# Square RootFast Math Functions

## Functions

CMSIS_INLINE __STATIC_INLINE
arm_status
arm_sqrt_f32 (float32_t in, float32_t *pOut)
Floating-point square root function.

arm_status arm_sqrt_q31 (q31_t in, q31_t *pOut)
Q31 square root function.

arm_status arm_sqrt_q15 (q15_t in, q15_t *pOut)
Q15 square root function.

## Description

Computes the square root of a number. There are separate functions for Q15, Q31, and floating-point data types. The square root function is computed using the Newton-Raphson algorithm. This is an iterative algorithm of the form:

```     x1 = x0 - f(x0)/f'(x0)
```

where `x1` is the current estimate, `x0` is the previous estimate, and `f'(x0)` is the derivative of `f()` evaluated at `x0`. For the square root function, the algorithm reduces to:

```    x0 = in/2                         [initial guess]
x1 = 1/2 * ( x0 + in / x0)        [each iteration]
```

## Function Documentation

 CMSIS_INLINE __STATIC_INLINE arm_status arm_sqrt_f32 ( float32_t `in, ` float32_t * `pOut ` )
Parameters
 [in] `in` input value. [out] `pOut` square root of input value.
Returns
The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if `in` is negative value and returns zero output for negative values.

References ARM_MATH_ARGUMENT_ERROR, and ARM_MATH_SUCCESS.

Referenced by arm_cmplx_mag_f32(), arm_rms_f32(), and arm_std_f32().

 arm_status arm_sqrt_q15 ( q15_t `in, ` q15_t * `pOut ` )
Parameters
 [in] `in` input value. The range of the input value is [0 +1) or 0x0000 to 0x7FFF. [out] `pOut` square root of input value.
Returns
The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if `in` is negative value and returns zero output for negative values.
Parameters
 [in] `in` input value. The range of the input value is [0 +1) or 0x0000 to 0x7FFF. [out] `*pOut` square root of input value.
Returns
The function returns ARM_MATH_SUCCESS if the input value is positive and ARM_MATH_ARGUMENT_ERROR if the input is negative. For negative inputs, the function returns *pOut = 0.

References ARM_MATH_ARGUMENT_ERROR, and ARM_MATH_SUCCESS.

Referenced by arm_cmplx_mag_q15(), arm_rms_q15(), and arm_std_q15().

 arm_status arm_sqrt_q31 ( q31_t `in, ` q31_t * `pOut ` )
Parameters
 [in] `in` input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF. [out] `pOut` square root of input value.
Returns
The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if `in` is negative value and returns zero output for negative values.
Parameters
 [in] `in` input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF. [out] `*pOut` square root of input value.
Returns
The function returns ARM_MATH_SUCCESS if the input value is positive and ARM_MATH_ARGUMENT_ERROR if the input is negative. For negative inputs, the function returns *pOut = 0.

References ARM_MATH_ARGUMENT_ERROR, and ARM_MATH_SUCCESS.

Referenced by arm_cmplx_mag_q31(), arm_rms_q31(), and arm_std_q31().