shave some cycles off 16-bit squaring with shift instead of add

also fix the comments about how many cycles shift takes

readme.md

@@ -18,7 +18,7 @@ Enjoy! I'll probably work on this off and on for the next few weeks until I've g
 
 ## Current state
 
-Basic rendering is functional, with interactive zoom/pan (+/-/arrows) and 6 preset viewports via the number keys.
+Basic rendering is functional, with interactive zoom/pan (+/-/arrows) and 4 preset viewports via the number keys.
 
 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.
 
@@ -27,7 +27,7 @@ The 16-bit signed integer multiplication takes two 16-bit inputs and emits one 3
 * 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 3.13-precision fixed point numbers with 6.26-precision intermediates.
+The mandelbrot calculations are done using 4.12-precision fixed point numbers. It may be possible to squish this down to 3.13.
 
 Iterations are capped at 255.
 
@@ -47,4 +47,4 @@ Currently produces a `.xex` executable, which can be booted up in common Atari e
 
 ## Todo
 
-See ideas in `todo.md`.
+See ideas in `todo.md`.

tables.js

@@ -11,40 +11,19 @@ function db(func) {
     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
+.export mul_lobyte
+.export mul_hibyte
 
-; (i * i + 1) / 2 for the multiplier
+; (i * i) / 2 for the multiplier
 .align 256
-mul_lobyte256:
-${db((i) => squares[i] & 0xff)}
+mul_lobyte:
+${db((i) => ((i * i) >> 1) & 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)}
+mul_hibyte:
+${db((i) => ((i * i) >> 9) & 0xff)}
 
 `);

todo.md

@@ -1,17 +1,15 @@
 things to try:
 
-* fix status bar to show elapsed time, per-iter time, per-pixel iter count
-
-* 'turbo' mode disabling graphics in full or part
-
 * patch the entire expanded-ram imul8xe on top of imul8 to avoid the 3-cycle thunk penalty :D
 
-* maybe clean up the load/layout of the big mul table
-
-* consider alternate lookup tables in the top 16KB under ROM
+* try 3.13 fixed point instead of 4.12 for more precision
+  * can we get away without the extra bit?
 
 * 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