/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 16/10/14 6:01p $Revision:  V.1.4.5 a
*
* Project:      CMSIS DSP Library
* Title:        arm_sqrt_q31.c
*
* Description:  Q31 square root function.
*
* 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
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */
#include "arm_math.h"
#include "arm_common_tables.h"

/**
 * @ingroup groupFastMath
 */

/**
 * @addtogroup SQRT
 * @{
 */

/**
 * @brief Q31 square root function.
 * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
 * @param[out]  *pOut square root of input value.
 * @return The function returns ARM_MATH_SUCCESS if the input value is positive
 * and ARM_MATH_ARGUMENT_ERROR if the input is negative.  For
 * negative inputs, the function returns *pOut = 0.
 */

arm_status arm_sqrt_q31(
    q31_t in,
    q31_t * pOut)
{
    q31_t number, temp1, bits_val1, var1, signBits1, half;
    float32_t temp_float1;
    union
    {
        q31_t fracval;
        float32_t floatval;
    } tempconv;

    number = in;

    /* If the input is a positive number then compute the signBits. */
    if(number > 0)
    {
        signBits1 = __CLZ(number) - 1;

        /* Shift by the number of signBits1 */
        if((signBits1 % 2) == 0)
        {
            number = number << signBits1;
        }
        else
        {
            number = number << (signBits1 - 1);
        }

        /* Calculate half value of the number */
        half = number >> 1;
        /* Store the number for later use */
        temp1 = number;

        /*Convert to float */
        temp_float1 = number * 4.6566128731e-010f;
        /*Store as integer */
        tempconv.floatval = temp_float1;
        bits_val1 = tempconv.fracval;
        /* Subtract the shifted value from the magic number to give intial guess */
        bits_val1 = 0x5f3759df - (bits_val1 >> 1);  /* gives initial guess */
        /* Store as float */
        tempconv.fracval = bits_val1;
        temp_float1 = tempconv.floatval;
        /* Convert to integer format */
        var1 = (q31_t)(temp_float1 * 1073741824);

        /* 1st iteration */
        var1 = ((q31_t)((q63_t) var1 * (0x30000000 -
                                        ((q31_t)
                                         ((((q31_t)
                                            (((q63_t) var1 * var1) >> 31)) *
                                           (q63_t) half) >> 31))) >> 31)) << 2;
        /* 2nd iteration */
        var1 = ((q31_t)((q63_t) var1 * (0x30000000 -
                                        ((q31_t)
                                         ((((q31_t)
                                            (((q63_t) var1 * var1) >> 31)) *
                                           (q63_t) half) >> 31))) >> 31)) << 2;
        /* 3rd iteration */
        var1 = ((q31_t)((q63_t) var1 * (0x30000000 -
                                        ((q31_t)
                                         ((((q31_t)
                                            (((q63_t) var1 * var1) >> 31)) *
                                           (q63_t) half) >> 31))) >> 31)) << 2;

        /* Multiply the inverse square root with the original value */
        var1 = ((q31_t)(((q63_t) temp1 * var1) >> 31)) << 1;

        /* Shift the output down accordingly */
        if((signBits1 % 2) == 0)
        {
            var1 = var1 >> (signBits1 / 2);
        }
        else
        {
            var1 = var1 >> ((signBits1 - 1) / 2);
        }
        *pOut = var1;

        return (ARM_MATH_SUCCESS);
    }
    /* If the number is a negative number then store zero as its square root value */
    else
    {
        *pOut = 0;
        return (ARM_MATH_ARGUMENT_ERROR);
    }
}

/**
 * @} end of SQRT group
 */
