Press n or j to go to the next uncovered block, b, p or k for the previous block.
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// <script id="workerCode">
// Constants
const MAX_CHAOTIC_ITERATIONS = 100000;
// Helper function to check debug flags
function hasDebugFlag(config, flag) {
const debug = config?.debug;
if (!debug) return false;
const parts = debug.split(',').map(f => f.trim());
return parts.some(p => p === flag || p.startsWith(flag + '='));
}
// Utility class for managing precomputed pixel data inherited from parent views.
// Used by all board types to skip computation for pixels known from parent.
// Uses TypedArrays for efficient storage of pending data.
class PrecomputedPoints {
constructor(inheritedData) {
// Track which pixels are pre-known (for excluding from compute)
this.knownPixels = new Set();
this.knownMask = null;
this.knownCount = 0;
// Map<iter, {dStart, dCount, cStart, cCount}>
this.rangeMap = new Map();
if (!inheritedData) {
this.dIndices = new Uint32Array(0);
this.cIndices = new Uint32Array(0);
this.cP = new Uint32Array(0);
this.cZ = new Float64Array(0);
this.zStride = 2;
return;
}
if (inheritedData.packed) {
this.dIndices = inheritedData.dIndices || new Uint32Array(0);
this.cIndices = inheritedData.cIndices || new Uint32Array(0);
this.cP = inheritedData.cP || new Uint32Array(0);
this.cZ = inheritedData.cZ || new Float64Array(0);
this.zStride = inheritedData.zStride || 2;
this.knownMask = inheritedData.knownMask || null;
this.knownCount = this.dIndices.length + this.cIndices.length;
const ranges = inheritedData.ranges || new Uint32Array(0);
for (let i = 0; i + 4 < ranges.length; i += 5) {
const iter = ranges[i];
this.rangeMap.set(iter, {
dStart: ranges[i + 1],
dCount: ranges[i + 2],
cStart: ranges[i + 3],
cCount: ranges[i + 4]
});
}
return;
}
const diverged = inheritedData.diverged || [];
const converged = inheritedData.converged || [];
// Sort to ensure contiguous storage per iteration
// (Use stable sort if preserving index order matters, but here it doesn't)
diverged.sort((a, b) => a.iter - b.iter);
converged.sort((a, b) => a.iter - b.iter);
// Allocate storage
this.dIndices = new Uint32Array(diverged.length);
this.cIndices = new Uint32Array(converged.length);
this.cP = new Uint32Array(converged.length);
// Determine Z stride
this.zStride = 2;
if (converged.length > 0 && converged[0].z && converged[0].z.length > 2) {
this.zStride = converged[0].z.length;
}
this.cZ = new Float64Array(converged.length * this.zStride);
// Fill Diverged
let currentIter = -1;
let start = 0;
for (let i = 0; i < diverged.length; i++) {
const item = diverged[i];
this.knownPixels.add(item.index);
this.dIndices[i] = item.index;
if (item.iter !== currentIter) {
if (currentIter !== -1) {
this.getRange(currentIter).dCount = i - start;
}
currentIter = item.iter;
start = i;
this.getRange(currentIter).dStart = start;
}
}
if (currentIter !== -1) {
this.getRange(currentIter).dCount = diverged.length - start;
}
// Fill Converged
currentIter = -1;
start = 0;
for (let i = 0; i < converged.length; i++) {
const item = converged[i];
this.knownPixels.add(item.index);
this.cIndices[i] = item.index;
this.cP[i] = item.p;
const zOffset = i * this.zStride;
const zLen = Math.min(this.zStride, item.z ? item.z.length : 0);
for (let k = 0; k < zLen; k++) {
this.cZ[zOffset + k] = item.z[k];
}
if (item.iter !== currentIter) {
if (currentIter !== -1) {
this.getRange(currentIter).cCount = i - start;
}
currentIter = item.iter;
start = i;
this.getRange(currentIter).cStart = start;
}
}
if (currentIter !== -1) {
this.getRange(currentIter).cCount = converged.length - start;
}
this.knownCount = this.knownPixels.size;
}
getRange(iter) {
if (!this.rangeMap.has(iter)) {
this.rangeMap.set(iter, { dStart: 0, dCount: 0, cStart: 0, cCount: 0 });
}
return this.rangeMap.get(iter);
}
isPrecomputed(index) {
if (this.knownMask) {
return this.knownMask[index] === 1;
}
return this.knownPixels.has(index);
}
getPrecomputedCount() {
if (this.knownMask) {
return this.knownCount;
}
return this.knownPixels.size;
}
// Get count of pending (not yet reported) precomputed points
getPendingCount() {
let count = 0;
for (const range of this.rangeMap.values()) {
count += range.dCount + range.cCount;
}
return count;
}
// Helper to reconstruct objects from TypedArrays
extractData(range) {
const diverged = [];
if (range.dCount > 0) {
for (let i = 0; i < range.dCount; i++) {
diverged.push(this.dIndices[range.dStart + i]);
}
}
const converged = [];
if (range.cCount > 0) {
for (let i = 0; i < range.cCount; i++) {
const idx = range.cStart + i;
const z = new Array(this.zStride);
for (let k = 0; k < this.zStride; k++) {
z[k] = this.cZ[idx * this.zStride + k];
}
converged.push({
index: this.cIndices[idx],
z: z,
p: this.cP[idx]
});
}
}
return { diverged, converged };
}
// Called each iteration to inject pending reports into changeList.
// Reports pixels that completed at this iteration count.
flushAtIteration(iter, board) {
const range = this.rangeMap.get(iter);
if (!range) return;
const { diverged, converged } = this.extractData(range);
// Queue the changes for reporting to main thread
// Note: diverged is just indices (nn), converged is objects (vv)
board.queueChanges({
iter,
nn: diverged,
vv: converged
});
// Update board's internal counters
board.di += diverged.length;
board.un -= diverged.length + converged.length;
// Mark pixels as done in nn[]
for (const idx of diverged) {
board.nn[idx] = iter;
}
for (const c of converged) {
board.nn[c.index] = -iter;
}
this.rangeMap.delete(iter);
}
// Get and remove pending reports for a specific iteration.
// Returns {diverged: [...], converged: [...]} or null if none.
// Does NOT update board counters - caller is responsible for that.
extractAtIteration(iter) {
const range = this.rangeMap.get(iter);
if (!range) return null;
const data = this.extractData(range);
this.rangeMap.delete(iter);
// Consumers expect {diverged: [indices], converged: [objects]}
// extractData provides exactly this.
return data;
}
// Get all iterations that have pending reports, optionally below maxIter.
getPendingIterations(maxIter = null) {
const keys = Array.from(this.rangeMap.keys());
const filtered = maxIter === null ? keys : keys.filter(iter => iter < maxIter);
return filtered.sort((a, b) => a - b);
}
// Extract and remove ALL pending reports below maxIter.
extractBelowIteration(maxIter) {
const iters = this.getPendingIterations(maxIter);
if (iters.length === 0) return null;
const combined = { diverged: [], converged: [] };
for (const iter of iters) {
const range = this.rangeMap.get(iter);
const data = this.extractData(range);
for (const item of data.diverged) combined.diverged.push(item);
for (const item of data.converged) combined.converged.push(item);
this.rangeMap.delete(iter);
}
return combined.diverged.length > 0 || combined.converged.length > 0 ? combined : null;
}
// Flush all pending reports up to and including maxIter.
// Used by GPU boards that compute in batches.
flushUpToIteration(maxIter, board) {
// Get iterations in sorted order to maintain proper changeList ordering
const iterations = Array.from(this.rangeMap.keys())
.filter(iter => iter <= maxIter)
.sort((a, b) => a - b);
for (const iter of iterations) {
this.flushAtIteration(iter, board);
}
}
// Check if all pending reports have been flushed
isEmpty() {
return this.rangeMap.size === 0;
}
// Serialize for board transfer between workers
serialize() {
const diverged = [];
const converged = [];
for (const iter of this.rangeMap.keys()) {
const range = this.rangeMap.get(iter);
const data = this.extractData(range);
for (const idx of data.diverged) {
diverged.push({ index: idx, iter });
}
for (const item of data.converged) {
converged.push({
index: item.index,
iter,
z: item.z,
p: item.p
});
}
}
// knownPixels is redundant as it can be rebuilt from diverged/converged
return { diverged, converged };
}
// Restore from serialized state
static fromSerialized(data) {
if (!data) return null;
// Constructor rebuilds everything (TypedArrays, knownPixels, rangeMap)
// from the diverged/converged arrays
return new PrecomputedPoints(data);
}
}
// Abstract base class for Mandelbrot computation backends.
class Board {
constructor(k, size, re, im, config, id, inheritedData = null) {
this.k = k; // Number in explorer
// Store size as double (sufficient for scaling), coordinates as QD
this.sizesQD = [typeof size === 'number' ? size : qdToNumber(size), toQD(re), toQD(im)];
this.id = id; // Random ID
this.config = config; // Global config
this.it = 1; // Current iteration
this.un = config.dimsArea; // Unfinished pixels
this.di = 0; // Diverged pixels
this.ch = 0; // Chaotic pixels
this.effort = 100; // Benchmarked: 4.4 ns/px-iter (baseline)
this.pix = this.pixelSize;
this.epsilon = this.pix / 10;
this.epsilon2 = this.pix * 10;
this.lastTime = 0; // Time last message sent out
this.changeList = []; // List of new data to send
this.updateSize = 0; // Amount of data to send
// Initialize arrays
this.nn = new Array(this.config.dimsArea).fill(0);
this.pp = new Array(this.config.dimsArea).fill(0);
this.cc = [];
this.zz = [];
this.bb = [];
// Initialize precomputed points from parent view (if provided)
this.precomputed = inheritedData ? new PrecomputedPoints(inheritedData) : null;
}
// Getter properties that derive from sizesQD (the authoritative source)
// sizesQD format: [sizeDouble, reQD, imQD]
get size() { return this.sizesQD[0]; }
get re() { return this.sizesQD[1]; }
get im() { return this.sizesQD[2]; }
// Derived scalar property
get pixelSize() { return this.size / this.config.dimsWidth; }
async serialize() {
return {
type: this.constructor.name,
k: this.k,
sizesQD: this.sizesQD,
id: this.id,
config: this.config,
it: this.it,
un: this.un,
di: this.di,
ch: this.ch,
lastTime: this.lastTime,
changeList: this.changeList,
updateSize: this.updateSize,
precomputed: this.precomputed ? this.precomputed.serialize() : null
};
}
compact() {
}
queueChanges(changes) {
if (changes !== null) {
if (!this.changeMap) this.changeMap = new Map();
const existing = this.changeMap.get(changes.iter);
if (existing) {
// Use loop instead of spread to avoid stack overflow with large arrays
for (const item of changes.nn) existing.nn.push(item);
for (const item of changes.vv) existing.vv.push(item);
} else {
this.changeList.push(changes);
this.changeMap.set(changes.iter, changes);
}
this.updateSize += changes.nn.length + changes.vv.length;
}
}
static fromSerialized(serialized) {
const subclasses = new Map([
['CpuBoard', CpuBoard],
['QDCpuBoard', QDCpuBoard],
['DDZhuoranBoard', DDZhuoranBoard],
['QDZhuoranBoard', QDZhuoranBoard],
['GpuBoard', GpuBoard],
['GlBoard', GlBoard],
['GlZhuoranBoard', GlZhuoranBoard],
['GpuZhuoranBoard', GpuZhuoranBoard],
['GpuAdaptiveBoard', GpuAdaptiveBoard],
['GlAdaptiveBoard', GlAdaptiveBoard]
]);
const board = subclasses.get(serialized.type).fromSerialized(serialized);
return board;
}
inspike(re, im) {
// We do not iterate infinitely for chaotic points in the spike.
// -1.401155 is the Feigenbaum point boundary
return (im == 0.0 && re > -2.0 && re < -1.401155 &&
this.config.exponent == 2);
}
unfinished() {
// Chaotic points in the spike counted as finished after max iterations.
const result = Math.max(0, this.un + (this.it < MAX_CHAOTIC_ITERATIONS ? 0 : -this.ch));
return result;
}
}
// CPU board using double precision arithmetic for shallow zoom depths.
class CpuBoard extends Board {
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
const sizeScalar = this.size;
const reDD = qdToDD(this.re);
const imDD = qdToDD(this.im);
// Initialize board: cc = c values, zz = current z, bb = checkpoint z, ss = active pixel indices
for (let y = 0; y < this.config.dimsHeight; y++) {
const jFrac = (0.5 - (y / this.config.dimsHeight));
const j = jFrac * (sizeScalar / this.config.aspectRatio) + imDD[0]; // Scale by height
for (let x = 0; x < this.config.dimsWidth; x++) {
const rFrac = ((x / this.config.dimsWidth) - 0.5);
const r = rFrac * sizeScalar + reDD[0]; // Scale by width
this.cc.push(r, j);
if (this.inspike(r, j)) {
this.ch += 1;
}
}
}
this.zz = this.cc.slice(); // Start with z = c
this.bb = this.cc.slice(); // Initial checkpoint = c
// Initialize active pixel list, excluding precomputed pixels
this.ss = [];
for (let i = 0; i < this.config.dimsArea; i++) {
if (!this.precomputed || !this.precomputed.isPrecomputed(i)) {
this.ss.push(i);
}
}
// Note: don't adjust this.un here - it will be decremented by flushAtIteration
// when precomputed points are flushed, which properly updates di/un together
}
static fromSerialized(serialized) {
const board = new CpuBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Override initialized values with serialized data
Object.assign(board, serialized);
// Restore nn values for completed pixels
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
// Reconstruct sparse arrays from serialized data
const cc = board.cc;
board.cc = [];
board.zz = [];
board.bb = [];
board.pp = [];
for (let i = 0; i < serialized.ss.length; i++) {
const index = serialized.ss[i];
board.cc[index * 2] = cc[index * 2];
board.cc[index * 2 + 1] = cc[index * 2 + 1];
board.zz[index * 2] = serialized.zz[i * 2];
board.zz[index * 2 + 1] = serialized.zz[i * 2 + 1];
board.bb[index * 2] = serialized.bb[i * 2];
board.bb[index * 2 + 1] = serialized.bb[i * 2 + 1];
board.pp[index] = serialized.pp[i];
}
// Restore precomputed points state
if (serialized.precomputed) {
board.precomputed = PrecomputedPoints.fromSerialized(serialized.precomputed);
}
return board;
}
async serialize() {
// Build sparse nn array for completed pixels (non-zero nn values)
const completedIndexes = [];
const completedNn = [];
for (let i = 0; i < this.nn.length; i++) {
if (this.nn[i] !== 0) {
completedIndexes.push(i);
completedNn.push(this.nn[i]);
}
}
return {
...(await super.serialize()),
ss: this.ss,
zz: this.ss.flatMap(i => [this.zz[i*2], this.zz[i*2+1]]),
bb: this.ss.flatMap(i => [this.bb[i*2], this.bb[i*2+1]]),
pp: this.ss.map(index => this.pp[index]),
completedIndexes,
completedNn,
}
}
iterate(targetIters = 1) {
// Batch multiple iterations internally
for (let batch = 0; batch < targetIters && this.un > 0; batch++) {
let changes = null;
const results = [0, 0, 0];
let s = this.ss; // speedy list of active pixel indices to compute
// Update checkpoints at fibonacciPeriod intervals (returns 1 at Fibonacci points)
if (fibonacciPeriod(this.it) == 1) {
for (let t = 0; t < s.length; ++t) {
let m = s[t];
if (this.nn[m]) continue;
this.bb[m * 2] = this.zz[m * 2]; // bb = checkpoint z position
this.bb[m * 2 + 1] = this.zz[m * 2 + 1];
this.pp[m] = 0; // Reset pp (period = iter when convergence first detected)
}
}
for (let t = 0; t < s.length; ++t) {
const index = s[t];
const computeResult = this.compute(index);
if (computeResult !== 0) {
if (!changes) {
changes = { iter: this.it, nn: [], vv: [] };
}
if (computeResult < 0) {
changes.vv.push({
index: index,
z: [this.zz[index * 2], this.zz[index * 2 + 1]], // float64 pair
p: this.pp[index] // period
});
} else {
changes.nn.push(index);
}
}
}
if (changes) {
this.un -= changes.nn.length + changes.vv.length; // newly finished
this.di += changes.nn.length; // diverged
}
if (s.length > this.un * 1.25) {
this.compact();
if (this.ss.length > this.un + this.ch) {
// Debug: Check for overlap between ss and changes
if (changes) {
const ssSet = new Set(this.ss);
const changedIndexes = new Set([...changes.nn, ...changes.vv.map(v => v.index)]);
const overlap = [...ssSet].filter(x => changedIndexes.has(x));
if (overlap.length > 0) {
console.warn(`Overlap detected between ss and changes: ${overlap.length} items`);
console.warn(`Overlap indexes: ${overlap}`);
console.warn(`ss length: ${this.ss.length}, un: ${this.un}`);
console.warn(`changes: nn ${changes.nn.length}, vv ${changes.vv.length}`);
}
}
// Additional checks
const uniqueSS = new Set(this.ss);
if (uniqueSS.size !== this.ss.length) {
console.warn(
`Duplicate entries in ss detected. ss length: ${this.ss.length}, ` +
`unique entries: ${uniqueSS.size}`);
}
const invalidIndexes = this.ss.filter(i => this.nn[i]);
if (invalidIndexes.length > 0) {
console.warn(
`Found ${invalidIndexes.length} indexes in ss that are ` +
`already marked as finished in nn`);
}
if (this.ss.length !== this.un + this.ch) {
console.warn(`Mismatch between ss length (${this.ss.length}) and un (${this.un})`);
}
throw new Error(`excess ss ${s.length}, ${this.ss.length}, ${this.un}`);
}
}
// Flush precomputed points at this iteration
if (this.precomputed) {
this.precomputed.flushAtIteration(this.it, this);
}
this.queueChanges(changes);
this.it++;
}
}
compact() {
this.ss = this.ss.filter(i => !this.nn[i]);
}
compute(m) {
if (this.nn[m]) return 0;
const m2 = m * 2;
const m2i = m2 + 1;
const r = this.zz[m2];
const j = this.zz[m2i];
const r2 = r * r;
const j2 = j * j;
if (r2 + j2 > 4.0) {
this.nn[m] = this.it;
return 1; // Diverged
}
// Mandelbrot iteration: z = z^exponent + c
let ra = r2 - j2;
let ja = 2 * r * j;
for (let ord = 2; ord < this.config.exponent; ord++) {
let rt = r * ra - j * ja;
ja = r * ja + j * ra;
ra = rt;
}
ra += this.cc[m2];
ja += this.cc[m2i];
this.zz[m2] = ra;
this.zz[m2i] = ja;
// Check convergence: compare current z to checkpoint
const rb = this.bb[m2];
const jb = this.bb[m2i];
const db = Math.abs(rb - ra) + Math.abs(jb - ja); // distance from checkpoint
const epsilon = this.epsilon;
const epsilon2 = this.epsilon2;
if (db <= epsilon2) {
if (!this.pp[m]) { this.pp[m] = this.it; } // Record iter when first detected
if (db <= epsilon) {
this.nn[m] = -this.it;
if (this.inspike(this.cc[m2], this.cc[m2i]) && this.ch > 0) {
this.ch -= 1;
}
return -1; // Converged
}
}
return 0; // Continue iterating
}
}
// CPU board using direct QD-precision iteration (no perturbation).
// Very slow but maximally accurate - serves as ground truth for verification.
class QDCpuBoard extends Board {
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
// Override epsilon for QD precision - need much tighter thresholds
// to avoid false convergence detection at deep zoom.
// Base Board uses pix/10 and pix*10, but for direct QD iteration
// we need thresholds much smaller than pixel size.
this.epsilon = this.pix * 1e-20; // Final convergence threshold
this.epsilon2 = this.pix * 1e-15; // Getting close threshold
this.effort = 11200; // Benchmarked: 493 ns/px-iter, 112× slower than CPU
// Use QD-precision values from getters
// IMPORTANT: At deep zoom (z > 1e30), double precision cannot represent
// the pixel size or offset accurately. Must use QD precision throughout.
const reQD = this.re;
const imQD = this.im;
// Pre-compute size/aspectRatio in QD precision for y offsets
// Use toQDMul instead of toQDScale to capture error terms at deep zoom
const aspectRecipQD = toQD(1 / this.config.aspectRatio);
const sizeOverAspect = toQDMul(this.size, aspectRecipQD);
// Temps for loop to avoid allocation
const tempQD = new Array(4);
const jQD = new Array(4);
const rQD = new Array(4);
// Initialize board: cc = c values (8 floats per pixel), zz = current z (8 floats per pixel)
// bb = checkpoint z, ss = active pixel indices
// Format: [r0, r1, r2, r3, i0, i1, i2, i3] for each complex number
for (let y = 0; y < this.config.dimsHeight; y++) {
const jFrac = (0.5 - (y / this.config.dimsHeight));
// Use arQdMul instead of toQDScale to capture error terms
// jFrac is treated as QD [jFrac, 0, 0, 0]
arQdMul(tempQD, 0, sizeOverAspect[0], sizeOverAspect[1], sizeOverAspect[2], sizeOverAspect[3], jFrac, 0, 0, 0);
arQdAdd(jQD, 0, imQD[0], imQD[1], imQD[2], imQD[3], tempQD[0], tempQD[1], tempQD[2], tempQD[3]);
for (let x = 0; x < this.config.dimsWidth; x++) {
const rFrac = ((x / this.config.dimsWidth) - 0.5);
// Use arQdMul instead of toQDScale to capture error terms
// size (if double) is [size, 0, 0, 0] as QD
const sz = this.size;
arQdMul(tempQD, 0, sz, 0, 0, 0, rFrac, 0, 0, 0);
arQdAdd(rQD, 0, reQD[0], reQD[1], reQD[2], reQD[3], tempQD[0], tempQD[1], tempQD[2], tempQD[3]);
// Store c as 8 floats: [r0, r1, r2, r3, i0, i1, i2, i3]
this.cc.push(rQD[0], rQD[1], rQD[2], rQD[3], jQD[0], jQD[1], jQD[2], jQD[3]);
const r = rQD[0] + rQD[1] + rQD[2] + rQD[3];
const j = jQD[0] + jQD[1] + jQD[2] + jQD[3];
if (this.inspike(r, j)) {
this.ch += 1;
}
}
}
this.zz = this.cc.slice(); // Start with z = c
this.bb = this.cc.slice(); // Initial checkpoint = c
// Initialize active pixel list, excluding precomputed pixels
this.ss = [];
for (let i = 0; i < this.config.dimsArea; i++) {
if (!this.precomputed || !this.precomputed.isPrecomputed(i)) {
this.ss.push(i);
}
}
// Note: don't adjust this.un here - it will be decremented by flushAtIteration
// when precomputed points are flushed, which properly updates di/un together
}
static fromSerialized(serialized) {
const board = new QDCpuBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Override initialized values with serialized data
Object.assign(board, serialized);
// Restore nn values for completed pixels
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
// Reconstruct sparse arrays from serialized data (8 floats per pixel)
const cc = board.cc;
board.cc = [];
board.zz = [];
board.bb = [];
board.pp = [];
for (let i = 0; i < serialized.ss.length; i++) {
const index = serialized.ss[i];
const i8 = index * 8;
for (let j = 0; j < 8; j++) {
board.cc[i8 + j] = cc[i8 + j];
board.zz[i8 + j] = serialized.zz[i * 8 + j];
board.bb[i8 + j] = serialized.bb[i * 8 + j];
}
board.pp[index] = serialized.pp[i];
}
// Restore precomputed points state
if (serialized.precomputed) {
board.precomputed = PrecomputedPoints.fromSerialized(serialized.precomputed);
}
return board;
}
async serialize() {
// Build sparse nn array for completed pixels (non-zero nn values)
const completedIndexes = [];
const completedNn = [];
for (let i = 0; i < this.nn.length; i++) {
if (this.nn[i] !== 0) {
completedIndexes.push(i);
completedNn.push(this.nn[i]);
}
}
return {
...(await super.serialize()),
ss: this.ss,
zz: this.ss.flatMap(i => {
const i8 = i * 8;
return [this.zz[i8], this.zz[i8+1], this.zz[i8+2], this.zz[i8+3],
this.zz[i8+4], this.zz[i8+5], this.zz[i8+6], this.zz[i8+7]];
}),
bb: this.ss.flatMap(i => {
const i8 = i * 8;
return [this.bb[i8], this.bb[i8+1], this.bb[i8+2], this.bb[i8+3],
this.bb[i8+4], this.bb[i8+5], this.bb[i8+6], this.bb[i8+7]];
}),
pp: this.ss.map(index => this.pp[index]),
completedIndexes,
completedNn,
}
}
iterate(targetIters = 1) {
// Batch multiple iterations internally
for (let batch = 0; batch < targetIters && this.un > 0; batch++) {
let changes = null;
let s = this.ss; // speedy list of active pixel indices to compute
// Update checkpoints at fibonacciPeriod intervals (returns 1 at Fibonacci points)
if (fibonacciPeriod(this.it) == 1) {
for (let t = 0; t < s.length; ++t) {
let m = s[t];
if (this.nn[m]) continue;
const m8 = m * 8;
for (let i = 0; i < 8; i++) {
this.bb[m8 + i] = this.zz[m8 + i];
}
this.pp[m] = 0; // Reset pp (period = iter when convergence first detected)
}
}
for (let t = 0; t < s.length; ++t) {
const index = s[t];
const computeResult = this.compute(index);
if (computeResult !== 0) {
if (!changes) {
changes = { iter: this.it, nn: [], vv: [] };
}
if (computeResult < 0) {
const m8 = index * 8;
// Preserve full QD precision (8 elements: 4 real + 4 imag)
changes.vv.push({
index: index,
z: [this.zz[m8], this.zz[m8+1], this.zz[m8+2], this.zz[m8+3],
this.zz[m8+4], this.zz[m8+5], this.zz[m8+6], this.zz[m8+7]],
p: this.pp[index] // period
});
} else {
changes.nn.push(index);
}
}
}
if (changes) {
this.un -= changes.nn.length + changes.vv.length; // newly finished
this.di += changes.nn.length; // diverged
}
if (s.length > this.un * 1.25) {
this.compact();
}
// Flush precomputed points at this iteration
if (this.precomputed) {
this.precomputed.flushAtIteration(this.it, this);
}
this.queueChanges(changes);
this.it++;
}
}
compact() {
this.ss = this.ss.filter(i => !this.nn[i]);
}
compute(m) {
if (this.nn[m]) return 0;
const m8 = m * 8;
// Extract z as QD complex: [r0, r1, r2, r3] and [i0, i1, i2, i3]
const zr = [this.zz[m8], this.zz[m8+1], this.zz[m8+2], this.zz[m8+3]];
const zi = [this.zz[m8+4], this.zz[m8+5], this.zz[m8+6], this.zz[m8+7]];
// Mandelbrot iteration: z = z² + c using QD precision
// z² = (zr + zi*i)² = zr² - zi² + 2*zr*zi*i
const zr2 = toQDSquare(zr); // zr²
const zi2 = toQDSquare(zi); // zi²
const zri = toQDMul(zr, zi); // zr * zi
// Check escape: |z|² > 4 using FULL QD precision comparison
// IMPORTANT: Cannot sum components to double and compare - this loses precision
// when |z|² ≈ 4 and differences are at 1e-34 scale. Adjacent pixels would escape
// at the same iteration, creating vertical stripes in the output.
// Instead, compute |z|² - 4 in QD precision and check if positive.
const mag2QD = toQDAdd(zr2, zi2); // |z|² in QD precision
const diffQD = toQDSub(mag2QD, [4, 0, 0, 0]); // |z|² - 4
// Check if diff > 0: find first non-zero component and check its sign
const escaped = diffQD[0] > 0 ||
(diffQD[0] === 0 && (diffQD[1] > 0 ||
(diffQD[1] === 0 && (diffQD[2] > 0 ||
(diffQD[2] === 0 && diffQD[3] > 0)))));
if (escaped) {
this.nn[m] = this.it;
return 1; // Diverged
}
const newZr = toQDSub(zr2, zi2); // zr² - zi²
const newZi = toQDDouble(zri); // 2 * zr * zi
// Add c
const cr = [this.cc[m8], this.cc[m8+1], this.cc[m8+2], this.cc[m8+3]];
const ci = [this.cc[m8+4], this.cc[m8+5], this.cc[m8+6], this.cc[m8+7]];
const finalZr = toQDAdd(newZr, cr);
const finalZi = toQDAdd(newZi, ci);
// Store back
this.zz[m8] = finalZr[0]; this.zz[m8+1] = finalZr[1];
this.zz[m8+2] = finalZr[2]; this.zz[m8+3] = finalZr[3];
this.zz[m8+4] = finalZi[0]; this.zz[m8+5] = finalZi[1];
this.zz[m8+6] = finalZi[2]; this.zz[m8+7] = finalZi[3];
// Check convergence: compare current z to checkpoint
// IMPORTANT: Must compute difference in QD precision FIRST, then convert to double.
// If we sum to double first and then subtract, we lose precision due to catastrophic
// cancellation when z ≈ 2 (fixed point) and differences are at 1e-35 scale.
const bbR = [this.bb[m8], this.bb[m8+1], this.bb[m8+2], this.bb[m8+3]];
const bbI = [this.bb[m8+4], this.bb[m8+5], this.bb[m8+6], this.bb[m8+7]];
const diffR = toQDSub(finalZr, bbR);
const diffI = toQDSub(finalZi, bbI);
const db = Math.abs(diffR[0] + diffR[1] + diffR[2] + diffR[3]) +
Math.abs(diffI[0] + diffI[1] + diffI[2] + diffI[3]);
const epsilon = this.epsilon;
const epsilon2 = this.epsilon2;
if (db <= epsilon2) {
if (!this.pp[m]) { this.pp[m] = this.it; } // Record iter when first detected
if (db <= epsilon) {
this.nn[m] = -this.it;
const cR = this.cc[m8] + this.cc[m8+1] + this.cc[m8+2] + this.cc[m8+3];
const cI = this.cc[m8+4] + this.cc[m8+5] + this.cc[m8+6] + this.cc[m8+7];
if (this.inspike(cR, cI) && this.ch > 0) {
this.ch -= 1;
}
return -1; // Converged
}
}
return 0; // Continue iterating
}
}
// Spatial bucket for O(1) lookup of nearby points in 2D
// Uses a grid with cell size = 2*bucketRadius to guarantee 4-bucket coverage
// Base class - subclasses implement precision-specific getF64Point and verifyAndGetDelta
class SpatialBucket {
// Minimum bucket size to avoid f64 precision issues
static MIN_BUCKET_SIZE = 1e-12;
/**
* @param {number} threadingEpsilon - L∞ distance threshold for "nearby"
*/
constructor(threadingEpsilon) {
this.threadingEpsilon = threadingEpsilon;
// Clamp bucket radius to avoid f64 precision problems
this.bucketRadius = Math.max(threadingEpsilon, SpatialBucket.MIN_BUCKET_SIZE);
this.gridSize = 2 * this.bucketRadius; // Grid cells are 2× radius for 4-bucket guarantee
this.buckets = new Map(); // "bx,by" -> Set of indices
}
// Subclasses must override: return {re, im} as f64 for coarse bucketing
getF64Point(i) { throw new Error("subclass must implement getF64Point"); }
// Subclasses must override: return {deltaRe, deltaIm} if within threadingEpsilon, else null
// Uses precision-aware subtraction to avoid catastrophic cancellation
verifyAndGetDelta(i, j) { throw new Error("subclass must implement verifyAndGetDelta"); }
getBucket(re, im) {
const bx = Math.floor(re / this.gridSize);
const by = Math.floor(im / this.gridSize);
return { bx, by };
}
getKey(bx, by) {
return `${bx},${by}`;
}
/**
* Add point at index i to the spatial structure
*/
add(i) {
const pt = this.getF64Point(i);
if (!pt) return;
const { bx, by } = this.getBucket(pt.re, pt.im);
const key = this.getKey(bx, by);
if (!this.buckets.has(key)) {
this.buckets.set(key, new Set());
}
this.buckets.get(key).add(i);
}
/**
* Find all points within threadingEpsilon L∞ distance of point i,
* remove them from the structure, and return [{index, deltaRe, deltaIm}, ...].
* Uses precision-aware verification via verifyAndGetDelta.
* Does NOT remove point i itself (it may not even be in the structure).
*/
findAndRemoveNear(i) {
const pt = this.getF64Point(i);
if (!pt) return [];
const { bx, by } = this.getBucket(pt.re, pt.im);
// Determine which 4 buckets to check based on position within bucket
// Since gridSize = 2*bucketRadius, checking 4 adjacent buckets guarantees
// we find all points within bucketRadius distance
const fracX = (pt.re / this.gridSize) - bx;
const fracY = (pt.im / this.gridSize) - by;
const dx = fracX < 0.5 ? -1 : 1;
const dy = fracY < 0.5 ? -1 : 1;
const bucketsToCheck = [
[bx, by],
[bx + dx, by],
[bx, by + dy],
[bx + dx, by + dy]
];
const found = [];
for (const [checkBx, checkBy] of bucketsToCheck) {
const key = this.getKey(checkBx, checkBy);
const bucket = this.buckets.get(key);
if (!bucket) continue;
const toRemove = [];
for (const j of bucket) {
if (j === i) continue; // Don't return the query point itself
// Use precision-aware verification
const delta = this.verifyAndGetDelta(i, j);
if (delta !== null) {
found.push({ index: j, deltaRe: delta.deltaRe, deltaIm: delta.deltaIm });
toRemove.push(j);
}
}
for (const j of toRemove) {
bucket.delete(j);
}
if (bucket.size === 0) {
this.buckets.delete(key);
}
}
return found;
}
/**
* Remove all indices older than (less than) minIndex
*/
removeOlderThan(minIndex) {
for (const [key, bucket] of this.buckets) {
for (const j of bucket) {
if (j < minIndex) {
bucket.delete(j);
}
}
if (bucket.size === 0) {
this.buckets.delete(key);
}
}
}
}
/**
* DDSpatialBucket - for quad-double precision points
* Point format: [re_hi, re_lo, im_hi, im_lo]
*/
class DDSpatialBucket extends SpatialBucket {
constructor(threadingEpsilon, getDDPoint) {
super(threadingEpsilon);
this.getDDPoint = getDDPoint;
}
getF64Point(i) {
const p = this.getDDPoint(i);
if (!p) return null;
return { re: p[0] + p[1], im: p[2] + p[3] };
}
verifyAndGetDelta(i, j) {
const pi = this.getDDPoint(i);
const pj = this.getDDPoint(j);
if (!pi || !pj) return null;
// Proper qd subtraction to avoid catastrophic cancellation
const deltaReQd = ddSub([pi[0], pi[1]], [pj[0], pj[1]]);
const deltaImQd = ddSub([pi[2], pi[3]], [pj[2], pj[3]]);
// Sum qd result to f64
const deltaRe = deltaReQd[0] + deltaReQd[1];
const deltaIm = deltaImQd[0] + deltaImQd[1];
// Check L∞ distance against actual threadingEpsilon
if (Math.max(Math.abs(deltaRe), Math.abs(deltaIm)) <= this.threadingEpsilon) {
return { deltaRe, deltaIm };
}
return null;
}
}
/**
* QDSpatialBucket - for quad-double precision points
* Point format: [re0, re1, re2, re3, im0, im1, im2, im3]
*/
class QDSpatialBucket extends SpatialBucket {
constructor(threadingEpsilon, getQDPoint) {
super(threadingEpsilon);
this.getQDPoint = getQDPoint;
}
getF64Point(i) {
const p = this.getQDPoint(i);
if (!p) return null;
return {
re: p[0] + p[1] + p[2] + p[3],
im: p[4] + p[5] + p[6] + p[7]
};
}
verifyAndGetDelta(i, j) {
const pi = this.getQDPoint(i);
const pj = this.getQDPoint(j);
if (!pi || !pj) return null;
// Proper QD subtraction to avoid catastrophic cancellation
const deltaReQD = toQDSub(
[pi[0], pi[1], pi[2], pi[3]],
[pj[0], pj[1], pj[2], pj[3]]
);
const deltaImQD = toQDSub(
[pi[4], pi[5], pi[6], pi[7]],
[pj[4], pj[5], pj[6], pj[7]]
);
// Sum QD result to f64
const deltaRe = qdToNumber(deltaReQD);
const deltaIm = qdToNumber(deltaImQD);
// Check L∞ distance against actual threadingEpsilon
if (Math.max(Math.abs(deltaRe), Math.abs(deltaIm)) <= this.threadingEpsilon) {
return { deltaRe, deltaIm };
}
return null;
}
}
// Reference Orbit Threading - enables robust cycle detection despite rebasing
class ReferenceOrbitThreading {
/**
* @param {SpatialBucket} spatialBucket - A precision-aware spatial bucket
* (DDSpatialBucket or QDSpatialBucket)
*/
constructor(spatialBucket) {
const maxCycleLength = 1e5;
// Window size limits bucket growth
this.windowSize = Math.min(1024, Math.floor(maxCycleLength));
// Threading links: {next: index, deltaRe: f32, deltaIm: f32}
this.threads = [];
// Spatial index for finding nearby points (precision-aware)
this.spatialBucket = spatialBucket;
}
/**
* Add a new orbit point and create threading links.
* All nearby past points are threaded to point at this new point.
* The spatial bucket handles precision-aware distance checking and delta computation.
*/
addPoint(currentIndex) {
// Find and remove all nearby past points from the bucket
// Returns [{index, deltaRe, deltaIm}, ...] with precision-aware deltas
const nearbyPast = this.spatialBucket.findAndRemoveNear(currentIndex);
// Add placeholder for this point's thread
this.threads.push({next: -1, deltaRe: 0, deltaIm: 0});
// Thread all nearby past points to this new point
// Note: deltaRe/deltaIm are (current - past), but we want (past -> current) delta
// So we negate the deltas returned by the bucket
for (const match of nearbyPast) {
this.threads[match.index] = {
next: currentIndex,
deltaRe: Math.fround(-match.deltaRe), // Negate: bucket returns (query - candidate)
deltaIm: Math.fround(-match.deltaIm)
};
}
// Add this point to the bucket for future lookups
this.spatialBucket.add(currentIndex);
// Cleanup old entries outside the window
if (currentIndex >= this.windowSize) {
this.spatialBucket.removeOlderThan(currentIndex - this.windowSize);
}
}
/**
* Get thread info for iteration i
*/
getThread(i) {
return this.threads[i] || null;
}
/**
* Manually set a thread (used for loop configuration)
*/
setThread(i, next, deltaRe, deltaIm) {
this.threads[i] = {
next,
deltaRe: Math.fround(deltaRe),
deltaIm: Math.fround(deltaIm)
};
}
get length() {
return this.threads.length;
}
}
// Single reference orbit perturbation method.
// Based on Zhuoran Li's 2021 approach:
// https://mathr.co.uk/blog/2021-05-14_stretching_deep_zoom.html
// Rebasing implementation follows Imagina: https://github.com/ImaginaFractal/Imagina
// Mixin that adds DD-precision reference orbit methods to any board class.
// Used by both DDZhuoranBoard (CPU) and GpuZhuoranBoard (GPU) to share
// the reference orbit computation logic.
const DDReferenceOrbitMixin = (Base) => class extends Base {
// Initialize DD reference orbit state. Call from constructor after super().
initDDReferenceOrbit(refC) {
// Reference point in DD precision [r_hi, r_lo, i_hi, i_lo]
this.refC = refC;
// Reference orbit array - each entry is [r_hi, r_lo, i_hi, i_lo]
this.refOrbit = [];
this.refOrbit.push([0, 0, 0, 0]); // Iteration 0: z = 0
this.refOrbit.push(this.refC.slice()); // Iteration 1: z = c
// Reference orbit state
this.refOrbitEscaped = false;
this.refIterations = 1;
this.maxRefIterations = 10000;
// Working array for DD precision operations
this.tt = new Array(16);
// Build threading structure
this.rebuildDDThreading();
}
// Rebuild threading structure from reference orbit (for serialization restore)
rebuildDDThreading() {
const threadingEpsilon = 10000 * this.epsilon;
const getDDPoint = (i) => this.refOrbit[i] || null;
const spatialBucket = new DDSpatialBucket(threadingEpsilon, getDDPoint);
this.threading = new ReferenceOrbitThreading(spatialBucket);
// Add all points from reference orbit
for (let i = 0; i <= this.refIterations; i++) {
this.threading.addPoint(i);
}
}
// DD accessor methods
getRefReal(ref) { return ref[0] + ref[1]; }
getRefImag(ref) { return ref[2] + ref[3]; }
getRefOrbit(iter) { return this.refOrbit[iter]; }
getRefOrbitLength() { return this.refOrbit.length; }
getRefCReal() { return this.refC[0] + this.refC[1]; }
getRefCImag() { return this.refC[2] + this.refC[3]; }
// Compute z = ref + dz in native DDc format (4 elements)
refDzNative(ref, dzr, dzi) {
// ref is DD: [r_hi, r_lo, i_hi, i_lo], returns DDc with proper DD addition
// Optimized to avoid allocations
const out = new Array(4);
arDdAdd(out, 0, ref[0], ref[1], dzr, 0);
arDdAdd(out, 2, ref[2], ref[3], dzi, 0);
return out;
}
// Extend reference orbit by one iteration in DD precision
extendReferenceOrbit() {
const lastIndex = this.refIterations;
const last = this.refOrbit[lastIndex];
const tt = this.tt;
const r1 = last[0];
const r2 = last[1];
const j1 = last[2];
const j2 = last[3];
// Check for escape
arDdSquare(tt, 0, r1, r2); // rsq = r**2
arDdSquare(tt, 2, j1, j2); // jsq = j**2
arDdAdd(tt, 4, tt[0], tt[1], tt[2], tt[3]); // d = rsq + jsq
if (tt[4] > 1e10) {
this.refOrbitEscaped = true;
return;
}
// Compute z^n for general exponent
arDdMul(tt, 6, 2 * r1, 2 * r2, j1, j2); // ja = 2*r*j
arDdAdd(tt, 8, tt[0], tt[1], -tt[2], -tt[3]); // ra = rsq - jsq
for (let ord = 2; ord < this.config.exponent; ord++) {
arDdMul(tt, 0, j1, j2, tt[6], tt[7]); // j * ja
arDdMul(tt, 2, r1, r2, tt[8], tt[9]); // r * ra
arDdAdd(tt, 4, -tt[0], -tt[1], tt[2], tt[3]); // rt = r*ra - j*ja
arDdMul(tt, 0, r1, r2, tt[6], tt[7]); // r * ja
arDdMul(tt, 2, j1, j2, tt[8], tt[9]); // j * ra
arDdAdd(tt, 6, tt[0], tt[1], tt[2], tt[3]); // ja = r*ja + j*ra
arDdSet(tt, 8, tt[4], tt[5]); // ra = rt
}
// Add c to get next z
const newZ = [0, 0, 0, 0];
arDdAdd(newZ, 0, tt[8], tt[9], this.refC[0], this.refC[1]); // real part
arDdAdd(newZ, 2, tt[6], tt[7], this.refC[2], this.refC[3]); // imag part
this.refOrbit.push(newZ);
this.refIterations++;
// Build thread-following map
this.threading.addPoint(this.refIterations);
// Grow array if needed
if (this.refIterations >= this.maxRefIterations) {
this.maxRefIterations *= 2;
}
}
};
// Mixin that adds QD-precision reference orbit methods to any board class.
