Press n or j to go to the next uncovered block, b, p or k for the previous block.
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5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x 5274x | // Linefeeds to align line numbers with HTML.
// <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 + '='));
}
// Abstract base class for Mandelbrot computation backends.
class Board {
constructor(k, size, re, im, config, id) {
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 = 1; // Work-per pixel
this.pix = this.pixelSize;
this.epsilon = Math.min(1e-12, this.pix / 10);
this.epsilon2 = Math.min(1e-9, 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 = [];
}
// 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
};
}
compact() {
}
queueChanges(changes) {
if (changes !== null) {
this.changeList.push(changes);
this.updateSize += changes.nn.length + changes.vv.length;
}
}
static fromSerialized(serialized) {
const subclasses = new Map([
['CpuBoard', CpuBoard],
['QDCpuBoard', QDCpuBoard],
['PerturbationBoard', PerturbationBoard],
['QDPerturbationBoard', QDPerturbationBoard],
['DDZhuoranBoard', DDZhuoranBoard],
['QDZhuoranBoard', QDZhuoranBoard],
['GpuBoard', GpuBoard],
['GpuZhuoranBoard', GpuZhuoranBoard],
['AdaptiveGpuBoard', AdaptiveGpuBoard]
]);
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);
}
inspikeDDA(re1, re2, im1, im2) {
// We do not iterate infinitely for chaotic points in the spike.
// -1.401155 is the Feigenbaum point boundary
return (im1 + im2 == 0.0 && re1 >= -2.0 && re1 < -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) {
super(k, size, re, im, config, id);
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
this.ss = Array(this.config.dimsArea).fill(null).map((_, i) => i); // All pixels active
}
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];
}
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() {
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}`);
}
}
this.it++;
this.queueChanges(changes);
}
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
if (db <= this.epsilon2) {
if (!this.pp[m]) { this.pp[m] = this.it; } // Record iter when first detected
if (db <= this.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) {
super(k, size, re, im, config, id);
// 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
// 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);
// 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 toQDMul instead of toQDScale to capture error terms
const jQD = toQDAdd(imQD, toQDMul(sizeOverAspect, toQD(jFrac)));
for (let x = 0; x < this.config.dimsWidth; x++) {
const rFrac = ((x / this.config.dimsWidth) - 0.5);
// Use toQDMul instead of toQDScale to capture error terms
const rQD = toQDAdd(reQD, toQDMul(this.size, toQD(rFrac)));
// 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
this.ss = Array(this.config.dimsArea).fill(null).map((_, i) => i); // All pixels active
}
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];
}
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() {
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();
}
this.it++;
this.queueChanges(changes);
}
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]);
if (db <= this.epsilon2) {
if (!this.pp[m]) { this.pp[m] = this.it; } // Record iter when first detected
if (db <= this.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
}
}
// CPU board using perturbation theory with sparse DD precision anchors.
class PerturbationBoard extends Board {
constructor(k, size, re, im, config, id) {
super(k, size, re, im, config, id);
this.ddIndexes = []; // Pixels computed in DD precision
this.pertIndexes = []; // Pixels computed as perturbations from DD points
this.tt = []; // Working array for DD precision operations
this.perturbationThreshold = Math.min(0.1, Math.sqrt(1e15 * (size / config.dimsWidth)));
this.effort = 3;
this.initPerturbationBoard(size, re, im);
}
initPerturbationBoard(size, re, im) {
this.cc = new Array(this.config.dimsArea * 4).fill(NaN);
// Odd grid ensures that center point corresponds to a DD precision pixel
const gridSizeX = Math.floor(this.config.dimsWidth / 17 / 2) * 2 + 1;
const gridSizeY = Math.floor(this.config.dimsHeight / 17 / 2) * 2 + 1;
const stepX = this.config.dimsWidth / gridSizeX;
const stepY = this.config.dimsHeight / gridSizeY;
const offsetX = stepX / 2;
const offsetY = stepY / 2;
const pixW = size / this.config.dimsWidth;
const pixH = (size / this.config.aspectRatio) / this.config.dimsHeight;
const cc = this.cc;
re = toDD(re);
im = toDD(im);
// Initialize reference points and perturbations
for (let gy = 0; gy < gridSizeY; gy++) {
const ry = Math.round(gy * stepY + offsetY);
const jFrac = (0.5 - (ry / this.config.dimsHeight));
const cj = ddAdd(im, ddScale(toDD(jFrac), size / this.config.aspectRatio))
for (let gx = 0; gx < gridSizeX; gx++) {
const rx = Math.round(gx * stepX + offsetX);
const rFrac = ((rx / this.config.dimsWidth) - 0.5);
const refIndex = (ry * this.config.dimsWidth + rx);
const ri = refIndex * 4;
const cr = ddAdd(re, ddScale(toDD(rFrac), size));
// Initialize reference point
cc[ri] = cr[0];
cc[ri+1] = cr[1];
cc[ri+2] = cj[0];
cc[ri+3] = cj[1];
this.ddIndexes.push(refIndex);
let refspike = this.inspikeDDA(cr[0], cr[1], cj[0], cj[1]);
if (refspike) {
this.ch += 1;
}
// Initialize perturbations around this reference point
const minY = Math.max(0, Math.floor(ry - offsetY));
const maxY = Math.min(this.config.dimsHeight - 1, Math.ceil(ry + offsetY));
const minX = Math.max(0, Math.floor(rx - offsetX));
const maxX = Math.min(this.config.dimsWidth - 1, Math.ceil(rx + offsetX));
for (let py = minY; py <= maxY; py++) {
const dci = (ry - py) * pixH;
for (let px = minX; px <= maxX; px++) {
const dcr = (px - rx) * pixW;
const pertIndex = (py * this.config.dimsWidth + px);
const pi = pertIndex * 4;
if (isNaN(cc[pi+3])) { // Avoid double-initialization
cc[pi] = dcr;
cc[pi+1] = dci;
cc[pi+2] = refIndex;
cc[pi+3] = Infinity;
this.pertIndexes.push(pertIndex);
if (refspike && py == ry) {
this.ch += 1;
}
}
}
}
}
}
this.zz = this.cc.slice();
this.bb = [];
this.nz = [];
}
static fromSerialized(serialized) {
const board = new PerturbationBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
const cc = board.cc;
// Override initialized values with serialized data
Object.assign(board, serialized);
delete board.pertZZ;
// 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 arrays from serialized data, leaving empty spots
board.cc = [];
board.zz = [];
board.nz = [];
board.bb = [];
board.pp = [];
const ddIdx = serialized.ddIndexes || [];
for (let i = 0; i < ddIdx.length; i++) {
const index = ddIdx[i];
for (let j = 0; j < 4; j++) {
board.zz[index * 4 + j] = board.nz[index * 4 + j] = serialized.zz[i * 4 + j];
board.bb[index * 4 + j] = serialized.bb[i * 4 + j];
board.cc[index * 4 + j] = cc[index * 4 + j];
}
if (!isFinite(cc[index * 4 + 3])) {
board.initAsDDPrecision(index, cc);
}
board.pp[index] = serialized.pp[i];
}
for (let i = 0; i < serialized.pertIndexes.length; i++) {
const index = serialized.pertIndexes[i];
for (let j = 0; j < 3; j++) {
board.zz[index * 4 + j] = serialized.pertZZ[i * 3 + j];
board.cc[index * 4 + j] = cc[index * 4 + j];
}
board.zz[index * 4 + 3] = board.cc[index * 4 + 3] = Infinity;
board.pp[index] = 0;
}
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()),
ddIndexes: this.ddIndexes,
pertIndexes: this.pertIndexes,
zz: this.ddIndexes.flatMap(i =>
[this.zz[i*4], this.zz[i*4+1], this.zz[i*4+2], this.zz[i*4+3]]),
bb: this.ddIndexes.flatMap(i =>
[this.bb[i*4], this.bb[i*4+1], this.bb[i*4+2], this.bb[i*4+3]]),
pp: this.ddIndexes.map(index => this.pp[index]),
pertZZ: this.pertIndexes.flatMap(i => [this.zz[i*4], this.zz[i*4+1], this.zz[i*4+2]]),
completedIndexes,
completedNn,
};
}
iterate() {
let changes = null;
let results = [0, 0, 0];
// Precompute DD precision point escape without updating z
// Update checkpoints at Fibonacci intervals
const isCheckpoint = fibonacciPeriod(this.it) === 1;
for (const index of this.ddIndexes) {
if (isCheckpoint && !this.nn[index]) {
ArddcCopy(this.bb, index*4, this.zz, index*4); // bb = checkpoint z
this.pp[index] = 0; // Reset pp (period = iter when convergence first detected)
}
let r = this.precomputeDD(index);
results[r + 1] += 1;
if (r !== 0) {
if (!changes) {
changes = { iter: this.it, nn: [], vv: [] };
}
if (r < 0) {
changes.vv.push({
index: index,
z: ArddcGet(this.nz, index*4), // DDc format
p: this.pp[index] // period
});
} else {
changes.nn.push(index);
}
}
}
// Iterate perturbation points that use the old z
const newDDIndexes = [];
let cache = { refIndex: null, binZpow: [] };
for (const index of this.pertIndexes) {
if (!this.computePerturbation(index, cache)) {
this.convertToDDPrecision(index);
let r = this.precomputeDD(index);
results[r + 1] += 1;
newDDIndexes.push(index);
if (r !== 0) {
if (!changes) {
changes = { iter: this.it, nn: [], vv: [] };
}
if (r < 0) {
changes.vv.push({
index: index,
z: ArddcGet(this.nz, index*4), // DDc format
p: this.pp[index] // period
});
} else {
changes.nn.push(index);
}
}
}
}
// Update index arrays
if (newDDIndexes.length > 0) {
const newPertIndexes = [];
let qi = 0;
for (const index of this.pertIndexes) {
if (newDDIndexes[qi] == index) {
qi += 1;
} else {
newPertIndexes.push(index);
}
}
this.ddIndexes = this.ddIndexes.concat(newDDIndexes);
this.pertIndexes = newPertIndexes;
}
// Finally update DD precision z with precomputed values
for (const index of this.ddIndexes) {
ArddcCopy(this.zz, index*4, this.nz, index*4);
}
// Tally progress
let diverged = results[2];
let count = results[0] + diverged;
this.un -= count;
this.di += diverged;
// Trim finished pixels from array.
if (this.pertIndexes.length + this.ddIndexes.length > this.un * 1.25) {
this.compact();
// Switch to full DD when perturbations are a small fraction of the work
if (this.pertIndexes.length < this.ddIndexes.length * 0.5) {
for (const index of this.pertIndexes) {
this.convertToDDPrecision(index);
this.ddIndexes.push(index);
}
this.pertIndexes = [];
}
}
this.it++;
this.queueChanges(changes);
}
compact() {
const trimmedDDIndexes = this.ddIndexes.filter(i => !this.nn[i]);
this.ddIndexes = trimmedDDIndexes;
}
precomputeDD(m) {
// DD precision Mandelbrot iteration with convergence detection
if (this.nn[m]) return 0;
const m4 = m * 4;
const tt = this.tt;
const nz = this.nz;
const r1 = this.zz[m4];
const r2 = this.zz[m4+1];
const j1 = this.zz[m4+2];
const j2 = this.zz[m4+3];
const cr1 = this.cc[m4];
const cr2 = this.cc[m4+1];
const cj1 = this.cc[m4+2];
const cj2 = this.cc[m4+3];
const br1 = this.bb[m4]; // bb = checkpoint z (DD precision)
const br2 = this.bb[m4+1];
const bj1 = this.bb[m4+2];
const bj2 = this.bb[m4+3];
ArddSquare(tt, 0, r1, r2); // 0: rsq = r**2
ArddSquare(tt, 2, j1, j2); // 2: jsq = j**2
ArddAdd(tt, 4, tt[0], tt[1], tt[2], tt[3]); // 4: d = rsq+jsq
if (tt[4] > 4) { // Check divergence: |z|² > 4
this.nn[m] = this.it;
ArddcCopy(nz, m4, this.zz, m4);
return 1; // Diverged
}
ArddMul(tt, 6, 2 * r1, 2 * r2, j1, j2); // 6: ja = 2*r*j
ArddAdd(tt, 8, tt[0], tt[1], -tt[2], -tt[3]); // 8: ra = rsq-jsq
for (let ord = 2; ord < this.config.exponent; ord++) {
ArddMul(tt, 0, j1, j2, tt[6], tt[7]); // 0: j * ja
ArddMul(tt, 2, r1, r2, tt[8], tt[9]); // 2: r * ra
ArddAdd(tt, 4, -tt[0], -tt[1], tt[2], tt[3]); // 4: rt = r*ra - j*ja
ArddMul(tt, 0, r1, r2, tt[6], tt[7]); // 0: r * ja
ArddMul(tt, 2, j1, j2, tt[8], tt[9]); // 2: j * ra
ArddAdd(tt, 6, tt[0], tt[1], tt[2], tt[3]); // 6: ja = r*ja + j*ra
ArddSet(tt, 8, tt[4], tt[5]); // 8: ra = rt
}
ArddAdd(nz, m4, tt[8], tt[9], cr1, cr2); // nz: nzr = ra + cr
ArddAdd(nz, m4+2, tt[6], tt[7], cj1, cj2); // nz+2: nzj = ja + cj
// Check convergence: compare new z to checkpoint
ArddAbsSub(tt, 0, br1, br2, nz[m4], nz[m4+1]); // 0: abs(nzr - br)
ArddAbsSub(tt, 2, bj1, bj2, nz[m4+2], nz[m4+3]);// 2: abs(nzj - bj)
ArddAdd(tt, 4, tt[0], tt[1], tt[2], tt[3]); // 4: db = abs(nzr-br)+abs(nzj-bj)
const db = tt[4] + tt[5] // distance from checkpoint
if (db <= this.epsilon2) {
if (!this.pp[m]) { this.pp[m] = this.it; } // Record iter when first detected
if (db <= this.epsilon) {
this.nn[m] = -this.it;
if (this.inspikeDDA(cr1, cr2, cj1, cj2) && this.ch > 0) {
this.ch -= 1;
}
return -1; // Converged
}
}
return 0; // Continue iterating
}
computePerturbation(index, cache) {
const m4 = index * 4;
const cr = this.cc[m4]
const ci = this.cc[m4+1]
const refIndex = this.cc[m4+2]
const ri4 = refIndex * 4;
const dr = this.zz[m4];
const di = this.zz[m4+1];
// Switch to quad when approaching convergence.
