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+--- Thread: (49G) Egyptian Fraction (Random) Programme (/thread-3971.html)
(49G) Egyptian Fraction (Random) Programme - Gerald H - 05-25-2015 02:24 PM
The programme EGYRAND takes a fraction expressed as the division of two integers from the stack & returns a random decomposition into Egyptian fractions.
eg For entry
'77/73'
the programme returns
:6: { 1 '1/19' '1/464' '1/128715' '1/11833836446' '1/490138897595538851760' }
or
:5: { 1 '1/19' '1/463' '1/321091' '1/206198539471' }
or
:5: { 1 '1/19' '1/464' '1/128714' '1/41418105776' }
or
:5: { 1 '1/20' '1/209' '1/101715' '1/6207463020' }
or a different list.
Here the programme in a box:
Code:
::
CK1&Dispatch
BINT10
::
BINT1
Z0_
FPTR2 ^2LAMBIND
FPTR2 ^SIMP1ext
FPTR2 ^FLAGPROPFRAC
FPTR2 ^DUPTYPEZ?
?SKIP
::
EXPR>_
SWAPDROP
'
x/
EQUAL
IT
::
Z0_
3UNROLL
FPTR2 ^QDiv
;
BEGIN
2GETLAM
#1+
2PUTLAM
DUP
FPTR2 ^FXNDext
SWAP
FPTR2 ^DupZIsOne?
NOT_WHILE
::
FPTR2 ^ZQUOText
%RAN
%.5
%>
ITE
Z1_
Z2_
FPTR2 ^RADDext
DUP
1GETLAM
Z<=
IT
::
DROP
1GETLAM
Z2_
FPTR2 ^RADDext
;
DUP1PUTLAM_
Z1_
FPTR2 ^SWAPRDIV
DUPUNROT
FPTR2 ^QSub
;
REPEAT
2DROP
;
2GETLAM
{}N
2GETLAM
ABND
#>$
>TAG
;
;& again the programme (which depiction do you prefer?)
::
CK1&Dispatch
BINT10
::
BINT1
Z0_
FPTR2 ^2LAMBIND
FPTR2 ^SIMP1ext
FPTR2 ^FLAGPROPFRAC
FPTR2 ^DUPTYPEZ?
?SKIP
::
EXPR>_
SWAPDROP
'
x/
EQUAL
IT
::
Z0_
3UNROLL
FPTR2 ^QDiv
;
BEGIN
2GETLAM
#1+
2PUTLAM
DUP
FPTR2 ^FXNDext
SWAP
FPTR2 ^DupZIsOne?
NOT_WHILE
::
FPTR2 ^ZQUOText
%RAN
%.5
%>
ITE
Z1_
Z2_
FPTR2 ^RADDext
DUP
1GETLAM
Z<=
IT
::
DROP
1GETLAM
Z2_
FPTR2 ^RADDext
;
DUP1PUTLAM_
Z1_
FPTR2 ^SWAPRDIV
DUPUNROT
FPTR2 ^QSub
;
REPEAT
2DROP
;
2GETLAM
{}N
2GETLAM
ABND
#>$
>TAG
;
;