CMSIS-DSP/Source/MatrixFunctions/arm_mat_mult_f32.c

/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_mat_mult_f32.c
 * Description:  Floating-point matrix multiplication
 *
 * $Date:        23 April 2021
 * $Revision:    V1.9.0
 *
 * Target Processor: Cortex-M and Cortex-A cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2021 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 "dsp/matrix_functions.h"

#if defined(ARM_MATH_NEON)
#define GROUPOFROWS 8
#endif

/**
 * @ingroup groupMatrix
 */

/**
 * @defgroup MatrixMult Matrix Multiplication
 *
 * Multiplies two matrices.
 *
 * @par Multiplication of two 3x3 matrices:
 * 
 * \f[
 * \begin{pmatrix}
 *  a_{1,1} & a_{1,2} & a_{1,3} \\
 *  a_{2,1} & a_{2,2} & a_{2,3} \\
 *  a_{3,1} & a_{3,2} & a_{3,3} \\
 * \end{pmatrix}
 * 
 * \begin{pmatrix}
 *  b_{1,1} & b_{1,2} & b_{1,3} \\
 *  b_{2,1} & b_{2,2} & b_{2,3} \\
 *  b_{3,1} & b_{3,2} & b_{3,3} \\
 * \end{pmatrix}
 * =
 * \begin{pmatrix}
 *  a_{1,1} b_{1,1}+a_{1,2} b_{2,1}+a_{1,3} b_{3,1} & a_{1,1} b_{1,2}+a_{1,2} b_{2,2}+a_{1,3} b_{3,2} & a_{1,1} b_{1,3}+a_{1,2} b_{2,3}+a_{1,3} b_{3,3} \\
 *  a_{2,1} b_{1,1}+a_{2,2} b_{2,1}+a_{2,3} b_{3,1} & a_{2,1} b_{1,2}+a_{2,2} b_{2,2}+a_{2,3} b_{3,2} & a_{2,1} b_{1,3}+a_{2,2} b_{2,3}+a_{2,3} b_{3,3} \\
 *  a_{3,1} b_{1,1}+a_{3,2} b_{2,1}+a_{3,3} b_{3,1} & a_{3,1} b_{1,2}+a_{3,2} b_{2,2}+a_{3,3} b_{3,2} & a_{3,1} b_{1,3}+a_{3,2} b_{2,3}+a_{3,3} b_{3,3} \\
 * \end{pmatrix}
 * \f]

 * Matrix multiplication is only defined if the number of columns of the
 * first matrix equals the number of rows of the second matrix.
 * Multiplying an <code>M x N</code> matrix with an <code>N x P</code> matrix results
 * in an <code>M x P</code> matrix.
 * When matrix size checking is enabled, the functions check: (1) that the inner dimensions of
 * <code>pSrcA</code> and <code>pSrcB</code> are equal; and (2) that the size of the output
 * matrix equals the outer dimensions of <code>pSrcA</code> and <code>pSrcB</code>.
 */


/**
 * @addtogroup MatrixMult
 * @{
 */



#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)

#define MATRIX_DIM3 3 
#define MATRIX_DIM4 4 

__STATIC_INLINE  arm_status arm_mat_mult_f32_2x2_mve(
    const arm_matrix_instance_f32 *pSrcA,
    const arm_matrix_instance_f32 *pSrcB,
    arm_matrix_instance_f32 *pDst)
{
    /* {a00, a00, a10, a10} */
    static const uint32_t  offsetA0[4] = { 0, 0, 2, 2 };
    /* {b00, b01, b00, b01} */
    static const uint32_t  offsetB0[4] = { 0, 1, 0, 1 };
    /* {a01, a01, a11, a11} */
    static const uint32_t  offsetA1[4] = { 1, 1, 3, 3 };
    /* {b10, b11, b10, b11} */
    static const uint32_t  offsetB1[4] = { 2, 3, 2, 3 };

    uint32x4_t vecOffsA, vecOffsB;
    f32x4_t vecInA, vecInB, vecDst;

    vecOffsA = vldrwq_u32((uint32_t const *) offsetA0);
    vecOffsB = vldrwq_u32((uint32_t const *) offsetB0);

    vecInA = vldrwq_gather_shifted_offset((float32_t const *) pSrcA->pData, vecOffsA);
    vecInB = vldrwq_gather_shifted_offset((float32_t const *) pSrcB->pData, vecOffsB);

    vecDst = vmulq(vecInA, vecInB);

    vecOffsA = vldrwq_u32((uint32_t const *) offsetA1);
    vecOffsB = vldrwq_u32((uint32_t const *) offsetB1);

    vecInA = vldrwq_gather_shifted_offset((float32_t const *) pSrcA->pData, vecOffsA);
    vecInB = vldrwq_gather_shifted_offset((float32_t const *) pSrcB->pData, vecOffsB);

    vecDst = vfmaq(vecDst, vecInA, vecInB);

    vstrwq_f32(pDst->pData, vecDst);

    return (ARM_MATH_SUCCESS);