// Used by both QDZhuoranBoard (CPU) and GpuAdaptiveBoard (GPU) to share
// the reference orbit computation logic.
const QDReferenceOrbitMixin = (Base) => class extends Base {
// Initialize QD reference orbit state. Call from constructor after super().
initQDReferenceOrbit(refC_qd) {
// Reference point in QD precision [re0, re1, re2, re3, im0, im1, im2, im3]
this.refC_qd = refC_qd;
// QD reference orbit array - each entry is [re0, re1, re2, re3, im0, im1, im2, im3]
this.qdRefOrbit = [
[0, 0, 0, 0, 0, 0, 0, 0], // Iteration 0: z = 0
[...refC_qd] // Iteration 1: z = c
];
// Reference orbit state
this.refOrbitEscaped = false;
this.refIterations = 1;
this.maxRefIterations = 10000;
// Working array for QD precision operations
this.tt = new Array(32);
// Build threading structure
this.rebuildQDThreading();
}
// Rebuild threading structure from reference orbit (for serialization restore)
rebuildQDThreading() {
const threadingEpsilon = 10000 * this.epsilon;
const getQDPoint = (i) => this.qdRefOrbit[i] || null;
const spatialBucket = new QDSpatialBucket(threadingEpsilon, getQDPoint);
this.threading = new ReferenceOrbitThreading(spatialBucket);
// Add all points from reference orbit
for (let i = 0; i <= this.refIterations; i++) {
this.threading.addPoint(i);
}
}
// QD accessor methods
getRefReal(ref) { return ref[0] + ref[1] + ref[2] + ref[3]; }
getRefImag(ref) { return ref[4] + ref[5] + ref[6] + ref[7]; }
getRefOrbit(iter) { return this.qdRefOrbit[iter]; }
getRefOrbitLength() { return this.qdRefOrbit.length; }
getRefCReal() { return this.refC_qd[0] + this.refC_qd[1] + this.refC_qd[2] + this.refC_qd[3]; }
getRefCImag() { return this.refC_qd[4] + this.refC_qd[5] + this.refC_qd[6] + this.refC_qd[7]; }
// Compute z = ref + dz in native QDc format (8 elements)
refDzNative(ref, dzr, dzi) {
// ref is QD: [r0,r1,r2,r3, i0,i1,i2,i3], returns QDc
// Optimized to avoid allocations
const out = new Array(8);
arQdAdd(out, 0, ref[0], ref[1], ref[2], ref[3], dzr, 0, 0, 0);
arQdAdd(out, 4, ref[4], ref[5], ref[6], ref[7], dzi, 0, 0, 0);
return out;
}
// Extend reference orbit by one iteration in QD precision
extendReferenceOrbit() {
const last = this.qdRefOrbit[this.refIterations];
const rr = [last[0], last[1], last[2], last[3]];
const ri = [last[4], last[5], last[6], last[7]];
const tt = this.tt;
// Check for escape using sum of QD components
const rSum = rr[0] + rr[1] + rr[2] + rr[3];
const iSum = ri[0] + ri[1] + ri[2] + ri[3];
const mag = rSum * rSum + iSum * iSum;
if (mag > 1e10) {
this.refOrbitEscaped = true;
return;
}
// Compute z^n for general exponent
// z^2 = (zr + zi*i)^2 = zr^2 - zi^2 + 2*zr*zi*i
arQdSquare(tt, 0, rr[0], rr[1], rr[2], rr[3]); // rsq = r^2
arQdSquare(tt, 4, ri[0], ri[1], ri[2], ri[3]); // jsq = j^2
arQdMul(tt, 8, 2*rr[0], 2*rr[1], 2*rr[2], 2*rr[3],
ri[0], ri[1], ri[2], ri[3]); // ja = 2*r*j
arQdAdd(tt, 16, tt[0], tt[1], tt[2], tt[3],
-tt[4], -tt[5], -tt[6], -tt[7]); // ra = rsq - jsq
for (let ord = 2; ord < this.config.exponent; ord++) {
arQdMul(tt, 0, ri[0], ri[1], ri[2], ri[3],
tt[8], tt[9], tt[10], tt[11]); // j * ja
arQdMul(tt, 4, rr[0], rr[1], rr[2], rr[3],
tt[16], tt[17], tt[18], tt[19]); // r * ra
arQdAdd(tt, 12, -tt[0], -tt[1], -tt[2], -tt[3],
tt[4], tt[5], tt[6], tt[7]); // rt = r*ra - j*ja
arQdMul(tt, 0, rr[0], rr[1], rr[2], rr[3],
tt[8], tt[9], tt[10], tt[11]); // r * ja
arQdMul(tt, 4, ri[0], ri[1], ri[2], ri[3],
tt[16], tt[17], tt[18], tt[19]); // j * ra
arQdAdd(tt, 8, tt[0], tt[1], tt[2], tt[3],
tt[4], tt[5], tt[6], tt[7]); // ja = r*ja + j*ra
arQdSet(tt, 16, tt[12], tt[13], tt[14], tt[15]); // ra = rt
}
// Add c to get next z
const nzrQD = new Array(4);
const nziQD = new Array(4);
arQdAdd(nzrQD, 0, tt[16], tt[17], tt[18], tt[19],
this.refC_qd[0], this.refC_qd[1], this.refC_qd[2], this.refC_qd[3]);
arQdAdd(nziQD, 0, tt[8], tt[9], tt[10], tt[11],
this.refC_qd[4], this.refC_qd[5], this.refC_qd[6], this.refC_qd[7]);
this.qdRefOrbit.push([nzrQD[0], nzrQD[1], nzrQD[2], nzrQD[3],
nziQD[0], nziQD[1], nziQD[2], nziQD[3]]);
this.refIterations++;
// Build thread-following map
this.threading.addPoint(this.refIterations);
// Grow array if needed
if (this.refIterations >= this.maxRefIterations) {
this.maxRefIterations *= 2;
}
}
};
// Base class for CPU-based Zhuoran perturbation boards (DD and QD precision)
// Subclasses implement precision-specific reference orbit computation
class CpuZhuoranBaseBoard extends Board {
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
// Per-pixel thread tracking for convergence detection
this.currentThreadIter = new Array(this.config.dimsArea).fill(0);
this.threadDeltaRe = new Array(this.config.dimsArea).fill(0);
this.threadDeltaIm = new Array(this.config.dimsArea).fill(0);
// Reference orbit management
this.maxRefIterations = 10000; // Will grow dynamically
this.refOrbitEscaped = false;
this.refIterations = 1; // Start with iterations 0 and 1
// Per-pixel data (double precision) - shared by all subclasses
this.dc = []; // Delta c from reference point [real, imag] pairs
this.dz = []; // Current perturbation delta [real, imag] pairs
this.refIter = []; // Which iteration of reference each pixel is following
this.pixelIndexes = []; // Active pixel indices
this.maxRefIter = 1; // Track maximum refIter to avoid scanning all pixels
this.effort = 100; // Default for CPU Zhuoran boards, overridden by subclasses
}
// Abstract methods - subclasses must implement these
// Get the double value of the real part from a ref orbit entry
getRefReal(refEntry) { throw new Error('Abstract method'); }
// Get the double value of the imaginary part from a ref orbit entry
getRefImag(refEntry) { throw new Error('Abstract method'); }
// Get the reference orbit entry at the given iteration
getRefOrbit(iter) { throw new Error('Abstract method'); }
// Get the current length of the reference orbit
getRefOrbitLength() { throw new Error('Abstract method'); }
// Get reference C real part as double
getRefCReal() { throw new Error('Abstract method'); }
// Get reference C imaginary part as double
getRefCImag() { throw new Error('Abstract method'); }
// Extend reference orbit by one iteration (precision-specific)
extendReferenceOrbit() { throw new Error('Abstract method'); }
// Initialize pixels (shared by DD and QD subclasses)
initPixels() {
// Compute delta c directly without precision loss.
// At deep zoom, computing cr = center + offset loses precision.
// Since the reference point IS the view center, dc is just the pixel offset from center.
const sizeScalar = this.size;
const dimsWidth = this.config.dimsWidth;
const dimsHeight = this.config.dimsHeight;
const aspectRatio = this.config.aspectRatio;
// Convert reference point to double for spike detection
// Subclasses implement these accessors via mixins
const refRe = this.getRefCReal();
const refIm = this.getRefCImag();
for (let y = 0; y < dimsHeight; y++) {
const yFrac = (0.5 - y / dimsHeight);
const dci = yFrac * (sizeScalar / aspectRatio);
for (let x = 0; x < dimsWidth; x++) {
const xFrac = (x / dimsWidth - 0.5);
const dcr = xFrac * sizeScalar;
const index = y * dimsWidth + x;
this.dc[index * 2] = dcr;
this.dc[index * 2 + 1] = dci;
// Start with z = c, so dz = dc
this.dz[index * 2] = dcr;
this.dz[index * 2 + 1] = dci;
// Start at iteration 1 (z = c)
this.refIter[index] = 1;
// Skip precomputed pixels - they'll be flushed at their iteration
if (!this.precomputed || !this.precomputed.isPrecomputed(index)) {
this.pixelIndexes.push(index);
}
// Count spike pixels
const cr = refRe + dcr;
const ci = refIm + dci;
if (this.inspike(cr, ci)) {
this.ch += 1;
}
}
}
}
// Shared iterate() method - works for both DD and QD
iterate(targetIters = 1) {
// Step 1: Extend reference orbit for entire batch upfront (not ahead)
const targetRefIterations = Math.max(this.it + targetIters, this.maxRefIter + targetIters);
while (!this.refOrbitEscaped && this.refIterations < targetRefIterations) {
this.extendReferenceOrbit();
}
// Batch multiple iterations internally
for (let batch = 0; batch < targetIters && this.un > 0; batch++) {
let changes = null;
// Step 2: Iterate all active pixels using perturbation
const newPixelIndexes = [];
for (const index of this.pixelIndexes) {
if (this.nn[index]) continue; // Skip finished pixels
const result = this.iteratePixel(index);
if (result !== 0) {
if (!changes) {
changes = { iter: this.it, nn: [], vv: [] };
}
if (result > 0) {
// Diverged
changes.nn.push(index);
this.nn[index] = this.it;
this.di += 1;
this.un -= 1;
} else {
// Converged
const index2 = index * 2;
const nextRefIter = this.refIter[index] + 1;
const ref = this.getRefOrbit(Math.min(nextRefIter, this.getRefOrbitLength() - 1));
const dzr = this.dz[index2];
const dzi = this.dz[index2 + 1];
changes.vv.push({
index: index,
z: this.refDzNative(ref, dzr, dzi), // Native format (DDc or QDc)
p: this.pp[index]
});
this.nn[index] = -this.it;
this.un -= 1;
if (this.inspike(
this.dc[index2] + this.getRefCReal(),
this.dc[index2 + 1] + this.getRefCImag()
) && this.ch > 0) {
this.ch -= 1;
}
}
} else {
newPixelIndexes.push(index);
}
}
this.pixelIndexes = newPixelIndexes;
// Compact if needed
if (this.pixelIndexes.length > this.un * 1.25) {
this.pixelIndexes = this.pixelIndexes.filter(i => !this.nn[i]);
}
// Flush precomputed points at this iteration
if (this.precomputed) {
this.precomputed.flushAtIteration(this.it, this);
}
this.it++;
this.queueChanges(changes);
}
}
// Shared iteratePixel() method - works for both DD and QD
iteratePixel(index) {
const index2 = index * 2;
let refIter = this.refIter[index];
// Check if current z has escaped BEFORE doing iteration
if (refIter < this.getRefOrbitLength()) {
const ref = this.getRefOrbit(refIter);
const refR = this.getRefReal(ref);
const refI = this.getRefImag(ref);
const dr = this.dz[index2];
const di = this.dz[index2 + 1];
const currentZR = refR + dr;
const currentZI = refI + di;
const currentMag2 = currentZR * currentZR + currentZI * currentZI;
if (currentMag2 > 4) {
return 1; // Diverged
}
}
// Ensure reference orbit exists
if (refIter >= this.getRefOrbitLength()) {
if (this.refOrbitEscaped) {
// Rebase to beginning
const lastRef = this.getRefOrbit(this.getRefOrbitLength() - 1);
const lastRefR = this.getRefReal(lastRef);
const lastRefI = this.getRefImag(lastRef);
const dr = this.dz[index2];
const di = this.dz[index2 + 1];
this.dz[index2] = lastRefR + dr;
this.dz[index2 + 1] = lastRefI + di;
this.refIter[index] = 0;
refIter = 0;
} else {
return 1; // Mark as diverged if unexpected
}
}
// Check if we need to rebase (Zhuoran's key innovation)
if (this.shouldRebase(index)) {
const ref = this.getRefOrbit(refIter);
const refR = this.getRefReal(ref);
const refI = this.getRefImag(ref);
const dr = this.dz[index2];
const di = this.dz[index2 + 1];
this.dz[index2] = refR + dr;
this.dz[index2 + 1] = refI + di;
this.refIter[index] = 0;
refIter = 0;
}
// Get reference orbit value
const ref = this.getRefOrbit(refIter);
if (!ref) {
return 0;
}
const refR = this.getRefReal(ref);
const refI = this.getRefImag(ref);
// Perturbation iteration using binomial expansion (Horner's method)
const dr = this.dz[index2];
const di = this.dz[index2 + 1];
const exponent = this.config.exponent || 2;
// Build binomial powers: coeff * z_ref^power for each term
let zPowR = refR;
let zPowI = refI;
let coeff = exponent;
// Start Horner's method with innermost term (just dz)
let resultR = dr;
let resultI = di;
// Horner's method: accumulate terms from highest to lowest power of z_ref
for (let k = 1; k < exponent; k++) {
// Add coeff * z_ref^power term
const termR = coeff * zPowR;
const termI = coeff * zPowI;
resultR = resultR + termR;
resultI = resultI + termI;
// Multiply by dz (complex multiplication)
const tempR = resultR * dr - resultI * di;
resultI = resultR * di + resultI * dr;
resultR = tempR;
// Update z_ref power: z_pow = z_pow * z_ref
const newZPowR = zPowR * refR - zPowI * refI;
zPowI = zPowR * refI + zPowI * refR;
zPowR = newZPowR;
// Update coefficient: coeff *= (n-k) / (k+1)
coeff *= (exponent - k) / (k + 1);
}
// Add perturbation in c
const newDr = resultR + this.dc[index2];
const newDi = resultI + this.dc[index2 + 1];
this.dz[index2] = newDr;
this.dz[index2 + 1] = newDi;
// CONVERGENCE DETECTION: fibonacciPeriod returns 1 at Fibonacci checkpoints
const justUpdatedCheckpoint = (fibonacciPeriod(this.it) == 1);
if (justUpdatedCheckpoint) {
this.bb[index2] = dr;
this.bb[index2 + 1] = di;
this.pp[index] = 0;
this.currentThreadIter[index] = refIter;
this.threadDeltaRe[index] = 0;
this.threadDeltaIm[index] = 0;
} else {
// Incrementally advance threads when thread.next == refIter
let currentThread = this.currentThreadIter[index];
const thread = this.threading.getThread(currentThread);
if (thread.next == refIter) {
this.threadDeltaRe[index] += thread.deltaRe;
this.threadDeltaIm[index] += thread.deltaIm;
currentThread = thread.next;
this.currentThreadIter[index] = currentThread;
}
// Check convergence when currentThreadIter matches refIter
if (this.currentThreadIter[index] === refIter) {
const checkpoint_dr = this.bb[index2];
const checkpoint_di = this.bb[index2 + 1];
const dzDiffR = dr - checkpoint_dr;
const dzDiffI = di - checkpoint_di;
const totalDiffR = this.threadDeltaRe[index] + dzDiffR;
const totalDiffI = this.threadDeltaIm[index] + dzDiffI;
const db = Math.max(Math.abs(totalDiffR), Math.abs(totalDiffI));
const epsilon = this.epsilon;
const epsilon2 = this.epsilon2;
if (db <= epsilon2) {
if (!this.pp[index]) {
this.pp[index] = this.it - 1;
}
if (db <= epsilon) {
return -1; // Converged via threading!
}
}
}
}
// Update reference iteration counter
this.refIter[index]++;
if (this.refIter[index] > this.maxRefIter) {
this.maxRefIter = this.refIter[index];
}
return 0; // Continue iterating
}
// Shared shouldRebase() method - works for both DD and QD
shouldRebase(index) {
const index2 = index * 2;
const dr = this.dz[index2];
const di = this.dz[index2 + 1];
const refIter = this.refIter[index];
if (refIter === 0) return false;
if (refIter >= this.getRefOrbitLength()) return false;
const ref = this.getRefOrbit(refIter);
if (!ref) return false;
const refR = this.getRefReal(ref);
const refI = this.getRefImag(ref);
const dzNorm = Math.max(Math.abs(dr), Math.abs(di));
const totalR = refR + dr;
const totalI = refI + di;
const totalNorm = Math.max(Math.abs(totalR), Math.abs(totalI));
return totalNorm < dzNorm * 2.0;
}
async serialize() {
// Build sparse nn array for completed pixels (non-zero nn values)
const completedIndexes = [];
const completedNn = [];
for (let i = 0; i < this.nn.length; i++) {
if (this.nn[i] !== 0) {
completedIndexes.push(i);
completedNn.push(this.nn[i]);
}
}
return {
...(await super.serialize()),
// Per-pixel state (sparse - only for active pixels)
pixelIndexes: this.pixelIndexes,
dc: this.pixelIndexes.flatMap(i => [this.dc[i*2], this.dc[i*2+1]]),
dz: this.pixelIndexes.flatMap(i => [this.dz[i*2], this.dz[i*2+1]]),
refIter: this.pixelIndexes.map(i => this.refIter[i]),
pp: this.pixelIndexes.map(i => this.pp[i]),
// Convergence detection state
currentThreadIter: this.pixelIndexes.map(i => this.currentThreadIter[i]),
threadDeltaRe: this.pixelIndexes.map(i => this.threadDeltaRe[i]),
threadDeltaIm: this.pixelIndexes.map(i => this.threadDeltaIm[i]),
// Reference orbit state
refOrbitEscaped: this.refOrbitEscaped,
refIterations: this.refIterations,
maxRefIter: this.maxRefIter,
// Completed pixels
completedIndexes,
completedNn,
};
}
static restoreBaseState(board, serialized) {
// Restore nn values for completed pixels
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
// Restore per-pixel state from sparse serialized data
board.dc = new Array(serialized.config.dimsArea * 2).fill(0);
board.dz = new Array(serialized.config.dimsArea * 2).fill(0);
board.refIter = new Array(serialized.config.dimsArea).fill(0);
board.pp = new Array(serialized.config.dimsArea).fill(0);
board.currentThreadIter = new Array(serialized.config.dimsArea).fill(0);
board.threadDeltaRe = new Array(serialized.config.dimsArea).fill(0);
board.threadDeltaIm = new Array(serialized.config.dimsArea).fill(0);
const pixelIndexes = serialized.pixelIndexes || [];
for (let i = 0; i < pixelIndexes.length; i++) {
const index = pixelIndexes[i];
board.dc[index * 2] = serialized.dc[i * 2];
board.dc[index * 2 + 1] = serialized.dc[i * 2 + 1];
board.dz[index * 2] = serialized.dz[i * 2];
board.dz[index * 2 + 1] = serialized.dz[i * 2 + 1];
board.refIter[index] = serialized.refIter[i];
board.pp[index] = serialized.pp[i];
board.currentThreadIter[index] = serialized.currentThreadIter[i];
board.threadDeltaRe[index] = serialized.threadDeltaRe[i];
board.threadDeltaIm[index] = serialized.threadDeltaIm[i];
}
board.pixelIndexes = pixelIndexes.slice();
// Restore reference orbit state
board.refOrbitEscaped = serialized.refOrbitEscaped || false;
board.refIterations = serialized.refIterations || 1;
board.maxRefIter = serialized.maxRefIter || 1;
// Restore scalar values
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
}
}
// DD-precision implementation of CpuZhuoranBaseBoard
// Uses DDReferenceOrbitMixin for reference orbit computation
class DDZhuoranBoard extends DDReferenceOrbitMixin(CpuZhuoranBaseBoard) {
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
this.effort = 450; // Benchmarked: 19.6 ns/px-iter, 4.5× slower than CPU
// Initialize DD reference orbit (refC, refOrbit, threading, etc.)
const refRe = qdToDD(this.re);
const refIm = qdToDD(this.im);
this.initDDReferenceOrbit([refRe[0], refRe[1], refIm[0], refIm[1]]);
this.initPixels();
}
static fromSerialized(serialized) {
const board = new DDZhuoranBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Restore base Zhuoran state (nn, dc, dz, refIter, etc.)
CpuZhuoranBaseBoard.restoreBaseState(board, serialized);
// Restore DD reference orbit
board.refOrbit = serialized.refOrbit || [];
board.refC = serialized.refC || [0, 0, 0, 0];
// Rebuild threading structure from restored reference orbit
board.rebuildDDThreading();
return board;
}
async serialize() {
return {
...(await super.serialize()),
refOrbit: this.refOrbit,
refC: this.refC,
};
}
getCurrentRefZ(index) {
const refIter = this.refIter[index];
if (refIter <= this.refIterations && this.refOrbit[refIter]) {
return this.refOrbit[refIter];
}
return [0, 0, 0, 0];
}
}
// QD-precision implementation of CpuZhuoranBaseBoard
// Provides higher precision (~212 bits) reference for very deep zooms
// Uses QDReferenceOrbitMixin for reference orbit computation
class QDZhuoranBoard extends QDReferenceOrbitMixin(CpuZhuoranBaseBoard) {
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
this.effort = 480; // Benchmarked: 21.0 ns/px-iter, 4.8× slower than CPU
// Initialize QD reference orbit (refC_qd, qdRefOrbit, threading, etc.)
const refReQD = this.re.slice();
const refImQD = this.im.slice();
this.initQDReferenceOrbit([...refReQD, ...refImQD]);
this.initPixels();
}
async serialize() {
return {
...(await super.serialize()),
refC_qd: this.refC_qd,
qdRefOrbit: this.qdRefOrbit,
};
}
static fromSerialized(serialized) {
const board = new QDZhuoranBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Restore base Zhuoran state (nn, dc, dz, refIter, etc.)
CpuZhuoranBaseBoard.restoreBaseState(board, serialized);
// Restore QD reference orbit
board.refC_qd = serialized.refC_qd || new Array(8).fill(0);
board.qdRefOrbit = serialized.qdRefOrbit || [];
// Rebuild threading structure from restored reference orbit
board.rebuildQDThreading();
return board;
}
}
// WebGPU-accelerated Mandelbrot computation using single-precision float32
// GPU computes all pixels in parallel using standard Mandelbrot iteration
// Base class for WebGPU-accelerated boards
// Provides shared GPU infrastructure for different computation strategies
class GpuBaseBoard extends Board {
static GPU_DEFAULT_MAX_BUFFER = 200 * 1024 * 1024; // 200MB
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
// Note: size, re, im are available via inherited getters from Board (computed from sizesQD)
// WebGPU state (shared by all GPU board implementations)
this.device = null;
this.pipeline = null;
this.buffers = {};
this.isGPUReady = false;
this.gpuInitPromise = null;
this.isComputing = false;
this.computePromise = null; // Track current async computation
this.lastReportedIters = null;
this.cpuStatus = null;
this.readPixelBufferPromise = null; // Lock for readPixelBuffer
this.effort = 20; // Default for GPU boards, overridden by subclasses
this.minBatchIters = 17; // GPU boards need minimum iterations per batch to amortize overhead
this.maxBatchIters = 134567; // Cap to avoid very long batches with few pixels
// Initialize batch tracking state (will be fully setup in initResultsReadback)
// This ensures batchesToReadback is defined for precomputed points processed before GPU init.
// When empty, queueChanges() uses the fallback path that adds directly to changeList.
this.batchesToReadback = [];
this.batchResultsRead = [];
this.previousBatchEndIter = 1; // First batch starts at iter=1
this.lastFlushedPrecomputedIter = 0;
}
checkSpike(size, re, im) {
// Count chaotic pixels in spike region and track which pixels are in spike
const dimsWidth = this.config.dimsWidth;
const dimsHeight = this.config.dimsHeight;
const size_double = Array.isArray(size) ? size.reduce((a, b) => a + (b || 0), 0) : size;
const re_double = Array.isArray(re) ? (re[0] + re[1]) : re;
const im_double = Array.isArray(im) ? (im[0] + im[1]) : im;
// Only allocate inSpike array if we find spike pixels (common case: none)
this.inSpike = null;
for (let y = 0; y < dimsHeight; y++) {
const yFrac = (0.5 - y / dimsHeight);
const ci = im_double + yFrac * (size_double / this.config.aspectRatio);
for (let x = 0; x < dimsWidth; x++) {
const index = y * dimsWidth + x;
const xFrac = (x / dimsWidth - 0.5);
const cr = re_double + xFrac * size_double;
if (this.inspike(cr, ci)) {
// Lazily allocate array only when we find the first spike pixel
if (!this.inSpike) {
this.inSpike = new Uint8Array(this.config.dimsArea);
}
this.ch += 1;
this.inSpike[index] = 1;
}
}
}
}
async initGPU() {
try {
const t0 = performance.now();
// Check WebGPU availability
if (!navigator.gpu) {
console.warn('WebGPU not supported');
return false;
}
// Request adapter (note: adapters are consumed after creating a device, so can't cache)
const adapter = await navigator.gpu.requestAdapter();
if (!adapter) {
console.warn('No WebGPU adapter found');
return false;
}
const t1 = performance.now();
// Request device with higher buffer limits if supported
const requiredLimits = {};
if (adapter.limits.maxStorageBufferBindingSize > 134217728) {
// Request higher limit if adapter supports it (default is 128MB)
requiredLimits.maxStorageBufferBindingSize = adapter.limits.maxStorageBufferBindingSize;
}
if (adapter.limits.maxBufferSize > 134217728) {
requiredLimits.maxBufferSize = adapter.limits.maxBufferSize;
}
this.device = await adapter.requestDevice({
requiredLimits: Object.keys(requiredLimits).length > 0 ? requiredLimits : undefined
});
if (!this.device) {
console.warn('Failed to get WebGPU device');
return false;
}
const t2 = performance.now();
// Subclass-specific initialization
await this.createComputePipeline();
const t3 = performance.now();
await this.createBuffers();
const t4 = performance.now();
this.createBindGroup();
const t5 = performance.now();
if (hasDebugFlag(this.config, 't')) {
console.log(`[gpu-init] adapter=${(t1-t0).toFixed(0)}ms device=${(t2-t1).toFixed(0)}ms pipeline=${(t3-t2).toFixed(0)}ms buffers=${(t4-t3).toFixed(0)}ms bindgroup=${(t5-t4).toFixed(0)}ms total=${(t5-t0).toFixed(0)}ms`);
}
this.isGPUReady = true;
return true;
} catch (error) {
console.error(`Board ${this.id}: WebGPU initialization failed:`, error.message || error);
// Check if this is a buffer size error
if (error.message && error.message.includes('exceeds WebGPU safe limit')) {
console.warn(
`Board ${this.id}: Dimensions too large for GPU ` +
`(${this.config.dimsWidth}x${this.config.dimsHeight}). ` +
`This board will NOT compute any pixels!`);
}
return false;
}
}
async ensureGPUReady() {
if (this.gpuInitPromise) {
await this.gpuInitPromise;
this.gpuInitPromise = null;
}
return this.isGPUReady;
}
async iterate(targetIters = null) {
if (!this.isGPUReady) {
return;
}
// Block if already computing (prevents scheduler spin on GPU boards)
if (this.computePromise) {
await this.computePromise;
return;
}
this.computePromise = this.compute(targetIters);
try {
await this.computePromise;
} finally {
this.computePromise = null;
}
}
async readBuffer(buffer, TypedArrayConstructor) {
const size = buffer.size;
const stagingBuffer = this.device.createBuffer({
size,
usage: GPUBufferUsage.COPY_DST | GPUBufferUsage.MAP_READ,
label: 'Staging buffer'
});
const commandEncoder = this.device.createCommandEncoder();
commandEncoder.copyBufferToBuffer(buffer, 0, stagingBuffer, 0, size);
this.device.queue.submit([commandEncoder.finish()]);
await stagingBuffer.mapAsync(GPUMapMode.READ);
const data = new TypedArrayConstructor(stagingBuffer.getMappedRange()).slice();
stagingBuffer.unmap();
stagingBuffer.destroy();
return data;
}
static isAvailable() {
return typeof navigator !== 'undefined' && 'gpu' in navigator;
}
static async queryMaxBufferSize() {
if (GpuBaseBoard.cachedMaxBufferSize !== undefined) {
return GpuBaseBoard.cachedMaxBufferSize;
}
try {
// Query adapter limits directly - no need to create a device
const adapter = await navigator.gpu.requestAdapter();
if (!adapter) {
console.warn('WebGPU adapter not available, falling back to CPU/WebGL2');
GpuBaseBoard.cachedMaxBufferSize = null;
return null;
}
const limit = Math.min(
adapter.limits.maxBufferSize,
adapter.limits.maxStorageBufferBindingSize);
GpuBaseBoard.cachedMaxBufferSize = Math.floor(limit * 0.9); // 90% for safety
return GpuBaseBoard.cachedMaxBufferSize;
} catch (e) {
console.warn('WebGPU query failed, falling back to CPU/WebGL2:', e.message || e);
GpuBaseBoard.cachedMaxBufferSize = null;
return null;
}
}
// ================================================================
// Double-buffering and compaction infrastructure
// Subclasses must define: static BYTES_PER_PIXEL, static STRIDE
// ================================================================
/**
* Initialize double-buffering and compaction state.
* Call from subclass constructor after super().
*/
initDoubleBuffering() {
this.stagingBufferIndex = 0;
this.hasPendingResults = false;
this.pendingIterationsPerBatch = 0;
this.baseIt = 1; // Committed iteration count
// Compaction state - uses bandwidth cost model
this.activeCount = this.config.dimsArea;
this.deadSinceCompaction = 0;
this.wastedBandwidth = 0;
this.compactionCount = 0;
this.pendingActiveCount = this.config.dimsArea;
this.lastBatchCompacted = false;
this.cumulativeWastedReads = 0;
}
initResultsReadback(recordBytes, maxCount) {
const safeMax = Math.max(1, maxCount);
this.resultsRecordBytes = recordBytes;
this.resultsHeaderBytes = 32; // 8 u32 fields: count, lastStaged, active_count, start_iter, iterations_per_batch, pad x3
this.resultsMaxCount = safeMax;
// Chunk size for incremental readback
this.resultsReadbackMaxRecords = Math.max(256, Math.floor(safeMax * 0.01));
// Pre-staging area layout (written by staging shader, copied to staging buffer):
// - Header: 16 bytes (firstEmpty, countInChunk, chunkStartIndex, reserved)
// - Records: chunkSize * recordBytes
// Two pre-staging areas (one per staging buffer) to prevent race conditions
// when command buffers overlap in execution.
this.preStagingHeaderBytes = 16;
this.preStagingSize = this.preStagingHeaderBytes + (recordBytes * this.resultsReadbackMaxRecords);
const preStagingBase = this.resultsHeaderBytes + (recordBytes * safeMax);
this.preStagingOffsets = [preStagingBase, preStagingBase + this.preStagingSize];
// Total results buffer: header + main records + TWO pre-staging areas
this.resultsBufferSize = preStagingBase + (this.preStagingSize * 2);
// Staging buffer matches pre-staging area size
this.resultsReadbackBufferSize = this.preStagingSize;
// Reset buffer: 8 u32s for header (count=0, lastStaged=0, others don't matter)
this.resultsCounterReset = new Uint32Array([0, 0, 0, 0, 0, 0, 0, 0]);
if (this.buffers.results?.destroy) {
this.buffers.results.destroy();
}
if (this.buffers.resultsStaging) {
for (const buf of this.buffers.resultsStaging) {
if (buf?.destroy) buf.destroy();
}
}
this.buffers.results = this.device.createBuffer({
size: this.resultsBufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST,
label: 'Results buffer'
});
const stagingSize = this.resultsReadbackBufferSize;
this.buffers.resultsStaging = [
this.device.createBuffer({
size: stagingSize,
usage: GPUBufferUsage.MAP_READ | GPUBufferUsage.COPY_DST,
label: 'Results staging 0'
}),
this.device.createBuffer({
size: stagingSize,
usage: GPUBufferUsage.MAP_READ | GPUBufferUsage.COPY_DST,
label: 'Results staging 1'
})
];
this.resultsReadIndex = 0;
this.resultsTotalCount = 0;
this.readbackBufferIndex = 0;
this.pendingReadbackIndex = null;
this.pendingReadbackPromise = null;
this.hasPendingResults = false;
this.resultsReadbackBytes = 0;
this.resultsReadbackBatches = 0;
this.lastResultsCount = 0;
// Batch tracking for ordered results (see docs/gpu-results-readback-design.md)
this.batchesToReadback = []; // Queue of {startIter, endIter, remainingPixelCount}
this.batchResultsRead = []; // Accumulated results for current head batch
this.previousBatchEndIter = 1; // First batch starts at iter=1
this.previousFirstEmpty = 0; // Track firstEmpty for batch size computation
this.lastFlushedPrecomputedIter = 0;
this.device.queue.writeBuffer(this.buffers.results, 0, this.resultsCounterReset);
// Batch locking buffer (see docs/gpu-batch-locking.md)
// Layout: lock(u32), batch_active(u32), collision_count(u32), reserved(u32)
// Used to prevent shader race conditions between overlapping batches
if (this.buffers.lock?.destroy) {
this.buffers.lock.destroy();
}
this.buffers.lock = this.device.createBuffer({
size: 16, // 4 u32s
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST,
label: 'Batch lock buffer'
});
// Initialize: lock=0 (unlocked), batch_active=0, collision_count=0, reserved=0
this.lockBufferReset = new Uint32Array([0, 0, 0, 0]);
this.device.queue.writeBuffer(this.buffers.lock, 0, this.lockBufferReset);
// Collision stats tracking (CPU-side)
this.batchCollisionCount = 0;
this.batchTotalCount = 0;
// Create staging shader pipeline (see docs/gpu-results-readback-design.md)
this.createStagingPipeline();
}
createStagingPipeline() {
const chunkSize = this.resultsReadbackMaxRecords;
const recordBytes = this.resultsRecordBytes;
const recordU32s = recordBytes / 4;
// Guard shader: tries to acquire batch lock (see docs/gpu-batch-locking.md)
// Uses atomicCompareExchange to prevent race conditions between overlapping batches
// Uses per-buffer-index batch_active to avoid race between Guard2 overwriting batch_active
// before Compute1 reads it (see design doc for details)
const guardShaderCode = `
struct GuardParams {
buffer_index: u32, // 0 or 1, matches double-buffering index
}
// Lock buffer layout:
// [0]=lock, [1]=batch_active[0], [2]=batch_active[1], [3]=collision_count
struct LockBuffer {
lock: atomic<u32>,
batch_active_0: atomic<u32>,
batch_active_1: atomic<u32>,
collision_count: atomic<u32>,
}
@group(0) @binding(0) var<uniform> params: GuardParams;
@group(0) @binding(1) var<storage, read_write> lockBuf: LockBuffer;
@compute @workgroup_size(1)
fn guard_main() {
// Try to acquire lock: atomicCompareExchange(expected=0, desired=1)
let prev = atomicCompareExchangeWeak(&lockBuf.lock, 0u, 1u).old_value;
let is_active = select(0u, 1u, prev == 0u);
// Write to per-buffer-index batch_active to avoid cross-batch race
if (params.buffer_index == 0u) {
atomicStore(&lockBuf.batch_active_0, is_active);
} else {
atomicStore(&lockBuf.batch_active_1, is_active);
}
if (prev != 0u) {
atomicAdd(&lockBuf.collision_count, 1u);
}
}
`;
const guardModule = this.device.createShaderModule({
code: guardShaderCode,
label: 'Guard shader'
});
this.guardPipeline = this.device.createComputePipeline({
layout: 'auto',
compute: {
module: guardModule,
entryPoint: 'guard_main'
},
label: 'Guard pipeline'
});
// Create guard params buffers for each buffer index
this.buffers.guardParams = [
this.device.createBuffer({
size: 4, // 1 u32
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Guard params 0'
}),
this.device.createBuffer({
size: 4, // 1 u32
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Guard params 1'
})
];
this.device.queue.writeBuffer(this.buffers.guardParams[0], 0, new Uint32Array([0]));
this.device.queue.writeBuffer(this.buffers.guardParams[1], 0, new Uint32Array([1]));
// Create guard bind groups for each buffer index
this.guardBindGroups = [
this.device.createBindGroup({
layout: this.guardPipeline.getBindGroupLayout(0),
entries: [
{ binding: 0, resource: { buffer: this.buffers.guardParams[0] } },
{ binding: 1, resource: { buffer: this.buffers.lock } }
],
label: 'Guard bind group 0'
}),
this.device.createBindGroup({
layout: this.guardPipeline.getBindGroupLayout(0),
entries: [
{ binding: 0, resource: { buffer: this.buffers.guardParams[1] } },
{ binding: 1, resource: { buffer: this.buffers.lock } }
],
label: 'Guard bind group 1'
})
];
// Staging shader: copies results from main area to pre-staging area
// All threads copy records in parallel, then atomicMin finds first not-ready record.
// This handles the race where atomicAdd claims a slot before data is written.
// Also handles batch locking: releases lock after copying, marks skipped batches.
const stagingShaderCode = `
struct StagingParams {
chunkSize: u32,
maxResults: u32,
recordU32s: u32,
preStagingOffset: u32,
bufferIndex: u32, // 0 or 1, for checking batch_active
_pad0: u32,
_pad1: u32,
_pad2: u32,
}
// Lock buffer layout matches guard shader:
// [0]=lock, [1]=batch_active[0], [2]=batch_active[1], [3]=collision_count
struct LockBuffer {
lock: atomic<u32>,
batch_active_0: atomic<u32>,
batch_active_1: atomic<u32>,
collision_count: atomic<u32>,
}
@group(0) @binding(0) var<uniform> params: StagingParams;
@group(0) @binding(1) var<storage, read_write> buffer: array<u32>;
@group(0) @binding(2) var<storage, read_write> lockBuf: LockBuffer;
// Buffer layout:
// [0]: count (firstEmpty)
// [1]: lastStaged
// [2..7]: other header fields
// [8..]: main records (status at offset 2 within each record)
// [preStagingOffset/4..]: pre-staging header + records
// Pre-staging header: [0]=firstEmpty, [1]=countInChunk, [2]=chunkStartIndex, [3]=skipped
const STATUS_OFFSET: u32 = 2u;
var<workgroup> sharedFirstEmpty: u32;
var<workgroup> sharedLastStaged: u32;
var<workgroup> sharedMaxToCheck: u32;
var<workgroup> sharedBatchSkipped: u32;
var<workgroup> firstNotReady: atomic<u32>;
@compute @workgroup_size(256)
fn staging_main(@builtin(local_invocation_id) local_id: vec3<u32>) {
let tid = local_id.x;
// Thread 0 reads header and initializes shared state
if (tid == 0u) {
sharedFirstEmpty = buffer[0];
sharedLastStaged = buffer[1];
sharedMaxToCheck = min(sharedFirstEmpty - sharedLastStaged, params.chunkSize);
atomicStore(&firstNotReady, sharedMaxToCheck); // "all ready" sentinel
// Check if batch was skipped due to collision
var batch_active: u32;
if (params.bufferIndex == 0u) {
batch_active = atomicLoad(&lockBuf.batch_active_0);
} else {
batch_active = atomicLoad(&lockBuf.batch_active_1);
}
sharedBatchSkipped = select(0u, 1u, batch_active == 0u);
}
workgroupBarrier();
let lastStaged = sharedLastStaged;
let maxToCheck = sharedMaxToCheck;
// Each thread copies multiple records (strided) and checks status
for (var i = tid; i < maxToCheck; i = i + 256u) {
let srcRecordStart = 8u + (lastStaged + i) * params.recordU32s;
let dstRecordStart = (params.preStagingOffset / 4u) + 4u + i * params.recordU32s;
// Copy the record
for (var j = 0u; j < params.recordU32s; j++) {
buffer[dstRecordStart + j] = buffer[srcRecordStart + j];
}
// Check status - if not ready, atomicMin to find earliest not-ready
let status = buffer[srcRecordStart + STATUS_OFFSET];
if (status == 0u) {
atomicMin(&firstNotReady, i);
}
}
workgroupBarrier();
// Thread 0 writes header, updates lastStaged, and releases lock
if (tid == 0u) {
let actualCount = atomicLoad(&firstNotReady);
let skipped = sharedBatchSkipped;
let headerBase = params.preStagingOffset / 4u;
buffer[headerBase + 0u] = sharedFirstEmpty;
buffer[headerBase + 1u] = actualCount;
buffer[headerBase + 2u] = lastStaged;
buffer[headerBase + 3u] = skipped; // 1 if batch was skipped due to collision
// Update lastStaged (only advance by ready records)
buffer[1] = lastStaged + actualCount;
// Release the batch lock (atomic provides memory ordering)
atomicStore(&lockBuf.lock, 0u);
}
}
`;
const stagingModule = this.device.createShaderModule({
code: stagingShaderCode,
label: 'Staging shader'
});
this.stagingPipeline = this.device.createComputePipeline({
layout: 'auto',
compute: {
module: stagingModule,
entryPoint: 'staging_main'
},
label: 'Staging pipeline'
});
// Create two staging params buffers (one per pre-staging area)
this.buffers.stagingParams = [
this.device.createBuffer({
size: 32, // 8 u32s (includes bufferIndex and padding)
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Staging params 0'
}),
this.device.createBuffer({
size: 32, // 8 u32s (includes bufferIndex and padding)
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Staging params 1'
})
];
// Write staging params for each pre-staging area
for (let i = 0; i < 2; i++) {
const stagingParamsData = new Uint32Array([
chunkSize,
this.resultsMaxCount,
recordU32s,
this.preStagingOffsets[i],
i, // bufferIndex: 0 or 1, for checking batch_active
0, // _pad0
0, // _pad1
0 // _pad2
]);
this.device.queue.writeBuffer(this.buffers.stagingParams[i], 0, stagingParamsData);
}
// Create two staging bind groups (one per pre-staging area)
// Each includes the lock buffer for batch collision handling
this.stagingBindGroups = [
this.device.createBindGroup({
layout: this.stagingPipeline.getBindGroupLayout(0),
entries: [
{ binding: 0, resource: { buffer: this.buffers.stagingParams[0] } },
{ binding: 1, resource: { buffer: this.buffers.results } },
{ binding: 2, resource: { buffer: this.buffers.lock } }
],
label: 'Staging bind group 0'
}),
this.device.createBindGroup({
layout: this.stagingPipeline.getBindGroupLayout(0),
entries: [
{ binding: 0, resource: { buffer: this.buffers.stagingParams[1] } },
{ binding: 1, resource: { buffer: this.buffers.results } },
{ binding: 2, resource: { buffer: this.buffers.lock } }
],
label: 'Staging bind group 1'
})
];
}
queueGuardPass(commandEncoder, bufferIndex) {
// Guard pass: try to acquire batch lock (see docs/gpu-batch-locking.md)
// Must run before compute pass to set batch_active[bufferIndex] flag
// Using per-buffer-index prevents Guard2 from corrupting Compute1's batch_active
const guardPass = commandEncoder.beginComputePass({ label: 'Guard pass' });
guardPass.setPipeline(this.guardPipeline);
guardPass.setBindGroup(0, this.guardBindGroups[bufferIndex]);
guardPass.dispatchWorkgroups(1);
guardPass.end();
}
queueResultsReadback(commandEncoder, index) {
// Run staging shader to copy results to pre-staging area
// Use index-specific bind group to write to the correct pre-staging area
// Staging shader also releases the batch lock after copying
const stagingPass = commandEncoder.beginComputePass({ label: 'Staging pass' });
stagingPass.setPipeline(this.stagingPipeline);
stagingPass.setBindGroup(0, this.stagingBindGroups[index]);
// Single workgroup - each thread handles multiple records via strided loop
stagingPass.dispatchWorkgroups(1);
stagingPass.end();
// Copy pre-staging area to staging buffer (each index uses its own pre-staging area)
commandEncoder.copyBufferToBuffer(
this.buffers.results, this.preStagingOffsets[index],
this.buffers.resultsStaging[index], 0,
this.preStagingSize
);
}
async readResultsChunk(index) {
// Read staging buffer which contains pre-staging header + records
// Header: firstEmpty (u32), countInChunk (u32), chunkStartIndex (u32), skipped (u32)
const staging = this.buffers.resultsStaging[index];
await staging.mapAsync(GPUMapMode.READ, 0, this.preStagingSize);
const mapped = staging.getMappedRange(0, this.preStagingSize);
// Parse header
const headerView = new Uint32Array(mapped, 0, 4);
const firstEmpty = Math.min(headerView[0], this.resultsMaxCount);
const countInChunk = headerView[1];
const chunkStartIndex = headerView[2];
const skipped = headerView[3] !== 0; // Batch collision flag (see docs/gpu-batch-locking.md)
// Copy records data (only if not skipped)
let data = null;
if (countInChunk > 0 && !skipped) {
const dataBytes = countInChunk * this.resultsRecordBytes;
data = new ArrayBuffer(dataBytes);
const src = new Uint8Array(mapped, this.preStagingHeaderBytes, dataBytes);
new Uint8Array(data).set(src);
}
staging.unmap();
return { firstEmpty, countInChunk, chunkStartIndex, skipped, data };
}
async processPendingReadback() {
if (this.pendingReadbackIndex === null) return;
await this.pendingReadbackPromise;
// Read chunk from staging buffer (see docs/gpu-results-readback-design.md)
const { firstEmpty, countInChunk, chunkStartIndex, skipped, data } = await this.readResultsChunk(
this.pendingReadbackIndex
);
// Track collision stats (see docs/gpu-batch-locking.md)
this.batchTotalCount++;
if (skipped) {
this.batchCollisionCount++;
// Skipped batch: no work was done, no results to process
// Don't update previousFirstEmpty or add to batchesToReadback
// Always log since collisions are rare and indicate GPU backpressure
console.log(`Board ${this.id}: Batch skipped (collision #${this.batchCollisionCount}/${this.batchTotalCount})`);
return;
}
this.resultsTotalCount = firstEmpty;
// Enqueue this batch with its pixel count and iteration range [start, end)
// Always enqueue, even with 0 GPU results - this ensures previousBatchEndIter
// gets updated for precomputed point flushing (batches with 0 results will
// immediately complete in flushCompleteBatches)
const batchPixelCount = firstEmpty - this.previousFirstEmpty;
this.batchesToReadback.push({
startIter: this.pendingBatchStartIter,
endIter: this.pendingBatchEndIter,
remainingPixelCount: batchPixelCount,
originalPixelCount: batchPixelCount // For invariant checking
});
this.previousFirstEmpty = firstEmpty;
// Process results through the batch-oriented loop
// (see docs/gpu-results-readback-design.md "Results Processing Loop Structure")
if (countInChunk > 0 && data) {
this.processResultsData(data, countInChunk);
} else if (countInChunk === 0) {
// No GPU results in this chunk, but still need to flush complete batches
this.flushCompleteBatches();
}
this.hasPendingResults = false;
this.pendingReadbackIndex = null;
this.pendingReadbackPromise = null;
this.pendingBatchStartIter = 0;
this.pendingBatchEndIter = 0;
}
/**
* Process results data with clean batch-oriented loop structure.
* See docs/gpu-results-readback-design.md "Results Processing Loop Structure" for design.
