/* =============================================================================
 * spreadsheet_functions_stat.ts  (주인 B · 3차 · 2026-09-27)
 * 통계 함수 — MEDIAN · MODE · STDEV(.S/.P) · VAR · RANK(.EQ) · LARGE · SMALL ·
 * PERCENTILE · QUARTILE · COUNTBLANK. 형 바꾸기 도우미는 `spreadsheet_functions_math.ts` 공용 것을 씀.
 * ========================================================================== */

import { ZERO, add, cmp, div, frac, mul, sub, type Frac } from "@ui/sheet/ui_template_sheet_frac";
import type {
  ErrorValue,
  EvalContext,
  EvalResult,
  LazyArg,
  RangeValue,
  SheetFunction,
} from "./spreadsheet_types";
import {
  collectNumbers,
  fracToDouble,
  fromDouble,
  isErr,
  isFrac,
  isRange,
  mkErr,
  num,
} from "./spreadsheet_functions_math";

function rangeNumbers(range: RangeValue): Frac[] | ErrorValue {
  const out: Frac[] = [];
  for (let r = 0; r < range.rows; r++) {
    for (let c = 0; c < range.cols; c++) {
      const cell = range.at(r, c);
      if (isErr(cell)) return cell;
      if (isFrac(cell)) out.push(cell);
    }
  }
  return out;
}

function meanAndSumSq(values: Frac[]): { mean: Frac; sumSq: Frac } {
  const n = frac(BigInt(values.length));
  const mean = div(values.reduce(add, ZERO), n);
  const sumSq = values.reduce((acc, v) => add(acc, mul(sub(v, mean), sub(v, mean))), ZERO);
  return { mean, sumSq };
}

function sampleVariance(values: Frac[]): Frac | ErrorValue {
  if (values.length < 2) return mkErr("#DIV/0!");
  return div(meanAndSumSq(values).sumSq, frac(BigInt(values.length - 1)));
}

function populationVariance(values: Frac[]): Frac | ErrorValue {
  if (values.length < 1) return mkErr("#DIV/0!");
  return div(meanAndSumSq(values).sumSq, frac(BigInt(values.length)));
}

function stdevOf(variance: Frac | ErrorValue): Frac | ErrorValue {
  if (isErr(variance)) return variance;
  return fromDouble(Math.sqrt(fracToDouble(variance)));
}

/** 정렬한 값에서 0 ≤ k ≤ 1 자리의 백분위(직선 보간 · 엑셀 PERCENTILE.INC 와 같음) */
function percentileOf(values: Frac[], k: number): Frac | ErrorValue {
  if (values.length === 0) return mkErr("#NUM!");
  if (k < 0 || k > 1) return mkErr("#NUM!");
  const sorted = [...values].sort((a, b) => cmp(a, b));
  const pos = k * (sorted.length - 1);
  const lowIdx = Math.floor(pos);
  const highIdx = Math.ceil(pos);
  if (lowIdx === highIdx) return sorted[lowIdx];
  const weight = fromDouble(pos - lowIdx);
  if (isErr(weight)) return weight;
  return add(sorted[lowIdx], mul(weight, sub(sorted[highIdx], sorted[lowIdx])));
}

function nthOrderStat(range: RangeValue, k: number, largest: boolean): Frac | ErrorValue {
  const values = rangeNumbers(range);
  if (isErr(values)) return values;
  if (k < 1 || k > values.length) return mkErr("#NUM!");
  const sorted = [...values].sort((a, b) => cmp(a, b));
  return sorted[largest ? sorted.length - k : k - 1];
}

function rankCall(args: LazyArg[], _ctx: EvalContext): EvalResult {
  const target = num(args[0]());
  if (isErr(target)) return target;
  const range = args[1]();
  if (!isRange(range)) return mkErr("#VALUE!");
  const orderArg = args.length > 2 ? num(args[2]()) : ZERO;
  if (isErr(orderArg)) return orderArg;
  const ascending = cmp(orderArg, ZERO) !== 0;
  let rank = 1;
  let found = false;
  for (let r = 0; r < range.rows; r++) {
    for (let c = 0; c < range.cols; c++) {
      const cell = range.at(r, c);
      if (!isFrac(cell)) continue;
      if (cmp(cell, target) === 0) found = true;
      if (ascending ? cmp(cell, target) < 0 : cmp(cell, target) > 0) rank++;
    }
  }
  return found ? frac(BigInt(rank)) : mkErr("#N/A");
}

