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/* ----------------------------------------------------------------------    

* 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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*   - Redistributions in binary form must reproduce the above copyright

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*     software without specific prior written permission.

*

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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    

   */