Restating EPS After a Stock Split: Preserve the Economics, Change the Unit

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/** Exact stock-split and share-consolidation EPS restatement. */

export type AccountingFramework = "IFRS" | "US_GAAP" | "OTHER_DECLARED";
export type RoundingMode = "half_even" | "half_up";
export type CapitalEventType = "stock_split" | "share_consolidation";

export interface CapitalEvent {
  event_id: string;
  effective_date: string;
  event_type: CapitalEventType;
  post_split_shares: string;
  pre_split_shares: string;
  event_is_effective: boolean;
  changes_resources: boolean;
}

export interface EpsPeriod {
  period_id: string;
  period_start: string;
  period_end: string;
  basis_date: string;
  basis_is_uniform: boolean;
  earnings_available_to_ordinary_shareholders: string;
  weighted_average_ordinary_shares: string;
  is_final: boolean;
}

export interface EpsRestatementInput {
  accounting_framework: AccountingFramework;
  currency: string;
  statements_authorized_for_issue_date: string;
  earnings_scale: string;
  share_scale: string;
  share_decimal_places: number;
  eps_decimal_places: number;
  rounding_mode: RoundingMode;
  restatement_policy: string;
  event_source_policy: string;
  events: CapitalEvent[];
  periods: EpsPeriod[];
}

export interface RestatedPeriod {
  period_id: string;
  period_start: string;
  period_end: string;
  source_basis_date: string;
  applied_event_ids: string[];
  factor_numerator: string;
  factor_denominator: string;
  earnings_available_to_ordinary_shareholders: string;
  pre_restatement_shares: string;
  restated_shares: string;
  pre_restatement_basic_eps: string;
  restated_basic_eps: string;
  share_rounding_adjusted: boolean;
  eps_rounding_adjusted: boolean;
  is_final: boolean;
}

export interface EpsRestatementResult {
  metric: "stock_split_consolidation_eps_restatement";
  accounting_framework: AccountingFramework;
  currency: string;
  statements_authorized_for_issue_date: string;
  status: "final" | "provisional";
  rows: RestatedPeriod[];
}

interface Rational {
  numerator: bigint;
  denominator: bigint;
}

const DECIMAL_RE = /^-?(?:0|[1-9]\d*)(?:\.\d+)?$/;
const POSITIVE_INTEGER_RE = /^[1-9]\d*$/;
const DATE_RE = /^\d{4}-\d{2}-\d{2}$/;

export class EpsRestatementValidationError extends Error {
  constructor(message: string) {
    super(message);
    this.name = "EpsRestatementValidationError";
  }
}

function abs(value: bigint): bigint {
  return value < 0n ? -value : value;
}

function gcd(left: bigint, right: bigint): bigint {
  let a = abs(left);
  let b = abs(right);
  while (b !== 0n) {
    [a, b] = [b, a % b];
  }
  return a;
}

function rational(numerator: bigint, denominator: bigint): Rational {
  if (denominator === 0n) throw new Error("rational denominator cannot be zero");
  if (denominator < 0n) {
    numerator = -numerator;
    denominator = -denominator;
  }
  const divisor = gcd(numerator, denominator);
  return {numerator: numerator / divisor, denominator: denominator / divisor};
}

function multiply(left: Rational, right: Rational): Rational {
  return rational(
    left.numerator * right.numerator,
    left.denominator * right.denominator,
  );
}

function divide(left: Rational, right: Rational): Rational {
  if (right.numerator === 0n) throw new Error("cannot divide by zero");
  return rational(
    left.numerator * right.denominator,
    left.denominator * right.numerator,
  );
}

