/EDVSBoardOS/MotionDriver/mllite/ml_math_func.c

/*

 $License:

    Copyright (C) 2011-2012 InvenSense Corporation, All Rights Reserved.

    See included License.txt for License information.

 $

 */



/*******************************************************************************

 *

 * $Id:$

 *

 ******************************************************************************/



/**

 *   @defgroup  ML_MATH_FUNC ml_math_func

 *   @brief     Motion Library - Math Functions

 *              Common math functions the Motion Library

 *

 *   @{

 *       @file ml_math_func.c

 *       @brief Math Functions.

 */



#include "mlmath.h"

#include "ml_math_func.h"

#include "mlinclude.h"

#include <string.h>



#ifdef EMPL

#define TABLE_SIZE (256)



/* TODO: If memory becomes a big issue, we can just store the data for a single

 * quadrant and transform the inputs and outputs of the lookup functions.

 */

const float sin_lookup[TABLE_SIZE] = {

    0.000000f, 0.024541f, 0.049068f, 0.073565f, 0.098017f, 0.122411f, 0.146730f, 0.170962f,

    0.195090f, 0.219101f, 0.242980f, 0.266713f, 0.290285f, 0.313682f, 0.336890f, 0.359895f,

    0.382683f, 0.405241f, 0.427555f, 0.449611f, 0.471397f, 0.492898f, 0.514103f, 0.534998f,

    0.555570f, 0.575808f, 0.595699f, 0.615232f, 0.634393f, 0.653173f, 0.671559f, 0.689541f,

    0.707107f, 0.724247f, 0.740951f, 0.757209f, 0.773010f, 0.788346f, 0.803208f, 0.817585f,

    0.831470f, 0.844854f, 0.857729f, 0.870087f, 0.881921f, 0.893224f, 0.903989f, 0.914210f,

    0.923880f, 0.932993f, 0.941544f, 0.949528f, 0.956940f, 0.963776f, 0.970031f, 0.975702f,

    0.980785f, 0.985278f, 0.989177f, 0.992480f, 0.995185f, 0.997290f, 0.998795f, 0.999699f,

    1.000000f, 0.999699f, 0.998795f, 0.997290f, 0.995185f, 0.992480f, 0.989177f, 0.985278f,

    0.980785f, 0.975702f, 0.970031f, 0.963776f, 0.956940f, 0.949528f, 0.941544f, 0.932993f,

    0.923880f, 0.914210f, 0.903989f, 0.893224f, 0.881921f, 0.870087f, 0.857729f, 0.844854f,

    0.831470f, 0.817585f, 0.803208f, 0.788346f, 0.773010f, 0.757209f, 0.740951f, 0.724247f,

    0.707107f, 0.689541f, 0.671559f, 0.653173f, 0.634393f, 0.615232f, 0.595699f, 0.575808f,

    0.555570f, 0.534998f, 0.514103f, 0.492898f, 0.471397f, 0.449611f, 0.427555f, 0.405241f,

    0.382683f, 0.359895f, 0.336890f, 0.313682f, 0.290285f, 0.266713f, 0.242980f, 0.219101f,

    0.195091f, 0.170962f, 0.146731f, 0.122411f, 0.098017f, 0.073565f, 0.049068f, 0.024541f,

    0.000000f, -0.024541f, -0.049067f, -0.073564f, -0.098017f, -0.122411f, -0.146730f, -0.170962f,

    -0.195090f, -0.219101f, -0.242980f, -0.266713f, -0.290284f, -0.313682f, -0.336890f, -0.359895f,

    -0.382683f, -0.405241f, -0.427555f, -0.449611f, -0.471397f, -0.492898f, -0.514103f, -0.534997f,

    -0.555570f, -0.575808f, -0.595699f, -0.615231f, -0.634393f, -0.653173f, -0.671559f, -0.689540f,

    -0.707107f, -0.724247f, -0.740951f, -0.757209f, -0.773010f, -0.788346f, -0.803207f, -0.817585f,

    -0.831469f, -0.844853f, -0.857729f, -0.870087f, -0.881921f, -0.893224f, -0.903989f, -0.914210f,

    -0.923880f, -0.932993f, -0.941544f, -0.949528f, -0.956940f, -0.963776f, -0.970031f, -0.975702f,

