Richard Suchenwirth 2002-04-27 - Periodic decimal fractions are numbers where a sequence of digits behind the decimal point (the period) is endlessly repeated, for example:
1/7 = 0.142857142857.. 1/3 = 0.3333..
The following routine tries to detect a period in a given number and returns the period (might be 0 for integers or non-strict periods like
1/2 = 0.5000..
or (implicitly) an empty string if no period could be detected - then the input number might be irrational (not representable by a nominator/divisor expression, e.g. sqrt(2)), or it has a period longer than 7 digits, which can not be confirmed at the maximum tcl_precision of 17, a limit imposed by the underlying double representation in C. For instance, 1/17 is certainly periodic, but the period is out of sight for Tcl's expr math..
proc period x {
set frac [expr {abs(double($x)-int($x))}]
if {!$frac || [string length $frac]<10} {return 0}
set digits [string range $frac 2 end]
foreach n {1 2 3 4 5 6 7} {
foreach offset {0 1 2 3 4 5 6} {
set try [string range $digits $offset [expr $offset+$n-1]]
if {[regexp .{0,$n}$try\($try)+.{0,$n}$ $digits]} {
return $try
}
}
}
}Arjen Markus As the fraction is contained in a string, there ought to be no problem with very long periods:
set long_fraction "0.123456789012345678901234567890"
As long, of course, as you avoid interpreting the string as a number! RS admits that he does, by letting expr compute the fractional part...
KBK In the spirit of Fraction math, let's do the period of a rational number whose numerator and denominator are integers. The following has no trouble finding out that 1/17 repeats with a period of 16 places.
proc period2 { n d } {
set x 0
while { 1 } {
set r [expr { $n % $d }]
if { $r == 0 } {
return 0
} elseif { [info exists seen($n)] } {
return [expr { $x - $seen($n) }]
} else {
set seen($n) $x
incr x
set n [expr { 10 * $r }]
}
}
}
for { set i 1 } { $i <= 20 } { incr i } {
puts [list $i [period2 1 $i]]
}There is some interesting number theory here, but I haven't the time to get into it; I've typed this in in about 15 minutes while waiting for a test to run.
Category Mathematics | Arts and crafts of Tcl-Tk programming