Now there are before there were not. Am 27.02.2017 10:07 schrieb "Lindsay John Lawrence" < lawrence.lindsayj...@gmail.com>:
> Hi, > > Are there scaled (fixed point) versions of division and sqrt in picolisp? > I may have missed them.. > > In any event I wrote a couple of functions to provide that functionality > that may be useful to others as well. Performance is reasonable. > > It is quite nice to be able to be able to do arbitrary precision > arithmetic in this way =) > > /Lindsay > > Code: > > # Scaled fixed point long division. (if necessary, round last digit) > # TODO: Brute force implementation... > # There is probably a better way to do it. > : (pp '/*) > (de /* (N D S) > (let (Q NIL R NIL Acc NIL Cnt 0) > (default S *Scl) > (setq S (+ 2 S)) > (do S > (T (>= Cnt S)) > (setq > Q (/ N D) > R (% N D) > Acc (cons Q Acc) > Cnt (inc Cnt) > N R ) > (when (and (gt0 N) (<= N D)) > (while (and (gt0 N) (<= N D)) > (setq > N (* N 10) > Acc (cons 0 Acc) > Cnt (inc Cnt) ) ) > (pop 'Acc) > (dec 'Cnt) ) ) > (setq R (pop 'Acc)) > (if (<= 5 R) > (setq Acc (cons (+ 1 (pop 'Acc)) Acc)) ) > (setq Acc (flip Acc)) > (format > (pack (cons (car Acc) "." (cdr Acc))) > (- S 2) ) ) ) > -> /* > > # Scaled fixed point sqrt(); no rounding > # TODO: Converges in 4-7 iterations in tests, 13 is probably overkill > : (pp 'sqrt*) > (de sqrt* (N S) > (let (P (/ N 2) M 13) > (default S *Scl) > (setq N (* N (** 10 S))) > (while (ge0 (dec 'M)) > (setq P (/ (+ P (/ N P)) 2)) ) > P ) ) > -> sqrt* > > > > Some Tests: > > # Arbitrary Fixed Precision Square Root > # Compare: bc. > # also: https://apod.nasa.gov/htmltest/gifcity/sqrt2.1mil > : (scl 64) (format (sqrt* 2.0) *Scl) > -> "1.4142135623730950488016887242096980785696718753769480731766797379" > : (scl 64) (format (sqrt* 0.5) *Scl) > -> "0.7071067811865475244008443621048490392848359376884740365883398689" > : (scl 64) (format (sqrt* 9967.0) *Scl) > -> "99.8348636499294268455686673311236280296661789737252407300182230035" > : (scl 100000) (bench (nil (sqrt* 2.0))) > 2.027 sec > > # Arbitrary Fixed Precision Long Division > # Compare: bc e.g. "scale=64 1/9967" > : (scl 64) (/* 1.0 9967.0) > -> 1003310926055984749673923949031804956355974716564663389184308 > : (scl 64) (format (/* 1.0 9967.0) *Scl) > -> "0.0001003310926055984749673923949031804956355974716564663389184308" > : (scl 64) (format (format (/* 1.0 9967.0) *Scl) *Scl) > -> 1003310926055984749673923949031804956355974716564663389184308 > : (scl 32) (/* 22.0 7.0) > -> 314285714285714285714285714285714 > : (scl 0) (/* 22.0 7.0) > -> 3 > : (scl 1) (/* 22.0 7.0) > -> 31 > : (scl 8) (/* 22.0 7.0) > -> 314285714 > : (scl 32) (/* 1.0 3.0) > -> 33333333333333333333333333333333 > : (scl 32) (/* 10.0 3.0) > -> 333333333333333333333333333333333 > : (scl 32) (format (/* 1.0 3.0) *Scl) > -> "0.33333333333333333333333333333333" > : (scl 32) (format (/* 10.0 3.0) *Scl) > -> "3.33333333333333333333333333333333" > : (scl 32) (format (/* 0.22 0.7) *Scl) > -> "0.31428571428571428571428571428571" > : (scl 32) (format (/* 9968.0 32.0) *Scl) > -> "311.50000000000000000000000000000000" > : (scl 10000) (bench (nil (format (/* 1.0 9967.0) *Scl))) > 7.685 sec >
