# SineFast Math Functions

## Functions

float32_t arm_sin_f32 (float32_t x)
Fast approximation to the trigonometric sine function for floating-point data.

q15_t arm_sin_q15 (q15_t x)
Fast approximation to the trigonometric sine function for Q15 data.

q31_t arm_sin_q31 (q31_t x)
Fast approximation to the trigonometric sine function for Q31 data.

## Description

Computes the trigonometric sine function using a combination of table lookup and linear interpolation. There are separate functions for Q15, Q31, and floating-point data types. The input to the floating-point version is in radians and in the range [0 2*pi) while the fixed-point Q15 and Q31 have a scaled input with the range [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a value of 2*pi wraps around to 0.

The implementation is based on table lookup using 256 values together with linear interpolation. The steps used are:

1. Calculation of the nearest integer table index
2. Compute the fractional portion (fract) of the table index.
3. The final result equals `(1.0f-fract)*a + fract*b;`

where

```   b=Table[index+0];
c=Table[index+1];
```

## Function Documentation

 float32_t arm_sin_f32 ( float32_t `x` )
Parameters
 [in] `x` input value in radians.
Returns
sin(x).

References FAST_MATH_TABLE_SIZE, and sinTable_f32.

Referenced by main().

 q15_t arm_sin_q15 ( q15_t `x` )
Parameters
 [in] `x` Scaled input value in radians.
Returns
sin(x).

The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi).

References FAST_MATH_Q15_SHIFT, and sinTable_q15.

 q31_t arm_sin_q31 ( q31_t `x` )
Parameters
 [in] `x` Scaled input value in radians.
Returns
sin(x).

The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi).

References FAST_MATH_Q31_SHIFT, and sinTable_q31.