/* =============================================================================
 * spreadsheet_functions_math.ts  (주인 B)
 * 수학 · 삼각 · 끝수 함수 + 함수 표 전체가 쓰는 형 바꾸기 도우미(공용은 여기서 export).
 * 뜻 · 경계값은 엑셀과 같게(Formula.js 는 시험 대조 답으로만 씀 · 속에 안 넣음).
 * 무리수(SQRT · 삼각 · PI · 소수 거듭제곱)는 double → 유효 15 자리 십진 → 분수.
 * ========================================================================== */

import {
  ZERO,
  add,
  cmp,
  div,
  frac,
  mul,
  parseDecimal,
  roundAt,
  sub,
  toInteger,
  type Frac,
} from "@ui/sheet/ui_template_sheet_frac";
import type {
  ErrorCode,
  ErrorValue,
  EvalResult,
  LazyArg,
  RangeValue,
  Scalar,
  SheetFunction,
} from "./spreadsheet_types";

const ONE = frac(1n);

// ── 공용 도우미(math · misc 둘 다 씀) ────────────────────────────────────────

export function mkErr(code: ErrorCode, why?: string): ErrorValue {
  return why === undefined ? { error: code } : { error: code, why };
}

export function isErr(v: unknown): v is ErrorValue {
  return typeof v === "object" && v !== null && "error" in (v as Record<string, unknown>);
}

export function isFrac(v: unknown): v is Frac {
  return typeof v === "object" && v !== null && "n" in (v as Record<string, unknown>);
}

export function isRange(v: EvalResult): v is RangeValue {
  return typeof v === "object" && v !== null && (v as RangeValue).kind === "range";
}

/** 범위면 1×1 일 때만 칸 하나로 · 아니면 `#VALUE!` */
export function toScalar(v: EvalResult): Scalar | ErrorValue {
  if (!isRange(v)) return v;
  if (v.rows === 1 && v.cols === 1) return v.at(0, 0);
  return mkErr("#VALUE!", "범위를 칸 하나 자리에 씀");
}

/** 빈 칸 0 · 참거짓 1/0 · 수 글 · 아니면 `#VALUE!` */
export function toNumber(v: Scalar): Frac | ErrorValue {
  if (v === null) return ZERO;
  if (isErr(v)) return v;
  if (typeof v === "boolean") return v ? ONE : ZERO;
  if (typeof v === "string") {
    try {
      return parseDecimal(v);
    } catch {
      return mkErr("#VALUE!", `글을 수로 못 읽음: ${v}`);
    }
  }
  return v;
}

/** 인자 하나(범위는 1×1 만) → 수 */
export function num(v: EvalResult): Frac | ErrorValue {
  const s = toScalar(v);
  return isErr(s) ? s : toNumber(s);
}

/** 글로 — 수는 일반 형식(간단 십진) · 참거짓 TRUE/FALSE */
export function toText(v: Scalar): string | ErrorValue {
  if (v === null) return "";
  if (isErr(v)) return v;
  if (typeof v === "string") return v;
  if (typeof v === "boolean") return v ? "TRUE" : "FALSE";
  return generalNumberText(v);
}

export function str(v: EvalResult): string | ErrorValue {
  const s = toScalar(v);
  return isErr(s) ? s : toText(s);
}

export function toBool(v: Scalar): boolean | ErrorValue {
  if (v === null) return false;
  if (isErr(v)) return v;
  if (typeof v === "boolean") return v;
  if (typeof v === "string") {
    const up = v.trim().toUpperCase();
    if (up === "TRUE") return true;
    if (up === "FALSE") return false;
    return mkErr("#VALUE!", `글을 참거짓으로 못 읽음: ${v}`);
  }
  return cmp(v, ZERO) !== 0;
}

export function bool(v: EvalResult): boolean | ErrorValue {
  const s = toScalar(v);
  return isErr(s) ? s : toBool(s);
}

/** double → 유효 15 자리 십진 → 분수 · NaN · 무한은 `#NUM!` */
export function fromDouble(x: number): Frac | ErrorValue {
  if (!Number.isFinite(x)) return mkErr("#NUM!");
  if (x === 0) return ZERO;
  return parseDecimal(x.toPrecision(15));
}

export function fracToDouble(x: Frac): number {
  return Number(x.n) / Number(x.d);
}

