| /* ---------------------------------------------------------------------- |
| * 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_q31.c |
| * |
| * Description: Processing function of DCT4 & IDCT4 Q31. |
| * |
| * 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" |
| |
| /** |
| * @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_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 = 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_FAMILY */ |
| |
| } |
| |
| /** |
| * @} end of DCT4_IDCT4 group |
| */ |