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author | px4dev <px4@purgatory.org> | 2013-01-06 12:52:05 -0800 |
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committer | px4dev <px4@purgatory.org> | 2013-01-06 12:52:05 -0800 |
commit | 4447282260be0780eb6e36f5e953bf56888a5688 (patch) | |
tree | 3ba1e976d998d433397343b79a0612af52075aef /apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c | |
parent | 659543f852d18197f68fafee5db5671567b74f4b (diff) | |
download | px4-firmware-4447282260be0780eb6e36f5e953bf56888a5688.tar.gz px4-firmware-4447282260be0780eb6e36f5e953bf56888a5688.tar.bz2 px4-firmware-4447282260be0780eb6e36f5e953bf56888a5688.zip |
Integrate the interesting parts of the CMSIS 3.01 (r3p1) DSP library
Diffstat (limited to 'apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c')
-rw-r--r-- | apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c | 553 |
1 files changed, 553 insertions, 0 deletions
diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c new file mode 100644 index 000000000..82d6164ee --- /dev/null +++ b/apps/mathlib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c @@ -0,0 +1,553 @@ +/* ----------------------------------------------------------------------
+* Copyright (C) 2010 ARM Limited. All rights reserved.
+*
+* $Date: 15. February 2012
+* $Revision: V1.1.0
+*
+* Project: CMSIS DSP Library
+* Title: arm_biquad_cascade_df1_32x64_q31.c
+*
+* Description: High precision Q31 Biquad cascade filter processing function
+*
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*
+* Version 1.1.0 2012/02/15
+* Updated with more optimizations, bug fixes and minor API changes.
+*
+* Version 1.0.10 2011/7/15
+* Big Endian support added and Merged M0 and M3/M4 Source code.
+*
+* Version 1.0.3 2010/11/29
+* Re-organized the CMSIS folders and updated documentation.
+*
+* Version 1.0.2 2010/11/11
+* Documentation updated.
+*
+* Version 1.0.1 2010/10/05
+* Production release and review comments incorporated.
+*
+* Version 1.0.0 2010/09/20
+* Production release and review comments incorporated.
+*
+* Version 0.0.7 2010/06/10
+* Misra-C changes done
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**
+ * @ingroup groupFilters
+ */
+
+/**
+ * @defgroup BiquadCascadeDF1_32x64 High Precision Q31 Biquad Cascade Filter
+ *
+ * This function implements a high precision Biquad cascade filter which operates on
+ * Q31 data values. The filter coefficients are in 1.31 format and the state variables
+ * are in 1.63 format. The double precision state variables reduce quantization noise
+ * in the filter and provide a cleaner output.
+ * These filters are particularly useful when implementing filters in which the
+ * singularities are close to the unit circle. This is common for low pass or high
+ * pass filters with very low cutoff frequencies.
+ *
+ * The function operates on blocks of input and output data
+ * and each call to the function processes <code>blockSize</code> samples through
+ * the filter. <code>pSrc</code> and <code>pDst</code> points to input and output arrays
+ * containing <code>blockSize</code> Q31 values.
+ *
+ * \par Algorithm
+ * Each Biquad stage implements a second order filter using the difference equation:
+ * <pre>
+ * y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
+ * </pre>
+ * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
+ * \image html Biquad.gif "Single Biquad filter stage"
+ * 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 use the difference equation
+ * <pre>
+ * y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
+ * </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.
+ * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad 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
+ * The <code>pState</code> points to state variables array .
+ * Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code> and each state variable in 1.63 format to improve precision.
+ * The state variables are arranged in the array as:
+ * <pre>
+ * {x[n-1], x[n-2], y[n-1], y[n-2]}
+ * </pre>
+ *
+ * \par
+ * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
+ * The state array has a total length of <code>4*numStages</code> values of data in 1.63 format.
+ * The state variables are updated after each block of data is processed; the coefficients are untouched.
+ *
+ * \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 Function
+ * There is also an associated initialization function which performs the following operations:
+ * - Sets the values of the internal structure fields.
+ * - Zeros out the values in the state buffer.
+ * \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 filter instance structure use
+ * <pre>
+ * arm_biquad_cas_df1_32x64_ins_q31 S1 = {numStages, pState, pCoeffs, postShift};
+ * </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; <code>postShift</code> shift to be applied which is described in detail below.
+ * \par Fixed-Point Behavior
+ * Care must be taken while using Biquad Cascade 32x64 filter function.
