Hi, this is a new version of the lib - combination of amforth's look-up table sinus calculus (see examples) within the 0-pi/2 range, and, the actual sinus calculated by the taylor series. VERY GOOD precision (6+ digits) and still fast. Pito.
\ fsin fcos ftan library \ amforth 4.0 \ Pito 25-9-2010 \ v 3.0. \ based on 4tH library by J.L. Bezemer \ and amforth's sinus.frt example \ 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 ; : _fsin fdup >taylor ( x x2 x ) _taylor $0000 $40C0 -taylor ( x-3 x2 x3 ) _taylor $0000 $42F0 +taylor ( x+5 x2 x5 ) _taylor $8000 $459D -taylor ( x-7 x2 x7 ) _taylor $3000 $48B1 +taylor ( x+9 x2 x9 ) _taylor $4540 $4C18 -taylor ( x-11 x2 x11 ) _taylor $9466 $4FB9 +taylor ( x+13 x2 x13 ) _taylor $3BBC $5398 -taylor ( x-15 x2 x15 ) _taylor $BF77 $57A1 +taylor ( x+17 x2 x17 ) _taylor $15CA $5BD8 -taylor ( x-19 x2 x19 ) fdrop fdrop ; ( x-19 ) \ calculate fsin : fsin ( RAD -- sinus ) fdup f0< >r fabs >range fdup $0FDB $4049 f> if $0FDB $4049 f- 1 >r else 0 >r then fdup $0FDB $3FC9 f> if $0FDB $4049 fswap f- then _fsin r> if fnegate then r> if fnegate then ; \ calculate fcos : fcos ( RAD -- cosinus ) $0FDB $3FC9 f+ fsin ; \ calculate ftan : ftan ( RAD -- tangens ) fdup fsin fswap fcos fdup f0= if abort else f/ then ; ************************************************ Ex: > _pi fsin fs. 0.0 ok > _pi fcos fs. -9.999999E-1 ok > _-pi fsin fs. 0.0 ok > _-pi fcos fs. -1.0 ok > _pihalf fsin fs. 9.999999E-1 ok > _pihalf fcos fs. 0.0 ok > _-pihalf fsin fs. -9.999999E-1 ok > _-pihalf fcos fs. 0.0 ok > 1 s>f fsin fs. 8.414711E-1 ok > 1 s>f fcos fs. 5.4030247E-1 ok > 10 s>f fsin fs. -5.4402137E-1 ok > 10 s>f fcos fs. -8.3907166E-1 ok > -1 s>f fsin fs. -8.414711E-1 ok > -1 s>f fcos fs. 5.4030237E-1 ok > -10 s>f fsin fs. 5.4402137E-1 ok > -10 s>f fcos fs. -8.3907127E-1 ok > _pi ftan fs. 0.0 ok > _-pi ftan fs. 0.0 ok > _pihalf ftan fs. > _-pihalf ftan fs. > 1 s>f ftan fs. 1.5574075 ok > 10 s>f ftan fs. 6.4836102E-1 ok > -1 s>f ftan fs. -1.5574076 ok > -10 s>f ftan fs. -6.483613E-1 ok > ------------------------------------------------------------------------------ Start uncovering the many advantages of virtual appliances and start using them to simplify application deployment and accelerate your shift to cloud computing. http://p.sf.net/sfu/novell-sfdev2dev _______________________________________________ Amforth-devel mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/amforth-devel
