www-lib-markdown/php/spreadsheet.php

<?php
/**
 * Base spreadsheet calculation error class.
 */
class CellException extends Error {
	/**
	 * Brief symbol to show in the cell to signify an error occurred during
	 * evaluation.
	 *
	 * @$string
	 */
	public string $errorSymbol;

	/**
	 * @param string $message  error message
	 * @param string $errorSymbol  symbol to show in the cell to indicate an error
	 */
	public function __construct(string $message, string $errorSymbol='#ERROR') {
		parent::__construct($message);
		$this->errorSymbol = $errorSymbol;
	}
}

/**
 * Exception thrown when a spreadsheet expression is invalid.
 */
class CellSyntaxException extends CellException {
	public function __construct(string $message, string $errorSymbol='#SYNTAX') {
		parent::__construct($message, $errorSymbol);
	}
}

/**
 * Exception thrown when a problem occurrs during evaluation.
 */
class CellEvaluationException extends CellException {}

/**
 * Exception thrown when cell dependencies cannot be resolved.
 */
class CellDependencyException extends CellException {
	public function __construct(string $message, string $errorSymbol='#REF') {
		parent::__construct($message, $errorSymbol);
	}
}

/**
 * Expression parsing token types.
 */
enum CellExpressionTokenType {
	case Name;
	case Address;
	case NameOrAddress;
	case String;
	case Number;
	case OpenParen;
	case CloseParen;
	case Colon;
	case Plus;
	case Minus;
	case Multiply;
	case Divide;
	case Comma;
	case Semicolon;
	case Ampersand;
	case LessThan;
	case LessThanEqual;
	case GreaterThan;
	case GreaterThanEqual;
	case Equal;
	case Unequal;
	case Not;

	public function isPotentialName(): bool {
		return $this === self::Name || $this === self::NameOrAddress;
	}

	public function isPotentialAddress(): bool {
		return $this === self::Address || $this === self::NameOrAddress;
	}
}

/**
 * Type of operation for a `CellExpression`. Named functions all fall under
 * `Function`.
 */
enum CellExpressionOperation {
	/** Arg is `number` */
	case Number;
	/** Arg is `string` without quotes */
	case String;
	/** Arg is `boolean` */
	case Boolean;
	/** Arg is `CellAddress` */
	case Reference;
	/** Args are start and end `CellAddress`es (e.g. "A5", "C7") */
	case Range;

	/** Args are two operand `CellExpression`s. */
	case Add;
	/** Args are two operand `CellExpression`s */
	case Subtract;
	/** Args are two operand `CellExpression`s */
	case Multiply;
	/** Args are two operand `CellExpression`s */
	case Divide;

	/** Args are two operand `CellExpression`s. */
	case Concatenate;

	/** Arg is operand `CellExpression` */
	case UnaryMinus;

	/** Args are two operand `CellExpression`s. */
	case GreaterThan;
	/** Args are two operand `CellExpression`s. */
	case GreaterThanEqual;
	/** Args are two operand `CellExpression`s. */
	case LessThan;
	/** Args are two operand `CellExpression`s. */
	case LessThanEqual;
	/** Args are two operand `CellExpression`s. */
	case Equal;
	/** Args are two operand `CellExpression`s. */
	case Unequal;

	/** Arg is operand `CellExpression`. */
	case UnaryNot;

	/** Args are 0+ `CellExpression`s */
	case Function;
}

/**
 * Collection of all calculated cells in a table. Evaluates formulas.
 */
class CellExpressionSet {
	private SpreadsheetGrid $grid;

	public function __construct(SpreadsheetGrid $grid) {
		$this->grid = $grid;
	}

	/**
	 * Populates the `outputValue` fields of every cell in the table. Cells
	 * with formulas will attempt to be calculated or populated with error
	 * values.
	 */
	public function calculateCells() {
		$rowCount = $this->grid->rowCount;
		$colCount = $this->grid->columnCount;

		// Make queue of cell addresses with expressions in them
		/** @$CellAddress[] */
		$expressionAddressQueue = [];
		$range = new CellAddressRange(new CellAddress(0, 0), new CellAddress($colCount - 1, $rowCount - 1));
		foreach ($range->cellsIn($this->grid) as $address) {
			$cell = $this->grid->cellAt($address);
			$value = $cell->originalValue;
			if ($value->type != CellValue::TYPE_FORMULA) {
				$cell->outputValue = $value;
				$cell->isCalculated = false;
				continue;
			}
			try {
				$expression = CellExpression::parse($value->formattedValue, $address);
				if (!$expression) {
					throw new CellSyntaxException("Invalid expression");
				}
				$cell->parsedExpression = $expression;
				$cell->isCalculated = true;
				array_push($expressionAddressQueue, $address);
				$this->enqueueFilledBlanks($expression, $expressionAddressQueue);
			} catch (CellException $e) {
				$cell->outputValue = CellValue::fromValue($e);
			}
		}

		// Try to evaluate each cell. If one depends on cells not yet calculated,
		// move it to the back of the queue and try again later.
		$this->processExpressionQueue($expressionAddressQueue);
		// Anything left in the queue is a circular reference.
		$this->processCircularReferences($expressionAddressQueue);
	}

	/**
	 * Attempts to evaluate expressions at the given `addresses`. If an
	 * expression has unevaluated references, the expression is moved to the
	 * end of the queue and tried again later. When this method returns, any
	 * elements left in `addresses` can be considered circular references.
	 * 
	 * @param CellAddress[] $addresses  mutable queue of formula addresses
	 */
	private function processExpressionQueue(array &$addresses) {
		$requeueCount = 0;
		while (sizeof($addresses) > 0 && $requeueCount < sizeof($addresses)) {
			$address = $addresses[0];
			array_splice($addresses, 0, 1);
			$cell = $this->grid->cellAt($address);
			try {
				$result = $this->evaluate($cell->parsedExpression, $address);
				$cell->isCalculated = true;
				if ($result instanceof CellValue) {
					$cell->outputValue = $result;
					$requeueCount = 0;
				} elseif (is_array($result)) {
					if (sizeof($result) == 1) {
						$cell->outputValue = $result[0];
						$requeueCount = 0;
					} else {
						throw new CellEvaluationException("Expression resolved to " . sizeof($result) . " values, single value expected");
					}
				} else {
					$typename = gettype($result) == 'object' ? get_class($result) : gettype($result);
					throw new CellEvaluationException("Expression resolved to {$typename}, expected CellValue");
				}
			} catch (CellDependencyException $e) {
				// Depends on a value that hasn't been calculated yet
				array_push($addresses, $address);
				$requeueCount++;
			} catch (CellSyntaxException | CellEvaluationException $e) {
				$cell->outputValue = CellValue::fromValue($e);
				$requeueCount = 0;
			}
		}
	}

	/**
	 * Autofills a formula, transposing the formula to each affected cell and
	 * stored in `parsedExpression`, and each address is queued in `addresses`
	 * for evaluation.
	 *
	 * @param CellExpression $expression  autofilled formula
	 * @param CellAddress[] $addresses  mutable address queue
	 */
	private function enqueueFilledBlanks(CellExpression $expression, array &$addresses) {
		foreach ($expression->fillRanges ?? [] as $range) {
			foreach ($range->cellsIn($this->grid) as $filledAddress) {
				$filledCell = $this->grid->cellAt($filledAddress);
				if ($filledCell->originalValue->type === CellValue::TYPE_BLANK &&
						(!$filledCell->outputValue ||
						$filledCell->outputValue->type === CellValue::TYPE_BLANK)) {
					$filledCell->parsedExpression = $expression->transpose($expression->location, $filledAddress);
					$filledCell->isCalculated = true;
					array_push($addresses, $filledAddress);
				}
			}
		}
	}

	/**
	 * Marks all cells at the given addresses as circular references.
	 *
	 * @param CellAddress[] $addresses  mutable address queue
	 */
	private function processCircularReferences(array $addresses) {
		foreach ($addresses as $address) {
			$cell = $this->grid->cellAt($address);
			$cell->outputValue = CellValue::fromValue(new CellDependencyException("Circular reference at {$address->name}"));
		}
	}

	/**
	 * Evaluates an expression if possible.
	 *
	 * @param CellExpression $expr  expression to evaluate
	 * @param CellAddress $address  location of expression
	 * @return CellValue|CellValue[]  results
	 */
	private function evaluate(CellExpression $expr, CellAddress $address) {
		$result = $this->preevaluate($expr, $address);
		if ($result instanceof CellValue) {
			// Expression included formatting override. Apply it to value.
			if ($expr->outputType !== null) {
				return CellValue::fromValue($result->value, $expr->outputType ??
					$result->type, $expr->outputDecimals);
			}
		}
		return $result;
	}

	/**
	 * Evaluates an expression if possible. No custom formatting is applied to
	 * result.
	 *
	 * @param CellExpression $expr  expression to evaluate
	 * @param CellAddress $address  location of expression
	 * @return CellValue|CellValue[]  results
	 * @throws CellException if evaluation fails for any reason
	 */
	private function preevaluate(CellExpression $expr, CellAddress $address) {
		switch ($expr->op) {
			case CellExpressionOperation::Number:
			case CellExpressionOperation::String:
			case CellExpressionOperation::Boolean:
				return $expr->arguments[0];

			case CellExpressionOperation::Reference: {
				$refAddress = $expr->arguments[0];
				$cell = $this->grid->cellAt($refAddress);
				if ($cell === null) {
					throw new CellEvaluationException("No cell at {$refAddress->name}", '#REF');
				}
				if ($cell->outputValue === null) {
					throw new CellDependencyException("Need calculated value for {$refAddress} to evaluate");
				}
				return $cell->outputValue;
			}
			case CellExpressionOperation::Range: {
				$range = $expr->arguments[0];
				$values = [];
				foreach ($range->cellsIn($this->grid) as $rAddress) {
					$cell = $this->grid->cellAt($rAddress);
					if ($rAddress->equals($address)) continue;
					$val = $this->grid->outputValueAt($rAddress);
					if ($val === null) {
						throw new CellDependencyException("Need calculated value for {$rAddress->name} to evaluate");
					}
					array_push($values, $val);
				}
				return $values;
			}

			case CellExpressionOperation::Add: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->add($op2);
			}
			case CellExpressionOperation::Subtract: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->subtract($op2);
			}
			case CellExpressionOperation::Multiply: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->multiply($op2);
			}
			case CellExpressionOperation::Divide: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->divide($op2);
			}
			case CellExpressionOperation::UnaryMinus: {
				$op = $this->evaluate($expr->arguments[0], $address);
				return CellValue::fromValue(0)->subtract($op);
			}

			case CellExpressionOperation::GreaterThan: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->gt($op2);
			}
			case CellExpressionOperation::GreaterThanEqual: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->gte($op2);
			}
			case CellExpressionOperation::LessThan: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->lt($op2);
			}
			case CellExpressionOperation::LessThanEqual: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->lte($op2);
			}
			case CellExpressionOperation::Equal: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->eq($op2);
			}
			case CellExpressionOperation::Unequal: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->neq($op2);
			}

			case CellExpressionOperation::UnaryNot: {
				$op = $this->evaluate($expr->arguments[0], $address);
				return $op->not();
			}

			case CellExpressionOperation::Concatenate: {
				$op1 = $this->evaluate($expr->arguments[0], $address);
				$op2 = $this->evaluate($expr->arguments[1], $address);
				return $op1->concatenate($op2);
			}

			case CellExpressionOperation::Function:
				return $this->callFunction($expr->qualifier, $expr->arguments, $address);
		}
		throw new CellSyntaxException("Unhandled operation {$expr->op->name}");
	}