if (this.nn[refIndex] || this.pp[refIndex]) return false;
// Compute binomial powers of z
if (cache.refIndex !== refIndex) {
cache.refIndex = refIndex;
const ri4 = refIndex * 4;
const zr = this.zz[ri4];
const zi = this.zz[ri4+2];
this.fillBinZpow(cache.binZpow, zr, zi);
}
const binZpow = cache.binZpow;
// Compute in (z+d)^n - z^n = nz^(n-1) d + (n(n-1)/2)z^(n-2) d^2...
let r = dr;
let i = di;
for (let ord = 0; ord < binZpow.length; ord += 2) {
r += binZpow[ord];
i += binZpow[ord+1];
const rNew = r * dr - i * di;
i = r * di + i * dr;
r = rNew;
}
// Add perturbation in c
r += cr;
i += ci;
if (this.isThresholdExceeded(r, i, refIndex)) {
return false;
}
this.zz[m4] = r;
this.zz[m4+1] = i;
return true;
}
fillBinZpow(binZpow, zr, zi) {
let zrCurrent = zr, ziCurrent = zi;
let coeff = this.config.exponent;
for (let k = 1; k < this.config.exponent - 1; k++) {
binZpow[k*2-2] = coeff * zrCurrent;
binZpow[k*2-1] = coeff * ziCurrent;
// Update z power
const zrNew = zrCurrent * zr - ziCurrent * zi;
ziCurrent = zrCurrent * zi + ziCurrent * zr;
zrCurrent = zrNew;
// Update coefficient for next iteration
coeff *= (this.config.exponent - k) / (k + 1);
}
// Add the last element without computing the next z power or coefficient
if (this.config.exponent > 1) {
binZpow[this.config.exponent*2 - 4] = coeff * zrCurrent;
binZpow[this.config.exponent*2 - 3] = coeff * ziCurrent;
}
}
isThresholdExceeded(dr, di, refIndex) {
const mag = Math.max(Math.abs(dr), Math.abs(di));
if (mag > this.perturbationThreshold) return true;
// If orbit is getting large, then be more careful.
if (mag * 10 < this.perturbationThreshold) return false;
const zr = this.zz[refIndex * 4];
const zi = this.zz[refIndex * 4 + 2];
return ((dr + zr) ** 2 + (di + zi) ** 2 > 3);
}
convertToDDPrecision(index) {
const m4 = index * 4;
const dr = this.zz[m4];
const di = this.zz[m4+1];
const cr = this.cc[m4];
const ci = this.cc[m4+1];
const refIndex = this.cc[m4+2];
const ri4 = refIndex * 4;
ArddAdd(this.zz, m4, dr, 0, this.zz[ri4], this.zz[ri4+1])
ArddAdd(this.zz, m4+2, di, 0, this.zz[ri4+2], this.zz[ri4+3])
ArddAdd(this.cc, m4, cr, 0, this.cc[ri4], this.cc[ri4+1])
ArddAdd(this.cc, m4+2, ci, 0, this.cc[ri4+2], this.cc[ri4+3])
}
initAsDDPrecision(index, refcc) {
const m4 = index * 4;
const cr = this.cc[m4];
const ci = this.cc[m4+1];
const refIndex = this.cc[m4+2];
const ri4 = refIndex * 4;
ArddAdd(this.cc, m4, cr, 0, refcc[ri4], refcc[ri4+1])
ArddAdd(this.cc, m4+2, ci, 0, refcc[ri4+2], refcc[ri4+3])
}
}
// QD-precision CPU board using perturbation theory (quad-double anchors)
class QDPerturbationBoard extends Board {
constructor(k, size, re, im, config, id) {
super(k, size, re, im, config, id);
this.qdIndexes = []; // Pixels computed in QD precision
this.tt = new Array(32).fill(0); // Working array for QD operations
this.effort = 4; // Higher cost than quad perturbation
this.initQDBoard(size, re, im);
}
initQDBoard(size, re, im) {
const dimsArea = this.config.dimsArea;
this.cc = new Array(dimsArea * 8).fill(0);
this.zz = new Array(dimsArea * 8).fill(0);
this.bb = new Array(dimsArea * 8).fill(0);
this.ss = Array.from({length: dimsArea}, (_, i) => i);
this.nn = new Array(dimsArea).fill(0);
this.pp = new Array(dimsArea).fill(0);
this.un = dimsArea;
this.di = 0;
const re_o = Array.isArray(re) && re.length === 4 ? re : [re, 0, 0, 0];
const im_o = Array.isArray(im) && im.length === 4 ? im : [im, 0, 0, 0];
for (let y = 0; y < this.config.dimsHeight; y++) {
const jFrac = (0.5 - (y / this.config.dimsHeight));
const cj = toQDAdd(im_o, toQDScale(toQD(jFrac), size / this.config.aspectRatio));
for (let x = 0; x < this.config.dimsWidth; x++) {
const rFrac = ((x / this.config.dimsWidth) - 0.5);
const cr = toQDAdd(re_o, toQDScale(toQD(rFrac), size));
const idx = y * this.config.dimsWidth + x;
const m8 = idx * 8;
this.cc[m8] = cr[0]; this.cc[m8+1] = cr[1];
this.cc[m8+2] = cr[2]; this.cc[m8+3] = cr[3];
this.cc[m8+4] = cj[0]; this.cc[m8+5] = cj[1];
this.cc[m8+6] = cj[2]; this.cc[m8+7] = cj[3];
this.zz[m8] = cr[0]; this.zz[m8+1] = cr[1];
this.zz[m8+2] = cr[2]; this.zz[m8+3] = cr[3];
this.zz[m8+4] = cj[0]; this.zz[m8+5] = cj[1];
this.zz[m8+6] = cj[2]; this.zz[m8+7] = cj[3];
this.bb[m8] = cr[0]; this.bb[m8+1] = cr[1];
this.bb[m8+2] = cr[2]; this.bb[m8+3] = cr[3];
this.bb[m8+4] = cj[0]; this.bb[m8+5] = cj[1];
this.bb[m8+6] = cj[2]; this.bb[m8+7] = cj[3];
this.qdIndexes.push(idx);
if (this.inspikeDDA(cr[0], cr[1], cj[0], cj[1])) {
this.ch += 1;
}
}
}
}
static fromSerialized(serialized) {
const board = new QDPerturbationBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
const cc = board.cc;
// 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 arrays from serialized data (8 floats per pixel for QD)
board.cc = [];
board.zz = [];
board.bb = [];
board.pp = [];
const qdIdx = serialized.qdIndexes || [];
for (let i = 0; i < qdIdx.length; i++) {
const index = qdIdx[i];
for (let j = 0; j < 8; j++) {
board.zz[index * 8 + j] = serialized.zz[i * 8 + j];
board.bb[index * 8 + j] = serialized.bb[i * 8 + j];
board.cc[index * 8 + j] = cc[index * 8 + j];
}
board.pp[index] = serialized.pp[i];
}
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()),
qdIndexes: this.qdIndexes,
zz: this.qdIndexes.flatMap(i => this.zz.slice(i*8, i*8+8)),
bb: this.qdIndexes.flatMap(i => this.bb.slice(i*8, i*8+8)),
pp: this.qdIndexes.map(index => this.pp[index]),
completedIndexes,
completedNn,
};
}
initAsQDPrecision(index, refcc) {
const m8 = index * 8;
for (let j = 0; j < 4; j++) {
this.cc[m8 + j] = refcc[m8 + j];
this.cc[m8 + 4 + j] = refcc[m8 + 4 + j];
}
}
iterate() {
let changes = null;
const s = this.ss;
const isCheckpoint = fibonacciPeriod(this.it) === 1;
if (isCheckpoint) {
for (let t = 0; t < s.length; ++t) {
const m = s[t];
if (this.nn[m]) continue;
ArqdcCopy(this.bb, m*8, this.zz, m*8); // bb = checkpoint z position
this.pp[m] = 0; // Reset pp
}
}
for (let t = 0; t < s.length; ++t) {
const index = s[t];
const result = this.compute(index);
if (result !== 0) {
if (!changes) {
changes = { iter: this.it, nn: [], vv: [] };
}
if (result < 0) {
changes.vv.push({
index: index,
z: ArqdcGet(this.zz, index*8),
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) {
throw new Error(`excess ss ${s.length}, ${this.ss.length}, ${this.un}`);
}
}
this.it++;
this.queueChanges(changes);
}
compact() {
this.ss = this.ss.filter(i => !this.nn[i]);
}
compute(m) {
if (this.nn[m]) return 0;
const m8 = m * 8;
const tt = this.tt;
const r1 = this.zz[m8];
const r2 = this.zz[m8+1];
const r3 = this.zz[m8+2];
const r4 = this.zz[m8+3];
const j1 = this.zz[m8+4];
const j2 = this.zz[m8+5];
const j3 = this.zz[m8+6];
const j4 = this.zz[m8+7];
const cr1 = this.cc[m8];
const cr2 = this.cc[m8+1];
const cr3 = this.cc[m8+2];
const cr4 = this.cc[m8+3];
const cj1 = this.cc[m8+4];
const cj2 = this.cc[m8+5];
const cj3 = this.cc[m8+6];
const cj4 = this.cc[m8+7];
ArqdSquare(tt, 0, r1, r2, r3, r4);
ArqdSquare(tt, 4, j1, j2, j3, j4);
ArqdAdd(tt, 8, tt[0], tt[1], tt[2], tt[3], tt[4], tt[5], tt[6], tt[7]);
if (tt[8] > 4) {
this.nn[m] = this.it;
return 1; // Diverged
}
ArqdMul(tt, 12, 2 * r1, 2 * r2, 2 * r3, 2 * r4, j1, j2, j3, j4);
ArqdAdd(tt, 20, tt[0], tt[1], tt[2], tt[3], -tt[4], -tt[5], -tt[6], -tt[7]);
for (let ord = 2; ord < this.config.exponent; ord++) {
ArqdMul(tt, 0, j1, j2, j3, j4, tt[12], tt[13], tt[14], tt[15]);
ArqdMul(tt, 4, r1, r2, r3, r4, tt[20], tt[21], tt[22], tt[23]);
ArqdAdd(tt, 8, -tt[0], -tt[1], -tt[2], -tt[3], tt[4], tt[5], tt[6], tt[7]);
ArqdMul(tt, 0, r1, r2, r3, r4, tt[12], tt[13], tt[14], tt[15]);
ArqdMul(tt, 4, j1, j2, j3, j4, tt[20], tt[21], tt[22], tt[23]);
ArqdAdd(tt, 12, tt[0], tt[1], tt[2], tt[3], tt[4], tt[5], tt[6], tt[7]);
ArqdSet(tt, 20, tt[8], tt[9], tt[10], tt[11]);
}
ArqdAdd(this.zz, m8, tt[20], tt[21], tt[22], tt[23], cr1, cr2, cr3, cr4);
ArqdAdd(this.zz, m8+4, tt[12], tt[13], tt[14], tt[15], cj1, cj2, cj3, cj4);
// Check convergence: compare current z to checkpoint
const br1 = this.bb[m8];
const br2 = this.bb[m8+1];
const bj1 = this.bb[m8+4];
const bj2 = this.bb[m8+5];
ArqdAbsSub(tt, 0, br1, br2, this.zz[m8], this.zz[m8+1]);
ArqdAbsSub(tt, 4, bj1, bj2, this.zz[m8+4], this.zz[m8+5]);
ArqdAdd(tt, 8, tt[0], tt[1], tt[2], tt[3], tt[4], tt[5], tt[6], tt[7]);
const db = tt[8] + tt[9];
if (db <= this.epsilon2) {
if (!this.pp[m]) { this.pp[m] = this.it; }
if (db <= this.epsilon) {
this.nn[m] = -this.it;
if (this.inspikeDDA(cr1, cr2, cj1, cj2) && this.ch > 0) {
this.ch -= 1;
}
return -1; // Converged
}
}
return 0;
}
}
// 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
const zr = toDDAdd([ref[0], ref[1]], dzr);
const zi = toDDAdd([ref[2], ref[3]], dzi);
return [zr[0], zr[1], zi[0], zi[1]];
}
// 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 AdaptiveGpuBoard (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
const zrQD = toQDAdd([ref[0], ref[1], ref[2], ref[3]], [dzr, 0, 0, 0]);
const ziQD = toQDAdd([ref[4], ref[5], ref[6], ref[7]], [dzi, 0, 0, 0]);
return [...zrQD, ...ziQD];
}
// 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) {
super(k, size, re, im, config, id);
// 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 = 2; // Effort level for scheduling
}
// 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 (precision-specific)
initPixels() { throw new Error('Abstract method'); }
// Shared iterate() method - works for both DD and QD
iterate() {
let changes = null;
// Step 1: Extend reference orbit if needed and not escaped
const targetRefIterations = Math.max(this.it + 100, this.maxRefIter + 100);
while (!this.refOrbitEscaped && this.refIterations < targetRefIterations) {
this.extendReferenceOrbit();
}
// 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]);
}
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));
if (db <= this.epsilon2) {
if (!this.pp[index]) {
this.pp[index] = this.it - 1;
}
if (db <= this.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) {
super(k, size, re, im, config, id);
// 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();
}
initPixels() {
const sizeScalar = this.size;
const reDD = qdToDD(this.re);
const imDD = qdToDD(this.im);
const pixW = sizeScalar / this.config.dimsWidth;
const pixH = (sizeScalar / this.config.aspectRatio) / this.config.dimsHeight;
const dimsWidth = this.config.dimsWidth;
const dimsHeight = this.config.dimsHeight;
const refRe = this.refC[0] + this.refC[1];
const refIm = this.refC[2] + this.refC[3];
// Convert DD precision arrays to doubles for perturbation deltas
const re_double = reDD[0] + reDD[1];
const im_double = imDD[0] + imDD[1];
// Initialize all pixels as perturbations from the reference point
for (let y = 0; y < dimsHeight; y++) {
const yFrac = (0.5 - y / dimsHeight);
const ci = im_double + yFrac * (sizeScalar / this.config.aspectRatio);
const dci = ci - refIm;
for (let x = 0; x < dimsWidth; x++) {
const xFrac = (x / dimsWidth - 0.5);
const cr = re_double + xFrac * sizeScalar;
const dcr = cr - refRe;
const index = y * dimsWidth + x;
this.dc[index * 2] = dcr;
this.dc[index * 2 + 1] = dci;
// Start with z = c (skipping trivial first iteration where 0^2+c=c)
// At refIter=1 where refOrbit[1] = c_ref, with dz = dc: z = c_ref + dc = c
this.dz[index * 2] = dcr;
this.dz[index * 2 + 1] = dci;
this.refIter[index] = 1; // Start at iteration 1 (z = c)
this.pixelIndexes.push(index);
if (this.inspike(cr, ci)) {
this.ch += 1;
}
}
}
}
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) {
super(k, size, re, im, config, id);
// 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();
}
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
const refRe = this.refC_qd[0] + this.refC_qd[1] + this.refC_qd[2] + this.refC_qd[3];
const refIm = this.refC_qd[4] + this.refC_qd[5] + this.refC_qd[6] + this.refC_qd[7];
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;
this.pixelIndexes.push(index);
// Count spike pixels
const cr = refRe + dcr;
const ci = refIm + dci;
if (this.inspike(cr, ci)) {
this.ch += 1;
}
}
}
}
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) {
super(k, size, re, im, config, id);
// 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.selfBatching = true; // GPU boards handle batching internally
}
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 {
// Check WebGPU availability
if (!navigator.gpu) {
console.warn('WebGPU not supported');
return false;
}
// Request adapter and device
const adapter = await navigator.gpu.requestAdapter();
if (!adapter) {
console.warn('No WebGPU adapter found');
return false;
}
// 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;
}
// Subclass-specific initialization
await this.createComputePipeline();
await this.createBuffers();
this.createBindGroup();
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() {
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();
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 {
const adapter = await navigator.gpu.requestAdapter();
if (!adapter) return GpuBaseBoard.GPU_DEFAULT_MAX_BUFFER;
// Request device with higher limits if supported
const requiredLimits = {};
if (adapter.limits.maxStorageBufferBindingSize > 134217728) {
requiredLimits.maxStorageBufferBindingSize = adapter.limits.maxStorageBufferBindingSize;
}
if (adapter.limits.maxBufferSize > 134217728) {
requiredLimits.maxBufferSize = adapter.limits.maxBufferSize;
}
const device = await adapter.requestDevice({
requiredLimits: Object.keys(requiredLimits).length > 0 ? requiredLimits : undefined
});
const limit = Math.min(
device.limits.maxBufferSize,
device.limits.maxStorageBufferBindingSize);
GpuBaseBoard.cachedMaxBufferSize = Math.floor(limit * 0.9); // 90% for safety
return GpuBaseBoard.cachedMaxBufferSize;
} catch (e) {
GpuBaseBoard.cachedMaxBufferSize = GpuBaseBoard.GPU_DEFAULT_MAX_BUFFER;
return GpuBaseBoard.cachedMaxBufferSize;
}
}
// 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.
