fix fix

in prep for bigger pixels

.gitignore

@@ -1,3 +1,4 @@
 *.o
 *.xex
+tables.s
 .DS_Store

Makefile

@@ -2,13 +2,17 @@
 
 all : mandel.xex
 
-%.xex : %.o
+mandel.xex : mandel.o tables.o atari-asm-xex.cfg
-	ld65 -C atari-asm-xex.cfg -o $@ $<
+	ld65 -C ./atari-asm-xex.cfg -o $@ mandel.o tables.o
 
 %.o : %.s
 	ca65 -o $@ $<
 
+tables.s : tables.js
+	node tables.js > tables.s
+
 clean :
+	rm -f tables.s
 	rm -f *.o
 	rm -f *.xex
 

atari-asm-xex.cfg

@@ -0,0 +1,28 @@
+FEATURES {
+    STARTADDRESS: default = $2E00;
+}
+SYMBOLS {
+    __STARTADDRESS__: type = export, value = %S;
+}
+MEMORY {
+    ZP:      file = "", define = yes, start = $0082, size = $007E;
+    MAIN:    file = %O, define = yes, start = %S,    size = $4000 - %S;
+    # Keep $4000-7fff clear for expanded RAM access window
+    TABLES:  file = %O, define = yes, start = $8000, size = $a000 - $8000;
+    # Keep $a000-$bfff clear for BASIC cartridge
+}
+FILES {
+    %O: format = atari;
+}
+FORMATS {
+    atari: runad = start;
+}
+SEGMENTS {
+    ZEROPAGE: load = ZP,      type = zp,  optional = yes;
+    EXTZP:    load = ZP,      type = zp,  optional = yes; # to enable modules to be able to link to C and assembler programs
+    CODE:     load = MAIN,    type = rw,                  define = yes;
+    RODATA:   load = MAIN,    type = ro   optional = yes;
+    DATA:     load = MAIN,    type = rw   optional = yes;
+    BSS:      load = MAIN,    type = bss, optional = yes, define = yes;
+    TABLES:   load = TABLES,  type = ro,  optional = yes, align = 256;
+}

readme.md

@@ -14,32 +14,37 @@ Non-goals:
 
 Enjoy! I'll probably work on this off and on for the next few weeks until I've got it producing fractals.
 
--- brooke, january 2023 - february 2024
+-- brooke, january 2023 - december 2024
 
 ## Current state
 
-Basic rendering is functional, but no interactive behavior (zoom/pan) or benchmarking is done yet.
+Basic rendering is functional, with interactive zoom/pan (+/-/arrows) and 4 preset viewports via the number keys.
 
-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.
+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.
 
-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.
+* 16-bit multiplies are decomposed into 4 8-bit unsigned multiplies and some addition
+* an optimized case for squares uses a table of 8-bit squares to reduce the number of 8-bit multiplication sub-ops
+* when expanded RAM is available as on 130XE, a 64KB 8-bit multiplication table accelerates the remaining multiplications
+* without expanded RAM, a table of half-squares is used to implement the algorithm from https://everything2.com/title/Fast+6502+multiplication
 
-The mandelbrot calculations are done using 4.12-precision fixed point numbers. It may be possible to squish this down to 3.13.
+The mandelbrot calculations are done using 4.12-precision fixed point numbers with 8.24-precision intermediates. It may be possible to squish this down to 3.13/6.26.
 
 Iterations are capped at 255.
 
 The pixels are run in a progressive layout to get the basic shape on screen faster.
 
-## Next steps
+There is a running counter of ms/px using the vertical blank interrupts as a timer, used to track our progress. :D
 
-Add a running counter of ms/px using the vertical blank interrupts as a timer. This'll show how further work improves it!
+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.
 
-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.
+There's some cute color cycling.
-
-I may be able to do a faster multiply using tables of squares for 8-bit component multiplication.
 
 ## Deps and build instructions
 
 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.
 