	/**
	 * Evaluates a named function, e.g. `ABS`, `SUM`, etc.
	 *
	 * @param string $functionName  function name
	 * @param array $args  raw arguments
	 * @param CellAddress $address  location of the expression
	 * @return CellValue  result
	 * @throws CellException if evaluation fails for any reason
	 */
	private function callFunction(string $functionName, array $args, CellAddress $address): CellValue {
		switch (mb_strtoupper($functionName)) {
			case 'ABS': return $this->funcAbs($args, $address);
			case 'AND': return $this->funcAnd($args, $address);
			case 'AVERAGE': return $this->funcAverage($args, $address);
			case 'CEILING': return $this->funcCeiling($args, $address);
			case 'EXP': return $this->funcExp($args, $address);
			case 'FLOOR': return $this->funcFloor($args, $address);
			case 'IF': return $this->funcIf($args, $address);
			case 'IFS': return $this->funcIfs($args, $address);
			case 'LN': return $this->funcLn($args, $address);
			case 'LOG': return $this->funcLog($args, $address);
			case 'LOWER': return $this->funcLower($args, $address);
			case 'MAX': return $this->funcMax($args, $address);
			case 'MIN': return $this->funcMin($args, $address);
			case 'MOD': return $this->funcMod($args, $address);
			case 'NOT': return $this->funcNot($args, $address);
			case 'OR': return $this->funcOr($args, $address);
			case 'POWER': return $this->funcPower($args, $address);
			case 'ROUND': return $this->funcRound($args, $address);
			case 'SQRT': return $this->funcSqrt($args, $address);
			case 'SUBSTITUTE': return $this->funcSubstitute($args, $address);
			case 'SUM': return $this->funcSum($args, $address);
			case 'UPPER': return $this->funcUpper($args, $address);
			case 'XOR': return $this->funcXor($args, $address);
			default:
				throw new CellSyntaxException("Unknown function \"{$functionName}\"");
		}
	}

	/**
	 * Checks and evaluates arguments for a numeric function. If successful,
	 * an array of `CellValue`s with numeric values is returned.
	 *
	 * @param string $functionName  name of the function (for debugging)
	 * @param int $minArgs  minimum required arguments
	 * @param int $maxArgs  maximum required arguments
	 * @param array $args  raw arguments
	 * @param CellAddress $address  address of the formula
	 * @return CellValue[]  numeric arguments
	 * @throws CellSyntaxException if wrong number of arguments is passed
	 * @throws CellEvaluationException if an argument does not resolve to a numeric value
	 */
	private function assertNumericArguments(string $functionName, int $minArgs,
			int $maxArgs, array $args, CellAddress $address): array {
		$argCount = sizeof($args);
		if ($argCount < $minArgs || $argCount > $maxArgs) {
			if ($minArgs == $maxArgs) {
				throw new CellSyntaxException("{$functionName}() expects {$minArgs} arguments, got {$argCount}");
			}
			throw new CellSyntaxException("{$functionName}() expects between {$minArgs} and {$maxArgs} arguments, got {$argCount}");
		}
		$out = [];
		foreach ($args as $argument) {
			$evaled = $this->evaluate($argument, $address);
			if (!($evaled instanceof CellValue) || !$evaled->isNumeric()) {
				throw new CellEvaluationException("{$functionName}() expects numeric arguments");
			}
			array_push($out, $evaled);
		}
		return $out;
	}

	/**
	 * Evaluates and flattens numeric arguments. For functions that can take
	 * arbitrary numbers of values including whole cell ranges.
	 *
	 * @param string $functionName  function name (for debugging)
	 * @param array $args  raw arguments
	 * @param CellAddress $address  location of expression
	 * @param bool $errorOnNonnumeric  whether to throw an exception if
	 *   non-numeric arguments are encountered, otherwise they're skipped silently
	 * @return CellValue[]  flattened array of numeric values
	 */
	private function flattenedNumericArguments(string $functionName, array $args,
			CellAddress $address, bool $errorOnNonnumeric=true): array {
		$flattened = [];
		foreach ($args as $argument) {
			$evaled = $this->evaluate($argument, $address);
			if ($evaled instanceof CellValue) {
				if (!$evaled->isNumeric()) {
					if ($errorOnNonnumeric) {
						throw new CellEvaluationException("{$functionName} requires numeric arguments");
					}
					continue;
				}
				array_push($flattened, $evaled);
			} elseif (is_array($evaled)) {
				$arr = $evaled;
				foreach ($arr as $arrayArgument) {
					if ($arrayArgument instanceof CellValue) {
						if (!$arrayArgument->isNumeric()) {
							if ($errorOnNonnumeric) {
								throw new CellEvaluationException("{$functionName} requires numeric arguments");
							}
							continue;
						}
						array_push($flattened, $arrayArgument);
					}
				}
			}
		}
		return $flattened;
	}

	/**
	 * `ABS(value)` - absolute value of a numeric argument
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcAbs(array $args, CellAddress $address): CellValue {
		$arg = $this->assertNumericArguments('ABS', 1, 1, $args, $address)[0];
		if ($arg->value < 0.0) {
			return CellValue::fromValue(0)->subtract($arg);
		}
		return $arg;
	}

	/**
	 * `AND(arg, arg, ..., arg)` - Boolean AND of any number of Boolean arguments
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcAnd(array $args, CellAddress $address): CellValue {
		if (sizeof($args) == 0) {
			throw new CellEvaluationException("AND requires one or more arguments");
		}
		$values = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		foreach ($values as $value) {
			$result = $value->booleanValue();
			if ($result === null) {
				throw new CellEvaluationException("AND requires boolean arguments");
			}
			if (!$result) return CellValue::fromValue(false);
		}
		return CellValue::fromValue(true);
	}

	/**
	 * `AVERAGE(arg, arg, ..., arg)` - Averages values. Non-numeric values are
	 * omitted from the calculation.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcAverage(array $args, CellAddress $address): CellValue {
		$sum = CellValue::fromValue(0);
		$count = 0;
		foreach ($args as $arg) {
			$val = $this->evaluate($arg, $address);
			if (is_array($val)) {
				foreach ($val as $elem) {
					if (!$elem->isNumeric()) continue;
					$sum = $sum->add($elem);
					$count++;
				}
			} elseif ($val->isNumeric()) {
				$sum = $sum->add($val);
				$count++;
			}
		}
		return ($count > 0) ? $sum->divide(CellValue::fromValue($count)) : CellValue::fromValue(0);
	}

	/**
	 * `CEILING(value)` - Ceiling of a numeric value.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcCeiling(array $args, CellAddress $address): CellValue {
		$arg = $this->assertNumericArguments('CEILING', 1, 1, $args, $address)[0];
		$newValue = ceil($arg->value);
		return CellValue::fromValue($newValue, $arg->type);
	}

	/**
	 * `EXP(value)` - Computes _e_ raised to the given exponent.
	 * 
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcExp(array $args, CellAddress $address): CellValue {
		$arg = $this->assertNumericArguments('EXP', 1, 1, $args, $address)[0];
		$newValue = exp($arg->value);
		return CellValue::fromValue($newValue, $arg->type);
	}

	/**
	 * `FLOOR(value)` - Numeric value rounded down.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcFloor(array $args, CellAddress $address): CellValue {
		$arg = $this->assertNumericArguments('FLOOR', 1, 1, $args, $address)[0];
		$newValue =floor($arg->value);
		return CellValue::fromValue($newValue, $arg->type);
	}

	/**
	 * `IF(test, trueVal, falseVal)` - Conditional test.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcIf(array $args, CellAddress $address): CellValue {
		if (sizeof($args) != 3) {
			throw new CellEvaluationException("IF expects three arguments");
		}
		$evaled = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		$test = $evaled[0]->booleanValue();
		if ($test === null) {
			throw new CellEvaluationException("IF expects a boolean for the first argument");
		}
		if ($test) {
			return $evaled[1];
		} else {
			return $evaled[2];
		}
	}

	/**
	 * `IFS(test1, result1, test2, result2, ..., fallbackResult)` - Multiple if
	 * statement. Takes 3 or more arguments of an odd number consisting of pairs
	 * of a Boolean test followed by the value to return if true. The very last
	 * value is the fallback value to return if none of the Boolean tests are true.
	 * 
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcIfs(array $args, CellAddress $address): CellValue {
		if (sizeof($args) < 3) {
			throw new CellEvaluationException("IFS expects at least 3 arguments");
		}
		if ((sizeof($args) % 2) != 1) {
			throw new CellEvaluationException("IFS expects an odd number of arguments");
		}
		$evaled = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		for ($i = 0; $i < sizeof($evaled) - 1; $i += 2) {
			$test = $evaled[i].booleanValue();
			if ($test === null) {
				throw new CellEvaluationException("IFS expects a boolean for argument " . ($i + 1));
			}
			if ($test) {
				return $evaled[$i + 1];
			}
		}
		return $evaled[sizeof($evaled) - 1];
	}

	/**
	 * `LN(value)` - Natural log.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcLn(array $args, CellAddress $address): CellValue {
		$arg = $this->assertNumericArguments('LN', 1, 1, $args, $address)[0];
		$newValue = log($arg->value);
		return CellValue::fromValue($newValue, $arg->type);
	}

	/**
	 * `LOG(value, [base])` - Logarithm. Base is 10 if not provided.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcLog(array $args, CellAddress $address): CellValue {
		$evaled = $this->assertNumericArguments('LOG', 1, 2, $args, $address);
		$exponent = $evaled[0];
		$base = (sizeof($evaled) > 1) ? $evaled[1]->value : 10.0;
		$newValue = log($exponent->value) / log($base);
		return CellValue::fromValue($newValue, $exponent->type);
	}

	/**
	 * `LOWER(text)` - Lowercase version of a string.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcLower(array $args, CellAddress $address): CellValue {
		if (sizeof($args) != 1) {
			throw new CellEvaluationException("LOWER requires one argument");
		}
		$evaled = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		$s = $evaled[0]->stringValue(true);
		if ($s === null) {
			throw new CellEvaluationException("LOWER requires one string argument");
		}
		return CellValue::fromValue(mb_strtolower($s));
	}

