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base: brooke:c3c5968749a7b74f0365018869cd33e97c3dabd6
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brooke:fastmul2
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compare: brooke:8044dbfc21fa1f9cf334060b7919ab106c990f71
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brooke:main
brooke:fastmul2
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3 commits
c3c5968749 ... 8044dbfc21

Author SHA1 Message Date
Brion Vibber
8044dbfc21 whee 2023-01-07 22:57:18 -08:00
Brion Vibber
a47836a39a mwahahah 2023-01-07 22:02:26 -08:00
Brion Vibber
c5a62cfa1d wip 2023-01-07 21:19:40 -08:00
3 changed files with 256 additions and 11 deletions
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28
fixed.js
View file

@ -4,24 +4,26 @@ let bits = 16;
// max Mandelbrot zx/zy addition range prior to checking distance // max Mandelbrot zx/zy addition range prior to checking distance
let inputRange = 4; let inputRange = 4;
let reduction = 0;
let roundOffset = (2 ** (reduction - 1)) + 1;
// Room to hold power up to -12/+4 for 16-bit mandelbrot // Room to hold power up to -12/+4 for 16-bit mandelbrot
let shift = 4; let shift = 5;
let base = 2 ** (bits - shift); let base = 2 ** (bits - shift);
let reduction = 4;
let roundOffset = (2 ** (reduction - 1)) + 1;
let entries = 2 ** (bits - reduction); let entries = 2 ** (bits - reduction);
let bytes = Math.ceil(bits / 8) * entries; let bytes = Math.ceil(bits / 8) * entries;
// try to keep all but the last few bits semi-accurate // try to keep all but the last few bits semi-accurate
let epsilonBits = 1 ; let epsilonBits = 1;
let epsilon = 2 ** epsilonBits; let epsilon = 2 ** epsilonBits;
function toFixed(float) { export function toFixed(float) {
return Math.round(float * base); return Math.round(float * base);
} }
function toFloat(fixed) { export function toFloat(fixed) {
return fixed / base; return fixed / base;
} }
@ -48,12 +50,12 @@ for (let i = 0; i < entries * 2; i++) {
// returns fixed point // returns fixed point
function log2(fixed) { export function log2(fixed) {
return enloggen[toIndex(fixed)]; return enloggen[toIndex(fixed)];
} }
// returns rounded integer // returns rounded integer
function pow2(fixed) { export function pow2(fixed) {
let n = toIndex(fixed); let n = toIndex(fixed);
if (n > empower.length) { if (n > empower.length) {
n = empower.length - 1; n = empower.length - 1;
@ -61,7 +63,7 @@ function pow2(fixed) {
return empower[entries + n]; return empower[entries + n];
} }
function mul(a, b) { export function mul(a, b) {
if (a == 0) return 0; if (a == 0) return 0;
if (b == 0) return 0; if (b == 0) return 0;
let la = log2(a)|0; let la = log2(a)|0;
@ -93,6 +95,7 @@ for (let i = 0; i < powEntries; i++) {
} }
*/ */
/*
// now just try multipling numbers // now just try multipling numbers
let deltas = 0; let deltas = 0;
let deltaAvg = 0; let deltaAvg = 0;
@ -145,11 +148,14 @@ deltaCount = 0;
console.log('done'); console.log('done');
console.log(`size of enloggen table: ${entries} entries, ${bytes} bytes`);
console.log(`size of empower table: ${entries * 2} entries, ${bytes * 2} bytes`);
let m = 0; let m = 0;
for (let i = 0; i < enloggen.length; i++) { for (let i = 0; i < enloggen.length; i++) {
m = Math.max(m, enloggen[i]); m = Math.max(m, enloggen[i]);
} }
console.log(`max enloggen entry is ${m}`); console.log(`max enloggen entry is ${m}`);
*/
console.log(`size of enloggen table: ${entries} entries, ${bytes} bytes`);
console.log(`size of empower table: ${entries * 2} entries, ${bytes * 2} bytes`);

36
sim.html Normal file
View file

@ -0,0 +1,36 @@
<!DOCTYPE html>
<html>
<meta charset="utf-8">
<title>Mandelbrot fixed-point test</title>
<style type="text/css">
/* */
</style>
<body>
<h1>Mandelbrot fixed-point test</h1>
<table>
<tr>
<th>Float</th>
<th>Fixed-point imul</th>
<th>Fixed-point log</th>
</tr>
<tr>
<td><canvas id="float" width="256" height="256"></canvas></td>
<td><canvas id="imul" width="256" height="256"></canvas></td>
<td><canvas id="log" width="256" height="256"></canvas></td>
</tr>
<tr>
<td colspan=3>
<button id="zoom-in">Zoom in</button>
<button id="zoom-out">Zoom out</button>
<button id="left">Left</button>
<button id="right">Right</button>
<button id="up">Up</button>
<button id="down">Down</button>
</td>
</tr>
</table>
<script async type="module" src="sim.js"></script>
</body>
</html>