*
* Structure:
* 1. Outer loop over batches in batchesToReadback
* 2. Flush precomputed points before the head batch's start iteration
* 3. Inner loop: parse results, accumulate into batchResultsRead
* 4. On batch completion: merge precomputed, sort, queue to changeList
*/
processResultsData(data, count) {
const STRIDE = 8; // 8 u32s per record for GpuBoard
const pixelU32 = new Uint32Array(data);
const pixelF32 = new Float32Array(data);
const debugReadback = hasDebugFlag(this.config, 'rb');
// Update readback stats
this.lastResultsCount = count;
this.resultsReadbackBatches += 1;
this.resultsReadbackBytes += count * this.resultsRecordBytes;
let dataIndex = 0;
// OUTER LOOP: Process batches in order (Step 1)
while (this.batchesToReadback.length > 0) {
const batch = this.batchesToReadback[0];
// Step 2: Flush precomputed points before this batch's iteration range
if (this.precomputed) {
this.flushPrecomputedUpTo(this.previousBatchEndIter - 1);
}
// Step 3: INNER LOOP - Process available data for this batch
while (batch.remainingPixelCount > 0 && dataIndex < count) {
const idx8 = dataIndex * STRIDE;
const origIndex = pixelU32[idx8 + 0];
const iters = pixelU32[idx8 + 1];
const status = pixelU32[idx8 + 2];
const period = pixelU32[idx8 + 3];
const zr = pixelF32[idx8 + 4];
const zi = pixelF32[idx8 + 5];
// Skip already processed pixels (can happen with staging overlap race)
if (this.nn[origIndex] !== 0) {
if (debugReadback) {
const same = this.nn[origIndex] === iters ? ' (SAME VALUE)' : ' (DIFFERENT VALUE)';
console.error(`Duplicate result for pixel ${origIndex}, existing nn=${this.nn[origIndex]}, new iters=${iters}${same}`);
}
dataIndex++;
continue;
}
// Skip non-finished pixels (status 0 = record not ready due to race)
if (status === 0) {
if (debugReadback) {
console.error(`status=0 in results buffer at origIndex=${origIndex}`);
}
dataIndex++;
continue;
}
// INVARIANT checks (gated by debug=rb flag)
if (debugReadback) {
if (iters < batch.startIter) {
console.error(`INVARIANT VIOLATION: iter=${iters} < batchStart=${batch.startIter}`);
}
if (iters >= batch.endIter) {
console.error(`INVARIANT VIOLATION: Future result! iter=${iters} >= batchEnd=${batch.endIter}`);
}
}
// Update board state
if (status === 1) { // Diverged
this.nn[origIndex] = iters;
this.pp[origIndex] = 1;
this.di++;
if (this.inSpike && this.inSpike[origIndex] && this.ch > 0) this.ch -= 1;
} else if (status === 2) { // Converged
this.nn[origIndex] = -iters;
this.pp[origIndex] = period; // Use GPU period directly (matches CpuBoard convention)
if (this.inSpike && this.inSpike[origIndex] && this.ch > 0) this.ch -= 1;
}
// Accumulate into batchResultsRead
const change = status === 1
? { iter: iters, nn: [origIndex], vv: [] }
: { iter: iters, nn: [], vv: [{ index: origIndex, z: [zr, zi], p: this.pp[origIndex] }] };
this.batchResultsRead.push(change);
this.deadSinceCompaction++;
batch.remainingPixelCount--;
dataIndex++;
}
// Check if batch is complete
if (batch.remainingPixelCount > 0) {
// Batch not complete yet - exit and wait for more data
break;
}
// Step 4: FLUSHING LOGIC - Batch is complete
// INVARIANT CHECK: batchResultsRead should have exactly originalPixelCount GPU results
if (this.batchResultsRead.length !== batch.originalPixelCount) {
console.error(`INVARIANT VIOLATION: batchResultsRead.length=${this.batchResultsRead.length} but originalPixelCount=${batch.originalPixelCount}`);
}
// Flush precomputed points up to this batch's end iteration
// With half-open [startIter, endIter), max iter in batch is endIter - 1
if (this.precomputed) {
this.flushPrecomputedIntoResults(batch.endIter - 1);
}
// INVARIANT CHECK: All results must be in half-open interval [startIter, endIter)
// AND iter >= previousBatchEndIter (no late results from earlier batches)
for (const change of this.batchResultsRead) {
if (change.iter < this.previousBatchEndIter) {
console.error(`INVARIANT VIOLATION at flush: iter=${change.iter} < previousEnd=${this.previousBatchEndIter}`);
}
if (change.iter < batch.startIter) {
console.error(`INVARIANT VIOLATION at flush: iter=${change.iter} < batchStart=${batch.startIter}`);
}
if (change.iter >= batch.endIter) {
console.error(`INVARIANT VIOLATION at flush: iter=${change.iter} >= batchEnd=${batch.endIter}`);
}
// Queue to changeList
this.queueChanges(change);
}
// Clear for next batch
this.batchResultsRead.length = 0;
this.previousBatchEndIter = batch.endIter;
this.batchesToReadback.shift();
}
// Update un count
// deadSinceCompaction includes results in batchResultsRead that aren't flushed yet
// Add them back since they're not in changeList yet (view won't see them)
const pendingPrecomputed = this.precomputed ? this.precomputed.getPendingCount() : 0;
const pendingInBatchResults = this.batchResultsRead.length;
this.un = (this.activeCount - this.deadSinceCompaction) + pendingPrecomputed + pendingInBatchResults;
}
/**
* Flush precomputed points with iterations <= maxIter directly to changeList.
* Called before processing a batch's iteration range.
*/
flushPrecomputedUpTo(maxIter) {
if (!this.precomputed || maxIter <= this.lastFlushedPrecomputedIter) return;
this.lastFlushedPrecomputedIter = maxIter;
this.precomputed.flushUpToIteration(maxIter, this);
}
/**
* Flush precomputed points with iterations <= maxIter into batchResultsRead.
* Called when a batch is complete to merge precomputed with GPU results.
*/
flushPrecomputedIntoResults(maxIter) {
if (!this.precomputed) return;
// With half-open intervals: flush precomputed with iter in [previousBatchEndIter, maxIter]
// (maxIter is inclusive because it's the last iter of the current batch)
const iterations = Array.from(this.precomputed.rangeMap.keys())
.filter(iter => iter >= this.previousBatchEndIter && iter <= maxIter)
.sort((a, b) => a - b);
for (const iter of iterations) {
const data = this.precomputed.extractAtIteration(iter);
if (!data) continue;
// Add diverged pixels
for (const idx of data.diverged) {
this.nn[idx] = iter;
this.di++;
this.batchResultsRead.push({ iter, nn: [idx], vv: [] });
}
// Add converged pixels
for (const c of data.converged) {
this.nn[c.index] = -iter;
this.batchResultsRead.push({ iter, nn: [], vv: [c] });
}
}
}
// Note: drainResultsBacklog is no longer needed.
// The staging shader automatically handles backlog via the lastStaged counter,
// ensuring each batch reads the next chunk of unprocessed results.
/**
* Return iteration count for submitted GPU batches.
*/
get it() {
return this.baseIt;
}
set it(value) {
this.baseIt = value;
}
/**
* Flush complete batches that have no remaining GPU results expected.
* Called when no GPU data in chunk but batches may be complete.
*/
flushCompleteBatches() {
while (this.batchesToReadback.length > 0 &&
this.batchesToReadback[0].remainingPixelCount <= 0) {
const batch = this.batchesToReadback[0];
// Flush precomputed points for this batch's range
// With half-open [startIter, endIter), max iter in batch is endIter - 1
if (this.precomputed) {
this.flushPrecomputedIntoResults(batch.endIter - 1);
}
// Queue results to changeList
// FractalWorker sorts changeList by iteration before sending, so we don't need to sort here
for (const change of this.batchResultsRead) {
this.queueChanges(change);
}
this.batchResultsRead.length = 0;
this.previousBatchEndIter = batch.endIter;
this.batchesToReadback.shift();
}
// Update un count
const pendingPrecomputed = this.precomputed ? this.precomputed.getPendingCount() : 0;
this.un = (this.activeCount - this.deadSinceCompaction) + pendingPrecomputed;
}
// Abstract methods - subclasses must implement these
async createComputePipeline() {
throw new Error('createComputePipeline() must be implemented by subclass');
}
async createBuffers() {
throw new Error('createBuffers() must be implemented by subclass');
}
createBindGroup() {
throw new Error('createBindGroup() must be implemented by subclass');
}
async compute() {
throw new Error('compute() must be implemented by subclass');
}
/**
* Read the pixels buffer from GPU and return as ArrayBuffer.
* Creates a temporary staging buffer on-demand to avoid persistent memory use.
* Uses a lock to prevent concurrent mapAsync calls.
* @returns {Promise<ArrayBuffer>} The pixel buffer data
*/
async readPixelBuffer() {
// Read GPU pixel buffer for serialization - creates temporary staging buffer on-demand
if (!this.isGPUReady || !this.buffers.pixels) {
return null;
}
// Wait for any pending read to complete before starting a new one
if (this.readPixelBufferPromise) {
await this.readPixelBufferPromise;
}
// Create the actual read operation as a promise we can track
const doRead = async () => {
const bytesPerPixel = this.constructor.BYTES_PER_PIXEL;
const dimsArea = this.config.dimsWidth * this.config.dimsHeight;
const bufferSize = dimsArea * bytesPerPixel;
// Create temporary staging buffer (only needed during serialization)
const stagingBuffer = this.device.createBuffer({
size: bufferSize,
usage: GPUBufferUsage.MAP_READ | GPUBufferUsage.COPY_DST,
label: 'Temp staging for serialization'
});
// Copy pixels buffer to staging
const commandEncoder = this.device.createCommandEncoder();
commandEncoder.copyBufferToBuffer(this.buffers.pixels, 0, stagingBuffer, 0, bufferSize);
this.device.queue.submit([commandEncoder.finish()]);
await this.device.queue.onSubmittedWorkDone();
// Read back the data
await stagingBuffer.mapAsync(GPUMapMode.READ);
const pixelData = new ArrayBuffer(bufferSize);
const srcData = stagingBuffer.getMappedRange();
new Uint8Array(pixelData).set(new Uint8Array(srcData));
stagingBuffer.unmap();
// Destroy temporary buffer immediately
stagingBuffer.destroy();
return pixelData;
};
this.readPixelBufferPromise = doRead();
try {
return await this.readPixelBufferPromise;
} finally {
this.readPixelBufferPromise = null;
}
}
/**
* Write ArrayBuffer data back to the GPU pixels buffer.
* @param {ArrayBuffer} data - The pixel buffer data to write
*/
async writePixelBuffer(data) {
if (!this.isGPUReady || !this.buffers.pixels) {
return false;
}
this.device.queue.writeBuffer(this.buffers.pixels, 0, data);
await this.device.queue.onSubmittedWorkDone();
return true;
}
}
// WebGPU board using float32 arithmetic for shallow zoom depths.
// Uses sparse buffer compaction to improve performance as pixels complete.
class GpuBoard extends GpuBaseBoard {
static BYTES_PER_PIXEL = 32; // 8 fields: orig_index + iter/status/period + zr/zi/base_r/base_i
static STRIDE = 8; // 8 u32/f32 fields per pixel
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
this.effort = 10; // Doubled to reduce batch sizes after GPU readback improvements
const pix = this.pixelSize;
this.epsilon = pix / 10;
this.epsilon2 = pix * 10;
this.checkSpike(size, re, im);
// Initialize double-buffering (from GpuBaseBoard)
this.initDoubleBuffering();
this.gpuInitPromise = this.initGPU();
}
async createComputePipeline() {
// Same shader as GpuBoard but adapted for compacted buffers
const shaderCode = `
struct Params {
center_re: f32,
center_im: f32,
pixel_size: f32,
aspect_ratio: f32,
dims_width: u32,
dims_height: u32,
iterations_per_batch: u32,
active_count: u32,
epsilon: f32,
epsilon2: f32,
exponent: u32,
workgroups_x: u32,
start_iter: u32,
checkpoint_count: u32,
buffer_index: u32, // 0 or 1, for per-buffer batch_active
_pad_bi: u32, // padding to maintain alignment
ckpt0: u32, ckpt1: u32, ckpt2: u32, ckpt3: u32,
ckpt4: u32, ckpt5: u32, ckpt6: u32, ckpt7: u32,
ckpt8: u32, ckpt9: u32, ckpt10: u32, ckpt11: u32,
ckpt12: u32, ckpt13: u32, ckpt14: u32, ckpt15: u32,
ckpt16: u32, ckpt17: u32, ckpt18: u32, ckpt19: u32,
ckpt20: u32, ckpt21: u32, ckpt22: u32, ckpt23: u32,
ckpt24: u32, ckpt25: u32, ckpt26: u32, ckpt27: u32,
ckpt28: u32, ckpt29: u32, ckpt30: u32, ckpt31: u32,
}
struct PixelState {
orig_index: u32, // Original pixel index (for coordinate computation)
iter: u32,
status: u32,
period: u32,
zr: f32,
zi: f32,
base_r: f32,
base_i: f32,
}
// Results buffer header: 32 bytes (8 u32 fields)
// Offset 0: count (atomic) - firstEmpty, next write slot
// Offset 4: lastStaged (atomic) - last staged index
// Offset 8: active_count
// Offset 12: start_iter
// Offset 16: iterations_per_batch
// Offset 20-28: padding
// Offset 32: records[0..N]
struct Results {
count: atomic<u32>,
lastStaged: atomic<u32>,
active_count: u32,
start_iter: u32,
iterations_per_batch: u32,
_pad0: u32,
_pad1: u32,
_pad2: u32,
records: array<PixelState>,
}
// Lock buffer for batch collision prevention (see docs/gpu-batch-locking.md)
// Uses per-buffer-index batch_active to avoid cross-batch race conditions
struct LockBuffer {
lock: atomic<u32>,
batch_active_0: atomic<u32>,
batch_active_1: atomic<u32>,
collision_count: atomic<u32>,
}
@group(0) @binding(0) var<uniform> params: Params;
@group(0) @binding(1) var<storage, read_write> pixels: array<PixelState>;
@group(0) @binding(2) var<storage, read_write> results: Results;
@group(0) @binding(3) var<storage, read_write> lockBuf: LockBuffer;
@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
// Check per-buffer-index batch_active - skip if guard didn't acquire lock
// Using buffer_index avoids race where Guard2 overwrites before Compute1 reads
var batch_active: u32;
if (params.buffer_index == 0u) {
batch_active = atomicLoad(&lockBuf.batch_active_0);
} else {
batch_active = atomicLoad(&lockBuf.batch_active_1);
}
if (batch_active == 0u) {
return; // Batch skipped due to collision
}
if (global_id.x == 0u && global_id.y == 0u && global_id.z == 0u) {
results.active_count = params.active_count;
results.start_iter = params.start_iter;
results.iterations_per_batch = params.iterations_per_batch;
}
let active_idx = global_id.y * params.workgroups_x + global_id.x;
if (active_idx >= params.active_count) {
return;
}
// Skip already-finished pixels (simple check in compacted buffer)
if (pixels[active_idx].status != 0u) {
return;
}
let orig_index = pixels[active_idx].orig_index;
let x = orig_index % params.dims_width;
let y = orig_index / params.dims_width;
let xFrac = f32(i32(x) - i32(params.dims_width / 2u)) / f32(params.dims_width);
let yFrac = f32(i32(params.dims_height / 2u) - i32(y)) / f32(params.dims_height);
let cr = params.center_re + xFrac * params.pixel_size;
let ci = params.center_im + yFrac * (params.pixel_size / params.aspect_ratio);
var zr = pixels[active_idx].zr;
var zi = pixels[active_idx].zi;
var iter = pixels[active_idx].iter;
var base_r = pixels[active_idx].base_r;
var base_i = pixels[active_idx].base_i;
var p = pixels[active_idx].period;
var finished = false;
// Initialize fresh pixels: iter=0 means uninitialized
// Set z=c (first iteration z₀=0 → z₁=c) and iter=1
if (iter == 0u) {
zr = cr;
zi = ci;
base_r = cr;
base_i = ci;
iter = 1u;
}
var next_checkpoint_idx = 0u;
// Fixed epsilon derived from pixel size (no iteration-based escalation)
let epsilon = params.epsilon;
let epsilon2 = params.epsilon2;
for (var i = 0u; i < params.iterations_per_batch; i++) {
if (next_checkpoint_idx < params.checkpoint_count) {
var checkpoint_offset = 0u;
switch (next_checkpoint_idx) {
case 0u: { checkpoint_offset = params.ckpt0; }
case 1u: { checkpoint_offset = params.ckpt1; }
case 2u: { checkpoint_offset = params.ckpt2; }
case 3u: { checkpoint_offset = params.ckpt3; }
case 4u: { checkpoint_offset = params.ckpt4; }
case 5u: { checkpoint_offset = params.ckpt5; }
case 6u: { checkpoint_offset = params.ckpt6; }
case 7u: { checkpoint_offset = params.ckpt7; }
case 8u: { checkpoint_offset = params.ckpt8; }
case 9u: { checkpoint_offset = params.ckpt9; }
case 10u: { checkpoint_offset = params.ckpt10; }
case 11u: { checkpoint_offset = params.ckpt11; }
case 12u: { checkpoint_offset = params.ckpt12; }
case 13u: { checkpoint_offset = params.ckpt13; }
case 14u: { checkpoint_offset = params.ckpt14; }
case 15u: { checkpoint_offset = params.ckpt15; }
case 16u: { checkpoint_offset = params.ckpt16; }
case 17u: { checkpoint_offset = params.ckpt17; }
case 18u: { checkpoint_offset = params.ckpt18; }
case 19u: { checkpoint_offset = params.ckpt19; }
case 20u: { checkpoint_offset = params.ckpt20; }
case 21u: { checkpoint_offset = params.ckpt21; }
case 22u: { checkpoint_offset = params.ckpt22; }
case 23u: { checkpoint_offset = params.ckpt23; }
case 24u: { checkpoint_offset = params.ckpt24; }
case 25u: { checkpoint_offset = params.ckpt25; }
case 26u: { checkpoint_offset = params.ckpt26; }
case 27u: { checkpoint_offset = params.ckpt27; }
case 28u: { checkpoint_offset = params.ckpt28; }
case 29u: { checkpoint_offset = params.ckpt29; }
case 30u: { checkpoint_offset = params.ckpt30; }
case 31u: { checkpoint_offset = params.ckpt31; }
default: {}
}
if (i == checkpoint_offset) {
base_r = zr;
base_i = zi;
p = 0u;
next_checkpoint_idx++;
}
}
let zr2 = zr * zr;
let zi2 = zi * zi;
let mag_sq = zr2 + zi2;
if (mag_sq > 4.0 || !(mag_sq <= 1e38)) {
pixels[active_idx].status = 1u;
finished = true;
break;
}
var ra = zr2 - zi2;
var ja = 2.0 * zr * zi;
for (var ord = 2u; ord < params.exponent; ord++) {
let rt = zr * ra - zi * ja;
ja = zr * ja + zi * ra;
ra = rt;
}
zr = ra + cr;
zi = ja + ci;
let dr = zr - base_r;
let di = zi - base_i;
let db = abs(dr) + abs(di);
if (db <= epsilon2) {
if (p == 0u) {
p = iter;
}
if (db <= epsilon) {
pixels[active_idx].status = 2u;
finished = true;
break;
}
}
iter++;
}
pixels[active_idx].zr = zr;
pixels[active_idx].zi = zi;
pixels[active_idx].base_r = base_r;
pixels[active_idx].base_i = base_i;
pixels[active_idx].iter = iter;
pixels[active_idx].period = p;
if (finished) {
let outIndex = atomicAdd(&results.count, 1u);
results.records[outIndex] = pixels[active_idx];
}
}
`;
const shaderModule = this.device.createShaderModule({
code: shaderCode,
label: 'SparseGpu compute shader'
});
this.pipeline = this.device.createComputePipeline({
layout: 'auto',
compute: {
module: shaderModule,
entryPoint: 'main'
},
label: 'SparseGpu compute pipeline'
});
}
async createBuffers() {
const dimsArea = this.config.dimsWidth * this.config.dimsHeight;
const BYTES_PER_PIXEL = 32; // 8 fields × 4 bytes
const maxBufferSize = Math.min(
this.device.limits.maxBufferSize,
this.device.limits.maxStorageBufferBindingSize
);
// Count active pixels (excluding precomputed)
const precomputedCount = this.precomputed ? this.precomputed.getPrecomputedCount() : 0;
const activePixelCount = dimsArea - precomputedCount;
// Allocate buffer for active pixels only
// WebGPU requires non-zero buffer size, so use at least 1 pixel worth
const pixelBufferSize = Math.max(BYTES_PER_PIXEL, activePixelCount * BYTES_PER_PIXEL);
if (pixelBufferSize > maxBufferSize) {
throw new Error(`Buffer size exceeds WebGPU limit`);
}
const resultsBufferSize = 16 + (activePixelCount * BYTES_PER_PIXEL);
if (resultsBufferSize > maxBufferSize) {
throw new Error(`Results buffer size exceeds WebGPU limit`);
}
// Uniform buffer for parameters
this.buffers.params = this.device.createBuffer({
size: 256, // 14 fields + 32 checkpoints = 184 bytes, rounded to 256
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Parameters buffer'
});
// Pixel state buffer (compacted - excludes precomputed pixels)
// Each pixel carries its orig_index, so no separate mapping buffer needed
// Use mappedAtCreation to avoid separate writeBuffer call
const tb0 = performance.now();
this.buffers.pixels = this.device.createBuffer({
size: pixelBufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST,
label: 'Pixel state buffer',
mappedAtCreation: true
});
const tb1 = performance.now();
// Note: stagingPixels buffers are created on-demand in readPixelBuffer() for serialization
// This saves ~2x pixel buffer size in GPU memory during normal operation
// Initialize directly into the mapped buffer (avoids separate CPU buffer + writeBuffer)
const pixelU32 = new Uint32Array(this.buffers.pixels.getMappedRange());
let activeIdx = 0;
if (this.precomputed) {
// With precomputed pixels, need to skip them
for (let i = 0; i < dimsArea; i++) {
if (!this.precomputed.isPrecomputed(i)) {
pixelU32[activeIdx * 8] = i; // orig_index only, rest is already 0
activeIdx++;
}
}
} else {
// No precomputed pixels - fast path: orig_index = sequential index
for (let i = 0; i < dimsArea; i++) {
pixelU32[i * 8] = i;
}
activeIdx = dimsArea;
}
const tb2 = performance.now();
this.buffers.pixels.unmap();
const tb3 = performance.now();
if (hasDebugFlag(this.config, 't')) {
console.log(`[buffer-init] create=${(tb1-tb0).toFixed(0)}ms loop=${(tb2-tb1).toFixed(0)}ms unmap=${(tb3-tb2).toFixed(0)}ms total=${(tb3-tb0).toFixed(0)}ms`);
}
this.activeCount = activePixelCount;
// Note: don't adjust this.un here - it will be decremented by flushUpToIteration
// when precomputed points are flushed, which properly updates di/un together
this.deadSinceCompaction = 0;
this.initResultsReadback(BYTES_PER_PIXEL, activePixelCount);
}
createBindGroup() {
this.bindGroup = this.device.createBindGroup({
layout: this.pipeline.getBindGroupLayout(0),
entries: [
{ binding: 0, resource: { buffer: this.buffers.params } },
{ binding: 1, resource: { buffer: this.buffers.pixels } },
{ binding: 2, resource: { buffer: this.buffers.results } },
{ binding: 3, resource: { buffer: this.buffers.lock } }
],
label: 'SparseGpu bind group'
});
}
// processResultsData inherited from GpuBaseBoard - uses batch tracking
async compute(targetIters = null) {
if (this.isComputing) return;
this.isComputing = true;
this.lastBatchCompacted = false;
const BYTES_PER_PIXEL = 32; // 8 fields × 4 bytes
const workgroupSize = 64;
try {
// STEP 1: Check if done (before submitting new work)
if (this.activeCount === 0 || this.un === 0) {
// Push sentinel batch to flush any remaining precomputed points
// (see docs/gpu-results-readback-design.md "Step 5: Sentinel Batch")
if (this.precomputed && this.precomputed.getPendingCount() > 0) {
this.batchesToReadback.push({
startIter: this.previousBatchEndIter,
endIter: Infinity, // Signals "all done" - flush all remaining precomputed
remainingPixelCount: 0 // No GPU results expected
});
this.flushCompleteBatches();
}
this.un = 0;
// Flush any pending results before returning
if (this.hasPendingResults) {
await this.flushPendingResults();
}
return;
}
// STEP 2: Submit new GPU batch FIRST (non-blocking)
// This starts the GPU working while we process previous results
const re_double = qdToNumber(this.re);
const im_double = qdToNumber(this.im);
const pixel_size = this.size;
let iterationsPerBatch;
if (targetIters !== null) {
iterationsPerBatch = targetIters;
} else {
const targetWork = 333337;
iterationsPerBatch = Math.max(17, Math.floor(targetWork / Math.max(this.un, 1)));
}
// Accelerating batch sizes for fast first paint at shallow zoom:
// - Batch 1: 1 iter, Batch 2: 2 iters, Batch 3: 4 iters, Batch 4: 8 iters
// - Only applies at zoom < 30 (size > 0.1) where early escapes are visible
const baseIt = this.baseIt;
if (this.size > 0.1) {
if (baseIt === 1) iterationsPerBatch = 1;
else if (baseIt <= 3) iterationsPerBatch = Math.min(iterationsPerBatch, 3 - baseIt + 1);
else if (baseIt <= 7) iterationsPerBatch = Math.min(iterationsPerBatch, 7 - baseIt + 1);
else if (baseIt <= 15) iterationsPerBatch = Math.min(iterationsPerBatch, 15 - baseIt + 1);
}
const numWorkgroups = Math.ceil(this.activeCount / workgroupSize);
const workgroupsX = Math.ceil(Math.sqrt(numWorkgroups));
const workgroupsY = Math.ceil(numWorkgroups / workgroupsX);
const checkpointOffsets = [];
const bufferIter = this.it;
for (let i = 0; i < iterationsPerBatch; i++) {
if (fibonacciPeriod(bufferIter + i) === 1) checkpointOffsets.push(i);
}
const checkpointCount = Math.min(checkpointOffsets.length, 32);
const paramsBuffer = new ArrayBuffer(256);
const paramsF32 = new Float32Array(paramsBuffer);
const paramsU32 = new Uint32Array(paramsBuffer);
paramsF32[0] = re_double;
paramsF32[1] = im_double;
paramsF32[2] = pixel_size;
paramsF32[3] = this.config.aspectRatio;
paramsU32[4] = this.config.dimsWidth;
paramsU32[5] = this.config.dimsHeight;
paramsU32[6] = iterationsPerBatch;
paramsU32[7] = this.activeCount;
paramsF32[8] = this.epsilon;
paramsF32[9] = this.epsilon2;
paramsU32[10] = this.config.exponent;
paramsU32[11] = workgroupsX * workgroupSize;
paramsU32[12] = bufferIter;
paramsU32[13] = checkpointCount;
const bufferIndex = this.readbackBufferIndex;
paramsU32[14] = bufferIndex; // buffer_index for per-buffer batch_active
paramsU32[15] = 0; // _pad_bi
for (let i = 0; i < 32; i++) {
paramsU32[16 + i] = i < checkpointCount ? checkpointOffsets[i] : 0;
}
this.device.queue.writeBuffer(this.buffers.params, 0, paramsBuffer);
const commandEncoder = this.device.createCommandEncoder({ label: 'GpuBoard compute' });
// Guard pass: try to acquire batch lock (see docs/gpu-batch-locking.md)
this.queueGuardPass(commandEncoder, bufferIndex);
// Compute pass: iterate pixels (will skip if lock not acquired)
const passEncoder = commandEncoder.beginComputePass({ label: 'GpuBoard pass' });
passEncoder.setPipeline(this.pipeline);
passEncoder.setBindGroup(0, this.bindGroup);
passEncoder.dispatchWorkgroups(workgroupsX, workgroupsY);
passEncoder.end();
// Queue staging shader pass and copy to staging buffer
// (see docs/gpu-results-readback-design.md)
// Staging shader releases the lock after copying
this.queueResultsReadback(commandEncoder, bufferIndex);
this.device.queue.submit([commandEncoder.finish()]);
// Save batch iter range using half-open interval [start, end)
// - start = first iter processed in this batch
// - end = first iter of the next batch (one past the last iter of this batch)
// Results from this batch have iter in [start, end)
const batchStartIter = this.baseIt;
this.baseIt += iterationsPerBatch;
const batchEndIter = this.baseIt; // = start + iterationsPerBatch
const currentPromise = this.device.queue.onSubmittedWorkDone();
// GPU is now computing in parallel!
// STEP 3: Process pending results from PREVIOUS batch (overlaps with GPU work)
if (this.pendingReadbackIndex !== null) {
await this.processPendingReadback();
}
// Set up state for THIS batch (to be processed next frame)
this.pendingReadbackIndex = bufferIndex;
this.pendingReadbackPromise = currentPromise;
this.readbackBufferIndex = 1 - bufferIndex;
this.pendingIterationsPerBatch = iterationsPerBatch;
this.hasPendingResults = true;
// Batch tracking: half-open interval [start, end) for proper invariant checking
this.pendingBatchStartIter = batchStartIter;
this.pendingBatchEndIter = batchEndIter;
} catch (error) {
console.error(`GpuBoard.compute() ERROR:`, error);
} finally {
this.isComputing = false;
}
}
async serialize() {
// Wait for any in-progress compute() to finish to avoid mapAsync race condition
while (this.isComputing) {
await new Promise(resolve => setTimeout(resolve, 10));
}
// CRITICAL: Flush pending results before serializing
// The double-buffered staging has results that haven't been processed yet
if (this.hasPendingResults) {
await this.flushPendingResults();
}
// Read the compacted GPU pixel buffer
await this.ensureGPUReady();
const gpuPixelData = await this.readCompactedPixelBuffer();
// Build sparse nn array for completed pixels
const completedIndexes = [];
const completedNn = [];
for (let i = 0; i < this.nn.length; i++) {
if (this.nn[i] !== 0) {
completedIndexes.push(i);
completedNn.push(this.nn[i]);
}
}
return {
...(await super.serialize()),
gpuPixelData: gpuPixelData ? Array.from(new Uint8Array(gpuPixelData)) : null,
effort: this.effort,
completedIndexes,
completedNn,
// Compaction state (orig_index is embedded in pixel data, no separate mapping needed)
activeCount: this.activeCount,
deadSinceCompaction: this.deadSinceCompaction,
cumulativeWastedReads: this.cumulativeWastedReads,
};
}
async flushPendingResults() {
// Process pending results from the staging buffer without starting a new batch
if (!this.hasPendingResults) return;
// Process the pending batch if there is one
if (this.pendingReadbackIndex !== null) {
await this.processPendingReadback();
}
// Continue draining results until all are read
// The staging shader reads from lastStaged which advances each time we read a chunk
let moreData = true;
while (moreData) {
// Run another staging shader pass and copy to staging buffer
const readbackIndex = this.readbackBufferIndex;
const commandEncoder = this.device.createCommandEncoder({ label: 'Drain readback' });
this.queueResultsReadback(commandEncoder, readbackIndex);
this.device.queue.submit([commandEncoder.finish()]);
await this.device.queue.onSubmittedWorkDone();
// Read and process the chunk
const { firstEmpty, countInChunk, chunkStartIndex, data } = await this.readResultsChunk(readbackIndex);
if (countInChunk === 0) {
moreData = false; // No more results to read
} else if (data) {
this.processResultsData(data, countInChunk);
}
this.readbackBufferIndex = 1 - readbackIndex;
}
// Batches should complete naturally as results are processed.
// If batches remain incomplete after draining all results, that's a bug.
}
async readCompactedPixelBuffer() {
if (!this.isGPUReady || !this.buffers?.pixels) return null;
const BYTES_PER_PIXEL = 32; // 8 fields × 4 bytes
const bufferSize = this.activeCount * BYTES_PER_PIXEL;
const readBuffer = this.device.createBuffer({
size: bufferSize,
usage: GPUBufferUsage.COPY_DST | GPUBufferUsage.MAP_READ
});
const commandEncoder = this.device.createCommandEncoder();
commandEncoder.copyBufferToBuffer(this.buffers.pixels, 0, readBuffer, 0, bufferSize);
this.device.queue.submit([commandEncoder.finish()]);
await readBuffer.mapAsync(GPUMapMode.READ);
const data = new ArrayBuffer(bufferSize);
new Uint8Array(data).set(new Uint8Array(readBuffer.getMappedRange()));
readBuffer.unmap();
readBuffer.destroy();
return data;
}
static fromSerialized(serialized) {
const board = new GpuBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Schedule async restoration after GPU init
board.gpuInitPromise = board.gpuInitPromise.then(async () => {
// Restore compaction state
if (serialized.activeCount !== undefined) {
board.activeCount = serialized.activeCount;
board.deadSinceCompaction = serialized.deadSinceCompaction || 0;
board.cumulativeWastedReads = serialized.cumulativeWastedReads || 0;
// Recreate buffers at the compacted size
const BYTES_PER_PIXEL = 32; // 8 fields × 4 bytes
const bufferSize = board.activeCount * BYTES_PER_PIXEL;
board.buffers.pixels?.destroy();
board.buffers.pixels = board.device.createBuffer({
size: bufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST,
label: 'Pixel state buffer (restored)'
});
// Restore GPU pixel buffer (includes orig_index for each pixel)
if (serialized.gpuPixelData) {
const pixelData = new Uint8Array(serialized.gpuPixelData).buffer;
board.device.queue.writeBuffer(board.buffers.pixels, 0, new Uint8Array(pixelData));
}
// Note: stagingPixels are created on-demand in readPixelBuffer() for serialization
board.initResultsReadback(BYTES_PER_PIXEL, board.activeCount);
// Recreate bind group with restored buffer
board.createBindGroup();
}
board.effort = serialized.effort || 5;
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
// Restore nn array
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
// Restore precomputed points state
if (serialized.precomputed) {
board.precomputed = PrecomputedPoints.fromSerialized(serialized.precomputed);
}
});
return board;
}
}
// WebGL2 board using fragment shaders for gap-free GPU iteration.
// Unlike WebGPU, WebGL's driver manages cross-command synchronization,
// allowing continuous GPU pipelining without CPU round-trips between batches.
// See docs/webgl-pingpong-design.md for detailed design rationale.
class GlBoard extends Board {
static TILE_SIZE = 16; // Tile size for hierarchical reduction
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
this.effort = 10; // Similar to GpuBoard
// Cap iterations per batch - can do up to 327680 in a single draw call
this.maxBatchIters = 327680;
// WebGL state
this.gl = null;
this.canvas = null;
this.iterProgram = null;
this.reduction1Program = null;
this.reduction2Program = null;
// Ping-pong state textures (MRT: state + checkpoint)
// State texture: (zr, zi, iter, status)
// Checkpoint texture: (checkpoint_zr, checkpoint_zi, period, reserved)
this.pingStateTex = null;
this.pingCheckpointTex = null;
this.pongStateTex = null;
this.pongCheckpointTex = null;
this.pingFB = null;
this.pongFB = null;
this.isPingRead = true;
// Hierarchy textures for sparse readback
this.level1Tex = null;
this.level1FB = null;
this.prevLevel1Tex = null;
this.prevLevel1FB = null;
this.level2Tex = null;
this.level2FB = null;
// Dimensions
this.texWidth = config.dimsWidth;
this.texHeight = config.dimsHeight;
this.level1Width = Math.ceil(this.texWidth / GlBoard.TILE_SIZE);
this.level1Height = Math.ceil(this.texHeight / GlBoard.TILE_SIZE);
this.level2Width = Math.ceil(this.level1Width / GlBoard.TILE_SIZE);
this.level2Height = Math.ceil(this.level1Height / GlBoard.TILE_SIZE);
// Track reported pixels to avoid duplicates
this.reported = new Uint8Array(config.dimsArea);
// Tile-based dispatch optimization
const totalTiles = this.level1Width * this.level1Height;
this.activeTileMask = new Uint8Array(totalTiles); // 1 = active, 0 = inactive
this.activeTileMask.fill(1); // All tiles start active
this.activeTileCount = totalTiles;
this.useTileDispatch = false; // Enable after first reduction
this.escapedSinceUpdate = 0; // Track escapes since last tile mask update
// Convergence detection thresholds (like CpuBoard)
this.epsilon = this.pix / 10; // Final convergence threshold
this.epsilon2 = this.pix * 10; // "Getting close" threshold
// Fibonacci sequence for checkpoint updates
this.fibCache = [1, 2];
this.nextFibIndex = 2;
// Full-screen quad VAO
this.quadVAO = null;
// Uniform locations (cached after shader compilation)
this.iterUniforms = {};
this.reduction1Uniforms = {};
this.reduction2Uniforms = {};
// Async readback state (PBO-based to avoid blocking)
// Double-buffered PBOs to avoid write-before-read warnings
this.pendingReadback = null; // { sync, pboIndex }
this.pendingBatchEndIter = null; // End iteration for pending batch (for precomputed flushing)
this.level2PBOs = [null, null]; // Ping-pong PBOs
this.currentPBOIndex = 0;
// Complex plane bounds (set in start())
this.cMinRe = 0;
this.cMinIm = 0;
this.cMaxRe = 0;
this.cMaxIm = 0;
// Initialize WebGL
this.glInitPromise = this.initWebGL();
}
// Check if iteration is a Fibonacci number (checkpoint point)
isFibonacci(n) {
// Extend cache if needed
while (this.fibCache[this.fibCache.length - 1] < n) {
const len = this.fibCache.length;
this.fibCache.push(this.fibCache[len - 1] + this.fibCache[len - 2]);
}
// Binary search
let lo = 0, hi = this.fibCache.length - 1;
while (lo <= hi) {
const mid = (lo + hi) >> 1;
if (this.fibCache[mid] === n) return true;
if (this.fibCache[mid] < n) lo = mid + 1;
else hi = mid - 1;
}
return false;
}
async initWebGL() {
// Create offscreen canvas for WebGL context
this.canvas = new OffscreenCanvas(this.texWidth, this.texHeight);
this.gl = this.canvas.getContext('webgl2', {
alpha: false,
antialias: false,
depth: false,
stencil: false,
powerPreference: 'high-performance',
preserveDrawingBuffer: true
});
if (!this.gl) {
throw new Error('WebGL2 not available');
}
const gl = this.gl;
// Required extension for float textures as render targets
const ext = gl.getExtension('EXT_color_buffer_float');
if (!ext) {
throw new Error('EXT_color_buffer_float not available');
}
// Initialize shaders
this.initShaders();
// Initialize textures and framebuffers
this.initPingPongBuffers();
this.initHierarchyBuffers();
// Initialize full-screen quad
this.initQuad();
// Initialize state texture with starting values
this.initStateTexture();
}
initShaders() {
const gl = this.gl;
// Vertex shader (shared by all passes)
const vsSource = `#version 300 es
in vec2 a_position;
out vec2 v_texCoord;
void main() {
gl_Position = vec4(a_position, 0.0, 1.0);
v_texCoord = (a_position + 1.0) * 0.5;
}
`;
// Fragment shader for Mandelbrot iteration with convergence detection
// Uses MRT: output 0 = state (zr, zi, iter, status)
// output 1 = checkpoint (checkpoint_zr, checkpoint_zi, period, reserved)
const fsIterSource = `#version 300 es
precision highp float;
uniform sampler2D u_state;
uniform sampler2D u_checkpoint;
uniform vec2 u_resolution;
uniform vec2 u_cMin;
uniform vec2 u_cMax;
uniform int u_iterations;
uniform float u_escapeRadius;
uniform int u_exponent;
uniform float u_epsilon; // Final convergence threshold
uniform float u_epsilon2; // "Getting close" threshold
uniform int u_startIter; // Global iteration at batch start
// Fibonacci info for checkpoint updates
uniform int u_fibPrev; // Previous Fibonacci number <= startIter
uniform int u_fibCurr; // Current Fibonacci number > startIter
in vec2 v_texCoord;
layout(location = 0) out vec4 outState;
layout(location = 1) out vec4 outCheckpoint;
void main() {
vec4 state = texture(u_state, v_texCoord);
vec4 checkpoint = texture(u_checkpoint, v_texCoord);
float zr = state.r;
float zi = state.g;
float iter = state.b;
float pixelIndex = state.a; // Grid index (static)
float cp_zr = checkpoint.r;
float cp_zi = checkpoint.g;
float period = checkpoint.b;
float status = checkpoint.a; // 0=active, 1=escaped, 2=converged, 4=precomputed (skip)
// c from pixel position
vec2 c = mix(u_cMin, u_cMax, v_texCoord);
// Track Fibonacci for checkpoint updates
int fibPrev = u_fibPrev;
int fibCurr = u_fibCurr;
if (status == 0.0) { // Active pixel
for (int i = 0; i < 327680; i++) { // Max iterations per draw call
if (i >= u_iterations) break;
int globalIter = u_startIter + i + 1;
// z = z^n + c (support exponent 2-5)
float zr2, zi2;
if (u_exponent == 2) {
zr2 = zr * zr - zi * zi + c.x;
zi2 = 2.0 * zr * zi + c.y;
} else if (u_exponent == 3) {
float zr_sq = zr * zr;
float zi_sq = zi * zi;
zr2 = zr * (zr_sq - 3.0 * zi_sq) + c.x;
zi2 = zi * (3.0 * zr_sq - zi_sq) + c.y;
} else if (u_exponent == 4) {
float zr_sq = zr * zr;
float zi_sq = zi * zi;
float zr_4 = zr_sq * zr_sq;
float zi_4 = zi_sq * zi_sq;
zr2 = zr_4 - 6.0 * zr_sq * zi_sq + zi_4 + c.x;
zi2 = 4.0 * zr * zi * (zr_sq - zi_sq) + c.y;
} else {
// Fallback for exponent 5+
float r = sqrt(zr * zr + zi * zi);
float theta = atan(zi, zr);
float rn = pow(r, float(u_exponent));
float ntheta = float(u_exponent) * theta;
zr2 = rn * cos(ntheta) + c.x;
zi2 = rn * sin(ntheta) + c.y;
}
zr = zr2;
zi = zi2;
iter += 1.0;
// Check for escape
if (zr * zr + zi * zi > u_escapeRadius) {
status = 1.0; // Escaped
break;
}
// Check for Fibonacci checkpoint update
if (globalIter == fibCurr) {
// Update checkpoint: save current z, reset period
cp_zr = zr;
cp_zi = zi;
period = 0.0;
// Advance Fibonacci sequence
int nextFib = fibPrev + fibCurr;
fibPrev = fibCurr;
fibCurr = nextFib;
// Skip convergence check this iteration - checkpoint was just set
// (z == checkpoint trivially when we just set checkpoint = z)
} else {
// Check for convergence (compare to checkpoint)
float dist = abs(zr - cp_zr) + abs(zi - cp_zi);
if (dist <= u_epsilon2) {
// Getting close - record period if not already set
if (period == 0.0) {
period = iter;
}
if (dist <= u_epsilon) {
// Converged!