	/**
	 * `MAX(arg, arg, ... arg)` - Returns the maximum numeric value.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcMax(array $args, CellAddress $address): CellValue {
		$maxValue = null;
		$flattened = $this->flattenedNumericArguments('MAX', $args, $address);
		if (sizeof($flattened) == 0) {
			throw new CellEvaluationException("MAX requires at least one numeric argument");
		}
		foreach ($flattened as $argument) {
			if ($maxValue === null || $argument->value > $maxValue->value) {
				$maxValue = $argument;
			}
		}
		return $maxValue ?? CellValue::fromValue(0);
	}

	/**
	 * `MIN(arg, arg, ... arg)` - Returns the minimum numeric value.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcMin(array $args, CellAddress $address): CellValue {
		$minValue = null;
		$flattened = $this->flattenedNumericArguments('MIN', $args, $address);
		if (sizeof($flattened) == 0) {
			throw new CellEvaluationException("MIN requires at least one numeric argument");
		}
		foreach ($flattened as $argument) {
			if ($minValue === null || $argument->value < $minValue->value) {
				$minValue = $argument;
			}
		}
		return $minValue ?? CellValue::fromValue(0);
	}

	/**
	 * `MOD(value, divisor)` - Returns the remainder after a division.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcMod(array $args, CellAddress $address): CellValue {
		if (sizeof($args) != 2) {
			throw new CellEvaluationException("MOD requires two numeric arguments");
		}
		$values = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		return $values[0]->modulo($values[1]);
	}

	/**
	 * `NOT(value)` - Boolean NOT of a Boolean value.
	 * 
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcNot(array $args, CellAddress $address): CellValue {
		if (sizeof($args) != 1) {
			throw new CellEvaluationException("NOT expects one argument");
		}
		$evaled = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		$b = $evaled[0].booleanValue();
		if ($b === null) {
			throw new CellEvaluationException("NOT expects boolean argument");
		}
		return CellValue::fromValue(!$b);
	}

	/**
	 * `OR(arg, arg, ... arg)` - Boolean OR of one or more Boolean arguments.
	 * 
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcOr(array $args, CellAddress $address): CellValue {
		if (sizeof($args) == 0) {
			throw new CellEvaluationException("OR requires one or more arguments");
		}
		$values = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		foreach ($values as $value) {
			$result = $value->booleanValue();
			if ($result === null) {
				throw new CellEvaluationException("OR requires boolean arguments");
			}
			if ($result) return CellValue::fromValue(true);
		}
		return CellValue::fromValue(false);
	}

	/**
	 * `POWER(base, exponent)` - Raises a base to an exponent.
	 * 
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcPower(array $args, CellAddress $address): CellValue {
		$evaled = $this->assertNumericArguments('POWER', 2, 2, $args, $address);
		$base = $evaled[0];
		$exp = $evaled[1];
		$val = pow($base->value, $exp->value);
		return CellValue::fromValue($val, $base->type);
	}

	/**
	 * `ROUND(value, [places])` - Rounds a number, optionally to the given number
	 * of digits after the decimal place. Negative places round to the nearest
	 * 10, 100, 1000, etc.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcRound(array $args, CellAddress $address): CellValue {
		$evaled = $this->assertNumericArguments('ROUND', 1, 2, $args, $address);
		$val = $evaled[0];
		$places = sizeof($evaled) > 1 ? $evaled[1]->value : 0;
		$divider = pow(10.0, $places);
		$newValue = round($val->value * $divider) / $divider;
		return CellValue::fromValue($newValue, $val->type);
	}

	/**
	 * `SQRT(value)` - Square root.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcSqrt(array $args, CellAddress $address): CellValue {
		$arg = $this->assertNumericArguments('SQRT', 1, 1, $args, $address)[0];
		$val = $arg->numericValue();
		return CellValue::fromValue(sqrt($val));
	}

	/**
	 * `SUBSTITUTE(text, pattern, replacement)` - Substitutes all occurrences of
	 * `pattern` within `text` with `replacement`.
	 * 
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcSubstitute(array $args, CellAddress $address): CellValue {
		if (sizeof($args) != 3) {
			throw new CellEvaluationException("SUBSTITUTE expects 3 string arguments");
		}
		$values = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		$text = $values[0]->stringValue();
		$search = $values[1]->stringValue();
		$replace = $values[2]->stringValue();
		if ($text === null || $search === null || $replace === null) {
			throw new CellEvaluationException("SUBSTITUTE expects 3 string arguments");
		}
		$result = str_replace($search, $replace, $text);
		return CellValue::fromValue($result);
	}

	/**
	 * `SUM(arg, arg, ... arg)` - Calculates the sum of numeric arguments.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcSum(array $args, CellAddress $address): CellValue {
		$sum = CellValue::fromValue(0);
		foreach ($args as $arg) {
			$val = $this->evaluate($arg, $address);
			if (is_array($val)) {
				foreach ($val as $elem) {
					if ($elem->isNumeric()) $sum = $sum->add($elem);
				}
			} elseif ($val->isNumeric()) {
				$sum = $sum->add($val);
			}
		}
		return $sum;
	}

	/**
	 * `UPPER(text)` - Uppercase of a text argument.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcUpper(array $args, CellAddress $address): CellValue {
		if (sizeof($args) != 1) {
			throw new CellEvaluationException("UPPER requires one argument");
		}
		$evaled = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		$s = $evaled[0]->stringValue(true);
		if ($s === null) {
			throw new CellEvaluationException("UPPER requires one string argument");
		}
		return CellValue::fromValue(mb_strtoupper($s));
	}

	/**
	 * `XOR(arg, arg, ... arg)` - Boolean XOR of one or more Boolean arguments.
	 *
	 * @param array $args  raw arguments
	 * @param CellAddress $address  expression location
	 * @return CellValue  result
	 */
	private function funcXor(array $args, CellAddress $address): CellValue {
		if (sizeof($args) == 0) {
			throw new CellEvaluationException("XOR requires one or more arguments");
		}
		$values = array_map(fn($arg) => $this->evaluate($arg, $address), $args);
		$result = null;
		foreach ($values as $value) {
			$b = $value->booleanValue();
			if ($b === null) {
				throw new CellEvaluationException("XOR requires boolean arguments");
			}
			$result = ($result === null) ? $b : ($result ^ $b);
		}
		return CellValue::fromValue($result != 0);
	}
}

/**
 * A spreadsheet formula expression. Evaluation is done by `CellExpressionSet`.
 */
class CellExpression {
	/**
	 * Operation.
	 */
	public CellExpressionOperation $op;

	/**
	 * Mixed array of `CellValue`, `CellAddress`, `CellAddressRange`,
	 * `CellExpression`, perhaps more.
	 */
	public array $arguments;

	/**
	 * For `Function`, the function name.
	 */
	public ?string $qualifier;

	/**
	 * Optional format override. One of `number`, `currency`, `percent`.
	 */
	public ?string $outputType = null;

	/**
	 * Optional decimal place formatting override.
	 */
	public ?int $outputDecimals = null;

	/**
	 * Address ranges to copy this expression into for any blank cells. Used
	 * by formulas with the `FILL` modifier.
	 * @var CellAddressRange[]|null $fillRanges
	 */
	public ?array $fillRanges = null;

	/**
	 * Source address of the formula.
	 */
	public ?CellAddress $location = null;

	/**
	 * @param CellExpressionOperation $op
	 * @param array $args
	 * @param ?string $qualifier
	 */
	public function __construct(CellExpressionOperation $op, array $args,
			?string $qualifier = null) {
		$this->op = $op;
		$this->arguments = $args;
		$this->qualifier = $qualifier;
	}

	/**
	 * Attempts to parse a formula expression.
	 *
	 * @param string $expression  formula string, including leading `=`
	 * @param CellAddress $address  location of the formula
	 * @return ?CellExpression  parsed expression, or `null` if it failed
	 */
	public static function parse(string $expression, CellAddress $address): ?CellExpression {
		$tokens = $this->expressionToTokens($expression);
		if (sizeof($tokens) == 0) return null;
		$expr = $this->expressionFromTokens($tokens, $address);
		$expr->location = $address;
		return $expr;
	}

	/**
	 * Writes an expression tree to `error_log` for debugging purposes.
	 * 
	 * @param CellExpression $expression
	 * @param string $indent
	 */
	public static function dumpExpression(CellExpression $expression, string $indent = '') {
		if (sizeof($expression->arguments) == 0) {
			error_log($indent . "expr " . $expression->op->name . "()");
		} else {
			error_log($indent . $expression->op->name . '(');
			foreach ($expression->arguments as $argument) {
				if (is_numeric($argument)) {
					error_log($indent . "\t{$argument}");
				} elseif (is_string($argument)) {
					error_log($indent . "\t\"{$argument}\"");
				} elseif (is_bool($argument)) {
					error_log($indent . "\t" . ($argument ? "true" : "false"));
				} elseif ($argument instanceof CellAddress) {
					error_log($indent . "\t" . $argument->name);
				} elseif ($argument instanceof CellAddressRange) {
					error_log($indent . "\t" . $argument->name);
				} elseif ($argument instanceof CellValue) {
					error_log($indent . "\t" . $argument->type . " " . $argument->formattedValue);
				} elseif ($argument instanceof CellExpression) {
					$this->dumpExpression($argument, $indent + "\t");
				} else {
					error_log($indent . "\t" . gettype($argument));
				}
			}
			error_log($indent . ')');
		}
	}

	private function clone(): CellExpression {
		$cp = new CellExpression();
		$cp->op = $this->op;
		$cp->arguments = array($this->arguments);
		$cp->qualifier = $this->qualifier;
		$cp->outputType = $this->outputType;
		$cp->outputDecimals = $this->outputDecimals;
		$cp->fillRanges = $this->fillRanges !== null ? array($this->fillRanges) : null;
		$cp->location = $this->location;
		return $cp;
	}

	/**
	 * Returns a copy of this expression with cell references transposed by
	 * the delta between `$start` and `$end` addresses. Used for repeating an
	 * autofilled formula into blank cells.
	 */
	public function transpose(CellAddress $start, CellAddress $end): ?CellExpression {
		$transposed = $this->clone(); // structuredClone makes a mess of typing
		$transposed->arguments = [];
		foreach ($this->arguments as $argument) {
			if ($argument instanceof CellExpression) {
				array_push($transposed->arguments, $argument->transpose($start, $end));
			} elseif ($argument instanceof CellAddress) {
				array_push($transposed->arguments, $argument->transpose($start, $end));
			} elseif ($argument instanceof CellAddressRange) {
				array_push($transposed->arguments, $argument->transpose($start, $end));
			} else {
				array_push($transposed->arguments, $argument);
			}
		}
		return $transposed;
	}

	// -- Tokenizing --------------------------------------------------------

	/**
	 * Converts an expression into an array of tokens.
	 * @param string $text  expression
	 * @return CellExpressionToken[]  tokens
	 */
	public static function expressionToTokens(string $text): array {
		$tokens = [];
		$pos = [0];
		$this->skipWhitespace($text, $pos);
		if (mb_substr($text, $pos[0], 1) == '=') {
			// Ignore equals
			$pos[0]++;
		}
		$this->skipWhitespace($text, $pos);
		$l = mb_strlen($text);
		while ($pos[0] < $l) {
			array_push($tokens, $this->readNextToken($text, $pos));
			$this->skipWhitespace($text, $pos);
		}
		return $tokens;
	}

