/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_dct4_f32.c
* Description: Processing function of DCT4 & IDCT4 F32
*
* $Date: 27. January 2017
* $Revision: V.1.5.1
*
* Target Processor: Cortex-M cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2017 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"
/**
* @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 128, 512, 2048 and 8192.
* 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;
#if defined (ARM_MATH_DSP)
/* 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 /* #if defined (ARM_MATH_DSP) */
}
/**
* @} end of DCT4_IDCT4 group
*/