status = 2.0;
break;
}
}
}
}
}
outState = vec4(zr, zi, iter, pixelIndex);
outCheckpoint = vec4(cp_zr, cp_zi, period, status);
}
`;
// Fragment shader for Level 0 → Level 1 reduction (tile summary)
// Tracks both escaped (status=1) and converged (status=2) pixels
// Status is now in checkpoint.a (not state.a)
const fsReduction1Source = `#version 300 es
precision highp float;
uniform sampler2D u_checkpoint;
uniform sampler2D u_prevTiles;
uniform vec2 u_stateSize;
uniform vec2 u_tileSize;
in vec2 v_texCoord;
out vec4 tileInfo;
void main() {
ivec2 tileCoord = ivec2(gl_FragCoord.xy);
ivec2 basePixel = tileCoord * 16;
float finishedCount = 0.0; // Both escaped and converged
float hasFinished = 0.0;
// Sample all 256 pixels in this 16x16 tile
for (int dy = 0; dy < 16; dy++) {
for (int dx = 0; dx < 16; dx++) {
ivec2 pixel = basePixel + ivec2(dx, dy);
if (pixel.x < int(u_stateSize.x) && pixel.y < int(u_stateSize.y)) {
vec4 checkpoint = texelFetch(u_checkpoint, pixel, 0);
if (checkpoint.a > 0.0) { // Escaped (1.0) or Converged (2.0)
finishedCount += 1.0;
hasFinished = 1.0;
}
}
}
}
// Compare with previous count to find newly finished
vec4 prev = texelFetch(u_prevTiles, tileCoord, 0);
float newlyFinished = finishedCount - prev.r;
tileInfo = vec4(finishedCount, newlyFinished, 0.0, hasFinished);
}
`;
// Fragment shader for Level 1 → Level 2 reduction (super-tile summary)
const fsReduction2Source = `#version 300 es
precision highp float;
uniform sampler2D u_tiles;
uniform vec2 u_tilesSize;
in vec2 v_texCoord;
out vec4 superTileInfo;
void main() {
ivec2 superCoord = ivec2(gl_FragCoord.xy);
ivec2 baseTile = superCoord * 16;
float totalFinished = 0.0;
float totalNew = 0.0;
float hasFinished = 0.0;
// Sample all 256 tiles in this 16x16 super-tile
for (int dy = 0; dy < 16; dy++) {
for (int dx = 0; dx < 16; dx++) {
ivec2 tile = baseTile + ivec2(dx, dy);
if (tile.x < int(u_tilesSize.x) && tile.y < int(u_tilesSize.y)) {
vec4 tileData = texelFetch(u_tiles, tile, 0);
totalFinished += tileData.r;
totalNew += tileData.g;
if (tileData.a > 0.0) hasFinished = 1.0;
}
}
}
superTileInfo = vec4(totalFinished, totalNew, 0.0, hasFinished);
}
`;
// Compile shaders
this.iterProgram = this.compileProgram(vsSource, fsIterSource);
this.reduction1Program = this.compileProgram(vsSource, fsReduction1Source);
this.reduction2Program = this.compileProgram(vsSource, fsReduction2Source);
// Cache uniform locations
this.cacheIterUniforms();
this.cacheReductionUniforms();
}
compileProgram(vsSource, fsSource) {
const gl = this.gl;
const vs = gl.createShader(gl.VERTEX_SHADER);
gl.shaderSource(vs, vsSource);
gl.compileShader(vs);
if (!gl.getShaderParameter(vs, gl.COMPILE_STATUS)) {
throw new Error('Vertex shader compile error: ' + gl.getShaderInfoLog(vs));
}
const fs = gl.createShader(gl.FRAGMENT_SHADER);
gl.shaderSource(fs, fsSource);
gl.compileShader(fs);
if (!gl.getShaderParameter(fs, gl.COMPILE_STATUS)) {
throw new Error('Fragment shader compile error: ' + gl.getShaderInfoLog(fs));
}
const program = gl.createProgram();
gl.attachShader(program, vs);
gl.attachShader(program, fs);
gl.linkProgram(program);
if (!gl.getProgramParameter(program, gl.LINK_STATUS)) {
throw new Error('Program link error: ' + gl.getProgramInfoLog(program));
}
gl.deleteShader(vs);
gl.deleteShader(fs);
return program;
}
cacheIterUniforms() {
const gl = this.gl;
gl.useProgram(this.iterProgram);
this.iterUniforms = {
u_state: gl.getUniformLocation(this.iterProgram, 'u_state'),
u_checkpoint: gl.getUniformLocation(this.iterProgram, 'u_checkpoint'),
u_resolution: gl.getUniformLocation(this.iterProgram, 'u_resolution'),
u_cMin: gl.getUniformLocation(this.iterProgram, 'u_cMin'),
u_cMax: gl.getUniformLocation(this.iterProgram, 'u_cMax'),
u_iterations: gl.getUniformLocation(this.iterProgram, 'u_iterations'),
u_escapeRadius: gl.getUniformLocation(this.iterProgram, 'u_escapeRadius'),
u_exponent: gl.getUniformLocation(this.iterProgram, 'u_exponent'),
u_epsilon: gl.getUniformLocation(this.iterProgram, 'u_epsilon'),
u_epsilon2: gl.getUniformLocation(this.iterProgram, 'u_epsilon2'),
u_startIter: gl.getUniformLocation(this.iterProgram, 'u_startIter'),
u_fibPrev: gl.getUniformLocation(this.iterProgram, 'u_fibPrev'),
u_fibCurr: gl.getUniformLocation(this.iterProgram, 'u_fibCurr')
};
}
cacheReductionUniforms() {
const gl = this.gl;
gl.useProgram(this.reduction1Program);
this.reduction1Uniforms = {
u_checkpoint: gl.getUniformLocation(this.reduction1Program, 'u_checkpoint'),
u_prevTiles: gl.getUniformLocation(this.reduction1Program, 'u_prevTiles'),
u_stateSize: gl.getUniformLocation(this.reduction1Program, 'u_stateSize'),
u_tileSize: gl.getUniformLocation(this.reduction1Program, 'u_tileSize')
};
gl.useProgram(this.reduction2Program);
this.reduction2Uniforms = {
u_tiles: gl.getUniformLocation(this.reduction2Program, 'u_tiles'),
u_tilesSize: gl.getUniformLocation(this.reduction2Program, 'u_tilesSize')
};
}
createTexture(width, height, internalFormat = null) {
const gl = this.gl;
internalFormat = internalFormat || gl.RGBA32F;
const tex = gl.createTexture();
gl.bindTexture(gl.TEXTURE_2D, tex);
gl.texImage2D(gl.TEXTURE_2D, 0, internalFormat, width, height, 0, gl.RGBA, gl.FLOAT, null);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
return tex;
}
createFramebuffer(texture) {
const gl = this.gl;
const fb = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, fb);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, texture, 0);
const status = gl.checkFramebufferStatus(gl.FRAMEBUFFER);
if (status !== gl.FRAMEBUFFER_COMPLETE) {
throw new Error('Framebuffer incomplete: ' + status);
}
return fb;
}
initPingPongBuffers() {
const gl = this.gl;
// Create state and checkpoint textures for ping-pong
this.pingStateTex = this.createTexture(this.texWidth, this.texHeight);
this.pingCheckpointTex = this.createTexture(this.texWidth, this.texHeight);
this.pongStateTex = this.createTexture(this.texWidth, this.texHeight);
this.pongCheckpointTex = this.createTexture(this.texWidth, this.texHeight);
// Create MRT framebuffers (2 color attachments each)
this.pingFB = this.createMRTFramebuffer(this.pingStateTex, this.pingCheckpointTex);
this.pongFB = this.createMRTFramebuffer(this.pongStateTex, this.pongCheckpointTex);
// Start with ping as read, pong as write
this.isPingRead = true;
}
createMRTFramebuffer(stateTex, checkpointTex) {
const gl = this.gl;
const fb = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, fb);
// Attach state texture to COLOR_ATTACHMENT0
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, stateTex, 0);
// Attach checkpoint texture to COLOR_ATTACHMENT1
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT1, gl.TEXTURE_2D, checkpointTex, 0);
// Enable both attachments for MRT
gl.drawBuffers([gl.COLOR_ATTACHMENT0, gl.COLOR_ATTACHMENT1]);
const status = gl.checkFramebufferStatus(gl.FRAMEBUFFER);
if (status !== gl.FRAMEBUFFER_COMPLETE) {
throw new Error('MRT Framebuffer incomplete: ' + status);
}
return fb;
}
initHierarchyBuffers() {
// Level 1: tile summaries
this.level1Tex = this.createTexture(this.level1Width, this.level1Height);
this.prevLevel1Tex = this.createTexture(this.level1Width, this.level1Height);
this.level1FB = this.createFramebuffer(this.level1Tex);
this.prevLevel1FB = this.createFramebuffer(this.prevLevel1Tex);
// Level 2: super-tile summaries
this.level2Tex = this.createTexture(this.level2Width, this.level2Height);
this.level2FB = this.createFramebuffer(this.level2Tex);
// Clear BOTH level1 textures to avoid garbage values after swap
const gl = this.gl;
gl.clearColor(0, 0, 0, 0);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level1FB);
gl.clear(gl.COLOR_BUFFER_BIT);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.prevLevel1FB);
gl.clear(gl.COLOR_BUFFER_BIT);
}
initQuad() {
const gl = this.gl;
// Full-screen quad vertices
const positions = new Float32Array([
-1, -1, 1, -1, -1, 1,
-1, 1, 1, -1, 1, 1
]);
this.quadVAO = gl.createVertexArray();
gl.bindVertexArray(this.quadVAO);
const posBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, posBuffer);
gl.bufferData(gl.ARRAY_BUFFER, positions, gl.STATIC_DRAW);
const posLoc = gl.getAttribLocation(this.iterProgram, 'a_position');
gl.enableVertexAttribArray(posLoc);
gl.vertexAttribPointer(posLoc, 2, gl.FLOAT, false, 0, 0);
gl.bindVertexArray(null);
}
initStateTexture() {
const gl = this.gl;
const sizeScalar = this.size;
const reDD = qdToDD(this.re);
const imDD = qdToDD(this.im);
// Calculate complex plane bounds
const halfWidth = sizeScalar / 2;
const halfHeight = halfWidth / this.config.aspectRatio;
this.cMinRe = reDD[0] - halfWidth;
this.cMaxRe = reDD[0] + halfWidth;
this.cMinIm = imDD[0] - halfHeight;
this.cMaxIm = imDD[0] + halfHeight;
// Initialize state texture: z=0, iter=0, index=gridIndex
// State layout: (zr, zi, iter, index) - index is the View's grid index
// WebGL y=0 is at bottom, but View y=0 is at top, so flip Y
const stateData = new Float32Array(this.texWidth * this.texHeight * 4);
// Set grid index in state.a for each pixel
for (let texY = 0; texY < this.texHeight; texY++) {
for (let x = 0; x < this.texWidth; x++) {
const texOffset = (texY * this.texWidth + x) * 4;
// Flip Y: texture y=0 (bottom) -> grid y=height-1, texture y=height-1 (top) -> grid y=0
const gridY = this.texHeight - 1 - texY;
const gridIndex = gridY * this.texWidth + x;
// stateData[texOffset + 0] = 0; // zr = 0
// stateData[texOffset + 1] = 0; // zi = 0
// stateData[texOffset + 2] = 0; // iter = 0
stateData[texOffset + 3] = gridIndex; // index = View's grid index
}
}
gl.bindTexture(gl.TEXTURE_2D, this.pingStateTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, this.texWidth, this.texHeight,
gl.RGBA, gl.FLOAT, stateData);
// Initialize checkpoint texture with sentinel values
// Checkpoint layout: (checkpoint_zr, checkpoint_zi, period, status)
// checkpoint_z must be far from any valid z value to prevent false convergence
// on the first iterations (before the first Fibonacci checkpoint is set)
// status: 0=active, 1=escaped, 2=converged, 4=precomputed
const checkpointData = new Float32Array(this.texWidth * this.texHeight * 4);
// Fast initialization: build pattern then copy with doubling
const sentinel = 1e30;
// Start with one pixel pattern
checkpointData[0] = sentinel; // checkpoint_zr
checkpointData[1] = sentinel; // checkpoint_zi
// checkpointData[2] = 0; // period = 0
// checkpointData[3] = 0; // status = 0 (active)
// Copy doubling: 1->2->4->8->... pixels at a time
let filled = 4; // 1 pixel = 4 floats
while (filled < checkpointData.length) {
const copyLen = Math.min(filled, checkpointData.length - filled);
checkpointData.copyWithin(filled, 0, copyLen);
filled += copyLen;
}
// Mark precomputed pixels with status=4 (and mark them as reported)
// These pixels won't be computed by the GPU and will be flushed separately
if (this.precomputed) {
const precomputedCount = this.precomputed.getPrecomputedCount();
if (precomputedCount > 0) {
const pp = this.precomputed;
// Iterate through all precomputed pixels
for (const [iter, range] of pp.rangeMap) {
// Mark diverged pixels
for (let i = 0; i < range.dCount; i++) {
const gridIndex = pp.dIndices[range.dStart + i];
// Convert grid index to texture offset (flip Y)
const gridY = Math.floor(gridIndex / this.texWidth);
const gridX = gridIndex % this.texWidth;
const texY = this.texHeight - 1 - gridY;
const texOffset = (texY * this.texWidth + gridX) * 4;
checkpointData[texOffset + 3] = 4.0; // status = precomputed
this.reported[gridIndex] = 1; // Mark as reported so we don't read it back
}
// Mark converged pixels
for (let i = 0; i < range.cCount; i++) {
const gridIndex = pp.cIndices[range.cStart + i];
const gridY = Math.floor(gridIndex / this.texWidth);
const gridX = gridIndex % this.texWidth;
const texY = this.texHeight - 1 - gridY;
const texOffset = (texY * this.texWidth + gridX) * 4;
checkpointData[texOffset + 3] = 4.0; // status = precomputed
this.reported[gridIndex] = 1; // Mark as reported
}
}
// Note: don't adjust un here - it will be decremented by flushUpToIteration
// when precomputed points are flushed, which properly updates di/un together
}
}
// Initialize BOTH ping and pong checkpoint textures with the same data
// This ensures precomputed pixels have status=4 regardless of which buffer is read first
gl.bindTexture(gl.TEXTURE_2D, this.pingCheckpointTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, this.texWidth, this.texHeight,
gl.RGBA, gl.FLOAT, checkpointData);
gl.bindTexture(gl.TEXTURE_2D, this.pongCheckpointTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, this.texWidth, this.texHeight,
gl.RGBA, gl.FLOAT, checkpointData);
// Also initialize both state textures with pixel indices
gl.bindTexture(gl.TEXTURE_2D, this.pongStateTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, this.texWidth, this.texHeight,
gl.RGBA, gl.FLOAT, stateData);
}
swapPingPong() {
this.isPingRead = !this.isPingRead;
}
// Helper to get current read textures
getReadTextures() {
return this.isPingRead
? { state: this.pingStateTex, checkpoint: this.pingCheckpointTex }
: { state: this.pongStateTex, checkpoint: this.pongCheckpointTex };
}
// Helper to get current write framebuffer
getWriteFB() {
return this.isPingRead ? this.pongFB : this.pingFB;
}
// Main entry point for scheduler - matches GpuBoard interface
async iterate(targetIters = null) {
// Wait for WebGL initialization
await this.glInitPromise;
// Process any pending readback from previous iteration
// This blocks until complete, but allows OTHER boards to work in parallel
this.waitForPendingReadback();
if (this.un <= 0) return;
// Calculate iterations based on effort if not specified
if (targetIters === null) {
const pixels = this.texWidth * this.texHeight;
const effort = Math.max(this.effort, 1);
targetIters = Math.max(1, Math.floor(100000 / (pixels * effort)));
}
// Run GPU iterations
this.doGpuIterations(targetIters);
// Store end iteration for precomputed flushing when readback completes
this.pendingBatchEndIter = this.it;
// Start async readback - results processed at start of next iterate()
this.startAsyncReadback();
}
// Start async readback using PBO
// The PBO read is async - GPU copies data in background
// getBufferSubData() will block until complete
startAsyncReadback() {
const gl = this.gl;
// Run reduction passes
this.runReductionPasses();
// Use ping-pong PBOs
const pboIndex = this.currentPBOIndex;
this.currentPBOIndex = 1 - this.currentPBOIndex;
// Create PBO if not exists
if (!this.level2PBOs[pboIndex]) {
this.level2PBOs[pboIndex] = gl.createBuffer();
this.level2Size = this.level2Width * this.level2Height * 4 * 4; // RGBA float
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, this.level2PBOs[pboIndex]);
gl.bufferData(gl.PIXEL_PACK_BUFFER, this.level2Size, gl.STREAM_READ);
}
// Async read level2 into PBO
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level2FB);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, this.level2PBOs[pboIndex]);
gl.readPixels(0, 0, this.level2Width, this.level2Height, gl.RGBA, gl.FLOAT, 0);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, null);
// Create fence sync to wait for GPU completion before reading
const sync = gl.fenceSync(gl.SYNC_GPU_COMMANDS_COMPLETE, 0);
gl.flush();
// Store pending PBO index and sync object
this.pendingReadback = { pboIndex, sync };
}
// Wait for pending readback to complete
waitForPendingReadback() {
const gl = this.gl;
const pending = this.pendingReadback;
if (!pending) return;
const pbo = this.level2PBOs[pending.pboIndex];
if (!pbo) {
// PBO was never created or was lost - skip this readback
if (pending.sync) gl.deleteSync(pending.sync);
this.pendingReadback = null;
this.pendingBatchEndIter = null;
return;
}
const batchEndIter = this.pendingBatchEndIter;
this.pendingReadback = null;
this.pendingBatchEndIter = null;
// Wait for fence sync to complete before reading (avoids pipeline stall warning)
if (pending.sync) {
gl.clientWaitSync(pending.sync, 0, 0); // Don't actually wait, just signal intent
gl.deleteSync(pending.sync);
}
// getBufferSubData() reads data after sync is signaled
const level2Data = new Float32Array(this.level2Width * this.level2Height * 4);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, pbo);
gl.getBufferSubData(gl.PIXEL_PACK_BUFFER, 0, level2Data);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, null);
// Process level2 data (queues GPU results)
this.processLevel2Results(level2Data);
// Flush precomputed points for this batch's iteration range
// This ensures precomputed and GPU results go in the same message
if (this.precomputed && batchEndIter) {
this.precomputed.flushUpToIteration(batchEndIter, this);
}
}
// Process level2 results and trigger hierarchical readback if needed
processLevel2Results(superTiles) {
const gl = this.gl;
const totalPixels = this.texWidth * this.texHeight;
// Find super-tiles with new escapes
const activeSuperTiles = [];
let totalNew = 0;
for (let sy = 0; sy < this.level2Height; sy++) {
for (let sx = 0; sx < this.level2Width; sx++) {
const idx = (sy * this.level2Width + sx) * 4;
const newlyEscaped = superTiles[idx + 1];
if (newlyEscaped > 0) {
activeSuperTiles.push({ x: sx, y: sy, count: newlyEscaped });
totalNew += newlyEscaped;
}
}
}
// Track cumulative escapes and update tile mask when >10% since last update
this.escapedSinceUpdate += totalNew;
if (this.escapedSinceUpdate > totalPixels * 0.10) {
this.updateActiveTileMask();
this.escapedSinceUpdate = 0;
}
if (activeSuperTiles.length === 0) {
// No new escapes - swap buffers and return
this.swapLevel1Buffers();
return;
}
// Adaptive: if >10% escapes, just read full texture
if (totalNew > totalPixels * 0.1) {
this.readFullTexture();
return;
}
// Hierarchical read
this.readHierarchical(activeSuperTiles);
}
// Find Fibonacci numbers around a given iteration
// Returns { prev, curr } where prev <= iter < curr
getFibonacciBounds(iter) {
// Extend cache if needed
while (this.fibCache[this.fibCache.length - 1] <= iter) {
const len = this.fibCache.length;
this.fibCache.push(this.fibCache[len - 1] + this.fibCache[len - 2]);
}
// Find the first Fibonacci > iter
let i = 0;
while (this.fibCache[i] <= iter) i++;
return {
prev: i > 0 ? this.fibCache[i - 1] : 1,
curr: this.fibCache[i]
};
}
// Queue n iterations (non-blocking - driver pipelines internally)
// Batches up to 327680 iterations per draw call (shader loop limit)
// Uses tile-based dispatch when many tiles are inactive
doGpuIterations(n) {
const gl = this.gl;
const MAX_SHADER_ITERS = 327680; // Shader's internal loop limit
const TILE_SIZE = GlBoard.TILE_SIZE;
const totalTiles = this.level1Width * this.level1Height;
// Decide whether to use tile dispatch
// Use tiles if <30% tiles active (overhead of many draws vs savings)
const useTiles = this.useTileDispatch && this.activeTileCount < totalTiles * 0.3;
gl.useProgram(this.iterProgram);
gl.bindVertexArray(this.quadVAO);
// Set static uniforms
gl.uniform2f(this.iterUniforms.u_resolution, this.texWidth, this.texHeight);
gl.uniform2f(this.iterUniforms.u_cMin, this.cMinRe, this.cMinIm);
gl.uniform2f(this.iterUniforms.u_cMax, this.cMaxRe, this.cMaxIm);
gl.uniform1f(this.iterUniforms.u_escapeRadius, 4.0);
gl.uniform1i(this.iterUniforms.u_exponent, this.config.exponent);
gl.uniform1f(this.iterUniforms.u_epsilon, this.epsilon);
gl.uniform1f(this.iterUniforms.u_epsilon2, this.epsilon2);
// Enable scissor test for tile-based dispatch
if (useTiles) {
gl.enable(gl.SCISSOR_TEST);
}
// Batch iterations - shader handles up to 327680 per draw call
let remaining = n;
while (remaining > 0) {
const batchSize = Math.min(remaining, MAX_SHADER_ITERS);
const startIter = this.it;
const { prev: fibPrev, curr: fibCurr } = this.getFibonacciBounds(startIter);
// Set per-batch uniforms
gl.uniform1i(this.iterUniforms.u_startIter, startIter);
gl.uniform1i(this.iterUniforms.u_fibPrev, fibPrev);
gl.uniform1i(this.iterUniforms.u_fibCurr, fibCurr);
gl.uniform1i(this.iterUniforms.u_iterations, batchSize);
// Get current read textures
const readTextures = this.getReadTextures();
// Bind state texture to TEXTURE0
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, readTextures.state);
gl.uniform1i(this.iterUniforms.u_state, 0);
// Bind checkpoint texture to TEXTURE1
gl.activeTexture(gl.TEXTURE1);
gl.bindTexture(gl.TEXTURE_2D, readTextures.checkpoint);
gl.uniform1i(this.iterUniforms.u_checkpoint, 1);
// Bind write framebuffer (MRT with both state and checkpoint attachments)
gl.bindFramebuffer(gl.FRAMEBUFFER, this.getWriteFB());
gl.viewport(0, 0, this.texWidth, this.texHeight);
if (useTiles) {
// Tile-based dispatch: only render active tiles using scissor
for (let ty = 0; ty < this.level1Height; ty++) {
for (let tx = 0; tx < this.level1Width; tx++) {
const tileIdx = ty * this.level1Width + tx;
if (this.activeTileMask[tileIdx]) {
const x = tx * TILE_SIZE;
const y = ty * TILE_SIZE;
const w = Math.min(TILE_SIZE, this.texWidth - x);
const h = Math.min(TILE_SIZE, this.texHeight - y);
gl.scissor(x, y, w, h);
gl.drawArrays(gl.TRIANGLES, 0, 6);
}
}
}
} else {
// Full-screen dispatch
gl.drawArrays(gl.TRIANGLES, 0, 6);
}
// Swap and advance
this.swapPingPong();
this.it += batchSize;
remaining -= batchSize;
}
if (useTiles) {
gl.disable(gl.SCISSOR_TEST);
}
gl.bindVertexArray(null);
}
// Run reduction passes (GPU-side, pipelined)
runReductionPasses() {
const gl = this.gl;
const readTextures = this.getReadTextures();
// Pass 1: State → Level 1
gl.useProgram(this.reduction1Program);
gl.bindVertexArray(this.quadVAO);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, readTextures.checkpoint);
gl.uniform1i(this.reduction1Uniforms.u_checkpoint, 0);
gl.activeTexture(gl.TEXTURE1);
gl.bindTexture(gl.TEXTURE_2D, this.prevLevel1Tex);
gl.uniform1i(this.reduction1Uniforms.u_prevTiles, 1);
gl.uniform2f(this.reduction1Uniforms.u_stateSize, this.texWidth, this.texHeight);
gl.uniform2f(this.reduction1Uniforms.u_tileSize, GlBoard.TILE_SIZE, GlBoard.TILE_SIZE);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level1FB);
gl.viewport(0, 0, this.level1Width, this.level1Height);
gl.drawArrays(gl.TRIANGLES, 0, 6);
// Pass 2: Level 1 → Level 2
gl.useProgram(this.reduction2Program);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, this.level1Tex);
gl.uniform1i(this.reduction2Uniforms.u_tiles, 0);
gl.uniform2f(this.reduction2Uniforms.u_tilesSize, this.level1Width, this.level1Height);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level2FB);
gl.viewport(0, 0, this.level2Width, this.level2Height);
gl.drawArrays(gl.TRIANGLES, 0, 6);
gl.bindVertexArray(null);
}
// Update active tile mask based on level1 reduction data
// Called periodically to track which tiles are fully finished
updateActiveTileMask() {
const gl = this.gl;
const TILE_SIZE = GlBoard.TILE_SIZE;
const PIXELS_PER_TILE = TILE_SIZE * TILE_SIZE; // 256
// Read level1 texture to get per-tile finished counts
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level1FB);
const level1Data = new Float32Array(this.level1Width * this.level1Height * 4);
gl.readPixels(0, 0, this.level1Width, this.level1Height, gl.RGBA, gl.FLOAT, level1Data);
// Update active tile mask
let newActiveCount = 0;
for (let ty = 0; ty < this.level1Height; ty++) {
for (let tx = 0; tx < this.level1Width; tx++) {
const tileIdx = ty * this.level1Width + tx;
const dataIdx = tileIdx * 4;
const finishedCount = level1Data[dataIdx]; // .r = finished count
// Calculate expected pixels in this tile (edge tiles may be smaller)
const tileW = Math.min(TILE_SIZE, this.texWidth - tx * TILE_SIZE);
const tileH = Math.min(TILE_SIZE, this.texHeight - ty * TILE_SIZE);
const tilePixels = tileW * tileH;
// Tile is inactive if all pixels are finished
if (finishedCount >= tilePixels) {
this.activeTileMask[tileIdx] = 0;
} else {
this.activeTileMask[tileIdx] = 1;
newActiveCount++;
}
}
}
this.activeTileCount = newActiveCount;
this.useTileDispatch = true; // Enable tile dispatch after first update
}
// LEGACY: Synchronous readback (replaced by async PBO pipeline)
// Kept for reference - use startAsyncReadback() + processPendingReadback() instead
readResultsSync() {
const gl = this.gl;
// Run reduction passes
this.runReductionPasses();
// Read Level 2 (tiny - always read all)
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level2FB);
const superTiles = new Float32Array(this.level2Width * this.level2Height * 4);
gl.readPixels(0, 0, this.level2Width, this.level2Height, gl.RGBA, gl.FLOAT, superTiles);
// Find super-tiles with new escapes
const activeSuperTiles = [];
let totalNew = 0;
for (let sy = 0; sy < this.level2Height; sy++) {
for (let sx = 0; sx < this.level2Width; sx++) {
const idx = (sy * this.level2Width + sx) * 4;
const newlyEscaped = superTiles[idx + 1];
if (newlyEscaped > 0) {
activeSuperTiles.push({ x: sx, y: sy, count: newlyEscaped });
totalNew += newlyEscaped;
}
}
}
// Track cumulative escapes and update tile mask when >10% since last update
const totalPixels = this.texWidth * this.texHeight;
this.escapedSinceUpdate += totalNew;
if (this.escapedSinceUpdate > totalPixels * 0.10) {
this.updateActiveTileMask();
this.escapedSinceUpdate = 0;
}
if (activeSuperTiles.length === 0) {
// No new escapes - swap buffers and return empty
this.swapLevel1Buffers();
return null;
}
// Adaptive: if >10% escapes, just read full texture
if (totalNew > totalPixels * 0.1) {
return this.readFullTexture();
}
// Hierarchical read
return this.readHierarchical(activeSuperTiles);
}
// Create a temporary framebuffer for reading a single texture
createReadFB(texture) {
const gl = this.gl;
const fb = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, fb);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, texture, 0);
return fb;
}
readHierarchical(activeSuperTiles) {
const gl = this.gl;
// Group results: escaped by iteration, converged separately
const escapedByIter = new Map();
const convergedByIter = new Map();
// Read Level 1 for active super-tiles
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level1FB);
const activeTiles = [];
for (const st of activeSuperTiles) {
const x0 = st.x * GlBoard.TILE_SIZE;
const y0 = st.y * GlBoard.TILE_SIZE;
const w = Math.min(GlBoard.TILE_SIZE, this.level1Width - x0);
const h = Math.min(GlBoard.TILE_SIZE, this.level1Height - y0);
const tileData = new Float32Array(w * h * 4);
gl.readPixels(x0, y0, w, h, gl.RGBA, gl.FLOAT, tileData);
for (let ty = 0; ty < h; ty++) {
for (let tx = 0; tx < w; tx++) {
const idx = (ty * w + tx) * 4;
const newlyFinished = tileData[idx + 1];
if (newlyFinished > 0) {
activeTiles.push({ x: x0 + tx, y: y0 + ty, count: newlyFinished });
}
}
}
}
// Get read textures
const readTextures = this.getReadTextures();
// Create temporary read framebuffers for state and checkpoint
const stateReadFB = this.createReadFB(readTextures.state);
const checkpointReadFB = this.createReadFB(readTextures.checkpoint);
// Read both state and checkpoint textures for active tiles
// State: (zr, zi, iter, index), Checkpoint: (cp_zr, cp_zi, period, status)
for (const tile of activeTiles) {
const x0 = tile.x * GlBoard.TILE_SIZE;
const y0 = tile.y * GlBoard.TILE_SIZE;
const w = Math.min(GlBoard.TILE_SIZE, this.texWidth - x0);
const h = Math.min(GlBoard.TILE_SIZE, this.texHeight - y0);
// Read state texture (zr, zi, iter, index)
gl.bindFramebuffer(gl.FRAMEBUFFER, stateReadFB);
const statePixels = new Float32Array(w * h * 4);
gl.readPixels(x0, y0, w, h, gl.RGBA, gl.FLOAT, statePixels);
// Read checkpoint texture (cp_zr, cp_zi, period, status)
gl.bindFramebuffer(gl.FRAMEBUFFER, checkpointReadFB);
const checkpointPixels = new Float32Array(w * h * 4);
gl.readPixels(x0, y0, w, h, gl.RGBA, gl.FLOAT, checkpointPixels);
for (let py = 0; py < h; py++) {
for (let px = 0; px < w; px++) {
const localIdx = (py * w + px) * 4;
const status = checkpointPixels[localIdx + 3]; // status in checkpoint.a
const pixelIndex = Math.round(statePixels[localIdx + 3]); // index in state.a
if (this.reported[pixelIndex]) continue;
if (status === 4.0) continue; // Precomputed - handled separately
if (status === 1.0) { // Escaped
const iter = Math.round(statePixels[localIdx + 2]);
this.nn[pixelIndex] = iter;
this.reported[pixelIndex] = 1;
this.un--;
this.di++;
if (!escapedByIter.has(iter)) {
escapedByIter.set(iter, []);
}
escapedByIter.get(iter).push(pixelIndex);
} else if (status === 2.0) { // Converged
const iter = Math.round(statePixels[localIdx + 2]);
const zr = statePixels[localIdx];
const zi = statePixels[localIdx + 1];
const period = Math.round(checkpointPixels[localIdx + 2]);
this.nn[pixelIndex] = -iter; // Negative for converged
this.reported[pixelIndex] = 1;
this.un--;
if (!convergedByIter.has(iter)) {
convergedByIter.set(iter, []);
}
convergedByIter.get(iter).push({
index: pixelIndex,
z: [zr, zi],
p: period
});
}
}
}
}
// Clean up temporary framebuffers
gl.deleteFramebuffer(stateReadFB);
gl.deleteFramebuffer(checkpointReadFB);
// Swap level1 buffers for next "newly finished" tracking
this.swapLevel1Buffers();
// Queue changes grouped by iteration
if (escapedByIter.size === 0 && convergedByIter.size === 0) return null;
// Merge and sort by iteration
const allIters = new Set([...escapedByIter.keys(), ...convergedByIter.keys()]);
const sortedIters = Array.from(allIters).sort((a, b) => a - b);
for (const iter of sortedIters) {
const escaped = escapedByIter.get(iter) || [];
const converged = convergedByIter.get(iter) || [];
this.queueChanges({ iter, nn: escaped, vv: converged });
}
return { queued: true };
}
readFullTexture() {
const gl = this.gl;
// Group results: escaped by iteration, converged separately
const escapedByIter = new Map();
const convergedByIter = new Map();
// Get read textures
const readTextures = this.getReadTextures();
// Create temporary read framebuffers
const stateReadFB = this.createReadFB(readTextures.state);
const checkpointReadFB = this.createReadFB(readTextures.checkpoint);
// Read both full textures
// State: (zr, zi, iter, index), Checkpoint: (cp_zr, cp_zi, period, status)
gl.bindFramebuffer(gl.FRAMEBUFFER, stateReadFB);
const statePixels = new Float32Array(this.texWidth * this.texHeight * 4);
gl.readPixels(0, 0, this.texWidth, this.texHeight, gl.RGBA, gl.FLOAT, statePixels);
gl.bindFramebuffer(gl.FRAMEBUFFER, checkpointReadFB);
const checkpointPixels = new Float32Array(this.texWidth * this.texHeight * 4);
gl.readPixels(0, 0, this.texWidth, this.texHeight, gl.RGBA, gl.FLOAT, checkpointPixels);
for (let i = 0; i < this.texWidth * this.texHeight; i++) {
const status = checkpointPixels[i * 4 + 3]; // status in checkpoint.a
const pixelIndex = Math.round(statePixels[i * 4 + 3]); // index in state.a
if (this.reported[pixelIndex]) continue;
if (status === 4.0) continue; // Precomputed - handled separately
if (status === 1.0) { // Escaped
const iter = Math.round(statePixels[i * 4 + 2]);
this.nn[pixelIndex] = iter;
this.reported[pixelIndex] = 1;
this.un--;
this.di++;
if (!escapedByIter.has(iter)) {
escapedByIter.set(iter, []);
}
escapedByIter.get(iter).push(pixelIndex);
} else if (status === 2.0) { // Converged
const iter = Math.round(statePixels[i * 4 + 2]);
const zr = statePixels[i * 4];
const zi = statePixels[i * 4 + 1];
const period = Math.round(checkpointPixels[i * 4 + 2]);
this.nn[pixelIndex] = -iter; // Negative for converged
this.reported[pixelIndex] = 1;
this.un--;
if (!convergedByIter.has(iter)) {
convergedByIter.set(iter, []);
}
convergedByIter.get(iter).push({
index: pixelIndex,
z: [zr, zi],
p: period
});
}
}
// Clean up temporary framebuffers
gl.deleteFramebuffer(stateReadFB);
gl.deleteFramebuffer(checkpointReadFB);
// Swap level1 buffers
this.swapLevel1Buffers();
// Queue changes grouped by iteration
if (escapedByIter.size === 0 && convergedByIter.size === 0) return null;
// Merge and sort by iteration
const allIters = new Set([...escapedByIter.keys(), ...convergedByIter.keys()]);
const sortedIters = Array.from(allIters).sort((a, b) => a - b);
for (const iter of sortedIters) {
const escaped = escapedByIter.get(iter) || [];
const converged = convergedByIter.get(iter) || [];
this.queueChanges({ iter, nn: escaped, vv: converged });
}
return { queued: true };
}
swapLevel1Buffers() {
[this.level1FB, this.prevLevel1FB] = [this.prevLevel1FB, this.level1FB];
[this.level1Tex, this.prevLevel1Tex] = [this.prevLevel1Tex, this.level1Tex];
}
// Serialization support
async serialize() {
const base = await super.serialize();
// GlBoard-specific state
return {
...base,
type: 'GlBoard',
reported: Array.from(this.reported),
cMinRe: this.cMinRe,
cMinIm: this.cMinIm,
cMaxRe: this.cMaxRe,
cMaxIm: this.cMaxIm
};
}
static fromSerialized(serialized) {
const board = new GlBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
board.glInitPromise = board.glInitPromise.then(() => {
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
if (serialized.reported) {
board.reported = new Uint8Array(serialized.reported);
}
board.cMinRe = serialized.cMinRe;
board.cMinIm = serialized.cMinIm;
board.cMaxRe = serialized.cMaxRe;
board.cMaxIm = serialized.cMaxIm;
// Restore nn array
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
});
return board;
}
// Check if WebGL2 is available
static isAvailable() {
if (typeof OffscreenCanvas === 'undefined') return false;
try {
const canvas = new OffscreenCanvas(1, 1);
const gl = canvas.getContext('webgl2');
if (!gl) return false;
const ext = gl.getExtension('EXT_color_buffer_float');
return !!ext;
} catch (e) {
return false;
}
}
}
// Base class for WebGL2 perturbation boards
// Provides shared WebGL infrastructure for GlZhuoranBoard and GlAdaptiveBoard
class GlPerturbationBaseBoard extends Board {
static TILE_SIZE = 16;
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
this.effort = 18;
this.maxBatchIters = 100000;
// WebGL state
this.gl = null;
this.canvas = null;
this.iterProgram = null;
this.reduction1Program = null;
this.reduction2Program = null;
// Ping-pong state textures for perturbation
this.pingStateTex = null;
this.pingCheckpointTex = null;
this.pingLazyTex = null;
this.pongStateTex = null;
this.pongCheckpointTex = null;
this.pongLazyTex = null;
this.pingFB = null;
this.pongFB = null;
this.isPingRead = true;
// Delta C texture (constant per pixel)
this.deltaCTex = null;
// Reference orbit + threading texture
this.refOrbitTex = null;
this.refOrbitTexWidth = 2048;
this.refOrbitTexHeight = 512;
this.lastUploadedRefIter = 0;
// Hierarchy textures for sparse readback
this.level1Tex = null;
this.level1FB = null;
this.prevLevel1Tex = null;
this.prevLevel1FB = null;
this.level2Tex = null;
this.level2FB = null;
// Dimensions
this.texWidth = config.dimsWidth;
this.texHeight = config.dimsHeight;
this.level1Width = Math.ceil(this.texWidth / GlPerturbationBaseBoard.TILE_SIZE);
this.level1Height = Math.ceil(this.texHeight / GlPerturbationBaseBoard.TILE_SIZE);
this.level2Width = Math.ceil(this.level1Width / GlPerturbationBaseBoard.TILE_SIZE);
this.level2Height = Math.ceil(this.level1Height / GlPerturbationBaseBoard.TILE_SIZE);
// Track reported pixels
this.reported = new Uint8Array(config.dimsArea);
// Tile-based dispatch
const totalTiles = this.level1Width * this.level1Height;
this.activeTileMask = new Uint8Array(totalTiles);
this.activeTileMask.fill(1);
this.activeTileCount = totalTiles;
this.useTileDispatch = false;
this.escapedSinceUpdate = 0;
// Convergence thresholds
this.epsilon = this.pix / 10;
this.epsilon2 = this.pix * 10;
// Fibonacci checkpoints
this.fibCache = [1, 2];
this.nextFibIndex = 2;
// Full-screen quad VAO
this.quadVAO = null;
// Uniform locations
this.iterUniforms = {};
this.reduction1Uniforms = {};
this.reduction2Uniforms = {};
// Async readback
this.pendingReadback = null;
this.pendingBatchEndIter = null;
this.level2PBOs = [null, null];
this.currentPBOIndex = 0;
// Reference orbit loop (for very deep zoom)
this.refOrbitLoop = { enabled: false };
this.refOrbitLoopConfigured = false;
// Per-pixel perturbation data
this.dc = new Float32Array(config.dimsArea * 2);
this.dz = new Float32Array(config.dimsArea * 2);
}
async initGL() {
this.canvas = new OffscreenCanvas(this.texWidth, this.texHeight);
this.gl = this.canvas.getContext('webgl2', {
antialias: false,
depth: false,
stencil: false,
preserveDrawingBuffer: true
});
const gl = this.gl;
gl.getExtension('EXT_color_buffer_float');
gl.getExtension('OES_texture_float_linear');
await this.createShaders();
this.createTextures();
this.createQuad();
this.initializeStateTextures();
this.uploadDeltaC();
}
// Vertex shader source (shared by all GL perturbation boards)
getVertexShaderSource() {
return `#version 300 es
in vec2 a_position;
out vec2 v_texCoord;
void main() {
gl_Position = vec4(a_position, 0.0, 1.0);
v_texCoord = (a_position + 1.0) * 0.5;
}
`;
}
// Reduction shader sources (shared by all GL perturbation boards)
getReduction1ShaderSource() {
return `#version 300 es
precision highp float;
uniform sampler2D u_state;
uniform sampler2D u_prevTiles;
uniform vec2 u_stateSize;
uniform vec2 u_tileSize;
in vec2 v_texCoord;
out vec4 tileInfo;
void main() {
ivec2 tileCoord = ivec2(gl_FragCoord.xy);
ivec2 basePixel = tileCoord * 16;
float finishedCount = 0.0;
float hasFinished = 0.0;
for (int dy = 0; dy < 16; dy++) {
for (int dx = 0; dx < 16; dx++) {
ivec2 pixel = basePixel + ivec2(dx, dy);
if (pixel.x < int(u_stateSize.x) && pixel.y < int(u_stateSize.y)) {
vec4 state = texelFetch(u_state, pixel, 0);
if (state.a > 0.0) {
finishedCount += 1.0;
hasFinished = 1.0;
}
}
}
}
vec4 prev = texelFetch(u_prevTiles, tileCoord, 0);
float newlyFinished = finishedCount - prev.r;
tileInfo = vec4(finishedCount, newlyFinished, 0.0, hasFinished);
}
`;
}
getReduction2ShaderSource() {
return `#version 300 es
precision highp float;
uniform sampler2D u_tiles;
uniform vec2 u_tilesSize;
in vec2 v_texCoord;
out vec4 superTileInfo;
void main() {
ivec2 superCoord = ivec2(gl_FragCoord.xy);
ivec2 baseTile = superCoord * 16;
float totalFinished = 0.0;
float totalNew = 0.0;
float hasFinished = 0.0;
for (int dy = 0; dy < 16; dy++) {
for (int dx = 0; dx < 16; dx++) {
ivec2 tile = baseTile + ivec2(dx, dy);
if (tile.x < int(u_tilesSize.x) && tile.y < int(u_tilesSize.y)) {
vec4 tileData = texelFetch(u_tiles, tile, 0);
totalFinished += tileData.r;
totalNew += tileData.g;
if (tileData.a > 0.0) hasFinished = 1.0;
}
}
}
superTileInfo = vec4(totalFinished, totalNew, 0.0, hasFinished);
}
`;
}
// Abstract method - subclasses must implement
getIterationShaderSource() {
throw new Error('Subclass must implement getIterationShaderSource()');
}
async createShaders() {
const gl = this.gl;
const vsSource = this.getVertexShaderSource();
const fsIterSource = this.getIterationShaderSource();
const fsReduction1Source = this.getReduction1ShaderSource();
const fsReduction2Source = this.getReduction2ShaderSource();
this.iterProgram = this.compileProgram(vsSource, fsIterSource);
this.reduction1Program = this.compileProgram(vsSource, fsReduction1Source);
this.reduction2Program = this.compileProgram(vsSource, fsReduction2Source);
// Cache uniform locations for iteration shader
gl.useProgram(this.iterProgram);
this.iterUniforms = {
u_state: gl.getUniformLocation(this.iterProgram, 'u_state'),
u_checkpoint: gl.getUniformLocation(this.iterProgram, 'u_checkpoint'),
u_lazy: gl.getUniformLocation(this.iterProgram, 'u_lazy'),
u_deltaC: gl.getUniformLocation(this.iterProgram, 'u_deltaC'),
u_refOrbit: gl.getUniformLocation(this.iterProgram, 'u_refOrbit'),
u_resolution: gl.getUniformLocation(this.iterProgram, 'u_resolution'),
u_iterations: gl.getUniformLocation(this.iterProgram, 'u_iterations'),
u_exponent: gl.getUniformLocation(this.iterProgram, 'u_exponent'),
u_epsilon: gl.getUniformLocation(this.iterProgram, 'u_epsilon'),
u_epsilon2: gl.getUniformLocation(this.iterProgram, 'u_epsilon2'),
u_pixelSize: gl.getUniformLocation(this.iterProgram, 'u_pixelSize'),
u_startIter: gl.getUniformLocation(this.iterProgram, 'u_startIter'),
u_refOrbitLength: gl.getUniformLocation(this.iterProgram, 'u_refOrbitLength'),
u_refOrbitTexWidth: gl.getUniformLocation(this.iterProgram, 'u_refOrbitTexWidth'),
u_fibPrev: gl.getUniformLocation(this.iterProgram, 'u_fibPrev'),
u_fibCurr: gl.getUniformLocation(this.iterProgram, 'u_fibCurr'),
u_loopEnabled: gl.getUniformLocation(this.iterProgram, 'u_loopEnabled'),
u_loopThreshold: gl.getUniformLocation(this.iterProgram, 'u_loopThreshold'),
u_loopJump: gl.getUniformLocation(this.iterProgram, 'u_loopJump'),
u_loopDeltaR: gl.getUniformLocation(this.iterProgram, 'u_loopDeltaR'),
u_loopDeltaI: gl.getUniformLocation(this.iterProgram, 'u_loopDeltaI'),
};
gl.useProgram(this.reduction1Program);
this.reduction1Uniforms = {
u_state: gl.getUniformLocation(this.reduction1Program, 'u_state'),
u_prevTiles: gl.getUniformLocation(this.reduction1Program, 'u_prevTiles'),
u_stateSize: gl.getUniformLocation(this.reduction1Program, 'u_stateSize'),
u_tileSize: gl.getUniformLocation(this.reduction1Program, 'u_tileSize'),
};
gl.useProgram(this.reduction2Program);
this.reduction2Uniforms = {
u_tiles: gl.getUniformLocation(this.reduction2Program, 'u_tiles'),
u_tilesSize: gl.getUniformLocation(this.reduction2Program, 'u_tilesSize'),
};
}
compileProgram(vsSource, fsSource) {
const gl = this.gl;
const vs = gl.createShader(gl.VERTEX_SHADER);
gl.shaderSource(vs, vsSource);
gl.compileShader(vs);
if (!gl.getShaderParameter(vs, gl.COMPILE_STATUS)) {
throw new Error('Vertex shader: ' + gl.getShaderInfoLog(vs));
}
const fs = gl.createShader(gl.FRAGMENT_SHADER);
gl.shaderSource(fs, fsSource);
gl.compileShader(fs);
if (!gl.getShaderParameter(fs, gl.COMPILE_STATUS)) {
throw new Error('Fragment shader: ' + gl.getShaderInfoLog(fs));
}
const program = gl.createProgram();
gl.attachShader(program, vs);
gl.attachShader(program, fs);
gl.linkProgram(program);
if (!gl.getProgramParameter(program, gl.LINK_STATUS)) {
throw new Error('Program link: ' + gl.getProgramInfoLog(program));
}
return program;
}
createTextures() {
const gl = this.gl;
// Create ping-pong state textures
this.pingStateTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pingCheckpointTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pingLazyTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pongStateTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pongCheckpointTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pongLazyTex = this.createFloatTexture(this.texWidth, this.texHeight);
// Delta C texture (constant)
this.deltaCTex = this.createFloatTexture(this.texWidth, this.texHeight);
// Reference orbit texture
this.refOrbitTex = this.createFloatTexture(this.refOrbitTexWidth, this.refOrbitTexHeight);
// Create framebuffers with MRT for ping-pong
// pingFB writes to ping textures, pongFB writes to pong textures
this.pingFB = this.createMRTFramebuffer(this.pingStateTex, this.pingCheckpointTex, this.pingLazyTex);
this.pongFB = this.createMRTFramebuffer(this.pongStateTex, this.pongCheckpointTex, this.pongLazyTex);
// Hierarchy textures
this.level1Tex = this.createFloatTexture(this.level1Width, this.level1Height);
this.level1FB = this.createFramebuffer(this.level1Tex);
this.prevLevel1Tex = this.createFloatTexture(this.level1Width, this.level1Height);
this.prevLevel1FB = this.createFramebuffer(this.prevLevel1Tex);
this.level2Tex = this.createFloatTexture(this.level2Width, this.level2Height);
this.level2FB = this.createFramebuffer(this.level2Tex);
// Initialize prevLevel1 to zeros
gl.bindFramebuffer(gl.FRAMEBUFFER, this.prevLevel1FB);
gl.viewport(0, 0, this.level1Width, this.level1Height);
gl.clearColor(0, 0, 0, 0);
gl.clear(gl.COLOR_BUFFER_BIT);
}
createFloatTexture(width, height) {
const gl = this.gl;
const tex = gl.createTexture();
gl.bindTexture(gl.TEXTURE_2D, tex);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA32F, width, height, 0, gl.RGBA, gl.FLOAT, null);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE);
return tex;
}
createFramebuffer(colorTex) {
const gl = this.gl;
const fb = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, fb);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, colorTex, 0);
return fb;
}
createMRTFramebuffer(stateTex, checkpointTex, lazyTex) {
const gl = this.gl;
const fb = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, fb);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, stateTex, 0);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT1, gl.TEXTURE_2D, checkpointTex, 0);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT2, gl.TEXTURE_2D, lazyTex, 0);
gl.drawBuffers([gl.COLOR_ATTACHMENT0, gl.COLOR_ATTACHMENT1, gl.COLOR_ATTACHMENT2]);
return fb;
}
createQuad() {
const gl = this.gl;
this.quadVAO = gl.createVertexArray();
gl.bindVertexArray(this.quadVAO);
const vbo = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, vbo);
gl.bufferData(gl.ARRAY_BUFFER, new Float32Array([-1,-1, 1,-1, -1,1, 1,1]), gl.STATIC_DRAW);
const posLoc = gl.getAttribLocation(this.iterProgram, 'a_position');
gl.enableVertexAttribArray(posLoc);
gl.vertexAttribPointer(posLoc, 2, gl.FLOAT, false, 0, 0);
}
// Abstract - subclass should implement
initializeStateTextures() {
throw new Error('Subclass must implement initializeStateTextures()');
}
uploadDeltaC() {
const gl = this.gl;
const w = this.texWidth;
const h = this.texHeight;
const area = w * h;
const dcData = new Float32Array(area * 4);
for (let i = 0; i < area; i++) {
dcData[i * 4 + 0] = this.dc[i * 2];
dcData[i * 4 + 1] = this.dc[i * 2 + 1];
dcData[i * 4 + 2] = 0.0;
dcData[i * 4 + 3] = 0.0;
}
gl.bindTexture(gl.TEXTURE_2D, this.deltaCTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, dcData);
}
// Abstract - subclass should implement based on DD or QD precision
uploadRefOrbit() {
throw new Error('Subclass must implement uploadRefOrbit()');
}
async start() {
await this.glInitPromise;
this.startTime = Date.now();
const re = qdToNumber(this.re);
const im = qdToNumber(this.im);
console.log(`[GL] Board ${this.config.index}: ${this.constructor.name} @ c=(${re.toFixed(4)}, ${im.toFixed(4)}), dims=${this.texWidth}x${this.texHeight}, pixel=${this.pix.toExponential(3)}`);
}
async iterate(targetIters = null) {
await this.glInitPromise;
this.waitForPendingReadback();
if (this.un <= 0) return;
// Extend reference orbit if needed
const targetRefIter = this.it + (targetIters || 1000);
while (this.refIterations < targetRefIter + 100 && !this.refOrbitEscaped) {
this.extendReferenceOrbit(Math.min(10000, targetRefIter + 100 - this.refIterations));
}
this.uploadRefOrbit();
if (targetIters === null) {
