pigweed / third_party / github / STMicroelectronics / cmsis_core / 7dd288b23bf605a3a2fafa81a29d2c96a2fd83ce / . / DSP_Lib / Source / TransformFunctions / arm_dct4_f32.c

/* ---------------------------------------------------------------------- | |

* Copyright (C) 2010-2014 ARM Limited. All rights reserved. | |

* | |

* $Date: 19. March 2015 | |

* $Revision: V.1.4.5 | |

* | |

* Project: CMSIS DSP Library | |

* Title: arm_dct4_f32.c | |

* | |

* Description: Processing function of DCT4 & IDCT4 F32. | |

* | |

* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 | |

* | |

* Redistribution and use in source and binary forms, with or without | |

* modification, are permitted provided that the following conditions | |

* are met: | |

* - Redistributions of source code must retain the above copyright | |

* notice, this list of conditions and the following disclaimer. | |

* - Redistributions in binary form must reproduce the above copyright | |

* notice, this list of conditions and the following disclaimer in | |

* the documentation and/or other materials provided with the | |

* distribution. | |

* - Neither the name of ARM LIMITED nor the names of its contributors | |

* may be used to endorse or promote products derived from this | |

* software without specific prior written permission. | |

* | |

* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |

* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |

* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS | |

* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE | |

* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, | |

* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, | |

* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |

* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER | |

* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |

* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN | |

* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE | |

* POSSIBILITY OF SUCH DAMAGE. | |

* -------------------------------------------------------------------- */ | |

#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_FAMILY | |

/* 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_FAMILY */ | |

} | |

/** | |

* @} end of DCT4_IDCT4 group | |

*/ |