Thanks for your replies! I've come up with these ones, based on the
Taylor series. It requires a separate FP stack and can't be used for
large values as well, (which function should I use, Albert, to reduce
this one?), but it is rather simple and relatively accurate.

Hans Bezemer

[UNDEFINED] fsin [IF]
[UNDEFINED] floats [IF]
include lib/ansfloat.4th
[THEN]

: f-rot frot frot ; \ inverted frot
: >taylor fdup f* fover ; \ setup for Taylor series
: (taylor) fover f* frot fover s>f f/ ;
: +taylor (taylor) f+ f-rot ; \ add Taylor iteration
: -taylor (taylor) f- f-rot ; \ subtract Taylor iteration

In article <16edbcc0-0978-4a9c-aa82-d68c0773c9f4@34g2000hsf.googlegroups.com>,
The Beez' bigfoot.com> 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.

in the

On Apr 27, 12:30 pm, Albert van der Horst
wrote:

: 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 ;

Albert,

I think I figured it out (your routine). This feels quite good (and
the test ranges come back fine too ;-)

Hans Bezemer

[UNDEFINED] fsin [IF]
[UNDEFINED] floats [IF]
include lib/ansfloat.4th
[THEN]

: >range
pi fdup f+ \ x pi2
fover fover f/ \ x pi2 x/pi2
floor fover f* \ x pi2 mod(x,pi2)
frot fswap f- \ pi2 mod(x,pi2)
pi fover \ pi2 mod pi mod
f- f0< if fswap f- else fnip then
;

In article d1g2000hsg.googlegroups.com>,
The Beez' bigfoot.com> wrote:

On 27 apr, 19:04, Albert van der Horst
wrote:

I think it was the comment that triggered me, but it suddenly came to
me. I was confused by the "FOVER 2e0 F/" sequence, since in most
situations you rather insert the constant again than to calculate it.
First I thought of "2E" as a hexadecimal number, but that made no
sense in any context. I came pretty close to your word by myself, but
I couldn't get the PI adjustment just right. Now it works.

Many thanks, Albert! Now I can release 4tH with a pretty nice FP
wordset, including FSIN, FCOS and FTAN. I hope nobody will use it
outside a government environment ;-)

Hans