}


/*
 * A  =  {{a00, a01, a02},
 *        {a10, a11, a12},
 *        {a20, a21, a22}}
 * B  =  {{b00, b01, b02},
 *        {b10, b11, b12},
 *        {b20, b21, b22}}
 *
 * Dst = {{a00 b00 + a01 b10 + a02 b20, a00 b01 + a01 b11 + a02 b21, a00 b02 + a01 b12 + a02 b22},
 *        {a10 b00 + a11 b10 + a12 b20, a10 b01 + a11 b11 + a12 b21, a10 b02 + a11 b12 + a12 b22},
 *        {a20 b00 + a21 b10 + a22 b20, a20 b01 + a21 b11 + a22 b21, a20 b02 + a21 b12 + a22 b22}}
 */
__STATIC_INLINE  arm_status arm_mat_mult_f32_3x3_mve(
    const arm_matrix_instance_f32 *pSrcA,
    const arm_matrix_instance_f32 *pSrcB,
    arm_matrix_instance_f32 *pDst)
{
    float32_t   *pInB = pSrcB->pData; /* input data matrix pointer B */
    float32_t   *pInA = pSrcA->pData; /* input data matrix pointer A  */
    float32_t   *pOut = pDst->pData;  /* output data matrix pointer */
    float32_t   *pInA0, *pInA1, *pInA2;
    f32x4_t    vecMac0, vecMac1, vecMac2;
    f32x4_t    vecInB;
    float32_t const *pSrBVec;

    pSrBVec = (float32_t const *) pInB;

    pInA0 = pInA;
    pInA1 = pInA0 + MATRIX_DIM3;
    pInA2 = pInA1 + MATRIX_DIM3;
    /* enable predication to disable last (4th) vector element */
    mve_pred16_t p0 = vctp32q(MATRIX_DIM3);

    /*
     * load {b0,0, b0,1, b0,2, 0}
     */
    vecInB = vldrwq_z_f32(pSrBVec, p0);  
    pSrBVec += MATRIX_DIM3;

    vecMac0 = vmulq(vecInB, *pInA0++);
    vecMac1 = vmulq(vecInB, *pInA1++);
    vecMac2 = vmulq(vecInB, *pInA2++);
    /*
     * load {b1,0, b1,1, b1,2, 0}
     */
    vecInB = vldrwq_z_f32(pSrBVec, p0);  
    pSrBVec += MATRIX_DIM3;

    vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);
    vecMac1 = vfmaq(vecMac1, vecInB, *pInA1++);
    vecMac2 = vfmaq(vecMac2, vecInB, *pInA2++);
    /*
     * load {b2,0, b2,1 , b2,2, 0}
     */
    vecInB = vldrwq_z_f32(pSrBVec, p0);  
    pSrBVec += MATRIX_DIM3;

    vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);
    vecMac1 = vfmaq(vecMac1, vecInB, *pInA1++);
    vecMac2 = vfmaq(vecMac2, vecInB, *pInA2++);

    /* partial vector stores */
    vstrwq_p_f32(pOut, vecMac0, p0); 
    pOut += MATRIX_DIM3;
    vstrwq_p_f32(pOut, vecMac1, p0); 
    pOut += MATRIX_DIM3;
    vstrwq_p_f32(pOut, vecMac2, p0);
    /*
     * Return to application
     */
    return (ARM_MATH_SUCCESS);
}




__STATIC_INLINE arm_status arm_mat_mult_f32_4x4_mve(
    const arm_matrix_instance_f32 *pSrcA,
    const arm_matrix_instance_f32 *pSrcB,
    arm_matrix_instance_f32 *pDst)
{
    float32_t const *pSrBVec;
    float32_t *pInB = pSrcB->pData; /* input data matrix pointer B */
    float32_t *pInA = pSrcA->pData; /* input data matrix pointer A  */
    float32_t *pOut = pDst->pData;  /* output data matrix pointer */
    float32_t *pInA0, *pInA1, *pInA2, *pInA3;
    f32x4_t vecMac0, vecMac1, vecMac2, vecMac3;
    f32x4_t vecInB;