const pixels = this.texWidth * this.texHeight;
const effort = Math.max(this.effort, 1);
targetIters = Math.max(1, Math.floor(100000 / (pixels * effort)));
}
this.doGpuIterations(targetIters);
this.pendingBatchEndIter = this.it;
this.startAsyncReadback();
}
doGpuIterations(targetIters) {
const gl = this.gl;
// Get Fibonacci checkpoints
while (this.fibCache[this.fibCache.length - 1] < this.it + targetIters + 1000) {
const n = this.fibCache.length;
this.fibCache.push(this.fibCache[n - 1] + this.fibCache[n - 2]);
}
let fibIdx = 0;
while (this.fibCache[fibIdx] <= this.it) fibIdx++;
const fibPrev = fibIdx > 0 ? this.fibCache[fibIdx - 1] : 1;
const fibCurr = this.fibCache[fibIdx];
// Bind shader and set uniforms
gl.useProgram(this.iterProgram);
gl.activeTexture(gl.TEXTURE3);
gl.bindTexture(gl.TEXTURE_2D, this.deltaCTex);
gl.uniform1i(this.iterUniforms.u_deltaC, 3);
gl.activeTexture(gl.TEXTURE4);
gl.bindTexture(gl.TEXTURE_2D, this.refOrbitTex);
gl.uniform1i(this.iterUniforms.u_refOrbit, 4);
gl.uniform2f(this.iterUniforms.u_resolution, this.texWidth, this.texHeight);
gl.uniform1i(this.iterUniforms.u_iterations, targetIters);
gl.uniform1i(this.iterUniforms.u_exponent, this.config.exponent);
gl.uniform1f(this.iterUniforms.u_epsilon, this.epsilon);
gl.uniform1f(this.iterUniforms.u_epsilon2, this.epsilon2);
gl.uniform1f(this.iterUniforms.u_pixelSize, this.pix);
gl.uniform1i(this.iterUniforms.u_startIter, this.it);
gl.uniform1i(this.iterUniforms.u_refOrbitLength, this.refIterations);
gl.uniform1i(this.iterUniforms.u_refOrbitTexWidth, this.refOrbitTexWidth);
gl.uniform1i(this.iterUniforms.u_fibPrev, fibPrev);
gl.uniform1i(this.iterUniforms.u_fibCurr, fibCurr);
// Loop parameters
gl.uniform1i(this.iterUniforms.u_loopEnabled, this.refOrbitLoop.enabled ? 1 : 0);
gl.uniform1i(this.iterUniforms.u_loopThreshold, this.refOrbitLoop.threshold || 0);
gl.uniform1i(this.iterUniforms.u_loopJump, this.refOrbitLoop.jumpAmount || 0);
gl.uniform1f(this.iterUniforms.u_loopDeltaR, this.refOrbitLoop.deltaR || 0);
gl.uniform1f(this.iterUniforms.u_loopDeltaI, this.refOrbitLoop.deltaI || 0);
// Bind input textures
const readState = this.isPingRead ? this.pingStateTex : this.pongStateTex;
const readCheckpoint = this.isPingRead ? this.pingCheckpointTex : this.pongCheckpointTex;
const readLazy = this.isPingRead ? this.pingLazyTex : this.pongLazyTex;
// Write to the OPPOSITE buffer (ping-pong pattern)
const writeFB = this.isPingRead ? this.pongFB : this.pingFB;
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, readState);
gl.uniform1i(this.iterUniforms.u_state, 0);
gl.activeTexture(gl.TEXTURE1);
gl.bindTexture(gl.TEXTURE_2D, readCheckpoint);
gl.uniform1i(this.iterUniforms.u_checkpoint, 1);
gl.activeTexture(gl.TEXTURE2);
gl.bindTexture(gl.TEXTURE_2D, readLazy);
gl.uniform1i(this.iterUniforms.u_lazy, 2);
// Draw
gl.bindFramebuffer(gl.FRAMEBUFFER, writeFB);
gl.viewport(0, 0, this.texWidth, this.texHeight);
gl.bindVertexArray(this.quadVAO);
gl.drawArrays(gl.TRIANGLE_STRIP, 0, 4);
this.isPingRead = !this.isPingRead;
this.it += targetIters;
}
startAsyncReadback() {
const gl = this.gl;
this.runReductionPasses();
const pboIndex = this.currentPBOIndex;
this.currentPBOIndex = 1 - this.currentPBOIndex;
if (!this.level2PBOs[pboIndex]) {
this.level2PBOs[pboIndex] = gl.createBuffer();
this.level2Size = this.level2Width * this.level2Height * 4 * 4;
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, this.level2PBOs[pboIndex]);
gl.bufferData(gl.PIXEL_PACK_BUFFER, this.level2Size, gl.STREAM_READ);
}
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level2FB);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, this.level2PBOs[pboIndex]);
gl.readPixels(0, 0, this.level2Width, this.level2Height, gl.RGBA, gl.FLOAT, 0);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, null);
// Create fence sync to wait for GPU completion before reading
const sync = gl.fenceSync(gl.SYNC_GPU_COMMANDS_COMPLETE, 0);
gl.flush();
this.pendingReadback = { pboIndex, sync };
}
runReductionPasses() {
const gl = this.gl;
const readState = this.isPingRead ? this.pingStateTex : this.pongStateTex;
// Swap level1 textures
[this.level1Tex, this.prevLevel1Tex] = [this.prevLevel1Tex, this.level1Tex];
[this.level1FB, this.prevLevel1FB] = [this.prevLevel1FB, this.level1FB];
// Level 1 reduction
gl.useProgram(this.reduction1Program);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level1FB);
gl.viewport(0, 0, this.level1Width, this.level1Height);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, readState);
gl.uniform1i(this.reduction1Uniforms.u_state, 0);
gl.activeTexture(gl.TEXTURE1);
gl.bindTexture(gl.TEXTURE_2D, this.prevLevel1Tex);
gl.uniform1i(this.reduction1Uniforms.u_prevTiles, 1);
gl.uniform2f(this.reduction1Uniforms.u_stateSize, this.texWidth, this.texHeight);
gl.uniform2f(this.reduction1Uniforms.u_tileSize, this.level1Width, this.level1Height);
gl.bindVertexArray(this.quadVAO);
gl.drawArrays(gl.TRIANGLE_STRIP, 0, 4);
// Level 2 reduction
gl.useProgram(this.reduction2Program);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level2FB);
gl.viewport(0, 0, this.level2Width, this.level2Height);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, this.level1Tex);
gl.uniform1i(this.reduction2Uniforms.u_tiles, 0);
gl.uniform2f(this.reduction2Uniforms.u_tilesSize, this.level1Width, this.level1Height);
gl.drawArrays(gl.TRIANGLE_STRIP, 0, 4);
}
waitForPendingReadback() {
const gl = this.gl;
const pending = this.pendingReadback;
if (!pending) return;
const pbo = this.level2PBOs[pending.pboIndex];
if (!pbo) {
if (pending.sync) gl.deleteSync(pending.sync);
this.pendingReadback = null;
this.pendingBatchEndIter = null;
return;
}
this.pendingReadback = null;
const batchEndIter = this.pendingBatchEndIter;
this.pendingBatchEndIter = null;
// Wait for fence sync to complete before reading (avoids pipeline stall warning)
if (pending.sync) {
gl.clientWaitSync(pending.sync, 0, 0); // Don't actually wait, just signal intent
gl.deleteSync(pending.sync);
}
const level2Data = new Float32Array(this.level2Width * this.level2Height * 4);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, pbo);
gl.getBufferSubData(gl.PIXEL_PACK_BUFFER, 0, level2Data);
gl.bindBuffer(gl.PIXEL_PACK_BUFFER, null);
this.processLevel2Results(level2Data);
}
processLevel2Results(superTiles) {
const gl = this.gl;
const activeSuperTiles = [];
let totalNew = 0;
let totalFinished = 0;
for (let sy = 0; sy < this.level2Height; sy++) {
for (let sx = 0; sx < this.level2Width; sx++) {
const idx = (sy * this.level2Width + sx) * 4;
totalFinished += superTiles[idx];
const newlyEscaped = superTiles[idx + 1];
if (newlyEscaped > 0) {
activeSuperTiles.push({ x: sx, y: sy, count: newlyEscaped });
totalNew += newlyEscaped;
}
}
}
if (totalNew === 0) return;
// Read level1 tiles for active super-tiles
const level1Data = new Float32Array(this.level1Width * this.level1Height * 4);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.level1FB);
gl.readPixels(0, 0, this.level1Width, this.level1Height, gl.RGBA, gl.FLOAT, level1Data);
const activeTiles = [];
for (const st of activeSuperTiles) {
const baseX = st.x * 16;
const baseY = st.y * 16;
for (let dy = 0; dy < 16; dy++) {
for (let dx = 0; dx < 16; dx++) {
const tx = baseX + dx;
const ty = baseY + dy;
if (tx >= this.level1Width || ty >= this.level1Height) continue;
const idx = (ty * this.level1Width + tx) * 4;
if (level1Data[idx + 1] > 0) {
activeTiles.push({ x: tx, y: ty, count: level1Data[idx + 1] });
}
}
}
}
if (activeTiles.length === 0) return;
// Read pixel state for active tiles
const readState = this.isPingRead ? this.pingStateTex : this.pongStateTex;
const readCheckpoint = this.isPingRead ? this.pingCheckpointTex : this.pongCheckpointTex;
const stateData = new Float32Array(this.texWidth * this.texHeight * 4);
const checkpointData = new Float32Array(this.texWidth * this.texHeight * 4);
// Create temp framebuffer to read from state texture
const tempFB = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, tempFB);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, readState, 0);
gl.readPixels(0, 0, this.texWidth, this.texHeight, gl.RGBA, gl.FLOAT, stateData);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, readCheckpoint, 0);
gl.readPixels(0, 0, this.texWidth, this.texHeight, gl.RGBA, gl.FLOAT, checkpointData);
gl.deleteFramebuffer(tempFB);
// Process active tiles
const results = [];
for (const tile of activeTiles) {
const baseX = tile.x * 16;
const baseY = tile.y * 16;
for (let dy = 0; dy < 16; dy++) {
for (let dx = 0; dx < 16; dx++) {
const px = baseX + dx;
const py = baseY + dy;
if (px >= this.texWidth || py >= this.texHeight) continue;
const pixelIdx = py * this.texWidth + px;
const stateIdx = pixelIdx * 4;
const status = stateData[stateIdx + 3];
if (status > 0 && !this.reported[pixelIdx]) {
this.reported[pixelIdx] = 1;
const iter = Math.round(stateData[stateIdx + 2]);
const period = Math.round(checkpointData[stateIdx + 3]);
results.push({
index: pixelIdx,
iter: status === 2 ? -iter : iter,
period: period
});
}
}
}
}
// Update counters
this.di += results.length;
this.un -= results.length;
// Queue results to changeList, grouped by iteration
if (results.length > 0) {
const byIter = new Map();
for (const r of results) {
this.nn[r.index] = r.iter;
this.pp[r.index] = r.period;
const absIter = Math.abs(r.iter);
if (!byIter.has(absIter)) {
byIter.set(absIter, { diverged: [], converged: [] });
}
const group = byIter.get(absIter);
if (r.iter > 0) {
group.diverged.push(r.index);
} else {
group.converged.push({ index: r.index, z: 0, p: r.period });
}
}
const sortedIters = Array.from(byIter.keys()).sort((a, b) => a - b);
for (const iter of sortedIters) {
const group = byIter.get(iter);
this.queueChanges({
iter,
nn: group.diverged,
vv: group.converged
});
}
}
}
async serialize() {
const base = await super.serialize();
const completedIndexes = [];
const completedNn = [];
for (let i = 0; i < this.nn.length; i++) {
if (this.nn[i] !== 0) {
completedIndexes.push(i);
completedNn.push(this.nn[i]);
}
}
return {
...base,
reported: Array.from(this.reported),
completedIndexes,
completedNn,
cMinRe: this.cMinRe,
cMinIm: this.cMinIm,
cMaxRe: this.cMaxRe,
cMaxIm: this.cMaxIm
};
}
static isAvailable() {
if (typeof OffscreenCanvas === 'undefined') return false;
try {
const canvas = new OffscreenCanvas(1, 1);
const gl = canvas.getContext('webgl2');
if (!gl) return false;
const ext = gl.getExtension('EXT_color_buffer_float');
return !!ext;
} catch (e) {
return false;
}
}
}
// WebGL2 perturbation board using DD precision reference orbit
// Fallback for browsers without WebGPU support at medium zoom depths
class GlZhuoranBoard extends DDReferenceOrbitMixin(GlPerturbationBaseBoard) {
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
// Initialize DD reference orbit
const refRe = Array.isArray(re) ? re : toDD(re);
const refIm = Array.isArray(im) ? im : toDD(im);
this.initDDReferenceOrbit([refRe[0], refRe[1], refIm[0], refIm[1]]);
// Initialize per-pixel perturbation data
this.initPixels(size, re, im);
// Start GL initialization
this.glInitPromise = this.initGL();
}
initPixels(size, re, im) {
const dimsWidth = this.config.dimsWidth;
const dimsHeight = this.config.dimsHeight;
const dimsArea = this.config.dimsArea;
const re_dd = Array.isArray(re) ? re : toDD(re);
const im_dd = Array.isArray(im) ? im : toDD(im);
const size_scalar = Array.isArray(size) ? size.reduce((a, b) => a + (b || 0), 0) : size;
const size_dd = toDD(size_scalar);
const sizeY_dd = toDD(size_scalar / this.config.aspectRatio);
const cr_dd = new Array(4);
const ci_dd = new Array(4);
const dcr_dd = new Array(4);
const dci_dd = new Array(4);
const temp = new Array(4);
for (let y = 0; y < dimsHeight; y++) {
const yFrac = (dimsHeight / 2 - y) / dimsHeight;
arDdMul(temp, 0, yFrac, 0, sizeY_dd[0], sizeY_dd[1]);
arDdAdd(ci_dd, 0, im_dd[0], im_dd[1], temp[0], temp[1]);
arDdAdd(dci_dd, 0, ci_dd[0], ci_dd[1], -this.refC[2], -this.refC[3]);
for (let x = 0; x < dimsWidth; x++) {
const xFrac = (x - dimsWidth / 2) / dimsWidth;
arDdMul(temp, 0, xFrac, 0, size_dd[0], size_dd[1]);
arDdAdd(cr_dd, 0, re_dd[0], re_dd[1], temp[0], temp[1]);
arDdAdd(dcr_dd, 0, cr_dd[0], cr_dd[1], -this.refC[0], -this.refC[1]);
const index = y * dimsWidth + x;
const index2 = index * 2;
this.dc[index2] = Math.fround(dcr_dd[0] + dcr_dd[1]);
this.dc[index2 + 1] = Math.fround(dci_dd[0] + dci_dd[1]);
this.dz[index2] = this.dc[index2];
this.dz[index2 + 1] = this.dc[index2 + 1];
}
}
}
getIterationShaderSource() {
return `#version 300 es
precision highp float;
precision highp int;
uniform sampler2D u_state; // (dzr, dzi, iter, status)
uniform sampler2D u_checkpoint; // (bbr, bbi, ref_iter, period)
uniform sampler2D u_lazy; // (ckpt_refidx, pending_refidx, ckpt_bbr, ckpt_bbi)
uniform sampler2D u_deltaC; // (dcr, dci, 0, 0)
uniform sampler2D u_refOrbit; // Reference orbit + threading
uniform vec2 u_resolution;
uniform int u_iterations;
uniform int u_exponent;
uniform float u_epsilon;
uniform float u_epsilon2;
uniform float u_pixelSize;
uniform int u_startIter;
uniform int u_refOrbitLength;
uniform int u_refOrbitTexWidth;
uniform int u_fibPrev;
uniform int u_fibCurr;
uniform int u_loopEnabled;
uniform int u_loopThreshold;
uniform int u_loopJump;
uniform float u_loopDeltaR;
uniform float u_loopDeltaI;
layout(location = 0) out vec4 outState;
layout(location = 1) out vec4 outCheckpoint;
layout(location = 2) out vec4 outLazy;
in vec2 v_texCoord;
vec2 getRefOrbit(int idx) {
if (idx >= u_refOrbitLength) return vec2(0.0);
int texelIdx = idx * 2;
int row = texelIdx / u_refOrbitTexWidth;
int col = texelIdx - row * u_refOrbitTexWidth;
vec4 data = texelFetch(u_refOrbit, ivec2(col, row), 0);
return vec2(data.r, data.g);
}
vec3 getThread(int idx) {
if (idx >= u_refOrbitLength) return vec3(-1.0, 0.0, 0.0);
int texelIdx = idx * 2;
int row = texelIdx / u_refOrbitTexWidth;
int col = texelIdx - row * u_refOrbitTexWidth;
vec4 data1 = texelFetch(u_refOrbit, ivec2(col, row), 0);
vec4 data2 = texelFetch(u_refOrbit, ivec2(col + 1, row), 0);
return vec3(data1.b, data1.a, data2.r);
}
void main() {
ivec2 coord = ivec2(gl_FragCoord.xy);
vec4 state = texelFetch(u_state, coord, 0);
vec4 checkpoint = texelFetch(u_checkpoint, coord, 0);
vec4 lazy = texelFetch(u_lazy, coord, 0);
vec4 dc = texelFetch(u_deltaC, coord, 0);
float dzr = state.r;
float dzi = state.g;
float iter = state.b;
float status = state.a;
float bbr = checkpoint.r;
float bbi = checkpoint.g;
int ref_iter = int(checkpoint.b);
float period = checkpoint.a;
int ckpt_refidx = int(lazy.r);
int pending_refidx = int(lazy.g);
float ckpt_bbr = lazy.b;
float ckpt_bbi = lazy.a;
float dcr = dc.r;
float dci = dc.g;
int fibPrev = u_fibPrev;
int fibCurr = u_fibCurr;
if (status == 0.0) {
for (int i = 0; i < 100000; i++) {
if (i >= u_iterations) break;
int globalIter = u_startIter + i + 1;
float dz_norm = max(abs(dzr), abs(dzi));
if (ref_iter > 0 && ref_iter < u_refOrbitLength) {
vec2 ref_check = getRefOrbit(ref_iter);
float total_r = ref_check.x + dzr;
float total_i = ref_check.y + dzi;
float total_norm = max(abs(total_r), abs(total_i));
if (total_norm < dz_norm * 2.0) {
dzr = total_r;
dzi = total_i;
ref_iter = 0;
if (ckpt_refidx >= 0) {
pending_refidx = ckpt_refidx;
bbr = ckpt_bbr;
bbi = ckpt_bbi;
}
}
}
if (ref_iter >= u_refOrbitLength) break;
vec2 ref_val = getRefOrbit(ref_iter);
float refr = ref_val.x;
float refi = ref_val.y;
float curr_r = refr + dzr;
float curr_i = refi + dzi;
float curr_mag_sq = curr_r * curr_r + curr_i * curr_i;
if (curr_mag_sq > 4.0 || curr_mag_sq != curr_mag_sq) {
status = 1.0;
break;
}
float old_dzr = dzr;
float old_dzi = dzi;
int old_ref_iter = ref_iter;
if (u_exponent == 2) {
float new_dzr = 2.0 * (refr * dzr - refi * dzi) + dzr * dzr - dzi * dzi + dcr;
float new_dzi = 2.0 * (refr * dzi + refi * dzr) + 2.0 * dzr * dzi + dci;
dzr = new_dzr;
dzi = new_dzi;
} else {
float z_pow_r = refr;
float z_pow_i = refi;
float coeff = float(u_exponent);
float result_r = dzr;
float result_i = dzi;
for (int k = 1; k < 10; k++) {
if (k >= u_exponent) break;
result_r += coeff * z_pow_r;
result_i += coeff * z_pow_i;
float temp_r = result_r * dzr - result_i * dzi;
result_i = result_r * dzi + result_i * dzr;
result_r = temp_r;
float new_z_pow_r = z_pow_r * refr - z_pow_i * refi;
z_pow_i = z_pow_r * refi + z_pow_i * refr;
z_pow_r = new_z_pow_r;
coeff *= float(u_exponent - k) / float(k + 1);
}
dzr = result_r + dcr;
dzi = result_i + dci;
}
iter += 1.0;
ref_iter++;
if (u_loopEnabled != 0 && ref_iter >= u_loopThreshold) {
dzr += u_loopDeltaR;
dzi += u_loopDeltaI;
ref_iter -= u_loopJump;
}
bool just_updated = false;
if (globalIter == fibCurr) {
just_updated = true;
bbr = old_dzr;
bbi = old_dzi;
ckpt_bbr = old_dzr;
ckpt_bbi = old_dzi;
ckpt_refidx = old_ref_iter;
pending_refidx = old_ref_iter;
period = 0.0;
int nextFib = fibPrev + fibCurr;
fibPrev = fibCurr;
fibCurr = nextFib;
}
if (ckpt_refidx >= 0 && !just_updated) {
if (ref_iter == ckpt_refidx) {
float diff_r = old_dzr - bbr;
float diff_i = old_dzi - bbi;
float db = max(abs(diff_r), abs(diff_i));
if (db <= u_epsilon2) {
if (period == 0.0) period = iter;
if (db <= u_epsilon) {
status = 2.0;
break;
}
}
}
if (pending_refidx >= 2584 && pending_refidx < u_refOrbitLength) {
vec3 thread = getThread(pending_refidx);
if (thread.x >= 0.0 && int(thread.x) == ref_iter) {
float diff_r = old_dzr - bbr + thread.y;
float diff_i = old_dzi - bbi + thread.z;
float db = max(abs(diff_r), abs(diff_i));
if (db <= u_epsilon2) {
if (period == 0.0) period = iter;
if (db <= u_epsilon) {
status = 2.0;
break;
}
}
bbr -= thread.y;
bbi -= thread.z;
pending_refidx = ref_iter;
}
}
}
}
}
outState = vec4(dzr, dzi, iter, status);
outCheckpoint = vec4(bbr, bbi, float(ref_iter), period);
outLazy = vec4(float(ckpt_refidx), float(pending_refidx), ckpt_bbr, ckpt_bbi);
}
`;
}
initializeStateTextures() {
const gl = this.gl;
const w = this.texWidth;
const h = this.texHeight;
const area = w * h;
const stateData = new Float32Array(area * 4);
const checkpointData = new Float32Array(area * 4);
const lazyData = new Float32Array(area * 4);
for (let i = 0; i < area; i++) {
stateData[i * 4 + 0] = this.dz[i * 2];
stateData[i * 4 + 1] = this.dz[i * 2 + 1];
stateData[i * 4 + 2] = 1.0;
stateData[i * 4 + 3] = 0.0;
checkpointData[i * 4 + 0] = 0.0;
checkpointData[i * 4 + 1] = 0.0;
checkpointData[i * 4 + 2] = 1.0;
checkpointData[i * 4 + 3] = 0.0;
lazyData[i * 4 + 0] = -1.0;
lazyData[i * 4 + 1] = -1.0;
lazyData[i * 4 + 2] = 0.0;
lazyData[i * 4 + 3] = 0.0;
}
gl.bindTexture(gl.TEXTURE_2D, this.pingStateTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, stateData);
gl.bindTexture(gl.TEXTURE_2D, this.pingCheckpointTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, checkpointData);
gl.bindTexture(gl.TEXTURE_2D, this.pingLazyTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, lazyData);
}
uploadRefOrbit() {
const gl = this.gl;
const refLen = this.refIterations;
if (refLen <= this.lastUploadedRefIter) return;
const texelsNeeded = refLen * 2;
const texWidth = this.refOrbitTexWidth;
const rowsNeeded = Math.ceil(texelsNeeded / texWidth);
if (rowsNeeded > this.refOrbitTexHeight) {
console.warn('Reference orbit exceeds texture size');
return;
}
const data = new Float32Array(texWidth * rowsNeeded * 4);
// Fill from 0, not lastUploadedRefIter, to avoid overwriting existing data with zeros
// when texSubImage2D uploads full rows
for (let i = 0; i < refLen; i++) {
const orbit = this.refOrbit[i];
const thread = this.threading.getThread(i);
const texelIdx = i * 2;
const dataIdx1 = texelIdx * 4;
data[dataIdx1 + 0] = orbit[0] + orbit[1];
data[dataIdx1 + 1] = orbit[2] + orbit[3];
data[dataIdx1 + 2] = thread.next;
data[dataIdx1 + 3] = thread.deltaRe;
const dataIdx2 = (texelIdx + 1) * 4;
data[dataIdx2 + 0] = thread.deltaIm;
data[dataIdx2 + 1] = 0.0;
data[dataIdx2 + 2] = 0.0;
data[dataIdx2 + 3] = 0.0;
}
gl.bindTexture(gl.TEXTURE_2D, this.refOrbitTex);
// Upload only new rows (rows that weren't fully uploaded before)
const startRow = Math.floor(this.lastUploadedRefIter * 2 / texWidth);
const endRow = Math.ceil(refLen * 2 / texWidth);
for (let row = startRow; row < endRow; row++) {
const rowOffset = row * texWidth * 4;
const rowData = data.subarray(rowOffset, rowOffset + texWidth * 4);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, row, texWidth, 1, gl.RGBA, gl.FLOAT, rowData);
}
this.lastUploadedRefIter = refLen;
}
async serialize() {
const base = await super.serialize();
return {
...base,
refC: this.refC,
refOrbit: this.refOrbit
};
}
static fromSerialized(serialized) {
const board = new GlZhuoranBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
board.glInitPromise = board.glInitPromise.then(() => {
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
if (serialized.reported) {
board.reported = new Uint8Array(serialized.reported);
}
board.cMinRe = serialized.cMinRe;
board.cMinIm = serialized.cMinIm;
board.cMaxRe = serialized.cMaxRe;
board.cMaxIm = serialized.cMaxIm;
if (serialized.refC) {
board.refC = serialized.refC;
}
if (serialized.refOrbit) {
board.refOrbit = serialized.refOrbit;
board.refIter = serialized.refOrbit.length / 2;
}
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
});
return board;
}
}
// WebGL2 adaptive perturbation board using QD precision reference orbit
// For extreme deep zoom when DD precision is insufficient
class GlAdaptiveBoard extends QDReferenceOrbitMixin(GlPerturbationBaseBoard) {
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
// Initialize QD reference orbit
const refReQD = toQD(re);
const refImQD = toQD(im);
this.initQDReferenceOrbit([...refReQD, ...refImQD]);
// Initialize per-pixel perturbation data with adaptive scaling
this.initPixels(size, re, im);
// Start GL initialization
this.glInitPromise = this.initGL();
}
initPixels(size, re, im) {
// Adaptive scaling: store dc as mantissa with separate scale exponent
// δc_actual = dc_stored × 2^scale, where dc_stored is in range ~[-2, 2]
const dimsWidth = this.config.dimsWidth;
const dimsHeight = this.config.dimsHeight;
const dimsArea = this.config.dimsArea;
// Convert size to scalar if it's a QD array
const size_scalar = Array.isArray(size) ? size.reduce((a, b) => a + (b || 0), 0) : size;
const pixelSize = size_scalar / dimsWidth;
// Compute initial scale: k = floor(log2(pixelSize))
const log2_pixelSize = Math.log2(pixelSize);
this.initialScale = Math.floor(log2_pixelSize);
// Mantissa factor: 2^(log2(pixelSize) - k) is in [1, 2)
const mantissa = Math.pow(2, log2_pixelSize - this.initialScale);
// Per-pixel scale array
this.pixelScale = new Int32Array(dimsArea);
// Initialize each pixel
for (let y = 0; y < dimsHeight; y++) {
const yOffset = dimsHeight / 2 - y;
for (let x = 0; x < dimsWidth; x++) {
const xOffset = x - dimsWidth / 2;
const index = y * dimsWidth + x;
const index2 = index * 2;
// δc_stored = mantissa × pixel_offset (normalized to range ~[-dimsWidth/2, +dimsWidth/2] * mantissa)
this.dc[index2] = Math.fround(mantissa * xOffset);
this.dc[index2 + 1] = Math.fround(mantissa * yOffset);
// Start with dz = dc
this.dz[index2] = this.dc[index2];
this.dz[index2 + 1] = this.dc[index2 + 1];
// All pixels start with the same scale
this.pixelScale[index] = this.initialScale;
}
}
}
// Override to create additional scale textures
createTextures() {
const gl = this.gl;
// Create ping-pong state textures (inherited)
this.pingStateTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pingCheckpointTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pingLazyTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pingScaleTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pongStateTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pongCheckpointTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pongLazyTex = this.createFloatTexture(this.texWidth, this.texHeight);
this.pongScaleTex = this.createFloatTexture(this.texWidth, this.texHeight);
// Delta C texture (constant)
this.deltaCTex = this.createFloatTexture(this.texWidth, this.texHeight);
// Reference orbit texture
this.refOrbitTex = this.createFloatTexture(this.refOrbitTexWidth, this.refOrbitTexHeight);
// Create 4-MRT framebuffers for ping-pong
this.pingFB = this.createMRTFramebuffer4(this.pingStateTex, this.pingCheckpointTex, this.pingLazyTex, this.pingScaleTex);
this.pongFB = this.createMRTFramebuffer4(this.pongStateTex, this.pongCheckpointTex, this.pongLazyTex, this.pongScaleTex);
// Hierarchy textures
this.level1Tex = this.createFloatTexture(this.level1Width, this.level1Height);
this.level1FB = this.createFramebuffer(this.level1Tex);
this.prevLevel1Tex = this.createFloatTexture(this.level1Width, this.level1Height);
this.prevLevel1FB = this.createFramebuffer(this.prevLevel1Tex);
this.level2Tex = this.createFloatTexture(this.level2Width, this.level2Height);
this.level2FB = this.createFramebuffer(this.level2Tex);
// Initialize prevLevel1 to zeros
gl.bindFramebuffer(gl.FRAMEBUFFER, this.prevLevel1FB);
gl.viewport(0, 0, this.level1Width, this.level1Height);
gl.clearColor(0, 0, 0, 0);
gl.clear(gl.COLOR_BUFFER_BIT);
}
createMRTFramebuffer4(stateTex, checkpointTex, lazyTex, scaleTex) {
const gl = this.gl;
const fb = gl.createFramebuffer();
gl.bindFramebuffer(gl.FRAMEBUFFER, fb);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, stateTex, 0);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT1, gl.TEXTURE_2D, checkpointTex, 0);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT2, gl.TEXTURE_2D, lazyTex, 0);
gl.framebufferTexture2D(gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT3, gl.TEXTURE_2D, scaleTex, 0);
gl.drawBuffers([gl.COLOR_ATTACHMENT0, gl.COLOR_ATTACHMENT1, gl.COLOR_ATTACHMENT2, gl.COLOR_ATTACHMENT3]);
const status = gl.checkFramebufferStatus(gl.FRAMEBUFFER);
if (status !== gl.FRAMEBUFFER_COMPLETE) {
throw new Error('4-MRT Framebuffer incomplete: ' + status);
}
return fb;
}
async createShaders() {
// Call parent to compile shaders and set up standard uniforms
await super.createShaders();
// Add GlAdaptiveBoard-specific uniforms for scaling
const gl = this.gl;
gl.useProgram(this.iterProgram);
this.iterUniforms.u_scale = gl.getUniformLocation(this.iterProgram, 'u_scale');
this.iterUniforms.u_initialScale = gl.getUniformLocation(this.iterProgram, 'u_initialScale');
}
// Adaptive scaling iteration shader - uses ldexp for deep zoom support
getIterationShaderSource() {
return `#version 300 es
precision highp float;
precision highp int;
uniform sampler2D u_state; // (dzr, dzi, iter, status)
uniform sampler2D u_checkpoint; // (bbr, bbi, ref_iter, period)
uniform sampler2D u_lazy; // (ckpt_refidx, pending_refidx, ckpt_bbr, ckpt_bbi)
uniform sampler2D u_scale; // (scale, 0, 0, 0)
uniform sampler2D u_deltaC; // (dcr, dci, 0, 0)
uniform sampler2D u_refOrbit; // Reference orbit + threading
uniform vec2 u_resolution;
uniform int u_iterations;
uniform int u_exponent;
uniform float u_epsilon;
uniform float u_epsilon2;
uniform float u_pixelSize;
uniform int u_startIter;
uniform int u_refOrbitLength;
uniform int u_refOrbitTexWidth;
uniform int u_fibPrev;
uniform int u_fibCurr;
uniform int u_loopEnabled;
uniform int u_loopThreshold;
uniform int u_loopJump;
uniform float u_loopDeltaR;
uniform float u_loopDeltaI;
uniform int u_initialScale;
layout(location = 0) out vec4 outState;
layout(location = 1) out vec4 outCheckpoint;
layout(location = 2) out vec4 outLazy;
layout(location = 3) out vec4 outScale;
in vec2 v_texCoord;
// ldexp(x, n) = x * 2^n
float ldexp(float x, int n) {
return x * exp2(float(n));
}
vec2 getRefOrbit(int idx) {
if (idx >= u_refOrbitLength) return vec2(0.0);
int texelIdx = idx * 2;
int row = texelIdx / u_refOrbitTexWidth;
int col = texelIdx - row * u_refOrbitTexWidth;
vec4 data = texelFetch(u_refOrbit, ivec2(col, row), 0);
return vec2(data.r, data.g);
}
vec3 getThread(int idx) {
if (idx >= u_refOrbitLength) return vec3(-1.0, 0.0, 0.0);
int texelIdx = idx * 2;
int row = texelIdx / u_refOrbitTexWidth;
int col = texelIdx - row * u_refOrbitTexWidth;
vec4 data1 = texelFetch(u_refOrbit, ivec2(col, row), 0);
vec4 data2 = texelFetch(u_refOrbit, ivec2(col + 1, row), 0);
return vec3(data1.b, data1.a, data2.r);
}
void main() {
ivec2 coord = ivec2(gl_FragCoord.xy);
vec4 state = texelFetch(u_state, coord, 0);
vec4 checkpoint = texelFetch(u_checkpoint, coord, 0);
vec4 lazy = texelFetch(u_lazy, coord, 0);
vec4 scaleVec = texelFetch(u_scale, coord, 0);
vec4 dc = texelFetch(u_deltaC, coord, 0);
float dzr = state.r;
float dzi = state.g;
float iter = state.b;
float status = state.a;
float bbr = checkpoint.r;
float bbi = checkpoint.g;
int ref_iter = int(checkpoint.b);
float period = checkpoint.a;
int ckpt_refidx = int(lazy.r);
int pending_refidx = int(lazy.g);
float ckpt_bbr = lazy.b;
float ckpt_bbi = lazy.a;
int scale = int(scaleVec.r);
float dcr = dc.r;
float dci = dc.g;
int fibPrev = u_fibPrev;
int fibCurr = u_fibCurr;
if (status == 0.0) {
for (int i = 0; i < 100000; i++) {
if (i >= u_iterations) break;
int globalIter = u_startIter + i + 1;
// Rebase check: compute actual dz and see if rebasing helps
float dzr_actual = ldexp(dzr, scale);
float dzi_actual = ldexp(dzi, scale);
float dz_norm = max(abs(dzr_actual), abs(dzi_actual));
if (ref_iter > 0 && ref_iter < u_refOrbitLength) {
vec2 ref_check = getRefOrbit(ref_iter);
float total_r = ref_check.x + dzr_actual;
float total_i = ref_check.y + dzi_actual;
float total_norm = max(abs(total_r), abs(total_i));
if (total_norm < dz_norm * 2.0) {
// Rebase: dz = Z + dz, reset ref_iter to 0
dzr_actual = total_r;
dzi_actual = total_i;
ref_iter = 0;
// Renormalize the rebased dz back to scaled form
float mag = max(abs(dzr_actual), abs(dzi_actual));
if (mag > 0.0 && mag < 1e30) {
int new_scale = int(floor(log2(mag)));
dzr = ldexp(dzr_actual, -new_scale);
dzi = ldexp(dzi_actual, -new_scale);
scale = new_scale;
} else {
dzr = dzr_actual;
dzi = dzi_actual;
scale = 0;
}
if (ckpt_refidx >= 0) {
pending_refidx = ckpt_refidx;
bbr = ckpt_bbr;
bbi = ckpt_bbi;
}
}
}
if (ref_iter >= u_refOrbitLength) break;
vec2 ref_val = getRefOrbit(ref_iter);
float refr = ref_val.x;
float refi = ref_val.y;
// Escape check using actual values
dzr_actual = ldexp(dzr, scale);
dzi_actual = ldexp(dzi, scale);
float curr_r = refr + dzr_actual;
float curr_i = refi + dzi_actual;
float curr_mag_sq = curr_r * curr_r + curr_i * curr_i;
if (curr_mag_sq > 4.0 || curr_mag_sq != curr_mag_sq) {
status = 1.0;
break;
}
float old_dzr = dzr;
float old_dzi = dzi;
int old_ref_iter = ref_iter;
int old_scale = scale;
// === PERTURBATION ITERATION with scaling ===
// For z² + c: new_dz = 2*Z*dz + dz² + dc
// Linear term (2*Z*dz) stays in scaled coordinates
// Quadratic term (dz²) needs ldexp(dz*dz, scale) since (dz*2^s)² = dz²*2^(2s)
// dc needs ldexp(dc, initial_scale - scale) to match current scale
float new_dzr;
float new_dzi;
int scale_diff = u_initialScale - scale;
float dc_r = ldexp(dcr, scale_diff);
float dc_i = ldexp(dci, scale_diff);
if (u_exponent == 2) {
float linear_r = 2.0 * (refr * dzr - refi * dzi);
float linear_i = 2.0 * (refr * dzi + refi * dzr);
float dz2_r = ldexp(dzr * dzr - dzi * dzi, scale);
float dz2_i = ldexp(2.0 * dzr * dzi, scale);
new_dzr = linear_r + dz2_r + dc_r;
new_dzi = linear_i + dz2_i + dc_i;
} else if (u_exponent == 3) {
// z³ + c: 3*Z²*dz + 3*Z*dz² + dz³
float ref2_r = refr * refr - refi * refi;
float ref2_i = 2.0 * refr * refi;
float t1_r = 3.0 * (ref2_r * dzr - ref2_i * dzi);
float t1_i = 3.0 * (ref2_r * dzi + ref2_i * dzr);
float dz2_r = dzr * dzr - dzi * dzi;
float dz2_i = 2.0 * dzr * dzi;
float t2_r = ldexp(3.0 * (refr * dz2_r - refi * dz2_i), scale);
float t2_i = ldexp(3.0 * (refr * dz2_i + refi * dz2_r), scale);
float dz3_r = dzr * dz2_r - dzi * dz2_i;
float dz3_i = dzr * dz2_i + dzi * dz2_r;
float t3_r = ldexp(dz3_r, scale + scale);
float t3_i = ldexp(dz3_i, scale + scale);
new_dzr = t1_r + t2_r + t3_r + dc_r;
new_dzi = t1_i + t2_i + t3_i + dc_i;
} else {
// Higher exponents: use direct computation
float zr = refr + dzr_actual;
float zi = refi + dzi_actual;
float zn_r = zr;
float zn_i = zi;
for (int p = 1; p < 10; p++) {
if (p >= u_exponent) break;
float temp_r = zn_r * zr - zn_i * zi;
zn_i = zn_r * zi + zn_i * zr;
zn_r = temp_r;
}
float refn_r = refr;
float refn_i = refi;
for (int p = 1; p < 10; p++) {
if (p >= u_exponent) break;
float temp_r = refn_r * refr - refn_i * refi;
refn_i = refn_r * refi + refn_i * refr;
refn_r = temp_r;
}
new_dzr = (zn_r - refn_r) + dc_r;
new_dzi = (zn_i - refn_i) + dc_i;
}
int new_scale = scale;
// === ADAPTIVE RESCALING ===
float dz_mag = max(abs(new_dzr), abs(new_dzi));
if (dz_mag > 0.0 && dz_mag < 1e30) {
float log2_mag = floor(log2(dz_mag));
if (log2_mag >= 1.0) {
int steps = int(log2_mag);
if (new_scale + steps <= 100) {
new_dzr = ldexp(new_dzr, -steps);
new_dzi = ldexp(new_dzi, -steps);
new_scale = new_scale + steps;
}
} else if (log2_mag < -1.0 && new_scale > u_initialScale) {
int steps = min(int(-log2_mag) - 1, new_scale - u_initialScale);
if (steps > 0) {
new_dzr = ldexp(new_dzr, steps);
new_dzi = ldexp(new_dzi, steps);
new_scale = new_scale - steps;
}
}
}
dzr = new_dzr;
dzi = new_dzi;
scale = new_scale;
iter += 1.0;
ref_iter++;
if (u_loopEnabled != 0 && ref_iter >= u_loopThreshold) {
// Loop delta is in actual units, need to convert to scaled
float loop_dzr = ldexp(u_loopDeltaR, -scale);
float loop_dzi = ldexp(u_loopDeltaI, -scale);
dzr += loop_dzr;
dzi += loop_dzi;
ref_iter -= u_loopJump;
}
// Bounding box updates use old values (before this iteration)
bool just_updated = false;
if (globalIter == fibCurr) {
just_updated = true;
bbr = old_dzr;
bbi = old_dzi;
ckpt_bbr = old_dzr;
ckpt_bbi = old_dzi;
ckpt_refidx = old_ref_iter;
pending_refidx = old_ref_iter;
period = 0.0;
int nextFib = fibPrev + fibCurr;
fibPrev = fibCurr;
fibCurr = nextFib;
}
if (ckpt_refidx >= 0 && !just_updated) {
if (ref_iter == ckpt_refidx) {
float diff_r = old_dzr - bbr;
float diff_i = old_dzi - bbi;
float db = max(abs(diff_r), abs(diff_i));
// Scale epsilon to match the stored scale
float eps = ldexp(u_epsilon, -old_scale);
float eps2 = ldexp(u_epsilon2, -old_scale);
if (db <= eps2) {
if (period == 0.0) period = iter;
if (db <= eps) {
status = 2.0;
break;
}
}
}
if (pending_refidx >= 2584 && pending_refidx < u_refOrbitLength) {
vec3 thread = getThread(pending_refidx);
if (thread.x >= 0.0 && int(thread.x) == ref_iter) {
// Thread deltas are in actual units, convert to old_scale
float thread_r = ldexp(thread.y, -old_scale);
float thread_i = ldexp(thread.z, -old_scale);
float diff_r = old_dzr - bbr + thread_r;
float diff_i = old_dzi - bbi + thread_i;
float db = max(abs(diff_r), abs(diff_i));
float eps = ldexp(u_epsilon, -old_scale);
float eps2 = ldexp(u_epsilon2, -old_scale);
if (db <= eps2) {
if (period == 0.0) period = iter;
if (db <= eps) {
status = 2.0;
break;
}
}
bbr -= thread_r;
bbi -= thread_i;
pending_refidx = ref_iter;
}
}
}
}
}
outState = vec4(dzr, dzi, iter, status);
outCheckpoint = vec4(bbr, bbi, float(ref_iter), period);
outLazy = vec4(float(ckpt_refidx), float(pending_refidx), ckpt_bbr, ckpt_bbi);
outScale = vec4(float(scale), 0.0, 0.0, 0.0);
}
`;
}
initializeStateTextures() {
const gl = this.gl;
const w = this.texWidth;
const h = this.texHeight;
const area = w * h;
const stateData = new Float32Array(area * 4);
const checkpointData = new Float32Array(area * 4);
const lazyData = new Float32Array(area * 4);
const scaleData = new Float32Array(area * 4);
for (let i = 0; i < area; i++) {
stateData[i * 4 + 0] = this.dz[i * 2];
stateData[i * 4 + 1] = this.dz[i * 2 + 1];
stateData[i * 4 + 2] = 1.0; // iter
stateData[i * 4 + 3] = 0.0; // status
checkpointData[i * 4 + 0] = 0.0;
checkpointData[i * 4 + 1] = 0.0;
checkpointData[i * 4 + 2] = 1.0;
checkpointData[i * 4 + 3] = 0.0;
lazyData[i * 4 + 0] = -1.0;
lazyData[i * 4 + 1] = -1.0;
lazyData[i * 4 + 2] = 0.0;
lazyData[i * 4 + 3] = 0.0;
// Scale texture: (scale, 0, 0, 0)
scaleData[i * 4 + 0] = this.pixelScale[i];
scaleData[i * 4 + 1] = 0.0;
scaleData[i * 4 + 2] = 0.0;
scaleData[i * 4 + 3] = 0.0;
}
gl.bindTexture(gl.TEXTURE_2D, this.pingStateTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, stateData);
gl.bindTexture(gl.TEXTURE_2D, this.pingCheckpointTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, checkpointData);
gl.bindTexture(gl.TEXTURE_2D, this.pingLazyTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, lazyData);
gl.bindTexture(gl.TEXTURE_2D, this.pingScaleTex);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, 0, w, h, gl.RGBA, gl.FLOAT, scaleData);
}
doGpuIterations(targetIters) {
const gl = this.gl;
// Get Fibonacci checkpoints
while (this.fibCache[this.fibCache.length - 1] < this.it + targetIters + 1000) {
const n = this.fibCache.length;
this.fibCache.push(this.fibCache[n - 1] + this.fibCache[n - 2]);
}
let fibIdx = 0;
while (this.fibCache[fibIdx] <= this.it) fibIdx++;
const fibPrev = fibIdx > 0 ? this.fibCache[fibIdx - 1] : 1;
const fibCurr = this.fibCache[fibIdx];
// Bind shader and set uniforms
gl.useProgram(this.iterProgram);
gl.activeTexture(gl.TEXTURE3);
gl.bindTexture(gl.TEXTURE_2D, this.deltaCTex);
gl.uniform1i(this.iterUniforms.u_deltaC, 3);
gl.activeTexture(gl.TEXTURE4);
gl.bindTexture(gl.TEXTURE_2D, this.refOrbitTex);
gl.uniform1i(this.iterUniforms.u_refOrbit, 4);
gl.uniform2f(this.iterUniforms.u_resolution, this.texWidth, this.texHeight);
gl.uniform1i(this.iterUniforms.u_iterations, targetIters);
gl.uniform1i(this.iterUniforms.u_exponent, this.config.exponent);
gl.uniform1f(this.iterUniforms.u_epsilon, this.epsilon);
gl.uniform1f(this.iterUniforms.u_epsilon2, this.epsilon2);
gl.uniform1f(this.iterUniforms.u_pixelSize, this.pix);
gl.uniform1i(this.iterUniforms.u_startIter, this.it);
gl.uniform1i(this.iterUniforms.u_refOrbitLength, this.refIterations);
gl.uniform1i(this.iterUniforms.u_refOrbitTexWidth, this.refOrbitTexWidth);
gl.uniform1i(this.iterUniforms.u_fibPrev, fibPrev);
gl.uniform1i(this.iterUniforms.u_fibCurr, fibCurr);
// Loop parameters
gl.uniform1i(this.iterUniforms.u_loopEnabled, this.refOrbitLoop.enabled ? 1 : 0);
gl.uniform1i(this.iterUniforms.u_loopThreshold, this.refOrbitLoop.threshold || 0);
gl.uniform1i(this.iterUniforms.u_loopJump, this.refOrbitLoop.jumpAmount || 0);
gl.uniform1f(this.iterUniforms.u_loopDeltaR, this.refOrbitLoop.deltaR || 0);
gl.uniform1f(this.iterUniforms.u_loopDeltaI, this.refOrbitLoop.deltaI || 0);
// GlAdaptiveBoard-specific: initial scale uniform
gl.uniform1i(this.iterUniforms.u_initialScale, this.initialScale);
// Bind input textures
const readState = this.isPingRead ? this.pingStateTex : this.pongStateTex;
const readCheckpoint = this.isPingRead ? this.pingCheckpointTex : this.pongCheckpointTex;
const readLazy = this.isPingRead ? this.pingLazyTex : this.pongLazyTex;
const readScale = this.isPingRead ? this.pingScaleTex : this.pongScaleTex;
// Write to the OPPOSITE buffer (ping-pong pattern)
const writeFB = this.isPingRead ? this.pongFB : this.pingFB;
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, readState);
gl.uniform1i(this.iterUniforms.u_state, 0);
gl.activeTexture(gl.TEXTURE1);
gl.bindTexture(gl.TEXTURE_2D, readCheckpoint);
gl.uniform1i(this.iterUniforms.u_checkpoint, 1);
gl.activeTexture(gl.TEXTURE2);
gl.bindTexture(gl.TEXTURE_2D, readLazy);
gl.uniform1i(this.iterUniforms.u_lazy, 2);
// GlAdaptiveBoard-specific: bind scale texture
gl.activeTexture(gl.TEXTURE5);
gl.bindTexture(gl.TEXTURE_2D, readScale);
gl.uniform1i(this.iterUniforms.u_scale, 5);
// Draw
gl.bindFramebuffer(gl.FRAMEBUFFER, writeFB);
gl.viewport(0, 0, this.texWidth, this.texHeight);
gl.bindVertexArray(this.quadVAO);
gl.drawArrays(gl.TRIANGLE_STRIP, 0, 4);
this.isPingRead = !this.isPingRead;
this.it += targetIters;
}
uploadRefOrbit() {
const gl = this.gl;
const refLen = this.refIterations;
if (refLen <= this.lastUploadedRefIter) return;
const texelsNeeded = refLen * 2;
const texWidth = this.refOrbitTexWidth;
const rowsNeeded = Math.ceil(texelsNeeded / texWidth);
if (rowsNeeded > this.refOrbitTexHeight) {
console.warn('Reference orbit exceeds texture size');
return;
}
const data = new Float32Array(texWidth * rowsNeeded * 4);
// Fill from 0, not lastUploadedRefIter, to avoid overwriting existing data with zeros
// when texSubImage2D uploads full rows
for (let i = 0; i < refLen; i++) {
const orbit = this.qdRefOrbit[i];
const thread = this.threading.getThread(i);
const texelIdx = i * 2;
const dataIdx1 = texelIdx * 4;
// Sum QD components to get f32 value for ref orbit
data[dataIdx1 + 0] = orbit ? orbit[0] + orbit[1] + orbit[2] + orbit[3] : 0;
data[dataIdx1 + 1] = orbit ? orbit[4] + orbit[5] + orbit[6] + orbit[7] : 0;
data[dataIdx1 + 2] = thread.next;
data[dataIdx1 + 3] = thread.deltaRe;
const dataIdx2 = (texelIdx + 1) * 4;
data[dataIdx2 + 0] = thread.deltaIm;
data[dataIdx2 + 1] = 0.0;
data[dataIdx2 + 2] = 0.0;
data[dataIdx2 + 3] = 0.0;
}
gl.bindTexture(gl.TEXTURE_2D, this.refOrbitTex);
// Upload only new rows (rows that weren't fully uploaded before)
const startRow = Math.floor(this.lastUploadedRefIter * 2 / texWidth);
const endRow = Math.ceil(refLen * 2 / texWidth);
for (let row = startRow; row < endRow; row++) {
const rowOffset = row * texWidth * 4;
const rowData = data.subarray(rowOffset, rowOffset + texWidth * 4);
gl.texSubImage2D(gl.TEXTURE_2D, 0, 0, row, texWidth, 1, gl.RGBA, gl.FLOAT, rowData);
}
this.lastUploadedRefIter = refLen;
}
async serialize() {
const base = await super.serialize();
return {
...base,
refC_qd: this.refC_qd,
qdRefOrbit: this.qdRefOrbit,
initialScale: this.initialScale,
pixelScale: Array.from(this.pixelScale)
};
}
static fromSerialized(serialized) {
const board = new GlAdaptiveBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
board.glInitPromise = board.glInitPromise.then(() => {
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
if (serialized.reported) {
board.reported = new Uint8Array(serialized.reported);
}
board.cMinRe = serialized.cMinRe;
board.cMinIm = serialized.cMinIm;
board.cMaxRe = serialized.cMaxRe;
board.cMaxIm = serialized.cMaxIm;
if (serialized.refC_qd) {
board.refC_qd = serialized.refC_qd;
}
if (serialized.qdRefOrbit) {
board.qdRefOrbit = serialized.qdRefOrbit;
board.refIterations = serialized.qdRefOrbit.length;
}
if (serialized.initialScale !== undefined) {
board.initialScale = serialized.initialScale;
}
if (serialized.pixelScale) {
board.pixelScale = new Int32Array(serialized.pixelScale);
}
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
});
return board;
}
}
// Base class for double-buffered GPU perturbation boards (GpuZhuoranBoard, GpuAdaptiveBoard)
// Provides shared double-buffering infrastructure and result processing
class GpuZhuoranBaseBoard extends GpuBaseBoard {
// Subclasses must define: static BYTES_PER_PIXEL, static STRIDE
// PixelState layout: orig_index, iter, status, period, ... (orig_index at offset 0)
// Initialize double-buffering and compaction state (call from subclass constructor)
initDoubleBuffering() {
this.stagingBufferIndex = 0;
this.hasPendingResults = false;
this.pendingIterationsPerBatch = 0;
this.baseIt = 1; // Committed iteration count
// Compaction state - uses bandwidth cost model
// Compact when cumulative wasted bandwidth > compaction cost
this.activeCount = this.config.dimsArea;
this.deadSinceCompaction = 0;
this.wastedBandwidth = 0; // Cumulative bytes wasted copying dead pixels
this.compactionCount = 0; // Number of compactions performed
this.pendingActiveCount = this.config.dimsArea;
this.lastBatchCompacted = false;
this.cumulativeWastedReads = 0;
}
// Return iteration count for submitted GPU batches (same as GpuBoard)
get it() {
return this.baseIt;
}
set it(value) {
this.baseIt = value;
}
async flushPendingResults() {
// Process pending results from the staging buffer without starting a new batch
if (!this.hasPendingResults) return;
if (this.pendingReadbackIndex !== null) {
await this.processPendingReadback();
}
// Continue draining results until all are read
// The staging shader reads from lastStaged which advances each time we read a chunk
let moreData = true;
while (moreData) {
const readbackIndex = this.readbackBufferIndex;
const commandEncoder = this.device.createCommandEncoder({ label: 'GpuZhuoran drain readback' });
this.queueResultsReadback(commandEncoder, readbackIndex);
this.device.queue.submit([commandEncoder.finish()]);
await this.device.queue.onSubmittedWorkDone();
// Read and process the chunk
const { countInChunk, data } = await this.readResultsChunk(readbackIndex);
if (countInChunk === 0) {
moreData = false; // No more results to read
} else if (data) {
this.processResultsData(data, countInChunk);
}
this.readbackBufferIndex = 1 - readbackIndex;
}
}
async readPixelBuffer() {
// Read GPU pixel buffer for serialization - creates temporary staging buffer on-demand
if (!this.isGPUReady || !this.buffers.pixels) {
return null;
}
const BYTES_PER_PIXEL = this.constructor.BYTES_PER_PIXEL;
const bufferSize = this.activeCount * BYTES_PER_PIXEL;
// Create temporary staging buffer (only needed during serialization)
const stagingBuffer = this.device.createBuffer({
size: bufferSize,
usage: GPUBufferUsage.MAP_READ | GPUBufferUsage.COPY_DST,
label: 'Temp staging for serialization'
});
// Copy pixels buffer to staging
const commandEncoder = this.device.createCommandEncoder();
commandEncoder.copyBufferToBuffer(this.buffers.pixels, 0, stagingBuffer, 0, bufferSize);
this.device.queue.submit([commandEncoder.finish()]);
await this.device.queue.onSubmittedWorkDone();
// Read back the data
await stagingBuffer.mapAsync(GPUMapMode.READ, 0, bufferSize);
const pixelData = new ArrayBuffer(bufferSize);
const srcData = stagingBuffer.getMappedRange(0, bufferSize);
new Uint8Array(pixelData).set(new Uint8Array(srcData));
stagingBuffer.unmap();
// Destroy temporary buffer immediately
stagingBuffer.destroy();
return pixelData;
}
}
// WebGPU-accelerated perturbation board using Zhuoran's approach
// Computes high-precision reference orbit on CPU, perturbations on GPU
// Uses DDReferenceOrbitMixin for reference orbit computation
class GpuZhuoranBoard extends DDReferenceOrbitMixin(GpuZhuoranBaseBoard) {
static BYTES_PER_PIXEL = 60; // 7 u32 + 8 f32 (with orig_index for compaction)
static STRIDE = 15; // 15 fields per pixel
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
this.effort = 18; // Doubled to reduce batch sizes after GPU readback improvements
// Initialize DD reference orbit (refC, refOrbit, threading, etc.)
