feat(functions): add statistical functions

lib/src/functions/stats.dart

@@ -0,0 +1,124 @@
+import 'dart:math' as math;
+
+import '../evaluator.dart';
+import '../values.dart';
+import 'helpers.dart';
+
+void registerStats(Map<String, CellFunction> registry) {
+  registry['AVERAGE'] = (args, ctx) {
+    final numbers = ctx.numbersFrom(args);
+    if (numbers.isEmpty) throw const EvalException(ErrorValue(ErrorKind.divZero));
+    return NumberValue(numbers.reduce((a, b) => a + b) / numbers.length);
+  };
+  registry['AVG'] = registry['AVERAGE']!;
+
+  registry['COUNT'] = (args, ctx) {
+    var count = 0;
+    for (final value in ctx.flatten(args)) {
+      if (value is NumberValue) count++;
+    }
+    return NumberValue(count.toDouble());
+  };
+
+  registry['COUNTA'] = (args, ctx) {
+    var count = 0;
+    for (final value in ctx.flatten(args)) {
+      if (value is! BlankValue) count++;
+    }
+    return NumberValue(count.toDouble());
+  };
+
+  registry['COUNTBLANK'] = (args, ctx) {
+    var count = 0;
+    for (final value in ctx.flatten(args)) {
+      if (value is BlankValue) count++;
+    }
+    return NumberValue(count.toDouble());
+  };
+
+  registry['MEDIAN'] = (args, ctx) {
+    final numbers = ctx.numbersFrom(args)..sort();
+    if (numbers.isEmpty) throw const EvalException(ErrorValue(ErrorKind.numError));
+    final middle = numbers.length ~/ 2;
+    if (numbers.length.isOdd) return NumberValue(numbers[middle]);
+    return NumberValue((numbers[middle - 1] + numbers[middle]) / 2);
+  };
+
+  registry['MODE'] = (args, ctx) {
+    final numbers = ctx.numbersFrom(args);
+    final counts = <double, int>{};
+    for (final value in numbers) {
+      counts[value] = (counts[value] ?? 0) + 1;
+    }
+    double? best;
+    var bestCount = 1;
+    for (final value in numbers) {
+      final count = counts[value]!;
+      if (count > bestCount) {
+        bestCount = count;
+        best = value;
+      }
+    }
+    if (best == null) throw const EvalException(ErrorValue(ErrorKind.na));
+    return NumberValue(best);
+  };
+
+  registry['VAR'] = (args, ctx) => NumberValue(_variance(ctx.numbersFrom(args), sample: true));
+  registry['VARP'] = (args, ctx) => NumberValue(_variance(ctx.numbersFrom(args), sample: false));
+  registry['STDEV'] = (args, ctx) =>
+      NumberValue(math.sqrt(_variance(ctx.numbersFrom(args), sample: true)));
+  registry['STDEVP'] = (args, ctx) =>
+      NumberValue(math.sqrt(_variance(ctx.numbersFrom(args), sample: false)));
+
+  registry['LARGE'] = (args, ctx) {
+    arity(args, 2, 2);
+    final numbers = ctx.numbersFrom([args[0]])..sort((a, b) => b.compareTo(a));
+    final k = intArg(args[1], ctx);
+    if (k < 1 || k > numbers.length) throw const EvalException(ErrorValue(ErrorKind.numError));
+    return NumberValue(numbers[k - 1]);
+  };
+
+  registry['SMALL'] = (args, ctx) {
+    arity(args, 2, 2);
+    final numbers = ctx.numbersFrom([args[0]])..sort();
+    final k = intArg(args[1], ctx);
+    if (k < 1 || k > numbers.length) throw const EvalException(ErrorValue(ErrorKind.numError));
+    return NumberValue(numbers[k - 1]);
+  };
+
+  registry['RANK'] = (args, ctx) {
+    arity(args, 2, 3);
+    final target = numberArg(args[0], ctx);
+    final numbers = ctx.numbersFrom([args[1]]);
+    final ascending = args.length > 2 && intArg(args[2], ctx) != 0;
+    numbers.sort(ascending ? (a, b) => a.compareTo(b) : (a, b) => b.compareTo(a));
+    final index = numbers.indexOf(target);
+    if (index < 0) throw const EvalException(ErrorValue(ErrorKind.na));
+    return NumberValue((index + 1).toDouble());
+  };
+
+  registry['PERCENTILE'] = (args, ctx) {
+    arity(args, 2, 2);
+    final numbers = ctx.numbersFrom([args[0]])..sort();
+    if (numbers.isEmpty) throw const EvalException(ErrorValue(ErrorKind.numError));
+    final fraction = numberArg(args[1], ctx);
+    if (fraction < 0 || fraction > 1) throw const EvalException(ErrorValue(ErrorKind.numError));
+    final position = fraction * (numbers.length - 1);
+    final lower = position.floor();
+    final upper = position.ceil();
+    if (lower == upper) return NumberValue(numbers[lower]);
+    final weight = position - lower;
+    return NumberValue(numbers[lower] * (1 - weight) + numbers[upper] * weight);
+  };
+}
+
+double _variance(List<double> numbers, {required bool sample}) {
+  final divisor = sample ? numbers.length - 1 : numbers.length;
+  if (divisor <= 0) throw const EvalException(ErrorValue(ErrorKind.divZero));
+  final mean = numbers.reduce((a, b) => a + b) / numbers.length;
+  var sum = 0.0;
+  for (final value in numbers) {
+    sum += (value - mean) * (value - mean);
+  }
+  return sum / divisor;
+}