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

Geoff Canyon gcanyon at gmail.com
Thu Dec 5 08:56:25 EST 2013

```Nice, thanks! I did something very similar about two days ago, except that,
since I thought LC wouldn't handle more than 6 digits of precision to the
right of the decimal point, I allowed for mantissas up to 10^7 (so that
multiplication would not overflow the standard math/numeric * function. It
turned out to be something like 100x slower than simple * which is perhaps
understandable, but given that I'm talking about doing gravity for (at
least) all the round bodies in the solar system (50 or so) for each update,
I gave it up for a different method.

You definitely need a bounds check so

1.,23

9.99999999999999945575230987042816,22

doesn't happen.

On Thu, Dec 5, 2013 at 4:17 AM, Michael Julian Lew
<michaell at unimelb.edu.au>wrote:

> 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
>
> function sciFormSubtract x,y
>    multiply item 1 of y by -1
> end sciFormSubtract
>
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```