Knuth's power tree: Difference between revisions
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/*────── X LP HP X LP HP X LP ◄── X, low power, high power ··· repeat*/ |
/*────── X LP HP X LP HP X LP ◄── X, low power, high power ··· repeat*/ |
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do until XP='' |
do until XP='' |
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parse var XP x pL pH XP; x=x/ |
parse var XP x pL pH XP; x= x / 1 /*get X, lowP, highP; and normalize X. */ |
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if pH='' then pH= |
if pH='' then pH= pL /*No highPower? Then assume lowPower. */ |
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do e=pL to pH; |
do e=pL to pH; p= abs(e) / 1 /*use a range of powers; use │E│ */ |
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$=powerTree(p); |
$= powerTree(p); w= length(pH) /*construct the power tree, (pow list).*/ |
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/* [↑] W≡length for an aligned display*/ |
/* [↑] W≡length for an aligned display*/ |
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do i=1 for words($); @.i= word($, i) /*build a fast Knuth's power tree array*/ |
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end /*i*/ |
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if p==0 then do; z=1; call show; iterate; end |
if p==0 then do; z= 1; call show; iterate; end /*handle case of zero power.*/ |
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!.=.; z=x; !.1=z; |
!.= .; z= x; !.1= z; prv= z /*define/construct the first power of X*/ |
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do k=2 to words($); n=@.k |
do k=2 to words($); n= @.k /*obtain the power (number) to be used.*/ |
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prev=k-1; diff=n-@.prev |
prev= k - 1; diff= n - @.prev /*these are used for the odd powers. */ |
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if n//2==0 then z=prv** |
if n//2==0 then z= prv ** 2 /*Even power? Then square the number.*/ |
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else z=z*!.diff |
else z= z * !.diff /* Odd " " mult. by pow diff.*/ |
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!.n= |
!.n= z /*remember for other multiplications. */ |
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prv= |
prv= z /*remember for squaring the numbers. */ |
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end /*k*/ |
end /*k*/ |
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call show /*display the expression and its value.*/ |
call show /*display the expression and its value.*/ |
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end /*e*/ |
end /*e*/ |
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end /*until XP ···*/ |
end /*until XP ···*/ |
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exit |
exit 0 /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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powerTree: arg y 1 oy; $= /*Z is the result; $ is the power tree.*/ |
powerTree: arg y 1 oy; $= /*Z is the result; $ is the power tree.*/ |
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if y=0 | y=1 then return y /*handle special cases for zero & unity*/ |
if y=0 | y=1 then return y /*handle special cases for zero & unity*/ |
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#.=0; @.=0; #.0= |
#.= 0; @.= 0; #.0= 1 /*define default & initial array values*/ |
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/* [↓] add blank "flag" thingy──►list.*/ |
/* [↓] add blank "flag" thingy──►list.*/ |
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do while \(y//2); $= |
do while \(y//2); $= $ ' ' /*reduce "front" even power #s to odd #*/ |
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if y\==oy then $=y $ |
if y\==oy then $= y $ /*(only) ignore the first power number*/ |
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y=y% |
y= y % 2 /*integer divide the power (it's even).*/ |
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end /*while*/ |
end /*while*/ |
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if $\=='' then $=y $ |
if $\=='' then $= y $ /*re─introduce the last power number. */ |
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$=$ oy |
$= $ oy /*insert last power number 1st in list.*/ |
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if y>1 then do while @.y==0; n=#.0; m=0 |
if y>1 then do while @.y==0; n= #.0; m= 0 |
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do while n\==0; q=0; s=n |
do while n\==0; q= 0; s= n |
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do while s\==0; _=n+s |
do while s\==0; _= n + s |
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if @._==0 then do; if q==0 then m_= |
if @._==0 then do; if q==0 then m_= _; |
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#._= q; @._= n; q= _ |
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end |
end |
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s=@.s |
s= @.s |
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end /*while s¬==0*/ |
end /*while s¬==0*/ |
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if q\==0 then do; #.m=q; m=m_; end |
if q\==0 then do; #.m= q; m= m_; end |
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n=#.n |
n= #.n |
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end /*while n¬==0*/ |
end /*while n¬==0*/ |
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#.m=0 |
#.m= 0 |
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end /*while @.y==0*/ |
end /*while @.y==0*/ |
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z=@.y |
z= @.y |
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do while z\==0; $=z $; z=@.z; end |
do while z\==0; $= z $; z= @.z; end /*build power list*/ |
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return space($) /*del extra blanks*/ |
return space($) /*del extra blanks*/ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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show: if e<0 then z=format(1/z, , 40)/1; _=right(e, w) /*use reciprocal? */ |
show: if e<0 then z=format(1/z, , 40)/1; _=right(e, w) /*use reciprocal? */ |
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say left('power tree for ' _ " is: " $,60) '═══' x"^"_ ' is: ' z; return</lang> |
say left('power tree for ' _ " is: " $,60) '═══' x"^"_ ' is: ' z; return</lang> |
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{{out|output|text= when using the default inputs:}} |
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<pre> |
<pre> |
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power tree for -4 is: 1 2 4 ═══ 2^-4 is: 0.0625 |
power tree for -4 is: 1 2 4 ═══ 2^-4 is: 0.0625 |
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