arm_dct4_f32.c
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r41 | /* ---------------------------------------------------------------------- | ||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_dct4_f32.c | ||||
* | ||||
* Description: Processing function of DCT4 & IDCT4 F32. | ||||
* | ||||
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 | ||||
* | ||||
* Version 1.0.10 2011/7/15 | ||||
* Big Endian support added and Merged M0 and M3/M4 Source code. | ||||
* | ||||
* Version 1.0.3 2010/11/29 | ||||
* Re-organized the CMSIS folders and updated documentation. | ||||
* | ||||
* Version 1.0.2 2010/11/11 | ||||
* Documentation updated. | ||||
* | ||||
* Version 1.0.1 2010/10/05 | ||||
* Production release and review comments incorporated. | ||||
* | ||||
* Version 1.0.0 2010/09/20 | ||||
* Production release and review comments incorporated. | ||||
* -------------------------------------------------------------------- */ | ||||
#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 supported by arm_rfft_f32(). | ||||
* 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: | ||||
* <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) | ||||
{ | ||||
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; | ||||
#ifndef ARM_MATH_CM0 | ||||
/* 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 /* #ifndef ARM_MATH_CM0 */ | ||||
} | ||||
/** | ||||
* @} end of DCT4_IDCT4 group | ||||
*/ | ||||