	/**
	 * @param string $text
	 * @param int $pos
	 * @return CellExpressionToken
	 */
	private static function readNextToken(string $text, int &$pos): CellExpressionToken {
		// Single char tokens
		if ($token = $this->readNextSimpleToken($text, $pos, '==', CellExpressionTokenType::Equal)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '!=', CellExpressionTokenType::Unequal)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '<=', CellExpressionTokenType::LessThanEqual)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '>=', CellExpressionTokenType::GreaterThanEqual)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '<', CellExpressionTokenType::LessThan)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '>', CellExpressionTokenType::GreaterThan)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '!', CellExpressionTokenType::Not)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '+', CellExpressionTokenType::Plus)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '-', CellExpressionTokenType::Minus)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '*', CellExpressionTokenType::Multiply)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '/', CellExpressionTokenType::Divide)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, ',', CellExpressionTokenType::Comma)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '(', CellExpressionTokenType::OpenParen)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, ')', CellExpressionTokenType::CloseParen)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, ':', CellExpressionTokenType::Colon)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, ';', CellExpressionTokenType::Semicolon)) return $token;
		if ($token = $this->readNextSimpleToken($text, $pos, '&', CellExpressionTokenType::Ampersand)) return $token;
		// Other tokens
		if ($token = $this->readNextAddressToken($text, $pos)) return $token;
		if ($token = $this->readNextNameToken($text, $pos)) return $token;
		if ($token = $this->readNextNumberToken($text, $pos)) return $token;
		if ($token = $this->readNextStringToken($text, $pos)) return $token;
		$ch = mb_substr($text, $pos, 1);
		throw new CellSyntaxException("Unexpected character \"{$ch}\" at {$pos}");
	}

	private static function skipWhitespace(string $text, int &$pos) {
		$l = mb_strlen($text);
		while ($pos < $l) {
			$ch = mb_substr($text, $pos, 1);
			if ($ch == ' ' || $ch == "\t" || $ch == "\n" || $ch == "\r") {
				$pos++;
			} else {
				return;
			}
		}
	}

	private static function readNextSimpleToken(string $text, int &$pos,
			string $target, CellExpressionTokenType $type): ?CellExpressionToken {
		$remaining = mb_strlen($text) - $pos;
		$l = mb_strlen($target);
		if ($l > $remaining) return null;
		$test = mb_substr($text, $pos, $l);
		if (mb_strtoupper($test) != mb_strtoupper($target)) return null;
		$pos += $l;
		return new CellExpressionToken($type, $test);
	}

	private static function readNextAddressToken(string $text, int &$pos): ?CellExpressionToken {
		$p = $pos;
		$ch = mb_substr($text, $p, 1);
		$address = '';
		$isName = true;
		if ($ch == '$') {
			$address += $ch;
			$isName = false;
			$p++;
		}
		$col = $this->readChars($text, $p, fn($s) => $this->isLetter($s), 1, 2);
		if ($col === null) return null;
		$address += $col;
		$ch = mb_substr($text, $p, 1);
		if ($ch == '$') {
			$address += $ch;
			$isName = false;
			$p++;
			$row = $this->readChars($text, $p, $this->isDigit, 1);
			if ($row === null) return null;
			$address += $row;
		} else {
			$row = $this->readChars($text, $p, $this->isDigit, 0);
			if ($row === null) return null;
			$address += $row;
		}
		$pos = $p;
		return new CellExpressionToken(
			$isName ? CellExpressionTokenType::NameOrAddress : CellExpressionTokenType::Address,
			$address);
	}

	private static function readNextNameToken(string $text, int &$pos): ?CellExpressionToken {
		$p = $pos;
		$name = $this->readChars($text, $p, fn($s) => $this->isLetter($s), 1);
		if ($name === null) return null;
		$pos = $p;
		if (CellAddress::isAddress($name)) {
			return new CellExpressionToken(CellExpressionTokenType::NameOrAddress, $name);
		}
		return new CellExpressionToken(CellExpressionTokenType::Name, $name);
	}

	private static function readNextNumberToken(string $text, int &$pos): ?CellExpressionToken {
		$ch = mb_substr($text, $pos, 1);
		if (!$this->isDigit($ch)) return null;
		$l = mb_strlen($text);
		$numStr = $ch;
		$pos++;
		while ($pos < $l) {
			$ch = mb_substr($text, $pos, 1);
			if ($this->isDigit($ch)) {
				$pos++;
				$numStr .= $ch;
			} else {
				break;
			}
		}
		if ($pos < $l) {
			$ch = mb_substr($text, $pos, 1);
			if ($ch == '.') {
				$numStr .= $ch;
				$pos[0]++;
				while ($pos < $l) {
					$ch = mb_substr($text, $pos[0], 1);
					if ($this->isDigit($ch)) {
						$pos++;
						$numStr .= $ch;
					} else {
						break;
					}
				}
			}
		}
		return new CellExpressionToken(CellExpressionTokenType::Number, $numStr);
	}

	private static function readNextStringToken(string $text, int &$pos): ?CellExpressionToken {
		$ch = mb_substr($text, $pos, 1);
		if ($ch !== '"') return null;
		$str = '';
		$pos++;
		$l = mb_strlen($text);
		$inEscape = false;
		while ($pos < $l) {
			$ch = mb_substr($text, $pos[0], $pos[0] + 1);
			$pos++;
			if ($inEscape) {
				$inEscape = false;
				if ($ch == '\\' || $ch == '"') {
					$str .= $ch;
				} else {
					throw new CellSyntaxException("Bad string escape sequence \"\\{$ch}\"");
				}
			} elseif ($ch == '\\') {
				$inEscape = true;
			} elseif ($ch == '"') {
				return new CellExpressionToken(CellExpressionTokenType::String, $str);
			} else {
				$str += $ch;
			}
		}
		throw new CellSyntaxException('Unterminated string');
	}

	/**
	 * Reads the next chars that pass a test function and returns the result.
	 *
	 * @param string $text
	 * @param int $pos
	 * @param callable $charTest
	 * @param ?int $minimumLength
	 * @param ?int $maximumLength
	 * @return ?string
	 */
	private static function readChars(string $text, int &$pos, callable $charTest,
			?int $minimumLength = null, ?int $maximumLength = null): ?string {
		$p = $pos;
		$l = mb_strlen($text);
		$s = '';
		$sl = 0;
		while ($p < $l && ($maximumLength === null || $sl < $maximumLength)) {
			$ch = mb_substr($text, $p, 1);
			if (!$charTest($ch)) break;
			$s += $ch;
			$sl++;
			$p++;
		}
		if ($p < $l && $charTest(mb_substr($text, $p, $p + 1))) {
			return null;
		}
		if ($minimumLength !== null && $sl < $minimumLength) {
			return null;
		}
		$pos = $p;
		return $s;
	}

	/**
	 * @param string $ch
	 * @return bool
	 */
	private static function isLetter(string $ch): bool {
		$ord = ord($ch);
		return ($ord >= 65 && $ord <= 90) || ($ord >= 97 && $ord <= 122);
	}

	/**
	 * @param string $ch
	 * @return bool
	 */
	private static function isDigit(string $ch): bool {
		$ord = ord($ch);
		return ($ord >= 48 && $ord <= 57);
	}

	// -- Parsing -----------------------------------------------------------

	/**
	 * @param array $tokens
	 * @param CellAddress $address
	 * @return ?CellExpression
	 */
	public static function expressionFromTokens(array $tokens, CellAddress $address): ?CellExpression {
		if ($expr = $this->tryExpressionAndFormat($tokens, 0, sizeof($tokens) - 1, $address)) return $expr;
		if ($expr = $this->tryExpressionAndFill($tokens, 0, sizeof($tokens) - 1, $address)) return $expr;
		if ($expr = $this->tryExpression($tokens, 0, sizeof($tokens) - 1, $address)) return $expr;
		return null;
	}

	/**
	 * @param array $tokens
	 * @param int $start
	 * @param int $end
	 * @param CellAddress $address
	 * @return ?CellExpression
	 */
	private static function tryExpressionAndFormat(array $tokens, int $start,
			int $end, CellAddress $address): ?CellExpression {
		for ($t = $start + 1; $t < $end; $t++) {
			if ($tokens[t]->type == CellExpressionTokenType::Semicolon) {
				$expr = $this->tryExpressionAndFill($tokens, $start, $t - 1, $address) ??
					$this->tryExpression($tokens, $start, $t - 1, $address);
				if ($expr === null) return null;
				$format = $this->tryFormat($tokens, $t + 1, $end, $address);
				if ($format === null) return null;
				[ $expr->outputType, $expr->outputDecimals ] = $format;
				return $expr;
			}
		}
		return null;
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param int $start
	 * @param int $end
	 * @param CellAddress $address
	 * @return ?CellExpression
	 */
	private static function tryExpressionAndFill(array $tokens, int $start,
			int $end, CellAddress $address): ?CellExpression {
		$count = $end - $start + 1;
		if ($count < 2) return null;
		if (!$tokens[$end]->type->isPotentialName()) return null;
		$name = mb_strtoupper($tokens[$end]->content);
		if ($name != 'FILL') return null;
		$exp = $this->tryExpression($tokens, $start, $end - 1, $address);
		$columnIndex = $address->columnIndex;
		$exp->fillRanges = [
			new CellAddressRange(new CellAddress($columnIndex, -1), new CellAddress($columnIndex, -1)),
		];
		return $exp;
	}