    pSrBVec = (float32_t const *) pInB;

    pInA0 = pInA;
    pInA1 = pInA0 + MATRIX_DIM4;
    pInA2 = pInA1 + MATRIX_DIM4;
    pInA3 = pInA2 + MATRIX_DIM4;
    /*
     * load {b0,0, b0,1, b0,2, b0,3}
     */
    vecInB = vld1q(pSrBVec);  
    pSrBVec += MATRIX_DIM4;

    vecMac0 = vmulq(vecInB, *pInA0++);
    vecMac1 = vmulq(vecInB, *pInA1++);
    vecMac2 = vmulq(vecInB, *pInA2++);
    vecMac3 = vmulq(vecInB, *pInA3++);
    /*
     * load {b1,0, b1,1, b1,2, b1,3}
     */
    vecInB = vld1q(pSrBVec);  
    pSrBVec += MATRIX_DIM4;

    vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);
    vecMac1 = vfmaq(vecMac1, vecInB, *pInA1++);
    vecMac2 = vfmaq(vecMac2, vecInB, *pInA2++);
    vecMac3 = vfmaq(vecMac3, vecInB, *pInA3++);
    /*
     * load {b2,0, b2,1, b2,2, b2,3}
     */
    vecInB = vld1q(pSrBVec);  
    pSrBVec += MATRIX_DIM4;

    vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);
    vecMac1 = vfmaq(vecMac1, vecInB, *pInA1++);
    vecMac2 = vfmaq(vecMac2, vecInB, *pInA2++);
    vecMac3 = vfmaq(vecMac3, vecInB, *pInA3++);
    /*
     * load {b3,0, b3,1, b3,2, b3,3}
     */
    vecInB = vld1q(pSrBVec);  
    pSrBVec += MATRIX_DIM4;

    vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);
    vecMac1 = vfmaq(vecMac1, vecInB, *pInA1++);
    vecMac2 = vfmaq(vecMac2, vecInB, *pInA2++);
    vecMac3 = vfmaq(vecMac3, vecInB, *pInA3++);

    vst1q(pOut, vecMac0);  
    pOut += MATRIX_DIM4;
    vst1q(pOut, vecMac1);  
    pOut += MATRIX_DIM4;
    vst1q(pOut, vecMac2);  
    pOut += MATRIX_DIM4;
    vst1q(pOut, vecMac3);
    /*
     * Return to application
     */
    return (ARM_MATH_SUCCESS);
}


/**
 * @brief Floating-point matrix multiplication.
 * @param[in]       *pSrcA points to the first input matrix structure
 * @param[in]       *pSrcB points to the second input matrix structure
 * @param[out]      *pDst points to output matrix structure
 * @return          The function returns either
 * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
 */
arm_status arm_mat_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst)
{
    float32_t  *pInB = pSrcB->pData;        /* input data matrix pointer B */
    float32_t  *pInA = pSrcA->pData;        /* input data matrix pointer A  */
    float32_t  *pOut = pDst->pData;         /* output data matrix pointer */
    int         numRowsA = pSrcA->numRows;  /* number of rows of input matrix A */
    int         numColsB = pSrcB->numCols;  /* number of columns of input matrix B */
    int         numColsA = pSrcA->numCols;  /* number of columns of input matrix A */
    uint32_t    blkCnt;                     /* loop counters */
    uint32_t    i;
    arm_status status; 

#ifdef ARM_MATH_MATRIX_CHECK

  /* Check for matrix mismatch condition */
  if ((pSrcA->numCols != pSrcB->numRows) ||
     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else
#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
  {
      /* small squared matrix specialized routines */
    if(numRowsA == numColsB && numColsB == numColsA) {
        if (numRowsA == 1)
        {
           pOut[0] = pInA[0] * pInB[0];
           return(ARM_MATH_SUCCESS);
        }
        else if(numRowsA == 2)
            return arm_mat_mult_f32_2x2_mve(pSrcA, pSrcB, pDst);
        else if(numRowsA == 3)
            return arm_mat_mult_f32_3x3_mve(pSrcA, pSrcB, pDst);
        else if(numRowsA == 4)
            return arm_mat_mult_f32_4x4_mve(pSrcA, pSrcB, pDst);
    }

    /* main loop process 4 rows */
    i = numRowsA >> 2;
    while (i > 0U)
    {
        float32_t *pInA0, *pInA1, *pInA2, *pInA3;
        float32_t *pInB0;
        float32_t *pOut0, *pOut1, *pOut2, *pOut3;
        f32x4_t vecMac0, vecMac1, vecMac2, vecMac3;
        f32x4_t vecInB;