+ * Following issues must be considered:
+ * - Scaling of coefficients
+ * - Filter gain
+ * - Overflow and saturation
+ *
+ * \par
+ * Filter coefficients are represented as fractional values and
+ * restricted to lie in the range <code>[-1 +1)</code>.
+ * The processing function has an additional scaling parameter <code>postShift</code>
+ * which allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
+ * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
+ * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"
+ * This essentially scales the filter coefficients by <code>2^postShift</code>.
+ * For example, to realize the coefficients
+ * <pre>
+ * {1.5, -0.8, 1.2, 1.6, -0.9}
+ * </pre>
+ * set the Coefficient array to:
+ * <pre>
+ * {0.75, -0.4, 0.6, 0.8, -0.45}
+ * </pre>
+ * and set <code>postShift=1</code>
+ *
+ * \par
+ * The second thing to keep in mind is the gain through the filter.
+ * The frequency response of a Biquad filter is a function of its coefficients.
+ * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.
+ * This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.
+ * To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.
+ *
+ * \par
+ * The third item to consider is the overflow and saturation behavior of the fixed-point Q31 version.
+ * This is described in the function specific documentation below.
+ */
+
+/**
+ * @addtogroup BiquadCascadeDF1_32x64
+ * @{
+ */
+
+/**
+ * @details
+
+ * @param[in] *S points to an instance of the high precision Q31 Biquad cascade filter.
+ * @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.
+ *
+ * \par
+ * The function is implemented using an internal 64-bit accumulator.
+ * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
+ * Thus, if the accumulator result overflows it wraps around rather than clip.
+ * In order to avoid overflows completely the input signal must be scaled down by 2 bits and lie in the range [-0.25 +0.25).
+ * After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by <code>postShift</code> bits and the result truncated to
+ * 1.31 format by discarding the low 32 bits.
+ *
+ * \par
+ * Two related functions are provided in the CMSIS DSP library.
+ * <code>arm_biquad_cascade_df1_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q63 accumulator.
+ * <code>arm_biquad_cascade_df1_fast_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q31 accumulator.
+ */
+
+void arm_biquad_cas_df1_32x64_q31(
+ const arm_biquad_cas_df1_32x64_ins_q31 * S,
+ q31_t * pSrc,
+ q31_t * pDst,
+ uint32_t blockSize)
+{
+ q31_t *pIn = pSrc; /* input pointer initialization */
+ q31_t *pOut = pDst; /* output pointer initialization */
+ q63_t *pState = S->pState; /* state pointer initialization */
+ q31_t *pCoeffs = S->pCoeffs; /* coeff pointer initialization */
+ q63_t acc; /* accumulator */
+ q31_t Xn1, Xn2; /* Input Filter state variables */
+ q63_t Yn1, Yn2; /* Output Filter state variables */
+ q31_t b0, b1, b2, a1, a2; /* Filter coefficients */
+ q31_t Xn; /* temporary input */
+ int32_t shift = (int32_t) S->postShift + 1; /* Shift to be applied to the output */
+ uint32_t sample, stage = S->numStages; /* loop counters */
+ q31_t acc_l, acc_h; /* temporary output */
+ uint32_t uShift = ((uint32_t) S->postShift + 1u);
+ uint32_t lShift = 32u - uShift; /* Shift to be applied to the output */
+
+
+#ifndef ARM_MATH_CM0
+
+ /* 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 */
+ Xn1 = (q31_t) (pState[0]);
+ Xn2 = (q31_t) (pState[1]);
+ Yn1 = pState[2];
+ Yn2 = pState[3];
+
+ /* Apply loop unrolling and compute 4 output values simultaneously. */
+ /* The variable acc hold output value that is being computed and
+ * stored in the destination buffer
+ * acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
+ */
+