/** 엑셀 「일반」 형식과 같은 십진 글(수식 `&` · TEXT 안 형식 자리가 없을 때) */
export function generalNumberText(x: Frac): string {
  const scaled = toInteger(mul(x, frac(10n ** 15n)), "round");
  const negative = scaled < 0n;
  const digits = (negative ? -scaled : scaled).toString().padStart(16, "0");
  const whole = digits.slice(0, -15).replace(/^0+(?=\d)/, "");
  const fraction = digits.slice(-15).replace(/0+$/, "");
  const body = fraction ? `${whole}.${fraction}` : whole;
  return negative && body !== "0" ? `-${body}` : body;
}

/** 인자 목록에서 수만 모음 — 범위는 수 아닌 값 조용히 건너뜀 · 낱값은 형 바꿈(실패시 strict 면 오류)
 * `propagateErrors` = 범위 · 낱값 오류를 그대로 돌려줄지(COUNT 는 false) */
export function collectNumbers(
  args: LazyArg[],
  propagateErrors: boolean,
  strictScalar: boolean,
): Frac[] | ErrorValue {
  const out: Frac[] = [];
  for (const a of args) {
    const v = a();
    if (isRange(v)) {
      for (let r = 0; r < v.rows; r++) {
        for (let c = 0; c < v.cols; c++) {
          const cell = v.at(r, c);
          if (isErr(cell)) {
            if (propagateErrors) return cell;
            continue;
          }
          if (isFrac(cell)) out.push(cell);
        }
      }
    } else if (isErr(v)) {
      if (propagateErrors) return v;
    } else if (v !== null) {
      const n = toNumber(v);
      if (isErr(n)) {
        if (strictScalar) return n;
      } else {
        out.push(n);
      }
    }
  }
  return out;
}

function digitsArg(args: LazyArg[], index: number, fallback: number): number | ErrorValue {
  if (index >= args.length) return fallback;
  const n = num(args[index]());
  return isErr(n) ? n : Math.trunc(fracToDouble(n));
}

function unaryDouble(fn: (x: number) => number): SheetFunction {
  return {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      return fromDouble(fn(fracToDouble(n)));
    },
  };
}