	/**
	 * Tries to parse a format suffix after a semicolon. Examples:
	 *
	 * ```
	 * ; number
	 * ; number 3
	 * ; currency 2
	 * ; percent 0
	 * ```
	 *
	 * @param CellExpressionToken[] $tokens
	 * @param int $start
	 * @param int $end
	 * @param CellAddress $address
	 * @return ?array CellValue type and decimal places
	 */
	private static function tryFormat(array $tokens, int $start, int $end,
			CellAddress $address): ?array {
		$count = $end - $start + 1;
		if ($count < 0 || $count > 2) return null;
		if (!$tokens[$start]->type->isPotentialName()) return null;
		$type = mb_strtolower($tokens[$start]);
		if (!CellValue::isTypeNumeric($type)) return null;
		if ($count > 1) {
			if ($tokens[$start + 1]->type != CellExpressionTokenType::Number) return null;
			$decimals = intval($tokens[$start + 1]->content);
		} else {
			$decimals = null;
		}
		return [ $type, $decimals ];
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param int $start
	 * @param int $end
	 * @param CellAddress $address
	 * @return CellExpression
	 */
	private static function tryExpression(array $tokens, int $start, int $end,
			CellAddress $address): CellExpression {
		if ($expr = $this->tryParenExpression($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryNumber($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryString($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryBoolean($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryFunction($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryRange($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryReference($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryInfix($tokens, $start, $end, $address)) return $expr;
		if ($expr = $this->tryUnary($tokens, $start, $end, $address)) return $expr;
		throw new CellSyntaxException("Invalid expression");
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryParenExpression(array $tokens, int $start,
			int $end, CellAddress $address): ?CellExpression {
		if ($tokens[$start]->type != CellExpressionTokenType::OpenParen) return null;
		if ($tokens[$end]->type != CellExpressionTokenType::CloseParen) return null;
		$parenLevel = 0;
		for ($t = $start + 1; $t < $end; $t++) {
			if ($tokens[$t]->type == CellExpressionTokenType::OpenParen) {
				$parenLevel++;
			} elseif ($tokens[$t]->type == CellExpressionTokenType::CloseParen) {
				$parenLevel--;
			}
			if ($parenLevel < 0) return null;
		}
		if ($parenLevel != 0) return null;
		return $this->tryExpression($tokens, $start + 1, $end - 1, $address);
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryNumber(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		if ($tokens[$end]->type != CellExpressionTokenType::Number) return null;
		if ($end > $start + 1) return null;
		$val = CellValue::fromCellString($tokens[$end]->content);
		if ($end > $start) {
			if ($tokens[$start]->type != CellExpressionTokenType::Minus) return null;
			$val->value = -$val->value;
		}
		return new CellExpression(CellExpressionOperation::Number, [ $val ]);
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryString(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		if ($start != $end) return null;
		if ($tokens[$start]->type != CellExpressionTokenType::String) return null;
		$str = $tokens[$start]->content;
		return new CellExpression(CellExpressionOperation::String,
			[ new CellValue($str, $str, CellValue::TYPE_STRING, 0) ]);
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryBoolean(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		if ($start != $end) return null;
		if (!$tokens[$start]->type->isPotentialName()) return null;
		$str = mb_strtoupper($tokens[$start]->content);
		if ($str != 'TRUE' && $str != 'FALSE') return null;
		return new CellExpression(CellExpressionOperation::Boolean,
			[ new CellValue($str, $str == 'TRUE', CellValue::TYPE_BOOLEAN) ]);
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryFunction(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		$count = $end - $start + 1;
		if ($count < 3) return null;
		if (!$tokens[$start]->type->isPotentialName()) return null;
		$qualifier = $tokens[$start]->content;
		if ($tokens[$start + 1]->type != CellExpressionTokenType::OpenParen) return null;
		if ($tokens[$end]->type != CellExpressionTokenType::CloseParen) return null;
		$argList = $this->tryArgumentList($tokens, $start + 2, $end - 1, $address);
		if ($argList === null) return null;
		return new CellExpression(CellExpressionOperation::Function, $argList, $qualifier);
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression[]|null
	 */
	private static function tryArgumentList(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		$count = $end - $start + 1;
		if ($count == 0) return [];
		$parenDepth = 0;
		$argCount = 1;

		// Populate argTokens with tuples of start and end token indices for each arg.
		/** @type {int[][]} */
		$argTokens = []; // argindex -> [ start, end ]
		$exprStartToken = $start;
		for ($i = $start; $i <= $end; $i++) {
			if ($tokens[$i]->type == CellExpressionTokenType::OpenParen) {
				$parenDepth++;
			} elseif ($tokens[$i]->type == CellExpressionTokenType::CloseParen) {
				$parenDepth--;
			} elseif ($tokens[$i]->type == CellExpressionTokenType::Comma && $parenDepth == 0) {
				$exprEndToken = $i - 1;
				array_push($argTokens, [ $exprStartToken, $exprEndToken ]);
				$exprStartToken = $i + 1;
			}
		}
		array_push($argTokens, [ $exprStartToken, $end ]);

		// Convert token ranges to expressions
		$args = [];
		foreach ($argTokens as $argToken) {
			$arg = $this->tryExpression($tokens, $argToken[0], $argToken[1], $address);
			if ($arg === null) return null;
			$args.push($arg);
		}
		return $args;
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryRange(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		$count = $end - $start + 1;
		if ($count != 3) return null;
		if (!$tokens[$start]->type->isPotentialAddress()) return null;
		$first = mb_strtoupper($tokens[$start]->content);
		if ($tokens[$start + 1]->type != CellExpressionTokenType::Colon) return null;
		if (!$tokens[$end]->type->isPotentialAddress()) return null;
		$last = mb_strtoupper($tokens[$end]->content);
		$firstAddress = CellAddress::fromString($first);
		$lastAddress = CellAddress::fromString($last);
		$range = new CellAddressRange($firstAddress, $lastAddress);
		return new CellExpression(CellExpressionOperation::Range, [ $range ]);
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryReference(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		if ($start != $end) return null;
		if (!$tokens[$start]->type->isPotentialAddress()) return null;
		$ref = mb_strtoupper($tokens[$start]->content);
		$refAddress = CellAddress::fromString($ref, $address, true);
		return new CellExpression(CellExpressionOperation::Reference, [ $refAddress ]);
	}

	private const infixPriority = [
		'Minus' => 1,
		'Plus' => 2,
		'Divide' => 3,
		'Multiply' => 4,
		'Ampersand' => 10,
		'GreaterThan' => 20,
		'GreaterThanEqual' => 20,
		'LessThan' => 20,
		'LessThanEqual' => 20,
		'Equal' => 20,
		'Unequal' => 20,
	];

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryInfix(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		$count = $end - $start + 1;
		if ($count < 3) return null;
		$candidates = [];
		$parenLevel = 0;
		for ($i = $start; $i <= $end; $i++) {
			if ($tokens[$i]->type == CellExpressionTokenType::OpenParen) {
				$parenLevel++;
			} elseif ($tokens[$i]->type == CellExpressionTokenType::CloseParen) {
				$parenLevel--;
			} elseif ($parenLevel == 0 && $i > $start && $i < $end) {
				$op = $tokens[$i]->type->name;
				$priority = $this->infixPriority[$op] ?? false;
				if ($priority === false) continue;
				array_push($candidates, [ 'priority' => priority, 'i' => $i ]);
			}
		}
		usort($candidates, fn($a, $b) => $a['priority'] - $b['priority']);
		$bestCandidate = null;
		foreach ($candidates as $candidate) {
			try {
				$i = $candidate['i'];
				$operand1 = $this->tryExpression($tokens, $start, $i - 1, $address);
				if ($operand1 === null) continue;
				$operand2 = $this->tryExpression($tokens, $i + 1, $end, $address);
				if ($operand2 === null) continue;
				$bestCandidate = $candidate;
				break;
			} catch (e) {
				if (!($e instanceof CellSyntaxException)) {
					throw $e;
				}
			}
		}
		if ($bestCandidate === null) {
			return null;
		}
		$i = $bestCandidate->i;
		switch ($tokens[$bestCandidate['i']]->type) {
			case CellExpressionTokenType::Plus:
				return new CellExpression(CellExpressionOperation::Add, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::Minus:
				return new CellExpression(CellExpressionOperation::Subtract, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::Multiply:
				return new CellExpression(CellExpressionOperation::Multiply, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::Divide:
				return new CellExpression(CellExpressionOperation::Divide, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::GreaterThan:
				return new CellExpression(CellExpressionOperation::GreaterThan, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::GreaterThanEqual:
				return new CellExpression(CellExpressionOperation::GreaterThanEqual, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::LessThan:
				return new CellExpression(CellExpressionOperation::LessThan, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::LessThanEqual:
				return new CellExpression(CellExpressionOperation::LessThanEqual, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::Equal:
				return new CellExpression(CellExpressionOperation::Equal, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::Unequal:
				return new CellExpression(CellExpressionOperation::Unequal, [ $operand1, $operand2 ]);
			case CellExpressionTokenType::Ampersand:
				return new CellExpression(CellExpressionOperation::Concatenate, [ $operand1, $operand2 ]);
		}
		return null;
	}

	/**
	 * @param CellExpressionToken[] $tokens
	 * @param number $start
	 * @param number $end
	 * @param CellAddress $address
	 * @return CellExpression|null
	 */
	private static function tryUnary(array $tokens, int $start, int $end,
			CellAddress $address): ?CellExpression {
		$count = $end - $start + 1;
		if ($count < 2) return null;
		$ops = [
			[ CellExpressionTokenType::Minus, CellExpressionOperation::UnaryMinus ],
			[ CellExpressionTokenType::Not, CellExpressionOperation::UnaryNot ],
		];
		foreach ($ops as $op) {
			if ($tokens[$start]->type != $op[0]) continue;
			$operand = $this->tryExpression($tokens, $start + 1, $end, $address);
			if ($operand === null) return null;
			return new CellExpression($op[1], [ $operand ]);
		}
		return null;
	}
}

/**
 * Parsing token for an expression.
 */
class CellExpressionToken {
	public CellExpressionTokenType $type;
	public string $content;

	/**
	 * @param CellExpressionTokenType $type
	 * @param string $content
	 */
	public function __construct(CellExpressionTokenType $type, string $content) {
		$this->type = $type;
		$this->content = $content;
	}
}

/**
 * The location of a cell in a table. If the address was specified without a
 * row, the address is considered "unresolved" and needs more context to
 * uniquely identify a cell.
 */
class CellAddress {
	public string $name;

	/** 
	 * Whether the column should remain unchanged when transposed. This is
	 * symbolized by prefixing the column name with a `$` (e.g. `$C3`).
	 */
	public bool $isColumnFixed = false;

	/**
	 * Zero-based column index.
	 */
	public int $columnIndex = -1;

	/**
	 * Letter code for the column.
	 */
	public function columnLetter(): string { return CellAddress::columnIndexToLetters($this->columnIndex); }

	/**
	 * Whether the row should remain unchanged when transposed. This is
	 * symbolized by prefixing the row number with a `$` (e.g. `C$3`).
	 */
	public bool $isRowFixed = false;

	/**
	 * Zero-based row index.
	 */
	public int $rowIndex = -1;

	/**
	 * One-based row number. This is the human-facing row number.
	 */
	public function rowNumber(): ?int { return $this->rowIndex >= 0 ? $this->rowIndex + 1 : null; }

	/**
	 * Whether this address has both a definite column and row.
	 */
	public function isResolved(): bool { return $this->columnIndex >= 0 && $this->rowIndex >= 0; }

	/**
	 * @param int $columnIndex  0-based column index
	 * @param int $rowIndex  0-based row index
	 * @param bool $isColumnFixed  whether the column name is fixed in
	 *   place during transpositions. Denoted with a `$` in front of the column letters.
	 * @param bool $isRowFixed  whether the row number is fixed in place
	 *   during transpositions. Denoted with a `$` in front of the row digits.
	 */
	public function __construct(int $columnIndex, int $rowIndex,
			bool $isColumnFixed=false, bool $isRowFixed=false) {
		if (!is_numeric($columnIndex)) {
			throw new Error("columnIndex must be number, got " . gettype($columnIndex));
		}
		if (!is_numeric($rowIndex)) {
			throw new Error("rowIndex must be number, got " . gettype($rowIndex));
		}
		$this->columnIndex = $columnIndex;
		$this->rowIndex = $rowIndex;
		$this->isColumnFixed = $isColumnFixed;
		$this->isRowFixed = $isRowFixed;
		$this->name = self::formatAddress($columnIndex, $rowIndex, $isColumnFixed, $isRowFixed);
	}

