Re: The Crisis with Remailers
At 11:58 1996-05-22 +0200, bryce@digicash.com wrote:
Matts, _floating_ point numbers are _not_ useful if you want to handle a number with a lot of precision, nor indeed, if you want to be able to _know_ the precision! If you have a number that represents money, you want to know the precision!
As I said yesterday, there are in fact people dealing with billions in all major currencies that keep their money in 64 bit floats. The precision is far better than anything you can do in 32 bit integers. Trust me, this is a fact and can easily be proven.
I shall try to refrain from taking umbrage at your comment that DigiCash is "not real".
The "get real" was a pun on floats. Many languages, such as Pascal, calls them real numbers. Sorry I forgot the smiley.
Also that DigiCash doesn't "do" currency. What could you possibly mean by that?
In my client (2.1.5a MT) there is no way to do currency conversion. If I go to a FIM or DEM merchant I can't buy anything in the store. This will probably change in the near future when a new client is released, and then we'll have the question of how to represent these currencies in one wallet. What do you think will happen if you have a one italian lira coin and you try to deposit it with Mark Twain's USD account? With integer math it won't be pretty.
For further reading on floating point and other representations of numbers in computing, I recommend any good introductory university text on mathematical computing. Sorry I don't have mine handy or I'd give you a specific reference.
Maybe you should start looking for it. You'll need it when the lira arrives... Regards, Matts
Despite the ugliness of floating point arithmetic (lack of associativity, for example) and my general distaste for it, I would have to agree that 64-bit floats are higher precision than 32-bit fixed-points, since more than half the bits are mantissa. Do major currency traders really store money as 64-bit floats? It surprises me. By the way, I thought the "get real" pun was funny and not at all disparaging. But I hope that "get rational" is good enough for currency exchange.
R.Hirschfeld@cwi.nl writes:
Despite the ugliness of floating point arithmetic (lack of associativity, for example) and my general distaste for it, I would have to agree that 64-bit floats are higher precision than 32-bit fixed-points, since more than half the bits are mantissa.
However, accounting systems DO NOT use 32 bit fixed point arithmetic. One client of mine had around $10Billion under management. Do you think they were doing their accounting on a system that could only deal with fixed point numbers of 45Million or so? Hell, individual trades are larger. Floating point systems are built to do approximate math on a very wide range of number sizes. Accounting systems require exact math -- down to the cent. Floats aren't suitable. Anyone who needs to understand why should go off and read Knuth, Volume 2. {erru
Date: Wed, 22 May 1996 15:04:04 -0400 From: "Perry E. Metzger" <perry@piermont.com>
Floating point systems are built to do approximate math on a very wide range of number sizes. Accounting systems require exact math -- down to the cent. Floats aren't suitable.
I completely agree. But are the usual fixed-point representations adequate for exchange rates, where it's not a matter of "down to the cent" but of ratios of cents and centimes? Is an exact representation of rationals (e.g., pairs of integers) needed?
R.Hirschfeld@cwi.nl writes:
Date: Wed, 22 May 1996 15:04:04 -0400 From: "Perry E. Metzger" <perry@piermont.com>
Floating point systems are built to do approximate math on a very wide range of number sizes. Accounting systems require exact math -- down to the cent. Floats aren't suitable.
I completely agree. But are the usual fixed-point representations adequate for exchange rates, where it's not a matter of "down to the cent" but of ratios of cents and centimes?
It depends on the number of significant figures you need to represent. Forex usually involves numbers with five significant figures, which can be represented fairly conveniently in fixed point. Perry
Perry Writes:
Floating point systems are built to do approximate math on a very wide range of number sizes. Accounting systems require exact math -- down to the cent. Floats aren't suitable.
Calling floating point math "approximate" is a bit of a misnomer. Floating point numbers all correspond to exact points on the real number line. The floating point number taken as the result of an operation, if that result is not another floating point number, is always chosen consistantly in a way which has minimum error and zero bias. Floating point numbers can be used to do exact integer arithmetic quite easily. A 48 bit mantissa can represent 14 decimal digit signed integers with no loss of precision, and $999,999,999,999.99 is more than enough magnitude for most bean counters. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd@netcom.com $ via Finger. $
On Wed, 22 May 1996, Mike Duvos wrote:
Perry Writes:
Floating point systems are built to do approximate math on a very wide range of number sizes. Accounting systems require exact math -- down to the cent. Floats aren't suitable.
