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  1. /* ----------------------------------------------------------------------    
  2. * Copyright (C) 2010-2014 ARM Limited. All rights reserved.  
  3. *    
  4. * $Date:        19. October 2015
  5. * $Revision:    V.1.4.5 a
  6. *    
  7. * Project:      CMSIS DSP Library  
  8. * Title:                arm_sqrt_q31.c    
  9. *    
  10. * Description:  Q31 square root function.    
  11. *    
  12. * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  13. *  
  14. * Redistribution and use in source and binary forms, with or without
  15. * modification, are permitted provided that the following conditions
  16. * are met:
  17. *   - Redistributions of source code must retain the above copyright
  18. *     notice, this list of conditions and the following disclaimer.
  19. *   - Redistributions in binary form must reproduce the above copyright
  20. *     notice, this list of conditions and the following disclaimer in
  21. *     the documentation and/or other materials provided with the
  22. *     distribution.
  23. *   - Neither the name of ARM LIMITED nor the names of its contributors
  24. *     may be used to endorse or promote products derived from this
  25. *     software without specific prior written permission.
  26. *
  27. * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  28. * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  29. * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  30. * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  31. * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  32. * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  33. * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  34. * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  35. * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  36. * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  37. * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  38. * POSSIBILITY OF SUCH DAMAGE.
  39. * -------------------------------------------------------------------- */
  40. #include "arm_math.h"
  41. #include "arm_common_tables.h"
  42.  
  43. /**    
  44.  * @ingroup groupFastMath    
  45.  */
  46.  
  47. /**    
  48.  * @addtogroup SQRT    
  49.  * @{    
  50.  */
  51.  
  52. /**    
  53.  * @brief Q31 square root function.    
  54.  * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.    
  55.  * @param[out]  *pOut square root of input value.    
  56.  * @return The function returns ARM_MATH_SUCCESS if the input value is positive
  57.  * and ARM_MATH_ARGUMENT_ERROR if the input is negative.  For
  58.  * negative inputs, the function returns *pOut = 0.
  59.  */
  60.  
  61. arm_status arm_sqrt_q31(
  62.   q31_t in,
  63.   q31_t * pOut)
  64. {
  65.   q31_t number, temp1, bits_val1, var1, signBits1, half;
  66.   float32_t temp_float1;
  67.   union
  68.   {
  69.       q31_t fracval;
  70.       float32_t floatval;
  71.   } tempconv;
  72.  
  73.   number = in;
  74.  
  75.   /* If the input is a positive number then compute the signBits. */
  76.   if(number > 0)
  77.   {
  78.     signBits1 = __CLZ(number) - 1;
  79.  
  80.     /* Shift by the number of signBits1 */
  81.     if((signBits1 % 2) == 0)
  82.     {
  83.       number = number << signBits1;
  84.     }
  85.     else
  86.     {
  87.       number = number << (signBits1 - 1);
  88.     }
  89.  
  90.     /* Calculate half value of the number */
  91.     half = number >> 1;
  92.     /* Store the number for later use */
  93.     temp1 = number;
  94.  
  95.     /*Convert to float */
  96.     temp_float1 = number * 4.6566128731e-010f;
  97.     /*Store as integer */
  98.     tempconv.floatval = temp_float1;
  99.     bits_val1 = tempconv.fracval;
  100.     /* Subtract the shifted value from the magic number to give intial guess */
  101.     bits_val1 = 0x5f3759df - (bits_val1 >> 1);  /* gives initial guess */
  102.     /* Store as float */
  103.     tempconv.fracval = bits_val1;
  104.     temp_float1 = tempconv.floatval;
  105.     /* Convert to integer format */
  106.     var1 = (q31_t) (temp_float1 * 1073741824);
  107.  
  108.     /* 1st iteration */
  109.     var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
  110.                                      ((q31_t)
  111.                                       ((((q31_t)
  112.                                          (((q63_t) var1 * var1) >> 31)) *
  113.                                         (q63_t) half) >> 31))) >> 31)) << 2;
  114.     /* 2nd iteration */
  115.     var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
  116.                                      ((q31_t)
  117.                                       ((((q31_t)
  118.                                          (((q63_t) var1 * var1) >> 31)) *
  119.                                         (q63_t) half) >> 31))) >> 31)) << 2;
  120.     /* 3rd iteration */
  121.     var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
  122.                                      ((q31_t)
  123.                                       ((((q31_t)
  124.                                          (((q63_t) var1 * var1) >> 31)) *
  125.                                         (q63_t) half) >> 31))) >> 31)) << 2;
  126.  
  127.     /* Multiply the inverse square root with the original value */
  128.     var1 = ((q31_t) (((q63_t) temp1 * var1) >> 31)) << 1;
  129.  
  130.     /* Shift the output down accordingly */
  131.     if((signBits1 % 2) == 0)
  132.     {
  133.       var1 = var1 >> (signBits1 / 2);
  134.     }
  135.     else
  136.     {
  137.       var1 = var1 >> ((signBits1 - 1) / 2);
  138.     }
  139.     *pOut = var1;
  140.  
  141.     return (ARM_MATH_SUCCESS);
  142.   }
  143.   /* If the number is a negative number then store zero as its square root value */
  144.   else
  145.   {
  146.     *pOut = 0;
  147.     return (ARM_MATH_ARGUMENT_ERROR);
  148.   }
  149. }
  150.  
  151. /**    
  152.  * @} end of SQRT group    
  153.  */
  154.