	/**
	 * Tests if a string is formatted like an address.
	 */
	public static function isAddress(string $text): bool {
		return self::fromString($text) != null;
	}

	/**
	 * Returns a converted form of this address reference in a formula that has
	 * been copied from its original location. In other words, if a formula
	 * refers to a cell one to the left and that formula is copied to the next
	 * cell down, that copy's reference should point to the cell on the next
	 * row as well. Addresses with an absolute column or row (e.g. "A5") will
	 * not be altered on that axis.
	 *
	 * Examples:
	 * - C6.transpose(A5, A9) = C10  (A9-A5 = +4 rows, C6 + 4 rows = C10)
	 * - C6.transpose(A5, B9) = D10  (B9-A5 = +4 rows +1 cols, C6 + 4 rows + 1
	 *   col = D10)
	 * - C$6.transpose(A5, A9) = C6  (A9-A5 = +4 rows, but row is fixed, so
	 *   still C6)
	 * - B.transpose(A5, A9) = B9  (A9-A4 = +4 rows, B has no row so last row
	 *   used = B9)
	 * - A1.transpose(C3, A1) = null (out of bounds)
	 * 
	 * @param CellAddress $relativeFrom  original address of the formula
	 * @param CellAddress $relativeTo  address where the formula is being
	 *   repeated
	 * @param boolean $resolveToRow  whether to fill in a row number if this
	 *   address doesn't have one
	 * @return CellAddress|null   resolved address, or `null` if out of bounds
	 */
	public function transpose(CellAddress $relativeFrom, CellAddress $relativeTo,
			bool $resolveToRow = true): ?CellAddress {
		if (!$relativeFrom->isResolved() || !$relativeTo->isResolved()) {
			throw new CellEvaluationException("Can only transpose to and from resolved addresses");
		}
		$newColumnIndex = $this->columnIndex;
		if (!$this->isColumnFixed) {
			$columnDelta = $relativeTo->columnIndex - $relativeFrom->columnIndex;
			$newColumnIndex += $columnDelta;
		}
		$newRowIndex = $this->rowIndex;
		if (!$this->isResolved && $resolveToRow) {
			$newRowIndex = $relativeFrom->rowIndex;
		}
		if ($newRowIndex != -1 && !$this->isRowAbsolute) {
			$rowDelta = $relativeTo->rowIndex - $relativeFrom->rowIndex;
			$newRowIndex += $rowDelta;
		}
		if ($newColumnIndex < 0 || $newRowIndex < 0) return null;
		return new CellAddress($newColumnIndex, $newRowIndex);
	}

	public function equals($other): bool {
		if (!($other instanceof CellAddress)) return false;
		return $other->columnIndex == $this->columnIndex && $other->rowIndex == $this->rowIndex;
	}

	public function exactlyEquals($other): bool {
		if (!($other instanceof CellAddress)) return false;
		return $other->name == $this->name;
	}

	public function __toString(): string {
		return $this->name;
	}

	/**
	 * Converts column letters (e.g. `A`, `C`, `AA`) to a 0-based column index.
	 * Assumes a validated well-formed column letter or else behavior is undefined.
	 */
	public static function lettersToColumnIndex(string $letters): int {
		$ACodepoint = ord('A');
		$columnIndex = 0;
		for ($i = mb_strlen($letters) - 1; $i >= 0; $i--) {
			$letterIndex = ord(mb_substr($letters, $i, 1)) - $ACodepoint;
			$columnIndex = $columnIndex * 26 + $letterIndex;
		}
		return $columnIndex;
	}

	/**
	 * Converts a column index to column letters (e.g. index 0 = `A`).
	 */
	private static function columnIndexToLetters(int $columnIndex): string {
		$letters = '';
		if ($columnIndex >= 0) {
			$ACodepoint = ord('A');
			$remaining = $columnIndex;
			do {
				$letters = chr(ACodepoint + (remaining % 26)) . $letters;
				$remaining = floor($remaining / 26);
			} while ($remaining > 0);
		}
		return $letters;
	}

	private static function formatAddress(int $columnIndex, int $rowIndex,
			bool $isColumnFixed, bool $isRowFixed): string {
		$addr = '';
		if ($isColumnFixed && $columnIndex >= 0) $addr .= '$';
		if ($columnIndex >= 0) $addr .= self::columnIndexToLetters($columnIndex);
		if ($isRowFixed && $rowIndex >= 0) $addr .= '$';
		if ($rowIndex >= 0) $addr .= "${rowIndex + 1}";
		return $addr;
	}

	/**
	 * Attempts to convert a cell address string to a `CellAddress`.
	 *
	 * @param string $address  cell address string
	 * @param ?CellAddress $relativeTo  address to resolve relative
	 *   addresses against
	 * @param boolean $throwIfInvalid  whether to throw an error if address
	 *   is invalid
	 * @return ?CellAddress  address, if parsable
	 * @throws CellEvaluationException  if the address is invalid and
	 *   `$throwIfInvalid` is `true`
	 */
	public static function fromString(string $address, ?CellAddress $relativeTo=null,
			bool $throwIfInvalid=false): ?CellAddress {
		if (!mb_eregi('^(\\$?)([A-Z]{1,2}?)((?:\\$(?=[0-9]))?)([0-9]*)$/', $address, $groups)) {
			if ($throwIfInvalid) throw new CellEvaluationException("Bad address \"{$address}\"", '#REF');
			return null;
		}
		$isColumnFixed = ($groups[1] == '$');
		$letters = mb_strtoupper($groups[2]);
		$isRowFixed = ($groups[3] == '$');
		$numbers = $groups[4];
		$columnIndex = $this->lettersToColumnIndex($letters);
		$rowIndex = (mb_strlen($numbers) == 0) ? -1 : intval($numbers) - 1;
		if ($columnIndex < 0 && $relativeTo !== null) $columnIndex = $relativeTo->columnIndex;
		if ($rowIndex < 0 && $relativeTo !== null) $rowIndex = $relativeTo->rowIndex;
		return new CellAddress($columnIndex, $rowIndex, $isColumnFixed, $isRowFixed);
	}
}

/**
 * Range of cells addresses. Can be iterated via `cellsIn`.
 */
class CellAddressRange {
	public bool $isResolved;
	public int $minColumnIndex;
	public int $maxColumnIndex;
	public int $minRowIndex;
	public int $maxRowIndex;
	public string $name;

	/**
	 * Creates a rectangular range between two corner cells. They can be in
	 * any order. The given cells must either both be resolved or both unresolved.
	 * 
	 * @param CellAddress $fromCell
	 * @param CellAddress $toCell
	 */
	public function __construct(CellAddress $fromCell, CellAddress $toCell) {
		if ($fromCell->isResolved() != $toCell->isResolved()) {
			throw new CellEvaluationException("Cannot mix resolved and unresolved cell addresses in range: {$fromCell->name} and {$toCell->name}");
		}
		$this->minColumnIndex = min($fromCell->columnIndex, $toCell->columnIndex);
		$this->maxColumnIndex = max($fromCell->columnIndex, $toCell->columnIndex);
		$this->minRowIndex = min($fromCell->rowIndex, $toCell->rowIndex);
		$this->maxRowIndex = max($fromCell->rowIndex, $toCell->rowIndex);
		$this->isResolved = $fromCell->isResolved;
		$this->name = (new CellAddress($this->minColumnIndex, $this->minRowIndex))->name .
				':' .
				(new CellAddress($this->maxColumnIndex, $this->maxRowIndex))->name;
	}

	/**
	 * Creates an iterator for every `CellAddress` in this range within the
	 * confines of the given grid's dimensions. Iterates each row in the first
	 * column, then each row in the second, etc. Iteration range is inclusive
	 * of the min and max extents.
	 * 
	 * Example:
	 * ```
	 * foreach (range.cellsIn(grid) as $address) {
	 *     ...
	 * }
	 * ```
	 *
	 * @param SpreadsheetGrid $grid
	 * @return object iterable object
	 */
	public function cellsIn(SpreadsheetGrid $grid): Iterator {
		$min_col = $this->minColumnIndex;
		$max_col = $this->maxColumnIndex;
		$min_row = $this->minRowIndex;
		$max_row = $this->maxRowIndex;
		if ($min_row == -1) {
			$min_row = $grid->getHeaderRowCount();
		}
		if ($max_row == -1) {
			$max_row = $grid->getRowCount() - 1;
		}
		$max_col = min($max_col, $grid->getColumnCount());
		return new class($grid, $min_col, $max_col, $min_row, $max_row) implements Iterator {
			private SpreadsheetGrid $grid;
			private int $min_col;
			private int $max_col;
			private int $min_row;
			private int $max_row;
			private int $col;
			private int $row;
			private ?CellAddress $address = null;
			private ?SpreadsheetCell $cell = null;
			function __construct($grid, $min_col, $max_col, $min_row, $max_row) {
				$this->grid = $grid;
				$this->min_col = $min_col;
				$this->max_col = $max_col;
				$this->min_row = $min_row;
				$this->max_row = $max_row;
				$this->col = $min_col;
				$this->row = $min_row;
				$this->setValues();
			}

			private function setValues() {
				if ($this->col >= $this->min_col && $this->col <= $this->max_col &&
						$this->row >= $this->min_row && $this->row <= $this->max_row) {
					$this->address = new CellAddress($this->col, $this->row);
					$this->cell = $this->grid->getCell($this->address);
					if (!$this->cell) {
						error_log("WARNING: Iterator found no cell at {$this->address->name}");
					}
				} else {
					$this->address = null;
					$this->cell = null;
				}
			}

			private function increment(): void {
				$this->row++;
				if ($this->row > $this->max_row) {
					$this->row = $this->min_row;
					$this->col++;
				}
				$this->setValues();
			}

			function current(): ?SpreadsheetCell {
				return $this->cell;
			}

			function key(): string {
				return $this->address->name;
			}

			function next(): void {
				$this->increment();
			}

			function rewind(): void {
				$this->row = $this->min_row;
				$this->col = $this->min_col;
				$this->setValues();
			}

			function valid(): bool {
				return $this->address != null;
			}
		};
	}
}

/**
 * A value in a spreadsheet or calculation.
 */
class CellValue {
	/**
	 * Blank cell. `value` is `null`.
	 */
	public const TYPE_BLANK = 'blank';
	/**
	 * Currency value. `value` is `number`.
	 */
	public const TYPE_CURRENCY = 'currency';
	/**
	 * Regular number value. `value` is `number`.
	 */
	public const TYPE_NUMBER = 'number';
	/**
	 * Percentage. `value` is `number`, represented as a ratio (100% = 1.0).
	 */
	public const TYPE_PERCENT = 'percent';
	/**
	 * Unaltered text value. `value` is `string`.
	 */
	public const TYPE_STRING = 'string';
	/**
	 * Boolean. `value` is `boolean`.
	 */
	public const TYPE_BOOLEAN = 'boolean';
	/**
	 * A formula that has resulted in an error during parsing or evaluation.
	 * `value` is `string` error message.
	 */
	public const TYPE_ERROR = 'error';
	/**
	 * A formula expression. `value` is `string` and includes the leading `=`.
	 */
	public const TYPE_FORMULA = 'formula';

