how to find the fractional representation of a decimal number
Posted: Mon Oct 03, 2016 3:34 pm
for non periodic numbers the algorithm is pretty simple ...
for a periodic number ( OOREXX ONLY )
quick and dirty just to show the algorithms.
Code: Select all
#! /usr/bin/env rexx
/* REXX
*/
Trace "O"
numeric digits 32
signal on novalue
f.1 = 1.25
f.2 = 0.25
f.0 = 2
do f = 1 to f.0
parse var f.f i "." d
p = length(d)
n = i || d
d = 10 ** p
rn = n / gcd(n,d)
rd = d / gcd(n,d)
say "numerator="rn", denominator="rd
end
exit
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
logic_error:
say "++"copies(" -",35)
say "++ Logic error at line '"sigl"' "
say "++"copies(" -",35)
exit
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
novalue:
say "++"copies(" -",35)
say "++ Novalue trapped, line '"sigl"' var '"condition("D")"' "
exit
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
gcd: procedure
parse arg x, y
if y > x then do
r = x; x = y; y = r
end
do until r = 0
r = x // y; x = y; y = r
end
return x
for a periodic number ( OOREXX ONLY )
Code: Select all
#! /usr/bin/env rexx
/* REXX
*/
Trace "O"
numeric digits 32
signal on novalue
n = 1.333333333
parse var n i "." f
p = lrs(f)
say n i f p
say length(f)
say length(p)
d = copies("9", length(p) )
n = i*d + p
rn = n / gcd(n,d)
rd = d / gcd(n,d)
say "numerator="rn", denominator="rd
exit
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
logic_error:
say "++"copies(" -",35)
say "++ Logic error at line '"sigl"' "
exit
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
novalue:
say "++"copies(" -",35)
say "++ Novalue trapped, line '"sigl"' var '"condition("D")"' "
exit
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
lrs:procedure
use strict arg s
m = s~length()
k = 0
L = .array~new
r = ""
do i = 1 to m
do j = i + 1 to m
if substr(s,i,1) = substr(s,j,1) then do
if i = 1 then ,
L[i,j] = 1
else do
if j-i > L[i-1,j-1] then do
L[i,j] = L[i-1,j-1] + 1
if L[i,j] > k then do
k = L[i,j]
r = substr(s,i-k+1,k)
end
end
else do
L[i,j] = 0
end
end
end
else do
L[i,j] = 0
end
end /* do j = i + 1 to m */
end /* do i = 1 to m */
return r
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
gcd: procedure
parse arg x, y
if y > x then do
r = x; x = y; y = r
end
do until r = 0
r = x // y
x = y
y = r
end
say x y r
return x