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-/* ----------------------------------------------------------------------
- * Project: CMSIS DSP Library
- * Title: arm_biquad_cascade_df2T_f64.c
- * Description: Processing function for floating-point transposed direct form II Biquad cascade filter
- *
- * $Date: 27. January 2017
- * $Revision: V.1.5.1
- *
- * Target Processor: Cortex-M cores
- * -------------------------------------------------------------------- */
-/*
- * Copyright (C) 2010-2017 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"
-
-/**
-* @ingroup groupFilters
-*/
-
-/**
-* @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
-*
-* This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
-* The filters are implemented as a cascade of second order Biquad sections.
-* These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
-* Only floating-point data is supported.
-*
-* This function operate on blocks of input and output data and each call to the function
-* processes <code>blockSize</code> samples through the filter.
-* <code>pSrc</code> points to the array of input data and
-* <code>pDst</code> points to the array of output data.
-* Both arrays contain <code>blockSize</code> values.
-*
-* \par Algorithm
-* Each Biquad stage implements a second order filter using the difference equation:
-* <pre>
-* y[n] = b0 * x[n] + d1
-* d1 = b1 * x[n] + a1 * y[n] + d2
-* d2 = b2 * x[n] + a2 * y[n]
-* </pre>
-* where d1 and d2 represent the two state values.
-*
-* \par
-* A Biquad filter using a transposed Direct Form II structure is shown below.
-* \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
-* Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
-* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
-* Pay careful attention to the sign of the feedback coefficients.
-* Some design tools flip the sign of the feedback coefficients:
-* <pre>
-* y[n] = b0 * x[n] + d1;
-* d1 = b1 * x[n] - a1 * y[n] + d2;
-* d2 = b2 * x[n] - a2 * y[n];
-* </pre>
-* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
-*
-* \par
-* Higher order filters are realized as a cascade of second order sections.
-* <code>numStages</code> refers to the number of second order stages used.
-* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
-* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the
-* coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
-*
-* \par
-* <code>pState</code> points to the state variable array.
-* Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.
-* The state variables are arranged in the <code>pState</code> array as:
-* <pre>
-* {d11, d12, d21, d22, ...}
-* </pre>
-* where <code>d1x</code> refers to the state variables for the first Biquad and
-* <code>d2x</code> refers to the state variables for the second Biquad.
-* The state array has a total length of <code>2*numStages</code> values.
-* The state variables are updated after each block of data is processed; the coefficients are untouched.
-*
-* \par
-* The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
-* The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
-* That is why the Direct Form I structure supports Q15 and Q31 data types.
-* The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables <code>d1</code> and <code>d2</code>.
-* Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
-* The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.
-*
-* \par Instance Structure
-* The coefficients and state variables for a filter are stored together in an instance data structure.
-* A separate instance structure must be defined for each filter.
-* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
-*
-* \par Init Functions
-* There is also an associated initialization function.
-* The initialization function performs following operations:
-* - Sets the values of the internal structure fields.
-* - Zeros out the values in the state buffer.
-* To do this manually without calling the init function, assign the follow subfields of the instance structure:
-* numStages, pCoeffs, pState. Also set all of the values in pState to zero.
-*
-* \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.
-* Set the values in the state buffer to zeros before static initialization.
-* For example, to statically initialize the instance structure use
-* <pre>
-* arm_biquad_cascade_df2T_instance_f64 S1 = {numStages, pState, pCoeffs};
-* </pre>
-* where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer.
-* <code>pCoeffs</code> is the address of the coefficient buffer;
-*
-*/
-
-/**
-* @addtogroup BiquadCascadeDF2T
-* @{
-*/
-
-/**
-* @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
-* @param[in] *S points to an instance of the filter data structure.
-* @param[in] *pSrc points to the block of input data.
-* @param[out] *pDst points to the block of output data
-* @param[in] blockSize number of samples to process.
-* @return none.
