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Electronics Pit Message Board :: Electronics Pit :: Console BASIC 1.0 :: Math
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Eddy-B
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Math
« Thread Started on Sept 17, 2008, 7:00pm »
I've picked up the project again, and started implementing more math capabilities.

Uptill now, the Console BASIC was able to do simple calculations using only the most basic operators (+ - * / %). One of my goals was to create a BASIC that allows for some more complex graphics than just plotting a few points and lines. To do circles i'd need Sine and Cosine functions, which brings me to the number system: the current Console BASIC has only 16bit integers to work with. In order to use fractions i will need either a floating point or a fixed point number system.

I soon figured that 16bit floating-point was rather useless, since it would have ridiculously little accuracy, and i don't want to use 32 bits because of the limited SRAM of the microcontroller.

So i'm left with 16bit fixed-point.
Question is: where do i put this fixed point ?
There are two favorable 16bit fixed-point systems: Q5.11 and Q8.8
The first one giving me 3 significant digits after the decimal point leaving 4 bits and a signbit for the integer part (-15.999 ~ 15.999).
The second gives me only 2 significant digits, BUT i have a full byte for the integer part (-127.99 ~ 127.99).
There is a third possibility: Q9.7 which gives me a range of -255.99 ~ 255.99 but the second digit behind the decimal point is questionable, and may have a 1-bit error after a calculation... I'd have to look into that. For now it seems like it will work fine.
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Eddy-B
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« Reply #1 on Sept 17, 2008, 8:11pm »
I've tested a CORDIC sine/cosine algorythm that i'm planning to implement in the Console BASIC, using both the Q8.8 and Q9.7 systems:

The Q8.8 system never has more than 1 bit error (due to rounding), where the Q9.7 has errors upto 2 bits.
So i think i'm going with the Q8.8 system.


I need to implement these functions for sure.. maybe others
SIN
COS
TAN
SQR ( SQR(16384) and higher will result in overflow in Q8.8)


[image] Here a test run of the SIN function with CORDIC on a Q8.8 fixed point system
« Last Edit: Sept 18, 2008, 5:38pm by Eddy-B »Link to Post - Back to Top  IP: Logged
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Eddy-B
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Re: Math
« Reply #2 on Sept 20, 2008, 9:56pm »
I've added the SIN, COS and TAN functinos to my BASIC.
I've also included two SQR variants: one that returns an integer, and one that returns a fixed-point number.

I also added conversion functions to and from fixed-point plus a ROUND function, that rounds a FP number to the nearest integer equivalent.

So far, everything works fine, be it that SIN(1o) and as a result also COS(89o) and TAN(89o) has a significant error due to the limited accuracy of the Q8.8 system.
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