        /* pointers to 4 consecutive output rows */
        pOut0 = pOut;
        pOut1 = pOut0 + numColsB;
        pOut2 = pOut1 + numColsB;
        pOut3 = pOut2 + numColsB;
        pInB0 = pInB;

        uint32_t  k = numColsB >> 2;
        while (k > 0U)
        {
            /* pointers to 4 consecutive Matrix A rows */
            pInA0 = pInA;
            pInA1 = pInA0 + numColsA;
            pInA2 = pInA1 + numColsA;
            pInA3 = pInA2 + numColsA;

            vecMac0 = vdupq_n_f32(0.0f);
            vecMac1 = vdupq_n_f32(0.0f);
            vecMac2 = vdupq_n_f32(0.0f);
            vecMac3 = vdupq_n_f32(0.0f);

            blkCnt = numColsA;

            while (blkCnt > 0U)
            {
                /*
                 * load {bi,4n+0, bi,4n+1, bi,4n+2, bi,4n+3}
                 */
                vecInB = *(f32x4_t *)pInB0; /* vldrwq_f32(pInB0, 0); */

                vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);
                vecMac1 = vfmaq(vecMac1, vecInB, *pInA1++);
                vecMac2 = vfmaq(vecMac2, vecInB, *pInA2++);
                vecMac3 = vfmaq(vecMac3, vecInB, *pInA3++);

                pInB0 = pInB0 + numColsB;
                /*
                 * Decrement the blockSize loop counter
                 */
                blkCnt--;
            }

            /* Store the results (4 x 4 block) in the destination buffer */
            vst1q(pOut0, vecMac0);  
            pOut0 += 4;
            vst1q(pOut1, vecMac1);  
            pOut1 += 4;
            vst1q(pOut2, vecMac2);  
            pOut2 += 4;
            vst1q(pOut3, vecMac3);  
            pOut3 += 4;

            /*
             * rewind
             */
            pInB0 -= (numColsB * numColsA) - 4;
            k--;
        }

        int       colBLeft = numColsB & 3;
        if (colBLeft)
        {
            pInA0 = pInA;
            pInA1 = pInA0 + numColsA;
            pInA2 = pInA1 + numColsA;
            pInA3 = pInA2 + numColsA;
            mve_pred16_t p0 = vctp32q(colBLeft);

            vecMac0 = vdupq_n_f32(0.0f);
            vecMac1 = vdupq_n_f32(0.0f);
            vecMac2 = vdupq_n_f32(0.0f);
            vecMac3 = vdupq_n_f32(0.0f);

            blkCnt = numColsA;

            while (blkCnt > 0U)
            {
                /*
                 * load {bi,4n+0, bi,4n+1, bi,4n+2, bi,4n+3}
                 */
                vecInB = vldrwq_z_f32(pInB0, p0);

                vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);
                vecMac1 = vfmaq(vecMac1, vecInB, *pInA1++);
                vecMac2 = vfmaq(vecMac2, vecInB, *pInA2++);
                vecMac3 = vfmaq(vecMac3, vecInB, *pInA3++);

                pInB0 = pInB0 + numColsB;
                /*
                 * Decrement the blockSize loop counter
                 */
                blkCnt--;
            }

            /* Store the results (4 x colBLeft block) in the destination buffer */
            vstrwq_p_f32(pOut0, vecMac0, p0);
            vstrwq_p_f32(pOut1, vecMac1, p0);
            vstrwq_p_f32(pOut2, vecMac2, p0);
            vstrwq_p_f32(pOut3, vecMac3, p0);
        }

        /* move to next rows */
        pInA += 4 * numColsA;
        pOut += 4 * numColsB;
        i--;
    }

    /*
     * non multiple of 4 rows for Matrix A
     * process single row
     */
    if (numRowsA & 3)
    {
        i = numRowsA & 3;
        while (i > 0U)
        {
            float32_t   *pInA0;
            float32_t   *pInB0;
            float32_t   *pOut0;
            f32x4_t    vecInB;
            f32x4_t    vecMac0;

            pOut0 = pOut;
            pInB0 = pInB;

            uint32_t       k = numColsB >> 2;
            while (k > 0U)
            {
                pInA0 = pInA;

                vecMac0 = vdupq_n_f32(0.0f);
                blkCnt = numColsA;
                while (blkCnt > 0U)
                {
                    /*
                     * load {bi,4n+0, bi,4n+1, bi,4n+2, bi,4n+3}
                     */
                    vecInB = *(f32x4_t *)pInB0; /* vldrwq_f32(pInB0, 0); */

                    vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);

                    pInB0 = pInB0 + numColsB;
                    /*
                     * Decrement the blockSize loop counter
                     */
                    blkCnt--;
                }

