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/* ----------------------------------------------------------------------    
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* Copyright (C) 2010-2014 ARM Limited. All rights reserved.  
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*    
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* $Date:        19. March 2015
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* $Revision:    V.1.4.5
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*    
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* Project:      CMSIS DSP Library  
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* Title:                arm_sqrt_q31.c    
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*    
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* Description:  Q31 square root function.    
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*    
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*  
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*   - Redistributions of source code must retain the above copyright
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*     notice, this list of conditions and the following disclaimer.
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*   - Redistributions in binary form must reproduce the above copyright
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*     notice, this list of conditions and the following disclaimer in
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*     the documentation and/or other materials provided with the
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*     distribution.
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*   - Neither the name of ARM LIMITED nor the names of its contributors
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*     may be used to endorse or promote products derived from this
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*     software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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* -------------------------------------------------------------------- */
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#include "arm_math.h"
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#include "arm_common_tables.h"
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/**    
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 * @ingroup groupFastMath    
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 */
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/**    
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 * @addtogroup SQRT    
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 * @{    
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 */
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/**    
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 * @brief Q31 square root function.    
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 * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.    
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 * @param[out]  *pOut square root of input value.    
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 * @return The function returns ARM_MATH_SUCCESS if the input value is positive
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 * and ARM_MATH_ARGUMENT_ERROR if the input is negative.  For
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 * negative inputs, the function returns *pOut = 0.
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 */
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arm_status arm_sqrt_q31(
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  q31_t in,
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  q31_t * pOut)
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{
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  q31_t number, temp1, bits_val1, var1, signBits1, half;
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  float32_t temp_float1;
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  union
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  {
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      q31_t fracval;
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      float32_t floatval;
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  } tempconv;
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  number = in;
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  /* If the input is a positive number then compute the signBits. */
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  if(number > 0)
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  {
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    signBits1 = __CLZ(number) - 1;
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    /* Shift by the number of signBits1 */
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    if((signBits1 % 2) == 0)
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    {
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      number = number << signBits1;
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    }
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    else
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    {
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      number = number << (signBits1 - 1);
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    }
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    /* Calculate half value of the number */
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    half = number >> 1;
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    /* Store the number for later use */
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    temp1 = number;
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    /*Convert to float */
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    temp_float1 = number * 4.6566128731e-010f;
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    /*Store as integer */
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    tempconv.floatval = temp_float1;
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    bits_val1 = tempconv.fracval;
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    /* Subtract the shifted value from the magic number to give intial guess */
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    bits_val1 = 0x5f3759df - (bits_val1 >> 1);  // gives initial guess  
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    /* Store as float */
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    tempconv.fracval = bits_val1;
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    temp_float1 = tempconv.floatval;
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    /* Convert to integer format */
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    var1 = (q31_t) (temp_float1 * 1073741824);
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    /* 1st iteration */
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    var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
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                                     ((q31_t)
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                                      ((((q31_t)
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                                         (((q63_t) var1 * var1) >> 31)) *
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                                        (q63_t) half) >> 31))) >> 31)) << 2;
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    /* 2nd iteration */
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    var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
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                                     ((q31_t)
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                                      ((((q31_t)
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                                         (((q63_t) var1 * var1) >> 31)) *
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                                        (q63_t) half) >> 31))) >> 31)) << 2;
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    /* 3rd iteration */
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    var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
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                                     ((q31_t)
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                                      ((((q31_t)
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                                         (((q63_t) var1 * var1) >> 31)) *
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                                        (q63_t) half) >> 31))) >> 31)) << 2;
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    /* Multiply the inverse square root with the original value */
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    var1 = ((q31_t) (((q63_t) temp1 * var1) >> 31)) << 1;
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    /* Shift the output down accordingly */
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    if((signBits1 % 2) == 0)
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    {
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      var1 = var1 >> (signBits1 / 2);
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    }
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    else
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    {
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      var1 = var1 >> ((signBits1 - 1) / 2);
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    }
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    *pOut = var1;
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    return (ARM_MATH_SUCCESS);
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  }
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  /* If the number is a negative number then store zero as its square root value */
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  else
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  {
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    *pOut = 0;
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    return (ARM_MATH_ARGUMENT_ERROR);
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  }
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}
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/**    
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 * @} end of SQRT group    
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 */