math.h library

[mightywombat]

I need to use some trig functions in some code that I'm writing for our kiwi drive train. Does anyone know where to find C libraries (specifically the math.h)? I've found the GNU C library but didn't think it would work because it said that it only ran on GNU systems. All I need is simple sin cos and tan funcs.
peace.
bill

[EricS-Team180]

Hi.
I recall that Mike Betts and Dr. Joe had some good comments on trig functions in this thread:
http://www.chiefdelphi.com/forums/sh...highlight=trig

(named "Edurobot and arrays" from November, in this forum)

For just sin, cos and tan, you might want to make a linear table lookup.

I've downloaded the cmath library from www.netlib.org/cephes, but I haven't tried it out on the edu rc

Eric

[mightywombat]

thanks alot. i'll check it out. although i did find that math.h does in fact come with the compiler after doing a search on my comp.

[mightywombat]

whats a linear table lookup?

[seanwitte]

Originally Posted by mightywombat

whats a linear table lookup?

The only issue with a table lookup is that you're confined to the values you put in your table.

You can use an approximation called the Maclaurin series for Sine, Cosine, and Tangent. The formulas are listed below. The angle, x, is in radians. There are 2*Pi radians in a circle, so 360 degrees = 2*Pi radians. These formulas match the actual Sine, Cosine, and Tangent to three decimal points.

Sine(x) = x - x^3/3! + x^5/5!
Cosine(x) = 1 - x^2/2! + x^4/4!
Tangent(x) = x + 2x^3/3! + 16x^5/5!

This is a special case of the Taylor series, which I'll leave to you look up. The Taylor series would allow you to reduce the number of terms you're calculating by using know values of Sin/Cos/Tan near the angle you're looking for.

The ! is the factorial operator and just means to take the number and multiple it by every number between it and 0.

3! = 3*2*1 = 6
4! = 4*3*2*1 = 24

[Mike Betts]

A Taylor Series expansion solution for sine and cosine would look like this (if you are doing floating point arithmetic) with angle in radians:

angle_pow_2 = angle * angle;

sin_angle = -0.0001984127 + (angle_pow_2 * 0.0000027557);
sin_angle = 0.0083333333 + (angle_pow_2 * sin_angle);
sin_angle = -0.1666666667 + (angle_pow_2 * sin_angle);
sin_angle = 1.0 + (angle_pow_2 * sin_angle);
sin_angle = angle * sin_angle;

cos_angle = -0.0013888889 + (angle_pow_2 * 0.0000248016);
cos_angle = 0.0416666667 + (angle_pow_2 * cos_angle);
cos_angle = -0.5000000000 + (angle_pow_2 * cos_angle);
cos_angle = 1.0 + (angle_pow_2 * cos_angle);

Since our team will be using integer arithmetic exclusively on the PIC, we generated a table using Excel (saved as a CSV file) and imported into the PIC code as a table of constants existing in ROM space.

Note that only sine from 0 to 90 degrees is required as the function is symmetrical. Both cosine and tangent can be mathematically generated from the sine.

The problem with math.h is that it returns a double and you really do not want to do floating point on your 'bot. The nice thing about a table lookup is that you control the format of the stored (returned) variable. In our case, an integer in 2FX14 format.

Hope this helps.

[mightywombat]

sweeeeetness. this rocks. i've got a few questions.
do you suggest reading all of the values from 0-90 (in fact you'd only need 0-45 because sin (46-90) = 1 - sin (0-45)) into a matrix or actually calculating them?
I'm also confused as to the difference between ROM and RAM space. I know what the acronyms stand for but thats about it.
why no floating points? is it too much for it to handle? are there any other things i should stay away from calculation/variable wise?

[Kevin Watson]

Originally Posted by mightywombat

are there any other things i should stay away from calculation/variable wise?

Division is very painful without hardware support.

-Kevin

[mightywombat]

whoa.. that CORDIC is rather confusing stuff. I'm going to play with it and see if i can figure it out a little more.
so you are saying that I should stay away from dividing two numbers?
(the question sounds dumb but i'm very surprised that it would be so tough)
I remember reading that it can handle addition VERY well but doesn't do much else as quick. thanks for the quick reply.

[Kevin Watson]

Originally Posted by mightywombat

whoa.. that CORDIC is rather confusing stuff. I'm going to play with it and see if i can figure it out a little more.

Yeah, you gotta be a math geek to like the CORDIC .

Originally Posted by mightywombat

so you are saying that I should stay away from dividing two numbers? (the question sounds dumb but i'm very surprised that it would be so tough) I remember reading that it can handle addition VERY well but doesn't do much else as quick. thanks for the quick reply.

Well, I shouldn't have made such a generalization. Integer division by powers of two is very fast (if the compiler is designed for such an optimization) because you only need to do a binary right shift to divide a number by two (multiplication works by shifting left). Division of two eighty-bit IEEE floating-point numbers on an eight-bit microcontroller is very painful.

-Kevin

[Kevin Watson]

Originally Posted by Kevin Watson

Well, I shouldn't have made such a generalization. Integer division by powers of two is very fast (if the compiler is designed for such an optimization) because you only need to do a binary right shift to divide a number by two (multiplication works by shifting left). Division of two eighty-bit IEEE floating-point numbers on an eight-bit microcontroller is very painful.

-Kevin

I forgot to point out that with timer support, it would be very easy to profile the different algorithms to see which is most efficient on the PIC18F8520. I just happened to have written some example timer code that might help.

-Kevin

[deltacoder1020]

Originally Posted by Kevin Watson

Well, I shouldn't have made such a generalization. Integer division by powers of two is very fast (if the compiler is designed for such an optimization) because you only need to do a binary right shift to divide a number by two (multiplication works by shifting left). Division of two eighty-bit IEEE floating-point numbers on an eight-bit microcontroller is very painful.

you could always hardcode the bitshift for the division to make sure that the optimization is in, even if the compiler doesn't automatically do it - just replace "x / 16" with "x >> 4"

[Mike Betts]

Originally Posted by deltacoder1020

you could always hardcode the bitshift for the division to make sure that the optimization is in, even if the compiler doesn't automatically do it - just replace "x / 16" with "x >> 4"

"x / 16" with "x >> 3"

[Mike Betts]

Originally Posted by mightywombat

do you suggest reading all of the values from 0-90 (in fact you'd only need 0-45 because sin (46-90) = 1 - sin (0-45)) into a matrix or actually calculating them?

Check your math... I think that 0-90 degrees is the minimum you want to try.

Originally Posted by mightywombat

I'm also confused as to the difference between ROM and RAM space. I know what the acronyms stand for but thats about it.

RAM is cleared to zero (at best) or random noise after a power up. ROM is non-volatile.

Originally Posted by mightywombat

why no floating points? is it too much for it to handle? are there any other things i should stay away from calculation/variable wise?

I would suggest you do a search of these fori (I still like that word, Dr. J!) for other discussions on floating point. Bottom line: The PIC18C is not a floating point processor...

[EricS-Team180]

Originally Posted by Mike Betts

In our case, an integer in 2FX14 format.

ummm...that's a new one me or maybe I'm just missing something obvious...

just what is an FX format? I typically think of x has hex and f as floating point???

Thanks,
Eric