	// -- Properties -----

	/**
	 * Type of value. One of the `TYPE_` constants.
	 */
	public string $type = CellValue::TYPE_STRING;
	/**
	 * Number of decimal places shown in the formatted value.
	 */
	public int $decimals = 0;
	/**
	 * The string shown in the table cell to the user.
	 */
	public string $formattedValue = '';
	/**
	 * The PHP data value. E.g. a `float` for currency values or an `Exception`
	 * for errors.
	 */
	public $value = null;

	/**
	 * Constructs a cell value explicitly. Values are not validated. Consider
	 * using `.fromCellString()` or `.fromValue()` to populate values more
	 * intelligently and consistently.
	 */
	public function __construct(
		string $formattedValue,
		mixed $value = null,
		string $type = CellValue::TYPE_STRING,
		int $decimals = 0
	) {
		$this->formattedValue = formattedValue;
		$this->value = value;
		$this->type = type;
		$this->decimals = decimals;
	}

	/**
	 * Returns whether this value is a numeric type.
	 */
	public function isNumeric(): bool {
		return CellValue::isTypeNumeric($this->type);
	}

	/**
	 * Creates a CellValue from formatted table cell contents. Attempts to
	 * detect formatted numbers including currency and percentages.
	 */
	public static function fromCellString(string $cellString): CellValue {
		$cv = new CellValue($cellString);
		$cv->populateFromCellString($cellString);
		return $cv;
	}

	/**
	 * Creates a CellValue from a value. Based off datatype, not string
	 * formatting; use `fromCellString` to parse formatted numbers.
	 * 
	 * @param mixed $value
	 * @param ?string $type  optional forced type
	 * @param ?int $decimals  optional number of decimal places to format to
	 * @return CellValue
	 * @throws CellEvaluationException  if `$value` is of an unsupported type
	 */
	public static function fromValue(mixed $value, ?string $type = null,
			?int $decimals = null): CellValue {
		if ($value === null) {
			return new CellValue('', null, CellValue::TYPE_BLANK);
		}
		if ($value instanceof Error) {
			if ($value instanceof CellException) {
				return new CellValue($value->errorSymbol, $value->message, CellValue::TYPE_ERROR);
			}
			return new CellValue('#ERROR', $value->message, CellValue::TYPE_ERROR);
		}
		if (is_bool($value)) {
			$formatted = CellValue::formatType($value, CellValue::TYPE_BOOLEAN, 0);
			return new CellValue($formatted, $value, CellValue::TYPE_BOOLEAN);
		}
		if (is_numeric($value)) {
			$resolvedType = $type || CellValue::TYPE_NUMBER;
			$resolvedDecimals = ($decimals !== null) ? $decimals :
				($resolvedType == CellValue::TYPE_CURRENCY ? 2 :
					CellValue::autodecimals($resolvedType == CellValue::TYPE_PERCENT ?
						$value * 100.0 : $value));
			$formatted = CellValue::formatType($value, $resolvedType, $resolvedDecimals);
			return new CellValue($formatted, $value, $resolvedType, $resolvedDecimals);
		}
		if (!is_string($value)) {
			throw new CellEvaluationException("Value of type " . gettype($value) . "unsupported");
		}
		$trimmed = trim($value);
		if (str_starts_with($trimmed, '=')) {
			return new CellValue($trimmed, $trimmed, CellValue::TYPE_FORMULA);
		}
		return new CellValue($trimmed, $trimmed, CellValue::TYPE_STRING);
	}

	private function populateFromCellString(?string $cellString) {
		$cellString = ($cellString !== null) ? trim($cellString) : null;
		$this->formattedValue = $cellString;
		// blank
		if ($cellString === null || $cellString == '') {
			$this->type = CellValue::TYPE_BLANK;
			$this->value = null;
			return;
		}
		// 'literal
		if (str_starts_with($cellString, "'")) {
			$stripped = trim(mb_substr($cellString, 1));
			$this->type = CellValue::TYPE_STRING;
			$this->formattedValue = $stripped;
			$this->value = $stripped;
			return;
		}
		// =TRUE
		$caps = mb_strtoupper($cellString);
		if ($caps == 'TRUE') {
			$this->type = CellValue::TYPE_BOOLEAN;
			$this->formattedValue = $caps;
			$this->value = true;
			$this->formattedValue = 'TRUE';
			return;
		}
		// =FALSE
		if ($caps == 'FALSE') {
			$this->type = CellValue::TYPE_BOOLEAN;
			$this->formattedValue = $caps;
			$this->value = false;
			$this->formattedValue = 'FALSE';
			return;
		}
		// =A*B
		if (str_starts_with($cellString, '=')) {
			$this->type = CellValue::TYPE_FORMULA;
			$this->value = $cellString;
			return;
		}
		// -$1,234.56
		if (mb_eregi('^([-]?)\\$(-?[0-9,]*\\.)([0-9]+)$', $cellString, $groups)) {
			$sign = $groups[1];
			$dollars = mb_eregi_replace(',', '', $groups[2]);
			$cents = $groups[3];
			$this->type = CellValue::TYPE_CURRENCY;
			$this->decimals = 2;
			$this->value = floatval($sign . $dollars . $cents);
			$this->formattedValue = CellValue::formatCurrency($this->value, $this->decimals);
			return;
		}
		// -$1,234
		if (mb_eregi('^([-]?)\\$(-?[0-9,]+)$', $cellString, $groups)) {
			$sign = $groups[1];
			$dollars = mb_eregi_replace(',', '', $groups[2]);
			$this->type = CellValue::TYPE_CURRENCY;
			$this->decimals = 0;
			$this->value = floatval($sign . $dollars);
			$this->formattedValue = CellValue::formatCurrency($this->value, $this->decimals);
			return;
		}
		// -1,234.56%
		if (mb_eregi('^([-]?[0-9,]*\\.)([0-9,]+)%$', $cellString, $groups)) {
			$wholes = mb_eregi_replace(',', '', $groups[1]);
			$decimals = $groups[2];
			$this->type = CellValue::TYPE_PERCENT;
			$this->decimals = mb_strlen($decimals);
			$this->value = floatval($wholes . $decimals) / 100.0;
			$this->formattedValue = CellValue::formatPercent($this->value, $this->decimals);
			return;
		}
		// -1,234%
		if (mb_eregi('^([-]?[0-9,]+)%$', $cellString, $groups)) {
			$wholes = mb_eregi_replace(',', '', $groups[1]);
			$this->type = CellValue::TYPE_PERCENT;
			$this->decimals = 0;
			$this->value = floatval($wholes) / 100.0;
			$this->formattedValue = CellValue::formatPercent($this->value, $this->decimals);
			return;
		}
		// -1,234.56
		if (mb_eregi('^([-]?[0-9,]*\\.)([0-9]+)$', $cellString, $groups)) {
			$wholes = mb_eregi_replace(',', '', $groups[1]);
			$decimals = $groups[2];
			$this->type = CellValue::TYPE_NUMBER;
			$this->decimals = mb_strlen($decimals);
			$this->value = floatval($wholes . $decimals);
			$this->formattedValue = CellValue::formatNumber($this->value, $this->decimals);
			return;
		}
		// -1,234
		if (mb_eregi('^([-]?[0-9,]+)$', $cellString, $groups)) {
			$wholes = mb_eregi_replace(',', '', $groups[1]);
			$this->type = CellValue::TYPE_NUMBER;
			$this->decimals = 0;
			$this->value = parseFloat($wholes);
			$this->formattedValue = CellValue::formatNumber($this->value, $this->decimals);
			return;
		}
		$this->type = CellValue::TYPE_STRING;
		$this->value = $cellString;
	}

	/**
	 * Returns the boolean equivalent of this value if possible.
	 */
	public function booleanValue(): ?bool {
		switch ($this->type) {
			case CellValue::TYPE_BLANK:
				return false;
			case CellValue::TYPE_BOOLEAN:
				return $this->value;
			case CellValue::TYPE_CURRENCY:
			case CellValue::TYPE_NUMBER:
			case CellValue::TYPE_PERCENT:
				return $this->value != 0;
			case CellValue::TYPE_ERROR:
			case CellValue::TYPE_FORMULA:
			case CellValue::TYPE_STRING:
				return null;
		}
	}

	/**
	 * Returns the numeric value of this value if possible.
	 */
	public function numericValue(): ?float {
		switch ($this->type) {
			case CellValue::TYPE_BLANK:
				return 0.0;
			case CellValue::TYPE_BOOLEAN:
				return $this->value ? 1.0 : 0.0;
			case CellValue::TYPE_CURRENCY:
			case CellValue::TYPE_NUMBER:
			case CellValue::TYPE_PERCENT:
				return $this->value;
			case CellValue::TYPE_ERROR:
			case CellValue::TYPE_FORMULA:
			case CellValue::TYPE_STRING:
				return null;
		}
	}

	/**
	 * Returns the string value of this value if possible.
	 */
	public function stringValue(bool $formatted = false): ?string {
		switch ($this->type) {
			case CellValue::TYPE_BLANK:
				return '';
			case CellValue::TYPE_BOOLEAN:
				return $this->value ? 'TRUE' : 'FALSE';
			case CellValue::TYPE_CURRENCY:
			case CellValue::TYPE_NUMBER:
			case CellValue::TYPE_PERCENT:
				return $formatted ? $this->formattedValue : "${$this->value}";
			case CellValue::TYPE_STRING:
				return $formatted ? $this->formattedValue : $this->value;
			case CellValue::TYPE_ERROR:
			case CellValue::TYPE_FORMULA:
				return null;
		}
	}

	// -- Operations --------------------------------------------------------

	/**
	 * Returns the result of this value plus `$b`.
	 */
	public function add(CellValue $b): CellValue {
		return self::binaryNumericOperation($this, $b, '+',
			fn($aVal, $bVal) => $aVal + $bVal);
	}

	/**
	 * Returns the result of this value minus `$b`.
	 */
	public function subtract(CellValue $b) {
		return self::binaryNumericOperation($this, $b, '-',
			fn($aVal, $bVal) => $aVal - $bVal);
	}

	/**
	 * Returns the result of this value multiplied by `$b`.
	 */
	public function multiply(CellValue $b): CellValue {
		return self::binaryNumericOperation($this, $b, '*',
			fn($aVal, $bVal) => $aVal * $bVal);
	}