export const STAT_FUNCTIONS: Record<string, SheetFunction> = {
  MEDIAN: {
    min: 1,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      if (isErr(values)) return values;
      if (values.length === 0) return mkErr("#NUM!");
      const sorted = [...values].sort((a, b) => cmp(a, b));
      const mid = Math.floor(sorted.length / 2);
      if (sorted.length % 2 === 1) return sorted[mid];
      return div(add(sorted[mid - 1], sorted[mid]), frac(2n));
    },
  },
  MODE: {
    min: 1,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      if (isErr(values)) return values;
      let bestIdx = -1;
      let bestCount = 1;
      for (let i = 0; i < values.length; i++) {
        let count = 0;
        for (const v of values) if (cmp(values[i], v) === 0) count++;
        if (count > bestCount) {
          bestCount = count;
          bestIdx = i;
        }
      }
      return bestIdx < 0 ? mkErr("#N/A") : values[bestIdx];
    },
  },
  STDEV: {
    min: 1,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      return isErr(values) ? values : stdevOf(sampleVariance(values));
    },
  },
  "STDEV.S": {
    min: 1,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      return isErr(values) ? values : stdevOf(sampleVariance(values));
    },
  },
  "STDEV.P": {
    min: 1,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      return isErr(values) ? values : stdevOf(populationVariance(values));
    },
  },
  VAR: {
    min: 1,
    call: (args) => {
      const values = collectNumbers(args, true, true);
      return isErr(values) ? values : sampleVariance(values);
    },
  },
  RANK: { min: 2, max: 3, call: rankCall },
  "RANK.EQ": { min: 2, max: 3, call: rankCall },
  LARGE: {
    min: 2,
    max: 2,
    call: (args) => {
      const range = args[0]();
      if (!isRange(range)) return mkErr("#VALUE!");
      const kArg = num(args[1]());
      if (isErr(kArg)) return kArg;
      return nthOrderStat(range, Math.trunc(fracToDouble(kArg)), true);
    },
  },
  SMALL: {
    min: 2,
    max: 2,
    call: (args) => {
      const range = args[0]();
      if (!isRange(range)) return mkErr("#VALUE!");
      const kArg = num(args[1]());
      if (isErr(kArg)) return kArg;
      return nthOrderStat(range, Math.trunc(fracToDouble(kArg)), false);
    },
  },
  PERCENTILE: {
    min: 2,
    max: 2,
    call: (args) => {
      const range = args[0]();
      if (!isRange(range)) return mkErr("#VALUE!");
      const kArg = num(args[1]());
      if (isErr(kArg)) return kArg;
      const values = rangeNumbers(range);
      if (isErr(values)) return values;
      return percentileOf(values, fracToDouble(kArg));
    },
  },
  QUARTILE: {
    min: 2,
    max: 2,
    call: (args) => {
      const range = args[0]();
      if (!isRange(range)) return mkErr("#VALUE!");
      const qArg = num(args[1]());
      if (isErr(qArg)) return qArg;
      const q = Math.trunc(fracToDouble(qArg));
      if (q < 0 || q > 4) return mkErr("#NUM!");
      const values = rangeNumbers(range);
      if (isErr(values)) return values;
      return percentileOf(values, q / 4);
    },
  },
  COUNTBLANK: {
    min: 1,
    max: 1,
    call: (args) => {
      const range = args[0]();
      if (!isRange(range)) return mkErr("#VALUE!");
      let count = 0;
      for (let r = 0; r < range.rows; r++) {
        for (let c = 0; c < range.cols; c++) if (range.at(r, c) === null) count++;
      }
      return frac(BigInt(count));
    },
  },
};