Reading from the SIN table in ROM

Harprit

When I use

sineval[Y]:=(word[(($E000+(2047)*Y/90))]*10000/65536)

to read from the sine tables in ROM, I do not get values that are
exact for some values from 0 to 90 in steps of 1.
This is for fast circular move segments for a CNC machine.

I should get numbers between 0 and 10000 so I can use integer math.
What am I doing wrong?

H

.

Tracy Allen

Does the value of Y go from 0 to 90 as integer?

The precision of the fraction 10000/65536 can be improved by using the ** operator. Note that 655360000 / (2^32) = 100000/65536. The sine table goes all the way 0 to 90 inclusive with a word at location 2048, so use 2048 instead of 2047.

sineval[Y] := word[ $E000][ 2048*Y/90] ** 655360000

Also maybe better roundoff in the division by 90.

sineval[Y] := word[ $E000][ (4096*Y/90 + 1)/2] ** 655360000

Harprit

Yes it goes from 0 to 90 as an integer.

I will put your suggestions in my program and get back to the forum.
Thanks
H

Harprit

We need to take it in steps so we can see where I go wrong.

The manual says there are 2049 16 bit values in the table starting at $E000
These 2049 values (in 4098 bytes) cover 90 degrees inclusive but go to a wee bit under 90 degrees
So each degree starting address is 2049/90 words apart. (90 16 bit values =180 8 bit values).
The best value for 45 degrees would start at byte $E000+1024 or $E000+1025 or be the average of the two values.
So the formula for each degree is

sine(Y):=(word[(($E000+(2049)*Y/45))]*10000/65535)

This works fine but there is an error of between -2 and +7 parts per 10000 on the results as compared with my HP calculator.
This works OK for a CNC machine but it would be better if it could be eliminated. We need to get things as right as possible.
There will be plenty of other mechanical problems.

Using your formula

sineval[Y] := word[ $E000+2048*Y/90] ** 655360000

modified to

sineval[Y] := word[ $E000+2048*Y/45] ** 655360000

works, the error shifts but the error is not eliminated.

H

Dave Hein

Since the table only has about 2000 entries you would expect an error of 1 out of 2000, which which is 5 out of 10000. You could get better results by adding the fractional bits times the slope. The slope of sin(x) is cos(x), so you could look up the slope from the table also. However, that's quite a bit of extra computation, and you might be better off using floating point routines running in a separate cog if you need higher accuracy.

Tracy Allen

Harprit, take a look at this thread and links within it, maybe some good insight for you.
http://forums.parallax.com/showthread.php/117437-Sin-Table-Printout

I don't understand, how did you manage
word[ $E000+2048*Y/90]
modified to
word[ $E000+2048*Y/45]
Those are quite different!
edit: the addresses have to be even numbers word[ $E000 + even number]
or use this syntax, word[ $E000][2048*Y/90]

My roundoff, word[ $E000][((4096*Y/90+1)/2)] was attempt to cut the error in half by rounding both up and down. To improve the result, I agree with Dave that you will need to interpolate.

Ariba

Here is a simple interpolating sine table read out:

    i := 65536*Y/90
    p := i>>4 + $E000
    i := i & 31
    sineval[Y] := ((word[p+2]-word[p])*i/32 + word[p]) ** 655360000

Andy

Mark_T

Harprit wrote: »

We need to take it in steps so we can see where I go wrong.

The manual says there are 2049 16 bit values in the table starting at $E000
These 2049 values (in 4098 bytes) cover 90 degrees inclusive but go to a wee bit under 90 degrees
So each degree starting address is 2049/90 words apart. (90 16 bit values =180 8 bit values).

No, the table covers 0 to 90 degrees inclusive, so the correct factor is 2048/90. The $FFFF value
represents 1.0, not 0.999985

Try

sineval[Y] := word[ $E000][ (4096*Y/90 + 1)/2] ** 655370000 ' or
sineval[Y] := word[ $E000][ (4096*Y/90 + 1)/2] * 10000 / 65535

Yes, 655370000 is correct, its the closest integer to 10000 * 2^32 / 65535

Mark_T

By the way why it's not actually necessary to use sin/cos to do circles - Bressenham's and similar DDA algorithms will do.
Yes, there is an issue with constant velocity, but there are ways to handle that.

With the Prop the sin table is extremely useful of course, and good enough for all but most exacting CNC applications. However
the multiply you need to do after looking up the table is a big hit.

Harprit

Thanks to all for the enlightening help.
I continue to be amazed by the Prop forum.
H

Phil Pilgrim (PhiPi)

Late to the party, but here's a thread that might be of interest:

http://forums.parallax.com/showthread.php/116047-Renormalizing-the-Sine-Table

-Phil