* Subclasses must have created buffers.pixels and buffers.stagingPixels.
* Uses a lock to prevent concurrent mapAsync calls.
* @returns {Promise<ArrayBuffer>} The pixel buffer data
*/
async readPixelBuffer() {
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 staging buffer if not present
if (!this.buffers.stagingPixels) {
this.buffers.stagingPixels = this.device.createBuffer({
size: bufferSize,
usage: GPUBufferUsage.MAP_READ | GPUBufferUsage.COPY_DST,
label: 'Staging pixels buffer (serialization)'
});
}
// Copy pixels buffer to staging
const commandEncoder = this.device.createCommandEncoder();
commandEncoder.copyBufferToBuffer(
this.buffers.pixels, 0, this.buffers.stagingPixels, 0, bufferSize);
this.device.queue.submit([commandEncoder.finish()]);
await this.device.queue.onSubmittedWorkDone();
// Read back the data
await this.buffers.stagingPixels.mapAsync(GPUMapMode.READ);
const pixelData = new ArrayBuffer(bufferSize);
const srcData = this.buffers.stagingPixels.getMappedRange();
new Uint8Array(pixelData).set(new Uint8Array(srcData));
this.buffers.stagingPixels.unmap();
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.
class GpuBoard extends GpuBaseBoard {
static BYTES_PER_PIXEL = 28; // 3 u32 + 4 f32 (consolidated PixelState struct)
constructor(k, size, re, im, config, id) {
super(k, size, re, im, config, id);
this.effort = 1;
// Epsilon values for convergence detection scale with pixel size
const pix = this.pixelSize;
// GPU uses float32 precision, so thresholds must be larger than CPU's float64
this.epsilon = Math.min(1e-7, pix / 10); // Final convergence threshold
this.epsilon2 = Math.min(1e-5, pix * 10); // Getting close threshold
this.checkSpike(size, re, im);
// Start GPU initialization (async)
this.gpuInitPromise = this.initGPU();
}
async createComputePipeline() {
// Mandelbrot shader with period detection for convergence
// Consolidated 3-binding layout: params, pixels (PixelState struct), active_pixels
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,
ckpt0: u32,
ckpt1: u32,
ckpt2: u32,
ckpt3: u32,
ckpt4: u32,
ckpt5: u32,
ckpt6: u32,
ckpt7: u32,
}
// Per-pixel state: 3 u32 + 4 f32 = 28 bytes
// Layout (u32 view):
// [0] iter: u32
// [1] status: u32
// [2] period: u32
// [3] zr: f32
// [4] zi: f32
// [5] base_r: f32
// [6] base_i: f32
struct PixelState {
iter: u32,
status: u32,
period: u32,
zr: f32,
zi: f32,
base_r: f32,
base_i: f32,
}
@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> active_pixels: array<u32>;
@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
// 2D dispatch: calculate linear index from 2D coordinates
let active_idx = global_id.y * params.workgroups_x + global_id.x;
if (active_idx >= params.active_count) {
return;
}
let index = active_pixels[active_idx];
let x = index % params.dims_width;
let y = index / params.dims_width;
// Compute c for this pixel
// Use integer arithmetic to avoid float32 rounding: (coord - dims/2) / dims
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);
// Load pixel state
var zr = pixels[index].zr;
var zi = pixels[index].zi;
var iter = pixels[index].iter;
var base_r = pixels[index].base_r;
var base_i = pixels[index].base_i;
var p = pixels[index].period;
// If this is the first batch and base is still zero, initialize it
if (iter == 0u && base_r == 0.0 && base_i == 0.0) {
base_r = zr; // Initialize to starting z (which is 0,0)
base_i = zi;
}
// Track next checkpoint using O(1) counter for adaptive Fibonacci checkpoints
var next_checkpoint_idx = 0u;
// Iterate for this batch
for (var i = 0u; i < params.iterations_per_batch; i++) {
// Check if this iteration is a Fibonacci checkpoint
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; }
default: {}
}
if (i == checkpoint_offset) {
base_r = zr;
base_i = zi;
p = 0u; // Reset p (period = iter when convergence first detected)
next_checkpoint_idx++;
}
}
let zr2 = zr * zr;
let zi2 = zi * zi;
let mag_sq = zr2 + zi2;
// Check divergence (escape radius 2, or NaN/Infinity from numerical errors)
if (mag_sq > 4.0 || !(mag_sq <= 1e38)) { // NaN/Inf check: !(x <= large) catches both
pixels[index].status = 1u; // Diverged
break;
}
// z = z^exponent + c (generalized Mandelbrot)
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;
// Check convergence: compare new z to checkpoint
let dr = zr - base_r;
let di = zi - base_i;
let db = abs(dr) + abs(di); // distance from checkpoint
if (db <= params.epsilon2) {
if (p == 0u) {
p = iter; // Record iter when convergence first detected
}
if (db <= params.epsilon) {
pixels[index].status = 2u; // Converged (periodic)
break;
}
}
iter++;
}
// Save state
pixels[index].zr = zr;
pixels[index].zi = zi;
pixels[index].base_r = base_r;
pixels[index].base_i = base_i;
pixels[index].iter = iter;
pixels[index].period = p;
}
`;
const shaderModule = this.device.createShaderModule({
code: shaderCode,
label: 'Mandelbrot compute shader'
});
this.pipeline = this.device.createComputePipeline({
layout: 'auto',
compute: {
module: shaderModule,
entryPoint: 'main'
},
label: 'Mandelbrot compute pipeline'
});
}
async createBuffers() {
const dimsArea = this.config.dimsWidth * this.config.dimsHeight;
// Check buffer size limits before creating (safety margin applied upstream)
const maxBufferSize = Math.min(
this.device.limits.maxBufferSize,
this.device.limits.maxStorageBufferBindingSize
);
// PixelState struct: 3 u32 + 4 f32 = 28 bytes per pixel
const BYTES_PER_PIXEL = 28;
const pixelBufferSize = dimsArea * 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.`);
}
// Uniform buffer for shader parameters
this.buffers.params = this.device.createBuffer({
size: 128,
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Parameters buffer'
});
// Consolidated pixel state buffer
// (PixelState struct: iter, status, period, zr, zi, base_r, base_i)
this.buffers.pixels = this.device.createBuffer({
size: pixelBufferSize,
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_SRC | GPUBufferUsage.COPY_DST,
label: 'Pixel state buffer'
});
// Storage buffer for active pixel indices (sparse list, max size = dimsArea)
this.buffers.activePixels = this.device.createBuffer({
size: dimsArea * 4, // 4 bytes per u32
usage: GPUBufferUsage.STORAGE | GPUBufferUsage.COPY_DST,
label: 'Active pixels buffer'
});
// Staging buffer for reading pixel state back to CPU
this.buffers.stagingPixels = this.device.createBuffer({
size: pixelBufferSize,
usage: GPUBufferUsage.MAP_READ | GPUBufferUsage.COPY_DST,
label: 'Staging pixels buffer'
});
// Initialize pixel state buffer using overlapping typed array views
// PixelState struct layout: [iter(u32), status(u32), period(u32),
// zr(f32), zi(f32), base_r(f32), base_i(f32)]
const pixelData = new ArrayBuffer(pixelBufferSize);
const pixelU32 = new Uint32Array(pixelData);
const pixelF32 = new Float32Array(pixelData);
for (let i = 0; i < dimsArea; i++) {
const idx7 = i * 7; // 7 x 4-byte values per pixel
// Integer fields (offsets 0-2)
pixelU32[idx7 + 0] = 0; // iter
pixelU32[idx7 + 1] = 0; // status (0 = computing)
pixelU32[idx7 + 2] = 0; // period
// Float fields (offsets 3-6)
pixelF32[idx7 + 3] = 0; // zr
pixelF32[idx7 + 4] = 0; // zi
pixelF32[idx7 + 5] = 0; // base_r
pixelF32[idx7 + 6] = 0; // base_i
}
this.device.queue.writeBuffer(this.buffers.pixels, 0, pixelData);
// Initialize active pixels list (all pixels start active)
const activePixels = new Uint32Array(dimsArea);
for (let i = 0; i < dimsArea; i++) {
activePixels[i] = i;
}
this.device.queue.writeBuffer(this.buffers.activePixels, 0, activePixels);
}
createBindGroup() {
// Consolidated 3-binding layout
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.activePixels } }
],
label: 'Mandelbrot bind group'
});
}
async compute() {
// Prevent concurrent compute() calls
if (this.isComputing) {
return;
}
this.isComputing = true;
try {
const dimsArea = this.config.dimsWidth * this.config.dimsHeight;
const workgroupSize = 64;
const BYTES_PER_PIXEL = 28; // 7 x 4-byte values per pixel
// Prepare parameters for GPU
const re_double = qdToNumber(this.re);
const im_double = qdToNumber(this.im);
const pixel_size = this.size;
// Initialize CPU-side status tracking if needed
if (!this.cpuStatus) {
this.cpuStatus = new Uint32Array(dimsArea).fill(0); // 0 = computing
}
// Build sparse active pixel list (only pixels still computing)
const activePixels = [];
for (let i = 0; i < dimsArea; i++) {
if (this.cpuStatus[i] === 0) {
activePixels.push(i);
}
}
const activeCount = activePixels.length;
if (activeCount === 0) {
this.un = 0;
return;
}
// Dynamic batch sizing: scale iterations inversely with active pixels
const targetWork = 333337; // Prime, reduced for better responsiveness
// Check for step mode debug flag 's'
const stepMode = hasDebugFlag(this.config, 's');
let iterationsPerBatch = stepMode ? 1 : Math.floor(targetWork / Math.max(activeCount, 1));
// Clamp to reasonable bounds (min 17) unless in step mode
if (!stepMode) {
iterationsPerBatch = Math.max(17, iterationsPerBatch);
}
// Update effort for scheduler (reflects actual iterations per call)
this.effort = iterationsPerBatch;
// Upload active pixel list to GPU
const activePixelsData = new Uint32Array(activePixels);
this.device.queue.writeBuffer(this.buffers.activePixels, 0, activePixelsData);
// 2D workgroup dispatch
const numWorkgroups = Math.ceil(activeCount / workgroupSize);
const workgroupsX = Math.ceil(Math.sqrt(numWorkgroups));
const workgroupsY = Math.ceil(numWorkgroups / workgroupsX);
// Precompute Fibonacci checkpoint offsets for this batch
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, 8);
// Upload parameters to uniform buffer
const paramsBuffer = new ArrayBuffer(128);
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] = activeCount;
paramsF32[8] = this.epsilon;
paramsF32[9] = this.epsilon2;
paramsU32[10] = this.config.exponent;
paramsU32[11] = workgroupsX * workgroupSize; // Total threads in X dimension
paramsU32[12] = bufferIter; // Starting iteration
paramsU32[13] = checkpointCount; // Number of checkpoints in this batch
// Pack all 8 checkpoint offsets (fill unused slots with 0)
for (let i = 0; i < 8; i++) {
paramsU32[14 + i] = i < checkpointCount ? checkpointOffsets[i] : 0;
}
this.device.queue.writeBuffer(this.buffers.params, 0, paramsBuffer);
// Create command encoder
const commandEncoder = this.device.createCommandEncoder({
label: 'Mandelbrot compute encoder'
});
// Compute pass
const passEncoder = commandEncoder.beginComputePass({
label: 'Mandelbrot compute pass'
});
passEncoder.setPipeline(this.pipeline);
passEncoder.setBindGroup(0, this.bindGroup);
passEncoder.dispatchWorkgroups(workgroupsX, workgroupsY); // 2D dispatch
passEncoder.end();
// Copy consolidated pixel buffer to staging
commandEncoder.copyBufferToBuffer(
this.buffers.pixels, 0, this.buffers.stagingPixels, 0, dimsArea * BYTES_PER_PIXEL);
// Submit compute + buffer copy in single batch
this.device.queue.submit([commandEncoder.finish()]);
await this.device.queue.onSubmittedWorkDone();
// Update iteration counter (before processing results, like CPU implementations)
this.it += iterationsPerBatch;
// Read consolidated pixel state buffer
await this.buffers.stagingPixels.mapAsync(GPUMapMode.READ);
const pixelData = new ArrayBuffer(dimsArea * BYTES_PER_PIXEL);
const srcData = this.buffers.stagingPixels.getMappedRange();
new Uint8Array(pixelData).set(new Uint8Array(srcData));
this.buffers.stagingPixels.unmap();
// Create typed array views for reading pixel state
const pixelU32 = new Uint32Array(pixelData);
const pixelF32 = new Float32Array(pixelData);
// Initialize lastReportedIters if needed
if (!this.lastReportedIters) {
this.lastReportedIters = new Uint32Array(dimsArea).fill(0);
}
// Find pixels that NEWLY diverged or converged this batch
const pixelsByIteration = new Map(); // For diverged: iter -> [indices]
const convergedByIteration = new Map(); // For converged: iter -> [{index, z, p}]
for (const i of activePixels) {
const idx7 = i * 7;
const iters = pixelU32[idx7 + 0]; // iter
const status = pixelU32[idx7 + 1]; // status
const period = pixelU32[idx7 + 2]; // period
const zr = pixelF32[idx7 + 3]; // zr
const zi = pixelF32[idx7 + 4]; // zi
const lastIters = this.lastReportedIters[i];
// Update CPU-side status tracking
this.cpuStatus[i] = status;
if (status === 1) {
// Diverged - newly diverged in this batch?
