John wrote: > I couldn't say which is 'better' out of Taylor series or > Chebyshev > polynomials, although the authors of Spectrum BASIC tended > to go for > small code size rather than ultimate speed in order to fit > a BASIC > interpreter into 16k.
The Chebyshev polynomials will spread the error more evenly than a Taylor series. (Technically, if expanded around x = 0 it's a Maclaurin series; a Taylor series can be expanded around any value of x.) Before the Spectrum existed, I played around with an early Sinclair scientific calculator. Mathematically, sin(x)/x --> 1 as x --> 0 but on this calculator sin(x)/x blew up for small values of x! This wouldn't have happened with a Maclaurin series approximation. David