    -0.980785f, -0.985278f, -0.989176f, -0.992480f, -0.995185f, -0.997290f, -0.998795f, -0.999699f,

    -1.000000f, -0.999699f, -0.998795f, -0.997290f, -0.995185f, -0.992480f, -0.989177f, -0.985278f,

    -0.980785f, -0.975702f, -0.970031f, -0.963776f, -0.956940f, -0.949528f, -0.941544f, -0.932993f,

    -0.923880f, -0.914210f, -0.903989f, -0.893224f, -0.881921f, -0.870087f, -0.857729f, -0.844854f,

    -0.831470f, -0.817585f, -0.803208f, -0.788347f, -0.773011f, -0.757209f, -0.740951f, -0.724247f,

    -0.707107f, -0.689541f, -0.671559f, -0.653173f, -0.634394f, -0.615232f, -0.595699f, -0.575808f,

    -0.555570f, -0.534998f, -0.514103f, -0.492898f, -0.471397f, -0.449612f, -0.427555f, -0.405241f,

    -0.382684f, -0.359895f, -0.336890f, -0.313682f, -0.290285f, -0.266713f, -0.242981f, -0.219102f,

    -0.195091f, -0.170962f, -0.146731f, -0.122411f, -0.098017f, -0.073565f, -0.049068f, -0.024542f

};



float inv_sinf(float x)

{

    int index = (unsigned int)((x * (TABLE_SIZE>>1)) / 3.14159f) % TABLE_SIZE;

    return sin_lookup[index];

}



float inv_cosf(float x)

{

    int index = ((unsigned int)((x * (TABLE_SIZE>>1)) / 3.14159f) + (TABLE_SIZE>>2)) % TABLE_SIZE;

    return sin_lookup[index];

}

#endif



/** @internal

 * Does the cross product of compass by gravity, then converts that

 * to the world frame using the quaternion, then computes the angle that

 * is made.

 *

 * @param[in] compass Compass Vector (Body Frame), length 3

 * @param[in] grav Gravity Vector (Body Frame), length 3

 * @param[in] quat Quaternion, Length 4

 * @return Angle Cross Product makes after quaternion rotation.

 */

float inv_compass_angle(const long *compass, const long *grav, const long *quat)

{

    long cgcross[4], q1[4], q2[4], qi[4];

    float angW;



    // Compass cross Gravity

    cgcross[0] = 0L;

    cgcross[1] = inv_q30_mult(compass[1], grav[2]) - inv_q30_mult(compass[2], grav[1]);

    cgcross[2] = inv_q30_mult(compass[2], grav[0]) - inv_q30_mult(compass[0], grav[2]);

    cgcross[3] = inv_q30_mult(compass[0], grav[1]) - inv_q30_mult(compass[1], grav[0]);



    // Now convert cross product into world frame

    inv_q_mult(quat, cgcross, q1);

    inv_q_invert(quat, qi);

    inv_q_mult(q1, qi, q2);



    // Protect against atan2 of 0,0

    if ((q2[2] == 0L) && (q2[1] == 0L))

        return 0.f;



    // This is the unfiltered heading correction

    angW = -atan2f(inv_q30_to_float(q2[2]), inv_q30_to_float(q2[1]));

    return angW;

}



/**

 *  @brief  The gyro data magnitude squared :

 *          (1 degree per second)^2 = 2^6 = 2^GYRO_MAG_SQR_SHIFT.

 * @param[in] gyro Gyro data scaled with 1 dps = 2^16

 *  @return the computed magnitude squared output of the gyroscope.

 */

unsigned long inv_get_gyro_sum_of_sqr(const long *gyro)

{

    unsigned long gmag = 0;

    long temp;

    int kk;



    for (kk = 0; kk < 3; ++kk) {

        temp = gyro[kk] >> (16 - (GYRO_MAG_SQR_SHIFT / 2));

        gmag += temp * temp;

    }



    return gmag;

}



/** Performs a multiply and shift by 29. These are good functions to write in assembly on

 * with devices with small memory where you want to get rid of the long long which some

 * assemblers don't handle well

 * @param[in] a

 * @param[in] b

 * @return ((long long)a*b)>>29

*/

long inv_q29_mult(long a, long b)

{

#ifdef EMPL_NO_64BIT

    long result;

    result = (long)((float)a * b / (1L << 29));

    return result;