if (lastIters === 0 || iters !== lastIters) {
this.nn[i] = iters;
this.pp[i] = 1;
if (!pixelsByIteration.has(iters)) {
pixelsByIteration.set(iters, []);
}
pixelsByIteration.get(iters).push(i);
this.lastReportedIters[i] = iters;
// Decrement ch if this pixel was in the spike
if (this.inSpike && this.inSpike[i] && this.ch > 0) {
this.ch -= 1;
}
}
} else if (status === 2) {
// Converged - newly converged in this batch?
if (lastIters === 0 || iters !== lastIters) {
this.nn[i] = -iters; // Negative iteration for converged pixels
// Add 1 because GPU shader increments iter before setting checkpoint,
// so period value is 1 less than what CPU board would store
this.pp[i] = period + 1;
if (!convergedByIteration.has(iters)) {
convergedByIteration.set(iters, []);
}
convergedByIteration.get(iters).push({
index: i,
z: [zr, zi], // float64 pair
p: this.pp[i]
});
this.lastReportedIters[i] = iters;
// Decrement ch if this pixel was in the spike
if (this.inSpike && this.inSpike[i] && this.ch > 0) {
this.ch -= 1;
}
}
}
}
// Count total finished pixels across entire grid (for statistics)
let totalDiverged = 0;
let totalConverged = 0;
let stillComputing = 0;
for (let i = 0; i < dimsArea; i++) {
const status = this.cpuStatus[i];
if (status === 1) totalDiverged++;
else if (status === 2) totalConverged++;
else stillComputing++;
}
// Create change objects for newly diverged and converged pixels
const allIterations = new Set([...pixelsByIteration.keys(),
...convergedByIteration.keys()]);
const sortedIterations = Array.from(allIterations).sort((a, b) => a - b);
let totalChanges = 0;
for (const iter of sortedIterations) {
const divergedIndices = pixelsByIteration.get(iter) || [];
const convergedData = convergedByIteration.get(iter) || [];
this.changeList.push({
iter: iter,
nn: divergedIndices,
vv: convergedData
});
totalChanges += divergedIndices.length + convergedData.length;
}
// Update board statistics
this.di = totalDiverged;
this.un = stillComputing;
this.updateSize = totalChanges;
} catch (error) {
console.error(`GpuBoard.compute() ERROR:`, error);
} finally {
this.isComputing = false;
}
}
async serialize() {
// 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 (like CPU boards)
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,
// CPU-side state
cpuStatus: this.cpuStatus ? Array.from(this.cpuStatus) : null,
lastReportedIters: this.lastReportedIters ? Array.from(this.lastReportedIters) : null,
effort: this.effort,
// Completed pixels (sparse format)
completedIndexes,
completedNn,
};
}
static async fromSerializedAsync(serialized) {
const board = new GpuBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Wait for GPU initialization
await board.ensureGPUReady();
// Restore GPU pixel buffer
if (serialized.gpuPixelData && board.isGPUReady) {
const pixelData = new Uint8Array(serialized.gpuPixelData).buffer;
await board.writePixelBuffer(pixelData);
}
// Restore CPU-side state
if (serialized.cpuStatus) {
board.cpuStatus = new Uint32Array(serialized.cpuStatus);
}
if (serialized.lastReportedIters) {
board.lastReportedIters = new Uint32Array(serialized.lastReportedIters);
}
board.effort = serialized.effort || 1;
// Restore Board state
board.it = serialized.it;
board.un = serialized.un;
board.di = serialized.di;
board.ch = serialized.ch || 0;
// Restore nn array from base serialization
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;
}
static fromSerialized(serialized) {
// For backwards compatibility with sync Board.fromSerialized
// GPU boards require async initialization, so this returns a board
// that will continue initializing in the background
const board = new GpuBoard(
serialized.k,
serialized.sizesQD[0],
serialized.sizesQD[1],
serialized.sizesQD[2],
serialized.config,
serialized.id
);
// Schedule async restoration
board.gpuInitPromise = board.gpuInitPromise.then(async () => {
// Restore GPU pixel buffer
if (serialized.gpuPixelData && board.isGPUReady) {
const pixelData = new Uint8Array(serialized.gpuPixelData).buffer;
await board.writePixelBuffer(pixelData);
}
// Restore CPU-side state
if (serialized.cpuStatus) {
board.cpuStatus = new Uint32Array(serialized.cpuStatus);
}
if (serialized.lastReportedIters) {
board.lastReportedIters = new Uint32Array(serialized.lastReportedIters);
}
board.effort = serialized.effort || 1;
// Restore Board state
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];
}
}
});
return board;
}
}
// 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(GpuBaseBoard) {
static BYTES_PER_PIXEL = 56; // 6 u32 + 8 f32 (unified PixelState struct)
constructor(k, size, re, im, config, id) {
super(k, size, re, im, config, id);
this.effort = 2; // Same as DDZhuoranBoard
// 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);
// 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, toDD(yFrac)[0], toDD(yFrac)[1], 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, toDD(xFrac)[0], toDD(xFrac)[1], 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;
// 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: 6 u32 + 8 f32 = 56 bytes per pixel
const pixelBufferSize = dimsArea * 56;
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.`);
}
// Single unified pixel state buffer (PixelState struct: 6 u32 + 8 f32 = 56 bytes per pixel)
// Layout per pixel: [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: 128,
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST,
label: 'Params buffer'
});
// Initialize pixel state buffer using overlapping typed array views
// ArrayBuffer holds 56 bytes per pixel (14 x 4 bytes)
const pixelData = new ArrayBuffer(pixelBufferSize);
const pixelU32 = new Uint32Array(pixelData); // For u32 fields (indices 0-5)
const pixelF32 = new Float32Array(pixelData); // For f32 fields (indices 6-13)
for (let i = 0; i < dimsArea; i++) {
const idx14 = i * 14; // 14 x 4-byte values per pixel
// Integer fields (offsets 0-5)
pixelU32[idx14 + 0] = 1; // iter (start at 1, z=c is iteration 1)
pixelU32[idx14 + 1] = 0; // status (0 = computing)
pixelU32[idx14 + 2] = 0; // period
pixelU32[idx14 + 3] = this.refIter[i]; // ref_iter
pixelU32[idx14 + 4] = 0xFFFFFFFF; // ckpt_refidx (sentinel)
pixelU32[idx14 + 5] = 0xFFFFFFFF; // pending_refidx (sentinel)
// Float fields (offsets 6-13)
pixelF32[idx14 + 6] = this.dz[i * 2]; // dzr
pixelF32[idx14 + 7] = this.dz[i * 2 + 1]; // dzi
pixelF32[idx14 + 8] = 0; // bbr
pixelF32[idx14 + 9] = 0; // bbi
pixelF32[idx14 + 10] = 0; // ckpt_bbr
pixelF32[idx14 + 11] = 0; // ckpt_bbi
pixelF32[idx14 + 12] = this.dc[i * 2]; // dcr
pixelF32[idx14 + 13] = this.dc[i * 2 + 1]; // dci
}
// 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
}
createBindGroup() {
// Unified 3-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 } }
],
label: 'Perturbation bind group'
});
}
// 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,
ckpt0: u32,
ckpt1: u32,
ckpt2: u32,
ckpt3: u32,
ckpt4: u32,
ckpt5: u32,
ckpt6: u32,
ckpt7: u32,
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
_padding: u32, // Alignment padding
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: 6 u32 + 8 f32 = 56 bytes
// Layout (u32 view):
// [0] iter: u32
// [1] status: u32
// [2] period: u32
// [3] ref_iter: u32
// [4] ckpt_refidx: u32
// [5] pending_refidx: u32
// [6] dzr: f32
// [7] dzi: f32
// [8] bbr: f32
// [9] bbi: f32
// [10] ckpt_bbr: f32
// [11] ckpt_bbi: f32
// [12] dcr: f32
// [13] dci: f32
struct PixelState {
// Integer fields (6 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,
}
// 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,
}
@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>;
// 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>) {
// 2D dispatch: calculate linear index from 2D coordinates
let index = global_id.y * params.workgroups_x + global_id.x;
let dimsArea = params.dims_width * params.dims_height;
if (index >= dimsArea) { 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;
// Convergence thresholds scale with pixel size for deep zooms
// GPU uses float32 precision, so thresholds must be larger than CPU's float64
let epsilon = min(1e-7, params.pixel_size / 10.0); // Final convergence threshold
let epsilon2 = min(1e-5, params.pixel_size * 10.0); // Getting close threshold
// 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;
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; }
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;
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;
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;
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;
}
`;
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() {
// Prevent concurrent compute() calls
if (this.isComputing) {
return;
}
this.isComputing = true;
const dimsArea = this.config.dimsWidth * this.config.dimsHeight;
try {
// Calculate batch size first (needed to determine reference orbit buffer)
const pixelsToIterate = this.un + this.ch;
// Check for step mode debug flag 's'
const stepMode = hasDebugFlag(this.config, 's');
const iterationsPerBatch = stepMode ? 1 : Math.max(17,
Math.floor(333337 / Math.max(pixelsToIterate, 1)));
// Update effort for scheduler (reflects actual iterations per call)
this.effort = iterationsPerBatch;
// Step 1: Extend reference orbit on CPU as needed
// Extend to what pixels need (this.it) plus enough buffer for next batch
const THREADING_CAPACITY = 1048576; // 2^20
const currentNeed = this.it + iterationsPerBatch;
// Also allow growth for thread-following, but cap to avoid waste
// Use proportional buffer (10%) for long periods, or fixed 10k buffer for short periods
const maxAllowedGrowth = Math.max(currentNeed + 10000, Math.round(currentNeed * 1.1));
const threadingBuffer = Math.min(this.refIterations + 100, maxAllowedGrowth);
// Cap at threading capacity - don't extend beyond this point
const targetRefIterations = Math.min(
Math.max(currentNeed, threadingBuffer),
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 2: Upload iteration state to GPU (INCREMENTAL UPLOADS)
// IterState struct: 5 f32 per iteration
// (ref_re, ref_im, thread_next, thread_delta_re, thread_delta_im)
const totalIters = this.refIterations + 1; // Include iteration 0
const BYTES_PER_ITER = 20; // 5 f32 = 20 bytes
// 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) {
// Only resize if we can actually allocate a larger buffer (not already at max cap)
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; // Reset after resize
this.createBindGroup();
}
// INCREMENTAL UPLOAD: Only upload new iteration data
if (this.lastUploadedIterLength < this.refIterations) {
const startIdx = Math.max(0, this.lastUploadedIterLength + 1);
// Cap to buffer capacity
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); // 5 floats per iteration
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;
// Reference orbit (DD precision -> f32)
iterF32[base + 0] = ref[0] + ref[1]; // ref_re
iterF32[base + 1] = ref[2] + ref[3]; // ref_im
// Threading data
if (!thread) {
iterF32[base + 2] = -1; // thread_next (-1 = no thread)
iterF32[base + 3] = 0; // thread_delta_re
iterF32[base + 4] = 0; // thread_delta_im
} 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 3: Check if all done
if (this.un === 0) {
this.isComputing = false;
return; // All pixels finished
}
// Step 4: Set up parameters
// Batch size already calculated above (before reference orbit extension)
const pixelSize = this.pixelSize;
// Step 4a: Precompute checkpoint offsets for this batch using fibonacciPeriod
const checkpointOffsets = [];
const bufferIter = this.it;
for (let i = 0; i < iterationsPerBatch; i++) {
const globalIter = bufferIter + i;
if (fibonacciPeriod(globalIter) === 1) {
checkpointOffsets.push(i);
}
}
// Cap at 8 checkpoints (hardware limit based on uniform buffer fields)
// Note: checkpointCount can be 0 if no checkpoints in this batch
// That's OK - we'll keep comparing to the last checkpoint from a previous batch
const checkpointCount = Math.min(checkpointOffsets.length, 8);
// Step 5: Dispatch GPU compute - process all pixels
const workgroupSize = 64;
const numWorkgroups = Math.ceil(dimsArea / workgroupSize);
// 2D workgroup dispatch
const workgroupsX = Math.ceil(Math.sqrt(numWorkgroups));
const workgroupsY = Math.ceil(numWorkgroups / workgroupsX);
// Pack params: dims_width, dims_height, iterations_per_batch, active_count,
// ref_orbit_length, exponent, workgroups_x, start_iter, checkpoint_count,
// ckpt0-7, loop params, pixel_size, aspect_ratio, loop deltas
const paramsBuffer = new ArrayBuffer(128); // Extended for new layout
const paramsU32 = new Uint32Array(paramsBuffer);
const paramsF32 = new Float32Array(paramsBuffer);
paramsU32[0] = this.config.dimsWidth;
paramsU32[1] = this.config.dimsHeight;
paramsU32[2] = iterationsPerBatch;
paramsU32[3] = dimsArea; // active_count: Process all pixels, skip finished ones in shader