Calling floating point math "approximate" is a bit of a misnomer. Floating point numbers all correspond to exact points on the real number line. The floating point number taken as the result of an operation, if that result is not another floating point number, is always chosen consistantly in a way which has minimum error and zero bias.
If floating point is implemented properly in *both* hardware and software, then the claim is valid. I have seen too many instances of floating point support and/or emulation from people like MS and Borland that would scare the bejeebers out of most competent programmers
Floating point numbers can be used to do exact integer arithmetic quite easily. A 48 bit mantissa can represent 14 decimal digit signed integers with no loss of precision, and $999,999,999,999.99 is more than enough magnitude for most bean counters.
Again, exact integer artimetic derived from floating point is dependant on how well the floating point "behaves". Mainframes dont suffer the same fate as some of the uP's do.
-- Mike Duvos $ PGP 2.6 Public Key available $ mpd@netcom.com $ via Finger. 7 $
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Mike: On Wed, 22 May 1996, Mike Duvos wrote:
quite easily. A 48 bit mantissa can represent 14 decimal digit signed integers with no loss of precision, and $999,999,999,999.99 is more than enough magnitude for most bean counters.
Not when that bean counter is a judge chasing down the $ 999 999 999 999.999 999 decimal, for an interest rate calculation. << You try defending that one to a judge who is looking for a reason to dismiss your case, with prejudice. >> xan jonathon grafolog@netcom.com ********************************************************************** * * * Opinions expressed don't necessarily reflect my own views. * * * * There is no way that they can be construed to represent * * any organization's views. * * * ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ * * * http://members.tripod.com/~graphology/index.html * * * ***********************************************************************
-----BEGIN PGP SIGNED MESSAGE----- Hi again Matts, This conversation has been thorough enough already that perhaps it is time to take it off-lists. I think that you are unaware of the difference between floating point numbers (e.g. the 'IEEE 754' 32 bit floating point number spec) and fixed-point numbers which are used to represent amounts other than "units" of a thing. (E.g., use a 32-bit integer and say that it represents millionths of an apple. You can now represent anything from 0.000001 apples to 4294.967295 apples with no loss of precision.) There are also many other ways to represent different kinds of numbers, including multi-precision integers and rationals, imaginary and complex numbers, etc. I reiterate that floating point numbers are for convenience when dealing with values whose precision is unimportant. Anyone who encodes real money into a float is dumb.
What do you think will happen if you have a one italian lira coin and you try to deposit it with Mark Twain's USD account? With integer math it won't be pretty.
It will be _very_ pretty. Stay tuned. :-) Regards, Bryce -----BEGIN PGP SIGNATURE----- Version: 2.6.2i Comment: Auto-signed under Unix with 'BAP' Easy-PGP v1.1b2 iQB1AwUBMaMp1kjbHy8sKZitAQFlBwMAwhwLBvPvKMwjzWMj/HMDrzlws9CRwPxd ylBIIWCnaChUafO9Gbjptd12A+nRlwgMJ27N+aY5GCcUu6jlVZz2j7jtxOqMMwNm VFHs0itk7hotPGAoFBF4i4iB0YG1C0Ih =y5zo -----END PGP SIGNATURE-----
Matts Kallioniemi writes:
What do you think will happen if you have a one italian lira coin and you try to deposit it with Mark Twain's USD account? With integer math it won't be pretty.
Fixed point math is not ugly. It is the only way to go if you are representing currency and thus cannot afford loss of precisions -- and isn't particularly onerous to use. Perry
participants (7)
-
bryce＠digicash.com -
jonathon -
Matts Kallioniemi -
mpd＠netcom.com -
Paul S. Penrod -
Perry E. Metzger -
R.Hirschfeld＠cwi.nl