#else

    long long temp;

    long result;

    temp = (long long)a * b;

    result = (long)(temp >> 29);

    return result;

#endif

}



/** Performs a multiply and shift by 30. These are good functions to write in assembly on

 * with devices with small memory where you want to get rid of the long long which some

 * assemblers don't handle well

 * @param[in] a

 * @param[in] b

 * @return ((long long)a*b)>>30

*/

long inv_q30_mult(long a, long b)

{

#ifdef EMPL_NO_64BIT

    long result;

    result = (long)((float)a * b / (1L << 30));

    return result;

#else

    long long temp;

    long result;

    temp = (long long)a * b;

    result = (long)(temp >> 30);

    return result;

#endif

}



#ifndef EMPL_NO_64BIT

long inv_q30_div(long a, long b)

{

    long long temp;

    long result;

    temp = (((long long)a) << 30) / b;

    result = (long)temp;

    return result;

}

#endif



/** Performs a multiply and shift by shift. These are good functions to write

 * in assembly on with devices with small memory where you want to get rid of

 * the long long which some assemblers don't handle well

 * @param[in] a First multicand

 * @param[in] b Second multicand

 * @param[in] shift Shift amount after multiplying

 * @return ((long long)a*b)<<shift

*/

#ifndef EMPL_NO_64BIT

long inv_q_shift_mult(long a, long b, int shift)

{

    long result;

    result = (long)(((long long)a * b) >> shift);

    return result;

}

#endif



/** Performs a fixed point quaternion multiply.

* @param[in] q1 First Quaternion Multicand, length 4. 1.0 scaled

*            to 2^30

* @param[in] q2 Second Quaternion Multicand, length 4. 1.0 scaled

*            to 2^30

* @param[out] qProd Product after quaternion multiply. Length 4.

*             1.0 scaled to 2^30.

*/

void inv_q_mult(const long *q1, const long *q2, long *qProd)

{

    INVENSENSE_FUNC_START;

    qProd[0] = inv_q30_mult(q1[0], q2[0]) - inv_q30_mult(q1[1], q2[1]) -

               inv_q30_mult(q1[2], q2[2]) - inv_q30_mult(q1[3], q2[3]);



    qProd[1] = inv_q30_mult(q1[0], q2[1]) + inv_q30_mult(q1[1], q2[0]) +

               inv_q30_mult(q1[2], q2[3]) - inv_q30_mult(q1[3], q2[2]);



    qProd[2] = inv_q30_mult(q1[0], q2[2]) - inv_q30_mult(q1[1], q2[3]) +

               inv_q30_mult(q1[2], q2[0]) + inv_q30_mult(q1[3], q2[1]);



    qProd[3] = inv_q30_mult(q1[0], q2[3]) + inv_q30_mult(q1[1], q2[2]) -

               inv_q30_mult(q1[2], q2[1]) + inv_q30_mult(q1[3], q2[0]);

}



/** Performs a fixed point quaternion addition.

* @param[in] q1 First Quaternion term, length 4. 1.0 scaled

*            to 2^30

* @param[in] q2 Second Quaternion term, length 4. 1.0 scaled

*            to 2^30

* @param[out] qSum Sum after quaternion summation. Length 4.

*             1.0 scaled to 2^30.

*/

void inv_q_add(long *q1, long *q2, long *qSum)

{

    INVENSENSE_FUNC_START;

    qSum[0] = q1[0] + q2[0];

    qSum[1] = q1[1] + q2[1];

    qSum[2] = q1[2] + q2[2];

    qSum[3] = q1[3] + q2[3];

}



void inv_vector_normalize(long *vec, int length)

{

    INVENSENSE_FUNC_START;

    double normSF = 0;

    int ii;

    for (ii = 0; ii < length; ii++) {

        normSF +=

            inv_q30_to_double(vec[ii]) * inv_q30_to_double(vec[ii]);

    }

    if (normSF > 0) {

        normSF = 1 / sqrt(normSF);

        for (ii = 0; ii < length; ii++) {

            vec[ii] = (int)((double)vec[ii] * normSF);

        }

    } else {

        vec[0] = 1073741824L;

        for (ii = 1; ii < length; ii++) {

            vec[ii] = 0;

        }

    }

}



void inv_q_normalize(long *q)

{

    INVENSENSE_FUNC_START;

    inv_vector_normalize(q, 4);

