Floating Point and Financial Software

[Bill Stewart]

Did that earlier posting really mean Digicash code uses 16-bit quantities
for moving money around?  Yow!  The API says 32 bits.

32 bits isn't enough precision; 64 bits is almost always enough.
Floating point gives you about 53 bits, which is usually enough,
but it fails badly for accounting.  The problem is that the amount
of precision in a floating-point calculation depends on the
magnitude of the numbers, so A+D and B-D may have different roundoff errors,
which is a Very Bad Thing when you're trying to move $D from A to B.
Floating point is fine for deciding how much money to move,
but you have to move the same amount in each calculation.

Otherwise, if there's no clever salami-attack programmer siphoning off the
roundoff error, little half-bits of salami get created or destroyed
on every transaction, leaving a random-walk amount of spam or anti-spam 
splattered all over the accounting system, which is Not Good.
And, of course, translating fractional decimal numbers of dollars
into floating-point binary creates another roundoff spam event,
while fixed-point systems would just use pennies or mills or microbucks
and operate integrally, only doing roundoff for multiplications
such as interest-rate calculation or /12s where you're deciding how
much money to move from account to account.*

Currency conversion is a good example - floating point may give you
the most accurate number of dollars to move for a transaction of
some integral number of yen, ecus, or zorkmids, which will generally
be non-integral.  Suppose Alice and Bob have ECU-denominated accounts,
and Alice pays Bob 1 dollar, or ECU 1/1.2299=0.8130742336775 **.
If Alice's account has, say, 3.1459265 million dollars' worth of ECUs,
and Bob's has 2.718128459045 ECUs, it's easy to lose 4.6566e-10 ECUS in
the transaction, and probably more if you didn't have decimal conversions.

64-bit integers let you use, say, millionths of a cent as your currency,
with values up to +/- 8 trillion, which will handle the US Federal Debt for
another couple of years, though more bits let you use the same code for
anything from micropayment to hyperinflated currencies.

One motivation for floating-point is historical computer power limits:
bignum arithmetics on 8086s takes lots of work, especially in languages
like Pascal or BASIC without abstract data types, and it's slow,
while the 8087 chip was far faster, and handled big enough chunks of
money for almost anybody who was doing their accounting on a PC
instead of a Mainframe.

[*My paycheck at AT&T often includes an Annual Penny Adjustment at the
end of the year to correct for the monthly payments for salaries that
aren't divisible by 3....]

[** ECU value from WSJ May 13.  Ukrainian Karbovanets were 183300/dollar.]




#					Thanks;  Bill
# Bill Stewart, stewarts at ix.netcom.com, +1-415-442-2215
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