paramsU32[4] = this.refIterations + 1; // ref_orbit_length: includes iteration 0
paramsU32[5] = this.config.exponent || 2;
paramsU32[6] = workgroupsX * workgroupSize; // Total threads in X dimension
// start_iter: Starting iteration (what's in the buffer before iter++)
paramsU32[7] = bufferIter;
paramsU32[8] = checkpointCount; // Number of checkpoints in this batch
// Pack all 8 checkpoint offsets (fill unused slots with 0)
for (let i = 0; i < 8; i++) {
paramsU32[9 + i] = i < checkpointCount ? checkpointOffsets[i] : 0;
}
// Pack reference orbit loop parameters
const loop = this.refOrbitLoop || { enabled: false };
paramsU32[17] = loop.enabled ? 1 : 0;
paramsU32[18] = loop.threshold || 0;
paramsU32[19] = loop.jumpAmount || 0;
paramsU32[20] = 0; // padding
paramsF32[21] = pixelSize;
paramsF32[22] = this.config.aspectRatio;
paramsF32[23] = loop.deltaR || 0;
paramsF32[24] = loop.deltaI || 0;
this.device.queue.writeBuffer(this.buffers.params, 0, paramsBuffer);
const commandEncoder = this.device.createCommandEncoder(
{ label: 'Perturbation compute' });
const passEncoder = commandEncoder.beginComputePass({ label: 'Perturbation pass' });
passEncoder.setPipeline(this.pipeline);
passEncoder.setBindGroup(0, this.bindGroup);
passEncoder.dispatchWorkgroups(workgroupsX, workgroupsY); // 2D dispatch
passEncoder.end();
this.device.queue.submit([commandEncoder.finish()]);
// Step 6: Read back results (unified PixelState buffer)
await this.device.queue.onSubmittedWorkDone();
// Read unified pixel buffer and create overlapping views
// PixelState struct: 6 u32 + 8 f32 = 14 x 4-byte values per pixel
const pixelBuffer = await this.readBuffer(this.buffers.pixels, Uint32Array);
const pixelU32 = pixelBuffer; // Already Uint32Array for u32 fields
const pixelF32 = new Float32Array(pixelBuffer.buffer); // Overlapping view for f32 fields
// Update global iteration counter (before processing results, like CPU implementations)
this.it += iterationsPerBatch;
// PixelState struct offsets (14 values per pixel, matching shader struct layout)
const INT_ITER = 0, INT_STATUS = 1, INT_PERIOD = 2, INT_REF_ITER = 3;
const FLOAT_DZR = 6, FLOAT_DZI = 7; // f32 fields start at offset 6
// Step 7: Update board state
const pixelsByIteration = new Map(); // Group diverged pixels by their exact iteration
const convergedByIteration = new Map(); // Group converged pixels by their exact iteration
let hasConverged = false;
// First pass: check for diverged pixels and count converged
let divergedCount = 0;
let convergedCount = 0;
for (let i = 0; i < dimsArea; i++) {
const idx14 = i * 14; // 14 values per pixel in unified struct
const status = pixelU32[idx14 + INT_STATUS];
const period = pixelU32[idx14 + INT_PERIOD];
if (this.nn[i] !== 0) continue; // Already finished
if (status === 1) {
// Newly diverged
const iters = pixelU32[idx14 + INT_ITER];
divergedCount++;
this.nn[i] = iters;
this.pp[i] = period;
if (!pixelsByIteration.has(iters)) {
pixelsByIteration.set(iters, []);
}
pixelsByIteration.get(iters).push(i);
this.di++;
this.un--;
// Decrement ch if this pixel was in the spike
if (this.inSpike && this.inSpike[i] && this.ch > 0) {
this.ch -= 1;
}
} else if (status === 2) {
convergedCount++;
hasConverged = true;
}
}
// Second pass: process converged pixels (f32 fields already available in pixelF32)
if (hasConverged) {
for (let i = 0; i < dimsArea; i++) {
const idx14 = i * 14;
const status = pixelU32[idx14 + INT_STATUS];
const period = pixelU32[idx14 + INT_PERIOD];
if (this.nn[i]) continue; // Already finished
if (status === 2) {
// Newly converged
const iters = pixelU32[idx14 + INT_ITER];
this.nn[i] = -iters;
// period from shader is pp (iteration when first within epsilon2)
// Store pp - 1 because fibonacciPeriod() adds 1 in its calculation
this.pp[i] = period - 1;
// Get converged position: refOrbit[refIter+1] + dz
// dz corresponds to refIter+1 because we computed new dz but didn't increment ref_iter
const refIter = pixelU32[idx14 + INT_REF_ITER];
const nextRefIter = refIter + 1;
const dzr = pixelF32[idx14 + FLOAT_DZR];
const dzi = pixelF32[idx14 + FLOAT_DZI];
const ref = this.refOrbit[Math.min(nextRefIter, this.refOrbit.length - 1)];
// Compute z = ref + dz with proper DD addition
const zr = toDDAdd([ref[0], ref[1]], dzr);
const zi = toDDAdd([ref[2], ref[3]], dzi);
if (!convergedByIteration.has(iters)) {
convergedByIteration.set(iters, []);
}
convergedByIteration.get(iters).push({
index: i,
z: [zr[0], zr[1], zi[0], zi[1]], // DDc format
p: this.pp[i] // Raw pp value (UI will call fibonacciPeriod to calculate period)
});
this.un--;
// Decrement ch if this pixel was in the spike
if (this.inSpike && this.inSpike[i] && this.ch > 0) {
this.ch -= 1;
}
}
}
}
// NOTE: When refOrbitEscaped is true, we do NOT mark remaining pixels as diverged.
// The GPU shader will continue iterating those pixels individually, and they will
// either diverge naturally or continue until maxiter. This matches the behavior
// of DDZhuoranBoard which rebases pixels when the reference orbit escapes.
// Create change objects grouped by iteration
const allIterations = new Set([...pixelsByIteration.keys(),
...convergedByIteration.keys()]);
const sortedIterations = Array.from(allIterations).sort((a, b) => a - b);
for (const iter of sortedIterations) {
const divergedIndices = pixelsByIteration.get(iter) || [];
const convergedData = convergedByIteration.get(iter) || [];
if (divergedIndices.length > 0 || convergedData.length > 0) {
this.queueChanges({
iter: iter,
nn: divergedIndices,
vv: convergedData
});
}
}
} catch (error) {
console.error(`GpuZhuoranBoard.compute() ERROR:`, error);
} finally {
this.isComputing = false;
}
}
async serialize() {
// 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,
};
}
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 () => {
// 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;
// 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 AdaptiveGpuBoard extends QDReferenceOrbitMixin(GpuBaseBoard) {
static BYTES_PER_PIXEL = 60; // 15 × 4 bytes (7 i32 + 8 f32)
constructor(k, size, re, im, config, id) {
super(k, size, re, im, config, id);
this.effort = 2; // Same as DDZhuoranBoard
// 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);
// Start GPU initialization (async)
this.gpuInitPromise = this.initGPU();
}
// 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;
// Consolidated 3-binding layout:
// 0: params (uniform)
// 1: pixels (PixelState): 7 i32 + 8 f32 = 60 bytes per pixel
// 2: iters (IterState): 5 f32 = 20 bytes per iteration (refOrbit + threading combined)
const PIXEL_BYTES = 60; // 15 × 4 bytes
const ITER_BYTES = 20; // 5 × 4 bytes
this.buffers = {
params: this.device.createBuffer({
size: 128,
usage: GPUBufferUsage.UNIFORM | GPUBufferUsage.COPY_DST
}),
pixels: this.device.createBuffer({
size: dimsArea * PIXEL_BYTES,
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: [iter, scale, status, period, ref_iter, ckpt_refidx, pending_refidx,
// dzr, dzi, bbr, bbi, ckpt_bbr, ckpt_bbi, dcr, dci]
const pixelBuffer = new ArrayBuffer(dimsArea * PIXEL_BYTES);
const pixelsI32 = new Int32Array(pixelBuffer);
const pixelsF32 = new Float32Array(pixelBuffer);
for (let i = 0; i < dimsArea; i++) {
const idx = i * 15; // 15 fields per pixel
// Integer fields (indices 0-6)
pixelsI32[idx + 0] = 1; // iter starts at 1
pixelsI32[idx + 1] = this.pixelScale[i]; // scale from initPixels
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
}
this.device.queue.writeBuffer(this.buffers.pixels, 0, pixelBuffer);
this.lastUploadedItersLength = -1;
}
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 } }
]
});
}
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,
ckpt0: u32,
ckpt1: u32,
ckpt2: u32,
ckpt3: u32,
ckpt4: u32,
ckpt5: u32,
ckpt6: u32,
ckpt7: u32,
loop_enabled: u32,
loop_threshold: u32,
loop_jump: u32,
initial_scale: i32, // Global scale for dc, bb, threaded_delta
pixel_size: f32,
aspect_ratio: f32,
loop_delta_r: f32,
loop_delta_i: f32,
}
// Per-pixel state: 7 i32 + 8 f32 = 60 bytes
// Layout (i32/u32 view):
// [0] iter: i32
// [1] scale: 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
struct PixelState {
// Integer fields (7 i32)
iter: i32,
scale: 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,
}
// 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,
}
@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>;
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>) {
let index = global_id.y * params.workgroups_x + global_id.x;
let dimsArea = params.dims_width * params.dims_height;
if (index >= dimsArea) { 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;
// Convergence thresholds - scaled by initialScale for comparison
let epsilon_actual = min(1e-7, params.pixel_size / 10.0);
let epsilon2_actual = min(1e-5, params.pixel_size * 10.0);
// Convert to initialScale for scaled comparisons
let epsilon = ldexp(epsilon_actual, -params.initial_scale);
let epsilon2 = ldexp(epsilon2_actual, -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);
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; }
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) {
const THREADING_CAPACITY = 1048576u;
if (ref_iter >= THREADING_CAPACITY) {
// Fallback: compare absolute positions (in actual coords)
let z_total_r = zr;
let z_total_i = zi;
let bbr_actual = ldexp(checkpoint_bb_r, params.initial_scale);
let bbi_actual = ldexp(checkpoint_bb_i, params.initial_scale);
let ref_ckpt = getRefOrbit(checkpoint_refidx);
let z_checkpoint_r = ref_ckpt.x + bbr_actual;
let z_checkpoint_i = ref_ckpt.y + bbi_actual;
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_actual) {
if (pp == 0u) { pp = iter; }
if (db <= epsilon_actual) {
pixels[index].status = 2;
pixels[index].period = i32(pp);
break;
}
}
} else {
// 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);
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);
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;
}
`;
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(`AdaptiveGpuBoard 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() {
// Prevent concurrent compute() calls
if (this.isComputing) return;
this.isComputing = true;
// Wait for async GPU initialization to complete
await this.gpuInitPromise;
// GPU required - if device unavailable, computation cannot proceed
if (!this.device) {
console.warn('AdaptiveGpuBoard: GPU device not available, cannot compute');
this.isComputing = false;
return;
}
try {
const dimsArea = this.config.dimsWidth * this.config.dimsHeight;
// Calculate batch size
const pixelsToIterate = this.un + this.ch;
// Check for step mode debug flag 's'
const stepMode = hasDebugFlag(this.config, 's');
const iterationsPerBatch = stepMode ? 1 : Math.max(17,
Math.floor(333337 / Math.max(pixelsToIterate, 1)));
this.effort = iterationsPerBatch;
// Extend reference orbit on CPU as needed
const THREADING_CAPACITY = 1048576;
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();
}
// Upload combined ref orbit + threading data
await this.uploadIters();
if (this.un === 0) {
this.isComputing = false;
return;
}
// Compute checkpoint offsets for convergence detection (enabled at all zoom levels)
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, 8);
// Get scalar size for pixelSize computation
const size_scalar = this.size;
const pixelSize = size_scalar / this.config.dimsWidth;
const workgroupSize = 64;
const numWorkgroups = Math.ceil(dimsArea / workgroupSize);
const workgroupsX = Math.ceil(Math.sqrt(numWorkgroups));
const workgroupsY = Math.ceil(numWorkgroups / workgroupsX);
// Pack params
const paramsBuffer = new ArrayBuffer(128);
const paramsU32 = new Uint32Array(paramsBuffer);
const paramsI32 = new Int32Array(paramsBuffer);
const paramsF32 = new Float32Array(paramsBuffer);
paramsU32[0] = this.config.dimsWidth;
paramsU32[1] = this.config.dimsHeight;
paramsU32[2] = iterationsPerBatch;
paramsU32[3] = dimsArea;
paramsU32[4] = this.refIterations + 1;
paramsU32[5] = this.config.exponent || 2;
paramsU32[6] = workgroupsX * workgroupSize;
paramsU32[7] = bufferIter;
paramsU32[8] = checkpointCount;
for (let i = 0; i < 8; i++) {
paramsU32[9 + i] = i < checkpointCount ? checkpointOffsets[i] : 0;
}
const loop = this.refOrbitLoop || { enabled: false };
paramsU32[17] = loop.enabled ? 1 : 0;
paramsU32[18] = loop.threshold || 0;
paramsU32[19] = loop.jumpAmount || 0;
paramsI32[20] = this.initialScale; // initial_scale for dc term in AdaptiveGpuBoard
paramsF32[21] = pixelSize;
paramsF32[22] = this.config.aspectRatio;
paramsF32[23] = loop.deltaR || 0;
paramsF32[24] = loop.deltaI || 0;
this.device.queue.writeBuffer(this.buffers.params, 0, paramsBuffer);
const commandEncoder = this.device.createCommandEncoder(
{ label: 'Adaptive perturbation compute' });
const passEncoder = commandEncoder.beginComputePass(