// ── 함수 표 ──────────────────────────────────────────────────────────────

export const MATH_FUNCTIONS: Record<string, SheetFunction> = {
  SUM: {
    min: 0,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      if (isErr(values)) return values;
      return values.reduce(add, ZERO);
    },
  },
  PRODUCT: {
    min: 0,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      if (isErr(values)) return values;
      return values.length === 0 ? ZERO : values.reduce(mul, ONE);
    },
  },
  SUMPRODUCT: {
    min: 1,
    call: (args) => {
      const arrays = args.map((a) => a());
      const grids = arrays.map((v) =>
        isRange(v) ? v : { rows: 1, cols: 1, at: () => (isErr(v) ? v : (v as Scalar)) },
      );
      const rows = grids[0].rows;
      const cols = grids[0].cols;
      for (const g of grids) {
        if (g.rows !== rows || g.cols !== cols) return mkErr("#VALUE!", "배열 크기가 다름");
      }
      let sum = ZERO;
      for (let r = 0; r < rows; r++) {
        for (let c = 0; c < cols; c++) {
          let prod = ONE;
          for (const g of grids) {
            const n = toNumber(g.at(r, c));
            if (isErr(n)) return n;
            prod = mul(prod, n);
          }
          sum = add(sum, prod);
        }
      }
      return sum;
    },
  },
  ROUND: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const d = digitsArg(args, 1, 0);
      if (isErr(d)) return d;
      return roundAt(n, d, "round");
    },
  },
  ROUNDUP: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const d = digitsArg(args, 1, 0);
      if (isErr(d)) return d;
      return roundAt(n, d, "away");
    },
  },
  ROUNDDOWN: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const d = digitsArg(args, 1, 0);
      if (isErr(d)) return d;
      return roundAt(n, d, "trunc");
    },
  },
  INT: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      return frac(toInteger(n, "floor"));
    },
  },
  TRUNC: {
    min: 1,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const d = digitsArg(args, 1, 0);
      if (isErr(d)) return d;
      return roundAt(n, d, "trunc");
    },
  },
  CEILING: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const sig = num(args[1]());
      if (isErr(sig)) return sig;
      if (cmp(sig, ZERO) === 0) return ZERO;
      if (cmp(n, ZERO) !== 0 && cmp(n, ZERO) > 0 !== cmp(sig, ZERO) > 0) {
        return mkErr("#NUM!", "수 · 기준의 부호가 다름");
      }
      return mul(frac(toInteger(div(n, sig), "away")), sig);
    },
  },
  FLOOR: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const sig = num(args[1]());
      if (isErr(sig)) return sig;
      if (cmp(sig, ZERO) === 0) return ZERO;
      if (cmp(n, ZERO) !== 0 && cmp(n, ZERO) > 0 !== cmp(sig, ZERO) > 0) {
        return mkErr("#NUM!", "수 · 기준의 부호가 다름");
      }
      return mul(frac(toInteger(div(n, sig), "trunc")), sig);
    },
  },
  ABS: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      return frac(n.n < 0n ? -n.n : n.n, n.d);
    },
  },
  MOD: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const d = num(args[1]());
      if (isErr(d)) return d;
      if (cmp(d, ZERO) === 0) return mkErr("#DIV/0!");
      const q = frac(toInteger(div(n, d), "floor"));
      return sub(n, mul(d, q));
    },
  },
  POWER: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const p = num(args[1]());
      if (isErr(p)) return p;
      if (p.d === 1n) {
        const exp = p.n;
        if (exp >= 0n) return frac(n.n ** exp, n.d ** exp);
        if (n.n === 0n) return mkErr("#DIV/0!");
        return frac(n.d ** -exp, n.n ** -exp);
      }
      return fromDouble(Math.pow(fracToDouble(n), fracToDouble(p)));
    },
  },
  SQRT: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      if (cmp(n, ZERO) < 0) return mkErr("#NUM!");
      return fromDouble(Math.sqrt(fracToDouble(n)));
    },
  },
  PI: { min: 0, max: 0, call: () => fromDouble(Math.PI) },
  SIN: unaryDouble(Math.sin),
  COS: unaryDouble(Math.cos),
  TAN: unaryDouble(Math.tan),
  ASIN: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const x = fracToDouble(n);
      if (x < -1 || x > 1) return mkErr("#NUM!");
      return fromDouble(Math.asin(x));
    },
  },
  ACOS: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const x = fracToDouble(n);
      if (x < -1 || x > 1) return mkErr("#NUM!");
      return fromDouble(Math.acos(x));
    },
  },
  ATAN: unaryDouble(Math.atan),
  RADIANS: unaryDouble((x) => (x * Math.PI) / 180),
  DEGREES: unaryDouble((x) => (x * 180) / Math.PI),
  MIN: {
    min: 0,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      if (isErr(values)) return values;
      return values.length === 0 ? ZERO : values.reduce((a, b) => (cmp(a, b) <= 0 ? a : b));
    },
  },
  MAX: {
    min: 0,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      if (isErr(values)) return values;
      return values.length === 0 ? ZERO : values.reduce((a, b) => (cmp(a, b) >= 0 ? a : b));
    },
  },
  AVERAGE: {
    min: 1,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      if (isErr(values)) return values;
      if (values.length === 0) return mkErr("#DIV/0!");
      return div(values.reduce(add, ZERO), frac(BigInt(values.length)));
    },
  },
  MROUND: {
    min: 2,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      const m = num(args[1]());
      if (isErr(m)) return m;
      if (cmp(m, ZERO) === 0) return ZERO;
      if (cmp(n, ZERO) !== 0 && cmp(n, ZERO) > 0 !== cmp(m, ZERO) > 0) {
        return mkErr("#NUM!", "수 · 배수의 부호가 다름");
      }
      return mul(frac(toInteger(div(n, m), "round")), m);
    },
  },
  ODD: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      let v = toInteger(n, "away");
      if (v === 0n) v = 1n;
      else if (v % 2n === 0n) v += v < 0n ? -1n : 1n;
      return frac(v);
    },
  },
  EVEN: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      let v = toInteger(n, "away");
      if (v % 2n !== 0n) v += v < 0n ? -1n : 1n;
      return frac(v);
    },
  },
  LOG: {
    min: 1,
    max: 2,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      if (cmp(n, ZERO) <= 0) return mkErr("#NUM!");
      const base = args.length > 1 ? num(args[1]()) : frac(10n);
      if (isErr(base)) return base;
      if (cmp(base, ZERO) <= 0 || cmp(base, ONE) === 0) return mkErr("#NUM!");
      return fromDouble(Math.log(fracToDouble(n)) / Math.log(fracToDouble(base)));
    },
  },
  LOG10: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      if (cmp(n, ZERO) <= 0) return mkErr("#NUM!");
      return fromDouble(Math.log10(fracToDouble(n)));
    },
  },
  LN: {
    min: 1,
    max: 1,
    call: (args) => {
      const n = num(args[0]());
      if (isErr(n)) return n;
      if (cmp(n, ZERO) <= 0) return mkErr("#NUM!");
      return fromDouble(Math.log(fracToDouble(n)));
    },
  },
  EXP: unaryDouble(Math.exp),
};