/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 16/10/14 6:01p $Revision:  V.1.4.5
*
* Project:      CMSIS DSP Library
* Title:        arm_lms_norm_f32.c
*
* Description:  Processing function for the floating-point Normalised LMS.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
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#include "arm_math.h"

/**
 * @ingroup groupFilters
 */

/**
 * @defgroup LMS_NORM Normalized LMS Filters
 *
 * This set of functions implements a commonly used adaptive filter.
 * It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization
 * factor which increases the adaptation rate of the filter.
 * The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.
 *
 * A normalized least mean square (NLMS) filter consists of two components as shown below.
 * The first component is a standard transversal or FIR filter.
 * The second component is a coefficient update mechanism.
 * The NLMS filter has two input signals.
 * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
 * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
 * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
 * This "error signal" tends towards zero as the filter adapts.
 * The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.
 * \image html LMS.gif "Internal structure of the NLMS adaptive filter"
 *
 * The functions operate on blocks of data and each call to the function processes
 * <code>blockSize</code> samples through the filter.
 * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
 * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
 * All arrays contain <code>blockSize</code> values.
 *
 * The functions operate on a block-by-block basis.
 * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
 * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
 *
 * \par Algorithm:
 * The output signal <code>y[n]</code> is computed by a standard FIR filter:
 * <pre>
 *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
 * </pre>
 *
 * \par
 * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
 * <pre>
 *     e[n] = d[n] - y[n].
 * </pre>
 *
 * \par
 * After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:
 * <pre>
 *    E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.
 * </pre>
 * The filter coefficients <code>b[k]</code> are then updated on a sample-by-sample basis:
 * <pre>
 *     b[k] = b[k] + e[n] * (mu/E) * x[n-k],  for k=0, 1, ..., numTaps-1
 * </pre>
 * where <code>mu</code> is the step size and controls the rate of coefficient convergence.
 *\par
 * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
 * Coefficients are stored in time reversed order.
 * \par
 * <pre>
 *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
 * </pre>
 * \par
 * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
 * Samples in the state buffer are stored in the order:
 * \par
 * <pre>
 *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
 * </pre>
 * \par
 * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
 * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
 * to be avoided and yields a significant speed improvement.
 * The state variables are updated after each block of data is processed.
 * \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 and
 * coefficient and state arrays cannot be shared among instances.
 * There are separate instance structure declarations for each of the 3 supported data types.
 *
 * \par Initialization Functions
 * There is also an associated initialization function for each data type.
 * The initialization function performs the 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:
 * numTaps, pCoeffs, mu, energy, x0, pState. Also set all of the values in pState to zero.
 * For Q7, Q15, and Q31 the following fields must also be initialized;
 * recipTable, postShift
 *
 * \par
 * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
 * \par Fixed-Point Behavior:
 * Care must be taken when using the Q15 and Q31 versions of the normalised LMS filter.
 * The following issues must be considered:
 * - Scaling of coefficients
 * - Overflow and saturation
 *
 * \par Scaling of Coefficients:
 * Filter coefficients are represented as fractional values and
 * coefficients are restricted to lie in the range <code>[-1 +1)</code>.
 * The fixed-point functions have an additional scaling parameter <code>postShift</code>.
 * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
 * This essentially scales the filter coefficients by <code>2^postShift</code> and
 * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
 * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
 *
 * \par Overflow and Saturation:
 * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
 * described separately as part of the function specific documentation below.
 */


/**
 * @addtogroup LMS_NORM
 * @{
 */


/**
 * @brief Processing function for floating-point normalized LMS filter.
 * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
 * @param[in] *pSrc points to the block of input data.
 * @param[in] *pRef points to the block of reference data.
 * @param[out] *pOut points to the block of output data.
 * @param[out] *pErr points to the block of error data.
 * @param[in] blockSize number of samples to process.
 * @return none.
 */

void arm_lms_norm_f32(
    arm_lms_norm_instance_f32 * S,
    float32_t * pSrc,
    float32_t * pRef,
    float32_t * pOut,
    float32_t * pErr,
    uint32_t blockSize)
{
    float32_t *pState = S->pState;                 /* State pointer */
    float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
    float32_t *pStateCurnt;                        /* Points to the current sample of the state */
    float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
    float32_t mu = S->mu;                          /* Adaptive factor */
    uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
    uint32_t tapCnt, blkCnt;                       /* Loop counters */
    float32_t energy;                              /* Energy of the input */
    float32_t sum, e, d;                           /* accumulator, error, reference data sample */
    float32_t w, x0, in;                           /* weight factor, temporary variable to hold input sample and state */

    /* Initializations of error,  difference, Coefficient update */
    e = 0.0f;
    d = 0.0f;
    w = 0.0f;

    energy = S->energy;
    x0 = S->x0;

    /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
    /* pStateCurnt points to the location where the new input data should be written */
    pStateCurnt = &(S->pState[(numTaps - 1u)]);

    /* Loop over blockSize number of values */
    blkCnt = blockSize;


#ifndef ARM_MATH_CM0_FAMILY

    /* Run the below code for Cortex-M4 and Cortex-M3 */

    while(blkCnt > 0u)
    {
        /* Copy the new input sample into the state buffer */
        *pStateCurnt++ = *pSrc;

        /* Initialize pState pointer */
        px = pState;

        /* Initialize coeff pointer */
        pb = (pCoeffs);

        /* Read the sample from input buffer */
        in = *pSrc++;

        /* Update the energy calculation */
        energy -= x0 * x0;
        energy += in * in;

        /* Set the accumulator to zero */
        sum = 0.0f;