{ label: 'Adaptive perturbation pass' });
passEncoder.setPipeline(this.pipeline);
passEncoder.setBindGroup(0, this.bindGroup);
passEncoder.dispatchWorkgroups(workgroupsX, workgroupsY);
passEncoder.end();
this.device.queue.submit([commandEncoder.finish()]);
await this.device.queue.onSubmittedWorkDone();
this.it += iterationsPerBatch;
// Read consolidated pixels buffer
// PixelState layout (15 fields × 4 bytes = 60 bytes/pixel):
// Int32 (indices 0-6): iter, scale, status, period, ref_iter, ckpt_refidx, pending_refidx
// Float32 (indices 7-14): dzr, dzi, bbr, bbi, ckpt_bbr, ckpt_bbi, dcr, dci
const pixelsU32 = await this.readBuffer(this.buffers.pixels, Uint32Array);
const pixelsI32 = new Int32Array(pixelsU32.buffer);
const pixelsF32 = new Float32Array(pixelsU32.buffer);
// Process GPU results
const pixelsByIteration = new Map();
const convergedByIteration = new Map();
let hasConverged = false;
// PixelState field indices (in units of 4 bytes)
const STRIDE = 15; // 15 fields per pixel
const P_ITER = 0, P_SCALE = 1, P_STATUS = 2, P_PERIOD = 3, P_REF_ITER = 4;
const P_DZR = 7, P_DZI = 8;
for (let i = 0; i < dimsArea; i++) {
const idx = i * STRIDE;
const status = pixelsI32[idx + P_STATUS];
const period = pixelsI32[idx + P_PERIOD];
if (this.nn[i] !== 0) continue;
if (status === 1) {
const iters = pixelsI32[idx + P_ITER];
this.nn[i] = iters;
this.pp[i] = period;
if (!pixelsByIteration.has(iters)) pixelsByIteration.set(iters, []);
pixelsByIteration.get(iters).push(i);
this.di++;
this.un--;
if (this.inSpike && this.inSpike[i] && this.ch > 0) this.ch -= 1;
} else if (status === 2) {
hasConverged = true;
}
}
if (hasConverged) {
for (let i = 0; i < dimsArea; i++) {
const idx = i * STRIDE;
const status = pixelsI32[idx + P_STATUS];
const period = pixelsI32[idx + P_PERIOD];
if (this.nn[i]) continue;
if (status === 2) {
const iters = pixelsI32[idx + P_ITER];
this.nn[i] = -iters;
this.pp[i] = period - 1;
const refIter = pixelsI32[idx + P_REF_ITER];
// AdaptiveGpuBoard stores dz BEFORE iteration (break before iter step),
// so dz corresponds to refIter, not refIter+1
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)];
// Compute z = ref + dz in full QD precision (8 elements for complex)
const zrQD = toQDAdd([ref[0], ref[1], ref[2], ref[3]], [dzr, 0, 0, 0]);
const ziQD = toQDAdd([ref[4], ref[5], ref[6], ref[7]], [dzi, 0, 0, 0]);
if (!convergedByIteration.has(iters)) convergedByIteration.set(iters, []);
convergedByIteration.get(iters).push(
{ index: i, z: [...zrQD, ...ziQD], p: this.pp[i] });
this.un--;
if (this.inSpike && this.inSpike[i] && this.ch > 0) this.ch -= 1;
}
}
}
const allIterations = new Set([...pixelsByIteration.keys(),
...convergedByIteration.keys()]);
for (const iter of Array.from(allIterations).sort((a, b) => a - b)) {
const divergedIndices = pixelsByIteration.get(iter) || [];
const convergedData = convergedByIteration.get(iter) || [];
if (divergedIndices.length > 0 || convergedData.length > 0) {
this.queueChanges({ iter: iter, nn: divergedIndices, vv: convergedData });
}
}
} catch (error) {
console.error('AdaptiveGpuBoard.compute() ERROR:',
error?.message || error, error?.stack || '');
} finally {
this.isComputing = false;
}
}
async serialize() {
// 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,
};
}
static fromSerialized(serialized) {
// GPU boards require async initialization, so this returns a board
// that will continue initializing in the background
const board = new AdaptiveGpuBoard(
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 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;
// 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;
}
}
function workerLog(message) {
self.postMessage({
type: 'log',
data: message
});
}
const forcedBoardTypes = {
'cpu': CpuBoard,
'ddz': DDZhuoranBoard,
'qdz': QDZhuoranBoard,
'pert': PerturbationBoard,
'qdpert': QDPerturbationBoard,
'gpu': GpuBoard,
'gpuz': GpuZhuoranBoard,
'adaptive': AdaptiveGpuBoard,
'qdcpu': QDCpuBoard
};
function selectBoardClass(pixelSize, dimsArea, gpuMaxBufferSize, forceBoard) {
if (forceBoard) {
if (forceBoard in forcedBoardTypes) {
return forcedBoardTypes[forceBoard];
} else {
throw new Error(`Unknown board type: ${forcedBoardType}.` +
` Valid types: ${Object.keys(forcedBoardTypes).join(', ')}`);
}
}
// First, try to select a GPU board.
if (gpuMaxBufferSize) {
// Select board type based on zoom level and float32 precision limits
// Float32 has ~7 decimal digits, so direct iteration works to ~1e-7 pixel size
// Shallow zooms (z < ~1e7): GpuBoard with simple float32 iteration
// Medium zooms (z ~1e7 to ~1e30): GpuZhuoranBoard with quad-precision reference
// Deep zooms (z > ~1e30): AdaptiveGpuBoard with QD-precision reference
// orbit and adaptive per-pixel scaling for correct escape detection
const GpuBoardClass = (
(pixelSize > 1e-7) ? GpuBoard :
(pixelSize > 1e-30) ? GpuZhuoranBoard :
AdaptiveGpuBoard);
const largestBufferSize = dimsArea * GpuBoardClass.BYTES_PER_PIXEL;
if (largestBufferSize <= gpuMaxBufferSize) {
return GpuBoardClass;
} else {
const bufferSizeMB = (largestBufferSize / (1024*1024)).toFixed(0);
const limitMB = (gpuMaxBufferSize / (1024*1024)).toFixed(0);
console.log(
`${GpuBoardClass}: dimsArea=${dimsArea} too large for GPU ` +
`(buffer size ${bufferSizeMB} MB > ${limitMB} MB), using CPU`);
}
}
// If GPU is not available, select a CPU board
const CpuBoardClass = (
(pixelSize > 1e-15) ? CpuBoard :
(pixelSize > 1e-30) ? PerturbationBoard :
QDZhuoranBoard);
return CpuBoardClass;
}
// FractalWorker manages board computation on both main thread and in workers
// Always defined on the main thread (for MockWorker to extend)
// and instantiated in real workers via workerStart
class FractalWorker {
constructor(workerNumber, name) {
this.workerNumber = workerNumber;
this.name = name;
this.boards = new Map();
this.hiddenBoards = new Set();
this.focusedBoardK = null;
this.computationPaused = false;
this.steps = 0;
this.startTime = 0;
this.endTime = -1;
this.timer = null;
this.gpuMaxBufferSize = null;
}
async handleMessage(type, data) {
switch (type) {
case 'addBoard':
this.workerNumber = data.workerNumber;
const enableGPU = data.config.enableGPU;
const webGPUAvailable = GpuBoard.isAvailable();
// Query GPU limits once on first use
if (enableGPU && webGPUAvailable && this.gpuMaxBufferSize === null) {
this.gpuMaxBufferSize = await GpuBaseBoard.queryMaxBufferSize();
}
// Explicit board selection via board= parameter
const forceBoard = data.config.forceBoard;
const size = data.size;
const dimsArea = data.config.dimsArea;
const pixelSize = size / data.config.dimsWidth;
const BoardClass = selectBoardClass(pixelSize, dimsArea, this.gpuMaxBufferSize, forceBoard);
// Construct the board instance
let board = new BoardClass(data.k, size, data.reQD, data.imQD, data.config, data.id);
this.boards.set(data.k, board);
// Store QD-precision coordinates
board.sizesQD = [size, data.reQD, data.imQD];
// Show coordinates
let coordStr;
const digits = Math.ceil(-Math.log10(pixelSize)) + 3;
const re_str = qdToDecimalString(data.reQD, digits);
const im_str = qdToDecimalString(data.imQD, digits);
coordStr = `c=(${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))
.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];
// In step mode, handle stepping behavior
if (this.stepMode) {
if (this.stepsRequested > 0) {
await board.iterate();
this.stepsRequested--; // Consume one step
// Call step callback if set
if (this.stepCallback) {
await this.stepCallback();
}
}
// If stepsRequested is 0, don't do anything (wait for step() call)
} else {
// Normal mode - loop until workDone threshold
// GPU boards handle batching internally, so only call iterate() once
if (board.selfBatching) {
await board.iterate();
} else {
for (let workDone = 0; workDone < 17377 && board.unfinished(); ) {
workDone += board.un * board.effort;
await board.iterate();
}
}
}
const now = (new Date()).getTime();
if (this.focusedBoardK == board.k ?
(board.updateSize >= 1429 || now - board.lastTime >= 100) :
(board.updateSize >= 4673 || now - board.lastTime >= 500)) {
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`);
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
}
});
board.lastTime = now;
board.updateSize = 0;
board.changeList = [];
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.timer = setTimeout(() => this.iterateBoards(), 0);
}
// 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">
//////////// DD (double-double) precision utilities ///////////
function toDD(x) {
return Array.isArray(x) ? x : [x, 0];
}
// Convert complex [real, imag] to DDc format [r_hi, r_lo, i_hi, i_lo]
function toDDc(c) {
if (c.length == 4) { return c; }
const r = toDD(c[0]);
const j = toDD(c[1]);
return [r[0], r[1], j[0], j[1]];
}
// Add two DD values, returning DD result
function toDDAdd(a, b) {
const aa = toDD(a);
const bb = toDD(b);
const out = [0, 0];
ArddAdd(out, 0, aa[0], aa[1], bb[0], bb[1]);
return out;
}
// Convert various complex formats to QDc format (8 elements)
// Handles: float64 pair [r, i], DDc [r_hi, r_lo, i_hi, i_lo], QDc [r0..r3, i0..i3]
function toQDc(c) {
if (!c) return null;
if (c.length === 8) return c; // Already QDc
if (c.length === 4) {
// DDc format: [r_hi, r_lo, i_hi, i_lo]
return [c[0], c[1], 0, 0, c[2], c[3], 0, 0];
}
if (c.length === 2) {
// Float64 pair: [real, imag]
return [c[0], 0, 0, 0, c[1], 0, 0, 0];
}
return null;
}
// Oct helpers for both main thread and workers (via mathCode)
function toQD(x) {
if (!Array.isArray(x)) return [x, 0, 0, 0];
if (x.length >= 4) return [x[0], x[1], x[2], x[3]];
if (x.length === 3) return [x[0], x[1], x[2], 0];
return [x[0], x[1] || 0, 0, 0];
}
function toQDScale(a, s) {
const o = toQD(a);
return [o[0] * s, o[1] * s, o[2] * s, o[3] * s];
}
function toQDAdd(a, b) {
const aa = toQD(a);
const bb = toQD(b);
const out = new Array(4);
ArqdAdd(out, 0, aa[0], aa[1], aa[2], aa[3], bb[0], bb[1], bb[2], bb[3]);
return out;
}
function toQDSub(a, b) {
const bb = toQD(b);
return toQDAdd(a, [-bb[0], -bb[1], -bb[2], -bb[3]]);
}
function toQDMul(a, b) {
const aa = toQD(a);
const bb = toQD(b);
const out = new Array(4);
ArqdMul(out, 0, aa[0], aa[1], aa[2], aa[3], bb[0], bb[1], bb[2], bb[3]);
return out;
}
function toQDSquare(a) {
const aa = toQD(a);
const out = new Array(4);
ArqdSquare(out, 0, aa[0], aa[1], aa[2], aa[3]);
return out;
}
function toQDDouble(a) {
const aa = toQD(a);
return [aa[0] * 2, aa[1] * 2, aa[2] * 2, aa[3] * 2];
}
function qdToNumber(o) {
const v = toQD(o);
return v[0] + v[1] + v[2] + v[3];
}
function qdToDD(o) {
const v = toQD(o);
return [v[0], v[1] + v[2] + v[3]];
}
// Convert a float64 to its exact BigInt representation, scaled by 10^scale.
function float64ToBigIntScaled(x, scale) {
if (x === 0) return 0n;
if (!Number.isFinite(x)) return 0n;
const sign = x < 0 ? -1n : 1n;
const absX = Math.abs(x);
const buffer = new ArrayBuffer(8);
const view = new DataView(buffer);
view.setFloat64(0, absX);
const bits = view.getBigUint64(0);
const expBits = Number((bits >> 52n) & 0x7FFn);
const mantissaBits = bits & 0xFFFFFFFFFFFFFn;
let binaryExp, mantissa;
if (expBits === 0) {
mantissa = mantissaBits;
binaryExp = -1022 - 52;
} else {
mantissa = (1n << 52n) | mantissaBits;
binaryExp = expBits - 1023 - 52;
}
const five = 5n, two = 2n;
let result = sign * mantissa * (five ** BigInt(scale));
const netBinaryExp = binaryExp + scale;
if (netBinaryExp >= 0) {
result = result * (two ** BigInt(netBinaryExp));
} else {
result = result / (two ** BigInt(-netBinaryExp));
}
return result;
}
function decimalToQD(decimalString) {
let s = decimalString.trim().toLowerCase();
const neg = s.startsWith('-');
if (neg) s = s.slice(1);
if (s.startsWith('+')) s = s.slice(1);
let exp = 0;
const eIdx = s.indexOf('e');
if (eIdx !== -1) {
exp = parseInt(s.slice(eIdx + 1), 10);
s = s.slice(0, eIdx);
}
const parts = s.split('.');
const intPart = parts[0] || '0';
const fracPart = parts[1] || '';
let scale = fracPart.length - exp;
const bigStr = intPart + fracPart;
let n = BigInt(bigStr.replace(/^0+/, '') || '0');
if (neg) n = -n;
if (scale < 0) {
n = n * (BigInt(10) ** BigInt(-scale));
scale = 0;
}
// Use internal scale of 60 decimal places for exact float64 representation
const internalScale = 60;
if (scale < internalScale) {
n = n * (BigInt(10) ** BigInt(internalScale - scale));
} else if (scale > internalScale) {
n = n / (BigInt(10) ** BigInt(scale - internalScale));
}
const limbs = [];
let residual = n;
const divisor = BigInt(10) ** BigInt(internalScale);
for (let i = 0; i < 4; i++) {
if (residual === 0n) { limbs.push(0); continue; }
const limb = Number(residual) / Number(divisor);
limbs.push(limb);
const limbBigInt = float64ToBigIntScaled(limb, internalScale);
residual = residual - limbBigInt;
}
// Normalize the result to ensure consistent representation across all QD operations.
