/** Half-way rounding offset used by the nearest-Nth reduction rule. */
const ROUNDING_HALF = 0.5;

/** Simple-fraction contract accepted by configuration parsing. */
const SIMPLE_FRACTION_PATTERN = /^\d+\/\d+$/u;

/** Fixed anchor so every model interprets one A4 page identically. */
export const A4_PAGE_ANCHOR_TEXT = "One A4 page is about 500 words.";

/** Formats one size target as a simple A4 page fraction, never as a decimal. */
export function formatA4Fraction(
	fraction: number,
	maxDenominator: number,
): string {
	if (fraction >= 1) {
		return "a full A4 page";
	}
	const { numerator, denominator } = toSimpleFraction(fraction, maxDenominator);
	return `${numerator}/${denominator} of an A4 page`;
}

/** Returns the next reduced size target for one retry step. */
export function nextReducedFraction(
	fraction: number,
	coefficient: number,
	maxDenominator: number,
): number {
	const reduced = fraction * coefficient;
	const partCount = Math.floor(
		reduced * maxDenominator + ROUNDING_HALF - Number.EPSILON,
	);
	const clamped = Math.max(1, Math.min(maxDenominator, partCount));
	return clamped / maxDenominator;
}

/** Parses one "n/d" fraction string with a denominator of at most maxDenominator. */
export function parseSimpleFraction(
	value: unknown,
	maxDenominator: number,
): number | string {
	if (typeof value !== "string" || !SIMPLE_FRACTION_PATTERN.test(value)) {
		return "must be a simple fraction like 2/3";
	}
	const [numeratorText, denominatorText] = value.split("/", 2);
	const numerator = Number(numeratorText);
	const denominator = Number(denominatorText);
	if (numerator < 1 || denominator < 1) {
		return "must be a simple fraction like 2/3";
	}
	if (numerator > denominator) {
		return "fraction must not exceed 1";
	}
	if (denominator > maxDenominator) {
		return `fraction denominator must not exceed ${maxDenominator}`;
	}
	return numerator / denominator;
}

/** Finds the closest simple fraction with a denominator of at most maxDenominator. */
function toSimpleFraction(
	value: number,
	maxDenominator: number,
): {
	readonly numerator: number;
	readonly denominator: number;
} {
	let bestNumerator = 1;
	let bestDenominator = 1;
	let bestError = Number.POSITIVE_INFINITY;
	for (let denominator = 1; denominator <= maxDenominator; denominator += 1) {
		const numerator = Math.round(value * denominator);
		if (numerator < 1 || numerator > denominator) {
			continue;
		}
		const error = Math.abs(numerator / denominator - value);
		if (error < bestError) {
			bestError = error;
			bestNumerator = numerator;
			bestDenominator = denominator;
		}
	}
	return { numerator: bestNumerator, denominator: bestDenominator };
}