# Quick & Dirty Sine¶

• Author or source: MisterToast
• Type: Sine Wave Synthesis
• Created: 2007-01-08 10:50:10
notes
```This is proof of concept only (but code works--I have it in my synth now).

Note that x must come in as 0<x<=4096. If you want to scale it to something else (like
0<x<=2*M_PI), do it in the call. Or do the math to scale the constants properly.

There's not much noise in here. A few little peaks here and there. When the signal is at
-20dB, the worst noise is at around -90dB.

For speed, you can go all floats without much difference. You can get rid of that unitary
negate pretty easily, as well. A couple other tricks can speed it up further--I went for
clarity in the code.

The result comes out a bit shy of the range -1<x<1. That is, the peak is something like
0.999.

Where did this come from? I'm experimenting with getting rid of my waveform tables, which
require huge amounts of memory. Once I had the Hamming anti-ringing code in, it looked
like all my waveforms were smooth enough to approximate with curves. So I started with
sine. Pulled my table data into Excel and then threw the data into a curve-fitting
application.

This would be fine for a synth. The noise is low enough that you could easily get away
with it. Ideal for a low-memory situation. My final code will be a bit harder to
understand, as I'll break the curve up and curve-fit smaller sections.
```
code
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```float xSin(double x) { //x is scaled 0<=x<4096 const double A=-0.015959964859; const double B=217.68468676; const double C=0.000028716332164; const double D=-0.0030591066066; const double E=-7.3316892871734489e-005; double y; bool negate=false; if (x>2048) { negate=true; x-=2048; } if (x>1024) x=2048-x; if (negate) y=-((A+x)/(B+C*x*x)+D*x-E); else y=(A+x)/(B+C*x*x)+D*x-E; return (float)y; } ```

```Improved version:

float xSin(double x)
{
//x is scaled 0<=x<4096
const double A=-0.40319426317E-08;
const double B=0.21683205691E+03;
const double C=0.28463350538E-04;
const double D=-0.30774648337E-02;
double y;

bool negate=false;
if (x>2048)
{
negate=true;
x-=2048;
}
if (x>1024)
x=2048-x;
y=(A+x)/(B+C*x*x)+D*x;
if (negate)
return (float)(-y);
else
return (float)y;
}
```
```%This is Matlab code. you can convert it to C
%All it take to make a high quality sine
%wave is 1 multiply and one subtract.
%You first have to initialize the 2 unit delays
% and the coefficient

Fs = 48000;      %Sample rate
oscfreq = 1000.0; %Oscillator frequency in Hz
c1 = 2 * cos(2 * pi * oscfreq / Fs);
%Initialize the unit delays
d1 = sin(2 * pi * oscfreq / Fs);
d2 = 0;
%Initialization done here is the oscillator loop
% which generates a sinewave
for j=1:100
output = d1;        %This is the sine value
fprintf(1, '%f\n', output);
%one multiply and one subtract is all it takes
d0 = d1 * c1 - d2;
d2 = d1;   %Shift the unit delays
d1 = d0;
end
```
```Hi,

Can I use this code in a GPL2 or GPL3 licensed program (a soft synth project called Snarl)? In other words, will you grant permission for me to re-license your code? And what name should I write down as copyright holder in the headers?

Thanks,
Juuso Alasuutari
```
```Juuso,

Absolutely!

Toast
```