 Currently produces a `.xex` executable, which can be booted up in common Atari emulators and some i/o devices.
+
+## Todo
+
+See ideas in `todo.md`.

tables.js

@@ -0,0 +1,50 @@
+function db(func) {
+    let lines = [];
+    for (let i = 0; i < 256; i += 16) {
+        let items = [];
+        for (let j = 0; j < 16; j++) {
+            let x = i + j;
+            items.push(func(x));
+        }
+        lines.push('    .byte ' + items.join(', '));
+    }
+    return lines.join('\n');
+}
+
+let squares = [];
+for (let i = 0; i < 512; i++) {
+    squares.push(Math.trunc((i * i + 1) / 2));
+}
+
+console.log(
+`.segment "TABLES"
+
+.export mul_lobyte256
+.export mul_hibyte256
+.export mul_hibyte512
+.export sqr_lobyte
+.export sqr_hibyte
+
+; (i * i + 1) / 2 for the multiplier
+.align 256
+mul_lobyte256:
+${db((i) => squares[i] & 0xff)}
+
+.align 256
+mul_hibyte256:
+${db((i) => (squares[i] >> 8) & 0xff)}
+
+.align 256
+mul_hibyte512:
+${db((i) => (squares[i + 256] >> 8) & 0xff)}
+
+; (i * i) for the plain squares
+.align 256
+sqr_lobyte:
+${db((i) => (i * i) & 0xff)}
+
+.align 256
+sqr_hibyte:
+${db((i) => ((i * i) >> 8) & 0xff)}
+
+`);

testme.js

@@ -0,0 +1,41 @@
+// ax = (a + x)2/2 - a2/2 - x2/2 
+
+function half_square(x) {
+    return Math.round(x * x / 2) & 0xffff >>> 0;
+}
+
+function mul8(a, b) {
+    let result = half_square(a + b) & 0xffff;
+    result = (result - half_square(a)) & 0xffff;
+    result = (result - half_square(b)) & 0xffff;
+    result = (result + (b & a & 1)) & 0xffff;
+    return result >>> 0;
+}
+
+function mul16(a, b) {
+    let ah = (a & 0xff00) >>> 8;
+    let al = (a & 0x00ff) >>> 0;
+    let bh = (b & 0xff00) >>> 8;
+    let bl = (b & 0x00ff) >>> 0;
+    let result = (mul8(al, bl) & 0xffff) >>> 0;
+    result = ((result + (mul8(ah, bl) << 8)) & 0x00ffffff) >>> 0;
+    result = ((result + (mul8(al, bh) << 8)) & 0x01ffffff) >>> 0;
+    result = ((result + (mul8(ah, bh) << 16)) & 0xffffffff) >>> 0;
+    return result;
+}
+
+let max = 65536;
+//let max = 256;
+//let max = 128;
+//let max = 8;
+
+for (let a = 0; a < max; a++) {
+    for (let b = 0; b < max; b++) {
+        let expected = Math.imul(a, b) >>> 0;
+        //let actual = mul8(a, b);
+        let actual = mul16(a, b);
+        if (expected !== actual) {
+            console.log(`wrong! ${a} * ${b} expected ${expected} got ${actual}`);
+        }
+    }
+}

todo.md

@@ -0,0 +1,19 @@
+things to try:
+
+* skip add on the top-byte multiply in sqr8/mul8
+  * should save a few cycles, suggestion by jamey
+
+* patch the entire expanded-ram imul8xe on top of imul8 to avoid the 3-cycle thunk penalty :D
+
+* try 3.13 fixed point instead of 4.12 for more precision
+  * can we get away without the extra bit?
+  * since exit compare space would be 6.26 i think so
+
+* y-axis mirror optimization
+
+* 'wide pixels' 2x and 4x for a fuller initial image in the tiered rendering
+  * maybe redo tiering to just 4x4, 2x2, 1x1?
+
+* extract viewport for display & re-input via keyboard
+
+* fujinet screenshot/viewport uploader