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* @packageDocumentation
*
* Pure, headless timing engine for computing measure boundaries, snap grid
* points, and pulse↔seconds conversion from BPM changes and time signature
* events.
*
* All functions operate on plain numeric pulse positions. There is no
* dependency on React, the DOM, or ECS entities.
*
* ## Design principles
*
* - **Measure-relative snap grid** — Snap points reset at every measure
* boundary, including interrupted measures.
* - **Time signatures interrupt immediately** — A new time signature at pulse
* `P` starts a new measure at `P`, cutting the previous measure short.
* - **BPM is independent from time signature** — Measure boundaries are
* determined solely by time signatures; BPM only affects real-time
* conversion.
* - **Precomputed arrays with binary search** — Measure boundaries and BPM
* segments are stored as sorted arrays. Queries use binary search for
* O(log n) lookup.
*/
import { bisectLeft, bisectRight, bisectRightBy } from "../binary-search";
const PPQN = 240;
export interface BpmChange {
pulse: number;
bpm: number;
}
export interface TimeSignature {
pulse: number;
numerator: number;
denominator: number;
}
export interface TimingEngine {
/** Returns measure start pulses in `[start, end)`. */
getMeasureBoundaries(range: { start: number; end: number }): number[];
/** Returns snap grid points in `[start, end)` for the given snap setting. */
getSnapPoints(snap: string, range: { start: number; end: number }): number[];
/** Converts a pulse position to seconds using the piecewise BPM curve. */
pulseToSeconds(pulse: number): number;
/** Converts seconds to the corresponding pulse position. */
secondsToPulse(seconds: number): number;
/** Snaps a pulse to the nearest grid point for the given snap setting. */
snapPulse(pulse: number, snap: string): number;
/** Returns the measure index (0-based) and measure start pulse for the given pulse. */
getMeasureAtPulse(pulse: number): {
measureIndex: number;
measureStart: number;
measureEnd: number;
};
/** Returns the BPM active at the given pulse. */
getBpmAtPulse(pulse: number): number;
/** Returns the time signature active at the given pulse. */
getTimeSignatureAtPulse(pulse: number): TimeSignature;
/** Formats seconds as `MM:SS.mmm`. */
formatTime(seconds: number): string;
}
function getMeasureLength(sig: TimeSignature): number {
return (sig.numerator * 4 * PPQN) / sig.denominator;
}
function parseSnapInterval(snap: string): number {
const match = snap.match(/^1\/(\d+)$/);
if (!match) {
throw new Error(`Invalid snap format: ${snap}`);
}
const n = parseInt(match[1], 10);
Iif (n <= 0) {
throw new Error(`Invalid snap denominator: ${n}`);
}
const interval = (4 * PPQN) / n;
if (!Number.isInteger(interval)) {
throw new Error(`Snap ${snap} does not produce an integer pulse interval`);
}
return interval;
}
interface BpmSegment {
startPulse: number;
startSeconds: number;
bpm: number;
}
export function createTimingEngine(
bpmChanges: BpmChange[],
timeSignatures: TimeSignature[],
): TimingEngine {
const sortedBpms = [...bpmChanges].sort((a, b) => a.pulse - b.pulse);
const sortedSigs = [...timeSignatures].sort((a, b) => a.pulse - b.pulse);
if (sortedBpms.length === 0) {
sortedBpms.push({ pulse: 0, bpm: 60 });
}
// Implicit 4/4 at pulse 0 when no explicit signature is present.
const effectiveSigs: TimeSignature[] =
sortedSigs.length > 0 && sortedSigs[0].pulse === 0
? sortedSigs
: [{ pulse: 0, numerator: 4, denominator: 4 }, ...sortedSigs];
// Precompute BPM segments.
const bpmSegments: BpmSegment[] = [];
let accumulatedSeconds = 0;
for (let i = 0; i < sortedBpms.length; i++) {
bpmSegments.push({
startPulse: sortedBpms[i].pulse,
startSeconds: accumulatedSeconds,
bpm: sortedBpms[i].bpm,
});
if (i + 1 < sortedBpms.length) {
const deltaPulse = sortedBpms[i + 1].pulse - sortedBpms[i].pulse;
accumulatedSeconds += (deltaPulse / PPQN) * (60 / sortedBpms[i].bpm);
}
}
// Lazily-computed measure boundaries.
const boundaries: number[] = [];
let boundariesComputedUpTo = -Infinity;
function findSigIndex(pulse: number): number {
let lo = 0;
let hi = effectiveSigs.length - 1;
while (lo < hi) {
const mid = Math.floor((lo + hi + 1) / 2);
if (effectiveSigs[mid].pulse <= pulse) {
lo = mid;
} else {
hi = mid - 1;
}
}
return lo;
}
function computeNextBoundary(measureStart: number, sigIndex: number): [number, number] {
// Advance to the time signature active at this measure start.