function parseDecimal(value: unknown, field: string): Rational {
  if (typeof value !== "string" || !DECIMAL_RE.test(value)) {
    throw new EpsRestatementValidationError(
      `${field} must be a canonical decimal string`,
    );
  }
  const unsigned = value.startsWith("-") ? value.slice(1) : value;
  const [whole, fraction = ""] = unsigned.split(".");
  if (whole.length + fraction.length > 30 || fraction.length > 12) {
    throw new EpsRestatementValidationError(
      `${field} exceeds the decimal size limit`,
    );
  }
  return rational(BigInt(value.replace(".", "")), 10n ** BigInt(fraction.length));
}

function parsePositiveInteger(value: unknown, field: string): bigint {
  if (
    typeof value !== "string" ||
    !POSITIVE_INTEGER_RE.test(value) ||
    value.length > 30
  ) {
    throw new EpsRestatementValidationError(
      `${field} must be a positive canonical integer string`,
    );
  }
  return BigInt(value);
}

function roundFixed(
  value: Rational,
  places: number,
  mode: RoundingMode,
): [string, boolean] {
  const negative = value.numerator < 0n;
  const scaled = abs(value.numerator) * 10n ** BigInt(places);
  let quotient = scaled / value.denominator;
  const remainder = scaled % value.denominator;
  const comparison = remainder * 2n - value.denominator;
  const increment = comparison > 0n ||
    (comparison === 0n &&
      (mode === "half_up" ||
        (mode === "half_even" && quotient % 2n === 1n)));
  if (increment) quotient += 1n;
  let digits = quotient.toString();
  if (places > 0) {
    digits = digits.padStart(places + 1, "0");
    const split = digits.length - places;
    digits = `${digits.slice(0, split)}.${digits.slice(split)}`;
  }
  if (negative && quotient !== 0n) digits = `-${digits}`;
  return [digits, remainder !== 0n];
}

function terminatingString(value: Rational): string {
  let denominator = value.denominator;
  let twos = 0;
  let fives = 0;
  while (denominator % 2n === 0n) {
    denominator /= 2n;
    twos++;
  }
  while (denominator % 5n === 0n) {
    denominator /= 5n;
    fives++;
  }
  if (denominator !== 1n) throw new Error("expected a terminating decimal");
  const scale = Math.max(twos, fives);
  let scaled = value.numerator *
    2n ** BigInt(scale - twos) *
    5n ** BigInt(scale - fives);
  const negative = scaled < 0n;
  if (negative) scaled = -scaled;
  let digits = scaled.toString();
  if (scale > 0) {
    digits = digits.padStart(scale + 1, "0");
    const split = digits.length - scale;
    digits = `${digits.slice(0, split)}.${digits.slice(split)}`
      .replace(/0+$/, "")
      .replace(/\.$/, "");
  }
  return negative && digits !== "0" ? `-${digits}` : digits;
}

function requireText(value: unknown, field: string): string {
  if (typeof value !== "string" || value.trim() === "") {
    throw new EpsRestatementValidationError(`${field} must be a non-empty string`);
  }
  return value;
}

function parseDate(value: unknown, field: string): string {
  if (typeof value !== "string" || !DATE_RE.test(value)) {
    throw new EpsRestatementValidationError(`${field} must use YYYY-MM-DD`);
  }
  const parsed = new Date(`${value}T00:00:00Z`);
  if (Number.isNaN(parsed.valueOf()) || parsed.toISOString().slice(0, 10) !== value) {
    throw new EpsRestatementValidationError(`${field} must be a real date`);
  }
  return value;
}

