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Re: gEDA-user: 23.99mil instead of 24mil in PCB

At 11:10 3-4-2006, you wrote:

Logic cannot be used to describe floating point numbers. We prove this by
contradiction. Let's suppose logic could be used to describe floating
point numbers. First we assume that the conversion algorithm from the
floating point number to the on-screen representation is deterministic,
this can be easily verified from the glibc source. From my experiment we
can then see that
a!=a
We also use an obvious tautology
a=a
and we got a contradiction. QED. [X]

Floating point numbers are like a remnant from the era of analog
computers with their ubiquitous noise - you write 1V into a sampling
amplifier and when you read once, you get 1V, second time you get 0.999V
etc.

I guess the name floating point numbers is derived from the fact that
the point on the number axis representing a variable value is constantly
moving up and down - like floating on a sea.

Floating point numbers are perfectly deterministic. Programmers are notoriously unwilling to think about the consequences of floating point to fixed point conversion, and equally unwilling to write their "equality" tests to cope with the consequences of the (perfectly determined) conversion procedures, but that is a problem in the formulation of the programmers (too lazy) rather than the number system.

Your notion that the floating refers to a constantly changing magnitude is poetic. but wrong.

The element that floats in a floating point number is the position of the decimal point - and in fact the crucial feature of floating point numbers was the changeover to a mantissa and exponent format, which allowed you to represent very small and very large numbers within a manageable number of bits.

--
Bill Sloman, Nijmegen