+ 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)
+ {
+ /* Read the input */
+ Xn = *pIn++;
+
+ /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+ /* acc = b0 * x[n] */
+ acc = (q63_t) Xn *b0;
+
+ /* acc += b1 * x[n-1] */
+ acc += (q63_t) Xn1 *b1;
+
+ /* acc += b[2] * x[n-2] */
+ acc += (q63_t) Xn2 *b2;
+
+ /* acc += a1 * y[n-1] */
+ acc += mult32x64(Yn1, a1);
+
+ /* acc += a2 * y[n-2] */
+ acc += mult32x64(Yn2, a2);
+
+ /* The result is converted to 1.63 , Yn2 variable is reused */
+ Yn2 = acc << shift;
+
+ /* Calc lower part of acc */
+ acc_l = acc & 0xffffffff;
+
+ /* Calc upper part of acc */
+ acc_h = (acc >> 32) & 0xffffffff;
+
+ /* Apply shift for lower part of acc and upper part of acc */
+ acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+ /* Store the output in the destination buffer in 1.31 format. */
+ *pOut = acc_h;
+
+ /* Read the second input into Xn2, to reuse the value */
+ Xn2 = *pIn++;
+
+ /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+ /* acc += b1 * x[n-1] */
+ acc = (q63_t) Xn *b1;
+
+ /* acc = b0 * x[n] */
+ acc += (q63_t) Xn2 *b0;
+
+ /* acc += b[2] * x[n-2] */
+ acc += (q63_t) Xn1 *b2;
+
+ /* acc += a1 * y[n-1] */
+ acc += mult32x64(Yn2, a1);
+
+ /* acc += a2 * y[n-2] */
+ acc += mult32x64(Yn1, a2);
+
+ /* The result is converted to 1.63, Yn1 variable is reused */
+ Yn1 = acc << shift;
+
+ /* Calc lower part of acc */
+ acc_l = acc & 0xffffffff;
+
+ /* Calc upper part of acc */
+ acc_h = (acc >> 32) & 0xffffffff;
+
+ /* Apply shift for lower part of acc and upper part of acc */
+ acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+ /* Read the third input into Xn1, to reuse the value */
+ Xn1 = *pIn++;
+
+ /* The result is converted to 1.31 */
+ /* Store the output in the destination buffer. */
+ *(pOut + 1u) = acc_h;
+
+ /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+ /* acc = b0 * x[n] */
+ acc = (q63_t) Xn1 *b0;
+
+ /* acc += b1 * x[n-1] */
+ acc += (q63_t) Xn2 *b1;
+
+ /* acc += b[2] * x[n-2] */
+ acc += (q63_t) Xn *b2;
+
+ /* acc += a1 * y[n-1] */
+ acc += mult32x64(Yn1, a1);
+
+ /* acc += a2 * y[n-2] */
+ acc += mult32x64(Yn2, a2);
+
+ /* The result is converted to 1.63, Yn2 variable is reused */
+ Yn2 = acc << shift;
+
+ /* Calc lower part of acc */
+ acc_l = acc & 0xffffffff;
+
+ /* Calc upper part of acc */
+ acc_h = (acc >> 32) & 0xffffffff;
+
+ /* Apply shift for lower part of acc and upper part of acc */
+ acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+ /* Store the output in the destination buffer in 1.31 format. */
+ *(pOut + 2u) = acc_h;
+
+ /* Read the fourth input into Xn, to reuse the value */
+ Xn = *pIn++;
+
+ /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+ /* acc = b0 * x[n] */
+ acc = (q63_t) Xn *b0;
+
+ /* acc += b1 * x[n-1] */
+ acc += (q63_t) Xn1 *b1;
+
+ /* acc += b[2] * x[n-2] */
+ acc += (q63_t) Xn2 *b2;
+
+ /* acc += a1 * y[n-1] */
+ acc += mult32x64(Yn2, a1);
+
+ /* acc += a2 * y[n-2] */
+ acc += mult32x64(Yn1, a2);
+
+ /* The result is converted to 1.63, Yn1 variable is reused */
+ Yn1 = acc << shift;
+
+ /* Calc lower part of acc */
+ acc_l = acc & 0xffffffff;
+
+ /* Calc upper part of acc */
+ acc_h = (acc >> 32) & 0xffffffff;
+
+ /* Apply shift for lower part of acc and upper part of acc */
+ acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+ /* Store the output in the destination buffer in 1.31 format. */
+ *(pOut + 3u) = acc_h;
+
+ /* Every time after the output is computed state should be updated. */
+ /* The states should be updated as: */
+ /* Xn2 = Xn1 */
+ /* Xn1 = Xn */
+ /* Yn2 = Yn1 */
+ /* Yn1 = acc */
+ Xn2 = Xn1;
+ Xn1 = Xn;
+
+ /* update output pointer */
+ pOut += 4u;
+
+ /* decrement the loop counter */
+ sample--;
+ }
+
+ /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
+ ** No loop unrolling is used. */