203
sim.js Normal file
View file

@ -0,0 +1,203 @@
import {toFixed, mul} from './fixed.js';
let toFixedLog = toFixed;
function toFixed16(val) {
// 4.12
return Math.round(val * (2 ** 12))
}
let four16 = toFixed16(4);
function imul(a, b) {
return Math.imul(a, b) >> 12;
}
function logmul(a, b) {
if ((a | b) == 0) {
return 0;
}
let neg = 0;
if (a < 0) {
a = -a;
neg++;
}
if (b < 0) {
b = -b;
neg++;
}
let product = mul(a, b);
if (neg == 1) {
product = -product;
}
return product;
}
let fourLog = toFixedLog(4);
let max = 256;
let width = 256;
let height = 256;
let zoom = 0;
let offsetX = 0;
let offsetY = 0;
function scale() {
return 1 / (2 ** zoom);
}
let cancelled = false;
async function cancel() {
cancelled = true;
return await nap(100);
}
let black = 0xff000000;
let tricolor = [
0xffff0000,
0xff00ff00,
0xff0000ff,
];
let palette = new Uint32Array(256);
palette[0] = black;
for (let i = 0; i < 255; i++) {
palette[i + 1] = tricolor[i % 3];
}
function nap(ms=0) {
return new Promise((resolve) => setTimeout(() => resolve(), ms));
}
function attach(id, func) {
document.getElementById(id).addEventListener('click', (_event) => {
cancel().then(() => {
func();
run();
});
});
}
attach('zoom-in', () => {
zoom++;
});
attach('zoom-out', () => {
if (zoom >= 1) {
zoom--;
}
});
attach('left', () => {
offsetX -= scale();
});
attach('right', () => {
offsetX += scale();
});
attach('up', () => {
offsetY -= scale();
});
attach('down', () => {
offsetY += scale();
});
async function setup(id, iterfunc) {
let canvas = document.getElementById(id);
let ctx = canvas.getContext('2d');
let imageData = ctx.createImageData(width, height);
let rgba = new Uint32Array(imageData.data.buffer);
cancelled = false;
for (let y = 0; y < height; y++) {
let cy = scale() * (y * 2 - height) / (height / 2) + offsetY;
for (let x = 0; x < width; x++) {
let cx = scale() * (x * 2 - width) / (width / 2) + offsetX;
let i = iterfunc(cx, cy);
let color = palette[i];
rgba[y * width + x] = color;
if (x % 256 == 255) {
ctx.putImageData(imageData, 0, 0);
await nap();
if (cancelled) {
return;
}
}
}
}
}
function run() {
setup('float', (cx, cy) => {
let zx = 0;
let zy = 0;
let zx_2 = 0;
let zy_2 = 0;
let zx_zy = 0;
for (let i = 1; i < max; i++) {
zx = zx_2 - zy_2 + cx;
zy = zx_zy + zx_zy + cy;
zx_2 = zx * zx;
zy_2 = zy * zy;
zx_zy = zx * zy;
if (zx_2 + zy_2 >= 4) {
return i;
}
}
return 0;
}).then(() => {
console.log('float done');
});
setup('imul', (cx, cy) => {
cx = toFixed16(cx);
cy = toFixed16(cy);
let zx = 0;
let zy = 0;
let zx_2 = 0;
let zy_2 = 0;
let zx_zy = 0;
for (let i = 1; i < max; i++) {
zx = zx_2 - zy_2 + cx;
zy = zx_zy + zx_zy + cy;
zx_2 = imul(zx, zx);
zy_2 = imul(zy, zy);
zx_zy = imul(zx, zy);
if (zx_2 + zy_2 >= four16) {
return i;
}
}
return 0;
}).then(() => {
console.log('imul done');
});
setup('log', (cx, cy) => {
cx = toFixedLog(cx);
cy = toFixedLog(cy);
let zx = 0;
let zy = 0;
let zx_2 = 0;
let zy_2 = 0;
let zx_zy = 0;
for (let i = 1; i < max; i++) {
zx = zx_2 - zy_2 + cx;
zy = zx_zy + zx_zy + cy;
zx_2 = logmul(zx, zx);
zy_2 = logmul(zy, zy);
zx_zy = logmul(zx, zy);
if (zx_2 + zy_2 >= fourLog) {
return i;
}
}
return 0;
}).then(() => {
console.log('log done');
});
}
run();