text: /* ----------------------------------------------------------------------    
  * Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
  *    
  * $Date:        31. July 2014 
  * $Revision: 	V1.4.4  
  *    
  * 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
  * are met:
  *   - Redistributions of source code must retain the above copyright
  *     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
  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  * POSSIBILITY OF SUCH DAMAGE.    
  * -------------------------------------------------------------------- */
  
  #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    
     */
  