384 lines
12 KiB
C
384 lines
12 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_dct4_q31.c
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* Description: Processing function of DCT4 & IDCT4 Q31
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*
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* $Date: 18. March 2019
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* $Revision: V1.6.0
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*
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* Target Processor: Cortex-M cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "arm_math.h"
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/**
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@addtogroup DCT4_IDCT4
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@{
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*/
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/**
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@brief Processing function for the Q31 DCT4/IDCT4.
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@param[in] S points to an instance of the Q31 DCT4 structure.
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@param[in] pState points to state buffer.
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@param[in,out] pInlineBuffer points to the in-place input and output buffer.
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@return none
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@par Input an output formats
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Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process,
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as the conversion from DCT2 to DCT4 involves one subtraction.
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Internally inputs are downscaled in the RFFT process function to avoid overflows.
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Number of bits downscaled, depends on the size of the transform.
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The input and output formats for different DCT sizes and number of bits to upscale are
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mentioned in the table below:
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\image html dct4FormatsQ31Table.gif
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*/
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void arm_dct4_q31(
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const arm_dct4_instance_q31 * S,
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q31_t * pState,
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q31_t * pInlineBuffer)
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{
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const q31_t *weights = S->pTwiddle; /* Pointer to the Weights table */
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const q31_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
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q31_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
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q31_t in; /* Temporary variable */
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uint32_t i; /* Loop counter */
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/* DCT4 computation involves DCT2 (which is calculated using RFFT)
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* along with some pre-processing and post-processing.
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* Computational procedure is explained as follows:
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* (a) Pre-processing involves multiplying input with cos factor,
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* r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
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* where,
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* r(n) -- output of preprocessing
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* u(n) -- input to preprocessing(actual Source buffer)
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* (b) Calculation of DCT2 using FFT is divided into three steps:
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* Step1: Re-ordering of even and odd elements of input.
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* Step2: Calculating FFT of the re-ordered input.
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* Step3: Taking the real part of the product of FFT output and weights.
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* (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
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* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
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* where,
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* Y4 -- DCT4 output, Y2 -- DCT2 output
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* (d) Multiplying the output with the normalizing factor sqrt(2/N).
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*/
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/*-------- Pre-processing ------------*/
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/* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
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arm_mult_q31 (pInlineBuffer, cosFact, pInlineBuffer, S->N);
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arm_shift_q31 (pInlineBuffer, 1, pInlineBuffer, S->N);
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/* ----------------------------------------------------------------
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* Step1: Re-ordering of even and odd elements as
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* pState[i] = pInlineBuffer[2*i] and
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* pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
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---------------------------------------------------------------------*/
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/* pS1 initialized to pState */
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pS1 = pState;
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/* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
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pS2 = pState + (S->N - 1U);
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/* pbuff initialized to input buffer */
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pbuff = pInlineBuffer;
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#if defined (ARM_MATH_LOOPUNROLL)
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/* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
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i = S->Nby2 >> 2U;
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/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
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** a second loop below computes the remaining 1 to 3 samples. */
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do
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{
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/* Re-ordering of even and odd elements */
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/* pState[i] = pInlineBuffer[2*i] */
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*pS1++ = *pbuff++;
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/* pState[N-i-1] = pInlineBuffer[2*i+1] */
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*pS2-- = *pbuff++;
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*pS1++ = *pbuff++;
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*pS2-- = *pbuff++;
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*pS1++ = *pbuff++;
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*pS2-- = *pbuff++;
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*pS1++ = *pbuff++;
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*pS2-- = *pbuff++;
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/* Decrement loop counter */
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i--;
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} while (i > 0U);
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/* pbuff initialized to input buffer */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Initializing the loop counter to N/4 instead of N for loop unrolling */
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i = S->N >> 2U;
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/* Processing with loop unrolling 4 times as N is always multiple of 4.
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* Compute 4 outputs at a time */
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do
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{
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/* Writing the re-ordered output back to inplace input buffer */
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*pbuff++ = *pS1++;
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*pbuff++ = *pS1++;
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*pbuff++ = *pS1++;
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*pbuff++ = *pS1++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* ---------------------------------------------------------
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* Step2: Calculate RFFT for N-point input
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* ---------------------------------------------------------- */
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/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
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arm_rfft_q31 (S->pRfft, pInlineBuffer, pState);
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/*----------------------------------------------------------------------
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* Step3: Multiply the FFT output with the weights.
