/* ----------------------------------------------------------------------
* 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
* 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;
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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
*/