export function restateEpsForCapitalEvents(
  input: EpsRestatementInput,
): EpsRestatementResult {
  if (input === null || typeof input !== "object" || Array.isArray(input)) {
    throw new EpsRestatementValidationError("input must be an object");
  }
  const required: (keyof EpsRestatementInput)[] = [
    "accounting_framework", "currency", "statements_authorized_for_issue_date",
    "earnings_scale", "share_scale", "share_decimal_places",
    "eps_decimal_places", "rounding_mode", "restatement_policy",
    "event_source_policy", "events", "periods",
  ];
  for (const field of required) {
    if (!(field in input)) {
      throw new EpsRestatementValidationError(`missing required field: ${field}`);
    }
  }
  if (!["IFRS", "US_GAAP", "OTHER_DECLARED"].includes(input.accounting_framework)) {
    throw new EpsRestatementValidationError("unsupported accounting_framework");
  }
  if (!/^[A-Z]{3}$/.test(input.currency)) {
    throw new EpsRestatementValidationError(
      "currency must be a three-letter uppercase code",
    );
  }
  const authorization = parseDate(
    input.statements_authorized_for_issue_date,
    "statements_authorized_for_issue_date",
  );
  requireText(input.restatement_policy, "restatement_policy");
  requireText(input.event_source_policy, "event_source_policy");
  const earningsScale = parseDecimal(input.earnings_scale, "earnings_scale");
  const shareScale = parseDecimal(input.share_scale, "share_scale");
  if (earningsScale.numerator <= 0n || shareScale.numerator <= 0n) {
    throw new EpsRestatementValidationError("unit scales must be positive");
  }
  for (const [value, field] of [
    [input.share_decimal_places, "share_decimal_places"],
    [input.eps_decimal_places, "eps_decimal_places"],
  ] as const) {
    if (!Number.isInteger(value) || value < 0 || value > 12) {
      throw new EpsRestatementValidationError(
        `${field} must be an integer from 0 to 12`,
      );
    }
  }
  if (!["half_even", "half_up"].includes(input.rounding_mode)) {
    throw new EpsRestatementValidationError(
      "rounding_mode must be half_even or half_up",
    );
  }
  if (!Array.isArray(input.events)) {
    throw new EpsRestatementValidationError("events must be an array");
  }
  if (!Array.isArray(input.periods) || input.periods.length === 0) {
    throw new EpsRestatementValidationError("periods must be a non-empty array");
  }

  const events: {id: string; effective: string; factor: Rational}[] = [];
  const eventIds = new Set<string>();
  let previousDate: string | null = null;
  input.events.forEach((raw, index) => {
    if (raw === null || typeof raw !== "object" || Array.isArray(raw)) {
      throw new EpsRestatementValidationError(`events[${index}] must be an object`);
    }
    const id = requireText(raw.event_id, `events[${index}].event_id`);
    if (eventIds.has(id)) {
      throw new EpsRestatementValidationError("event_id values must be unique");
    }
    eventIds.add(id);
    const effective = parseDate(
      raw.effective_date,
      `events[${index}].effective_date`,
    );
    if (effective > authorization) {
      throw new EpsRestatementValidationError(
        "events after authorization are outside this invocation",
      );
    }
    if (previousDate !== null && effective <= previousDate) {
      throw new EpsRestatementValidationError(
        "events must be strictly ordered by effective_date",
      );
    }
    previousDate = effective;
    if (typeof raw.event_is_effective !== "boolean" || !raw.event_is_effective) {
      throw new EpsRestatementValidationError("every event must be effective");
    }
    if (typeof raw.changes_resources !== "boolean") {
      throw new EpsRestatementValidationError(
        "every event must declare changes_resources",
      );
    }
    if (raw.changes_resources) {
      throw new EpsRestatementValidationError(
        "resource-changing combined transactions are outside this plain " +
          "split/consolidation engine",
      );
    }
    const post = parsePositiveInteger(
      raw.post_split_shares,
      `events[${index}].post_split_shares`,
    );
    const pre = parsePositiveInteger(
      raw.pre_split_shares,
      `events[${index}].pre_split_shares`,
    );
    const factor = rational(post, pre);
    if (raw.event_type === "stock_split" &&
        factor.numerator <= factor.denominator) {
      throw new EpsRestatementValidationError(
        "stock_split factor must be greater than one",
      );
    }
    if (raw.event_type === "share_consolidation" &&
        factor.numerator >= factor.denominator) {
      throw new EpsRestatementValidationError(
        "share_consolidation factor must be less than one",
      );
    }
    if (!["stock_split", "share_consolidation"].includes(raw.event_type)) {
      throw new EpsRestatementValidationError("unsupported event_type");
    }
    events.push({id, effective, factor});
  });

