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No commits in common. "main" and "status" have entirely different histories.
9 changed files with 299 additions and 1357 deletions
1
.gitignore
vendored
1
.gitignore
vendored
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@ -1,4 +1,3 @@
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*.o
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*.xex
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tables.s
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.DS_Store
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2
.mailmap
2
.mailmap
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@ -1,2 +0,0 @@
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Brooke Vibber <bvibber@pobox.com>
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Brooke Vibber <bvibber@pobox.com> <brion@pobox.com>
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8
Makefile
8
Makefile
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@ -2,17 +2,13 @@
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all : mandel.xex
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mandel.xex : mandel.o tables.o atari-asm-xex.cfg
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ld65 -C ./atari-asm-xex.cfg -o $@ mandel.o tables.o
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%.xex : %.o
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ld65 -C atari-asm-xex.cfg -o $@ $<
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%.o : %.s
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ca65 -o $@ $<
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tables.s : tables.js
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node tables.js > tables.s
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clean :
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rm -f tables.s
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rm -f *.o
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rm -f *.xex
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@ -1,28 +0,0 @@
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FEATURES {
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STARTADDRESS: default = $2E00;
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}
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SYMBOLS {
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__STARTADDRESS__: type = export, value = %S;
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}
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MEMORY {
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ZP: file = "", define = yes, start = $0082, size = $007E;
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MAIN: file = %O, define = yes, start = %S, size = $4000 - %S;
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# Keep $4000-7fff clear for expanded RAM access window
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TABLES: file = %O, define = yes, start = $8000, size = $a000 - $8000;
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# Keep $a000-$bfff clear for BASIC cartridge
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}
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FILES {
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%O: format = atari;
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}
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FORMATS {
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atari: runad = start;
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}
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SEGMENTS {
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ZEROPAGE: load = ZP, type = zp, optional = yes;
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EXTZP: load = ZP, type = zp, optional = yes; # to enable modules to be able to link to C and assembler programs
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CODE: load = MAIN, type = rw, define = yes;
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RODATA: load = MAIN, type = ro optional = yes;
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DATA: load = MAIN, type = rw optional = yes;
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BSS: load = MAIN, type = bss, optional = yes, define = yes;
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TABLES: load = TABLES, type = ro, optional = yes, align = 256;
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}
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25
readme.md
25
readme.md
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@ -14,37 +14,30 @@ Non-goals:
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Enjoy! I'll probably work on this off and on for the next few weeks until I've got it producing fractals.
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-- brooke, january 2023 - december 2024
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-- brion, january 2023
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## Current state
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Basic rendering is functional, with interactive zoom/pan (+/-/arrows) and 6 preset viewports via the number keys.
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Basic rendering is functional, but no interactive behavior (zoom/pan) or benchmarking is done yet.
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The 16-bit signed integer multiplication takes two 16-bit inputs and emits one 32-bit output in the zero page, using the Atari OS ROM's floating point registers as workspaces. Inputs are clobbered.
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The 16-bit signed integer multiplication works; it takes two 16-bit inputs and emits one 32-bit output in the zero page, using the Atari OS ROM's floating point registers as workspaces. Inputs are clobbered.
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* 16-bit multiplies are decomposed into 4 8-bit unsigned multiplies and some addition
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* an optimized case for squares uses a table of 8-bit squares to reduce the number of 8-bit multiplication sub-ops
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* when expanded RAM is available as on 130XE, a 64KB 8-bit multiplication table accelerates the remaining multiplications
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* without expanded RAM, a table of half-squares is used to implement the algorithm from https://everything2.com/title/Fast+6502+multiplication
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The main loop is a basic add-and-shift, using 16-bit adds which requires flipping the sign of negative inputs (otherwise you'd have to add all those sign-extension bits). Runs in 470-780 cycles depending on input.
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The mandelbrot calculations are done using 3.13-precision fixed point numbers with 6.26-precision intermediates.
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The mandelbrot calculations are done using 4.12-precision fixed point numbers. It may be possible to squish this down to 3.13.
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Iterations are capped at 255.
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The pixels are run in a progressive layout to get the basic shape on screen faster.
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## Next steps
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There is a running counter of ms/px using the vertical blank interrupts as a timer, used to track our progress. :D
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Add a running counter of ms/px using the vertical blank interrupts as a timer. This'll show how further work improves it!
