Re: A92: Trig Lib
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Re: A92: Trig Lib
Anton Ivanov wrote:
> A full blown, fast and compact trig library can be developed on the
> basis of an
> algorithm that I devised, requring a table of values in the range of
> only [0, pi/2]
>
> Let sin(x) be the operation of "looking up" in a table of values
> Assume positive angles
> if theta > 2pi a=theta mod 2pi
> if theta < 2pi a = theta
> if 0 =< a =< pi/2 return sin(a)
> if pi/2 < a =< pi return sin(pi-a)
> if pi < a =< 3pi/2 return -sin(a-pi)
> if 3pi/2 < a =< 2pi return -sin(3pi/2-a)
>
> Thus only the interval [0, pi/2] is really needed.
> At an increment of .01, that is less than 160 entries.
> If every entry is one byte, and it is agreed that sin(pi/2)=.999, then
> the eight
> bits guarantee three-digit (decimal) accuracy (11100111 would
> correspond to .999).
> This precision is entirely adequate for any application that I can
> concieve of,
> especially given the resolution of LCD. The sign can be represented
> with a bit in
> the system register, or anywhere else.
> The following identities can then be taken advantage of:
> cos(x) = sin(pi/2 -x)
> sin(-x) = -sin(x)
>
> So, would anyone be intrested in writing such a lib? It's size can
> probably be kept
> under 300 bytes, and, if properly coded, it should be rather fast.
What would be with taking more digits, and therefore compress the data?
Therefore a Initialization routinie would be possible, for uncompressing
the data
to a temporary memory area. (I try this over the weekend...)
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