// Without this, limbs may not satisfy |limb[i]| < ulp(limb[i-1])/2, causing
// ArqdAdd/toQDAdd to produce different representations when adding zero.
// Uses quickTwoSum cascade to renormalize (fully inlined to avoid dependency issues).
let s0 = limbs[0] + limbs[1], e0 = limbs[1] - (s0 - limbs[0]);
let s1 = e0 + limbs[2], e1 = limbs[2] - (s1 - e0);
let s2 = e1 + limbs[3], s3 = limbs[3] - (s2 - e1);
let t0 = s0 + s1; s1 = s1 - (t0 - s0); s0 = t0;
t0 = s1 + s2; s2 = s2 - (t0 - s1); s1 = t0;
t0 = s2 + s3; s3 = s3 - (t0 - s2); s2 = t0;
return [s0, s1, s2, s3];
}
// Parse a complex number string into QD precision real and imaginary parts.
// Accepts formats like: "-0.74543+0.11301i", "0.5i", "-i", "0.25", ""
// Returns { re: QD array, im: QD array } or null if parsing fails
function parseComplexToQD(coordString) {
const trimmed = coordString.trim();
// Empty string returns null to signal default/inherit behavior
if (trimmed === '') {
return null;
}
// Match: optional real part, then optional imaginary part (with 'i' or just 'i')
const match = trimmed.match(
/([-+]?\d*\.?\d+(?:e[-+]?\d+)?\b)?(?:([-+]?\d*\.?\d+(?:e[-+]?\d+)?)i|([-+]?i))?$/
);
if (!match) {
return null;
}
// Extract real part (default to '0' if not present)
const realStr = match[1] || '0';
// Extract imaginary part: either match[2] (number with 'i') or match[3] (just 'i' or '-i')
let imagStr = match[2] || (match[3] ? match[3].replace('i', '1') : '0');
return {
re: decimalToQD(realStr),
im: decimalToQD(imagStr)
};
}
// Convert QD value to decimal string with exact BigInt arithmetic.
function qdToDecimalString(qd, digits) {
const o = Array.isArray(qd) ? qd : [qd, 0, 0, 0];
const internalScale = 60;
let total = 0n;
for (let i = 0; i < 4; i++) {
if (o[i] !== 0) {
total += float64ToBigIntScaled(o[i], internalScale);
}
}
const neg = total < 0n;
if (neg) total = -total;
const divisor = BigInt(10) ** BigInt(internalScale);
const intPart = total / divisor;
let fracPart = total % divisor;
let result = intPart.toString();
if (digits > 0) {
let fracStr = fracPart.toString().padStart(internalScale, '0');
if (digits < fracStr.length) {
const roundDigit = parseInt(fracStr[digits]);
fracStr = fracStr.slice(0, digits);
if (roundDigit >= 5) {
let carry = 1;
let chars = fracStr.split('');
for (let i = chars.length - 1; i >= 0 && carry; i--) {
const d = parseInt(chars[i]) + carry;
chars[i] = (d % 10).toString();
carry = Math.floor(d / 10);
}
fracStr = chars.join('');
if (carry) result = (BigInt(result) + 1n).toString();
}
} else {
fracStr = fracStr.padEnd(digits, '0');
}
fracStr = fracStr.replace(/0+$/, '');
if (fracStr.length > 0) result += '.' + fracStr;
}
return result;
}
function fast2Sum(a, b) {
let s = a + b;
let t = b - (s - a);
return [s, t];
}
function slow2Sum(a, b) {
let s = a + b;
let c = s - a;
return [s, (a - (s - c)) + (b - c)];
}
function ddSplit(a) {
const c = (134217729) * a; // 2^27 + 1, Veltkamp-Dekker constant
const x = c - (c - a);
const y = a - x;
return [x, y];
}
function twoProduct(a, b) {
let p = a * b;
let [ah, al] = ddSplit(a);
let [bh, bl] = ddSplit(b);
let err = ((ah * bh - p) + ah * bl + al * bh) + al * bl;
return [p, err];
}
function twoSquare(a) {
let p = a * a;
let [ah, al] = ddSplit(a);
let err = ((ah * ah - p) + 2 * ah * al) + al * al;
return [p, err];
}
function ddAdd(a, b) {
let [a1, a0] = a;
let [b1, b0] = b;
let [h1, h2] = slow2Sum(a1, b1);
let [l1, l2] = slow2Sum(a0, b0);
let [v1, v2] = fast2Sum(h1, h2 + l1);
return fast2Sum(v1, v2 + l2);
}
function ddMul(a, b) {
let [a1, a0] = a;
let [b1, b0] = b;
let [p1, p2] = twoProduct(a1, b1);
return fast2Sum(p1, p2 + a1 * b0 + b1 * a0);
}
function ddDouble(a) {
return [a[0] * 2, a[1] * 2];
}
function ddScale(q, s) {
let [q1, q0] = q;
let [p1, p2] = twoProduct(q1, s);
return fast2Sum(p1, p2 + s * q0);
}
function ddSquare(a) {
let [a1, a0] = a;
let [p1, p2] = twoSquare(a1);
return fast2Sum(p1, p2 + 2 * a1 * a0);
}
function ddcPow(q, n) {
if (n === 1) return q;
if (n === 2) return ddcSquare(q);
if (n === 3) return ddcMul(ddcSquare(q), q);
let result = [1, 0, 0, 0];
let base = q;
while (n > 0) {
if (n % 2 === 1) { result = ddcMul(result, base); }
base = ddcSquare(base);
n = Math.floor(n / 2);
}
return result;
}
function ddNegate(a) {
let [a1, a0] = a;
return [-a1, -a0];
}
function ddSub(a, b) {
return ddAdd(a, ddNegate(b));
}
function qdDiv(a, b) {
let reciprocal = ddReciprocal(b);
return ddMul(a, reciprocal);
}
function ddReciprocal(b, iters = 2) {
if (b[0] === 0 && b[1] === 0) {
return [NaN, 0]; // Return NaN for division by zero
}
// Refine the approximation using Newton-Raphson iteration
let x = [1 / b[0], 0];
for (let i = 0; i < iters; i++) {
x = ddMul(x, ddSub([2, 0], ddMul(x, b)));
}
return x;
}
// Complex operations in DD precision
function ddcAdd(a, b) {
let realSum = ddAdd([a[0], a[1]], [b[0], b[1]]);
let imagSum = ddAdd([a[2], a[3]], [b[2], b[3]]);
return [realSum[0], realSum[1], imagSum[0], imagSum[1]];
}
// Complex subtraction in DD precision
function ddcSub(a, b) {
let realDiff = ddSub([a[0], a[1]], [b[0], b[1]]);
let imagDiff = ddSub([a[2], a[3]], [b[2], b[3]]);
return [realDiff[0], realDiff[1], imagDiff[0], imagDiff[1]];
}
// Complex multiplication in DD precision
function ddcMul(a, b) {
let ac = ddMul([a[0], a[1]], [b[0], b[1]]);
let bd = ddMul([a[2], a[3]], [b[2], b[3]]);
let adbc = ddMul(ddAdd([a[0], a[1]], [a[2], a[3]]), ddAdd([b[0], b[1]], [b[2], b[3]]));
let real = ddSub(ac, bd);
let imag = ddSub(adbc, ddAdd(ac, bd));
return [real[0], real[1], imag[0], imag[1]];
}
// Complex doubling in DD precision
function ddcDouble(a) {
let realDouble = ddDouble([a[0], a[1]]);
let imagDouble = ddDouble([a[2], a[3]]);
return [realDouble[0], realDouble[1], imagDouble[0], imagDouble[1]];
}
// Complex squaring in DD precision
function ddcSquare(a) {
let a0a0 = ddSquare([a[0], a[1]]);
let a1a1 = ddSquare([a[2], a[3]]);
let a0a1 = ddMul([a[0], a[1]], [a[2], a[3]]);
let real = ddSub(a0a0, a1a1);
let imag = ddDouble(a0a1);
return [real[0], real[1], imag[0], imag[1]];
}
// Complex absolute value in DD precision
function ddcAbs(a) {
let a0a0 = ddSquare([a[0], a[1]]);
let a1a1 = ddSquare([a[2], a[3]]);
return ddAdd(a0a0, a1a1);
}
function qdParse(s) {
s = s.trim().toLowerCase();
if (s === "infinity" || s === "+infinity") return [Infinity, 0];
if (s === "-infinity") return [-Infinity, 0];
if (s === "nan") return [NaN, 0];
let sign = 1;
if (s[0] === '-') {
sign = -1;
s = s.slice(1);
} else if (s[0] === '+') {
s = s.slice(1);
}
let e = 0;
let parts = s.split('e');
if (parts.length > 1) {
s = parts[0];
e = parseInt(parts[1]);
}
let decimalPos = s.indexOf('.');
if (decimalPos !== -1) {
s = s.replace('.', '');
e -= s.length - decimalPos;
}
s = s.replace(/^0+/, '');
if (s === '') return [0, 0];
let result = [0, 0];
for (let digit of s) {
result = ddAdd(ddMul(result, [10, 0]), [parseInt(digit), 0]);
}
if (e !== 0) {
result = ddMul(result, qdPow10(e));
}
if (sign === -1) {
result = ddNegate(result);
}
return result;
}
function qdPow10(e) {
if (e < 0) return ddReciprocal(qdPow10(-e));
// Up to 1e16, the second component is zero.
if (e <= 16) { return [10 ** e, 0]; }
if (e % 2) { return ddMul([1e15, 0], qdPow10(e - 15)) };
return ddSquare(qdPow10(e / 2));
}
function qdFloor(q) {
let [a, b] = q;
let fl = Math.floor(a);
let [r0, r1] = ddAdd([a, b], [-fl, 0]);
if (r0 < 0 || (r0 === 0 && r1 < 0)) {
fl -= 1;
}
return [fl, 0];
}
function ddCompare(a, b) {
if (a[0] < b[0]) return -1;
if (a[0] > b[0]) return 1;
if (a[1] < b[1]) return -1;
if (a[1] > b[1]) return 1;
return 0;
}
function qdCompare(a, b) {
if (a[0] < b[0]) return -1;
if (a[0] > b[0]) return 1;
if (a[1] < b[1]) return -1;
if (a[1] > b[1]) return 1;
if (a[2] < b[2]) return -1;
if (a[2] > b[2]) return 1;
if (a[3] < b[3]) return -1;
if (a[3] > b[3]) return 1;
return 0;
}
function qdLt(a, s) {
return a[0] < s || (a[0] == s && a[1] < 0);
}
function ddEq(a, s) {
return a[0] == s && a[1] == 0;
}
function qdEq(a, s) {
return a[0] === s && a[1] === 0 && a[2] === 0 && a[3] === 0;
}
function qdAbs(q) {
return (q[0] + q[1] < 0) ? ddNegate(q) : q;
}
function qdFixed(q, digits = 0) {
// With fixed-point notation, digits specifies the number of digits after the decimal point.
return qdFormat(q, digits, true);
}
const ddTen = [10, 0];
function qdFormat(q, digits = 'auto', useFixedPoint = false) {
// With scientific notation, digits specifies the number of significant digits.
let [a, b] = q;
let s = a < 0 || (a === 0 && b < 0) ? '-' : '';
let autoFormat = (digits == 'auto');
if (autoFormat) {
digits = 32;
}
q = qdAbs(q);
if (!isFinite(a) || !isFinite(b)) return a.toString();
if (a === 0 && b === 0) {
if (autoFormat) return '0';
if (useFixedPoint) digits += 1;
return '0' + (digits > 1 ? '.' + '0'.repeat(digits - 1) : '');
}
// Scale q to be between 1 and 10
let e = parseInt(q[0].toExponential().match(/e([+-]\d+)/)[1]);
if (ddCompare(q, qdPow10(e)) < 0) { e -= 1; }
if (ddCompare(q, qdPow10(1+e)) >= 0) { e += 1; }
if (e) { q = ddMul(q, qdPow10(-e)); }
if (!qdLt(q, 10)) { // Hit boundary condition
q = qdDiv(q, ddTen);
e += 1;
}
let result = '';
let nonzeroDigits = digits;
if (useFixedPoint && !autoFormat) {
nonzeroDigits = nonzeroDigits + e + 1;
}
for (let i = 0; i < nonzeroDigits + 1; i++) {
let floorQ = qdFloor(q);
let digit = floorQ[0];
result += digit;
q = ddSub(q, floorQ);
q = ddMul(q, ddTen);
}
// Rounding
if (nonzeroDigits < 0) {
// No nonzero signficant digits? Treat as zero.