while (
sigIndex + 1 < effectiveSigs.length &&
effectiveSigs[sigIndex + 1].pulse <= measureStart
) {
sigIndex++;
}
const sig = effectiveSigs[sigIndex];
const length = getMeasureLength(sig);
const nextMeasureStart = measureStart + length;
if (
sigIndex + 1 < effectiveSigs.length &&
effectiveSigs[sigIndex + 1].pulse < nextMeasureStart
) {
return [effectiveSigs[sigIndex + 1].pulse, sigIndex + 1];
}
return [nextMeasureStart, sigIndex];
}
function ensureBoundariesUpTo(targetPulse: number) {
if (targetPulse < boundariesComputedUpTo) return;
let measureStart: number;
let sigIndex: number;
if (boundaries.length === 0) {
measureStart = effectiveSigs[0].pulse;
sigIndex = 0;
} else {
measureStart = boundaries[boundaries.length - 1];
sigIndex = findSigIndex(measureStart);
[measureStart, sigIndex] = computeNextBoundary(measureStart, sigIndex);
}
while (measureStart <= targetPulse) {
boundaries.push(measureStart);
[measureStart, sigIndex] = computeNextBoundary(measureStart, sigIndex);
}
boundariesComputedUpTo = measureStart;
}
return {
getMeasureBoundaries({ start, end }) {
ensureBoundariesUpTo(end);
const left = bisectLeft(boundaries, start);
const right = bisectLeft(boundaries, end);
return boundaries.slice(left, right);
},
getSnapPoints(snap, { start, end }) {
const interval = parseSnapInterval(snap);
ensureBoundariesUpTo(end);
const points: number[] = [];
let measureIdx = bisectRight(boundaries, start) - 1;
Iif (measureIdx < 0) measureIdx = 0;
while (measureIdx < boundaries.length && boundaries[measureIdx] < end) {
const measureStart = boundaries[measureIdx];
const measureEnd =
measureIdx + 1 < boundaries.length
? boundaries[measureIdx + 1]
: computeNextBoundary(measureStart, findSigIndex(measureStart))[0];
const rangeStart = Math.max(start, measureStart);
let point = measureStart + Math.ceil((rangeStart - measureStart) / interval) * interval;
while (point < Math.min(end, measureEnd)) {
points.push(point);
point += interval;
}
measureIdx++;
}
return points;
},
pulseToSeconds(pulse) {
if (pulse <= 0) return 0;
const idx = Math.max(0, bisectRightBy(bpmSegments, pulse, (s) => s.startPulse) - 1);
const seg = bpmSegments[idx];
const deltaPulse = pulse - seg.startPulse;
return seg.startSeconds + (deltaPulse / PPQN) * (60 / seg.bpm);
},
secondsToPulse(seconds) {
if (seconds <= 0) return 0;
const idx = bisectRightBy(bpmSegments, seconds, (s) => s.startSeconds) - 1;
const seg = bpmSegments[idx];
const remaining = seconds - seg.startSeconds;
return seg.startPulse + (remaining / (60 / seg.bpm)) * PPQN;
},
snapPulse(pulse, snap) {
const interval = parseSnapInterval(snap);
ensureBoundariesUpTo(pulse);
const measureIdx = bisectRight(boundaries, pulse) - 1;
Iif (measureIdx < 0) return 0;
const measureStart = boundaries[measureIdx];
const measureEnd =
measureIdx + 1 < boundaries.length
? boundaries[measureIdx + 1]
: computeNextBoundary(measureStart, findSigIndex(measureStart))[0];
const snapped = measureStart + Math.round((pulse - measureStart) / interval) * interval;
return Math.max(measureStart, Math.min(snapped, measureEnd - interval));
},
getMeasureAtPulse(pulse) {
ensureBoundariesUpTo(pulse);
const measureIdx = bisectRight(boundaries, pulse) - 1;
Iif (measureIdx < 0) {
return { measureIndex: 0, measureStart: 0, measureEnd: boundaries[0] ?? 0 };
}
const measureStart = boundaries[measureIdx];
const measureEnd =
measureIdx + 1 < boundaries.length
? boundaries[measureIdx + 1]
: computeNextBoundary(measureStart, findSigIndex(measureStart))[0];
return { measureIndex: measureIdx, measureStart, measureEnd };
},
getBpmAtPulse(pulse) {
const idx = Math.max(0, bisectRightBy(bpmSegments, pulse, (s) => s.startPulse) - 1);
return bpmSegments[idx]?.bpm ?? 60;
},
getTimeSignatureAtPulse(pulse) {
const idx = Math.max(0, bisectRightBy(effectiveSigs, pulse, (s) => s.pulse) - 1);
return effectiveSigs[idx] ?? { pulse: 0, numerator: 4, denominator: 4 };
},
formatTime(seconds) {
const mins = Math.floor(seconds / 60);
const secs = Math.floor(seconds % 60);
const ms = Math.floor((seconds % 1) * 1000);
return `${String(mins).padStart(2, "0")}:${String(secs).padStart(2, "0")}.${String(ms).padStart(3, "0")}`;
},
};
}
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