From 86608c6770cf08c138a2bdab5855072f64be09ef Mon Sep 17 00:00:00 2001 From: joshua Date: Sat, 30 Dec 2023 23:54:31 -0500 Subject: initial commit --- .../DSP/Source/TransformFunctions/arm_dct4_f32.c | 448 +++++++++++++++++++++ 1 file changed, 448 insertions(+) create mode 100644 Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c (limited to 'Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c') diff --git a/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c new file mode 100644 index 0000000..729ebf1 --- /dev/null +++ b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c @@ -0,0 +1,448 @@ +/* ---------------------------------------------------------------------- + * 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 k = 0, 1, 2, ..., N-1 + @par + Its inverse is defined as follows: + \image html IDCT4Equation.gif + where n = 0, 1, 2, ..., N-1 + @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: + 
+      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};
+
+ 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 sqrt(2/N); + \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 + */ -- cgit v1.2.3