A general base-conversion procedure for arbitrary length string representations of numbers with integer and/or fraction.
#=============================================================================
# PROC : baseconvert
# PURPOSE : convert number in one base to another base
# AUTHOR : Richard Booth
# DATE : Fri Jul 14 10:40:50 EDT 2006
# ---------------------------------------------------------------------------
# ARGUMENTS :
# % base_from
# original base (expressed in base 10)
# % base_to
# base to convert number to (expressed in base 10)
# % number
# number expressed in base_from (must have form int.fra, int, or .fra)
# RESULTS :
# * returns number expressed in base_to
# EXAMPLE-CALL :
#{
# set num16 [baseconvert 10 16 3.1415926535]
#}
#=============================================================================
proc baseconvert {base_from base_to number} {
set number [string tolower $number]
if {![regexp {([0-9a-z]*)\.?([0-9a-z]*)} $number match sint sfra]} {
puts "baseconvert error: number \"$number\" is not in correct format"
return ""
}
set map 0123456789abcdefghijklmnopqrstuvwxyz
set i -1
foreach c [split $map ""] {
incr i
set D2I($c) $i
set I2D($i) $c
}
set lint [string length $sint]
set lfra [string length $sfra]
set converted_number 0
if {$lint > 0} {
set i -1
foreach c [split $sint ""] {
set B([incr i]) $D2I($c)
}
set aint ""
while {1} {
set s 0
set r 0
for {set i 0} {$i < $lint} {incr i} {
set v [expr $B($i) + $r*$base_from]
set B($i) [expr int($v/$base_to)]
set r [expr $v - $base_to*$B($i)]
set s [expr $s + $B($i)]
}
set aint "$I2D($r)$aint"
if {$s == 0} {break}
}
set converted_number $aint
}
if {$lfra > 0} {
set s [expr $lfra*int(1.0*log($base_from)/log($base_to))]
set i $lfra
foreach c [split $sfra ""] {
set B([incr i -1]) $D2I($c)
}
set afra ""
for {set j 0} {$j < $s} {incr j} {
set r 0
for {set i 0} {$i < $lfra} {incr i} {
set v [expr $base_to*$B($i) + $r]
set r [expr int($v/$base_from)]
set B($i) [expr $v - $r*$base_from]
}
set afra "$I2D($r)$afra"
}
append converted_number .$afra
}
return $converted_number
}
a small test script for baseconvert:
set fmt "%-10s (base %-2d) => %-10s (base %-2d)"
foreach number {12ff.abb 122. 125 .222 0.222 0.22 0.2 0.1} {
puts [format $fmt $number 16 [baseconvert 16 10 $number] 10]
puts [format $fmt $number 16 [baseconvert 16 8 $number] 8]
puts [format $fmt $number 16 [baseconvert 16 2 $number] 2]
}rvb A related problem is sampling a multi-dimensional grid:
#=============================================================================
# PROC : gridsample
# PURPOSE : uniformly sample a normalized hypercube
# AUTHOR : Richard Booth
# DATE : Tue Jul 18 11:19:10 EDT 2006
# ---------------------------------------------------------------------------
# ARGUMENTS :
# % ndiv
# number of divisions of the normalized hypercube
# (each independent variable range is [-1, 1])
# % nind
# number of independent variables
# RESULTS :
# * returns list of (normalized) samples
# EXAMPLE-CALL :
#{
# set samples [gridsample 5 2]
#}
#=============================================================================
proc gridsample {ndiv nind} {
if {$nind < 1 || $ndiv < 1} {
return {}
}
set samples {}
set base [expr $ndiv+1]
set npts [expr pow($base, $nind)]
for {set i 0} {$i < $npts} {incr i} {
set sample {}
set v $i
for {set j 0} {$j < $nind} {incr j} {
set w [expr int($v/$base)]
set r [expr $v - $base*$w]
set v $w
lappend sample [expr {2.0*$r/$ndiv-1}]
}
lappend samples [join $sample]
}
return $samples
}
a test script for gridsample:
set nind 3
set ndiv 6
set samples [gridsample $ndiv $nind]
puts "sample A B C"
set iexpt -1
foreach sample $samples {
puts "[incr iexpt] [join $sample]"
}See Also: Converting an integer to a base 2 string, Binary representation of numbers,