Double precision maths library

Hello Erik

The Cypress chip looked good & seemed to do all we needed (if the Keil tools had supported ANSI C we would hvave been happy). We found out too late that the Keil tools ignore double declarations. To change tracks now would costs fortune (re-designing & tooling a large multi-layer PCB). If only I we could re-run hstory with the benefit of hindsight... but sadly that isn't possible.

Anyway, I am happy that an 8-bit processor with a little extra code will eat the job (A-2B+C)/D-2E+F) in double precision floating-point once every 100ms.

thanks - Paul

Hello Erik

The Cypress chip looked good & seemed to do all we needed (if the Keil tools had supported ANSI C we would hvave been happy). We found out too late that the Keil tools ignore double declarations. To change tracks now would costs fortune (re-designing & tooling a large multi-layer PCB). If only I we could re-run hstory with the benefit of hindsight... but sadly that isn't possible.

Anyway, I am happy that an 8-bit processor with a little extra code will eat the job (A-2B+C)/D-2E+F) in double precision floating-point once every 100ms.

thanks - Paul

(if the Keil tools had supported ANSI C we would hvave been happy)
rather than missing "tools had supported" I think you missed "time to process using a slow 8 bitter".
Alas, that is water under the bridge. If you do a bit of paper calculations, you will see that fixed point with scaling really is not that big a deal.

in most cases you can, simply by knowing possible ranges, scale by fixed values.

If not, there always is the "floating fixed point" method.

let us have a look at x = ((a * b)/c)

you need one variable "fudge" set to zero before the calculation.

here we go (syntaxically incorrect)

if (a > one_half_max)
{
  a /= 2;
  fudge--;
}
if (b > one_half_max)
{
  b /= 2;
  fudge--;
}
temp = a*b
while (temp < one_half_max)
{
  temp *= 2;
  fudge ++;
}
x = temp/c

Hello Erik

Many thanks for he code ideas (gives me food for thought). I am now in the throws of coding functions with double precision floats... handling NaN, zero, +INF & -INF conditions for each variable & combination like +IN+ + -INF seems to take up most of the effort!.

best regards - Paul

I think you missed "time to process using a slow 8 bitter".<p>

Time is not an issue in some applications.

Not having the double datatype is probably just a way not to lead clueless programmers into the temptation of actually using them - which will then make them complain that their stuff does not work (especially when they try to cram heavy double crunching into ISRs).

Hello Christoph

You are right (& all the other contributors to this duscussion)... it is slow doing this on an 8-bitter. I have just started to test my first attempt & adds go from around 30us with floats to 300us for doubles (10 times slower!!). I hadn't expected such a big impact, but I am writing it in C rather than assembler (I thought C was supposed to be just about as fast as assembler!).

Back to the fun of testing...

thanks - Paul.

"I hadn't expected such a big impact..."

Maybe the $5000 is sounding a bit less unreasonable...?

"I thought C was supposed to be just about as fast as assembler!"

That does, of course, depend very largely upon your skill...
And there are some tasks for which 'C' is particularly unsuited - I guess this could well be one of them?

I hadn't expected such a big impact, but I am writing it in C rather than assembler (I thought C was supposed to be just about as fast as assembler!).<p>

This is one of the cases where hand-coded assembler will beat any kind of high-level language (even C) hands down.

Having access to the CPUs overflow- and carry-flag alone will speed up the calculations significantly since it makes checking for these conditions by doing actual comparisons unnecessary.

You can, of course, access these flags in C code ... however, this is an ugly hack at best (when you know exactly what you are doing and double-check the resulting compiler output, since the actual behavior of the compiler is pretty much undefined in this case), but much more likely it is a sure-fire way to make the program a horrible, bug-infested nightmare. (Read: Don't do it unless you're really willing to verify that the compiler output does what you want it to do, and don't expect anyone after you to do any maintenance on the code.)

If you need speed, it might be worth your while to familiarize yourself with '51 assembler (which, due to the simplicity of the CPU, isn't too bad, as you don't have to deal with pipelines and other things that make an assembler programmers life hard on more modern architectures) to optimize your double arithmetic routines.

"Maybe the $5000 is sounding a bit less unreasonable...?"

Have you seen how little of the standard math library you actually get for your $5000?

" ... double-check the resulting compiler output ... "

Of course, by the time you've done that, you might as well have writted it in assembler in the first place! :-0

The problem here is not just C.

The float implementation of C51 uses registers for float operations. It can do this because there are eight 1-byte registers and each float only uses 4 bytes. So, C51's implementation is actually pretty fast.

When you start to implement double operations, you need 8 bytes for each operand and 16 bytes for both. So, you can't do everything in registers. Assuming that you could do everything in registers, I'd expect most operations to be at least 4 times slower. Since you'll have to swap registers out to memory, a factor of 10x is probably not too bad.

Jon

Hello Jon

Thanks for the explanation - that makes perfect sense.

Coding now complete... into testing.

best regards - Paul

To change tracks now would costs fortune (re-designing & tooling a large multi-layer PCB).

well a "fortune" IS a relative term, but changhing a processor would cost one hour for my layout person and ~$500 for 2 new prototype boards from the contract manufacturer.

How must does it cost for you trying to find a way around the problem using the board you have?

Erik