Re: [Amforth-devel] Floating point - fsin, fcos, ftan

[pito <pi...@vo...>]

..more compact, faster by 25%.P.

\ fsin fcos ftan library
\ amforth 4.0
\ Pito 23-9-2010
\ based on 4tH library by J.L. Bezemer
\ needs Leon's flib (and Pito's asm flib v1.1 for speed)
-fsincostan
marker -fsincostan
\ the original JLB (taylor) does not work, a bug?
: >taylor fdup f* fover ;        \ setup for Taylor series
: _taylor fover f* frot fover ;
: +taylor f/ f+ frot frot ;      \ add Taylor iteration
: -taylor f/ f- frot frot ;      \ subtract Taylor iteration
\ put x in RADIANS within 2pi range                                 
   
: >range                              
$0FDB $4049 fdup f+                          ( x pi2 )
fover fover f/                       ( x pi2 x/pi2 )
ffloor fover f*                      ( x pi2 mod )
frot fswap f-                        ( pi2 mod )
$0FDB $4049 fover                            ( pi2 mod pi mod )
f< if fswap f- else fnip then ;
\ calculate fcos
: fcos
1 s>f fswap >range >taylor			( 1 x2 1 )
_taylor $0000 $4000 -taylor		( 1-2 x2 x2 )
_taylor $0000 $41C0 +taylor		( 1+4 x2 x4 )
_taylor $0000 $4434 -taylor		( 1-6 x2 x6 )
_taylor $8000 $471D +taylor		( 1+8 x2 x8 )
_taylor $7C00 $4A5D -taylor		( 1-10 x2 x10 )
_taylor $67E0 $4DE4 +taylor		( 1+12 x2 x12 )
\  _taylor $61D9 $51A2 +taylor		( 1-14 x2 x14 )
\  _taylor $3BBC $5598 +taylor		( 1+16 x2 x16 )
fdrop fdrop ;					( 1+12 )
\ calculate fsin 
: fsin $0FDB $3FC9 f- fcos ;
\ calculate ftan
: ftan fdup fsin fswap fcos f/ ;       \ ftan = fsin / fcos