}



void inv_q_invert(const long *q, long *qInverted)

{

    INVENSENSE_FUNC_START;

    qInverted[0] = q[0];

    qInverted[1] = -q[1];

    qInverted[2] = -q[2];

    qInverted[3] = -q[3];

}



double quaternion_to_rotation_angle(const long *quat) {

    double quat0 = (double )quat[0] / 1073741824;

    if (quat0 > 1.0f) {

        quat0 = 1.0;

    } else if (quat0 < -1.0f) {

        quat0 = -1.0;

    }



    return acos(quat0)*2*180/M_PI;

}



/** Rotates a 3-element vector by Rotation defined by Q

*/

void inv_q_rotate(const long *q, const long *in, long *out)

{

    long q_temp1[4], q_temp2[4];

    long in4[4], out4[4];



    // Fixme optimize

    in4[0] = 0;

    memcpy(&in4[1], in, 3 * sizeof(long));

    inv_q_mult(q, in4, q_temp1);

    inv_q_invert(q, q_temp2);

    inv_q_mult(q_temp1, q_temp2, out4);

    memcpy(out, &out4[1], 3 * sizeof(long));

}



void inv_q_multf(const float *q1, const float *q2, float *qProd)

{

    INVENSENSE_FUNC_START;

    qProd[0] =

        (q1[0] * q2[0] - q1[1] * q2[1] - q1[2] * q2[2] - q1[3] * q2[3]);

    qProd[1] =

        (q1[0] * q2[1] + q1[1] * q2[0] + q1[2] * q2[3] - q1[3] * q2[2]);

    qProd[2] =

        (q1[0] * q2[2] - q1[1] * q2[3] + q1[2] * q2[0] + q1[3] * q2[1]);

    qProd[3] =

        (q1[0] * q2[3] + q1[1] * q2[2] - q1[2] * q2[1] + q1[3] * q2[0]);

}



void inv_q_addf(const float *q1, const float *q2, float *qSum)

{

    INVENSENSE_FUNC_START;

    qSum[0] = q1[0] + q2[0];

    qSum[1] = q1[1] + q2[1];

    qSum[2] = q1[2] + q2[2];

    qSum[3] = q1[3] + q2[3];

}



void inv_q_normalizef(float *q)

{

    INVENSENSE_FUNC_START;

    float normSF = 0;

    float xHalf = 0;

    normSF = (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);

    if (normSF < 2) {

        xHalf = 0.5f * normSF;

        normSF = normSF * (1.5f - xHalf * normSF * normSF);

        normSF = normSF * (1.5f - xHalf * normSF * normSF);

        normSF = normSF * (1.5f - xHalf * normSF * normSF);

        normSF = normSF * (1.5f - xHalf * normSF * normSF);

        q[0] *= normSF;

        q[1] *= normSF;

        q[2] *= normSF;

        q[3] *= normSF;

    } else {

        q[0] = 1.0;

        q[1] = 0.0;

        q[2] = 0.0;

        q[3] = 0.0;

    }

    normSF = (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);

}



/** Performs a length 4 vector normalization with a square root.

* @param[in,out] q vector to normalize. Returns [1,0,0,0] is magnitude is zero.

*/

void inv_q_norm4(float *q)

{

    float mag;

    mag = sqrtf(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);

    if (mag) {

        q[0] /= mag;

        q[1] /= mag;

        q[2] /= mag;

        q[3] /= mag;

    } else {

        q[0] = 1.f;

        q[1] = 0.f;

        q[2] = 0.f;

        q[3] = 0.f;

    }

}



void inv_q_invertf(const float *q, float *qInverted)

{

    INVENSENSE_FUNC_START;

    qInverted[0] = q[0];

    qInverted[1] = -q[1];

    qInverted[2] = -q[2];

    qInverted[3] = -q[3];

}



/**

 * Converts a quaternion to a rotation matrix.

 * @param[in] quat 4-element quaternion in fixed point. One is 2^30.

 * @param[out] rot Rotation matrix in fixed point. One is 2^30. The

 *             First 3 elements of the rotation matrix, represent

 *             the first row of the matrix. Rotation matrix multiplied

 *             by a 3 element column vector transform a vector from Body

 *             to World.