+ sample = (blockSize & 0x3u);
+
+ while(sample > 0u)
+ {
+ /* Read the input */
+ Xn = *pIn++;
+
+ /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+
+ /* acc = b0 * x[n] */
+ acc = (q63_t) Xn *b0;
+ /* acc += b1 * x[n-1] */
+ acc += (q63_t) Xn1 *b1;
+ /* acc += b[2] * x[n-2] */
+ acc += (q63_t) Xn2 *b2;
+ /* acc += a1 * y[n-1] */
+ acc += mult32x64(Yn1, a1);
+ /* acc += a2 * y[n-2] */
+ acc += mult32x64(Yn2, a2);
+
+ /* Every time after the output is computed state should be updated. */
+ /* The states should be updated as: */
+ /* Xn2 = Xn1 */
+ /* Xn1 = Xn */
+ /* Yn2 = Yn1 */
+ /* Yn1 = acc */
+ Xn2 = Xn1;
+ Xn1 = Xn;
+ Yn2 = Yn1;
+ /* The result is converted to 1.63, Yn1 variable is reused */
+ Yn1 = acc << shift;
+
+ /* Calc lower part of acc */
+ acc_l = acc & 0xffffffff;
+
+ /* Calc upper part of acc */
+ acc_h = (acc >> 32) & 0xffffffff;
+
+ /* Apply shift for lower part of acc and upper part of acc */
+ acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+ /* Store the output in the destination buffer in 1.31 format. */
+ *pOut++ = acc_h;
+ //Yn1 = acc << shift;
+
+ /* Store the output in the destination buffer in 1.31 format. */
+// *pOut++ = (q31_t) (acc >> (32 - shift));
+
+ /* decrement the loop counter */
+ sample--;
+ }
+
+ /* The first stage output is given as input to the second stage. */
+ pIn = pDst;
+
+ /* Reset to destination buffer working pointer */
+ pOut = pDst;
+
+ /* Store the updated state variables back into the pState array */
+ /* Store the updated state variables back into the pState array */
+ *pState++ = (q63_t) Xn1;
+ *pState++ = (q63_t) Xn2;
+ *pState++ = Yn1;
+ *pState++ = Yn2;
+
+ } while(--stage);
+
+#else
+
+ /* 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 */
+ Xn1 = pState[0];
+ Xn2 = pState[1];
+ Yn1 = pState[2];
+ Yn2 = pState[3];
+
+ /* The variable acc hold output value that is being computed and
+ * stored in the destination buffer
+ * acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
+ */
+
+ sample = blockSize;
+
+ while(sample > 0u)
+ {
+ /* Read the input */
+ Xn = *pIn++;
+
+ /* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
+ /* acc = b0 * x[n] */
+ acc = (q63_t) Xn *b0;
+ /* acc += b1 * x[n-1] */
+ acc += (q63_t) Xn1 *b1;
+ /* acc += b[2] * x[n-2] */
+ acc += (q63_t) Xn2 *b2;
+ /* acc += a1 * y[n-1] */
+ acc += mult32x64(Yn1, a1);
+ /* acc += a2 * y[n-2] */
+ acc += mult32x64(Yn2, a2);
+
+ /* Every time after the output is computed state should be updated. */
+ /* The states should be updated as: */
+ /* Xn2 = Xn1 */
+ /* Xn1 = Xn */
+ /* Yn2 = Yn1 */
+ /* Yn1 = acc */
+ Xn2 = Xn1;
+ Xn1 = Xn;
+ Yn2 = Yn1;
+
+ /* The result is converted to 1.63, Yn1 variable is reused */
+ Yn1 = acc << shift;
+
+ /* Calc lower part of acc */
+ acc_l = acc & 0xffffffff;
+
+ /* Calc upper part of acc */
+ acc_h = (acc >> 32) & 0xffffffff;
+
+ /* Apply shift for lower part of acc and upper part of acc */
+ acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
+
+ /* Store the output in the destination buffer in 1.31 format. */
+ *pOut++ = acc_h;
+
+ //Yn1 = acc << shift;
+
+ /* Store the output in the destination buffer in 1.31 format. */
+ //*pOut++ = (q31_t) (acc >> (32 - shift));
+
+ /* decrement the loop counter */
+ sample--;
+ }
+
+ /* The first stage output is given as input to the second stage. */
+ pIn = pDst;
+
+ /* Reset to destination buffer working pointer */
+ pOut = pDst;
+
+ /* Store the updated state variables back into the pState array */
+ *pState++ = (q63_t) Xn1;
+ *pState++ = (q63_t) Xn2;
+ *pState++ = Yn1;
+ *pState++ = Yn2;
+
+ } while(--stage);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+}
+
+ /**
+ * @} end of BiquadCascadeDF1_32x64 group
+ */
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