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There's a check for cycles in (zx,zy) output when in the 'lake'; if values repeat, they cannot escape. This is a big time saver in fractint.
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Check for cycles in (zx,zy) output when in the 'lake'; if values repeat, they cannot escape. This is a big time saver in fractint.
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There's some cute color cycling.
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I may be able to do a faster multiply using tables of squares for 8-bit component multiplication.
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## Deps and build instructions
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I'm using `ca65` as a macro assembler, and have a Unix-style `Makefile` for building. Should work fairly easily on Linux and Mac. Might work on "raw" Windows but I use WSL for that.
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Currently produces a `.xex` executable, which can be booted up in common Atari emulators and some i/o devices.
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## Todo
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See ideas in `todo.md`.
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50
tables.js
50
tables.js
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@ -1,50 +0,0 @@
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function db(func) {
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let lines = [];
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for (let i = 0; i < 256; i += 16) {
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let items = [];
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for (let j = 0; j < 16; j++) {
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let x = i + j;
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items.push(func(x));
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}
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lines.push(' .byte ' + items.join(', '));
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}
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return lines.join('\n');
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}
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let squares = [];
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for (let i = 0; i < 512; i++) {
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squares.push(Math.trunc((i * i + 1) / 2));
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}
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console.log(
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`.segment "TABLES"
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.export mul_lobyte256
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.export mul_hibyte256
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.export mul_hibyte512
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.export sqr_lobyte
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.export sqr_hibyte
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; (i * i + 1) / 2 for the multiplier
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.align 256
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mul_lobyte256:
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${db((i) => squares[i] & 0xff)}
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.align 256
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mul_hibyte256:
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${db((i) => (squares[i] >> 8) & 0xff)}
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.align 256
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mul_hibyte512:
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${db((i) => (squares[i + 256] >> 8) & 0xff)}
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; (i * i) for the plain squares
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.align 256
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sqr_lobyte:
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${db((i) => (i * i) & 0xff)}
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.align 256
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sqr_hibyte:
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${db((i) => ((i * i) >> 8) & 0xff)}
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`);
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41
testme.js
41
testme.js
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// ax = (a + x)2/2 - a2/2 - x2/2
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function half_square(x) {
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return Math.round(x * x / 2) & 0xffff >>> 0;
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}
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function mul8(a, b) {
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let result = half_square(a + b) & 0xffff;
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result = (result - half_square(a)) & 0xffff;
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result = (result - half_square(b)) & 0xffff;
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result = (result + (b & a & 1)) & 0xffff;
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return result >>> 0;
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}
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function mul16(a, b) {
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let ah = (a & 0xff00) >>> 8;
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let al = (a & 0x00ff) >>> 0;
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let bh = (b & 0xff00) >>> 8;
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let bl = (b & 0x00ff) >>> 0;
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let result = (mul8(al, bl) & 0xffff) >>> 0;
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result = ((result + (mul8(ah, bl) << 8)) & 0x00ffffff) >>> 0;
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result = ((result + (mul8(al, bh) << 8)) & 0x01ffffff) >>> 0;
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result = ((result + (mul8(ah, bh) << 16)) & 0xffffffff) >>> 0;
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return result;
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}
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let max = 65536;
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//let max = 256;
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//let max = 128;
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//let max = 8;
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for (let a = 0; a < max; a++) {
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for (let b = 0; b < max; b++) {
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let expected = Math.imul(a, b) >>> 0;
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//let actual = mul8(a, b);
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let actual = mul16(a, b);
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if (expected !== actual) {
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console.log(`wrong! ${a} * ${b} expected ${expected} got ${actual}`);
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}
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}
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}
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17
todo.md
17
todo.md
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things to try:
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* fix status bar to show elapsed time, per-iter time, per-pixel iter count
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* 'turbo' mode disabling graphics in full or part
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* patch the entire expanded-ram imul8xe on top of imul8 to avoid the 3-cycle thunk penalty :D
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* maybe clean up the load/layout of the big mul table
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* consider alternate lookup tables in the top 16KB under ROM
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* y-axis mirror optimization
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* extract viewport for display & re-input via keyboard
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* fujinet screenshot/viewport uploader
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