Library of functions for complex numbers

[raymond]

I am considering the preparation of a library of functions which would cover the arithmetic, trigonometric, hyperbolic, logarithmic, exponential and a few other operations on COMPLEX NUMBERS.

The flag parameter would indicate the size of the operand(s) (and result), allowing either SINGLE, DOUBLE or EXTENDED DOUBLE precision. The flag parameter would also indicate if operand(s) (and result) are in cartesian or polar coordinates. The operand(s) source and the result destination would also be indicated by the flag parameter as from/to the FPU or memory.

A detailed Help file (API style) would also be made available along with the source code of all the modules.

The library would not be intended for beginners in assembly. The user will need to be familiar with the management of the FPU registers to insure that the required number of registers are free before calling any of the functions.

This is a survey to find out if it is worth my time and effort to prepare such a library.

Raymond

[hutch--]

Ray,

I understand that it is a lot of effort to develop functions of this type and do all the testing necessary but it would certainly be useful if such a library existed, especially if it was documented properly.

[MichaelW]

I think such a library would be useful, but it seems like you would be duplicating a lot of the functionality already available (well tested and reliable) in the CRTL.

[Vortex]

Hi Raymond,

If I remeber well, a member from Harold's forum, infinie was working on a library for complex numbers.

[raymond]

I do remember someone else trying to prepare a library for complex numbers. However, some of the posted code was a nightmare: operands were only taken from memory and sometimes transferred directly on the stack, and other times their address was transferred on the stack. (When using the FPU, it's always more efficient to use data already in FPU registers whenever possible instead of always transferring to/from memory.)

Furthermore, his approach only allowed the use of 32-bit operands, limiting the versatility when more precision would be necessary.

Raymond

[DaRetard]

Ray,

I understand that it is a lot of effort to develop functions of this type and do all the testing necessary but it would certainly be useful if such a library existed, especially if it was documented properly.

I second that :U

[raymond]

While developing my library of complex number functions, I needed something to test those functions. So, I whipped up this dialog box in the attached zip file to cover currently available functions.

If you are not familiar with complex numbers, some of the results may appear weird. If you have no knowledge of trigonometry, the result may appear even more weird.

If you think there may be errors in results, their report would be appreciated. Your contribution would also be appreciated if you think other functions may be useful.

This test box and its source file will be included in the ZLIB package when it is completed with the Help file.

Raymond

Edit: Corrected the test program after it was d/l once. The error was to accept negative numbers for the real coefficient of polar coordinates. Some functions were reporting an error and the result boxes were not being updated. When no error was reported, the displayed result would have been incorrect.

The modified version reverses a negative sign for the real coefficient of polar coordinates before feeding it to the function. If the source was z1, that edit control is also modified.

Edit2: Just before going to sleep, I realized that I had forgotten to do the same for the z2 source. The corrected test box is now attached.


[attachment deleted by admin]

[Titan]

Cool raymond, I lack the understanding of some of the math you are using in there. :red  But it looks like a job well done so far.

[raymond]

The complex number library is completed. You can get it from:

http://www.ray.masmcode.com/index.html#znum

If you don't know what complex numbers are, the above link also includes a brief description of that "complex" subject.

Within the next few weeks, I will also make my fractal program available from the same link. I'm currently reworking its help file to reflect the use of threads in the revised program. (Fractal art makes extensive use of complex numbers.)

Enjoy

Raymond

[NaN]

Hey Raymond,

Great work.  My only comment is to possibly correct for the use of negative numbers under Polar mode.  I only peaked into your zmul source, but I notice you're using FABS to clean things up.  Mathematically this is not the correct way of doing things:

-1<15 = -1 * e^j(15) = 1 * e^j(180) * e^j(15) = 1 * e^j(195) = 1<195

Your FABS operation basically is doing:

-1<15 = 1 * e^j(15) = 1<15 (Which is not correct!)

I notice in your sample program your also checking and cleaning up negative numbers before functions are applied.  My personal thought is since you already have the routines written, so you should conver negative polar radius' to positive radius' as shown above.  Likewise, another healthy check would be to convert polar angles greater than or equal to 360 degrees to its 0->359 deg equivalent (for best precision from FPU round off errors).

Anyways, Im still impressed with your handy work! I just thought I would add my 2 cents to make it better.
Regards,
:NaN:

[raymond]

Hi NaN

Thanks for the appreciation.

The only time that I would expect a negative real coefficient in polar coordinates is from user input. None of the functions would return such a negative coefficient. AFAIK, vectors should always be positive. You seem to be maintaining that the user could knowingly input a negative value for a vector along with the reverse angle. What would be a logical reason for that??
Or could a negative value be provided by some other computation (or generated by some instrument) which would thus need to be corrected appropriately??
If that is the case, how can it be differenciated from inadequate user input??

As for angles greater that 2*pi, none of the functions would return something greater. Again, could this be generated by some other computation?? And how often??

I know that complex numbers are used in scientific areas such as electricity. However, I am not familiar with any of the details of their use or generation. That's why I'm asking all those questions. There's no age limit for learning.

Raymond

[NaN]

Certainly glad to offer what I can.

I agree with you that most polar numbers have a positive value.  However, my point is there is no mathematical definition that says there shouldnt be.  Its more of a convention than a mathematical rule.

If i had a circuit that ran off a positive and negative voltage,  say an amplifier, it would be rational to have vector quantities and phase angle in both +9V<30 and -9V<30.  Phase shift is a result of non-linear devices in some combination (such as capacitors or inductors in combination with a resistance).  So the same capacitor/resistor combination acting as a separate filter on both supply voltages *could* be expressed as shown above.

However, your point is also true.  My negative voltages can be all expressed as 9V<210 instead of -9V<30.  But to be honest, the latter is easier to realize its actually a negative quantity. 

Anyways... Im not sugesting polar resultants should be expressed in negative quantities, just that the library be made as flexible as posible for negative inputs.  I can kinda see this being one of those 'murfy's law' type bugs in someone's source that take 3 days to track down, and finally relize that the numbers are being artifically adjusted.

Regards,
:NaN:

[raymond]

Thanks NaN for the explanation.

I'll modify it and inadequate input from a user will have to live with the consequences of a corrected angle.

Raymond

[raymond]

Done.

Added a paragraph in the Design Philosophy of the Help file to explain how the functions handle negative vectors. Modified the version to 1.1

Also modified the test box to do the same thing as the functions.

Raymond

[Mark Jones]

Nice work!  :U