Unit math

Richard Suchenwirth 2002-09-07 - Browsing the early chapters of a math book, the simple rules for arithmetics with units attracted me, just because I hadn't done such in Tcl before. For example, "A runner makes 5 km in 20 minutes - what is his average speed?" could be written as

 unitmath 5 km / 20 min

and should return 15 km/h. This involves both string and list manipulations, and finally a simple calculation, and returns the result with the matching unit. For more usage examples, see the "test suite" which comes before unitmath itself, as a hint that one should design tests before starting development:

 proc unitmath'test {} {
    set fail 0
    foreach {cmd                     expected} {
        {unitmath 5 km / 20 min}     {15 km/h}
        {unitmath {2 m * 3 m}}       {6 m2}
        {unitmath 60.00$ / 50.00$} 1.2
        {unitmath 2 m+60 cm}         {2.6 m}
        {unitmath 1 h / 4}           {15 min}
        {unitmath 2 ft / 3}          {8 in}
        {unitmath 2 ft 6 in * 3 ft}  {7.5 sq.ft}
        {unitmath 2m * 3m * 4m}      {24 m3}
    } {
        catch $cmd res ;# errors can't stop this test suite...
        puts [list $cmd $res]
        if [string compare $res $expected] {
            puts "[incr fail]. expected: $expected"
        }
    }
    if !$fail {puts "passed all tests"}
 }
 proc unitmath args {
    array set convert {
        m,cm 100 m,mm 1000 h,min 60 km/min,km/h 60 ft,in 12
    }
    if {[llength $args]==1} {set args [lindex $args 0]}
    regsub -all {([0-9])([a-zA-Z$])} "{$args}" {\1 \2} uexpr
    foreach op {+ - * /} {
        set uexpr [string map [list $op "\} $op \{"] $uexpr]
    } ;#-- grouping numbers and their units together
    set numUnits ""; set denUnits ""
    set multiplying 0
    set expr ""
    set where numUnits ;# "pointer" to where new units go
    #puts [list uexpr: $uexpr]
    foreach part $uexpr {
        switch -- $part {
            "+" - "-" {append expr $part}
            "*"       {append expr ")*("; set multiplying 1}
            "/"       {append expr ")/("; set where denUnits}
            default {
                foreach {value unit} [join $part] {;#break
                #puts [list part: $part value: $value unit: $unit]
                if $multiplying {
                    lappend $where $unit
                } else {
                    set targetUnit [set $where]
                    if {$targetUnit != ""} {
                        if {$unit != $targetUnit} {
                            set f $convert($targetUnit,$unit)
                            set value [expr {$value * 1.0 / $f}]
                        }
                    } else {set $where $unit}
                }
                append expr + $value
                }
            }
        }
    }
    if {$numUnits == $denUnits} {
        set units "" ;# cancel out ratios, e.g. $/$
    } else {
        set units [join $numUnits *]
        if {[llength $denUnits]} {append units / [join $denUnits *]}
    }
    puts [list expr: $expr]
    set res [expr 1.0*($expr)] ;# avoid integer division
    if {$res<1} {
        set convs [array names convert $units,*]
        if {[llength $convs]} {
            set f [lindex $convs 0] ;# simply pick first factor
            set res [expr $res * $convert($f)]
            regexp $units,(.+) $f -> units
        } ;# try to "upgrade" small results
    }
    string trim [string map {
        ".0 " " " m*m*m m3 m*m m2 ft*ft sq.ft
    } "$res $units"]
 }
 if {[file tail [info script]]==[file tail $argv0]} unitmath'test

2002-11-09 - Here's code to handle unit prefixes as used in decimal systems, e.g. m and k in

 0.001 m = 1 mm (millimeter)
 1000 m  = 1 km (kilometer)

These prefixes, which typically involve scaling by 10 to the n-th power, where n is a multiple of 3, are applicable to all units in the MKSA system (meter - kilogram - second - Ampere) and their derivations, e.g. Hz (Hertz, = 1/sec). Normalizing unit-dimensioned values is a simple operation on paper, but to implement it in Tcl involves some interesting leaps between types:

first we have a number (integer or float)
normalize to scientific representation with [format %e]
extract mantissa/exponent and their signs from the resulting string
look up a suitable unit in a pair list
finally adjust the amount (mantissa) and compose a result string

So here goes:

 proc unitprefix {amount unit} {
    set sci [format %e $amount]
    regexp {(.+)e(.)0*(.+)} $sci -> mantissa esign exponent
    set exponent $esign$exponent ;# avoid leading zeroes
    foreach {prefix order} {
        u -6 m -3 "" 0 k 3 M 6 G 9 T 12
    } {
        if {$exponent <= $order+2} break
    }
    return "[expr {$amount/pow(10,$order)}] $prefix$unit"
 }

The usual name for this is Dimensional Analysis.

See also edit