Heronian triangles: Difference between revisions
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m (→using SQRT table: added whitespace, optimized a DO loop, aligned the END with the DO loop..) |
m (→using iSQRT: added whitespace, aligned the END with the DO loop.) |
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<lang rexx>/*REXX program generates & displays primitive Heronian triangles by side length and area*/ |
<lang rexx>/*REXX program generates & displays primitive Heronian triangles by side length and area*/ |
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parse arg N first area . /*obtain optional arguments from the CL*/ |
parse arg N first area . /*obtain optional arguments from the CL*/ |
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if N=='' | N=="," then N= |
if N=='' | N=="," then N= 200 /*Not specified? Then use the default.*/ |
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if first=='' | first=="," then first= |
if first=='' | first=="," then first= 10 /* " " " " " " */ |
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if area=='' | area=="," then area= |
if area=='' | area=="," then area= 210 /* " " " " " " */ |
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numeric digits 99 |
numeric digits 99 /*ensure 'nuff dec. digs to calc. N**5.*/ |
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numeric digits max(9, 1 + length(N**5) ) /*minimize decimal digits for REXX pgm.*/ |
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call Heron; HT= 'Heronian triangles' /*invoke the Heron subroutine. */ |
call Heron; HT= 'Heronian triangles' /*invoke the Heron subroutine. */ |
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say # ' primitive' HT "found with sides up to " N ' (inclusive).' |
say # ' primitive' HT "found with sides up to " N ' (inclusive).' |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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Heron: @.= 0; minP= 9e9; maxP= 0; maxA= 0; minA= 9e9; Ln= length(N) /* __*/ |
Heron: @.= 0; minP= 9e9; maxP= 0; maxA= 0; minA= 9e9; Ln= length(N) /* __*/ |
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#= 0; #.= 0; #.2= 1; #.3= 1; #.7= 1; #.8= 1 /*digits ¬good √ */ |
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do a=3 to N /*start at a minimum side length of 3. */ |
do a=3 to N /*start at a minimum side length of 3. */ |
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Aeven= a//2==0 /*if A is even, B and C must be odd.*/ |
Aeven= a//2==0 /*if A is even, B and C must be odd.*/ |
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end /*c*/ /* [↑] keep each unique perimeter#*/ |
end /*c*/ /* [↑] keep each unique perimeter#*/ |
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end /*b*/ |
end /*b*/ |
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end /*a*/; return # |
end /*a*/; return # /*return # of Heronian triangles. */ |
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/*─────────────────────────────────────────────────────────────────────────────────────────────*/ |
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hGCD: x=a; do j=2 for 2; y=arg(j); do until y==0; parse value x//y y with y x; end; end; return x |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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hGCD: x=a; do j=2 for 2; y= arg(j); do until y==0; parse value x//y y with y x |
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end /*until*/ |
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end /*j*/; return x |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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hIsqrt: procedure; parse arg x; q= 1; r= 0; do while q<=x; q= q * 4 |
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end /*while q<=x*/ |
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do while q>1; q=q%4; _= x-r-q; r= r%2; if _>=0 then parse value _ r+q with x r |
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end /*while q>1*/; return r |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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show: m=0; say; say; parse arg ae; say arg(2); if ae\=='' then first= 9e9 |
show: m=0; say; say; parse arg ae; say arg(2); if ae\=='' then first= 9e9 |
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