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June 2018 Update

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Ingy döt Net 2018-06-22 20:57:24 +00:00
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commit 22f33d4004
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51
Task/Stern-Brocot-sequence/REXX/stern-brocot-sequence.rexx
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@ -1,44 +1,49 @@
/*REXX program generates & displays a Stern─Brocot sequence; finds 1─based indices; GCDs*/
parse arg N idx fix chk . /*get optional arguments from the C.L. */
if N=='' | N=="," then N= 15 /* N not defined? Then use default.*/
if idx=='' | idx=="," then idx= 10 /*IDX " " " " " */
if fix=='' | fix=="," then fix= 100 /*FIX " " " " " */
if chk=='' | chk=="," then chk=1000 /*CHK " " " " " */
if N=='' | N=="," then N= 15 /*Not specified? Then use the default.*/
if idx=='' | idx=="," then idx= 10 /* " " " " " " */
if fix=='' | fix=="," then fix= 100 /* " " " " " " */
if chk=='' | chk=="," then chk=1000 /* " " " " " " */
say center('the first' N "numbers in the Stern─Brocot sequence", 70, '═')
say center('the first' N "numbers in the Stern─Brocot sequence", 70, '═')
a=Stern_Brocot(N) /*invoke function to generate sequence.*/
say a /*display the sequence to the terminal.*/
say
say center('the 1-based index for the first' idx "integers", 70, '═')
say center('the 1─based index for the first' idx "integers", 70, '═')
a=Stern_Brocot(-idx) /*invoke function to generate sequence.*/
do i=1 for idx
say 'for ' right(i,length(idx))", the index is: " wordpos(i,a)
w=length(idx); do i=1 for idx
say 'for ' right(i, w)", the index is: " wordpos(i, a)
end /*i*/
say
say center('the 1-based index for' fix, 70, "═")
say center('the 1─based index for' fix, 70, "═")
a=Stern_Brocot(-fix) /*invoke function to generate sequence.*/
say 'for ' fix", the index is: " wordpos(fix, a)
say
say center('checking if all two consecutive members have a GCD=1', 70, '═')
a=Stern_Brocot(chk) /*invoke function to generate sequence.*/
do c=1 for chk-1; if gcd(subword(a,c,2))==1 then iterate
say 'GCD check failed at member' c"."; exit 13
do c=1 for chk-1; if gcd(subword(a, c, 2))==1 then iterate
say 'GCD check failed at index' c; exit 13
end /*c*/
say '───── All ' chk " two consecutive members have a GCD of unity."
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gcd: procedure; $=; do i=1 for arg(); $=$ arg(i); end /*i*/ /*arg list. */
parse var $ x z .; if x=0 then x=z; x=abs(x) /*zero case?*/
do j=2 to words($); y=abs(word($,j)); if y=0 then iterate /*ignore 0's*/
do until y==0; parse value x//y y with y x; end /*heavy work*/
end /*j*/
return x /*return GCD*/
gcd: procedure; $=; do i=1 for arg(); $=$ arg(i) /*get arg list. */
end /*i*/
parse var $ x z .; if x=0 then x=z /*is zero case? */
x=abs(x) /*use absolute x*/
do j=2 to words($); y=abs( word($, j) )
if y=0 then iterate /*ignore zeros. */
do until y==0; parse value x//y y with y x /* ◄──heavy work*/
end /*until*/
end /*j*/
return x /*return the GCD*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
Stern_Brocot: parse arg h 1 f; $=1 1; if h<0 then h=1e9
else f=0; f=abs(f)
do k=2 until words($)>=h | wordpos(f,$)\==0
_=word($,k); $=$ (_+word($,k-1)) _; if f==0 then iterate
end /*until*/
if f==0 then return subword($,1,h)
Stern_Brocot: parse arg h 1 f; $=1 1; if h<0 then h=1e9
else f=0
f=abs(f)
do k=2 until words($)>=h | wordpos(f, $)\==0; _=word($, k)
$=$ (_ + word($, k-1) ) _
end /*k*/
if f==0 then return subword($, 1, h)
return $