-*/
-
-
-LOW_OPTIMIZATION_ENTER
-void arm_biquad_cascade_df2T_f64(
-const arm_biquad_cascade_df2T_instance_f64 * S,
-float64_t * pSrc,
-float64_t * pDst,
-uint32_t blockSize)
-{
-
- float64_t *pIn = pSrc; /* source pointer */
- float64_t *pOut = pDst; /* destination pointer */
- float64_t *pState = S->pState; /* State pointer */
- float64_t *pCoeffs = S->pCoeffs; /* coefficient pointer */
- float64_t acc1; /* accumulator */
- float64_t b0, b1, b2, a1, a2; /* Filter coefficients */
- float64_t Xn1; /* temporary input */
- float64_t d1, d2; /* state variables */
- uint32_t sample, stage = S->numStages; /* loop counters */
-
-#if defined(ARM_MATH_CM7)
-
- float64_t Xn2, Xn3, Xn4, Xn5, Xn6, Xn7, Xn8; /* Input State variables */
- float64_t Xn9, Xn10, Xn11, Xn12, Xn13, Xn14, Xn15, Xn16;
- float64_t acc2, acc3, acc4, acc5, acc6, acc7; /* Simulates the accumulator */
- float64_t acc8, acc9, acc10, acc11, acc12, acc13, acc14, acc15, acc16;
-
- do
- {
- /* Reading the coefficients */
- b0 = pCoeffs[0];
- b1 = pCoeffs[1];
- b2 = pCoeffs[2];
- a1 = pCoeffs[3];
- /* Apply loop unrolling and compute 16 output values simultaneously. */
- sample = blockSize >> 4U;
- a2 = pCoeffs[4];
-
- /*Reading the state values */
- d1 = pState[0];
- d2 = pState[1];
-
- pCoeffs += 5U;
-
-
- /* First part of the processing with loop unrolling. Compute 16 outputs at a time.
- ** a second loop below computes the remaining 1 to 15 samples. */
- while (sample > 0U) {
-
- /* y[n] = b0 * x[n] + d1 */
- /* d1 = b1 * x[n] + a1 * y[n] + d2 */
- /* d2 = b2 * x[n] + a2 * y[n] */
-
- /* Read the first 2 inputs. 2 cycles */
- Xn1 = pIn[0 ];
- Xn2 = pIn[1 ];
-
- /* Sample 1. 5 cycles */
- Xn3 = pIn[2 ];
- acc1 = b0 * Xn1 + d1;
-
- Xn4 = pIn[3 ];
- d1 = b1 * Xn1 + d2;
-
- Xn5 = pIn[4 ];
- d2 = b2 * Xn1;
-
- Xn6 = pIn[5 ];
- d1 += a1 * acc1;
-
- Xn7 = pIn[6 ];
- d2 += a2 * acc1;
-
- /* Sample 2. 5 cycles */
- Xn8 = pIn[7 ];
- acc2 = b0 * Xn2 + d1;
-
- Xn9 = pIn[8 ];
- d1 = b1 * Xn2 + d2;
-
- Xn10 = pIn[9 ];
- d2 = b2 * Xn2;
-
- Xn11 = pIn[10];
- d1 += a1 * acc2;
-
- Xn12 = pIn[11];
- d2 += a2 * acc2;
-
- /* Sample 3. 5 cycles */
- Xn13 = pIn[12];
- acc3 = b0 * Xn3 + d1;
-
- Xn14 = pIn[13];
- d1 = b1 * Xn3 + d2;
-
- Xn15 = pIn[14];
- d2 = b2 * Xn3;
-
- Xn16 = pIn[15];
- d1 += a1 * acc3;
-
- pIn += 16;
- d2 += a2 * acc3;
-
- /* Sample 4. 5 cycles */
- acc4 = b0 * Xn4 + d1;
- d1 = b1 * Xn4 + d2;
- d2 = b2 * Xn4;
- d1 += a1 * acc4;
- d2 += a2 * acc4;
-
- /* Sample 5. 5 cycles */
- acc5 = b0 * Xn5 + d1;
- d1 = b1 * Xn5 + d2;
- d2 = b2 * Xn5;
- d1 += a1 * acc5;
- d2 += a2 * acc5;
-
- /* Sample 6. 5 cycles */
- acc6 = b0 * Xn6 + d1;
- d1 = b1 * Xn6 + d2;
- d2 = b2 * Xn6;
- d1 += a1 * acc6;
- d2 += a2 * acc6;
-
- /* Sample 7. 5 cycles */
- acc7 = b0 * Xn7 + d1;
- d1 = b1 * Xn7 + d2;
