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
  in = *pS1++ >> 1u;
  /* input buffer acts as inplace, so output values are stored in the input itself. */
  *pbuff++ = in;

  /* pState pointer is incremented twice as the real values are located alternatively in the array */
  pS1++;

  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
   ** a second loop below computes the remaining 1 to 3 samples. */
  do
  {
    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
    in = *pS1++ - in;
    *pbuff++ = in;
    /* points to the next real value */
    pS1++;

    in = *pS1++ - in;
    *pbuff++ = in;
    pS1++;

    in = *pS1++ - in;
    *pbuff++ = in;
    pS1++;

    in = *pS1++ - in;
    *pbuff++ = in;
    pS1++;

    /* Decrement the loop counter */
    i--;
  } while(i > 0u);

  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
   ** No loop unrolling is used. */
  i = (S->N - 1u) % 0x4u;

  while(i > 0u)
  {
    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
    in = *pS1++ - in;
    *pbuff++ = in;
    /* points to the next real value */
    pS1++;

    /* Decrement the loop counter */
    i--;
  }


        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/

  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
  i = S->N >> 2u;

  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
  pbuff = pInlineBuffer;

  /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
  do
  {
    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
    in = *pbuff;
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));

    in = *pbuff;
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));

    in = *pbuff;
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));

    in = *pbuff;
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));

    /* Decrement the loop counter */
    i--;
  } while(i > 0u);


#else

  /* Run the below code for Cortex-M0 */

  /* Initializing the loop counter to N/2 */
  i = S->Nby2;

  do
  {
    /* Re-ordering of even and odd elements */
    /* pState[i] =  pInlineBuffer[2*i] */
    *pS1++ = *pbuff++;
    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
    *pS2-- = *pbuff++;

    /* Decrement the loop counter */
    i--;
  } while(i > 0u);

  /* pbuff initialized to input buffer */
  pbuff = pInlineBuffer;

  /* pS1 initialized to pState */
  pS1 = pState;

  /* Initializing the loop counter */
  i = S->N;

  do
  {
    /* Writing the re-ordered output back to inplace input buffer */
    *pbuff++ = *pS1++;

    /* Decrement the loop counter */
    i--;
  } while(i > 0u);


  /* ---------------------------------------------------------    
   *     Step2: Calculate RFFT for N-point input    
   * ---------------------------------------------------------- */
  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
  arm_rfft_q31(S->pRfft, pInlineBuffer, pState);

  /*----------------------------------------------------------------------    
   *  Step3: Multiply the FFT output with the weights.    
   *----------------------------------------------------------------------*/
  arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);

  /* The output of complex multiplication is in 3.29 format.    
   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
  arm_shift_q31(pState, 2, pState, S->N * 2);

  /* ----------- Post-processing ---------- */
  /* DCT-IV can be obtained from DCT-II by the equation,    
   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
   *       Hence, Y4(0) = Y2(0)/2  */
  /* Getting only real part from the output and Converting to DCT-IV */

  /* pbuff initialized to input buffer. */
  pbuff = pInlineBuffer;

  /* pS1 initialized to pState */
  pS1 = pState;

  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
  in = *pS1++ >> 1u;
  /* input buffer acts as inplace, so output values are stored in the input itself. */
  *pbuff++ = in;

  /* pState pointer is incremented twice as the real values are located alternatively in the array */
  pS1++;

  /* Initializing the loop counter */
  i = (S->N - 1u);

  while(i > 0u)
  {
    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
    in = *pS1++ - in;
    *pbuff++ = in;
    /* points to the next real value */
    pS1++;

    /* Decrement the loop counter */
    i--;
  }


        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/

  /* Initializing the loop counter */
  i = S->N;

  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
  pbuff = pInlineBuffer;

  do
  {
    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
    in = *pbuff;
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));

    /* Decrement the loop counter */
    i--;
  } while(i > 0u);

#endif /* #ifndef ARM_MATH_CM0_FAMILY */

}

/**    
   * @} end of DCT4_IDCT4 group    
   */