# Is 0.000001 as small a number as can be worked with?

Michael Julian Lew michaell at unimelb.edu.au
Thu Dec 5 05:17:34 EST 2013

Ages ago I wrote some functions to allow arithmetic with arbitrarily large numbers of decimal places. (I think I debugged them, but it was a while ago so you should check them carefully!)

function SciForm x
--Returns the number in the form signed mantissa, comma, power of ten
put empty into tsign
if char 1 of x = "-" then
delete char 1 of x
put "-" into tsign
end if
if char 1 of x = "+" then delete char 1 of x
repeat
if char 1 of x <> "0" then exit repeat
delete char 1 of x
end repeat
if x is empty then
--value was zero!
return "0,0"
exit SciForm
end if
if "." is not in x then
put (the number of chars in x) -1 into tpower
put "." after char 1 of x
put x into tmant
else --contains .
if char 1 of x = "." then --decimal leading
replace "." with empty in x
put x into x2
put x into tmant
put "." after char 1 of tmant
repeat
if char 1 of x2 <> "0" then exit repeat
delete char 1 of x2
end repeat
if x2 is empty then
--value was zero!
return "0,0"
exit SciForm
end if
put the number of chars in x2- the number of chars in x -1 into tpower
if leadZeros > 0 then delete char 1 to leadZeros of x
put "." after char 1 of x
put x into tmant
else --decimal within
put offset(".",x)-2 into tpower
replace "." with empty in x
put "." after char 1 of x
put x into tmant
end if
end if
return tsign & tmant &"," & tpower
end SciForm

function SciFormMult x,y --returns x*y
put item 2 of x + item 2 of y into tpower
put item 1 of x*item 1 of y into tMantProd
put SciForm(tMantProd) into tProd
add tPower to item 2 of tProd
return tProd
end SciFormMult

function SciFormDivide x,y --returns x/y
put item 2 of x - item 2 of y into tpower
put item 1 of x/item 1 of y into tMantDiv
put SciForm(tMantDiv) into tDiv
add tPower to item 2 of tDiv
return tDiv
end SciFormDivide

put item 2 of x into xp
put item 2 of y into yp
put xp-yp into pdiff
put item 1 of x into xmant
put item 1 of y into ymant
multiply ymant by 10^-pdiff
put ymant + xmant into mantSum
put sciForm(mantSum) into tsum
add xp to item 2 of tsum
return tsum