| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_dct4_f32.c |
| * Description: Processing function of DCT4 & IDCT4 F32 |
| * |
| * $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" |
| |
| /** |
| @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 \ref 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) |
| { |
| const float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */ |
| const 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 */ |
| 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_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_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_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 = (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 = (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++ = 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 |
| |
| /* 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_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 = (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 loop counter */ |
| i--; |
| } while (i > 0U); |
| |
| /*------------ 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++ = in * S->normalize; |
| |
| /* Decrement loop counter */ |
| i--; |
| } while (i > 0U); |
| |
| #endif /* #if defined (ARM_MATH_LOOPUNROLL) */ |
| |
| } |
| |
| /** |
| @} end of DCT4_IDCT4 group |
| */ |