const refRe = Array.isArray(re) ? re : toDD(re);
const refIm = Array.isArray(im) ? im : toDD(im);
this.initDDReferenceOrbit([refRe[0], refRe[1], refIm[0], refIm[1]]);
// Initialize per-pixel perturbation data
this.initPixels(size, re, im);
// Initialize double-buffering (from GpuZhuoranBaseBoard)
this.initDoubleBuffering();
// Start GPU initialization (async)
this.gpuInitPromise = this.initGPU();
}
initPixels(size, re, im) {
const dimsWidth = this.config.dimsWidth;
const dimsHeight = this.config.dimsHeight;
const dimsArea = this.config.dimsArea;
// Convert re/im to DD precision if needed
const re_dd = Array.isArray(re) ? re : toDD(re);
const im_dd = Array.isArray(im) ? im : toDD(im);
// Convert size to scalar if it's a QD array (fixes NaN when size is array)
const size_scalar = Array.isArray(size) ? size.reduce((a, b) => a + (b || 0), 0) : size;
const size_dd = toDD(size_scalar);
const sizeY_dd = toDD(size_scalar / this.config.aspectRatio);
// Per-pixel data arrays
this.dc = new Float32Array(dimsArea * 2);
// Delta c from reference [real, imag] pairs
this.dz = new Float32Array(dimsArea * 2);
// Current perturbation delta [real, imag] pairs
this.refIter = new Uint32Array(dimsArea);
// Which iteration of reference each pixel is following
// Working arrays for DD precision arithmetic
const cr_dd = new Array(4);
const ci_dd = new Array(4);
const dcr_dd = new Array(4);
const dci_dd = new Array(4);
const temp = new Array(4);
// Initialize all pixels as perturbations from the reference point
for (let y = 0; y < dimsHeight; y++) {
// Use integer arithmetic to avoid float64 rounding: (dims/2 - y) / dims
const yFrac = (dimsHeight / 2 - y) / dimsHeight;
// ci_dd = im_dd + yFrac * sizeY_dd (in DD precision)
arDdMul(temp, 0, yFrac, 0, sizeY_dd[0], sizeY_dd[1]);
arDdAdd(ci_dd, 0, im_dd[0], im_dd[1], temp[0], temp[1]);
// dci_dd = ci_dd - refC_imag
arDdAdd(dci_dd, 0, ci_dd[0], ci_dd[1], -this.refC[2], -this.refC[3]);
for (let x = 0; x < dimsWidth; x++) {
// Use integer arithmetic to avoid float64 rounding: (x - dims/2) / dims
const xFrac = (x - dimsWidth / 2) / dimsWidth;
// cr_dd = re_dd + xFrac * size_dd (in DD precision)
arDdMul(temp, 0, xFrac, 0, size_dd[0], size_dd[1]);
arDdAdd(cr_dd, 0, re_dd[0], re_dd[1], temp[0], temp[1]);
// dcr_dd = cr_dd - refC_real
arDdAdd(dcr_dd, 0, cr_dd[0], cr_dd[1], -this.refC[0], -this.refC[1]);
const index = y * dimsWidth + x;
const index2 = index * 2;
// Convert DD precision deltas to float32 (Math.fround simulates GPU precision)
this.dc[index2] = Math.fround(dcr_dd[0] + dcr_dd[1]);
this.dc[index2 + 1] = Math.fround(dci_dd[0] + dci_dd[1]);
// Start with dz = dc (so z = c_ref + dc = c)
this.dz[index2] = this.dc[index2];
this.dz[index2 + 1] = this.dc[index2 + 1];
// Start at iteration 1 (where refOrbit[1] = c_ref)
this.refIter[index] = 1;
}
}
this.checkSpike(size, re, im);
}
async createBuffers() {
const dimsArea = this.config.dimsWidth * this.config.dimsHeight;
const BYTES_PER_PIXEL = GpuZhuoranBoard.BYTES_PER_PIXEL;
const STRIDE = GpuZhuoranBoard.STRIDE;
// Check buffer size limits before creating (safety margin applied upstream)
const maxBufferSize = Math.min(
this.device.limits.maxBufferSize,
this.device.limits.maxStorageBufferBindingSize
);
// Unified PixelState struct: 7 u32 + 8 f32 = 60 bytes per pixel (with orig_index)
const precomputedCount = this.precomputed ? this.precomputed.getPrecomputedCount() : 0;
const activePixelCount = dimsArea - precomputedCount;
const pixelBufferSize = Math.max(BYTES_PER_PIXEL, activePixelCount * BYTES_PER_PIXEL);
if (pixelBufferSize > maxBufferSize) {
throw new Error(
`Buffer size (${(pixelBufferSize / (1024 * 1024)).toFixed(1)} MB) ` +
`exceeds WebGPU limit (${(maxBufferSize / (1024 * 1024)).toFixed(1)} MB). ` +
`Board ${this.config.dimsWidth}x${this.config.dimsHeight} is too large ` +
`for GPU acceleration.`);
}
const resultsBufferSize = 16 + (activePixelCount * BYTES_PER_PIXEL);
if (resultsBufferSize > maxBufferSize) {
throw new Error(
`Results buffer size (${(resultsBufferSize / (1024 * 1024)).toFixed(1)} MB) ` +
`exceeds WebGPU limit (${(maxBufferSize / (1024 * 1024)).toFixed(1)} MB).`);
}
// Single unified pixel state buffer (PixelState struct: 7 u32 + 8 f32 = 60 bytes per pixel)
// Layout per pixel: [orig_index, iter, status, period, ref_iter, ckpt_refidx, pending_refidx,
// dzr, dzi, bbr, bbi, ckpt_bbr, ckpt_bbi, dcr, dci]
this.buffers.pixels = this.device.createBuffer({
size: pixelBufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST,
label: 'Pixel state buffer'
});
// Unified iteration state buffer (IterState struct: 5 f32 = 20 bytes per iteration)
// Combines reference orbit (re, im) and threading data (next, deltaRe, deltaIm)
// Start with 1MB, will grow by doubling up to 128MB cap
this.buffers.iters = this.device.createBuffer({
size: 1 * 1024 * 1024,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST,
label: 'Iteration state buffer'
});
// Track last uploaded iteration length
this.lastUploadedIterLength = -1; // -1 means nothing uploaded yet
// Uniform buffer for parameters
this.buffers.params = this.device.createBuffer({
size: 256, // Increased to hold 32 checkpoint slots
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Params buffer'
});
// Note: stagingPixels buffers are created on-demand in readPixelBuffer() for serialization
// This saves ~2x pixel buffer size in GPU memory during normal operation
// Initialize pixel state buffer using overlapping typed array views
// ArrayBuffer holds 60 bytes per pixel (15 x 4 bytes, with orig_index)
const pixelData = new ArrayBuffer(pixelBufferSize);
const pixelU32 = new Uint32Array(pixelData); // For u32 fields (indices 0-6)
const pixelF32 = new Float32Array(pixelData); // For f32 fields (indices 7-14)
let activeIdx = 0;
for (let i = 0; i < dimsArea; i++) {
if (this.precomputed && this.precomputed.isPrecomputed(i)) {
continue;
}
const idx = activeIdx * STRIDE; // 15 x 4-byte values per pixel
// Integer fields (offsets 0-6)
pixelU32[idx + 0] = i; // orig_index (for coordinate computation after compaction)
pixelU32[idx + 1] = 1; // iter (start at 1, z=c is iteration 1)
pixelU32[idx + 2] = 0; // status (0 = computing)
pixelU32[idx + 3] = 0; // period
pixelU32[idx + 4] = this.refIter[i]; // ref_iter
pixelU32[idx + 5] = 0xFFFFFFFF; // ckpt_refidx (sentinel)
pixelU32[idx + 6] = 0xFFFFFFFF; // pending_refidx (sentinel)
// Float fields (offsets 7-14)
pixelF32[idx + 7] = this.dz[i * 2]; // dzr
pixelF32[idx + 8] = this.dz[i * 2 + 1]; // dzi
pixelF32[idx + 9] = 0; // bbr
pixelF32[idx + 10] = 0; // bbi
pixelF32[idx + 11] = 0; // ckpt_bbr
pixelF32[idx + 12] = 0; // ckpt_bbi
pixelF32[idx + 13] = this.dc[i * 2]; // dcr
pixelF32[idx + 14] = this.dc[i * 2 + 1]; // dci
activeIdx++;
}
// Initialize unified iters buffer with initial data (iter 0 and 1)
// IterState struct: [ref_re, ref_im, thread_next, thread_delta_re, thread_delta_im] = 5 f32
const initialIterData = new Float32Array(10); // 2 iters * 5 floats
// iter 0: z=0, no thread
initialIterData[0] = 0; // ref_re
initialIterData[1] = 0; // ref_im
initialIterData[2] = -1; // thread_next (-1 = no thread)
initialIterData[3] = 0; // thread_delta_re
initialIterData[4] = 0; // thread_delta_im
// iter 1: z=c_ref, no thread
initialIterData[5] = this.refC[0] + this.refC[1]; // ref_re
initialIterData[6] = this.refC[2] + this.refC[3]; // ref_im
initialIterData[7] = -1; // thread_next
initialIterData[8] = 0; // thread_delta_re
initialIterData[9] = 0; // thread_delta_im
this.device.queue.writeBuffer(this.buffers.pixels, 0, pixelU32);
this.device.queue.writeBuffer(this.buffers.iters, 0, initialIterData);
// Mark initial data as uploaded
this.lastUploadedIterLength = 1; // Uploaded iters 0 and 1
this.activeCount = activePixelCount;
this.pendingActiveCount = activePixelCount;
this.deadSinceCompaction = 0;
this.wastedBandwidth = 0;
this.initResultsReadback(BYTES_PER_PIXEL, activePixelCount);
}
createBindGroup() {
// Unified 5-binding layout for maximum cache coherency
this.bindGroup = this.device.createBindGroup({
layout: this.pipeline.getBindGroupLayout(0),
entries: [
{ binding: 0, resource: { buffer: this.buffers.params } },
{ binding: 1, resource: { buffer: this.buffers.pixels } },
{ binding: 2, resource: { buffer: this.buffers.iters } },
{ binding: 3, resource: { buffer: this.buffers.results } },
{ binding: 4, resource: { buffer: this.buffers.lock } }
],
label: 'Perturbation bind group'
});
}
/**
* Process GPU results using batch-oriented approach (same as GpuBoard).
* This ensures results are only sent to changeList when batches complete,
* preventing out-of-order iteration delivery that causes striping.
*/
processResultsData(data, count) {
const STRIDE = GpuZhuoranBoard.STRIDE;
const pixelU32 = new Uint32Array(data);
const pixelF32 = new Float32Array(data);
const debugReadback = hasDebugFlag(this.config, 'rb');
this.lastResultsCount = count;
this.resultsReadbackBatches += 1;
this.resultsReadbackBytes += count * this.resultsRecordBytes;
const INT_ORIG_INDEX = 0, INT_ITER = 1, INT_STATUS = 2, INT_PERIOD = 3, INT_REF_ITER = 4;
const FLOAT_DZR = 7, FLOAT_DZI = 8;
let dataIndex = 0;
// OUTER LOOP: Process batches in order
while (this.batchesToReadback.length > 0) {
const batch = this.batchesToReadback[0];
// Flush precomputed points before this batch's iteration range
if (this.precomputed) {
this.flushPrecomputedUpTo(this.previousBatchEndIter - 1);
}
// INNER LOOP: Process available data for this batch
while (batch.remainingPixelCount > 0 && dataIndex < count) {
const idx = dataIndex * STRIDE;
const origIndex = pixelU32[idx + INT_ORIG_INDEX];
const status = pixelU32[idx + INT_STATUS];
const period = pixelU32[idx + INT_PERIOD];
const iters = pixelU32[idx + INT_ITER];
// Skip already processed pixels (shouldn't happen, but defensive)
if (this.nn[origIndex] !== 0) {
if (debugReadback) {
const same = this.nn[origIndex] === iters ? ' (SAME VALUE)' : ' (DIFFERENT VALUE)';
console.error(`INVARIANT VIOLATION: Duplicate result for pixel ${origIndex}, existing nn=${this.nn[origIndex]}, new iters=${iters}${same}`);
}
dataIndex++;
continue;
}
// Skip non-finished pixels (status 0 = still computing)
if (status === 0) {
dataIndex++;
continue;
}
if (status === 1) {
// Diverged
this.nn[origIndex] = iters;
this.pp[origIndex] = period;
this.di++;
if (this.inSpike && this.inSpike[origIndex] && this.ch > 0) this.ch -= 1;
// Accumulate into batchResultsRead
this.batchResultsRead.push({ iter: iters, nn: [origIndex], vv: [] });
} else if (status === 2) {
// Converged
this.nn[origIndex] = -iters;
this.pp[origIndex] = period - 1;
if (this.inSpike && this.inSpike[origIndex] && this.ch > 0) this.ch -= 1;
// Compute final z value using DD reference orbit
const refIter = pixelU32[idx + INT_REF_ITER];
const nextRefIter = refIter + 1;
const dzr = pixelF32[idx + FLOAT_DZR];
const dzi = pixelF32[idx + FLOAT_DZI];
const ref = this.refOrbit[Math.min(nextRefIter, this.refOrbit.length - 1)];
// Accumulate into batchResultsRead
this.batchResultsRead.push({
iter: iters,
nn: [],
vv: [{ index: origIndex, z: this.refDzNative(ref, dzr, dzi), p: this.pp[origIndex] }]
});
}
this.deadSinceCompaction++;
batch.remainingPixelCount--;
dataIndex++;
}
// Check if batch is complete
if (batch.remainingPixelCount > 0) {
// Batch not complete - exit and wait for more data
break;
}
// BATCH COMPLETE - Flush to changeList
// Flush precomputed points up to this batch's end iteration
if (this.precomputed) {
this.flushPrecomputedIntoResults(batch.endIter - 1);
}
// Queue results to changeList using queueChanges
for (const change of this.batchResultsRead) {
this.queueChanges(change);
}
// Clear for next batch
this.batchResultsRead.length = 0;
this.previousBatchEndIter = batch.endIter;
this.batchesToReadback.shift();
}
// Update un count
// deadSinceCompaction includes results in batchResultsRead that aren't flushed yet
// Add them back since they're not in changeList yet (view won't see them)
const pendingPrecomputed = this.precomputed ? this.precomputed.getPendingCount() : 0;
const pendingInBatchResults = this.batchResultsRead.length;
this.un = (this.activeCount - this.deadSinceCompaction) + pendingPrecomputed + pendingInBatchResults;
}
// extendReferenceOrbit() inherited from DDReferenceOrbitMixin
setupReferenceOrbitLoop() {
// When reference orbit hits threading limit, find a close point to loop back to
const THREADING_CAPACITY = 1048576; // 2^20
const SEARCH_WINDOW = 12000;
if (this.refIterations < THREADING_CAPACITY || this.refOrbitLoopConfigured) {
return; // Not at limit yet, or already configured
}
// Get endpoint (current position at threading limit)
const endpoint = this.refOrbit[THREADING_CAPACITY];
const endR = endpoint[0] + endpoint[1];
const endI = endpoint[2] + endpoint[3];
// Search back to find closest point
let closestIter = THREADING_CAPACITY - SEARCH_WINDOW;
let closestDist = Infinity;
for (let i = THREADING_CAPACITY - SEARCH_WINDOW; i < THREADING_CAPACITY; i++) {
const pt = this.refOrbit[i];
const ptR = pt[0] + pt[1];
const ptI = pt[2] + pt[3];
const dr = endR - ptR;
const di = endI - ptI;
const dist = Math.max(Math.abs(dr), Math.abs(di)); // Chebyshev distance
if (dist <= closestDist) { // Use <= to take latest point when tied
closestDist = dist;
closestIter = i;
}
}
// Compute delta in DD precision
const closestPt = this.refOrbit[closestIter];
const tt = this.tt;
arDdAdd(tt, 0, endpoint[0], endpoint[1], -closestPt[0], -closestPt[1]); // real delta
arDdAdd(tt, 2, endpoint[2], endpoint[3], -closestPt[2], -closestPt[3]); // imag delta
// Store loop parameters
this.refOrbitLoop = {
enabled: true,
threshold: THREADING_CAPACITY,
jumpAmount: THREADING_CAPACITY - closestIter,
deltaR: tt[0] + tt[1], // Convert to float64
deltaI: tt[2] + tt[3]
};
this.refOrbitLoopConfigured = true;
// Update threading for loop segment to wrap around
const loopDeltaR = this.refOrbitLoop.deltaR;
const loopDeltaI = this.refOrbitLoop.deltaI;
const epsilon3 = this.threading.epsilon3;
// For each iteration in the loop segment, check if it can thread to another iteration
// considering the loop wrap (iterations will repeat with a delta offset)
for (let i = closestIter; i <= THREADING_CAPACITY; i++) {
const iPt = this.refOrbit[i];
const iR = iPt[0] + iPt[1];
const iI = iPt[2] + iPt[3];
// Check if we can thread to same or later iteration (considering it will wrap with delta)
// Allow j = i for self-threading within the loop (period-N orbits repeat with delta)
for (let j = i; j <= THREADING_CAPACITY; j++) {
const jPt = this.refOrbit[j];
// After loop, iteration j will be at position refOrbit[j] + loop_delta
const jR = jPt[0] + jPt[1] + loopDeltaR;
const jI = jPt[2] + jPt[3] + loopDeltaI;
const dr = iR - jR;
const di = iI - jI;
const dist = Math.max(Math.abs(dr), Math.abs(di));
if (dist <= epsilon3) {
// Thread i -> j (wrapping through the loop)
this.threading.setThread(i, j, jR - iR, jI - iI);
break; // Take first match
}
}
}
}
async createComputePipeline() {
const shaderCode = `
struct Params {
dims_width: u32,
dims_height: u32,
iterations_per_batch: u32,
active_count: u32,
ref_orbit_length: u32,
exponent: u32,
workgroups_x: u32,
start_iter: u32,
checkpoint_count: u32,
buffer_index: u32, // 0 or 1, for per-buffer batch_active
ckpt0: u32, ckpt1: u32, ckpt2: u32, ckpt3: u32,
ckpt4: u32, ckpt5: u32, ckpt6: u32, ckpt7: u32,
ckpt8: u32, ckpt9: u32, ckpt10: u32, ckpt11: u32,
ckpt12: u32, ckpt13: u32, ckpt14: u32, ckpt15: u32,
ckpt16: u32, ckpt17: u32, ckpt18: u32, ckpt19: u32,
ckpt20: u32, ckpt21: u32, ckpt22: u32, ckpt23: u32,
ckpt24: u32, ckpt25: u32, ckpt26: u32, ckpt27: u32,
ckpt28: u32, ckpt29: u32, ckpt30: u32, ckpt31: u32,
_pad_ckpt: u32, // Padding after checkpoints
loop_enabled: u32, // 1 if loop enabled, 0 otherwise
loop_threshold: u32, // ref_iter threshold to trigger loop
loop_jump: u32, // Amount to subtract from ref_iter
pixel_size: f32,
aspect_ratio: f32,
loop_delta_r: f32, // Delta to add to dzr
loop_delta_i: f32, // Delta to add to dzi
}
// Per-pixel state: 7 u32 + 8 f32 = 60 bytes (with orig_index for compaction)
// Layout (u32 view):
// [0] orig_index: u32 (original pixel index for sparse processing)
// [1] iter: u32
// [2] status: u32
// [3] period: u32
// [4] ref_iter: u32
// [5] ckpt_refidx: u32
// [6] pending_refidx: u32
// [7] dzr: f32
// [8] dzi: f32
// [9] bbr: f32
// [10] bbi: f32
// [11] ckpt_bbr: f32
// [12] ckpt_bbi: f32
// [13] dcr: f32
// [14] dci: f32
struct PixelState {
// Integer fields (7 u32)
orig_index: u32,
iter: u32,
status: u32,
period: u32,
ref_iter: u32,
ckpt_refidx: u32,
pending_refidx: u32,
// Float fields (8 f32)
dzr: f32,
dzi: f32,
bbr: f32,
bbi: f32,
ckpt_bbr: f32,
ckpt_bbi: f32,
dcr: f32,
dci: f32,
}
// Results buffer with 32-byte header matching staging shader expectations
// Layout:
// Offset 0: count (firstEmpty) - atomic, GPU writes finished pixels atomically
// Offset 4: lastStaged - atomic, updated by staging shader
// Offset 8-28: active_count, start_iter, iterations_per_batch, padding
// Offset 32: records[0..N]
struct Results {
count: atomic<u32>,
lastStaged: atomic<u32>,
active_count: u32,
start_iter: u32,
iterations_per_batch: u32,
_pad0: u32,
_pad1: u32,
_pad2: u32,
records: array<PixelState>,
}
// Per-iteration state (reference orbit + threading): 5 f32 = 20 bytes
// Layout (f32 view):
// [0] ref_re: f32
// [1] ref_im: f32
// [2] thread_next: f32 (-1 = no thread)
// [3] thread_delta_re: f32
// [4] thread_delta_im: f32
struct IterState {
ref_re: f32, // Reference orbit real part
ref_im: f32, // Reference orbit imag part
thread_next: f32, // Next thread index (as f32, -1 = no thread)
thread_delta_re: f32,
thread_delta_im: f32,
}
// Lock buffer for batch collision prevention (see docs/gpu-batch-locking.md)
// Uses per-buffer-index batch_active to avoid cross-batch race conditions
struct LockBuffer {
lock: atomic<u32>,
batch_active_0: atomic<u32>,
batch_active_1: atomic<u32>,
collision_count: atomic<u32>,
}
@group(0) @binding(0) var<uniform> params: Params;
@group(0) @binding(1) var<storage, read_write> pixels: array<PixelState>;
@group(0) @binding(2) var<storage, read> iters: array<IterState>;
@group(0) @binding(3) var<storage, read_write> results: Results;
@group(0) @binding(4) var<storage, read_write> lockBuf: LockBuffer;
// Get threading data from unified iters buffer
// Returns vec3: [next_index_as_f32, deltaRe, deltaIm]
fn getThread(idx: u32) -> vec3<f32> {
if (idx >= params.ref_orbit_length) { return vec3<f32>(-1.0, 0.0, 0.0); }
let iter_data = iters[idx];
return vec3<f32>(iter_data.thread_next,
iter_data.thread_delta_re, iter_data.thread_delta_im);
}
// Get reference orbit values from unified iters buffer
fn getRefOrbit(idx: u32) -> vec2<f32> {
if (idx >= params.ref_orbit_length) { return vec2<f32>(0.0, 0.0); }
return vec2<f32>(iters[idx].ref_re, iters[idx].ref_im);
}
@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
// Check per-buffer-index batch_active - skip if guard didn't acquire lock
var batch_active: u32;
if (params.buffer_index == 0u) {
batch_active = atomicLoad(&lockBuf.batch_active_0);
} else {
batch_active = atomicLoad(&lockBuf.batch_active_1);
}
if (batch_active == 0u) {
return; // Batch skipped due to collision
}
if (global_id.x == 0u && global_id.y == 0u && global_id.z == 0u) {
results.active_count = params.active_count;
results.start_iter = params.start_iter;
results.iterations_per_batch = params.iterations_per_batch;
}
// 2D dispatch: calculate linear index from 2D coordinates
let index = global_id.y * params.workgroups_x + global_id.x;
if (index >= params.active_count) { return; }
// Skip if already finished
if (pixels[index].status != 0u) { return; }
// Load state from unified pixel struct
var iter = pixels[index].iter;
var pp = pixels[index].period;
var ref_iter = pixels[index].ref_iter;
var checkpoint_refidx = pixels[index].ckpt_refidx;
var pending_checkpoint_refidx = pixels[index].pending_refidx;
var dzr = pixels[index].dzr;
var dzi = pixels[index].dzi;
var bbr = pixels[index].bbr;
var bbi = pixels[index].bbi;
var checkpoint_bb_r = pixels[index].ckpt_bbr;
var checkpoint_bb_i = pixels[index].ckpt_bbi;
let dcr = pixels[index].dcr;
let dci = pixels[index].dci;
var finished = false;
// Convergence thresholds scale with pixel size for deep zooms (no iteration-based escalation)
// GPU uses float32 precision, so thresholds must be larger than CPU's float64
let epsilon_base = params.pixel_size / 10.0; // Final convergence threshold
let epsilon2_base = params.pixel_size * 10.0; // Getting close threshold
let epsilon = epsilon_base;
let epsilon2 = epsilon2_base;
// Track next checkpoint using O(1) counter for adaptive checkpoints
var next_checkpoint_idx = 0u;
// Iterate for the batch
for (var batch_iter = 0u; batch_iter < params.iterations_per_batch; batch_iter++) {
// Early exit if pixel already finished (converged/diverged)
if (pixels[index].status != 0u) {
break;
}
// Check rebasing before loading reference orbit values to avoid using stale data
let dz_norm = max(abs(dzr), abs(dzi));
// Peek at reference orbit to check rebasing condition
if (ref_iter < params.ref_orbit_length) {
let ref_check = getRefOrbit(ref_iter);
let total_r_pre = ref_check.x + dzr;
let total_i_pre = ref_check.y + dzi;
let total_norm = max(abs(total_r_pre), abs(total_i_pre));
// Rebase when orbit approaches critical point
if (ref_iter > 0u && total_norm < dz_norm * 2.0) {
dzr = total_r_pre; // Set dz = z_total (absolute position)
dzi = total_i_pre;
ref_iter = 0u; // Restart from beginning of reference orbit
// Reset lazy threading state after rebase:
// - pending_checkpoint_refidx back to checkpoint_refidx
// - bb back to checkpoint_bb (original dz at checkpoint)
if (checkpoint_refidx != 0xFFFFFFFFu) {
pending_checkpoint_refidx = checkpoint_refidx;
bbr = checkpoint_bb_r;
bbi = checkpoint_bb_i;
}
}
}
// Load reference orbit values for current (possibly rebased) ref_iter
if (ref_iter >= params.ref_orbit_length) {
break; // Reference orbit too short
}
let ref_val = getRefOrbit(ref_iter);
var refr = ref_val.x;
var refi = ref_val.y;
// Check current z for divergence
let curr_total_r = refr + dzr;
let curr_total_i = refi + dzi;
let curr_mag_sq = curr_total_r * curr_total_r + curr_total_i * curr_total_i;
// Check divergence (escape radius 2, or NaN/Infinity from numerical errors)
// NaN/Inf check: !(x <= large) catches both
if (curr_mag_sq > 4.0 || !(curr_mag_sq <= 1e38)) {
pixels[index].status = 1u;
pixels[index].period = pp;
finished = true;
break;
}
// Save dz before iteration (for checkpoint timing)
let old_dzr = dzr;
let old_dzi = dzi;
let old_ref_iter = ref_iter;
// Perturbation iteration using binomial expansion (Horner's method)
// (z_ref+dz)^n - z_ref^n = sum(k=1 to n) C(n,k) * z_ref^(n-k) * dz^k
// Computed as: dz * (C(n,1)*z_ref^(n-1) + dz * (C(n,2)*z_ref^(n-2) + ...))