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*----------------------------------------------------------------------*/
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arm_cmplx_mult_cmplx_q31 (pState, weights, pState, S->N);
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/* The output of complex multiplication is in 3.29 format.
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* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
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arm_shift_q31 (pState, 2, pState, S->N * 2);
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/* ----------- Post-processing ---------- */
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/* DCT-IV can be obtained from DCT-II by the equation,
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* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
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* Hence, Y4(0) = Y2(0)/2 */
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/* Getting only real part from the output and Converting to DCT-IV */
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/* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
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i = (S->N - 1U) >> 2U;
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/* pbuff initialized to input buffer. */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
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in = *pS1++ >> 1U;
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/* input buffer acts as inplace, so output values are stored in the input itself. */
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*pbuff++ = in;
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/* pState pointer is incremented twice as the real values are located alternatively in the array */
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pS1++;
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/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
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** a second loop below computes the remaining 1 to 3 samples. */
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do
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{
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/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
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/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
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in = *pS1++ - in;
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*pbuff++ = in;
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/* points to the next real value */
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pS1++;
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in = *pS1++ - in;
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*pbuff++ = in;
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pS1++;
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in = *pS1++ - in;
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*pbuff++ = in;
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pS1++;
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in = *pS1++ - in;
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*pbuff++ = in;
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pS1++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
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** No loop unrolling is used. */
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i = (S->N - 1U) % 0x4U;
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while (i > 0U)
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{
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/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
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/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
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in = *pS1++ - in;
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*pbuff++ = in;
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/* points to the next real value */
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pS1++;
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/* Decrement loop counter */
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i--;
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}
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/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
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/* Initializing the loop counter to N/4 instead of N for loop unrolling */
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i = S->N >> 2U;
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/* pbuff initialized to the pInlineBuffer(now contains the output values) */
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pbuff = pInlineBuffer;
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/* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */
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do
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{
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/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
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in = *pbuff;
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*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
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in = *pbuff;
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*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
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in = *pbuff;
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*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
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in = *pbuff;
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*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
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/* Decrement loop counter */
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i--;
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} while (i > 0U);
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#else
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/* Initializing the loop counter to N/2 */
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i = S->Nby2;
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do
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{
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/* Re-ordering of even and odd elements */
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/* pState[i] = pInlineBuffer[2*i] */
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*pS1++ = *pbuff++;
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/* pState[N-i-1] = pInlineBuffer[2*i+1] */
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*pS2-- = *pbuff++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* pbuff initialized to input buffer */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Initializing the loop counter */
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i = S->N;
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do
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{
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/* Writing the re-ordered output back to inplace input buffer */
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*pbuff++ = *pS1++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* ---------------------------------------------------------
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* Step2: Calculate RFFT for N-point input
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* ---------------------------------------------------------- */
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/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
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arm_rfft_q31 (S->pRfft, pInlineBuffer, pState);
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/*----------------------------------------------------------------------
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* Step3: Multiply the FFT output with the weights.
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*----------------------------------------------------------------------*/
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arm_cmplx_mult_cmplx_q31 (pState, weights, pState, S->N);
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/* The output of complex multiplication is in 3.29 format.
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* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
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arm_shift_q31(pState, 2, pState, S->N * 2);
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/* ----------- Post-processing ---------- */
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/* DCT-IV can be obtained from DCT-II by the equation,
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* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
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* Hence, Y4(0) = Y2(0)/2 */
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/* Getting only real part from the output and Converting to DCT-IV */
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/* pbuff initialized to input buffer. */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
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in = *pS1++ >> 1U;
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/* input buffer acts as inplace, so output values are stored in the input itself. */
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*pbuff++ = in;
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/* pState pointer is incremented twice as the real values are located alternatively in the array */
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pS1++;
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/* Initializing the loop counter */
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i = (S->N - 1U);
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while (i > 0U)
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{
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/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
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/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
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in = *pS1++ - in;
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*pbuff++ = in;
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/* points to the next real value */
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pS1++;
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/* Decrement loop counter */
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i--;
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}
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/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
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/* Initializing loop counter */
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i = S->N;
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/* pbuff initialized to the pInlineBuffer (now contains the output values) */
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pbuff = pInlineBuffer;
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do
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{
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/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
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in = *pbuff;
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*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
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/* Decrement loop counter */
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i--;
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} while (i > 0U);
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#endif /* #if defined (ARM_MATH_LOOPUNROLL) */
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}
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/**
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@} end of DCT4_IDCT4 group
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*/
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