Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!samsung!brutus.cs.uiuc.edu!jarthur!rspangle
From: rspangle@jarthur.Claremont.EDU (Randy Spangler)
Newsgroups: comp.graphics
Subject: Re: Mandelbrot algorithm summary
Keywords: mandelbrot algorithm
Message-ID: <4212@jarthur.Claremont.EDU>
Date: 7 Feb 90 18:20:12 GMT
References: <5480@vax1.tcd.ie> <536@dino.cs.iastate.edu>
Organization: Harvey Mudd College, Claremont, CA 91711
Lines: 44

>In article <5480@vax1.tcd.ie> cbuckley@vax1.tcd.ie (Colm Buckley) writes:
>      
>    [using 32bit fixed point for mandelbrot computations]
>
>}The numbers are stored multiplied by 2**28, ...
> 
>    [addition and subtraction work ok, but muliply...]
>
>}poses a problem. When two numbers stored in this fashion are multiplied
>}together, the result will be 2**28 times too big ( (x * 2**28) * (y * 2**28) =
>}(x * y * 2**56), not (x * y * 2**28). Therefore, when multiplication is
>}necessary, the multiplicand and multiplier must both be divided by (2**14).
>}This is easily and quickly accomplished by right-shifting x and y by 14 bits
>}(x >> 14 = x / (2**14) ).

Well, those of us with 80386's can multiply two 32-bit numbers and get a 
64-bit number in EDX:EAX (first 32 in EDX, next 32 in EAX) with the 
following code:

	MOV	eax,number1
	IMUL	number2

where number1 and number2 are 32-bit memory operands.  I don't know if the
68000 chips have similar instructions, but I would assume so.

The next is pretty system-specific (IBM 80x87 only).  I have a program I
wrote in assembly to plot mandelbrot sets using the floating point chip.
I optimized it so that all the calculations are done using the chip's
registers - no conversion to regular memory operands.  It's slower than 
32-bit integer math, but more accurate than any other program I've seen for
the IBM at high resolution, since the numbers never leave the 10-byte format
that the 80x87 stores them in (as opposed to 8-byte long floating point type
for memory operands).

Since the code only applies to a small segment of the readers, I'll email
copies to interested people, unless I get so many responses that I think it's
worth posting.


-- 
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|    Randy Spangler                    |    The less things change, the    |
|    rspangle@jarthur.claremont.edu    |    more they remain the same      |
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