1  /* ----------------------------------------------------------------------
  2   * Project:      CMSIS DSP Library
  3   * Title:        arm_sqrt_q15.c
  4   * Description:  Q15 square root function
  5   *
  6   * $Date:        23 April 2021
  7   * $Revision:    V1.9.0
  8   *
  9   * Target Processor: Cortex-M and Cortex-A cores
 10   * -------------------------------------------------------------------- */
 11  /*
 12   * Copyright (C) 2010-2021 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 "dsp/fast_math_functions.h"
 30  #include "arm_common_tables.h"
 31  
 32  /**
 33    @ingroup groupFastMath
 34   */
 35  
 36  /**
 37    @addtogroup SQRT
 38    @{
 39   */
 40  
 41  /**
 42    @brief         Q15 square root function.
 43    @param[in]     in    input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF
 44    @param[out]    pOut  points to square root of input value
 45    @return        execution status
 46                     - \ref ARM_MATH_SUCCESS        : input value is positive
 47                     - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
 48   */
 49  
 50  #define Q12QUARTER 0x2000
 51  arm_status arm_sqrt_q15(
 52    q15_t in,
 53    q15_t * pOut)
 54  {
 55    q15_t number, var1, signBits1,temp;
 56  
 57    number = in;
 58  
 59    /* If the input is a positive number then compute the signBits. */
 60    if (number > 0)
 61    {
 62      signBits1 = __CLZ(number) - 17;
 63  
 64      /* Shift by the number of signBits1 */
 65      if ((signBits1 % 2) == 0)
 66      {
 67        number = number << signBits1;
 68      }
 69      else
 70      {
 71        number = number << (signBits1 - 1);
 72      }
 73      /* Start value for 1/sqrt(x) for the Newton iteration */
 74      var1 = sqrt_initial_lut_q15[(number>> 11) - (Q12QUARTER >> 11)];
 75  
 76      /* 0.5 var1 * (3 - number * var1 * var1) */
 77      /* 1st iteration */
 78  
 79     temp = ((q31_t) var1 * var1) >> 12;
 80     temp = ((q31_t) number * temp) >> 15;
 81     temp = 0x3000 - temp; 
 82     var1 = ((q31_t) var1 * temp) >> 13;
 83  
 84     temp = ((q31_t) var1 * var1) >> 12;
 85     temp = ((q31_t) number * temp) >> 15;
 86     temp = 0x3000 - temp; 
 87     var1 = ((q31_t) var1 * temp) >> 13;
 88  
 89     temp = ((q31_t) var1 * var1) >> 12;
 90     temp = ((q31_t) number * temp) >> 15;
 91     temp = 0x3000 - temp; 
 92     var1 = ((q31_t) var1 * temp) >> 13;
 93  
 94      /* Multiply the inverse square root with the original value */
 95  
 96      var1 = ((q15_t) (((q31_t) number * var1) >> 12));
 97  
 98      /* Shift the output down accordingly */
 99      if ((signBits1 % 2) == 0)
100      {
101        var1 = var1 >> (signBits1 / 2);
102      }
103      else
104      {
105        var1 = var1 >> ((signBits1 - 1) / 2);
106      }
107      *pOut = var1;
108  
109  
110      return (ARM_MATH_SUCCESS);
111    }
112    /* If the number is a negative number then store zero as its square root value */
113    else
114    {
115      *pOut = 0;
116  
117      return (ARM_MATH_ARGUMENT_ERROR);
118    }
119  }
120  
121  /**
122    @} end of SQRT group
123   */