arm_dct4_q31.c
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CLexer
r71 | /* ---------------------------------------------------------------------- | |||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_dct4_q31.c | ||||
* | ||||
* Description: Processing function of DCT4 & IDCT4 Q31. | ||||
* | ||||
* 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" | ||||
/** | ||||
* @addtogroup DCT4_IDCT4 | ||||
* @{ | ||||
*/ | ||||
/** | ||||
* @brief Processing function for the Q31 DCT4/IDCT4. | ||||
* @param[in] *S points to an instance of the Q31 DCT4 structure. | ||||
* @param[in] *pState points to state buffer. | ||||
* @param[in,out] *pInlineBuffer points to the in-place input and output buffer. | ||||
* @return none. | ||||
* \par Input an output formats: | ||||
* Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process, | ||||
* as the conversion from DCT2 to DCT4 involves one subtraction. | ||||
* Internally inputs are downscaled in the RFFT process function to avoid overflows. | ||||
* Number of bits downscaled, depends on the size of the transform. | ||||
* The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below: | ||||
* | ||||
* \image html dct4FormatsQ31Table.gif | ||||
*/ | ||||
void arm_dct4_q31( | ||||
const arm_dct4_instance_q31 * S, | ||||
q31_t * pState, | ||||
q31_t * pInlineBuffer) | ||||
{ | ||||
uint16_t i; /* Loop counter */ | ||||
q31_t *weights = S->pTwiddle; /* Pointer to the Weights table */ | ||||
q31_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ | ||||
q31_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ | ||||
q31_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_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N); | ||||
arm_shift_q31(pInlineBuffer, 1, 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 = 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 = 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_q31(S->pRfft, pInlineBuffer, pState); | ||||
/*---------------------------------------------------------------------- | ||||
* Step3: Multiply the FFT output with the weights. | ||||
*----------------------------------------------------------------------*/ | ||||
arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N); | ||||
/* The output of complex multiplication is in 3.29 format. | ||||
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */ | ||||
arm_shift_q31(pState, 2, pState, S->N * 2); | ||||
/* ----------- 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++ >> 1u; | ||||
/* 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++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | ||||
in = *pbuff; | ||||
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | ||||
in = *pbuff; | ||||
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | ||||
in = *pbuff; | ||||
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | ||||
/* Decrement the loop counter */ | ||||
i--; | ||||
} while(i > 0u); | ||||
#else | ||||
/* Run the below code for Cortex-M0 */ | ||||
/* 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_q31(S->pRfft, pInlineBuffer, pState); | ||||
/*---------------------------------------------------------------------- | ||||
* Step3: Multiply the FFT output with the weights. | ||||
*----------------------------------------------------------------------*/ | ||||
arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N); | ||||
/* The output of complex multiplication is in 3.29 format. | ||||
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */ | ||||
arm_shift_q31(pState, 2, pState, S->N * 2); | ||||
/* ----------- 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++ >> 1u; | ||||
/* 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); | ||||
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 */ | ||||
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++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); | ||||
/* Decrement the loop counter */ | ||||
i--; | ||||
} while(i > 0u); | ||||
#endif /* #ifndef ARM_MATH_CM0 */ | ||||
} | ||||
/** | ||||
* @} end of DCT4_IDCT4 group | ||||
*/ | ||||