precision arithmetic

[mwf]

I have a project coming up that needs some high precision math. A fixed point format like 32bit.32bit (integer.fraction) would work as would double precision floating point. Does anyone have software/experience with this that they are willing to share? The hope is to do this with ZX-24 hardware.

[spamiam]

Well, it is definitely a ZBasic question, but I suppose not specifically ZX-24.

I am glad that you suggested fixed point math. It will be easier than trying to re-create 64 bit floating point math.

You must have need some considerable precision and/or large numbers to need these sorts of variables.

When I took my chemistry courses in college, they tried to pound into my head the principles of significant digits.

I do not think I ever really got it. I saw in your other post that you want to interface to some sensors. When you deal with sensors, you definitely need to be aware of the precision and accuracy.


Precision is the number of significant digits it will send to you. The accuracy is different. This is the error in the reading. They are somewhat related.

If you have a temp sensor which reads to 1/1000 degree, but the readings vary by 1/10 degree from one measurement to the next, then you really are only sure of the temp to 1/10 degree or so. The added precision is ficticious. These extra numbers do not represent real information.

The other issue is how to combine large and small numbers when adding.

If you have only a certain number of significant digits, (e.g. 3 sig. digits), then how do you add 1000 (1.00e3) and 1.00? The answer is still 1000.

This issue of significant digits might reduce your need to such high precision, and still result in calculations that are just as meaningful as those with more digits.

-Tony

[GTBecker]

Has anyone tried the Micromega uM-FPU V3 Floating Point Coprocessor?
http://www.micromegacorp.com/umfpu-v3.html


Tom

[dkinzer]

[stevech]

[GTBecker]

> ... equivalent to the math support in ZBasic...

Certainly the common math must be equivalent except, perhaps for speed;
and its matrix functions are very inviting. It goes beyond just math,
though, in that it can be programmed to run up to 64 user functions,
each a subroutine, macro or autonomous program.

It has two 10kHz 12-bit ADCs, a few timers, external trigger. It seems
to me that it could be programmed to be a smart sensor front-end,
implementing stuff like least-squares or Kalmans without burdening the
main process after initialization.

A little off-thread, but interesting, I think.

[mwf]

A little more on why I want this for the curious. I am computing the frequency for a direct digital synthesizer which needs a 32bit fraction (of its clock frequency). There are several steps in the calculation and intermediate values can range from 32bit integers to numbers with the binary point somewhere in the middle. The final answer is 27bits of precision with the useful bits in the middle of the 32 bit fraction. A few high bits should be zero and a few low bits are don't care. I will loose a couple bits in inexact divisions in the algorithm

This is a few more bits than FP can manage unless it is double precision. I could do the calculation in 32bit fixed point since I could predetermine the binary point throughout the calculation. Keeping track of the binary point is why they invented floating point. All the intermediate values have to fit the format if it is going to be the same for the entire calculation. Everything will fit in a 32.32 format. There are DDS chips that want 48 bits for the frequency fraction. Double precision floating point is barely adequate for these.

Absolute frequency is known to whatever precision your time base allows - maybe 20 to 24 bits. Relative frequency - is the synthesizer higher or lower than some other signal source - can easily be determined to millihertz. I'm not going that far....but every bit of resolution is useful if you are matching frequency between sources.

[mikep]