 */

void inv_quaternion_to_rotation(const long *quat, long *rot)

{

    rot[0] =

        inv_q29_mult(quat[1], quat[1]) + inv_q29_mult(quat[0],

                quat[0]) -

        1073741824L;

    rot[1] =

        inv_q29_mult(quat[1], quat[2]) - inv_q29_mult(quat[3], quat[0]);

    rot[2] =

        inv_q29_mult(quat[1], quat[3]) + inv_q29_mult(quat[2], quat[0]);

    rot[3] =

        inv_q29_mult(quat[1], quat[2]) + inv_q29_mult(quat[3], quat[0]);

    rot[4] =

        inv_q29_mult(quat[2], quat[2]) + inv_q29_mult(quat[0],

                quat[0]) -

        1073741824L;

    rot[5] =

        inv_q29_mult(quat[2], quat[3]) - inv_q29_mult(quat[1], quat[0]);

    rot[6] =

        inv_q29_mult(quat[1], quat[3]) - inv_q29_mult(quat[2], quat[0]);

    rot[7] =

        inv_q29_mult(quat[2], quat[3]) + inv_q29_mult(quat[1], quat[0]);

    rot[8] =

        inv_q29_mult(quat[3], quat[3]) + inv_q29_mult(quat[0],

                quat[0]) -

        1073741824L;

}



/**

 * Converts a quaternion to a rotation vector. A rotation vector is

 * a method to represent a 4-element quaternion vector in 3-elements.

 * To get the quaternion from the 3-elements, The last 3-elements of

 * the quaternion will be the given rotation vector. The first element

 * of the quaternion will be the positive value that will be required

 * to make the magnitude of the quaternion 1.0 or 2^30 in fixed point units.

 * @param[in] quat 4-element quaternion in fixed point. One is 2^30.

 * @param[out] rot Rotation vector in fixed point. One is 2^30.

 */

void inv_quaternion_to_rotation_vector(const long *quat, long *rot)

{

    rot[0] = quat[1];

    rot[1] = quat[2];

    rot[2] = quat[3];



    if (quat[0] < 0.0) {

        rot[0] = -rot[0];

        rot[1] = -rot[1];

        rot[2] = -rot[2];

    }

}



/** Converts a 32-bit long to a big endian byte stream */

unsigned char *inv_int32_to_big8(long x, unsigned char *big8)

{

    big8[0] = (unsigned char)((x >> 24) & 0xff);

    big8[1] = (unsigned char)((x >> 16) & 0xff);

    big8[2] = (unsigned char)((x >> 8) & 0xff);

    big8[3] = (unsigned char)(x & 0xff);

    return big8;

}



/** Converts a big endian byte stream into a 32-bit long */

long inv_big8_to_int32(const unsigned char *big8)

{

    long x;

    x = ((long)big8[0] << 24) | ((long)big8[1] << 16) | ((long)big8[2] << 8)

        | ((long)big8[3]);

    return x;

}



/** Converts a big endian byte stream into a 16-bit integer (short) */

short inv_big8_to_int16(const unsigned char *big8)

{

    short x;

    x = ((short)big8[0] << 8) | ((short)big8[1]);

    return x;

}



/** Converts a little endian byte stream into a 16-bit integer (short) */

short inv_little8_to_int16(const unsigned char *little8)

{

    short x;

    x = ((short)little8[1] << 8) | ((short)little8[0]);

    return x;

}



/** Converts a 16-bit short to a big endian byte stream */

unsigned char *inv_int16_to_big8(short x, unsigned char *big8)

{

    big8[0] = (unsigned char)((x >> 8) & 0xff);

    big8[1] = (unsigned char)(x & 0xff);

    return big8;

}



void inv_matrix_det_inc(float *a, float *b, int *n, int x, int y)

{

    int k, l, i, j;

    for (i = 0, k = 0; i < *n; i++, k++) {

        for (j = 0, l = 0; j < *n; j++, l++) {

            if (i == x)

                i++;

            if (j == y)

                j++;

            *(b + 6 * k + l) = *(a + 6 * i + j);

        }

    }

    *n = *n - 1;

}



void inv_matrix_det_incd(double *a, double *b, int *n, int x, int y)

{

    int k, l, i, j;

    for (i = 0, k = 0; i < *n; i++, k++) {

        for (j = 0, l = 0; j < *n; j++, l++) {

            if (i == x)

                i++;

            if (j == y)

                j++;

            *(b + 6 * k + l) = *(a + 6 * i + j);

