arm_dct4_f32.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_f32.c    
*    
* Description:	Processing function of DCT4 & IDCT4 F32.    
*    
* 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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*     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
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#include "arm_math.h"

/**    
 * @ingroup groupTransforms    
 */

/**    
 * @defgroup DCT4_IDCT4 DCT Type IV Functions    
 * Representation of signals by minimum number of values is important for storage and transmission.    
 * The possibility of large discontinuity between the beginning and end of a period of a signal    
 * in DFT can be avoided by extending the signal so that it is even-symmetric.    
 * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the    
 * spectrum and is very widely used in signal and image coding applications.    
 * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.    
 * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.    
 *    
 * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.    
 * Reordering of the input data makes the computation of DCT just a problem of    
 * computing the DFT of a real signal with a few additional operations.    
 * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.    
 *     
 * DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used.    
 * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.    
 * DCT2 implementation can be described in the following steps:    
 * - Re-ordering input    
 * - Calculating Real FFT    
 * - Multiplication of weights and Real FFT output and getting real part from the product.    
 *    
 * This process is explained by the block diagram below:    
 * \image html DCT4.gif "Discrete Cosine Transform - type-IV"    
 *    
 * \par Algorithm:    
 * The N-point type-IV DCT is defined as a real, linear transformation by the formula:    
 * \image html DCT4Equation.gif    
 * where <code>k = 0,1,2,.....N-1</code>    
 *\par    
 * Its inverse is defined as follows:    
 * \image html IDCT4Equation.gif    
 * where <code>n = 0,1,2,.....N-1</code>    
 *\par    
 * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).    
 * The symmetry of the transform matrix indicates that the fast algorithms for the forward    
 * and inverse transform computation are identical.    
 * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.    
 *    
 * \par Lengths supported by the transform:    
 *  As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().    
 * The library provides separate functions for Q15, Q31, and floating-point data types.    
 * \par Instance Structure    
 * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.    
 * A separate instance structure must be defined for each transform.    
 * There are separate instance structure declarations for each of the 3 supported data types.    
 *    
 * \par Initialization Functions    
 * There is also an associated initialization function for each data type.    
 * The initialization function performs the following operations:    
 * - Sets the values of the internal structure fields.    
 * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().    
 * \par    
 * Use of the initialization function is optional.    
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
 * To place an instance structure into a const data section, the instance structure must be manually initialized.    
 * Manually initialize the instance structure as follows:    
 * <pre>    
 *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};    
 *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};   
 *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};   
 * </pre>   
 * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;   
 * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;    
 * \c pTwiddle points to the twiddle factor table;   
 * \c pCosFactor points to the cosFactor table;   
 * \c pRfft points to the real FFT instance;   
 * \c pCfft points to the complex FFT instance;   
 * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()   
 * and arm_rfft_f32() respectively for details regarding static initialization.   
 *   
 * \par Fixed-Point Behavior    
 * Care must be taken when using the fixed-point versions of the DCT4 transform functions.    
 * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.    
 * Refer to the function specific documentation below for usage guidelines.    
 */

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

/**    
 * @brief Processing function for the floating-point DCT4/IDCT4.   
 * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.   
 * @param[in]       *pState        points to state buffer.   
 * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
 * @return none.   
 */

void arm_dct4_f32(
  const arm_dct4_instance_f32 * S,
  float32_t * pState,
  float32_t * pInlineBuffer)
{
  uint32_t i;                                    /* Loop counter */
  float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */
  float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */
  float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */
  float32_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_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
  arm_mult_f32(pInlineBuffer, cosFact, 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 = (uint32_t) 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 = (uint32_t) 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_f32(S->pRfft, pInlineBuffer, pState);

        /*----------------------------------------------------------------------    
	 *  Step3: Multiply the FFT output with the weights.    
	 *----------------------------------------------------------------------*/
  arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);

  /* ----------- 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 = ((uint32_t) 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++ * (float32_t) 0.5;
  /* 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 = ((uint32_t) 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 = (uint32_t) 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++ = in * S->normalize;

    in = *pbuff;
    *pbuff++ = in * S->normalize;

    in = *pbuff;
    *pbuff++ = in * S->normalize;

    in = *pbuff;
    *pbuff++ = in * S->normalize;

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


#else

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

  /* Initializing the loop counter to N/2 */
  i = (uint32_t) 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 = (uint32_t) 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_f32(S->pRfft, pInlineBuffer, pState);

        /*----------------------------------------------------------------------    
	 *  Step3: Multiply the FFT output with the weights.    
	 *----------------------------------------------------------------------*/
  arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);

  /* ----------- 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++ * (float32_t) 0.5;
  /* 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 = ((uint32_t) S->N - 1u);

  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++;


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


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

  /* Initializing the loop counter */
  i = (uint32_t) 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++ = in * S->normalize;

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

#endif /* #ifndef ARM_MATH_CM0_FAMILY */

}

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