- d2 = b2 * Xn7;
- d1 += a1 * acc7;
- d2 += a2 * acc7;
-
- /* Sample 8. 5 cycles */
- acc8 = b0 * Xn8 + d1;
- d1 = b1 * Xn8 + d2;
- d2 = b2 * Xn8;
- d1 += a1 * acc8;
- d2 += a2 * acc8;
-
- /* Sample 9. 5 cycles */
- acc9 = b0 * Xn9 + d1;
- d1 = b1 * Xn9 + d2;
- d2 = b2 * Xn9;
- d1 += a1 * acc9;
- d2 += a2 * acc9;
-
- /* Sample 10. 5 cycles */
- acc10 = b0 * Xn10 + d1;
- d1 = b1 * Xn10 + d2;
- d2 = b2 * Xn10;
- d1 += a1 * acc10;
- d2 += a2 * acc10;
-
- /* Sample 11. 5 cycles */
- acc11 = b0 * Xn11 + d1;
- d1 = b1 * Xn11 + d2;
- d2 = b2 * Xn11;
- d1 += a1 * acc11;
- d2 += a2 * acc11;
-
- /* Sample 12. 5 cycles */
- acc12 = b0 * Xn12 + d1;
- d1 = b1 * Xn12 + d2;
- d2 = b2 * Xn12;
- d1 += a1 * acc12;
- d2 += a2 * acc12;
-
- /* Sample 13. 5 cycles */
- acc13 = b0 * Xn13 + d1;
- d1 = b1 * Xn13 + d2;
- d2 = b2 * Xn13;
-
- pOut[0 ] = acc1 ;
- d1 += a1 * acc13;
-
- pOut[1 ] = acc2 ;
- d2 += a2 * acc13;
-
- /* Sample 14. 5 cycles */
- pOut[2 ] = acc3 ;
- acc14 = b0 * Xn14 + d1;
-
- pOut[3 ] = acc4 ;
- d1 = b1 * Xn14 + d2;
-
- pOut[4 ] = acc5 ;
- d2 = b2 * Xn14;
-
- pOut[5 ] = acc6 ;
- d1 += a1 * acc14;
-
- pOut[6 ] = acc7 ;
- d2 += a2 * acc14;
-
- /* Sample 15. 5 cycles */
- pOut[7 ] = acc8 ;
- pOut[8 ] = acc9 ;
- acc15 = b0 * Xn15 + d1;
-
- pOut[9 ] = acc10;
- d1 = b1 * Xn15 + d2;
-
- pOut[10] = acc11;
- d2 = b2 * Xn15;
-
- pOut[11] = acc12;
- d1 += a1 * acc15;
-
- pOut[12] = acc13;
- d2 += a2 * acc15;
-
- /* Sample 16. 5 cycles */
- pOut[13] = acc14;
- acc16 = b0 * Xn16 + d1;
-
- pOut[14] = acc15;
- d1 = b1 * Xn16 + d2;
-
- pOut[15] = acc16;
- d2 = b2 * Xn16;
-
- sample--;
- d1 += a1 * acc16;
-
- pOut += 16;
- d2 += a2 * acc16;
- }
-
- sample = blockSize & 0xFu;
- while (sample > 0U) {
- Xn1 = *pIn;
- acc1 = b0 * Xn1 + d1;
-
- pIn++;
- d1 = b1 * Xn1 + d2;
-
- *pOut = acc1;
- d2 = b2 * Xn1;
-
- pOut++;
- d1 += a1 * acc1;
-
- sample--;
- d2 += a2 * acc1;
- }
-
- /* Store the updated state variables back into the state array */
- pState[0] = d1;
- /* The current stage input is given as the output to the next stage */
- pIn = pDst;
-
- pState[1] = d2;
- /* decrement the loop counter */
- stage--;
-
- pState += 2U;
-
- /*Reset the output working pointer */
- pOut = pDst;
-
- } while (stage > 0U);
-
-#elif defined(ARM_MATH_CM0_FAMILY)
-
- /* Run the below code for Cortex-M0 */
-
- do
- {
- /* Reading the coefficients */
- b0 = *pCoeffs++;
- b1 = *pCoeffs++;
- b2 = *pCoeffs++;
- a1 = *pCoeffs++;
- a2 = *pCoeffs++;
-
- /*Reading the state values */
- d1 = pState[0];
- d2 = pState[1];
-
-
- sample = blockSize;
-
- while (sample > 0U)
- {
- /* Read the input */
- Xn1 = *pIn++;
-
- /* y[n] = b0 * x[n] + d1 */
- acc1 = (b0 * Xn1) + d1;
-
- /* Store the result in the accumulator in the destination buffer. */
- *pOut++ = acc1;
-
