Knuth's power tree: Difference between revisions

Content added Content deleted
m (changed a comment in the task's definition section.)
m (→‎{{header|REXX}}: changed/added comments and whitespace, changed indentations, made other cosmetic changes.)
Line 563: Line 563:


=={{header|REXX}}==
=={{header|REXX}}==
This REXX version supports results up to 1,000 decimal digits   (which can be expanded with the   '''numeric digits nnn'''   REXX statement.   Also, negative powers are supported.
This REXX version supports results up to 1,000 decimal digits   (which can be expanded with the   '''numeric digits nnn'''   REXX statement.
⚫
<lang rexx>/*REXX program produces & shows a power tree for P, and calculates & shows X^P*/
numeric digits 1000 /*be able to handle some large numbers.*/
⚫
parse arg nums /*get set stuff: sets of three numbers.*/
⚫
if nums='' then nums='2 -4 17 3 191 191 1.1 81' /*Not specified? Use defaults*/
⚫
/*X lowPow highPow ··· repeat*/
⚫
do until nums=''
⚫
parse var nums x pL pH nums; x=x/1 /*get X, lowP, highP; and normalize X. */
⚫
if pH='' then pH=pL /*No highPower? Then assume lowPower. */


Also, negative powers are supported.
do e=pL to pH; p=abs(e)/1 /*use a range of powers; use │E│ */
⚫
<lang rexx>/*REXX program produces & displays a power tree for P, and calculates & displays X^P.*/
$=powerTree(p); w=length(pH) /*construct the power tree, (pow list).*/
/* [↑] W≡length for show*/
numeric digits 1000 /*be able to handle some large numbers.*/
do i=1 for words($); @.i=word($,i); end /*build a fast pow array.*/
parse arg XP /*get sets: X, low power, high power.*/
⚫
if XP='' then XP='2 -4 17 3 191 191 1.1 81' /*Not specified? Then use the default.*/
/*────── X LP HP X LP HP X LP ◄── X, low power, high power ··· repeat*/
⚫
do until XP=''
⚫
parse var XP x pL pH XP; x=x/1 /*get X, lowP, highP; and normalize X. */
⚫
if pH='' then pH=pL /*No highPower? Then assume lowPower. */


if p==0 then do; z=1; call show; iterate; end /*handle case of 0 power.*/
do e=pL to pH; p=abs(e)/1 /*use a range of powers; use │E│ */
!.=.; z=x; !.1=z; prv=z /*define the first power of X. */
$=powerTree(p); w=length(pH) /*construct the power tree, (pow list).*/
⚫
/* [↑] W≡length for an aligned display*/
do i=1 for words($); @.i=word($,i) /*build a fast Knuth's power tree array*/
⚫
end /*i*/


do k=2 to words($); n=@.k /*obtain the power (number) to be used.*/
if p==0 then do; z=1; call show; iterate; end /*handle case of zero power.*/
prev=k-1; diff=n-@.prev /*these are used for the odd powers. */
!.=.; z=x; !.1=z; prv=z /*define/construct the first power of X*/
⚫
if n//2==0 then z=prv**2 /*Even power? Then square the number.*/
⚫
else z=z*!.diff /* Odd " " mult. by pow diff.*/
⚫
!.n=z /*remember for other multiplications. */
⚫
prv=z /*remember for squaring the numbers. */
⚫
end /*k*/
⚫
call show /*display the expression and its value.*/
⚫
end /*e*/
end /*until nums ···*/
⚫
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────POWERTREE subroutine────────────────────────*/
⚫
powerTree: arg y 1 oy; $= /*Z is the result; $ is the power tree.*/
if y=0 | y=1 then return y /*handle special cases for zero & unity*/
⚫
#.=0; @.=0; #.0=1 /*define default & initial array values*/
⚫
/* [↓] add blank "flag" thingy──►list.*/
⚫
do while \(y//2); $=$ ' ' /*reduce "front" even power #s to odd #*/
⚫
if y\==oy then $=y $ /*(only) ignore the first power number*/
⚫
y=y%2 /*integer divide the power (it's even).*/
end /*while ···*/


if $\=='' then $=y $ /*re─introduce the last power number. */
do k=2 to words($); n=@.k /*obtain the power (number) to be used.*/
$=$ oy /*insert last power number 1st in list.*/
prev=k-1; diff=n-@.prev /*these are used for the odd powers. */
if y>1 then do while @.y==0; n=#.0; m=0
if n//2==0 then z=prv**2 /*Even power? Then square the number.*/
do while n\==0; q=0; s=n
else z=z*!.diff /* Odd " " mult. by pow diff.*/
do while s\==0; _=n+s
!.n=z /*remember for other multiplications. */
if @._==0 then do; if q==0 then m_=_; #._=q; @._=n; q=_
prv=z /*remember for squaring the numbers. */
end
end /*k*/
⚫
call show /*display the expression and its value.*/
⚫
s=@.s
end /*while s¬==0*/
end /*e*/
if q\==0 then do; #.m=q; m=m_; end
end /*until XP ···*/
⚫
exit /*stick a fork in it, we're all done. */
⚫
n=#.n
/*──────────────────────────────────────────────────────────────────────────────────────*/
⚫
end /*while n¬==0*/
⚫
powerTree: arg y 1 oy; $= /*Z is the result; $ is the power tree.*/
#.m=0
end /*while @.y==0*/
if y=0 | y=1 then return y /*handle special cases for zero & unity*/
⚫
#.=0; @.=0; #.0=1 /*define default & initial array values*/
z=@.y
do while z\==0; $=z $; z=@.z; end /*build power list.*/
/* [↓] add blank "flag" thingy──►list.*/
⚫
do while \(y//2); $=$ ' ' /*reduce "front" even power #s to odd #*/
return space($)
⚫
if y\==oy then $=y $ /*(only) ignore the first power number*/
/*────────────────────────────────SHOW subroutine─────────────────────────────*/
⚫
y=y%2 /*integer divide the power (it's even).*/
⚫
show: if e<0 then z=format(1/z,,40)/1; _=right(e,w) /*use reciprocal ? */
say left('power tree for ' _ " is: " $,60) '═══' x"^"_ ' is: ' z; return</lang>
end /*while*/

⚫
if $\=='' then $=y $ /*re─introduce the last power number. */
⚫
$=$ oy /*insert last power number 1st in list.*/
if y>1 then do while @.y==0; n=#.0; m=0
do while n\==0; q=0; s=n
do while s\==0; _=n+s
if @._==0 then do; if q==0 then m_=_; #._=q; @._=n; q=_
⚫
end
⚫
s=@.s
⚫
end /*while s¬==0*/
if q\==0 then do; #.m=q; m=m_; end
⚫
n=#.n
⚫
end /*while n¬==0*/
⚫
#.m=0
⚫
end /*while @.y==0*/
⚫
z=@.y
do while z\==0; $=z $; z=@.z; end /*build power list*/
return space($) /*del extra blanks*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
⚫
show: if e<0 then z=format(1/z, , 40)/1; _=right(e, w) /*use reciprocal? */
say left('power tree for ' _ " is: " $,60) '═══' x"^"_ ' is: ' z; return</lang>
'''output''' when using the default inputs:
'''output''' when using the default inputs:
<pre>
<pre>
Retrieved from "https://rosettacode.org/wiki/Knuth%27s_power_tree"