result = '?';
nonzeroDigits = 0;
e = 0;
} else if (parseInt(result[nonzeroDigits]) >= 5) {
result = result.slice(0, nonzeroDigits) + '?';
let carry = 1;
for (let i = nonzeroDigits - 1; i >= 0; i--) {
let digit = parseInt(result[i]) + carry;
if (digit < 10) {
result = result.slice(0, i) + digit + result.slice(i + 1);
carry = 0;
break;
} else {
result = result.slice(0, i) + '0' + result.slice(i + 1);
carry = 1;
}
}
if (carry) {
result = '1' + result;
nonzeroDigits += 1;
e++;
}
}
result = result.slice(0, nonzeroDigits);
epart = '';
if (!useFixedPoint && (!autoFormat || e < -6 || e >= 32)) {
// Scientific notation
if (result.length > 1) {
result = result[0] + '.' + result.slice(1);
}
if (e !== 0) {
epart = 'e' + e;
}
} else {
// Fixed-point notation
if (e >= 0) {
result = result.padEnd(e + 1, '0');
result = result.slice(0, e + 1) + '.' + result.slice(e + 1);
} else {
result = '0.' + '0'.repeat(-e - 1) + result;
}
// Ensure the correct number of digits after the decimal point
let [intPart, fracPart] = result.split('.');
if (digits <= 0) {
result = intPart;
} else {
fracPart = (fracPart || '').padEnd(digits, '0');
result = intPart + '.' + fracPart;
}
}
if (autoFormat) {
// Auto digit selection: trim trailing zeros
result = result.replace(/\.0+$|(\.\d*[1-9])0+$/, "$1");
}
return s + result + epart;
}
// Array in-place DD precision, allows fast computation
// by avoiding array constructors
function Afast2Sum(r, i, a, b) {
let s = a + b;
r[i] = s;
r[i+1] = b - (s - a);
}
function Aslow2Sum(r, i, a, b) {
let s = a + b;
let c = s - a;
r[i] = s;
r[i+1] = (a - (s - c)) + (b - c);
}
function ArddSplit(r, i, a) {
const c = (134217729) * a; // 2^27 + 1, Veltkamp-Dekker constant
const x = c - (c - a);
const y = a - x;
r[i] = x;
r[i+1] = y;
}
function AtwoProduct(r, i, a, b) {
const p = a * b;
ArddSplit(r, i, a);
const ah = r[i];
const al = r[i+1];
ArddSplit(r, i, b);
const bh = r[i];
const bl = r[i+1];
const err = ((ah * bh - p) + ah * bl + al * bh) + al * bl;
r[i] = p;
r[i+1] = err;
}
function AtwoSquare(r, i, a) {
const p = a * a;
ArddSplit(r, i, a);
const ah = r[i];
const al = r[i+1];
const err = ((ah * ah - p) + 2 * ah * al) + al * al;
r[i] = p;
r[i+1] = err;
}
function AquickTwoSum(a, b) {
const s = a + b;
return [s, b - (s - a)];
}
function AsymmetricTwoSum(a, b) {
const s = a + b;
const bb = s - a;
return [s, (a - (s - bb)) + (b - bb)];
}
// Three-sum from QD library: combines three values with proper error propagation
// Returns [sum, err1, err2] where sum + err1 + err2 = a + b + c (exactly)
function ArqdThreeSum(a, b, c) {
let [t1, t2] = AsymmetricTwoSum(a, b);
let [newA, t3] = AsymmetricTwoSum(c, t1);
let [newB, newC] = AsymmetricTwoSum(t2, t3);
return [newA, newB, newC];
}
function ArddAdd(r, i, a1, a2, b1, b2) {
Aslow2Sum(r, i, a1, b1);
const h1 = r[i];
const h2 = r[i+1];
Aslow2Sum(r, i, a2, b2);
const l1 = r[i];
const l2 = r[i+1];
Afast2Sum(r, i, h1, h2 + l1);
const v1 = r[i];
const v2 = r[i+1];
Afast2Sum(r, i, v1, v2 + l2);
}
function ArddMul(r, i, a1, a2, b1, b2) {
AtwoProduct(r, i, a1, b1);
const p1 = r[i];
const p2 = r[i+1];
Afast2Sum(r, i, p1, p2 + a1 * b2 + b1 * a2);
}
function ArddSet(r, i, a1, a2) {
r[i] = a1;
r[i+1] = a2;
}
function ArddcCopy(r, i, s, si) {
r[i] = s[si];
r[i+1] = s[si+1];
r[i+2] = s[si+2];
r[i+3] = s[si+3];
}
function ArddcGet(s, si) {
return s.slice(si, si+4);
}
function ArddSquare(r, i, a1, a2) {
AtwoSquare(r, i, a1);
const p1 = r[i];
const p2 = r[i+1];
Afast2Sum(r, i, p1, p2 + 2 * a1 * a2);
}
function ArddAbsSub(r, i, a1, a2, b1, b2) {
ArddAdd(r, i, a1, a2, -b1, -b2);
if (r[i] + r[i+1] < 0) {
r[i] = -r[i];
r[i+1] = -r[i+1];
}
}
// Oct-double (four-limb) helpers for deeper precision
function ArqdTwoProduct(a, b) {
const tmp = [];
AtwoProduct(tmp, 0, a, b);
return [tmp[0], tmp[1]];
}
function ArqdTwoSquare(a) {
const tmp = [];
AtwoSquare(tmp, 0, a);
return [tmp[0], tmp[1]];
}
// Renormalization algorithm from QD library (Hida, Li, Bailey)
// Takes 5 inputs and produces 4 normalized outputs
function ArqdRenorm(r, i, c0, c1, c2, c3, c4) {
let t0, t1, t2, t3, s;
// First pass: propagate from bottom to top, collecting errors
[s, t3] = AquickTwoSum(c3, c4);
[s, t2] = AquickTwoSum(c2, s);
[s, t1] = AquickTwoSum(c1, s);
[c0, t0] = AquickTwoSum(c0, s);
// Second pass: combine error terms
[s, t2] = AquickTwoSum(t2, t3);
[s, t1] = AquickTwoSum(t1, s);
[c1, t0] = AquickTwoSum(t0, s);
// Third pass: final cleanup
[s, t1] = AquickTwoSum(t1, t2);
[c2, t0] = AquickTwoSum(t0, s);
c3 = t0 + t1;
ArqdSet(r, i, c0, c1, c2, c3);
}
function ArqdSet(r, i, a1, a2, a3, a4) {
r[i] = a1;
r[i+1] = a2;
r[i+2] = a3;
r[i+3] = a4;
}
function ArqdcCopy(r, i, s, si) {
r[i] = s[si];
r[i+1] = s[si+1];
r[i+2] = s[si+2];
r[i+3] = s[si+3];
r[i+4] = s[si+4];
r[i+5] = s[si+5];
r[i+6] = s[si+6];
r[i+7] = s[si+7];
}
function ArqdcGet(s, si) {
return s.slice(si, si+8);
}
function ArqdAdd(r, i, a1, a2, a3, a4, b1, b2, b3, b4) {
let s0, s1, s2, s3, s4, t0, t1, t2;
[s0, t0] = AsymmetricTwoSum(a1, b1);
[s1, t1] = AsymmetricTwoSum(a2, b2);
[s2, t2] = AsymmetricTwoSum(a3, b3);
s3 = a4 + b4;
[s1, t0] = AsymmetricTwoSum(s1, t0);
[s2, t1] = AsymmetricTwoSum(s2, t1);
s3 += t2;
[s2, t0] = AsymmetricTwoSum(s2, t0);
s3 += t1;
[s3, s4] = AsymmetricTwoSum(s3, t0);
[s0, s1] = AquickTwoSum(s0, s1);
[s1, s2] = AquickTwoSum(s1, s2);
[s2, s3] = AquickTwoSum(s2, s3);
[s3, s4] = AquickTwoSum(s3, s4);
s2 += s4;
[s2, s3] = AquickTwoSum(s2, s3);
[s1, s2] = AquickTwoSum(s1, s2);
ArqdSet(r, i, s0, s1, s2, s3);
}
// QD library sloppy_mul algorithm (Hida, Li, Bailey)
// Uses TwoProduct for 6 products (levels 0-2) for nearly full 212-bit precision
function ArqdMul(r, i, a1, a2, a3, a4, b1, b2, b3, b4) {
// Level 0: a[0]*b[0]
let [p0, q0] = ArqdTwoProduct(a1, b1);
// Level 1: a[0]*b[1], a[1]*b[0]
let [p1, q1] = ArqdTwoProduct(a1, b2);
let [p2, q2] = ArqdTwoProduct(a2, b1);
// Level 2: a[0]*b[2], a[1]*b[1], a[2]*b[0]
let [p3, q3] = ArqdTwoProduct(a1, b3);
let [p4, q4] = ArqdTwoProduct(a2, b2);
let [p5, q5] = ArqdTwoProduct(a3, b1);
// Accumulate terms using three_sum
[p1, p2, q0] = ArqdThreeSum(p1, p2, q0);
[p2, q1, q2] = ArqdThreeSum(p2, q1, q2);
[p3, p4, p5] = ArqdThreeSum(p3, p4, p5);
// Further combining
let [s0, t0] = AsymmetricTwoSum(p2, p3);
let [s1, t1] = AsymmetricTwoSum(q1, p4);
let s2 = q2 + p5;
[s1, t0] = AsymmetricTwoSum(s1, t0);
s2 += t0 + t1;
// Level 3 cross-products and remaining error terms
s1 += a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + q0 + q3 + q4 + q5;
// Renormalize
ArqdRenorm(r, i, p0, p1, s0, s1, s2);
}
// QD library optimized sqr algorithm (Hida, Li, Bailey)
// Exploits symmetry: a[i]*a[j] = a[j]*a[i], so compute once and double
// Uses TwoSquare (cheaper than TwoProduct) where possible
function ArqdSquare(r, i, a1, a2, a3, a4) {
// Level 0: a[0]² - use TwoSquare
let [p0, q0] = ArqdTwoSquare(a1);
// Level 1: 2*a[0]*a[1] - single TwoProduct with doubled arg
let [p1, q1] = ArqdTwoProduct(2 * a1, a2);
// Level 2: 2*a[0]*a[2] + a[1]²
let [p2, q2] = ArqdTwoProduct(2 * a1, a3);
let [p3, q3] = ArqdTwoSquare(a2);
// Accumulate level 1
[p1, p2, q0] = ArqdThreeSum(p1, q0, p2);
// Accumulate level 2
[p2, q1, q2] = ArqdThreeSum(p2, q1, q2);
[p3, q3] = AsymmetricTwoSum(p3, q3);
// Combine accumulated values
let [s0, t0] = AsymmetricTwoSum(p2, p3);
let [s1, t1] = AsymmetricTwoSum(q1, q3);
let s2 = q2;
[s1, t0] = AsymmetricTwoSum(s1, t0);
s2 += t0 + t1;
// Level 3: 2*a[0]*a[3] + 2*a[1]*a[2] (plain multiply)
s1 += 2 * a1 * a4 + 2 * a2 * a3 + q0;
// Renormalize
ArqdRenorm(r, i, p0, p1, s0, s1, s2);
}
// Oct-precision absolute difference: r = |a - b|
// Used for cycle detection in QDPerturbationBoard
function ArqdAbsSub(r, i, a1, a2, a3, a4, b1, b2, b3, b4) {
ArqdAdd(r, i, a1, a2, a3, a4, -b1, -b2, -b3, -b4);
if (r[i] + r[i+1] + r[i+2] + r[i+3] < 0) {
r[i] = -r[i];
r[i+1] = -r[i+1];
r[i+2] = -r[i+2];
r[i+3] = -r[i+3];
}
}
// Additional shared utility function for tracking cycles.
function fibonacciPeriod(iteration) {
// Returns 1 at Fibonacci checkpoints (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...)
// Otherwise returns distance from most recent Fibonacci checkpoint plus 1.
// Fibonacci growth (φ ≈ 1.618) reduces aliasing with periods compared to power-of-2.
if (iteration === 0) return 1;
if (iteration === 1) return 1;
// Find largest Fibonacci number <= iteration
let a = 1, b = 1;
while (b < iteration) {
const next = a + b;
a = b;
b = next;
}
// Return 1 if iteration is exact Fibonacci, else distance from previous
if (b === iteration) return 1;
return iteration - a + 1;
}
// Catmull-Rom spline interpolation for smooth movie camera paths.
// Uses quad-double precision for numerical stability at deep zoom.
function catmullRom1DQD(p0, p1, p2, p3, t) {
const t2 = t * t;
const t3 = t2 * t;
const c0 = (-t3 + 2*t2 - t) / 2;
const c2 = (-3*t3 + 4*t2 + t) / 2;
const c3 = (t3 - t2) / 2;
// Compute offsets from p1 for numerical stability
const s0 = toQDSub(p0, p1);
const s2 = toQDSub(p2, p1);
const s3 = toQDSub(p3, p1);
return toQDAdd(toQDAdd(toQDAdd(toQDScale(s0, c0),
toQDScale(s3, c3)), toQDScale(s2, c2)), p1);
}
function catmullRomSplineQD(p0, p1, p2, p3, t) {
return [
catmullRom1DQD(p0[0], p1[0], p2[0], p3[0], t),
catmullRom1DQD(p0[1], p1[1], p2[1], p3[1], t)
];
}
// </script>
if (typeof module !== 'undefined') module.exports = { hasDebugFlag, workerLog, selectBoardClass, toDD, toDDc, toDDAdd, toQDc, toQD, toQDScale, toQDAdd, toQDSub, toQDMul, toQDSquare, toQDDouble, qdToNumber, qdToDD, float64ToBigIntScaled, decimalToQD, parseComplexToQD, qdToDecimalString, fast2Sum, slow2Sum, ddSplit, twoProduct, twoSquare, ddAdd, ddMul, ddDouble, ddScale, ddSquare, ddcPow, ddNegate, ddSub, qdDiv, ddReciprocal, ddcAdd, ddcSub, ddcMul, ddcDouble, ddcSquare, ddcAbs, qdParse, qdPow10, qdFloor, ddCompare, qdCompare, qdLt, ddEq, qdEq, qdAbs, qdFixed, qdFormat, Afast2Sum, Aslow2Sum, ArddSplit, AtwoProduct, AtwoSquare, AquickTwoSum, AsymmetricTwoSum, ArqdThreeSum, ArddAdd, ArddMul, ArddSet, ArddcCopy, ArddcGet, ArddSquare, ArddAbsSub, ArqdTwoProduct, ArqdTwoSquare, ArqdRenorm, ArqdSet, ArqdcCopy, ArqdcGet, ArqdAdd, ArqdMul, ArqdSquare, ArqdAbsSub, fibonacciPeriod, catmullRom1DQD, catmullRomSplineQD, Board, CpuBoard, QDCpuBoard, PerturbationBoard, QDPerturbationBoard, SpatialBucket, DDSpatialBucket, QDSpatialBucket, ReferenceOrbitThreading, CpuZhuoranBaseBoard, DDZhuoranBoard, QDZhuoranBoard, GpuBaseBoard, GpuBoard, GpuZhuoranBoard, AdaptiveGpuBoard, FractalWorker }; |