        }

    }

    *n = *n - 1;

}



float inv_matrix_det(float *p, int *n)

{

    float d[6][6], sum = 0;

    int i, j, m;

    m = *n;

    if (*n == 2)

        return (*p ** (p + 7) - *(p + 1) ** (p + 6));

    for (i = 0, j = 0; j < m; j++) {

        *n = m;

        inv_matrix_det_inc(p, &d[0][0], n, i, j);

        sum =

            sum + *(p + 6 * i + j) * SIGNM(i +

                                            j) *

            inv_matrix_det(&d[0][0], n);

    }



    return (sum);

}



double inv_matrix_detd(double *p, int *n)

{

    double d[6][6], sum = 0;

    int i, j, m;

    m = *n;

    if (*n == 2)

        return (*p ** (p + 7) - *(p + 1) ** (p + 6));

    for (i = 0, j = 0; j < m; j++) {

        *n = m;

        inv_matrix_det_incd(p, &d[0][0], n, i, j);

        sum =

            sum + *(p + 6 * i + j) * SIGNM(i +

                                            j) *

            inv_matrix_detd(&d[0][0], n);

    }



    return (sum);

}



/** Wraps angle from (-M_PI,M_PI]

 * @param[in] ang Angle in radians to wrap

 * @return Wrapped angle from (-M_PI,M_PI]

 */

float inv_wrap_angle(float ang)

{

    if (ang > M_PI)

        return ang - 2 * (float)M_PI;

    else if (ang <= -(float)M_PI)

        return ang + 2 * (float)M_PI;

    else

        return ang;

}



/** Finds the minimum angle difference ang1-ang2 such that difference

 * is between [-M_PI,M_PI]

 * @param[in] ang1

 * @param[in] ang2

 * @return angle difference ang1-ang2

 */

float inv_angle_diff(float ang1, float ang2)

{

    float d;

    ang1 = inv_wrap_angle(ang1);

    ang2 = inv_wrap_angle(ang2);

    d = ang1 - ang2;

    if (d > M_PI)

        d -= 2 * (float)M_PI;

    else if (d < -(float)M_PI)

        d += 2 * (float)M_PI;

    return d;

}



/** bernstein hash, derived from public domain source */

uint32_t inv_checksum(const unsigned char *str, int len)

{

    uint32_t hash = 5381;

    int i, c;



    for (i = 0; i < len; i++) {

        c = *(str + i);

        hash = ((hash << 5) + hash) + c;	/* hash * 33 + c */

    }



    return hash;

}



static unsigned short inv_row_2_scale(const signed char *row)

{

    unsigned short b;



    if (row[0] > 0)

        b = 0;

    else if (row[0] < 0)

        b = 4;

    else if (row[1] > 0)

        b = 1;

    else if (row[1] < 0)

        b = 5;

    else if (row[2] > 0)

        b = 2;

    else if (row[2] < 0)

        b = 6;

    else

        b = 7;		// error

    return b;

}





/** Converts an orientation matrix made up of 0,+1,and -1 to a scalar representation.

* @param[in] mtx Orientation matrix to convert to a scalar.

* @return Description of orientation matrix. The lowest 2 bits (0 and 1) represent the column the one is on for the

* first row, with the bit number 2 being the sign. The next 2 bits (3 and 4) represent

* the column the one is on for the second row with bit number 5 being the sign.

* The next 2 bits (6 and 7) represent the column the one is on for the third row with

* bit number 8 being the sign. In binary the identity matrix would therefor be:

* 010_001_000 or 0x88 in hex.

*/

unsigned short inv_orientation_matrix_to_scalar(const signed char *mtx)

{



    unsigned short scalar;



    /*

       XYZ  010_001_000 Identity Matrix

       XZY  001_010_000

       YXZ  010_000_001

       YZX  000_010_001

       ZXY  001_000_010

       ZYX  000_001_010

     */



    scalar = inv_row_2_scale(mtx);

    scalar |= inv_row_2_scale(mtx + 3) << 3;

    scalar |= inv_row_2_scale(mtx + 6) << 6;





    return scalar;

}



/** Uses the scalar orientation value to convert from chip frame to body frame

* @param[in] orientation A scalar that represent how to go from chip to body frame

* @param[in] input Input vector, length 3

* @param[out] output Output vector, length 3

*/

void inv_convert_to_body(unsigned short orientation, const long *input, long *output)