        /* Loop unrolling.  Process 4 taps at a time. */
        tapCnt = numTaps >> 2;

        while(tapCnt > 0u)
        {
            /* Perform the multiply-accumulate */
            sum += (*px++) * (*pb++);
            sum += (*px++) * (*pb++);
            sum += (*px++) * (*pb++);
            sum += (*px++) * (*pb++);

            /* Decrement the loop counter */
            tapCnt--;
        }

        /* If the filter length is not a multiple of 4, compute the remaining filter taps */
        tapCnt = numTaps % 0x4u;

        while(tapCnt > 0u)
        {
            /* Perform the multiply-accumulate */
            sum += (*px++) * (*pb++);

            /* Decrement the loop counter */
            tapCnt--;
        }

        /* The result in the accumulator, store in the destination buffer. */
        *pOut++ = sum;

        /* Compute and store error */
        d = (float32_t)(*pRef++);
        e = d - sum;
        *pErr++ = e;

        /* Calculation of Weighting factor for updating filter coefficients */
        /* epsilon value 0.000000119209289f */
        w = (e * mu) / (energy + 0.000000119209289f);

        /* Initialize pState pointer */
        px = pState;

        /* Initialize coeff pointer */
        pb = (pCoeffs);

        /* Loop unrolling.  Process 4 taps at a time. */
        tapCnt = numTaps >> 2;

        /* Update filter coefficients */
        while(tapCnt > 0u)
        {
            /* Perform the multiply-accumulate */
            *pb += w * (*px++);
            pb++;

            *pb += w * (*px++);
            pb++;

            *pb += w * (*px++);
            pb++;

            *pb += w * (*px++);
            pb++;


            /* Decrement the loop counter */
            tapCnt--;
        }

        /* If the filter length is not a multiple of 4, compute the remaining filter taps */
        tapCnt = numTaps % 0x4u;

        while(tapCnt > 0u)
        {
            /* Perform the multiply-accumulate */
            *pb += w * (*px++);
            pb++;

            /* Decrement the loop counter */
            tapCnt--;
        }

        x0 = *pState;

        /* Advance state pointer by 1 for the next sample */
        pState = pState + 1;

        /* Decrement the loop counter */
        blkCnt--;
    }

    S->energy = energy;
    S->x0 = x0;

    /* Processing is complete. Now copy the last numTaps - 1 samples to the
       satrt of the state buffer. This prepares the state buffer for the
       next function call. */

    /* Points to the start of the pState buffer */
    pStateCurnt = S->pState;

    /* Loop unrolling for (numTaps - 1u)/4 samples copy */
    tapCnt = (numTaps - 1u) >> 2u;

    /* copy data */
    while(tapCnt > 0u)
    {
        *pStateCurnt++ = *pState++;
        *pStateCurnt++ = *pState++;
        *pStateCurnt++ = *pState++;
        *pStateCurnt++ = *pState++;

        /* Decrement the loop counter */
        tapCnt--;
    }

    /* Calculate remaining number of copies */
    tapCnt = (numTaps - 1u) % 0x4u;

    /* Copy the remaining q31_t data */
    while(tapCnt > 0u)
    {
        *pStateCurnt++ = *pState++;

        /* Decrement the loop counter */
        tapCnt--;
    }

#else

    /* Run the below code for Cortex-M0 */

    while(blkCnt > 0u)
    {
        /* Copy the new input sample into the state buffer */
        *pStateCurnt++ = *pSrc;

        /* Initialize pState pointer */
        px = pState;

        /* Initialize pCoeffs pointer */
        pb = pCoeffs;

        /* Read the sample from input buffer */
        in = *pSrc++;

        /* Update the energy calculation */
        energy -= x0 * x0;
        energy += in * in;

        /* Set the accumulator to zero */
        sum = 0.0f;

        /* Loop over numTaps number of values */
        tapCnt = numTaps;

        while(tapCnt > 0u)
        {
            /* Perform the multiply-accumulate */
            sum += (*px++) * (*pb++);

            /* Decrement the loop counter */
            tapCnt--;
        }

        /* The result in the accumulator is stored in the destination buffer. */
        *pOut++ = sum;

        /* Compute and store error */
        d = (float32_t)(*pRef++);
        e = d - sum;
        *pErr++ = e;

        /* Calculation of Weighting factor for updating filter coefficients */
        /* epsilon value 0.000000119209289f */
        w = (e * mu) / (energy + 0.000000119209289f);

        /* Initialize pState pointer */
        px = pState;

        /* Initialize pCcoeffs pointer */
        pb = pCoeffs;

        /* Loop over numTaps number of values */
        tapCnt = numTaps;

        while(tapCnt > 0u)
        {
            /* Perform the multiply-accumulate */
            *pb += w * (*px++);
            pb++;

            /* Decrement the loop counter */
            tapCnt--;
        }

        x0 = *pState;

        /* Advance state pointer by 1 for the next sample */
        pState = pState + 1;

        /* Decrement the loop counter */
        blkCnt--;
    }

    S->energy = energy;
    S->x0 = x0;

    /* Processing is complete. Now copy the last numTaps - 1 samples to the
       satrt of the state buffer. This prepares the state buffer for the
       next function call. */

    /* Points to the start of the pState buffer */
    pStateCurnt = S->pState;

    /* Copy (numTaps - 1u) samples  */
    tapCnt = (numTaps - 1u);

    /* Copy the remaining q31_t data */
    while(tapCnt > 0u)
    {
        *pStateCurnt++ = *pState++;

        /* Decrement the loop counter */
        tapCnt--;
    }

#endif /*   #ifndef ARM_MATH_CM0_FAMILY */

}

/**
   * @} end of LMS_NORM group
   */