                /* Store the results (1 x 4 block) in the destination buffer */
                vst1q(pOut0, vecMac0);  
                pOut0 += 4;

                /*
                 * rewind
                 */
                pInB0 -= (numColsB * numColsA) - 4;
                k--;
            }

            int       colBLeft = numColsB & 3;
            if (colBLeft)
            {
                pInA0 = pInA;
                mve_pred16_t p0 = vctp32q(colBLeft);

                vecMac0 = vdupq_n_f32(0.0f);
                blkCnt = numColsA;
                while (blkCnt > 0U)
                {
                    /*
                     * load {bi,4n+0, bi,4n+1, bi,4n+2, bi,4n+3}
                     */
                    vecInB = vldrwq_z_f32(pInB0, p0);

                    vecMac0 = vfmaq(vecMac0, vecInB, *pInA0++);

                    pInB0 = pInB0 + numColsB;
                    /*
                     * Decrement the blockSize loop counter
                     */
                    blkCnt--;
                }
                /* Store the results (1 x colBLeft block) in the destination buffer */
                vstrwq_p_f32(pOut0, vecMac0, p0);
            }

            /* move to next row */
            pInA += 1 * numColsA;
            pOut += 1 * numColsB;
            i--;
        }
        
      }
      status = ARM_MATH_SUCCESS;
  }

  /* Return to application */
  return (status);
}
#else

#if defined(ARM_MATH_NEON)
/**
 * @brief Floating-point matrix multiplication.
 * @param[in]       *pSrcA points to the first input matrix structure
 * @param[in]       *pSrcB points to the second input matrix structure
 * @param[out]      *pDst points to output matrix structure
 * @return          The function returns either
 * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
 */
arm_status arm_mat_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst)
{
  float32_t *pIn1 = pSrcA->pData;                /* input data matrix pointer A */
  float32_t *pIn2 = pSrcB->pData;                /* input data matrix pointer B */
  float32_t *pInA = pSrcA->pData;                /* input data matrix pointer A  */
  float32_t *pOut = pDst->pData;                 /* output data matrix pointer */
  float32_t *px;                                 /* Temporary output data matrix pointer */
  float32_t sum;                                 /* Accumulator */
  uint16_t numRowsA = pSrcA->numRows;            /* number of rows of input matrix A */
  uint16_t numColsB = pSrcB->numCols;            /* number of columns of input matrix B */
  uint16_t numColsA = pSrcA->numCols;            /* number of columns of input matrix A */


  uint32_t col, i = 0U, j, row = numRowsA, rowCnt, colCnt;      /* loop counters */
  arm_status status;                             /* status of matrix multiplication */

  float32x4_t a0V, a1V, a2V, a3V, a4V, a5V, a6V, a7V;
  float32x4_t acc0,acc1,acc2,acc3,acc4,acc5,acc6,acc7,temp;
  float32x2_t accum = vdup_n_f32(0);
  float32_t *pIn1B = pSrcA->pData;    
  float32_t *pIn1C = pSrcA->pData;    
  float32_t *pIn1D = pSrcA->pData;  
  float32_t *pIn1E = pSrcA->pData; 
  float32_t *pIn1F = pSrcA->pData; 
  float32_t *pIn1G = pSrcA->pData; 
  float32_t *pIn1H = pSrcA->pData;   

  float32_t *pxB,*pxC, *pxD, *pxE, *pxF, *pxG, *pxH;                                 /* Temporary output data matrix pointer */
  float32_t sum0,sum1, sum2,sum3, sum4, sum5 , sum6, sum7;

#ifdef ARM_MATH_MATRIX_CHECK

  /* Check for matrix mismatch condition */
  if ((pSrcA->numCols != pSrcB->numRows) ||
     (pSrcA->numRows != pDst->numRows) || (pSrcB->numCols != pDst->numCols))
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else
#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
  {
    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
    /* Row loop */
    rowCnt = row >> 3;

    while(rowCnt > 0)
    {
      /* Output pointer is set to starting address of the row being processed */
      px = pOut + GROUPOFROWS*i;
      pxB = px + numColsB;
      pxC = px + 2*numColsB;
      pxD = px + 3*numColsB;
      pxE = px + 4*numColsB;
      pxF = px + 5*numColsB;
      pxG = px + 6*numColsB;
      pxH = px + 7*numColsB;

