/* ---------------------------------------------------------------------- * 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 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 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) { 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 */