  const periodIds = new Set<string>();
  const rows = input.periods.map((raw, index): RestatedPeriod => {
    if (raw === null || typeof raw !== "object" || Array.isArray(raw)) {
      throw new EpsRestatementValidationError(`periods[${index}] must be an object`);
    }
    const periodId = requireText(raw.period_id, `periods[${index}].period_id`);
    if (periodIds.has(periodId)) {
      throw new EpsRestatementValidationError("period_id values must be unique");
    }
    periodIds.add(periodId);
    const start = parseDate(raw.period_start, `periods[${index}].period_start`);
    const end = parseDate(raw.period_end, `periods[${index}].period_end`);
    if (start > end) {
      throw new EpsRestatementValidationError(
        "period_start must not exceed period_end",
      );
    }
    const basis = parseDate(raw.basis_date, `periods[${index}].basis_date`);
    if (basis > authorization) {
      throw new EpsRestatementValidationError(
        "basis_date cannot exceed authorization",
      );
    }
    if (typeof raw.basis_is_uniform !== "boolean" || !raw.basis_is_uniform) {
      throw new EpsRestatementValidationError("every period basis must be uniform");
    }
    if (typeof raw.is_final !== "boolean") {
      throw new EpsRestatementValidationError("period is_final must be boolean");
    }
    const earningsReported = parseDecimal(
      raw.earnings_available_to_ordinary_shareholders,
      `periods[${index}].earnings_available_to_ordinary_shareholders`,
    );
    const sharesReported = parseDecimal(
      raw.weighted_average_ordinary_shares,
      `periods[${index}].weighted_average_ordinary_shares`,
    );
    if (sharesReported.numerator <= 0n) {
      throw new EpsRestatementValidationError(
        "weighted_average_ordinary_shares must be positive",
      );
    }
    const earnings = multiply(earningsReported, earningsScale);
    const originalShares = multiply(sharesReported, shareScale);
    let factor = rational(1n, 1n);
    const applied: string[] = [];
    for (const event of events) {
      if (event.effective > basis) {
        factor = multiply(factor, event.factor);
        applied.push(event.id);
      }
    }
    const restatedShares = multiply(originalShares, factor);
    const preEps = divide(earnings, originalShares);
    const restatedEps = divide(earnings, restatedShares);
    const [shareDisplay, shareAdjusted] = roundFixed(
      restatedShares,
      input.share_decimal_places,
      input.rounding_mode,
    );
    const [preEpsDisplay] = roundFixed(
      preEps,
      input.eps_decimal_places,
      input.rounding_mode,
    );
    const [restatedEpsDisplay, epsAdjusted] = roundFixed(
      restatedEps,
      input.eps_decimal_places,
      input.rounding_mode,
    );
    return {
      period_id: periodId,
      period_start: start,
      period_end: end,
      source_basis_date: basis,
      applied_event_ids: applied,
      factor_numerator: factor.numerator.toString(),
      factor_denominator: factor.denominator.toString(),
      earnings_available_to_ordinary_shareholders: terminatingString(earnings),
      pre_restatement_shares: terminatingString(originalShares),
      restated_shares: shareDisplay,
      pre_restatement_basic_eps: preEpsDisplay,
      restated_basic_eps: restatedEpsDisplay,
      share_rounding_adjusted: shareAdjusted,
      eps_rounding_adjusted: epsAdjusted,
      is_final: raw.is_final,
    };
  });

  return {
    metric: "stock_split_consolidation_eps_restatement",
    accounting_framework: input.accounting_framework,
    currency: input.currency,
    statements_authorized_for_issue_date: authorization,
    status: rows.every((row) => row.is_final) ? "final" : "provisional",
    rows,
  };
}