Re: Taylor series FSIN, FCOS, FTAN

In article
<ab4909ea-1f40-4f3d-92b3-0fab3aad2038@[EMAIL PROTECTED]
>,
The Beez' <hansoft@[EMAIL PROTECTED]
> wrote:
>On Apr 27, 12:30 pm, Albert van der Horst <alb...@[EMAIL PROTECTED]
>
>wrote:
>> For large values you should do range reduction. It amount to
>> subtraction multiples of 2*pi and such. At least try to land
>> in the [-PI, PI] interval.
>> It is wise to at least take that from the sources I supplied. This
>> greatly affects precision. If you omit range reduction, with your
>> Taylor series, it still works in principle.
>> For Chebychev it breaks down.
>
>: REDUCE.2PI                   \ x
>        PI*2                    \ x pi2
>        FOVER FOVER F/          \ x pi2 x/pi2
>        FLOOR                   \ x pi2 i(x/pi2)
>        FOVER F*                \ x pi2 mod(x,pi2)
>        FROT                    \ PI2 MOD(X,PI2) X
>        FSWAP F-                \ PI2 MOD(X,PI2)
>        FOVER 2E F/ FOVER       \ PI2 MOD PI MOD
>        F< IF FSWAP F- ELSE FNIP THEN ;
>
>I took this one from your source, but I'm unable to figure out what
>you're trying to do at:
>
>        FOVER 2E F/ FOVER       \ PI2 MOD PI MOD
>
>Where does "2E" come from all of a sudden? And why isn't it converted
>to a float before using it?

This is ugly shorthand for 2.0e0. That IS a float.
If the reduced number is greater than pi , another 2pi is
subtracted. You get pi by dividing by 2 (which need not
be an efficient thing to do in your situation).

>
>Hans Bezemer


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-- 
Albert van der Horst, UTRECHT,THE NETHERLANDS
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