{

    output[0] = input[orientation      & 0x03] * SIGNSET(orientation & 0x004);

    output[1] = input[(orientation>>3) & 0x03] * SIGNSET(orientation & 0x020);

    output[2] = input[(orientation>>6) & 0x03] * SIGNSET(orientation & 0x100);

}



/** Uses the scalar orientation value to convert from body frame to chip frame

* @param[in] orientation A scalar that represent how to go from chip to body frame

* @param[in] input Input vector, length 3

* @param[out] output Output vector, length 3

*/

void inv_convert_to_chip(unsigned short orientation, const long *input, long *output)

{

    output[orientation & 0x03]      = input[0] * SIGNSET(orientation & 0x004);

    output[(orientation>>3) & 0x03] = input[1] * SIGNSET(orientation & 0x020);

    output[(orientation>>6) & 0x03] = input[2] * SIGNSET(orientation & 0x100);

}





/** Uses the scalar orientation value to convert from chip frame to body frame and

* apply appropriate scaling.

* @param[in] orientation A scalar that represent how to go from chip to body frame

* @param[in] sensitivity Sensitivity scale

* @param[in] input Input vector, length 3

* @param[out] output Output vector, length 3

*/

void inv_convert_to_body_with_scale(unsigned short orientation, long sensitivity, const long *input, long *output)

{

    output[0] = inv_q30_mult(input[orientation & 0x03] *

                             SIGNSET(orientation & 0x004), sensitivity);

    output[1] = inv_q30_mult(input[(orientation>>3) & 0x03] *

                             SIGNSET(orientation & 0x020), sensitivity);

    output[2] = inv_q30_mult(input[(orientation>>6) & 0x03] *

                             SIGNSET(orientation & 0x100), sensitivity);

}



/** find a norm for a vector

* @param[in] a vector [3x1]

* @param[out] output the norm of the input vector

*/

double inv_vector_norm(const float *x)

{

    return sqrt(x[0]*x[0]+x[1]*x[1]+x[2]*x[2]);

}



void inv_init_biquad_filter(inv_biquad_filter_t *pFilter, float *pBiquadCoeff) {

    int i;

    // initial state to zero

    pFilter->state[0] = 0;

    pFilter->state[1] = 0;



    // set up coefficients

    for (i=0; i<5; i++) {

        pFilter->c[i] = pBiquadCoeff[i];

    }

}



void inv_calc_state_to_match_output(inv_biquad_filter_t *pFilter, float input)

{

    pFilter->input = input;

    pFilter->output = input;

    pFilter->state[0] = input / (1 + pFilter->c[2] + pFilter->c[3]);

    pFilter->state[1] = pFilter->state[0];

}



float inv_biquad_filter_process(inv_biquad_filter_t *pFilter, float input)  {

    float stateZero;



    pFilter->input = input;

    // calculate the new state;

    stateZero = pFilter->input - pFilter->c[2]*pFilter->state[0]

                               - pFilter->c[3]*pFilter->state[1];



    pFilter->output = stateZero + pFilter->c[0]*pFilter->state[0]

                                + pFilter->c[1]*pFilter->state[1];



    // update the output and state

    pFilter->output = pFilter->output * pFilter->c[4];

    pFilter->state[1] = pFilter->state[0];

    pFilter->state[0] = stateZero;

    return pFilter->output;

}



void inv_get_cross_product_vec(float *cgcross, float compass[3], float grav[3])  {



    cgcross[0] = (float)compass[1] * grav[2] - (float)compass[2] * grav[1];

    cgcross[1] = (float)compass[2] * grav[0] - (float)compass[0] * grav[2];

    cgcross[2] = (float)compass[0] * grav[1] - (float)compass[1] * grav[0];

}



void mlMatrixVectorMult(long matrix[9], const long vecIn[3], long *vecOut)  {

        // matrix format

        //  [ 0  3  6;

        //    1  4  7;

        //    2  5  8]



        // vector format:  [0  1  2]^T;

        int i, j;

        long temp;



        for (i=0; i<3; i++)	{

                temp = 0;

                for (j=0; j<3; j++)  {

                        temp += inv_q30_mult(matrix[i+j*3], vecIn[j]);

                }

                vecOut[i] = temp;

        }

}





/**

 * @}

 */