It seems You reimplemented `*/'.
How about something like:
# [name 'sqrt "isqrt"] # Somthing like that.
[scl [if native 17 8]]
[de sqrt [N]
[list [isqrt (** 100 *Scl) N] 'E [- *Scl]] ]
On 2/27/17, Joh-Tob Schäg <[email protected]> wrote:
> Now there are before there were not.
> Am 27.02.2017 10:07 schrieb "Lindsay John Lawrence" <
> [email protected]>:
>
>> 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
>>
>
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