/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_dct4_q31.c
* Description: Processing function of DCT4 & IDCT4 Q31
*
* $Date: 18. March 2019
* $Revision: V1.6.0
*
* Target Processor: Cortex-M cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
*
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#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)
{
const q31_t *weights = S->pTwiddle; /* Pointer to the Weights table */
const 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 */
uint32_t i; /* Loop counter */
/* 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;
#if defined (ARM_MATH_LOOPUNROLL)
/* 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 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 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 loop counter */
i--;
} while (i > 0U);
#else
/* 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 loop counter */
i--;
}
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing 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 loop counter */
i--;
} while (i > 0U);
#endif /* #if defined (ARM_MATH_LOOPUNROLL) */
}
/**
@} end of DCT4_IDCT4 group
*/
