Sine
[Fast Math Functions]

Computes the trigonometric sine function using a combination of table lookup and cubic interpolation. More...

Detailed Description

Computes the trigonometric sine function using a combination of table lookup and cubic interpolation.

There are separate functions for Q15, Q31, and floating-point data types. The input to the floating-point version is in radians 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 cubic interpolation. The steps used are:

1. Calculation of the nearest integer table index
2. Fetch the four table values a, b, c, and d
3. Compute the fractional portion (fract) of the table index.
4. Calculation of wa, wb, wc, wd
5. The final result equals a*wa + b*wb + c*wc + d*wd

where

    
    a=Table[index-1];    
    b=Table[index+0];    
    c=Table[index+1];    
    d=Table[index+2];    
 

and

    
    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;    
    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;    
    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;    
    wd=(1/6)*fract.^3 - (1/6)*fract;    
 

Function Documentation