pigweed / third_party / github / STMicroelectronics / cmsis_core / be0e91fb4ba19a2ee427ba8b6b75b43eb02b2810 / . / DSP / Source / TransformFunctions / arm_dct4_q15.c

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

* Project: CMSIS DSP Library | |

* Title: arm_dct4_q15.c | |

* Description: Processing function of DCT4 & IDCT4 Q15 | |

* | |

* $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" | |

/** | |

@addtogroup DCT4_IDCT4 | |

@{ | |

*/ | |

/** | |

@brief Processing function for the Q15 DCT4/IDCT4. | |

@param[in] S points to an instance of the Q15 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 | |

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 dct4FormatsQ15Table.gif | |

*/ | |

void arm_dct4_q15( | |

const arm_dct4_instance_q15 * S, | |

q15_t * pState, | |

q15_t * pInlineBuffer) | |

{ | |

const q15_t *weights = S->pTwiddle; /* Pointer to the Weights table */ | |

const q15_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ | |

q15_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ | |

q15_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_mult_q15 (pInlineBuffer, cosFact, pInlineBuffer, S->N); | |

arm_shift_q15 (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; | |

#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_q15 (S->pRfft, pInlineBuffer, pState); | |

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

* Step3: Multiply the FFT output with the weights. | |

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

arm_cmplx_mult_cmplx_q15 (pState, weights, pState, S->N); | |

/* The output of complex multiplication is in 3.13 format. | |

* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */ | |

arm_shift_q15 (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 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++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); | |

in = *pbuff; | |

*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); | |

in = *pbuff; | |

*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); | |

in = *pbuff; | |

*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); | |

/* Decrement 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_q15 (S->pRfft, pInlineBuffer, pState); | |

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

* Step3: Multiply the FFT output with the weights. | |

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

arm_cmplx_mult_cmplx_q15 (pState, weights, pState, S->N); | |

/* The output of complex multiplication is in 3.13 format. | |

* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */ | |

arm_shift_q15 (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); | |

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++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); | |

/* Decrement loop counter */ | |

i--; | |

} while (i > 0U); | |

#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ | |

} | |

/** | |

@} end of DCT4_IDCT4 group | |

*/ |