      /* For every row wise process, the column loop counter is to be initiated */
      col = numColsB;

      /* For every row wise process, the pIn2 pointer is set
       ** to the starting address of the pSrcB data */
      pIn2 = pSrcB->pData;

      j = 0U;

      /* Column loop */
      do
      {
        /* Set the variable sum, that acts as accumulator, to zero */
        sum0 = 0.0f;
        sum1 = 0.0f;
        sum2 = 0.0f;
        sum3 = 0.0f;
        sum4 = 0.0f;
        sum5 = 0.0f;
        sum6 = 0.0f;
        sum7 = 0.0f;

        /* Initiate the pointer pIn1 to point to the starting address of the column being processed */
        pIn1 = pInA;
        pIn1B = pIn1 + numColsA;
        pIn1C = pIn1 + 2*numColsA;
        pIn1D = pIn1 + 3*numColsA;
        pIn1E = pIn1 + 4*numColsA;
        pIn1F = pIn1 + 5*numColsA;
        pIn1G = pIn1 + 6*numColsA;
        pIn1H = pIn1 + 7*numColsA;

        acc0 = vdupq_n_f32(0.0);
        acc1 = vdupq_n_f32(0.0);
        acc2 = vdupq_n_f32(0.0);
        acc3 = vdupq_n_f32(0.0);
        acc4 = vdupq_n_f32(0.0);
        acc5 = vdupq_n_f32(0.0);
        acc6 = vdupq_n_f32(0.0);
        acc7 = vdupq_n_f32(0.0);

        /* Compute 4 MACs simultaneously. */
        colCnt = numColsA >> 2U;

        /* Matrix multiplication */
        while (colCnt > 0U)
        {
          /* c(m,n) = a(1,1)*b(1,1) + a(1,2)*b(2,1) + ... + a(m,p)*b(p,n) */
          a0V = vld1q_f32(pIn1);  
          a1V = vld1q_f32(pIn1B);  
          a2V = vld1q_f32(pIn1C); 
          a3V = vld1q_f32(pIn1D); 
          a4V = vld1q_f32(pIn1E); 
          a5V = vld1q_f32(pIn1F); 
          a6V = vld1q_f32(pIn1G); 
          a7V = vld1q_f32(pIn1H); 

	      pIn1 += 4;
          pIn1B += 4;
          pIn1C += 4;
          pIn1D += 4;
          pIn1E += 4;
          pIn1F += 4;
          pIn1G += 4;
          pIn1H += 4;
          
          temp = vsetq_lane_f32(*pIn2,temp,0);
          pIn2 += numColsB;
          temp = vsetq_lane_f32(*pIn2,temp,1);
          pIn2 += numColsB;
          temp = vsetq_lane_f32(*pIn2,temp,2);
          pIn2 += numColsB;
          temp = vsetq_lane_f32(*pIn2,temp,3);
          pIn2 += numColsB;

          acc0 = vmlaq_f32(acc0,a0V,temp);
          acc1 = vmlaq_f32(acc1,a1V,temp);
          acc2 = vmlaq_f32(acc2,a2V,temp);
          acc3 = vmlaq_f32(acc3,a3V,temp);
          acc4 = vmlaq_f32(acc4,a4V,temp);
          acc5 = vmlaq_f32(acc5,a5V,temp);
          acc6 = vmlaq_f32(acc6,a6V,temp);
          acc7 = vmlaq_f32(acc7,a7V,temp);

          /* Decrement the loop count */
          colCnt--;
        }

        accum = vpadd_f32(vget_low_f32(acc0), vget_high_f32(acc0));
        sum0 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        accum = vpadd_f32(vget_low_f32(acc1), vget_high_f32(acc1));
        sum1 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        accum = vpadd_f32(vget_low_f32(acc2), vget_high_f32(acc2));
        sum2 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        accum = vpadd_f32(vget_low_f32(acc3), vget_high_f32(acc3));
        sum3 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        accum = vpadd_f32(vget_low_f32(acc4), vget_high_f32(acc4));
        sum4 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        accum = vpadd_f32(vget_low_f32(acc5), vget_high_f32(acc5));
        sum5 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        accum = vpadd_f32(vget_low_f32(acc6), vget_high_f32(acc6));
        sum6 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        accum = vpadd_f32(vget_low_f32(acc7), vget_high_f32(acc7));
        sum7 += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        /* If the columns of pSrcA is not a multiple of 4, compute any remaining MACs here.
         ** No loop unrolling is used. */
        colCnt = numColsA & 3;

        while (colCnt > 0U)
        {
          /* c(m,n) = a(1,1)*b(1,1) + a(1,2)*b(2,1) + ... + a(m,p)*b(p,n) */
          sum0 += *pIn1++ * (*pIn2);
          sum1 += *pIn1B++ * (*pIn2);
          sum2 += *pIn1C++ * (*pIn2);
          sum3 += *pIn1D++ * (*pIn2);
          sum4 += *pIn1E++ * (*pIn2);
          sum5 += *pIn1F++ * (*pIn2);
          sum6 += *pIn1G++ * (*pIn2);
          sum7 += *pIn1H++ * (*pIn2);
          pIn2 += numColsB;

