Speex dev - Aug 2007 - math_approx.c

The section that establishes the MIME type is stating audio/x-speex.
Per the MIME Types and File Extensions it should be audio/ogg.

If the change will be made, there's no need to put it as audio/x-ogg
as the IETF values MIME types already in use.

-Ivo

Hi,
I started to optimize math_approx fixed point functions to ARM CPU. And 
found out that approximations are not Taylor series, for example:
spx_exp2(x) = D0 + D1*x + D2*x^2 +D3*x^3,
where D0 = 1, D1 = log(2), D2 = (log(2))^2 / 2, D3 = (log(2))^3 / 6 for 
Taylor serie,
but Speex source code uses different coefficients:
D0 = 1, D1 = log(2), D2 = 3 - 4*log(2), D3 = 3*log(2) - 2

Can anyone explain the difference? Was it done to equalize error along 
range? How were obtained D2 and D3?
Thanks,
Oleg Homenko

Oleg Homenko a ?crit :
> Hi,
> I started to optimize math_approx fixed point functions to ARM CPU. And
> found out that approximations are not Taylor series, 
That's right.

for example:
> spx_exp2(x) = D0 + D1*x + D2*x^2 +D3*x^3,
> where D0 = 1, D1 = log(2), D2 = (log(2))^2 / 2, D3 = (log(2))^3 / 6 for
> Taylor serie,
> but Speex source code uses different coefficients:
> D0 = 1, D1 = log(2), D2 = 3 - 4*log(2), D3 = 3*log(2) - 2
> 
> Can anyone explain the difference? Was it done to equalize error along
> range? How were obtained D2 and D3?
It's actually a polynomial fit. That's better than Taylor series
because, as you say, the error is better distributed.

	Jean-Marc