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/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_sqrt_q31.c
* Description: Q31 square root function
*
* $Date: 23 April 2021
* $Revision: V1.9.0
*
* Target Processor: Cortex-M and Cortex-A cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
*
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "dsp/fast_math_functions.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 points to square root of input value
@return execution status
- \ref ARM_MATH_SUCCESS : input value is positive
- \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
*/
#define Q28QUARTER 0x20000000
arm_status arm_sqrt_q31(
q31_t in,
q31_t * pOut)
{
q31_t number, var1, signBits1 ,temp;
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);
}
/* Start value for 1/sqrt(x) for the Newton iteration */
var1 = sqrt_initial_lut_q31[(number>> 26) - (Q28QUARTER >> 26)];
/* 0.5 var1 * (3 - number * var1 * var1) */
/* 1st iteration */
temp = ((q63_t) var1 * var1) >> 28;
temp = ((q63_t) number * temp) >> 31;
temp = 0x30000000 - temp;
var1 = ((q63_t) var1 * temp) >> 29;
/* 2nd iteration */
temp = ((q63_t) var1 * var1) >> 28;
temp = ((q63_t) number * temp) >> 31;
temp = 0x30000000 - temp;
var1 = ((q63_t) var1 * temp) >> 29;
/* 3nd iteration */
temp = ((q63_t) var1 * var1) >> 28;
temp = ((q63_t) number * temp) >> 31;
temp = 0x30000000 - temp;
var1 = ((q63_t) var1 * temp) >> 29;
/* Multiply the inverse square root with the original value */
var1 = ((q31_t) (((q63_t) number * var1) >> 28));
/* 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
*/
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