- /* Every time after the output is computed state should be updated. */
- /* d1 = b1 * x[n] + a1 * y[n] + d2 */
- d1 = ((b1 * Xn1) + (a1 * acc1)) + d2;
-
- /* d2 = b2 * x[n] + a2 * y[n] */
- d2 = (b2 * Xn1) + (a2 * acc1);
-
- /* decrement the loop counter */
- sample--;
- }
-
- /* Store the updated state variables back into the state array */
- *pState++ = d1;
- *pState++ = d2;
-
- /* The current stage input is given as the output to the next stage */
- pIn = pDst;
-
- /*Reset the output working pointer */
- pOut = pDst;
-
- /* decrement the loop counter */
- stage--;
-
- } while (stage > 0U);
-
-#else
-
- float64_t Xn2, Xn3, Xn4; /* Input State variables */
- float64_t acc2, acc3, acc4; /* accumulator */
-
-
- float64_t p0, p1, p2, p3, p4, A1;
-
- /* Run the below code for Cortex-M4 and Cortex-M3 */
- do
- {
- /* Reading the coefficients */
- b0 = *pCoeffs++;
- b1 = *pCoeffs++;
- b2 = *pCoeffs++;
- a1 = *pCoeffs++;
- a2 = *pCoeffs++;
-
-
- /*Reading the state values */
- d1 = pState[0];
- d2 = pState[1];
-
- /* Apply loop unrolling and compute 4 output values simultaneously. */
- sample = blockSize >> 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. */
- while (sample > 0U) {
-
- /* y[n] = b0 * x[n] + d1 */
- /* d1 = b1 * x[n] + a1 * y[n] + d2 */
- /* d2 = b2 * x[n] + a2 * y[n] */
-
- /* Read the four inputs */
- Xn1 = pIn[0];
- Xn2 = pIn[1];
- Xn3 = pIn[2];
- Xn4 = pIn[3];
- pIn += 4;
-
- p0 = b0 * Xn1;
- p1 = b1 * Xn1;
- acc1 = p0 + d1;
- p0 = b0 * Xn2;
- p3 = a1 * acc1;
- p2 = b2 * Xn1;
- A1 = p1 + p3;
- p4 = a2 * acc1;
- d1 = A1 + d2;
- d2 = p2 + p4;
-
- p1 = b1 * Xn2;
- acc2 = p0 + d1;
- p0 = b0 * Xn3;
- p3 = a1 * acc2;
- p2 = b2 * Xn2;
- A1 = p1 + p3;
- p4 = a2 * acc2;
- d1 = A1 + d2;
- d2 = p2 + p4;
-
- p1 = b1 * Xn3;
- acc3 = p0 + d1;
- p0 = b0 * Xn4;
- p3 = a1 * acc3;
- p2 = b2 * Xn3;
- A1 = p1 + p3;
- p4 = a2 * acc3;
- d1 = A1 + d2;
- d2 = p2 + p4;
-
- acc4 = p0 + d1;
- p1 = b1 * Xn4;
- p3 = a1 * acc4;
- p2 = b2 * Xn4;
- A1 = p1 + p3;
- p4 = a2 * acc4;
- d1 = A1 + d2;
- d2 = p2 + p4;
-
- pOut[0] = acc1;
- pOut[1] = acc2;
- pOut[2] = acc3;
- pOut[3] = acc4;
- pOut += 4;
-
- sample--;
- }
-
- sample = blockSize & 0x3U;
- while (sample > 0U) {
- Xn1 = *pIn++;
-
- p0 = b0 * Xn1;
- p1 = b1 * Xn1;
- acc1 = p0 + d1;
- p3 = a1 * acc1;
- p2 = b2 * Xn1;
- A1 = p1 + p3;
- p4 = a2 * acc1;
- d1 = A1 + d2;
- d2 = p2 + p4;
-
- *pOut++ = acc1;
-
- sample--;
- }
-
- /* Store the updated state variables back into the state array */
- *pState++ = d1;
- *pState++ = d2;
-
- /* The current stage input is given as the output to the next stage */
- pIn = pDst;
-
- /*Reset the output working pointer */
- pOut = pDst;
-
- /* decrement the loop counter */
- stage--;
-
- } while (stage > 0U);
-
-#endif
-
-}
-LOW_OPTIMIZATION_EXIT
-
-/**
- * @} end of BiquadCascadeDF2T group
- */