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Diff: cmsis_dsp/FilteringFunctions/arm_biquad_cascade_df2T_f64.c
- Revision:
- 5:3762170b6d4d
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/cmsis_dsp/FilteringFunctions/arm_biquad_cascade_df2T_f64.c Fri Nov 20 08:45:18 2015 +0000
@@ -0,0 +1,603 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
+*
+* $Date: 19. March 2015
+* $Revision: V.1.4.5
+*
+* Project: CMSIS DSP Library
+* Title: arm_biquad_cascade_df2T_f64.c
+*
+* Description: Processing function for the floating-point transposed
+* direct form II Biquad cascade filter.
+*
+* 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 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
+ */