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| author | joshua <joshua@joshuayun.com> | 2023-12-30 23:54:31 -0500 |
|---|---|---|
| committer | joshua <joshua@joshuayun.com> | 2023-12-30 23:54:31 -0500 |
| commit | 86608c6770cf08c138a2bdab5855072f64be09ef (patch) | |
| tree | 494a61b3ef37e76f9235a0d10f5c93d97290a35f /Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c | |
| download | sdr-software-master.tar.gz | |
Diffstat (limited to 'Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c')
| -rw-r--r-- | Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c | 448 |
1 files changed, 448 insertions, 0 deletions
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 <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
+ */
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