Sin & Cos Functions in VHDL

Hi everybody! I'm new on this world of FPGA's.

Well I'm trying to implement the function Sin and Cos in VHDL but I have a problem because my FPGA's doesn't works with float numbers and I can't use any kind of math libraries. I did a program in C language to calculate Sin() with the Taylor series aproximation but the question is...how can I translate this program to VHDL? I don't need to calculate exactly the Sin() value...only a relative good value of it. For example: Sin(30º)=0.45 or something like that

Thanks guys for your help! (and sorry for my english...)

#include <iostream>
using namespace std;
int main()
{
int c,square,d, fat, expden;
float x, seno, y;
seno=0;
expden=1; //Value of the exponent
cout <<"Insert value of the angle"<<endl;
cin >>x;
x=x*3.1415/180; //Degree to Rad
for(c=1;c<=5;c++) //Number of iterations
{
fat=1;
for(d=1;d<=expden;d++)
{fat=fat*d;}
y=1;
for(square=1;square<=expden;square++){ //Loop to elevate to square
y=x*y;
}
if(c%2==0)
{seno=seno-(y/fat);
}
else
{seno=seno+(y/fat);
}
expden=expden+2;
}
cout <<"Sinus = ";
cout <<seno<<endl;
system("pause");
return 0;
}

have you thought about using fixed point rather than floating? FPGAs can do floating point, but you have to use IP cores to do it, and they have longer latencies compared to fixed point.

If you only need an appriximate value, I suggest you look into generating a lookup table for the sin and cos values. This is the simplest way of implementing sign and cos. Your address is the X value, and the output of the table is sin(x).

Hey, thanks for your fast reply

Well, more or less I can understand what you mean...do you have an example? no all the code but something to start...or some link to learn it how can I start? because I'm a little bit lost...sorry and thanks again!

If you need high resolution for the input angle, use 2 tables and the formula

sin(A + B) = sin A * cos B + cos A * sin B

then use

cos A = 1 - sin A

to get the final formula

sin(A + B) = sin A * sin(1 - B) + sin(1 - A) * sin B

for-->std_match

Thanks again but I need to implement this function in VHDL...and I don't need to be exactly.

I don't need to calculate exactly the Sin() value...only a relative good value of it.

Click to expand...

A look-up-table would be the most easy solution. It's usually stored in internal ROM that's available with most FPGA families.

Cordic is another common method, also taylor series can work. You have to translate the C code to a sequential VHDL process, performing one iteration step per clock cycle. This is not achievable with a VHDL for loop.

a quick example - I hope it makes sense. It should generate a rom.


Input angle is an integer that may have to be scaled by 2^n appropriatly. But the output of the table are values in the range -1 to +1

Thank you so much guys!

now I have to go...but when it works I will tell you!

Check this code:
VHDL coding tips and tricks: Simple sine wave generator in VHDL

Note that the code is not optimized. The optimized code need only one quarter of the RAm used in the above code. But it just gives a intro.

I was trying to understand all the lines of your code but I can't....
could you comment what are you doing exactly line per line? thanks!

std_match said:

sin(A + B) = sin A * cos B + cos A * sin B

then use

cos A = 1 - sin A

to get the final formula

sin(A + B) = sin A * sin(1 - B) + sin(1 - A) * sin B

Click to expand...

I know this is an electronics forum, but don't forget about math!

The first formula is correct but not the second(and even less the third). This is the correct version of the second formula:

(cos A)^2 = 1 - (sin A)^2

Before post something....try to read first question of the subject...then if you want we can discus about math. Tros de quoniem!

I would also consider a lookup table.
But if you want to use taylor series (and the sine doesn't need to be exact), with a bunch of multipliers, a couple of adders and some dividers, you can do the trick...
sin(x) = x + x^3/6 could give a result close enough (if you known beforehand what angles you're dealing with).

regards

aethor said:

I know this is an electronics forum, but don't forget about math!

The first formula is correct but not the second(and even less the third). This is the correct version of the second formula:

(cos A)^2 = 1 - (sin A)^2

Click to expand...

This is embarassing....

The second formula I wanted to use is cos A = sin(90 - A) for degrees or the equivalent for radians.

A is the coarse angle 0-90 degrees. B is the fraction part of the angle.

For the fraction angle B we don't save any memory with this formula,
so I also use a cosinus table.

This gives the final result for degrees: sin(A + B) = sin A * cos B + sin(90 - A) * sin B

Replace 90 with pi/2 for radians.

Using one table for sin A, one for sin B and one for cos(B) can save a lot of memory. For example, A could be 0.0-89.9 degrees and B could be 0.0000-0.0999 degrees. The total no of memory entries is 2900 and you can have arbitrary precision for sin(X) where X is 0.0000-89.9999
With only 1 table, 900 000 values must be stored.

I wanted to show the basic principle. There are probably smart tricks to reduce the memory usage even more.