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

        /* Store the result in the destination buffer */
        *px++ = sum0;
        *pxB++ = sum1;
        *pxC++ = sum2;
        *pxD++ = sum3;
        *pxE++ = sum4;
        *pxF++ = sum5;
        *pxG++ = sum6;
        *pxH++ = sum7;

        /* Update the pointer pIn2 to point to the  starting address of the next column */
        j++;
        pIn2 = pSrcB->pData + j;

        /* Decrement the column loop counter */
        col--;

      } while (col > 0U);

      /* Update the pointer pInA to point to the  starting address of the next row */
      i = i + numColsB;
      pInA = pInA + GROUPOFROWS*numColsA;

      /* Decrement the row loop counter */
      rowCnt--;
    } 

    /*

    i was the index of a group of rows computed by previous loop.
    Now i is the index of a row since below code is computing row per row
    and no more group of row per group of rows.

    */

    i = GROUPOFROWS*i;
    rowCnt = row & 7;

    while(rowCnt > 0)
    {
      /* Output pointer is set to starting address of the row being processed */
      px = pOut + i;

      /* For every row wise process, the column loop counter is to be initiated */
      col = numColsB;

      /* For every row wise process, the pIn2 pointer is set
       ** to the starting address of the pSrcB data */
      pIn2 = pSrcB->pData;

      j = 0U;

      /* Column loop */
      do
      {
        /* Set the variable sum, that acts as accumulator, to zero */
        sum = 0.0f;

        /* Initiate the pointer pIn1 to point to the starting address of the column being processed */
        pIn1 = pInA;

        acc0 = vdupq_n_f32(0.0);

        /* Compute 4 MACs simultaneously. */
        colCnt = numColsA >> 2U;

        /* Matrix multiplication   */
        while (colCnt > 0U)
        {
          /* c(m,n) = a(1,1)*b(1,1) + a(1,2)*b(2,1) + ... + a(m,p)*b(p,n) */
          a0V = vld1q_f32(pIn1);  // load & separate real/imag pSrcA (de-interleave 2)
          pIn1 += 4;
          
          temp = vsetq_lane_f32(*pIn2,temp,0);
          pIn2 += numColsB;
          temp = vsetq_lane_f32(*pIn2,temp,1);
          pIn2 += numColsB;
          temp = vsetq_lane_f32(*pIn2,temp,2);
          pIn2 += numColsB;
          temp = vsetq_lane_f32(*pIn2,temp,3);
          pIn2 += numColsB;

          acc0 = vmlaq_f32(acc0,a0V,temp);

          /* Decrement the loop count */
          colCnt--;
        }

        accum = vpadd_f32(vget_low_f32(acc0), vget_high_f32(acc0));
        sum += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1);

        /* If the columns of pSrcA is not a multiple of 4, compute any remaining MACs here.
         ** No loop unrolling is used. */
        colCnt = numColsA % 0x4U;

        while (colCnt > 0U)
        {
          /* c(m,n) = a(1,1)*b(1,1) + a(1,2)*b(2,1) + ... + a(m,p)*b(p,n) */
          sum += *pIn1++ * (*pIn2);
          pIn2 += numColsB;

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

        /* Store the result in the destination buffer */
        *px++ = sum;

        /* Update the pointer pIn2 to point to the  starting address of the next column */
        j++;
        pIn2 = pSrcB->pData + j;

        /* Decrement the column loop counter */
        col--;

      } while (col > 0U);


      /* Update the pointer pInA to point to the  starting address of the next row */
      i = i + numColsB;
      pInA = pInA + numColsA;

      /* Decrement the row loop counter */
      rowCnt--;

