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  1. /* ----------------------------------------------------------------------
  2.  * Project:      CMSIS DSP Library
  3.  * Title:        arm_sqrt_q31.c
  4.  * Description:  Q31 square root function
  5.  *
  6.  * $Date:        27. January 2017
  7.  * $Revision:    V.1.5.1
  8.  *
  9.  * Target Processor: Cortex-M cores
  10.  * -------------------------------------------------------------------- */
  11. /*
  12.  * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
  13.  *
  14.  * SPDX-License-Identifier: Apache-2.0
  15.  *
  16.  * Licensed under the Apache License, Version 2.0 (the License); you may
  17.  * not use this file except in compliance with the License.
  18.  * You may obtain a copy of the License at
  19.  *
  20.  * www.apache.org/licenses/LICENSE-2.0
  21.  *
  22.  * Unless required by applicable law or agreed to in writing, software
  23.  * distributed under the License is distributed on an AS IS BASIS, WITHOUT
  24.  * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  25.  * See the License for the specific language governing permissions and
  26.  * limitations under the License.
  27.  */
  28.  
  29. #include "arm_math.h"
  30. #include "arm_common_tables.h"
  31.  
  32. /**
  33.  * @ingroup groupFastMath
  34.  */
  35.  
  36. /**
  37.  * @addtogroup SQRT
  38.  * @{
  39.  */
  40.  
  41. /**
  42.  * @brief Q31 square root function.
  43.  * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
  44.  * @param[out]  *pOut square root of input value.
  45.  * @return The function returns ARM_MATH_SUCCESS if the input value is positive
  46.  * and ARM_MATH_ARGUMENT_ERROR if the input is negative.  For
  47.  * negative inputs, the function returns *pOut = 0.
  48.  */
  49.  
  50. arm_status arm_sqrt_q31(
  51.   q31_t in,
  52.   q31_t * pOut)
  53. {
  54.   q31_t number, temp1, bits_val1, var1, signBits1, half;
  55.   float32_t temp_float1;
  56.   union
  57.   {
  58.       q31_t fracval;
  59.       float32_t floatval;
  60.   } tempconv;
  61.  
  62.   number = in;
  63.  
  64.   /* If the input is a positive number then compute the signBits. */
  65.   if (number > 0)
  66.   {
  67.     signBits1 = __CLZ(number) - 1;
  68.  
  69.     /* Shift by the number of signBits1 */
  70.     if ((signBits1 % 2) == 0)
  71.     {
  72.       number = number << signBits1;
  73.     }
  74.     else
  75.     {
  76.       number = number << (signBits1 - 1);
  77.     }
  78.  
  79.     /* Calculate half value of the number */
  80.     half = number >> 1;
  81.     /* Store the number for later use */
  82.     temp1 = number;
  83.  
  84.     /*Convert to float */
  85.     temp_float1 = number * 4.6566128731e-010f;
  86.     /*Store as integer */
  87.     tempconv.floatval = temp_float1;
  88.     bits_val1 = tempconv.fracval;
  89.     /* Subtract the shifted value from the magic number to give intial guess */
  90.     bits_val1 = 0x5f3759df - (bits_val1 >> 1);  /* gives initial guess */
  91.     /* Store as float */
  92.     tempconv.fracval = bits_val1;
  93.     temp_float1 = tempconv.floatval;
  94.     /* Convert to integer format */
  95.     var1 = (q31_t) (temp_float1 * 1073741824);
  96.  
  97.     /* 1st iteration */
  98.     var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
  99.                                      ((q31_t)
  100.                                       ((((q31_t)
  101.                                          (((q63_t) var1 * var1) >> 31)) *
  102.                                         (q63_t) half) >> 31))) >> 31)) << 2;
  103.     /* 2nd iteration */
  104.     var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
  105.                                      ((q31_t)
  106.                                       ((((q31_t)
  107.                                          (((q63_t) var1 * var1) >> 31)) *
  108.                                         (q63_t) half) >> 31))) >> 31)) << 2;
  109.     /* 3rd iteration */
  110.     var1 = ((q31_t) ((q63_t) var1 * (0x30000000 -
  111.                                      ((q31_t)
  112.                                       ((((q31_t)
  113.                                          (((q63_t) var1 * var1) >> 31)) *
  114.                                         (q63_t) half) >> 31))) >> 31)) << 2;
  115.  
  116.     /* Multiply the inverse square root with the original value */
  117.     var1 = ((q31_t) (((q63_t) temp1 * var1) >> 31)) << 1;
  118.  
  119.     /* Shift the output down accordingly */
  120.     if ((signBits1 % 2) == 0)
  121.     {
  122.       var1 = var1 >> (signBits1 / 2);
  123.     }
  124.     else
  125.     {
  126.       var1 = var1 >> ((signBits1 - 1) / 2);
  127.     }
  128.     *pOut = var1;
  129.  
  130.     return (ARM_MATH_SUCCESS);
  131.   }
  132.   /* If the number is a negative number then store zero as its square root value */
  133.   else
  134.   {
  135.     *pOut = 0;
  136.     return (ARM_MATH_ARGUMENT_ERROR);
  137.   }
  138. }
  139.  
  140. /**
  141.  * @} end of SQRT group
  142.  */
  143.