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Forums > C64 Coding > How easy is it to calculate sine tables from the bare bones in ML?
2008-08-05 09:52
Conrad

Registered: Nov 2006
Posts: 849
How easy is it to calculate sine tables from the bare bones in ML?

Hi!

I'd like to have a go at coding my own routine of calculating sine/cosine tables without use of the BASIC interpreters (pi, sin(), etc) and just use pure ML instead.

Can I ask, how easy (or how SMALL) is this to do? Do I need to do additional algorithms like factorial or are there KERNAL routines for that (if any)? Multiplication code is no problem as I've seen articles on those, I'm just thinking about the rest of math involved with sine calculation.

Thanx in advance.
 
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2008-08-05 11:36
Skate

Registered: Jul 2003
Posts: 494
@Cruzer: So, your source code comment is the liar! ;)

Well, I like using plain basic for sinus calculations (slow but more flexible with ranges) in small sized intros and precalculated tables in bigger projects.
2008-08-05 13:53
Cruzer

Registered: Dec 2001
Posts: 1048
"generate sine" - yeah, guess that's a stretch. :)

Well, sometimes these parabolic "sines" work pretty good, and other times it's obvious to see that something's wrong, especially in the middle, where it's hard to get the two parabolas to meet precisely. But this is based on 256b routines - it might be possible to tweak it better if the code doesn't have to be super small.
2008-08-05 15:33
doynax
Account closed

Registered: Oct 2004
Posts: 212
Quote: Anyone have an example on how to access the BASIC routines from asm to generate a sine? Also how compact is such a routine, are we talking like 50 bytes or 500 bytes?

Here's the best I could come up with on short notice (31 bytes):
table	= $0400		;; preferably a low page

loop	lda #<index
	ldy #>index
	jsr $bba2
	
	jsr $e277

	lda $61
	adc #7
	sta $61

	jsr $bc9b
	lda $65

index	.byte $90
	.byte $00
	sta table

	inc *-2
	bne loop
I suspect that the float-to-int portion could be shortened by making use of some sneaky ROM function somewhere. Interesting challenge though, anyone got a shorter implementation?
2008-08-05 18:03
Frantic

Registered: Mar 2003
Posts: 1648
@Doynax: Would it be OK to post that on Codebase?
2008-08-05 18:29
doynax
Account closed

Registered: Oct 2004
Posts: 212
Quote: @Doynax: Would it be OK to post that on Codebase?

Look.. It's a code snippet posted on a public forum, of course you can use it. Feel free to modify it, sell it, claim you wrote it yourself or print it out and use it as toilet paper.
There are few things as obnoxious as tutorial authors and the like thinking they've got some sort of claim to your program when you based your code on their work..

By the way personally I'd like to see a decent tutorial on the BASIC floating point library in the code base. This is a good beginning but it's incomplete and full of errors. For instance I'd like to know why taking sin(0) seems to crash the program.
2008-08-05 19:23
Frantic

Registered: Mar 2003
Posts: 1648
okok, I posted it and wrote that it was created by some lamer named Doynax (just kidding).
2008-08-05 22:08
Shadow
Account closed

Registered: Apr 2002
Posts: 355
Nice explanation that accompanied the codebase64 post, much appreciated!
2008-08-05 22:53
Frantic

Registered: Mar 2003
Posts: 1648
Credits for those goes to (some lamer called) Doynax. ;)
2008-08-06 02:39
doynax
Account closed

Registered: Oct 2004
Posts: 212
I managed to reduce the bloody thing by two bytes (to 29) by converting to integer through adding a 'magic' float. Well, it's actually a piece of code in the BASIC ROM but it works well enough as a float..
table	= $0400		;; Preferably a low page. Must be paged aligned!

loop	lda #<index	;; Load 5-byte float at 'index' into FAC, the fraction
	ldy #>index	;; of which is stepped between 0/256..255/256.
	jsr $bba2	;; However an integer bias is also added in order to fix
			;; the exponent and make hence it possible to increment the
			;; fraction as a normal binary byte, e.g. a version of the
			;; classic x86 float-to-int conversion trick.
	
	jsr $e277	;; Now calculate sine of FAC. Except skip the initial part
			;; of the BASIC function which divides by 2*PI to get
			;; a fraction out of radians since we've already got one.
			;; The integer bias is taken care by BASIC since sin()
			;; is supposed to be periodic.

	lda #<bias	;; Convert the output in FAC from a float in -1..+1 to a
	ldy #>bias	;; fixed-point value in -128..+127 at the LSB of the
	jsr $b867	;; mantissa by employing the same trick as before of
	lda $65		;; adding a high integer bias.

index	.byte $90	;; This is both a float *and* a piece of code. The exponent
	.byte $00	;; ($90 corresponds to 2^16) fixes our 8-bit fraction as the
	sta table	;; third byte of the mantissa and STA address' LSB (don't
			;; forget that BASIC floats are big-endian!). And $90/$00
			;; interpreted as code simply correspond to a harmless BCC *+2.
			;; Note that while the STA's opcode is an integer part which
			;; shouldn't affect the result, the table's high byte *does*
			;; serve as a small offset shifting the result by up to one
			;; index value. Some might even argue that placing the table
			;; at $8000 would produce the 'proper' rounding.

	inc *-2
	bne loop

bias	= $befa		;; A float with an exponent of $99 (2^25) and an LSB of
;;	.byte $99	;; zero is used to convert the output to binary. Such byte
;;	.byte $02	;; sequences can be found in six places in the BASIC/Kernal
;;	.byte $01	;; ROMs, at $befa/$bf04/$bf09/$fd53/$fd56/$ff38.
;;	.byte $a9	;; A version with an LSB of $80 would have been useful to
;;	.byte $00	;; create unsigned output (e.g. between $00 and $ff with the
			;; origin at $80) but unfortunately doesn't seem to exist.
2008-08-06 07:30
Cruzer

Registered: Dec 2001
Posts: 1048
Nice, much smaller than my faked routine. But how fast is it compared to Basic?
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