// Build binomial powers: coeff * z_ref^power for each term
var z_pow_r = refr;
var z_pow_i = refi;
var coeff = f32(params.exponent);
// Start Horner's method with innermost term
var result_r = dzr;
var result_i = dzi;
// Horner's method: accumulate terms from highest to lowest power of z_ref
for (var k = 1u; k < params.exponent; k++) {
// Add coeff * z_ref^power term
let term_r = coeff * z_pow_r;
let term_i = coeff * z_pow_i;
result_r = result_r + term_r;
result_i = result_i + term_i;
// Multiply by dz (complex multiplication)
let temp_r = result_r * dzr - result_i * dzi;
result_i = result_r * dzi + result_i * dzr;
result_r = temp_r;
// Update z_ref power: z_pow = z_pow * z_ref
let new_z_pow_r = z_pow_r * refr - z_pow_i * refi;
z_pow_i = z_pow_r * refi + z_pow_i * refr;
z_pow_r = new_z_pow_r;
// Update coefficient: coeff *= (n-k) / (k+1)
coeff *= f32(params.exponent - k) / f32(k + 1u);
}
// Add perturbation in c
dzr = result_r + dcr;
dzi = result_i + dci;
// Check if reference orbit is long enough for next iteration
let next_ref_check = (ref_iter + 1u) * 2u;
if (next_ref_check + 1u >= params.ref_orbit_length * 2u) {
break;
}
// CONVERGENCE DETECTION: Check if this iteration is a checkpoint
var just_updated = false;
if (next_checkpoint_idx < params.checkpoint_count) {
// Get the offset for the next checkpoint based on index
var checkpoint_offset = 0u;
switch (next_checkpoint_idx) {
case 0u: { checkpoint_offset = params.ckpt0; }
case 1u: { checkpoint_offset = params.ckpt1; }
case 2u: { checkpoint_offset = params.ckpt2; }
case 3u: { checkpoint_offset = params.ckpt3; }
case 4u: { checkpoint_offset = params.ckpt4; }
case 5u: { checkpoint_offset = params.ckpt5; }
case 6u: { checkpoint_offset = params.ckpt6; }
case 7u: { checkpoint_offset = params.ckpt7; }
case 8u: { checkpoint_offset = params.ckpt8; }
case 9u: { checkpoint_offset = params.ckpt9; }
case 10u: { checkpoint_offset = params.ckpt10; }
case 11u: { checkpoint_offset = params.ckpt11; }
case 12u: { checkpoint_offset = params.ckpt12; }
case 13u: { checkpoint_offset = params.ckpt13; }
case 14u: { checkpoint_offset = params.ckpt14; }
case 15u: { checkpoint_offset = params.ckpt15; }
case 16u: { checkpoint_offset = params.ckpt16; }
case 17u: { checkpoint_offset = params.ckpt17; }
case 18u: { checkpoint_offset = params.ckpt18; }
case 19u: { checkpoint_offset = params.ckpt19; }
case 20u: { checkpoint_offset = params.ckpt20; }
case 21u: { checkpoint_offset = params.ckpt21; }
case 22u: { checkpoint_offset = params.ckpt22; }
case 23u: { checkpoint_offset = params.ckpt23; }
case 24u: { checkpoint_offset = params.ckpt24; }
case 25u: { checkpoint_offset = params.ckpt25; }
case 26u: { checkpoint_offset = params.ckpt26; }
case 27u: { checkpoint_offset = params.ckpt27; }
case 28u: { checkpoint_offset = params.ckpt28; }
case 29u: { checkpoint_offset = params.ckpt29; }
case 30u: { checkpoint_offset = params.ckpt30; }
case 31u: { checkpoint_offset = params.ckpt31; }
default: {}
}
// Check if current batch_iter matches this checkpoint
if (batch_iter == checkpoint_offset) {
just_updated = true;
// Store both bb (current) and checkpoint_bb (original, for reset after rebase)
bbr = old_dzr; // dz real at checkpoint (BEFORE iteration)
bbi = old_dzi; // dz imag at checkpoint
checkpoint_bb_r = old_dzr; // Save original for reset
checkpoint_bb_i = old_dzi;
checkpoint_refidx = old_ref_iter; // Store reference iteration (fixed)
pending_checkpoint_refidx = old_ref_iter; // Start lazy threading at checkpoint
pp = 0u;
next_checkpoint_idx++; // Move to next checkpoint
}
}
// Check convergence (if we have a checkpoint and didn't just update it)
// Use 0xFFFFFFFF as sentinel for "no checkpoint yet"
if (checkpoint_refidx != 0xFFFFFFFFu && !just_updated) {
// Threading buffer capacity: 64MB / 16 bytes per iteration = 4,194,304 (2^22)
const THREADING_CAPACITY = 1048576u;
// Fallback: when ref_iter exceeds threading buffer, use absolute position comparison
if (ref_iter >= THREADING_CAPACITY) {
// Compute absolute positions (accepts float32 precision loss)
let z_total_r = refr + old_dzr;
let z_total_i = refi + old_dzi;
let checkpoint_ref = getRefOrbit(checkpoint_refidx);
let z_checkpoint_r = checkpoint_ref.x + checkpoint_bb_r;
let z_checkpoint_i = checkpoint_ref.y + checkpoint_bb_i;
let diff_r = z_total_r - z_checkpoint_r;
let diff_i = z_total_i - z_checkpoint_i;
let db = max(abs(diff_r), abs(diff_i));
if (db <= epsilon2) {
if (pp == 0u) {
pp = iter;
}
if (db <= epsilon) {
pixels[index].status = 2u;
pixels[index].period = pp;
finished = true;
break;
}
}
} else {
// LAZY THREADING convergence check (high precision)
// Case 1: ref_iter == checkpoint_refidx (after rebasing or naturally arriving)
// Compare dz - bb directly (bb equals checkpoint_bb at this point)
if (ref_iter == checkpoint_refidx) {
let dz_diff_r = old_dzr - bbr;
let dz_diff_i = old_dzi - bbi;
let db = max(abs(dz_diff_r), abs(dz_diff_i));
if (db <= epsilon2) {
if (pp == 0u) {
pp = iter;
}
if (db <= epsilon) {
pixels[index].status = 2u;
pixels[index].period = pp;
finished = true;
break;
}
}
}
// Case 2: Check if thread[pending_checkpoint_refidx].next == ref_iter
// This handles threading case where we lazily follow thread links
if (pending_checkpoint_refidx >= 2584u &&
pending_checkpoint_refidx < params.ref_orbit_length) {
let thread = getThread(pending_checkpoint_refidx);
if (thread.x >= 0.0 && u32(thread.x) == ref_iter) {
// Check convergence: add thread delta to diff (matches old code)
// total_diff = threaded_delta + dz_diff = thread.delta + (dz - bb)
let dz_diff_r = old_dzr - bbr + thread.y;
let dz_diff_i = old_dzi - bbi + thread.z;
let db = max(abs(dz_diff_r), abs(dz_diff_i));
if (db <= epsilon2) {
if (pp == 0u) {
pp = iter;
}
if (db <= epsilon) {
pixels[index].status = 2u;
pixels[index].period = pp;
finished = true;
break;
}
}
// Update bb for future checks: bb -= thread.delta
// So future: dz - bb_new + next_delta = dz - (bb - delta) + next_delta
// = (dz - bb) + delta + next_delta (accumulated)
bbr -= thread.y;
bbi -= thread.z;
pending_checkpoint_refidx = ref_iter;
}
}
}
}
iter++;
ref_iter++;
// Reference orbit loop: when ref_iter hits threshold, apply delta and jump back
if (params.loop_enabled != 0u && ref_iter >= params.loop_threshold) {
dzr += params.loop_delta_r;
dzi += params.loop_delta_i;
ref_iter -= params.loop_jump;
}
}
// Write back state to unified pixel struct
pixels[index].iter = iter;
pixels[index].period = pp;
pixels[index].ref_iter = ref_iter;
pixels[index].ckpt_refidx = checkpoint_refidx;
pixels[index].pending_refidx = pending_checkpoint_refidx;
pixels[index].dzr = dzr;
pixels[index].dzi = dzi;
pixels[index].bbr = bbr;
pixels[index].bbi = bbi;
pixels[index].ckpt_bbr = checkpoint_bb_r;
pixels[index].ckpt_bbi = checkpoint_bb_i;
if (finished) {
let outIndex = atomicAdd(&results.count, 1u);
results.records[outIndex] = pixels[index];
}
}
`;
const shaderModule = this.device.createShaderModule({
code: shaderCode,
label: 'Perturbation compute shader'
});
this.pipeline = this.device.createComputePipeline({
layout: 'auto',
compute: {
module: shaderModule,
entryPoint: 'main'
},
label: 'Perturbation compute pipeline'
});
}
async compute(targetIters = null) {
// Prevent concurrent compute() calls
if (this.isComputing) return;
this.isComputing = true;
this.lastBatchCompacted = false;
const BYTES_PER_PIXEL = GpuZhuoranBoard.BYTES_PER_PIXEL; // 60 bytes (7 u32 + 8 f32)
const STRIDE = GpuZhuoranBoard.STRIDE; // 15 fields per pixel
const THREADING_CAPACITY = 1048576; // 2^20
const BYTES_PER_ITER = 20; // 5 f32 = 20 bytes
try {
// ================================================================
// STEP 1: Check if done BEFORE submitting new work
// ================================================================
if (this.activeCount === 0) {
if (this.precomputed && this.precomputed.getPendingCount() > 0) {
const remainingIters = this.precomputed.getPendingIterations();
for (const iter of remainingIters) {
const pending = this.precomputed.extractAtIteration(iter);
if (pending) {
const divergedIndices = [];
const convergedData = [];
for (const idx of pending.diverged) {
this.nn[idx] = iter;
this.pp[idx] = 1;
this.di++;
this.un--;
divergedIndices.push(idx);
}
for (const c of pending.converged) {
this.nn[c.index] = -iter;
this.pp[c.index] = c.p;
this.un--;
convergedData.push({ index: c.index, z: c.z, p: c.p });
}
if (divergedIndices.length > 0 || convergedData.length > 0) {
this.queueChanges({ iter, nn: divergedIndices, vv: convergedData });
}
}
}
}
this.un = 0;
if (this.hasPendingResults) {
await this.flushPendingResults();
}
return;
}
if (this.un === 0) {
if (this.hasPendingResults) {
await this.flushPendingResults();
}
return;
}
// ================================================================
// STEP 2: Calculate batch size and extend reference orbit
// ================================================================
const pixelsToIterate = this.un + this.ch;
let iterationsPerBatch;
if (targetIters !== null) {
iterationsPerBatch = targetIters;
} else {
iterationsPerBatch = Math.max(17, Math.floor(333337 / Math.max(pixelsToIterate, 1)));
}
// Extend reference orbit to exactly what this batch needs
const currentNeed = this.it + iterationsPerBatch;
const targetRefIterations = Math.min(currentNeed, THREADING_CAPACITY);
while (!this.refOrbitEscaped && this.refIterations < targetRefIterations) {
this.extendReferenceOrbit();
}
// Setup reference orbit loop when we hit the threading capacity
if (this.refIterations >= THREADING_CAPACITY && !this.refOrbitLoopConfigured) {
this.setupReferenceOrbitLoop();
}
// ================================================================
// STEP 3: Upload iteration state to GPU (INCREMENTAL UPLOADS)
// ================================================================
const totalIters = this.refIterations + 1;
// Resize iters buffer if needed, cap at 128MB
const requiredIterSize = totalIters * BYTES_PER_ITER;
const maxBufferSize = 128 * 1024 * 1024;
const allocSize = Math.min(Math.max(requiredIterSize * 2, 1024), maxBufferSize);
if (this.buffers.iters.size < requiredIterSize &&
this.buffers.iters.size < allocSize) {
await this.device.queue.onSubmittedWorkDone();
this.buffers.iters.destroy();
this.buffers.iters = this.device.createBuffer({
size: allocSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST,
label: 'Iteration state buffer'
});
this.lastUploadedIterLength = -1;
this.createBindGroup();
}
// INCREMENTAL UPLOAD: Only upload new iteration data
if (this.lastUploadedIterLength < this.refIterations) {
const startIdx = Math.max(0, this.lastUploadedIterLength + 1);
const maxIters = Math.floor(this.buffers.iters.size / BYTES_PER_ITER);
const endIdx = Math.min(this.refIterations, maxIters - 1);
const count = endIdx - startIdx + 1;
if (count > 0) {
const iterF32 = new Float32Array(count * 5);
for (let i = 0; i < count; i++) {
const iterIdx = startIdx + i;
const ref = this.refOrbit[iterIdx];
const thread = this.threading.getThread(iterIdx);
const base = i * 5;
iterF32[base + 0] = ref[0] + ref[1];
iterF32[base + 1] = ref[2] + ref[3];
if (!thread) {
iterF32[base + 2] = -1;
iterF32[base + 3] = 0;
iterF32[base + 4] = 0;
} else {
iterF32[base + 2] = thread.next;
iterF32[base + 3] = thread.deltaRe;
iterF32[base + 4] = thread.deltaIm;
}
}
const byteOffset = startIdx * BYTES_PER_ITER;
this.device.queue.writeBuffer(this.buffers.iters, byteOffset, iterF32);
}
this.lastUploadedIterLength = this.refIterations;
}
// ================================================================
// STEP 4: Set up parameters and dispatch GPU (NON-BLOCKING)
// ================================================================
const pixelSize = this.pixelSize;
const checkpointOffsets = [];
const bufferIter = this.it;
for (let i = 0; i < iterationsPerBatch; i++) {
if (fibonacciPeriod(bufferIter + i) === 1) checkpointOffsets.push(i);
}
const checkpointCount = Math.min(checkpointOffsets.length, 32);
const workgroupSize = 64;
const numWorkgroups = Math.ceil(this.activeCount / workgroupSize);
const workgroupsX = Math.ceil(Math.sqrt(numWorkgroups));
const workgroupsY = Math.ceil(numWorkgroups / workgroupsX);
const paramsBuffer = new ArrayBuffer(256);
const paramsU32 = new Uint32Array(paramsBuffer);
const paramsF32 = new Float32Array(paramsBuffer);
const bufferIndex = this.readbackBufferIndex;
paramsU32[0] = this.config.dimsWidth;
paramsU32[1] = this.config.dimsHeight;
paramsU32[2] = iterationsPerBatch;
paramsU32[3] = this.activeCount;
paramsU32[4] = this.refIterations + 1;
paramsU32[5] = this.config.exponent || 2;
paramsU32[6] = workgroupsX * workgroupSize;
paramsU32[7] = bufferIter;
paramsU32[8] = checkpointCount;
paramsU32[9] = bufferIndex; // buffer_index for per-buffer batch_active
for (let i = 0; i < 32; i++) {
paramsU32[10 + i] = i < checkpointCount ? checkpointOffsets[i] : 0;
}
paramsU32[42] = 0; // _pad_ckpt
const loop = this.refOrbitLoop || { enabled: false };
paramsU32[43] = loop.enabled ? 1 : 0;
paramsU32[44] = loop.threshold || 0;
paramsU32[45] = loop.jumpAmount || 0;
paramsF32[46] = pixelSize;
paramsF32[47] = this.config.aspectRatio;
paramsF32[48] = loop.deltaR || 0;
paramsF32[49] = loop.deltaI || 0;
this.device.queue.writeBuffer(this.buffers.params, 0, paramsBuffer);
const commandEncoder = this.device.createCommandEncoder({ label: 'Perturbation compute' });
// Guard pass: try to acquire batch lock (see docs/gpu-batch-locking.md)
this.queueGuardPass(commandEncoder, bufferIndex);
// Compute pass: iterate pixels (will skip if lock not acquired)
const passEncoder = commandEncoder.beginComputePass({ label: 'Perturbation pass' });
passEncoder.setPipeline(this.pipeline);
passEncoder.setBindGroup(0, this.bindGroup);
passEncoder.dispatchWorkgroups(workgroupsX, workgroupsY);
passEncoder.end();
// Queue staging shader pass and copy to staging buffer
// Staging shader releases the lock after copying
this.queueResultsReadback(commandEncoder, bufferIndex);
const gpuStartTime = performance.now();
this.device.queue.submit([commandEncoder.finish()]);
// Save batch iter range using half-open interval [start, end)
const batchStartIter = this.baseIt;
this.baseIt += iterationsPerBatch;
const batchEndIter = this.baseIt;
const currentPromise = this.device.queue.onSubmittedWorkDone();
// GPU is now computing in parallel!
// ================================================================
// STEP 5: Process pending results from PREVIOUS batch (overlaps with GPU)
// ================================================================
if (this.pendingReadbackIndex !== null) {
await this.processPendingReadback();
}
// ================================================================
// STEP 6: Speculative reference orbit extension while GPU works
// ================================================================
const speculativeTimeLimit = 100; // ms
const nextBatchIt = this.it + iterationsPerBatch;
const nextBatchNeed = nextBatchIt + iterationsPerBatch;
const speculativeTarget = Math.min(
Math.max(nextBatchNeed + 10000, Math.round(nextBatchNeed * 1.1)),
THREADING_CAPACITY
);
while (!this.refOrbitEscaped &&
this.refIterations < speculativeTarget &&
(performance.now() - gpuStartTime) < speculativeTimeLimit) {
this.extendReferenceOrbit();
}
// ================================================================
// STEP 7: Update pending state for next iteration
// ================================================================
this.pendingReadbackIndex = bufferIndex;
this.pendingReadbackPromise = currentPromise;
this.readbackBufferIndex = 1 - bufferIndex;
this.pendingIterationsPerBatch = iterationsPerBatch;
this.hasPendingResults = true;
// Batch tracking: half-open interval [start, end) (see docs/gpu-results-readback-design.md)
this.pendingBatchStartIter = batchStartIter;
this.pendingBatchEndIter = batchEndIter;
} catch (error) {
console.error(`GpuZhuoranBoard.compute() ERROR:`, error);
} finally {
this.isComputing = false;
}
}
// flushPendingResults() and readPixelBuffer() inherited from GpuZhuoranBaseBoard
async serialize() {
// Wait for any in-progress compute() to finish to avoid mapAsync race condition
while (this.isComputing) {
await new Promise(resolve => setTimeout(resolve, 10));
}
// CRITICAL: Flush pending results before serializing
if (this.hasPendingResults) {
await this.flushPendingResults();
}
// Ensure GPU is ready before reading buffers
await this.ensureGPUReady();
// Read GPU pixel buffer
const gpuPixelData = await this.readPixelBuffer();
// Build sparse nn array for completed pixels
const completedIndexes = [];
const completedNn = [];
for (let i = 0; i < this.nn.length; i++) {
if (this.nn[i] !== 0) {
completedIndexes.push(i);
completedNn.push(this.nn[i]);
}
}
return {
...(await super.serialize()),
// GPU pixel buffer as array (for JSON serialization)
gpuPixelData: gpuPixelData ? Array.from(new Uint8Array(gpuPixelData)) : null,
// DD reference orbit state
refOrbit: this.refOrbit,
refC: this.refC,
refIterations: this.refIterations,
refOrbitEscaped: this.refOrbitEscaped,
refOrbitLoop: this.refOrbitLoop || null,
refOrbitLoopConfigured: this.refOrbitLoopConfigured || false,
// Board state
effort: this.effort,
completedIndexes,
completedNn,
activeCount: this.activeCount,
deadSinceCompaction: this.deadSinceCompaction,
wastedBandwidth: this.wastedBandwidth,
};
}
static fromSerialized(serialized) {
// GPU boards require async initialization, so this returns a board
// that will continue initializing in the background
const board = new GpuZhuoranBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Schedule async restoration after GPU init
board.gpuInitPromise = board.gpuInitPromise.then(async () => {
if (serialized.activeCount !== undefined) {
board.activeCount = serialized.activeCount;
board.deadSinceCompaction = serialized.deadSinceCompaction || 0;
board.wastedBandwidth = serialized.wastedBandwidth || 0;
board.pendingActiveCount = board.activeCount;
const bufferSize = board.activeCount * GpuZhuoranBoard.BYTES_PER_PIXEL;
board.buffers.pixels?.destroy();
board.buffers.pixels = board.device.createBuffer({
size: bufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST,
label: 'Pixel state buffer (restored)'
});
// Note: stagingPixels are created on-demand in readPixelBuffer() for serialization
board.initResultsReadback(GpuZhuoranBoard.BYTES_PER_PIXEL, board.activeCount);
board.createBindGroup();
}
// Restore GPU pixel buffer
if (serialized.gpuPixelData && board.isGPUReady) {
const pixelData = new Uint8Array(serialized.gpuPixelData).buffer;
await board.writePixelBuffer(pixelData);
}
// Restore DD reference orbit state
board.refOrbit = serialized.refOrbit || [];
board.refC = serialized.refC || [0, 0, 0, 0];
board.refIterations = serialized.refIterations || 1;
board.refOrbitEscaped = serialized.refOrbitEscaped || false;
board.refOrbitLoop = serialized.refOrbitLoop || null;
board.refOrbitLoopConfigured = serialized.refOrbitLoopConfigured || false;
// Rebuild threading structure from restored reference orbit
board.rebuildDDThreading();
// Restore Board state
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
board.effort = serialized.effort || 2;
if (serialized.precomputed) {
board.precomputed = PrecomputedPoints.fromSerialized(serialized.precomputed);
}
// Restore nn array
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
});
return board;
}
}
/**
* Adaptive Per-Pixel Scaling GPU Perturbation Board
*
* This board uses per-pixel adaptive scaling for deep zooms. It
* tracks a per-pixel scale exponent that adapts dynamically during iteration.
*
* Key insight: Each pixel's perturbation δ is stored as (dz, scale) where
* δ_actual = dz × 2^scale. When |dz| > 2, we halve dz and increment scale,
* keeping dz bounded while preserving the actual δ value.
*
* This enables accurate escape detection at extreme zoom depths (z=10^40+)
* where the quadratic term δ² underflows in fixed-scale approaches.
*
* See docs/ADAPTIVE-SCALING.md for full mathematical derivation.
*/
// Uses QDReferenceOrbitMixin for reference orbit computation
class GpuAdaptiveBoard extends QDReferenceOrbitMixin(GpuZhuoranBaseBoard) {
static BYTES_PER_PIXEL = 64; // 16 × 4 bytes (7 i32 + 8 f32 + 1 i32, with orig_index)
static STRIDE = 16; // 16 fields per pixel
constructor(k, size, re, im, config, id, inheritedData = null) {
super(k, size, re, im, config, id, inheritedData);
this.effort = 20; // Doubled to reduce batch sizes after GPU readback improvements
// Initialize QD reference orbit (refC_qd, qdRefOrbit, threading, etc.)
const refReQD = toQD(re);
const refImQD = toQD(im);
this.initQDReferenceOrbit([...refReQD, ...refImQD]);
// Initialize per-pixel perturbation data (sets initialScale and pixelScale)
this.initPixels(size, re, im);
// Initialize double-buffering (from GpuZhuoranBaseBoard)
this.initDoubleBuffering();
// Start GPU initialization (async)
this.gpuInitPromise = this.initGPU();
}
// get it(), set it() inherited from GpuZhuoranBaseBoard
// extendReferenceOrbit() inherited from QDReferenceOrbitMixin
// Setup reference orbit loop for very long orbits
setupReferenceOrbitLoop() {
// When reference orbit hits threading limit, find a close point to loop back to
const THREADING_CAPACITY = 1048576; // 2^20
const SEARCH_WINDOW = 12000;
if (this.refIterations < THREADING_CAPACITY || this.refOrbitLoopConfigured) {
return; // Not at limit yet, or already configured
}
// Get endpoint (current position at threading limit) - QD precision
const endpoint = this.qdRefOrbit[THREADING_CAPACITY];
// Search back to find closest point (using QD arithmetic)
let closestIter = THREADING_CAPACITY - SEARCH_WINDOW;
let closestDist = Infinity;
const tt = this.tt;
for (let i = THREADING_CAPACITY - SEARCH_WINDOW; i < THREADING_CAPACITY; i++) {
const pt = this.qdRefOrbit[i];
// Compute difference in QD precision
arQdAdd(tt, 0, endpoint[0], endpoint[1], endpoint[2], endpoint[3],
-pt[0], -pt[1], -pt[2], -pt[3]); // dr
arQdAdd(tt, 4, endpoint[4], endpoint[5], endpoint[6], endpoint[7],
-pt[4], -pt[5], -pt[6], -pt[7]); // di
// Chebyshev distance: max(|dr|, |di|)
const dr = tt[0] + tt[1] + tt[2] + tt[3];
const di = tt[4] + tt[5] + tt[6] + tt[7];
const dist = Math.max(Math.abs(dr), Math.abs(di));
if (dist <= closestDist) { // Use <= to take latest point when tied
closestDist = dist;
closestIter = i;
}
}
// Compute delta in QD precision
const closestPt = this.qdRefOrbit[closestIter];
arQdAdd(tt, 0, endpoint[0], endpoint[1], endpoint[2], endpoint[3],
-closestPt[0], -closestPt[1], -closestPt[2], -closestPt[3]); // real delta
arQdAdd(tt, 4, endpoint[4], endpoint[5], endpoint[6], endpoint[7],
-closestPt[4], -closestPt[5], -closestPt[6], -closestPt[7]); // imag delta
// Store loop parameters with QD precision delta
const deltaR_qd = [tt[0], tt[1], tt[2], tt[3]];
const deltaI_qd = [tt[4], tt[5], tt[6], tt[7]];
this.refOrbitLoop = {
enabled: true,
threshold: THREADING_CAPACITY,
jumpAmount: THREADING_CAPACITY - closestIter,
deltaR_qd: deltaR_qd,
deltaI_qd: deltaI_qd,
deltaR: deltaR_qd[0] + deltaR_qd[1] + deltaR_qd[2] + deltaR_qd[3], // f64 for GPU
deltaI: deltaI_qd[0] + deltaI_qd[1] + deltaI_qd[2] + deltaI_qd[3]
};
this.refOrbitLoopConfigured = true;
// Update threading for loop segment to wrap around (using QD precision)
const loopDeltaR = deltaR_qd[0] + deltaR_qd[1] + deltaR_qd[2] + deltaR_qd[3];
const loopDeltaI = deltaI_qd[0] + deltaI_qd[1] + deltaI_qd[2] + deltaI_qd[3];
const epsilon3 = this.threading.epsilon3;
// For each iteration in the loop segment, check if it can thread to another iteration
// considering the loop wrap (iterations will repeat with a delta offset)
for (let i = closestIter; i <= THREADING_CAPACITY; i++) {
const iPt = this.qdRefOrbit[i];
const iR = iPt[0] + iPt[1] + iPt[2] + iPt[3];
const iI = iPt[4] + iPt[5] + iPt[6] + iPt[7];
// Check if we can thread to same or later iteration (considering it will wrap with delta)
// Allow j = i for self-threading within the loop (period-N orbits repeat with delta)
for (let j = i; j <= THREADING_CAPACITY; j++) {
const jPt = this.qdRefOrbit[j];
// After loop, iteration j will be at position qdRefOrbit[j] + loop_delta
const jR = jPt[0] + jPt[1] + jPt[2] + jPt[3] + loopDeltaR;
const jI = jPt[4] + jPt[5] + jPt[6] + jPt[7] + loopDeltaI;
const dr = iR - jR;
const di = iI - jI;
const dist = Math.max(Math.abs(dr), Math.abs(di));
if (dist <= epsilon3) {
// Thread i -> j (wrapping through the loop)
this.threading.setThread(i, j, jR - iR, jI - iI);
break; // Take first match
}
}
}
}
// Upload combined ref orbit + threading to iters buffer
async uploadIters() {
const ITER_BYTES = 20; // 5 f32 per iteration
const threadingData = this.threading.threads;
const totalIters = this.refIterations + 1;
// Resize iters buffer if needed
const requiredSize = totalIters * ITER_BYTES;
if (this.buffers.iters.size < requiredSize) {
await this.device.queue.onSubmittedWorkDone();
this.buffers.iters.destroy();
this.buffers.iters = this.device.createBuffer({
size: Math.max(requiredSize * 2, 1024),
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST
});
this.createBindGroup();
this.lastUploadedItersLength = -1; // Force full re-upload after resize
}
// Upload incrementally from lastUploadedItersLength
if (this.lastUploadedItersLength < this.refIterations) {
const startIdx = Math.max(0, this.lastUploadedItersLength + 1);
const count = this.refIterations - startIdx + 1;
// IterState: [ref_re, ref_im, thread_next, thread_delta_re, thread_delta_im]
const itersF32 = new Float32Array(count * 5);
for (let i = 0; i < count; i++) {
const orbitIdx = startIdx + i;
const ref = this.qdRefOrbit[orbitIdx];
const thread = threadingData[orbitIdx] || { next: -1, deltaRe: 0, deltaIm: 0 };
const idx = i * 5;
// Sum QD components to get f32 value for ref orbit
itersF32[idx + 0] = ref ? ref[0] + ref[1] + ref[2] + ref[3] : 0; // ref_re
itersF32[idx + 1] = ref ? ref[4] + ref[5] + ref[6] + ref[7] : 0; // ref_im
itersF32[idx + 2] = thread.next; // thread_next
itersF32[idx + 3] = thread.deltaRe; // thread_delta_re
itersF32[idx + 4] = thread.deltaIm; // thread_delta_im
}
this.device.queue.writeBuffer(this.buffers.iters, startIdx * ITER_BYTES, itersF32);
this.lastUploadedItersLength = this.refIterations;
}
}
initPixels(size, re, im) {
const dimsWidth = this.config.dimsWidth;
const dimsHeight = this.config.dimsHeight;
const dimsArea = this.config.dimsArea;
// Convert size to scalar if it's a QD array
const size_scalar = Array.isArray(size) ? size.reduce((a, b) => a + (b || 0), 0) : size;
const pixelSize = size_scalar / dimsWidth;
// Compute initial scale: k = floor(log2(pixelSize))
const log2_pixelSize = Math.log2(pixelSize);
this.initialScale = Math.floor(log2_pixelSize);
// Mantissa factor: 2^(log2(pixelSize) - k) is in [1, 2)
const mantissa = Math.pow(2, log2_pixelSize - this.initialScale);
// Per-pixel data arrays
this.dc = new Float32Array(dimsArea * 2); // Delta c [real, imag] pairs
this.dz = new Float32Array(dimsArea * 2); // Current perturbation delta [real, imag]
this.pixelScale = new Int32Array(dimsArea); // Per-pixel scale exponent
this.refIter = new Uint32Array(dimsArea); // Reference iteration index
// Initialize each pixel
// Both x and y offsets are in raw pixel units. The pixelSize (size/dimsWidth) is
// already correct because sizeY = size/aspectRatio = size*dimsHeight/dimsWidth,
// and sizeY/dimsHeight = size/dimsWidth = pixelSize. So no extra scaling needed.
for (let y = 0; y < dimsHeight; y++) {
const yOffset = dimsHeight / 2 - y;
for (let x = 0; x < dimsWidth; x++) {
const xOffset = x - dimsWidth / 2;
const index = y * dimsWidth + x;
const index2 = index * 2;
// δc_stored = mantissa × pixel_offset (normalized to [~-1, ~+1] range)
this.dc[index2] = Math.fround(mantissa * xOffset);
this.dc[index2 + 1] = Math.fround(mantissa * yOffset);
// Start with dz = dc
this.dz[index2] = this.dc[index2];
this.dz[index2 + 1] = this.dc[index2 + 1];
// All pixels start with the same scale
this.pixelScale[index] = this.initialScale;
// Start at iteration 1
this.refIter[index] = 1;
}
}
this.checkSpike(size, re, im);
}
initPixelsQD() {
// Override to prevent parent from overwriting our scaled arrays
}
async createBuffers() {
const dimsArea = this.config.dimsArea;
const STRIDE = GpuAdaptiveBoard.STRIDE; // 16 fields per pixel
// Consolidated 3-binding layout:
// 0: params (uniform)
// 1: pixels (PixelState): 7 i32 + 8 f32 + 1 i32 = 64 bytes per pixel (with orig_index)
// 2: iters (IterState): 5 f32 = 20 bytes per iteration (refOrbit + threading combined)
const PIXEL_BYTES = GpuAdaptiveBoard.BYTES_PER_PIXEL; // 64 bytes
const ITER_BYTES = 20; // 5 × 4 bytes
const precomputedCount = this.precomputed ? this.precomputed.getPrecomputedCount() : 0;
const activePixelCount = dimsArea - precomputedCount;
const pixelBufferSize = Math.max(PIXEL_BYTES, activePixelCount * PIXEL_BYTES);
const resultsBufferSize = 16 + (activePixelCount * PIXEL_BYTES);
const maxBufferSize = Math.min(
this.device.limits.maxBufferSize,
this.device.limits.maxStorageBufferBindingSize
);
if (pixelBufferSize > maxBufferSize) {
throw new Error(`Buffer size exceeds WebGPU limit`);
}
if (resultsBufferSize > maxBufferSize) {
throw new Error(`Results buffer size exceeds WebGPU limit`);
}
// Note: stagingPixels buffers are created on-demand in readPixelBuffer() for serialization
// This saves ~2x pixel buffer size in GPU memory during normal operation
this.buffers = {
params: this.device.createBuffer({
size: 256, // Increased to hold 32 checkpoint slots
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST
}),
pixels: this.device.createBuffer({
size: pixelBufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST
}),
iters: this.device.createBuffer({
size: 1024 * ITER_BYTES, // Start small, will resize as needed
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST
})
};
// Initialize pixels buffer with overlapping typed array views
// PixelState layout: [orig_index, iter, status, period, ref_iter, ckpt_refidx, pending_refidx,
// dzr, dzi, bbr, bbi, ckpt_bbr, ckpt_bbi, dcr, dci, scale]
const pixelBuffer = new ArrayBuffer(pixelBufferSize);
const pixelsI32 = new Int32Array(pixelBuffer);
const pixelsF32 = new Float32Array(pixelBuffer);
let activeIdx = 0;
for (let i = 0; i < dimsArea; i++) {
if (this.precomputed && this.precomputed.isPrecomputed(i)) {
continue;
}
const idx = activeIdx * STRIDE; // 16 fields per pixel
// Integer fields (indices 0-6)
pixelsI32[idx + 0] = i; // orig_index (for coordinate computation after compaction)
pixelsI32[idx + 1] = 1; // iter starts at 1
pixelsI32[idx + 2] = 0; // status = computing
pixelsI32[idx + 3] = 0; // period = 0
pixelsI32[idx + 4] = this.refIter[i]; // ref_iter
pixelsI32[idx + 5] = -1; // ckpt_refidx (-1 = no checkpoint)
pixelsI32[idx + 6] = -1; // pending_refidx
// Float fields (indices 7-14)
pixelsF32[idx + 7] = this.dz[i * 2]; // dzr (scaled by per-pixel scale)
pixelsF32[idx + 8] = this.dz[i * 2 + 1]; // dzi
pixelsF32[idx + 9] = 0; // bbr (scaled by initialScale)
pixelsF32[idx + 10] = 0; // bbi
pixelsF32[idx + 11] = 0; // ckpt_bbr
pixelsF32[idx + 12] = 0; // ckpt_bbi
pixelsF32[idx + 13] = this.dc[i * 2]; // dcr (scaled by initialScale)
pixelsF32[idx + 14] = this.dc[i * 2 + 1]; // dci
// GpuAdaptiveBoard-specific field at end (index 15)
pixelsI32[idx + 15] = this.pixelScale[i]; // scale from initPixels
activeIdx++;
}
this.device.queue.writeBuffer(this.buffers.pixels, 0, pixelBuffer);
this.lastUploadedItersLength = -1;
this.activeCount = activePixelCount;
this.pendingActiveCount = activePixelCount;
this.deadSinceCompaction = 0;
this.wastedBandwidth = 0;
this.initResultsReadback(PIXEL_BYTES, activePixelCount);
}
createBindGroup() {
this.bindGroup = this.device.createBindGroup({
layout: this.pipeline.getBindGroupLayout(0),
entries: [
{ binding: 0, resource: { buffer: this.buffers.params } },
{ binding: 1, resource: { buffer: this.buffers.pixels } },
{ binding: 2, resource: { buffer: this.buffers.iters } },
{ binding: 3, resource: { buffer: this.buffers.results } },
{ binding: 4, resource: { buffer: this.buffers.lock } }
],
label: 'Adaptive perturbation bind group'
});
}
/**
* Process GPU results using batch-oriented approach (same as GpuBoard).
* This ensures results are only sent to changeList when batches complete,
* preventing out-of-order iteration delivery that causes striping.
*/
processResultsData(data, count) {
const STRIDE = GpuAdaptiveBoard.STRIDE;
const pixelsI32 = new Int32Array(data);
const pixelsF32 = new Float32Array(data);
const debugReadback = hasDebugFlag(this.config, 'rb');
this.lastResultsCount = count;
this.resultsReadbackBatches += 1;
this.resultsReadbackBytes += count * this.resultsRecordBytes;
const P_ORIG_INDEX = 0, P_ITER = 1, P_STATUS = 2, P_PERIOD = 3, P_REF_ITER = 4;
const P_DZR = 7, P_DZI = 8, P_SCALE = 15;
let dataIndex = 0;
// OUTER LOOP: Process batches in order
while (this.batchesToReadback.length > 0) {
const batch = this.batchesToReadback[0];
// Flush precomputed points before this batch's iteration range
if (this.precomputed) {
this.flushPrecomputedUpTo(this.previousBatchEndIter - 1);
}
// INNER LOOP: Process available data for this batch
while (batch.remainingPixelCount > 0 && dataIndex < count) {
const idx = dataIndex * STRIDE;
const origIndex = pixelsI32[idx + P_ORIG_INDEX];
const status = pixelsI32[idx + P_STATUS];
const period = pixelsI32[idx + P_PERIOD];
const iters = pixelsI32[idx + P_ITER];
// Skip already processed pixels (shouldn't happen, but defensive)
if (this.nn[origIndex] !== 0) {
if (debugReadback) {
const same = this.nn[origIndex] === iters ? ' (SAME VALUE)' : ' (DIFFERENT VALUE)';
console.error(`INVARIANT VIOLATION: Duplicate result for pixel ${origIndex}, existing nn=${this.nn[origIndex]}, new iters=${iters}${same}`);
}
dataIndex++;
continue;
}
// Skip non-finished pixels (status 0 = still computing)
if (status === 0) {
dataIndex++;
continue;
}
if (status === 1) {
// Diverged
this.nn[origIndex] = iters;
this.pp[origIndex] = period;
this.di++;
if (this.inSpike && this.inSpike[origIndex] && this.ch > 0) this.ch -= 1;
// Accumulate into batchResultsRead
this.batchResultsRead.push({ iter: iters, nn: [origIndex], vv: [] });
} else if (status === 2) {
// Converged
this.nn[origIndex] = -iters;
this.pp[origIndex] = period - 1;
if (this.inSpike && this.inSpike[origIndex] && this.ch > 0) this.ch -= 1;
// Compute final z value using QD reference orbit with adaptive scaling
const refIter = pixelsI32[idx + P_REF_ITER];
const scale = pixelsI32[idx + P_SCALE];
const dzr = pixelsF32[idx + P_DZR] * Math.pow(2, scale);
const dzi = pixelsF32[idx + P_DZI] * Math.pow(2, scale);
const ref = this.qdRefOrbit[Math.min(refIter, this.qdRefOrbit.length - 1)];
// Accumulate into batchResultsRead
this.batchResultsRead.push({
iter: iters,
nn: [],
vv: [{ index: origIndex, z: this.refDzNative(ref, dzr, dzi), p: this.pp[origIndex] }]
});
}
this.deadSinceCompaction++;
batch.remainingPixelCount--;
dataIndex++;
}
// Check if batch is complete
if (batch.remainingPixelCount > 0) {
// Batch not complete - exit and wait for more data
break;
}
// BATCH COMPLETE - Flush to changeList
// Flush precomputed points up to this batch's end iteration
if (this.precomputed) {
this.flushPrecomputedIntoResults(batch.endIter - 1);
}
// Queue results to changeList using queueChanges
for (const change of this.batchResultsRead) {
this.queueChanges(change);
}
// Clear for next batch
this.batchResultsRead.length = 0;
this.previousBatchEndIter = batch.endIter;
this.batchesToReadback.shift();
}
// Update un count
// deadSinceCompaction includes results in batchResultsRead that aren't flushed yet
// Add them back since they're not in changeList yet (view won't see them)
const pendingPrecomputed = this.precomputed ? this.precomputed.getPendingCount() : 0;
const pendingInBatchResults = this.batchResultsRead.length;
this.un = (this.activeCount - this.deadSinceCompaction) + pendingPrecomputed + pendingInBatchResults;
}
async createComputePipeline() {
// Consolidated 3-binding adaptive per-pixel scaling perturbation shader
// Scale conventions:
// dz: per-pixel adaptive scale
// bb, checkpoint_bb, dc: global initialScale (Option C)
// Lazy threading: bb gets modified by thread deltas, checkpoint_bb stores original for reset
const shaderCode = `
struct Params {
dims_width: u32,
dims_height: u32,
iterations_per_batch: u32,
active_count: u32,
ref_orbit_length: u32,
exponent: u32,
workgroups_x: u32,
start_iter: u32,
checkpoint_count: u32,
buffer_index: u32, // 0 or 1, for per-buffer batch_active
ckpt0: u32, ckpt1: u32, ckpt2: u32, ckpt3: u32,
ckpt4: u32, ckpt5: u32, ckpt6: u32, ckpt7: u32,
ckpt8: u32, ckpt9: u32, ckpt10: u32, ckpt11: u32,
ckpt12: u32, ckpt13: u32, ckpt14: u32, ckpt15: u32,
ckpt16: u32, ckpt17: u32, ckpt18: u32, ckpt19: u32,
ckpt20: u32, ckpt21: u32, ckpt22: u32, ckpt23: u32,
ckpt24: u32, ckpt25: u32, ckpt26: u32, ckpt27: u32,
ckpt28: u32, ckpt29: u32, ckpt30: u32, ckpt31: u32,
_pad_ckpt: u32, // Padding after checkpoints
loop_enabled: u32,
loop_threshold: u32,
loop_jump: u32,
initial_scale: i32, // Global scale for dc, bb, threaded_delta
_pad_scale: u32, // Padding for alignment
pixel_size: f32,
aspect_ratio: f32,
loop_delta_r: f32,
loop_delta_i: f32,
}
// Per-pixel state: 7 i32 + 8 f32 + 1 i32 = 64 bytes (with orig_index for compaction)
// Layout matches GpuZhuoranBoard for first 15 fields (scale at end)
// Layout (i32/u32 view):
// [0] orig_index: i32 (original pixel index for sparse processing)
// [1] iter: i32
// [2] status: i32
// [3] period: i32
// [4] ref_iter: i32
// [5] ckpt_refidx: i32
// [6] pending_refidx: i32
// [7] dzr: f32
// [8] dzi: f32
// [9] bbr: f32
// [10] bbi: f32
// [11] ckpt_bbr: f32
// [12] ckpt_bbi: f32
// [13] dcr: f32
// [14] dci: f32
// [15] scale: i32 (GpuAdaptiveBoard-specific, at end for layout compatibility)
struct PixelState {
// Integer fields (7 i32) - orig_index first, then matches GpuZhuoranBoard
orig_index: i32,
iter: i32,
status: i32,
period: i32,
ref_iter: i32,
ckpt_refidx: i32,
pending_refidx: i32,
// Float fields (8 f32)
dzr: f32,
dzi: f32,
bbr: f32,
bbi: f32,
ckpt_bbr: f32,
ckpt_bbi: f32,
dcr: f32,
dci: f32,
// GpuAdaptiveBoard-specific field at end
scale: i32,
}
// Results buffer with 32-byte header matching staging shader expectations
// Layout:
// Offset 0: count (firstEmpty) - atomic, GPU writes finished pixels atomically
// Offset 4: lastStaged - atomic, updated by staging shader
// Offset 8-28: active_count, start_iter, iterations_per_batch, padding
// Offset 32: records[0..N]
struct Results {
count: atomic<u32>,
lastStaged: atomic<u32>,
active_count: u32,
start_iter: u32,
iterations_per_batch: u32,
_pad0: u32,
_pad1: u32,
_pad2: u32,
records: array<PixelState>,
}
// Per-iteration state (reference orbit + threading): 5 f32 = 20 bytes
// Layout (f32 view):
// [0] ref_re: f32
// [1] ref_im: f32
// [2] thread_next: f32
// [3] thread_delta_re: f32
// [4] thread_delta_im: f32
struct IterState {
ref_re: f32,
ref_im: f32,
thread_next: f32,
thread_delta_re: f32,
thread_delta_im: f32,
}
// Lock buffer for batch collision prevention (see docs/gpu-batch-locking.md)
// Uses per-buffer-index batch_active to avoid cross-batch race conditions
struct LockBuffer {
lock: atomic<u32>,
batch_active_0: atomic<u32>,
batch_active_1: atomic<u32>,
collision_count: atomic<u32>,
}
@group(0) @binding(0) var<uniform> params: Params;
@group(0) @binding(1) var<storage, read_write> pixels: array<PixelState>;
@group(0) @binding(2) var<storage, read> iters: array<IterState>;
@group(0) @binding(3) var<storage, read_write> results: Results;
@group(0) @binding(4) var<storage, read_write> lockBuf: LockBuffer;
fn getThread(idx: u32) -> vec3<f32> {
if (idx >= params.ref_orbit_length) { return vec3<f32>(-1.0, 0.0, 0.0); }
let iter_data = iters[idx];
return vec3<f32>(iter_data.thread_next,
iter_data.thread_delta_re, iter_data.thread_delta_im);
}
fn getRefOrbit(idx: u32) -> vec2<f32> {
if (idx >= params.ref_orbit_length) { return vec2<f32>(0.0, 0.0); }
return vec2<f32>(iters[idx].ref_re, iters[idx].ref_im);
}
@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
// Check per-buffer-index batch_active - skip if guard didn't acquire lock
var batch_active: u32;
if (params.buffer_index == 0u) {
batch_active = atomicLoad(&lockBuf.batch_active_0);
} else {
batch_active = atomicLoad(&lockBuf.batch_active_1);
}
if (batch_active == 0u) {
return; // Batch skipped due to collision
}
if (global_id.x == 0u && global_id.y == 0u && global_id.z == 0u) {
results.active_count = params.active_count;
results.start_iter = params.start_iter;
results.iterations_per_batch = params.iterations_per_batch;
}
let index = global_id.y * params.workgroups_x + global_id.x;
if (index >= params.active_count) { return; }
// Read pixel state
let status = pixels[index].status;
if (status != 0) { return; }
var iter = u32(pixels[index].iter);
var scale = pixels[index].scale;
var pp = u32(pixels[index].period);
var ref_iter = u32(pixels[index].ref_iter);
var checkpoint_refidx = u32(pixels[index].ckpt_refidx);
var pending_checkpoint_refidx = u32(pixels[index].pending_refidx);
// Read float state (all checkpoint-related values in initialScale)
var dzr = pixels[index].dzr;
var dzi = pixels[index].dzi;
var bbr = pixels[index].bbr;
var bbi = pixels[index].bbi;
var checkpoint_bb_r = pixels[index].ckpt_bbr;
var checkpoint_bb_i = pixels[index].ckpt_bbi;
let dcr = pixels[index].dcr;
let dci = pixels[index].dci;
var finished = false;
// Convergence thresholds - scaled by initialScale for comparison (no iteration-based escalation)
let epsilon_base = params.pixel_size / 10.0;
let epsilon2_base = params.pixel_size * 10.0;
// Convert to initialScale for scaled comparisons
let epsilon = ldexp(epsilon_base, -params.initial_scale);
let epsilon2 = ldexp(epsilon2_base, -params.initial_scale);
// Track next checkpoint using O(1) counter for adaptive checkpoints
var next_checkpoint_idx = 0u;
for (var batch_iter = 0u; batch_iter < params.iterations_per_batch; batch_iter++) {
if (pixels[index].status != 0) { break; }
if (ref_iter >= params.ref_orbit_length) { break; }
let ref_orbit = getRefOrbit(ref_iter);
var refr = ref_orbit.x;
var refi = ref_orbit.y;
// Compute actual delta and position: z = Z_ref + δ_actual
var dzr_actual = 0.0;
var dzi_actual = 0.0;
if (scale >= -126) {
dzr_actual = ldexp(dzr, scale);
dzi_actual = ldexp(dzi, scale);
}
var zr = refr + dzr_actual;
var zi = refi + dzi_actual;
// === ESCAPE CHECK ===
// Check BEFORE rebasing to match QDZhuoranBoard behavior
let z_mag_sq = zr * zr + zi * zi;
// Check divergence (escape radius 2, or NaN/Infinity from numerical errors)
if (z_mag_sq > 4.0 || !(z_mag_sq <= 1e38)) { // NaN/Inf check: !(x <= large) catches both
pixels[index].status = 1;
pixels[index].period = i32(pp);
finished = true;
break;
}
// === REBASING ===
let z_norm = max(abs(zr), abs(zi));
let dz_norm = max(abs(dzr_actual), abs(dzi_actual));
if (ref_iter > 0u && z_norm < dz_norm * 2.0) {
let new_log2 = floor(log2(z_norm));
let new_scale = max(i32(new_log2), params.initial_scale);
dzr = ldexp(zr, -new_scale);
dzi = ldexp(zi, -new_scale);
scale = new_scale;
ref_iter = 0u;
// Reset lazy threading state after rebase
if (checkpoint_refidx != 0xFFFFFFFFu) {
pending_checkpoint_refidx = checkpoint_refidx;
bbr = checkpoint_bb_r;
bbi = checkpoint_bb_i;
}
let ref0 = getRefOrbit(0u);
refr = ref0.x;
refi = ref0.y;
dzr_actual = ldexp(dzr, scale);
dzi_actual = ldexp(dzi, scale);
zr = refr + dzr_actual;
zi = refi + dzi_actual;
}
// === CONVERGENCE DETECTION ===
// bb and threaded_delta are in initialScale, so convert dz to initialScale for comparison
var just_updated = false;
if (next_checkpoint_idx < params.checkpoint_count) {
var checkpoint_offset = 0u;
switch (next_checkpoint_idx) {
case 0u: { checkpoint_offset = params.ckpt0; }
case 1u: { checkpoint_offset = params.ckpt1; }
case 2u: { checkpoint_offset = params.ckpt2; }
case 3u: { checkpoint_offset = params.ckpt3; }
case 4u: { checkpoint_offset = params.ckpt4; }
case 5u: { checkpoint_offset = params.ckpt5; }