    } 
    /* Set status as ARM_MATH_SUCCESS */
    status = ARM_MATH_SUCCESS;
  }

  /* Return to application */
  return (status);
}
#else
/**
 * @brief Floating-point matrix multiplication.
 * @param[in]       *pSrcA points to the first input matrix structure
 * @param[in]       *pSrcB points to the second input matrix structure
 * @param[out]      *pDst points to output matrix structure
 * @return          The function returns either
 * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
 */
arm_status arm_mat_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
        arm_matrix_instance_f32 * pDst)
{
  float32_t *pIn1 = pSrcA->pData;                /* Input data matrix pointer A */
  float32_t *pIn2 = pSrcB->pData;                /* Input data matrix pointer B */
  float32_t *pInA = pSrcA->pData;                /* Input data matrix pointer A */
  float32_t *pInB = pSrcB->pData;                /* Input data matrix pointer B */
  float32_t *pOut = pDst->pData;                 /* Output data matrix pointer */
  float32_t *px;                                 /* Temporary output data matrix pointer */
  float32_t sum;                                 /* Accumulator */
  uint16_t numRowsA = pSrcA->numRows;            /* Number of rows of input matrix A */
  uint16_t numColsB = pSrcB->numCols;            /* Number of columns of input matrix B */
  uint16_t numColsA = pSrcA->numCols;            /* Number of columns of input matrix A */
  uint32_t col, i = 0U, row = numRowsA, colCnt;  /* Loop counters */
  arm_status status;                             /* Status of matrix multiplication */

#ifdef ARM_MATH_MATRIX_CHECK

  /* Check for matrix mismatch condition */
  if ((pSrcA->numCols != pSrcB->numRows) ||
      (pSrcA->numRows != pDst->numRows)  ||
      (pSrcB->numCols != pDst->numCols)    )
  {
    /* Set status as ARM_MATH_SIZE_MISMATCH */
    status = ARM_MATH_SIZE_MISMATCH;
  }
  else

#endif /* #ifdef ARM_MATH_MATRIX_CHECK */

  {
    /* The following loop performs the dot-product of each row in pSrcA with each column in pSrcB */
    /* row loop */
    do
    {
      /* Output pointer is set to starting address of row being processed */
      px = pOut + i;

      /* For every row wise process, column loop counter is to be initiated */
      col = numColsB;

      /* For every row wise process, pIn2 pointer is set to starting address of pSrcB data */
      pIn2 = pSrcB->pData;

      /* column loop */
      do
      {
        /* Set the variable sum, that acts as accumulator, to zero */
        sum = 0.0f;

        /* Initialize pointer pIn1 to point to starting address of column being processed */
        pIn1 = pInA;

#if defined (ARM_MATH_LOOPUNROLL)

        /* Loop unrolling: Compute 4 MACs at a time. */
        colCnt = numColsA >> 2U;

        /* matrix multiplication */
        while (colCnt > 0U)
        {
          /* c(m,p) = a(m,1) * b(1,p) + a(m,2) * b(2,p) + .... + a(m,n) * b(n,p) */

          /* Perform the multiply-accumulates */
          sum += *pIn1++ * *pIn2;
          pIn2 += numColsB;

          sum += *pIn1++ * *pIn2;
          pIn2 += numColsB;

          sum += *pIn1++ * *pIn2;
          pIn2 += numColsB;

          sum += *pIn1++ * *pIn2;
          pIn2 += numColsB;

          /* Decrement loop counter */
          colCnt--;
        }

        /* Loop unrolling: Compute remaining MACs */
        colCnt = numColsA % 0x4U;

#else

        /* Initialize cntCnt with number of columns */
        colCnt = numColsA;

#endif /* #if defined (ARM_MATH_LOOPUNROLL) */

        while (colCnt > 0U)
        {
          /* c(m,p) = a(m,1) * b(1,p) + a(m,2) * b(2,p) + .... + a(m,n) * b(n,p) */

          /* Perform the multiply-accumulates */
          sum += *pIn1++ * *pIn2;
          pIn2 += numColsB;

          /* Decrement loop counter */
          colCnt--;
        }

        /* Store result in destination buffer */
        *px++ = sum;

        /* Decrement column loop counter */
        col--;

        /* Update pointer pIn2 to point to starting address of next column */
        pIn2 = pInB + (numColsB - col);

      } while (col > 0U);

      /* Update pointer pInA to point to starting address of next row */
      i = i + numColsB;
      pInA = pInA + numColsA;

      /* Decrement row loop counter */
      row--;

    } while (row > 0U);

    /* Set status as ARM_MATH_SUCCESS */
    status = ARM_MATH_SUCCESS;
  }

  /* Return to application */
  return (status);
}

#endif /* #if defined(ARM_MATH_NEON) */
#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */

/**
 * @} end of MatrixMult group
 */