diff --git a/fixed.js b/fixed.js index 397de0f..2946dd1 100644 --- a/fixed.js +++ b/fixed.js @@ -4,24 +4,26 @@ let bits = 16; // max Mandelbrot zx/zy addition range prior to checking distance let inputRange = 4; +let reduction = 0; +let roundOffset = (2 ** (reduction - 1)) + 1; + // Room to hold power up to -12/+4 for 16-bit mandelbrot -let shift = 4; +let shift = 5; let base = 2 ** (bits - shift); -let reduction = 4; -let roundOffset = (2 ** (reduction - 1)) + 1; + let entries = 2 ** (bits - reduction); let bytes = Math.ceil(bits / 8) * entries; // try to keep all but the last few bits semi-accurate -let epsilonBits = 1 ; +let epsilonBits = 1; let epsilon = 2 ** epsilonBits; -function toFixed(float) { +export function toFixed(float) { return Math.round(float * base); } -function toFloat(fixed) { +export function toFloat(fixed) { return fixed / base; } @@ -48,12 +50,12 @@ for (let i = 0; i < entries * 2; i++) { // returns fixed point -function log2(fixed) { +export function log2(fixed) { return enloggen[toIndex(fixed)]; } // returns rounded integer -function pow2(fixed) { +export function pow2(fixed) { let n = toIndex(fixed); if (n > empower.length) { n = empower.length - 1; @@ -61,7 +63,7 @@ function pow2(fixed) { return empower[entries + n]; } -function mul(a, b) { +export function mul(a, b) { if (a == 0) return 0; if (b == 0) return 0; let la = log2(a)|0; @@ -93,6 +95,7 @@ for (let i = 0; i < powEntries; i++) { } */ +/* // now just try multipling numbers let deltas = 0; let deltaAvg = 0; @@ -145,11 +148,14 @@ deltaCount = 0; 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; for (let i = 0; i < enloggen.length; i++) { m = Math.max(m, enloggen[i]); } 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`); diff --git a/sim.html b/sim.html new file mode 100644 index 0000000..a260a0d --- /dev/null +++ b/sim.html @@ -0,0 +1,36 @@ + + + + Mandelbrot fixed-point test + + +

Mandelbrot fixed-point test

+ + + + + + + + + + + + + + + +
FloatFixed-point imulFixed-point log
+ + + + + + +
+ + + + \ No newline at end of file diff --git a/sim.js b/sim.js new file mode 100644 index 0000000..bc83348 --- /dev/null +++ b/sim.js @@ -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(); \ No newline at end of file