case 6u: { checkpoint_offset = params.ckpt6; }
case 7u: { checkpoint_offset = params.ckpt7; }
case 8u: { checkpoint_offset = params.ckpt8; }
case 9u: { checkpoint_offset = params.ckpt9; }
case 10u: { checkpoint_offset = params.ckpt10; }
case 11u: { checkpoint_offset = params.ckpt11; }
case 12u: { checkpoint_offset = params.ckpt12; }
case 13u: { checkpoint_offset = params.ckpt13; }
case 14u: { checkpoint_offset = params.ckpt14; }
case 15u: { checkpoint_offset = params.ckpt15; }
case 16u: { checkpoint_offset = params.ckpt16; }
case 17u: { checkpoint_offset = params.ckpt17; }
case 18u: { checkpoint_offset = params.ckpt18; }
case 19u: { checkpoint_offset = params.ckpt19; }
case 20u: { checkpoint_offset = params.ckpt20; }
case 21u: { checkpoint_offset = params.ckpt21; }
case 22u: { checkpoint_offset = params.ckpt22; }
case 23u: { checkpoint_offset = params.ckpt23; }
case 24u: { checkpoint_offset = params.ckpt24; }
case 25u: { checkpoint_offset = params.ckpt25; }
case 26u: { checkpoint_offset = params.ckpt26; }
case 27u: { checkpoint_offset = params.ckpt27; }
case 28u: { checkpoint_offset = params.ckpt28; }
case 29u: { checkpoint_offset = params.ckpt29; }
case 30u: { checkpoint_offset = params.ckpt30; }
case 31u: { checkpoint_offset = params.ckpt31; }
default: {}
}
if (batch_iter == checkpoint_offset) {
just_updated = true;
// Store bb and checkpoint_bb in initialScale: bb = dz_actual / 2^initialScale
let bb_val_r = ldexp(dzr_actual, -params.initial_scale);
let bb_val_i = ldexp(dzi_actual, -params.initial_scale);
bbr = bb_val_r;
bbi = bb_val_i;
checkpoint_bb_r = bb_val_r; // Save original for reset after rebase
checkpoint_bb_i = bb_val_i;
checkpoint_refidx = ref_iter;
pending_checkpoint_refidx = ref_iter; // Start lazy threading at checkpoint
pp = 0u;
next_checkpoint_idx = next_checkpoint_idx + 1u;
}
}
// Check convergence with lazy threading (all comparisons in initialScale)
if (checkpoint_refidx != 0xFFFFFFFFu && !just_updated && scale >= -126) {
// LAZY THREADING convergence check in initialScale
// Convert current dz to initialScale for comparison
let dzr_scaled = ldexp(dzr_actual, -params.initial_scale);
let dzi_scaled = ldexp(dzi_actual, -params.initial_scale);
// Case 1: ref_iter == checkpoint_refidx (after rebasing or naturally arriving)
if (ref_iter == checkpoint_refidx) {
let dz_diff_r = dzr_scaled - bbr;
let dz_diff_i = dzi_scaled - bbi;
let db = max(abs(dz_diff_r), abs(dz_diff_i));
if (db <= epsilon2) {
if (pp == 0u) { pp = iter; }
if (db <= epsilon) {
pixels[index].status = 2;
pixels[index].period = i32(pp);
finished = true;
break;
}
}
}
// Case 2: Check if thread[pending_checkpoint_refidx].next == ref_iter
if (pending_checkpoint_refidx >= 2584u &&
pending_checkpoint_refidx < params.ref_orbit_length) {
let thread = getThread(pending_checkpoint_refidx);
if (thread.x >= 0.0 && u32(thread.x) == ref_iter) {
// Check convergence: add thread delta to diff (convert to initialScale)
let thread_r_scaled = ldexp(thread.y, -params.initial_scale);
let thread_i_scaled = ldexp(thread.z, -params.initial_scale);
let dz_diff_r = dzr_scaled - bbr + thread_r_scaled;
let dz_diff_i = dzi_scaled - bbi + thread_i_scaled;
let db = max(abs(dz_diff_r), abs(dz_diff_i));
if (db <= epsilon2) {
if (pp == 0u) { pp = iter; }
if (db <= epsilon) {
pixels[index].status = 2;
pixels[index].period = i32(pp);
finished = true;
break;
}
}
// Update bb for future checks: bb -= thread.delta
bbr = bbr - thread_r_scaled;
bbi = bbi - thread_i_scaled;
pending_checkpoint_refidx = ref_iter;
}
}
}
// === PERTURBATION ITERATION ===
// Binomial expansion: (Z+δz)^n - Z^n = Σ C(n,k)·Z^(n-k)·δz^k
// All terms computed in scaled coordinates to avoid float32 overflow
var new_dzr: f32;
var new_dzi: f32;
let scale_diff = params.initial_scale - scale;
let dc_r = ldexp(dcr, scale_diff);
let dc_i = ldexp(dci, scale_diff);
if (params.exponent == 2u) {
// z² + c: 2·Z·δz + δz²
let linear_r = 2.0 * (refr * dzr - refi * dzi);
let linear_i = 2.0 * (refr * dzi + refi * dzr);
let dz2_r = ldexp(dzr * dzr - dzi * dzi, scale);
let dz2_i = ldexp(2.0 * dzr * dzi, scale);
new_dzr = linear_r + dz2_r + dc_r;
new_dzi = linear_i + dz2_i + dc_i;
} else if (params.exponent == 3u) {
// z³ + c: 3·Z²·δz + 3·Z·δz² + δz³
let ref2_r = refr * refr - refi * refi;
let ref2_i = 2.0 * refr * refi;
let t1_r = 3.0 * (ref2_r * dzr - ref2_i * dzi);
let t1_i = 3.0 * (ref2_r * dzi + ref2_i * dzr);
let dz2_r = dzr * dzr - dzi * dzi;
let dz2_i = 2.0 * dzr * dzi;
let t2_r = ldexp(3.0 * (refr * dz2_r - refi * dz2_i), scale);
let t2_i = ldexp(3.0 * (refr * dz2_i + refi * dz2_r), scale);
let dz3_r = dzr * dz2_r - dzi * dz2_i;
let dz3_i = dzr * dz2_i + dzi * dz2_r;
let t3_r = ldexp(dz3_r, scale + scale);
let t3_i = ldexp(dz3_i, scale + scale);
new_dzr = t1_r + t2_r + t3_r + dc_r;
new_dzi = t1_i + t2_i + t3_i + dc_i;
} else if (params.exponent == 4u) {
// z⁴ + c: 4·Z³·δz + 6·Z²·δz² + 4·Z·δz³ + δz⁴
let ref2_r = refr * refr - refi * refi;
let ref2_i = 2.0 * refr * refi;
let ref3_r = refr * ref2_r - refi * ref2_i;
let ref3_i = refr * ref2_i + refi * ref2_r;
let t1_r = 4.0 * (ref3_r * dzr - ref3_i * dzi);
let t1_i = 4.0 * (ref3_r * dzi + ref3_i * dzr);
let dz2_r = dzr * dzr - dzi * dzi;
let dz2_i = 2.0 * dzr * dzi;
let t2_r = ldexp(6.0 * (ref2_r * dz2_r - ref2_i * dz2_i), scale);
let t2_i = ldexp(6.0 * (ref2_r * dz2_i + ref2_i * dz2_r), scale);
let dz3_r = dzr * dz2_r - dzi * dz2_i;
let dz3_i = dzr * dz2_i + dzi * dz2_r;
let t3_r = ldexp(4.0 * (refr * dz3_r - refi * dz3_i), scale + scale);
let t3_i = ldexp(4.0 * (refr * dz3_i + refi * dz3_r), scale + scale);
let dz4_r = dz2_r * dz2_r - dz2_i * dz2_i;
let dz4_i = 2.0 * dz2_r * dz2_i;
let t4_r = ldexp(dz4_r, scale + scale + scale);
let t4_i = ldexp(dz4_i, scale + scale + scale);
new_dzr = t1_r + t2_r + t3_r + t4_r + dc_r;
new_dzi = t1_i + t2_i + t3_i + t4_i + dc_i;
} else {
// Higher exponents: use direct computation (less efficient)
let dzr_actual = ldexp(dzr, scale);
let dzi_actual = ldexp(dzi, scale);
var zr = refr + dzr_actual;
var zi = refi + dzi_actual;
var zn_r = zr;
var zn_i = zi;
for (var p = 1u; p < params.exponent; p++) {
let temp_r = zn_r * zr - zn_i * zi;
zn_i = zn_r * zi + zn_i * zr;
zn_r = temp_r;
}
var refn_r = refr;
var refn_i = refi;
for (var p = 1u; p < params.exponent; p++) {
let temp_r = refn_r * refr - refn_i * refi;
refn_i = refn_r * refi + refn_i * refr;
refn_r = temp_r;
}
new_dzr = (zn_r - refn_r) + dc_r;
new_dzi = (zn_i - refn_i) + dc_i;
}
var new_scale = scale;
// === ADAPTIVE RESCALING ===
let dz_mag = max(abs(new_dzr), abs(new_dzi));
if (dz_mag > 0.0 && dz_mag < 1e30) { // Guard against Infinity/NaN
let log2_mag = floor(log2(dz_mag));
if (log2_mag >= 1.0) {
let steps = i32(log2_mag);
// Clamp scale to prevent overflow (max scale ~100, min scale ~initial_scale)
if (new_scale + steps <= 100) {
new_dzr = ldexp(new_dzr, -steps);
new_dzi = ldexp(new_dzi, -steps);
new_scale = new_scale + steps;
}
} else if (log2_mag < -1.0 && new_scale > params.initial_scale) {
let steps = min(i32(-log2_mag) - 1, new_scale - params.initial_scale);
if (steps > 0) {
new_dzr = ldexp(new_dzr, steps);
new_dzi = ldexp(new_dzi, steps);
new_scale = new_scale - steps;
}
}
}
dzr = new_dzr;
dzi = new_dzi;
scale = new_scale;
ref_iter = ref_iter + 1u;
iter = iter + 1u;
}
// Write back integer state
pixels[index].iter = i32(iter);
pixels[index].scale = scale;
pixels[index].ref_iter = i32(ref_iter);
pixels[index].ckpt_refidx = i32(checkpoint_refidx);
pixels[index].pending_refidx = i32(pending_checkpoint_refidx);
if (pixels[index].status == 0) {
pixels[index].period = i32(pp);
}
// Write back float state
pixels[index].dzr = dzr;
pixels[index].dzi = dzi;
pixels[index].bbr = bbr;
pixels[index].bbi = bbi;
pixels[index].ckpt_bbr = checkpoint_bb_r;
pixels[index].ckpt_bbi = checkpoint_bb_i;
if (finished) {
let outIndex = atomicAdd(&results.count, 1u);
results.records[outIndex] = pixels[index];
}
}
`;
const shaderModule = this.device.createShaderModule({
code: shaderCode,
label: 'Adaptive per-pixel scaling perturbation shader'
});
// Check for shader compilation errors
const compilationInfo = await shaderModule.getCompilationInfo();
for (const msg of compilationInfo.messages) {
const level = msg.type === 'error' ? 'ERROR' : msg.type === 'warning' ? 'WARN' : 'INFO';
console.log(`GpuAdaptiveBoard shader ${level}: ${msg.message} ` +
`(line ${msg.lineNum}, col ${msg.linePos})`);
}
this.pipeline = this.device.createComputePipeline({
layout: 'auto',
compute: {
module: shaderModule,
entryPoint: 'main'
},
label: 'Adaptive perturbation pipeline'
});
}
async compute(targetIters = null) {
// Prevent concurrent compute() calls
if (this.isComputing) return;
this.isComputing = true;
this.lastBatchCompacted = false;
// Wait for async GPU initialization to complete
await this.gpuInitPromise;
// GPU required - if device unavailable, computation cannot proceed
if (!this.device) {
console.warn('GpuAdaptiveBoard: GPU device not available, cannot compute');
this.isComputing = false;
return;
}
try {
const THREADING_CAPACITY = 1048576;
const BYTES_PER_PIXEL = GpuAdaptiveBoard.BYTES_PER_PIXEL; // 64 bytes
const STRIDE = GpuAdaptiveBoard.STRIDE; // 16 fields
// ================================================================
// STEP 1: Check if done BEFORE submitting new work
// ================================================================
if (this.activeCount === 0) {
if (this.precomputed && this.precomputed.getPendingCount() > 0) {
const remainingIters = this.precomputed.getPendingIterations();
for (const iter of remainingIters) {
const pending = this.precomputed.extractAtIteration(iter);
if (pending) {
const divergedIndices = [];
const convergedData = [];
for (const idx of pending.diverged) {
this.nn[idx] = iter;
this.pp[idx] = 1;
this.di++;
this.un--;
divergedIndices.push(idx);
}
for (const c of pending.converged) {
this.nn[c.index] = -iter;
this.pp[c.index] = c.p;
this.un--;
convergedData.push({ index: c.index, z: c.z, p: c.p });
}
if (divergedIndices.length > 0 || convergedData.length > 0) {
this.queueChanges({ iter, nn: divergedIndices, vv: convergedData });
}
}
}
}
this.un = 0;
if (this.hasPendingResults) {
await this.flushPendingResults();
}
return;
}
if (this.un === 0) {
if (this.hasPendingResults) {
await this.flushPendingResults();
}
return;
}
// ================================================================
// STEP 2: Calculate batch size and extend reference orbit
// ================================================================
const pixelsToIterate = this.un + this.ch;
let iterationsPerBatch;
if (targetIters !== null) {
iterationsPerBatch = targetIters;
} else {
iterationsPerBatch = Math.max(17, Math.floor(333337 / Math.max(pixelsToIterate, 1)));
}
// Extend reference orbit to exactly what this batch needs
const currentNeed = this.it + iterationsPerBatch;
const targetRefIterations = Math.min(currentNeed, THREADING_CAPACITY);
while (!this.refOrbitEscaped && this.refIterations < targetRefIterations) {
this.extendReferenceOrbit();
}
// Setup reference orbit loop when we hit the threading capacity
if (this.refIterations >= THREADING_CAPACITY && !this.refOrbitLoopConfigured) {
this.setupReferenceOrbitLoop();
}
// ================================================================
// STEP 3: Upload iteration state to GPU
// ================================================================
await this.uploadIters();
// ================================================================
// STEP 4: Set up parameters and dispatch GPU (NON-BLOCKING)
// ================================================================
const checkpointOffsets = [];
const bufferIter = this.it;
for (let i = 0; i < iterationsPerBatch; i++) {
const globalIter = bufferIter + i;
if (fibonacciPeriod(globalIter) === 1) {
checkpointOffsets.push(i);
}
}
const checkpointCount = Math.min(checkpointOffsets.length, 32);
const size_scalar = this.size;
const pixelSize = size_scalar / this.config.dimsWidth;
const workgroupSize = 64;
const numWorkgroups = Math.ceil(this.activeCount / workgroupSize);
const workgroupsX = Math.ceil(Math.sqrt(numWorkgroups));
const workgroupsY = Math.ceil(numWorkgroups / workgroupsX);
const paramsBuffer = new ArrayBuffer(256);
const paramsU32 = new Uint32Array(paramsBuffer);
const paramsI32 = new Int32Array(paramsBuffer);
const paramsF32 = new Float32Array(paramsBuffer);
const bufferIndex = this.readbackBufferIndex;
paramsU32[0] = this.config.dimsWidth;
paramsU32[1] = this.config.dimsHeight;
paramsU32[2] = iterationsPerBatch;
paramsU32[3] = this.activeCount;
paramsU32[4] = this.refIterations + 1;
paramsU32[5] = this.config.exponent || 2;
paramsU32[6] = workgroupsX * workgroupSize;
paramsU32[7] = bufferIter;
paramsU32[8] = checkpointCount;
paramsU32[9] = bufferIndex; // buffer_index for per-buffer batch_active
for (let i = 0; i < 32; i++) {
paramsU32[10 + i] = i < checkpointCount ? checkpointOffsets[i] : 0;
}
paramsU32[42] = 0; // _pad_ckpt
const loop = this.refOrbitLoop || { enabled: false };
paramsU32[43] = loop.enabled ? 1 : 0;
paramsU32[44] = loop.threshold || 0;
paramsU32[45] = loop.jumpAmount || 0;
paramsI32[46] = this.initialScale;
paramsU32[47] = 0; // _pad_scale
paramsF32[48] = pixelSize;
paramsF32[49] = this.config.aspectRatio;
paramsF32[50] = loop.deltaR || 0;
paramsF32[51] = loop.deltaI || 0;
this.device.queue.writeBuffer(this.buffers.params, 0, paramsBuffer);
const commandEncoder = this.device.createCommandEncoder(
{ label: 'Adaptive perturbation compute' });
// Guard pass: try to acquire batch lock (see docs/gpu-batch-locking.md)
this.queueGuardPass(commandEncoder, bufferIndex);
// Compute pass: iterate pixels (will skip if lock not acquired)
const passEncoder = commandEncoder.beginComputePass(
{ label: 'Adaptive perturbation pass' });
passEncoder.setPipeline(this.pipeline);
passEncoder.setBindGroup(0, this.bindGroup);
passEncoder.dispatchWorkgroups(workgroupsX, workgroupsY);
passEncoder.end();
// Queue staging shader pass and copy to staging buffer
// Staging shader releases the lock after copying
this.queueResultsReadback(commandEncoder, bufferIndex);
const gpuStartTime = performance.now();
this.device.queue.submit([commandEncoder.finish()]);
// Save batch iter range using half-open interval [start, end)
const batchStartIter = this.baseIt;
this.baseIt += iterationsPerBatch;
const batchEndIter = this.baseIt;
const currentPromise = this.device.queue.onSubmittedWorkDone();
// GPU is now computing in parallel!
// ================================================================
// STEP 5: Process pending results from PREVIOUS batch (overlaps with GPU)
// ================================================================
if (this.pendingReadbackIndex !== null) {
await this.processPendingReadback();
}
// ================================================================
// STEP 6: Speculative reference orbit extension while GPU works
// ================================================================
const speculativeTimeLimit = 100; // ms
const nextBatchIt = this.it + iterationsPerBatch;
const nextBatchNeed = nextBatchIt + iterationsPerBatch;
const speculativeTarget = Math.min(
Math.max(nextBatchNeed + 10000, Math.round(nextBatchNeed * 1.1)),
THREADING_CAPACITY
);
while (!this.refOrbitEscaped &&
this.refIterations < speculativeTarget &&
(performance.now() - gpuStartTime) < speculativeTimeLimit) {
this.extendReferenceOrbit();
}
// ================================================================
// STEP 7: Update pending state for next iteration
// ================================================================
this.pendingReadbackIndex = bufferIndex;
this.pendingReadbackPromise = currentPromise;
this.readbackBufferIndex = 1 - bufferIndex;
this.pendingIterationsPerBatch = iterationsPerBatch;
this.hasPendingResults = true;
// Batch tracking: half-open interval [start, end) (see docs/gpu-results-readback-design.md)
this.pendingBatchStartIter = batchStartIter;
this.pendingBatchEndIter = batchEndIter;
} catch (error) {
console.error('GpuAdaptiveBoard.compute() ERROR:',
error?.message || error, error?.stack || '');
} finally {
this.isComputing = false;
}
}
// flushPendingResults() and readPixelBuffer() inherited from GpuZhuoranBaseBoard
async serialize() {
// Wait for any in-progress compute() to finish to avoid mapAsync race condition
while (this.isComputing) {
await new Promise(resolve => setTimeout(resolve, 10));
}
// CRITICAL: Flush pending results before serializing
if (this.hasPendingResults) {
await this.flushPendingResults();
}
// Ensure GPU is ready before reading buffers
await this.ensureGPUReady();
// Read GPU pixel buffer
const gpuPixelData = await this.readPixelBuffer();
// Build sparse nn array for completed pixels
const completedIndexes = [];
const completedNn = [];
for (let i = 0; i < this.nn.length; i++) {
if (this.nn[i] !== 0) {
completedIndexes.push(i);
completedNn.push(this.nn[i]);
}
}
return {
...(await super.serialize()),
// GPU pixel buffer as array (for JSON serialization)
gpuPixelData: gpuPixelData ? Array.from(new Uint8Array(gpuPixelData)) : null,
// QD reference orbit state
qdRefOrbit: this.qdRefOrbit,
refC_qd: this.refC_qd,
refIterations: this.refIterations,
refOrbitEscaped: this.refOrbitEscaped,
refOrbitLoop: this.refOrbitLoop || null,
refOrbitLoopConfigured: this.refOrbitLoopConfigured || false,
// Per-pixel adaptive scaling
initialScale: this.initialScale,
// Board state
effort: this.effort,
completedIndexes,
completedNn,
activeCount: this.activeCount,
deadSinceCompaction: this.deadSinceCompaction,
wastedBandwidth: this.wastedBandwidth,
};
}
static fromSerialized(serialized) {
// GPU boards require async initialization, so this returns a board
// that will continue initializing in the background
const board = new GpuAdaptiveBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Schedule async restoration after GPU init
board.gpuInitPromise = board.gpuInitPromise.then(async () => {
if (serialized.activeCount !== undefined) {
board.activeCount = serialized.activeCount;
board.deadSinceCompaction = serialized.deadSinceCompaction || 0;
board.wastedBandwidth = serialized.wastedBandwidth || 0;
board.pendingActiveCount = board.activeCount;
const bufferSize = board.activeCount * GpuAdaptiveBoard.BYTES_PER_PIXEL;
board.buffers.pixels?.destroy();
board.buffers.pixels = board.device.createBuffer({
size: bufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST
});
// Note: stagingPixels are created on-demand in readPixelBuffer() for serialization
board.initResultsReadback(GpuAdaptiveBoard.BYTES_PER_PIXEL, board.activeCount);
board.createBindGroup();
}
// Restore GPU pixel buffer
if (serialized.gpuPixelData && board.isGPUReady) {
const pixelData = new Uint8Array(serialized.gpuPixelData).buffer;
await board.writePixelBuffer(pixelData);
}
// Restore QD reference orbit state
board.qdRefOrbit = serialized.qdRefOrbit || [];
board.refC_qd = serialized.refC_qd || new Array(8).fill(0);
board.refIterations = serialized.refIterations || 1;
board.refOrbitEscaped = serialized.refOrbitEscaped || false;
board.refOrbitLoop = serialized.refOrbitLoop || null;
board.refOrbitLoopConfigured = serialized.refOrbitLoopConfigured || false;
// Restore per-pixel adaptive scaling
if (serialized.initialScale !== undefined) {
board.initialScale = serialized.initialScale;
}
// Rebuild threading structure from restored reference orbit
board.rebuildQDThreading();
// Restore Board state
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
board.effort = serialized.effort || 2;
if (serialized.precomputed) {
board.precomputed = PrecomputedPoints.fromSerialized(serialized.precomputed);
}
// Restore nn array
board.nn = new Array(serialized.config.dimsArea).fill(0);
if (serialized.completedIndexes) {
for (let i = 0; i < serialized.completedIndexes.length; i++) {
board.nn[serialized.completedIndexes[i]] = serialized.completedNn[i];
}
}
});
return board;
}
}
const forcedBoardTypes = {
'cpu': CpuBoard,
'ddz': DDZhuoranBoard,
'qdz': QDZhuoranBoard,
'gpu': GpuBoard,
'gl': GlBoard,
'glz': GlZhuoranBoard,
'gla': GlAdaptiveBoard,
'gpuz': GpuZhuoranBoard,
'gpua': GpuAdaptiveBoard,
'qdcpu': QDCpuBoard
};
// Cache WebGL2 availability check
let glBoardAvailable = null;
function isGlBoardAvailable() {
if (glBoardAvailable === null) {
glBoardAvailable = GlBoard.isAvailable();
// Logging is now done at point of use (see worker handleMessage)
}
return glBoardAvailable;
}
function selectBoardClass(pixelSize, dimsArea, gpuMaxBufferSize, forceBoard) {
if (forceBoard) {
if (forceBoard in forcedBoardTypes) {
// Check if forcing a GPU board type but GPU isn't available
const gpuBoardTypes = ['gpu', 'gpuz', 'gpua'];
if (gpuBoardTypes.includes(forceBoard) && !gpuMaxBufferSize) {
throw new Error(`board=${forceBoard} requested but WebGPU is not available. ` +
`Use a CPU board (cpu, ddz, qdz) or WebGL board (gl, glz, gla) instead.`);
}
return forcedBoardTypes[forceBoard];
} else {
throw new Error(`Unknown board type: ${forcedBoardType}.` +
` Valid types: ${Object.keys(forcedBoardTypes).join(', ')}`);
}
}
// Prefer WebGPU boards when available
if (gpuMaxBufferSize) {
// Select board type based on zoom level and float32 precision limits
// Float32 has ~7 decimal digits, so direct iteration works to ~1e-7 pixel size
// Shallow zooms (z < ~1e7): GpuBoard with simple float32 iteration
// Medium zooms (z ~1e7 to ~1e30): GpuZhuoranBoard with quad-precision reference
// Deep zooms (z > ~1e30): GpuAdaptiveBoard with QD-precision reference
// orbit and adaptive per-pixel scaling for correct escape detection
const GpuBoardClass = (
(pixelSize > 1e-7) ? GpuBoard :
(pixelSize > 1e-30) ? GpuZhuoranBoard :
GpuAdaptiveBoard);
const largestBufferSize = dimsArea * GpuBoardClass.BYTES_PER_PIXEL;
if (largestBufferSize <= gpuMaxBufferSize) {
return GpuBoardClass;
} else {
const bufferSizeMB = (largestBufferSize / (1024*1024)).toFixed(0);
const limitMB = (gpuMaxBufferSize / (1024*1024)).toFixed(0);
console.log(
`${GpuBoardClass}: dimsArea=${dimsArea} too large for GPU ` +
`(buffer size ${bufferSizeMB} MB > ${limitMB} MB)`);
// Fall through to try WebGL2 boards
}
}
// WebGPU not available or buffer too large - try WebGL2 boards as fallback
if (isGlBoardAvailable()) {
// Shallow zooms: GlBoard with simple float32 iteration
if (pixelSize > 1e-7) {
return GlBoard;
}
// Medium zooms: GlZhuoranBoard with DD-precision reference orbit
if (pixelSize > 1e-30 && GlZhuoranBoard.isAvailable()) {
return GlZhuoranBoard;
}
// Deep zooms: GlAdaptiveBoard with QD-precision reference orbit
if (GlAdaptiveBoard.isAvailable()) {
return GlAdaptiveBoard;
}
}
// No GPU available - fall back to CPU boards
const CpuBoardClass = (
(pixelSize > 1e-15) ? CpuBoard :
(pixelSize > 1e-30) ? DDZhuoranBoard :
QDZhuoranBoard);
return CpuBoardClass;
}
// FractalWorker manages board computation on both main thread and in workers
// Always defined on the main thread (for MockWorker to extend)
// and instantiated in real workers via workerStart
class FractalWorker {
constructor(workerNumber, name) {
this.workerNumber = workerNumber;
this.name = name;
this.boards = new Map();
this.hiddenBoards = new Set();
this.focusedBoardK = null;
this.computationPaused = false;
this.steps = 0;
this.startTime = 0;
this.endTime = -1;
this.timer = null;
this.gpuMaxBufferSize = null;
// Batch timing collection for benchmarking (debug=b)
// Maps board.k -> array of {pixels, iters, timeMs}
this.batchTimings = new Map();
this.collectBatchTimings = false;
// Console.log timing output (debug=t)
this.logTimings = false;
// Random batch sizes for benchmarking (debug=r)
this.randomBatching = false;
this.randomBatchMin = 1;
this.randomBatchMax = 16;
// Target time per batch in milliseconds (configurable)
this.batchTimeMs = 100;
// Fast scheduling using MessageChannel (faster than setTimeout(0))
// The message queue has higher priority than the timer queue
this.scheduleChannel = new MessageChannel();
this.schedulePending = false;
this.scheduleChannel.port1.onmessage = () => {
this.schedulePending = false;
this.iterateBoards();
};
}
// Schedule next iteration using MessageChannel (faster than setTimeout(0))
scheduleNextIteration() {
if (!this.schedulePending) {
this.schedulePending = true;
this.scheduleChannel.port2.postMessage(null);
}
}
// Record a batch timing sample for benchmarking
// startPixels should be board.un captured BEFORE iterate()
recordBatchTiming(board, startTime, startIter, startPixels) {
if (!this.collectBatchTimings) return;
const timeMs = performance.now() - startTime;
const iters = board.it - startIter;
// Use the pixel count from before the batch (some may have diverged during)
const pixels = startPixels;
if (iters > 0 && pixels > 0 && timeMs > 0) {
if (!this.batchTimings.has(board.k)) {
this.batchTimings.set(board.k, []);
}
this.batchTimings.get(board.k).push({ pixels, iters, timeMs });
}
}
// Get batch timings for regression analysis
getBatchTimings(k) {
return this.batchTimings.get(k) || [];
}
// Clear batch timings
clearBatchTimings(k) {
if (k !== undefined) {
this.batchTimings.delete(k);
} else {
this.batchTimings.clear();
}
}
async handleMessage(type, data) {
switch (type) {
case 'addBoard':
this.workerNumber = data.workerNumber;
// Debug flags to disable GPU backends for testing fallback chain
const noGPU = hasDebugFlag(data.config, 'nogpu');
const noGL = hasDebugFlag(data.config, 'nogl');
const webGPUAvailable = !noGPU && GpuBoard.isAvailable();
// Query GPU limits once on first use
if (webGPUAvailable && this.gpuMaxBufferSize === null) {
this.gpuMaxBufferSize = await GpuBaseBoard.queryMaxBufferSize();
}
// Cache WebGL2 availability override for selectBoardClass
if (noGL) {
glBoardAvailable = false;
}
// Log fallback chain status (only for first board)
if (data.k === 0) {
if (noGPU) {
if (noGL) {
console.log('WebGPU disabled, WebGL2 disabled - falling back to CPU boards');
} else if (isGlBoardAvailable()) {
console.log('WebGPU disabled - falling back to WebGL2 boards');
} else {
console.log('WebGPU disabled, WebGL2 not available - falling back to CPU boards');
}
} else if (!this.gpuMaxBufferSize) {
if (isGlBoardAvailable()) {
console.log('WebGPU not available - falling back to WebGL2 boards');
} else {
console.log('WebGPU and WebGL2 not available - falling back to CPU boards');
}
}
}
// Explicit board selection via board= parameter
const forceBoard = data.config.forceBoard;
const size = data.size;
const dimsArea = data.config.dimsArea;
const pixelSize = size / data.config.dimsWidth;
const BoardClass = selectBoardClass(pixelSize, dimsArea, this.gpuMaxBufferSize, forceBoard);
// Construct the board instance with optional inherited data
let board = new BoardClass(data.k, size, data.reQD, data.imQD, data.config, data.id, data.inheritedData);
this.boards.set(data.k, board);
// Log inheritance stats if debug=inherit is set
if (data.inheritedData && hasDebugFlag(data.config, 'inherit')) {
const inherited = data.inheritedData.packed ?
((data.inheritedData.dIndices?.length || 0) + (data.inheritedData.cIndices?.length || 0)) :
((data.inheritedData.diverged?.length || 0) + (data.inheritedData.converged?.length || 0));
console.log(`Board ${data.k} (${BoardClass.name}): received ${inherited} inherited pixels`);
}
// Enable batch timing collection if debug=b is set
if (hasDebugFlag(data.config, 'b')) {
this.collectBatchTimings = true;
}
// Enable console.log timing output if debug=t is set
if (hasDebugFlag(data.config, 't')) {
this.logTimings = true;
}
// Enable random batch sizes for benchmarking if debug=r is set
if (hasDebugFlag(data.config, 'r')) {
this.randomBatching = true;
this.logTimings = true; // Also enable timing output
}
// Store QD-precision coordinates
board.sizesQD = [size, data.reQD, data.imQD];
// Show coordinates
let coordStr;
const digits = Math.ceil(-Math.log10(pixelSize)) + 3;
const re_str = qdToDecimalString(data.reQD, digits);
const im_str = qdToDecimalString(data.imQD, digits);
coordStr = `c=(${re_str}, ${im_str})`;
console.log(
`Board ${data.k}: ${board.constructor.name} @ ${coordStr}, ` +
`dims=${data.config.dimsWidth}x${data.config.dimsHeight}, ` +
`pixel=${pixelSize.toExponential(3)}`
);
// Log refC_qd at full precision for deep zoom boards
// to debug click vs URL differences
if (board.refC_qd && pixelSize < 1e-45) {
const refReQD = [board.refC_qd[0], board.refC_qd[1],
board.refC_qd[2], board.refC_qd[3]];
const refImQD = [board.refC_qd[4], board.refC_qd[5],
board.refC_qd[6], board.refC_qd[7]];
const digits = Math.ceil(-Math.log10(pixelSize)) + 3;
console.log(` refC_qd: (${qdToDecimalString(refReQD, digits)}, ` +
`${qdToDecimalString(refImQD, digits)})`);
}
// Send board type info once on creation
this.sendToScheduler({
type: 'boardCreated',
data: {
k: data.k,
boardType: board.constructor.name
}
});
break;
case 'removeBoard':
this.boards.delete(data.k);
break;
case 'setFocusedBoard':
this.focusedBoardK = data.k;
break;
case 'setHiddenBoards':
this.hiddenBoards = new Set(data.hiddenBoards);
break;
case 'requestTransfer':
const transferredBoards = [];
for (const k of data.boardKeys) {
if (this.boards.has(k)) {
const board = this.boards.get(k);
board.compact();
const serializedBoard = await board.serialize();
this.boards.delete(k);
transferredBoards.push(serializedBoard);
}
}
// Send the serialized boards back to the scheduler
this.sendToScheduler({
type: 'downloadTransfer',
data: { transferredBoards }
});
break;
case 'uploadTransfer':
// Recreate the board from the serialized data and add it to this worker
const newBoard = Board.fromSerialized(data.boardData);
this.boards.set(newBoard.k, newBoard);
break;
case 'pause':
this.computationPaused = data.pause;
break;
}
// Start iteration loop if not running (check after every message)
if (!this.timer && this.boards.size && !this.computationPaused) {
this.iterateBoards();
} else {
const remainingWork = Array.from(this.boards.values()).
filter(board => !this.hiddenBoards.has(board.k)).
map(b => b.un * b.effort).reduce((a, b) => a + b, 0);
this.sendToScheduler({
type: 'update',
data: {
remainingWork,
}
});
}
}
async iterateBoards() {
this.timer = null;
if (this.computationPaused) {
return;
}
let pri = Array.from(this.boards.values())
.filter(board => (board.unfinished() || board.updateSize || board.hasPendingResults))
.filter(board => !this.hiddenBoards.has(board.k));
if (pri.length) {
// Start timer if it is not already running.
if (this.endTime) {
this.startTime = (new Date).getTime();
this.endTime = 0;
}
if (this.steps % 2) {
// Prioritize most unfinished half the time.
pri = pri.sort((a, b) => b.un - a.un);
} else {
// Prioritize the most recent half the time.
pri = pri.sort((a, b) => b.k - a.k);
// Allow the user to prioritize by pointing the mouse.
if (this.focusedBoardK !== null) {
pri.sort((a, b) => (a.k === this.focusedBoardK ? -1 : b.k === this.focusedBoardK ? 1 : 0));
}
}
// Exponential scheduling policy
let shift = Math.floor(this.steps++ / 2) + 1;
let p = 0;
while (shift & (1 << p)) { p += 1; }
const board = pri[Math.min(p, pri.length) % pri.length];
// Calculate targetIters based on time budget and effort
// Work threshold tuned for ~10-20ms CPU batches and ~50-100ms GPU batches
// Large batches improve throughput by amortizing per-batch overhead
const batchTimeMs = this.batchTimeMs || 100;
const workThreshold = batchTimeMs * 5000000;
let targetIters;
if (this.stepMode) {
// Step mode: always 1 iteration per step
targetIters = 1;
} else if (this.randomBatching) {
// Random batch sizes for benchmarking (debug=r)
// Produces varied iteration counts for regression analysis
targetIters = this.randomBatchMin + Math.floor(
Math.random() * (this.randomBatchMax - this.randomBatchMin + 1)
);
} else {
// Calculate iterations to fill time budget, respecting board limits
const pixels = Math.max(board.un, 1);
const effort = Math.max(board.effort, 1);
const minIters = board.minBatchIters || 1;
const maxIters = board.maxBatchIters || Infinity;
targetIters = Math.min(maxIters, Math.max(minIters, Math.floor(workThreshold / (pixels * effort))));
}
// In step mode, wait for step() to request iterations
if (this.stepMode && this.stepsRequested <= 0) {
// If stepsRequested is 0, don't do anything (wait for step() call)
} else {
const shouldTime = this.collectBatchTimings || this.logTimings;
const startTime = shouldTime ? performance.now() : 0;
const startIter = board.it;
const startPixels = board.un;
await board.iterate(targetIters);
if (shouldTime) {
const elapsedMs = performance.now() - startTime;
const actualIters = board.it - startIter;
if (this.collectBatchTimings) {
this.recordBatchTiming(board, startTime, startIter, startPixels);
}
if (this.logTimings && actualIters > 0) {
const boardType = board.constructor.name;
const elapsedUs = elapsedMs * 1000; // Convert to microseconds
const usPerPixelIter = elapsedUs / (startPixels * actualIters);
const compactedFlag = board.lastBatchCompacted ? ' C' : '';
console.log(`[timing] ${boardType} k=${board.k}: ${startPixels} px × ${actualIters} iters = ${elapsedUs.toFixed(1)}μs${compactedFlag}`);
}
}
if (this.stepMode) {
this.stepsRequested--; // Consume one step
// Call step callback if set
if (this.stepCallback) {
await this.stepCallback();
}
}
}
const now = (new Date()).getTime();
const timeSinceUpdate = now - board.lastTime;
const isFocused = this.focusedBoardK == board.k;
const hasChanges = board.updateSize > 0 || !board.unfinished();
// Send updates at least every 100ms, or earlier if enough pixels changed
const enoughPixels = isFocused ?
(board.updateSize >= 1429) : (board.updateSize >= 4673);
if (timeSinceUpdate >= 100 || (hasChanges && enoughPixels)) {
const boardEffort = board.un * board.effort;
const remainingWork = pri.map(b => b.un * b.effort).reduce((a, b) => a + b, 0);
const workerInfo = `${this.name}: ` + (board.unfinished() ?
`boards {${[...this.boards.keys()]}}, work: ${remainingWork}` :
`board finished`);
// Sort changeList by iteration for consistent histogram construction
board.changeList.sort((a, b) => a.iter - b.iter);
this.sendToScheduler({
type: 'iterations',
data: {
k: board.k,
id: board.id,
it: board.it,
un: board.un,
di: board.di,
ch: board.ch,
changeList: board.changeList,
boardEffort,
remainingWork,
workerInfo,
boardType: board.constructor.name,
compactionCount: board.compactionCount || 0,
activeCount: board.activeCount || board.config.dimsArea,
resultsReadbackBytes: board.resultsReadbackBytes || 0,
resultsReadbackBatches: board.resultsReadbackBatches || 0,
lastResultsCount: board.lastResultsCount || 0,
batchTotalCount: board.batchTotalCount || 0,
batchCollisionCount: board.batchCollisionCount || 0
}
});
board.lastTime = now;
board.updateSize = 0;
board.changeList = [];
board.changeMap = null;
if (!board.unfinished()) {
// Delete board when done.
this.boards.delete(board.k);
}
}
} else {
// End timer when there is no remaining work
if (!this.endTime) {
this.endTime = (new Date).getTime();
}
return;
}
this.scheduleNextIteration();
}
// Abstract method to be overridden by subclasses
// Sends messages from worker back to scheduler
sendToScheduler(msg) {
throw new Error('FractalWorker.sendToScheduler() must be implemented by subclass');
}
}
// </script>
// <script id="mathCode">
// Debug flag 'w': Define MockWorker for main thread debugging
// workerCode has type="text/webworker" so it's not parsed; eval it when needed for MockWorker
if (location.search.includes('debug=')) {
const debugValue = decodeURIComponent(location.search.match(/[?&]debug=([^&]*)/)?.[1] || '');
if (debugValue.split(',').includes('w')) {
// Insert workerCode as a script element to make all classes available in global scope
// (Using a script element instead of eval because class declarations are block-scoped in eval)
const workerCodeEl = document.getElementById('workerCode');
if (workerCodeEl) {
const script = document.createElement('script');
script.textContent = workerCodeEl.textContent;
document.head.appendChild(script);
}
// Define MockWorker class that extends FractalWorker
window.MockWorker = class MockWorker extends FractalWorker {
constructor(workerNumber) {
super(workerNumber, `MockWorker ${workerNumber}`);
this.onmessage = null; // Callback for sending messages back to Scheduler
// Step mode support (debug=s flag)
this.stepMode = false;
this.stepsRequested = 0;
}
// Override to add step mode support
async iterateBoards() {
this.timer = null;
// Step mode: only iterate if steps are requested
if (this.stepMode && this.stepsRequested === 0) {
// Wait for step() to be called
this.timer = setTimeout(() => this.iterateBoards(), 100);
return;
}
// Call parent implementation (it will check stepsRequested and decrement if needed)
await super.iterateBoards();
}
// Handle incoming messages from Scheduler (when Scheduler calls worker.postMessage())
// Real Workers receive messages via self.onmessage, but MockWorker receives via this method
postMessage(msg) {
// Schedule handleMessage asynchronously to match real Worker behavior
setTimeout(async () => {
const { type, data } = msg;
await this.handleMessage(type, data);
}, 0);
}
// Override abstract method to send messages back to Scheduler
sendToScheduler(msg) {
if (this.onmessage) {
this.onmessage({ data: msg });
}
}
};
console.log('MockWorker class defined for main thread debugging');
// Enable step mode if 's' flag is set
if (debugValue.split(',').includes('s')) {
// Set step mode flag on MockWorker initialization
const originalConstructor = window.MockWorker;
window.MockWorker = class extends originalConstructor {
constructor(workerNumber) {
super(workerNumber);
this.stepMode = true;
console.log(`MockWorker ${workerNumber} created in step mode`);
}
};
// Helper functions for stepping through iterations
window.step = function(n = 1, workerIndex = 0, callback = null) {
if (typeof workerIndex === 'function') {
callback = workerIndex;
workerIndex = 0;
}
const worker = window[`worker${workerIndex}`];
if (!worker || !worker.stepMode) {
console.log(`Step mode not active for worker${workerIndex}. Load page with ?debug=w,s`);
return;
}
worker.stepCallback = callback;
worker.stepsRequested += n;
if (!callback) {
console.log(`Stepping worker${workerIndex} ${n} iteration(s)...`);
}
return worker.boards;
};
window.stepAll = function(workerIndex = 0) {
const worker = window[`worker${workerIndex}`];
if (!worker) {
console.log(`No worker${workerIndex} available`);
return;
}
worker.stepMode = false;
worker.stepsRequested = 1; // Queue one step to trigger continuous iteration
console.log(`Resuming continuous iteration for worker${workerIndex}...`);
};
window.pause = function(workerIndex = 0) {
const worker = window[`worker${workerIndex}`];
if (!worker) {
console.log(`No worker${workerIndex} available`);
return;
}
worker.stepMode = true;
worker.stepsRequested = 0; // Clear any pending steps
console.log(`Paused worker${workerIndex}. Use step() or step(n) to continue.`);
};
window.inspectBoard = function(k = 0, workerIndex = 0) {
const worker = window[`worker${workerIndex}`];
if (!worker || !worker.boards.has(k)) {
console.log(`Board ${k} not found on worker${workerIndex}. Available:`, Array.from(worker?.boards?.keys() || []));
return null;
}
const board = worker.boards.get(k);
console.log(`Board ${k} on worker${workerIndex} (${board.constructor.name}):`);
console.log(` Iteration: ${board.it}`);
console.log(` Unfinished pixels: ${board.un}`);
console.log(` Diverged: ${board.di}`);
console.log(` Converged: ${board.ch}`);
return board;
};
window.tracePixel = async function(k, pixelIndex, workerIndex = 0) {
const worker = window[`worker${workerIndex}`];
if (!worker || !worker.boards.has(k)) {
console.log(`Board ${k} not found on worker${workerIndex}`);
return null;
}
const board = worker.boards.get(k);
const info = {
boardType: board.constructor.name,
iteration: board.it,
nn: board.nn[pixelIndex]
};
// For Adaptive boards, read GPU state
if (board.constructor.name === 'GpuAdaptiveBoard') {
const pixelData = await board.readBuffer(board.buffers.pixels, Uint8Array);
const offset = pixelIndex * 60;
const pixelU32 = new Uint32Array(pixelData.buffer, offset, 15);
const pixelF32 = new Float32Array(pixelData.buffer, offset, 15);
info.status = new Int32Array([pixelU32[0]])[0];
info.refIter = pixelU32[2];
info.scale = new Int32Array([pixelU32[4]])[0];
info.dzr = pixelF32[7];
info.dzi = pixelF32[8];
info.dzr_scaled = info.dzr * Math.pow(2, info.scale);
info.dzi_scaled = info.dzi * Math.pow(2, info.scale);
}
// For QDZ boards, read CPU state
if (board.constructor.name === 'QDZhuoranBoard') {
info.refIter = board.refIter[pixelIndex];
info.dzr = board.dz[pixelIndex * 2];
info.dzi = board.dz[pixelIndex * 2 + 1];
}
console.table(info);
return info;
};
// Analyze batch timings collected with debug=b
// In step mode, each batch does 1 iteration, so we can only measure:
// time = overhead + perPixel × pixels
// For multi-iteration batches (non-step mode), we could separate:
// time = perBatch + perIter × iters + perPixelIter × pixels × iters
window.analyzeBatchTimings = function(k = 0) {
const worker = window.worker0;
if (!worker) {
console.log('No worker available');
return null;
}
const timings = worker.getBatchTimings(k);
if (timings.length < 4) {
console.log(`Not enough timing data (${timings.length} samples). Run more iterations with debug=b,w,s`);
return null;
}
const board = worker.boards.get(k);
const boardName = board?.constructor.name || 'Unknown';
const n = timings.length;
// Check if we have iteration variation
const uniqueIters = [...new Set(timings.map(t => t.iters))];
const hasIterVariation = uniqueIters.length > 1;
// Simple linear regression: time = overhead + perPixel × pixels
let sum_p = 0, sum_y = 0, sum_pp = 0, sum_py = 0;
for (const t of timings) {
const p = t.pixels;
const y = t.timeMs * 1000; // μs
sum_p += p; sum_y += y; sum_pp += p*p; sum_py += p*y;
}
const det = n * sum_pp - sum_p * sum_p;
const perPixelUs = det !== 0 ? (n * sum_py - sum_p * sum_y) / det : 0;
const overheadUs = (sum_y - perPixelUs * sum_p) / n;
// Pixel count range
const minPixels = Math.min(...timings.map(t => t.pixels));
const maxPixels = Math.max(...timings.map(t => t.pixels));
console.log(`\nBatch Timing Analysis for Board ${k} (${boardName}):`);
console.log(` Samples: ${n}`);
console.log(` Pixel range: ${minPixels} - ${maxPixels}`);
console.log(` Model: time = ${overheadUs.toFixed(1)} μs + ${perPixelUs.toFixed(4)} μs × pixels`);
console.log(` Per-pixel cost: ${Math.max(0, perPixelUs).toFixed(4)} μs/pixel`);
console.log(` Overhead: ${Math.max(0, overheadUs).toFixed(1)} μs/batch`);
if (!hasIterVariation) {
console.log(`\n Note: In step mode, each batch does 1 iteration.`);
console.log(` The per-pixel cost is actually per-pixel-iteration.`);
}
// Show sample data
console.log(`\n Sample data (first 10):`);
console.table(timings.slice(0, 10).map(t => ({
pixels: t.pixels,
iters: t.iters,
timeMs: t.timeMs.toFixed(2),
'μs/pixel': (t.timeMs * 1000 / t.pixels).toFixed(3)
})));
return { perPixelUs: Math.max(0, perPixelUs), overheadUs: Math.max(0, overheadUs), samples: n };
};
window.clearBatchTimings = function(k) {
const worker = window.worker0;
if (worker) {
worker.clearBatchTimings(k);
console.log(k !== undefined ? `Cleared timings for board ${k}` : 'Cleared all timings');
}
};
console.log('Step mode enabled. Use step(), step(n), pause(), stepAll(), inspectBoard(k), tracePixel(k, pixelIndex)');
if (window.worker0?.collectBatchTimings) {
console.log('Batch timing enabled (debug=b). Use analyzeBatchTimings(k), clearBatchTimings(k)');
}
}
}
}
// </script>
if (typeof module !== 'undefined') module.exports = { hasDebugFlag, isGlBoardAvailable, selectBoardClass, PrecomputedPoints, Board, CpuBoard, QDCpuBoard, SpatialBucket, DDSpatialBucket, QDSpatialBucket, ReferenceOrbitThreading, CpuZhuoranBaseBoard, DDZhuoranBoard, QDZhuoranBoard, GpuBaseBoard, GpuBoard, GlBoard, GlPerturbationBaseBoard, GlZhuoranBoard, GlAdaptiveBoard, GpuZhuoranBaseBoard, GpuZhuoranBoard, GpuAdaptiveBoard, FractalWorker, declarations, that, MockWorker, defined }; |