	/**
	 * Returns the result of this value divided by `$b`.
	 *
	 * @throws CellEvaluationException  on divide by zero
	 */
	public function divide(CellValue $b): CellValue {
		return self::binaryNumericOperation($this, $b, '/', function($aVal, $bVal) {
			if ($bVal == 0) throw new CellEvaluationException("Division by zero", '#NAN');
			return $aVal / $bVal;
		});
	}

	/**
	 * Returns the result of this value modulo by `$b`.
	 *
	 * @throws CellEvaluationException  on divide by zero
	 */
	public function modulo($b) {
		return self::binaryNumericOperation($this, $b, '%', function($aVal, $bVal) {
			if ($bVal == 0) throw new CellEvaluationException("Division by zero", '#NAN');
			return $aVal % $bVal;
		});
	}

	/**
	 * Returns the result of whether this value is greater than `$b`.
	 */
	public function gt(CellValue $b): CellValue {
		return self::fromValue(CellValue::compare($this, $b) > 0);
	}

	/**
	 * Returns the result of whether tihs value is greater than or equal to `$b`.
	 */
	public function gte(CellValue $b): CellValue {
		return self::fromValue(CellValue::compare($this, $b) >= 0);
	}

	/**
	 * Returns the result of whether this value is less than `$b`.
	 */
	public function lt(CellValue $b): CellValue {
		return self::fromValue(CellValue::compare($this, $b) < 0);
	}

	/**
	 * Returns the result of whether this value is less than or equal to `$b`.
	 */
	public function lte(CellValue $b): CellValue {
		return self::fromValue(CellValue::compare($this, $b) <= 0);
	}

	/**
	 * Returns the result of whether this value is equal to `$b`.
	 */
	public function eq(CellValue $b): CellValue {
		return self::fromValue(CellValue::compare($this, $b) == 0);
	}

	/**
	 * Returns the result of whether this value is unequal to `$b`.
	 */
	public function neq(CellValue $b): CellValue {
		return self::fromValue(CellValue::compare($this, $b) != 0);
	}

	/**
	 * Returns the boolean not of this value.
	 */
	public function not(): CellValue {
		switch ($this->type) {
			case CellValue::TYPE_BLANK:
				return self::fromValue(true);
			case CellValue::TYPE_CURRENCY:
			case CellValue::TYPE_NUMBER:
			case CellValue::TYPE_PERCENT:
				return self::fromValue($this->value == 0);
			case CellValue::TYPE_STRING:
				throw new CellEvaluationException("Cannot perform NOT on string");
			case CellValue::TYPE_BOOLEAN:
				return self::fromValue(!$this->value);
			case CellValue::TYPE_ERROR:
				throw $this->value;
			case CellValue::TYPE_FORMULA:
				throw new CellEvaluationException("Cannot perform NOT on expression");
		}
	}

	/**
	 * Returns the string representation of a value concatenated to the string
	 * representation of this value.
	 */
	public function concatenate(CellValue $b): CellValue {
		$s1 = $this->stringValue(true);
		$s2 = $b->stringValue(true);
		if ($s1 === null || $s2 === null) {
			throw new CellEvaluationException("Concatenation requires string arguments");
		}
		return self::fromValue("{$s1}{$s2}");
	}

	/**
	 * Helper to resolve two numeric arguments and perform an operation on them.
	 *
	 * @param CellValue $a  operand A
	 * @param CellValue $b  operand B
	 * @param string $op  operator
	 * @param function $fn  takes two `float` arguments and returns a `float` result
	 * @return CellValue  result
	 * @throws CellEvaluationException
	 */
	public static function binaryNumericOperation(CellValue $a, CellValue $b,
			string $op, callable $fn): CellValue {
		$ops = self::resolveNumericOperands($a, $b, $op);
		$aNum = $ops[0];
		$bNum = $ops[1];
		$type = $ops[2];
		$result = $fn($aNum, $bNum);
		return self::fromValue($result, $type);
	}

	/**
	 * Determines what the result of a calculation with two operands should
	 * look like. Returns a tuple array of the A float value, the B float value,
	 * and the type of the result.
	 *
	 * @param CellValue $a  operand A
	 * @param CellValue $b  operand B
	 * @param string $op  operator symbol
	 * @return array  3-element tuple array with A number value, B number value,
	 *   and result type string
	 * @throws CellEvaluationException  if types are incompatible for numeric operations
	 */
	private static function resolveNumericOperands(CellValue $a, CellValue $b, string $op): array {
		if ($a->type == $this->TYPE_ERROR) throw $a->value;
		if ($b->type == $this->TYPE_ERROR) throw $b->value;
		if ($a->type == $this->TYPE_STRING || $b->type == $this->TYPE_STRING) {
			throw new CellEvaluationException("Cannot perform math on text values");
		}

		if ($a->type == $this->TYPE_BLANK) {
			if ($b->type == $this->TYPE_BLANK) {
				return [ 0, 0, $this->TYPE_NUMBER, 0 ];
			}
			return [ 0, $b->value, $b->type ];
		} elseif ($b->type == $this->TYPE_BLANK) {
			return [ $a->value, 0, $a->type ];
		}

		$isMultOrDiv = ($op == '*' || $op == '/' || $op == '%');

		if ($a->type == $b->type) {
			return [ $a->value, $b->value, $a->type ];
		}

		switch ($a->type . $b->type) {
			case $this->TYPE_CURRENCY . $this->TYPE_NUMBER:
			case $this->TYPE_CURRENCY . $this->TYPE_PERCENT:
				return [ $a->value, $b->value, $this->TYPE_CURRENCY ];
			case $this->TYPE_PERCENT . $this->TYPE_CURRENCY:
				return [ $a->value, $b->value,
						$isMultOrDiv ? $this->TYPE_CURRENCY : $this->TYPE_PERCENT ];
			case $this->TYPE_PERCENT . $this->TYPE_NUMBER:
				return [ $a->value, $b->value,
						$isMultOrDiv ? $this->TYPE_NUMBER : $this->TYPE_PERCENT ];
			case $this->TYPE_NUMBER . $this->TYPE_CURRENCY:
				return [ $a->value, $b->value, $b->type ];
			case $this->TYPE_NUMBER . $this->TYPE_PERCENT:
				return [ $a->value, $b->value,
						$isMultOrDiv ? $this->TYPE_NUMBER : $b->type ];
			case $this->TYPE_BOOLEAN . $this->TYPE_CURRENCY:
			case $this->TYPE_BOOLEAN . $this->TYPE_NUMBER:
			case $this->TYPE_BOOLEAN . $this->TYPE_PERCENT:
				return [ $a->value ? 1 : 0, $b->value, $b->type ];
			case $this->TYPE_CURRENCY . $this->TYPE_BOOLEAN:
			case $this->TYPE_NUMBER . $this->TYPE_BOOLEAN:
			case $this->TYPE_PERCENT . $this->TYPE_BOOLEAN:
				return [ $a->value, $b->value ? 1 : 0, $a->type ];
		}
		throw new CellEvaluationException(`Unhandled operand types "${a.type}" and "${b.type}"`);
	}

	/**
	 * Performs a comparison of two values.
	 *
	 * @param CellValue $a
	 * @param CellValue $b
	 * @return int `-1`, `0`, or `1` if a < b, a == b, or a > b, respectively
	 */
	private static function compare(CellValue $a, CellValue $b): int {
		$args = self::resolveComparableArguments($a, $b);
		$valueA = $args[0];
		$valueB = $args[1];
		if (is_string($valueA)) {
			return strcasecmp($valueA, $valueB);
		} else {
			if ($valueA < $valueB) return -1;
			if ($valueA > $valueB) return 1;
			return 0;
		}
	}

	/**
	 * @param CellValue $a
	 * @param CellValue $b
	 * @return array  two comparable values (strings or floats)
	 * @throws CellEvaluationException  if values are formulas
	 * @throws CellException  if `$a` or `$b` is of type `TYPE_ERROR`
	 */
	private static function resolveComparableArguments(CellValue $a, CellValue $b): array {
		if ($a->type == CellValue::TYPE_ERROR) throw $a->value;
		if ($b->type == CellValue::TYPE_ERROR) throw $b->value;
		if ($a->type == CellValue::TYPE_FORMULA) throw new CellEvaluationException("Can't compare formula values");
		if ($b->type == CellValue::TYPE_FORMULA) throw new CellEvaluationException("Can't compare formula values");
		$aNumValue = $a->value;
		$bNumValue = $b->value;
		$aStrValue = "{$a->value}";
		$bStrValue = "{$b->value}";
		switch ($a->type) {
			case CellValue::TYPE_BLANK:
				$aNumValue = 0;
				$aStrValue = '';
				break;
			case CellValue::TYPE_BOOLEAN:
				$aNumValue = ($aNumValue) ? 1 : 0;
				break;
		}
		switch ($b->type) {
			case CellValue::TYPE_BLANK:
				$bNumValue = 0;
				$bStrValue = '';
				break;
			case CellValue::TYPE_BOOLEAN:
				$bNumValue = ($bNumValue) ? 1 : 0;
				break;
		}
		if ($a->type == CellValue::TYPE_STRING || $b->type == CellValue::TYPE_STRING) {
			return [ $aStrValue, $bStrValue ];
		}
		return [ $aNumValue, $bNumValue ];
	}

	/**
	 * Returns a formatted string for the given raw value, value type, and
	 * decimal places.
	 */
	public static function formatType(mixed $value, string $type, int $decimals): string {
		switch ($type) {
			case CellValue::TYPE_BLANK: return '';
			case CellValue::TYPE_CURRENCY: return CellValue::formatCurrency($value, $decimals);
			case CellValue::TYPE_NUMBER: return CellValue::formatNumber($value, $decimals);
			case CellValue::TYPE_PERCENT: return CellValue::formatPercent($value, $decimals);
			case CellValue::TYPE_BOOLEAN: return $value ? 'TRUE' : 'FALSE';
			case CellValue::TYPE_STRING: return "{$value}";
			case CellValue::TYPE_FORMULA: return "{$value}";
		}
	}

	private static function formatNumber(float|int $value, int $decimals): string {
		return number_format($value, $decimals);
	}

	private static function formatCurrency(float|int $dollars, int $decimals): string {
		$s = number_format($dollars, $decimals);
		if (str_starts_with($s, '-')) {
			return '-$' . mb_substr($s, 1);
		}
		return '$' . s;
	}

	private static function formatPercent(float|int $value, int $decimals): string {
		$dec = $value * 100.0;
		return number_format($dec, $decimals) . '%';
	}

	/**
	 * Determines a good number of decimal places to format a value to.
	 */
	private static function autodecimals(mixed $value, int $maxDigits = 6): int {
		if ($value instanceof CellValue) {
			return CellValue::autodecimals($value->value);
		}
		if (is_numeric($value)) {
			$s = number_format($value, $maxDigits);
			if (strpos($s, '.') === false) return 0;
			$fraction = explode('.', $s)[1];
			return min($maxDigits, mb_strlen($fraction));
		}
		return 0;
	}

	/**
	 * Tests if a type is numeric.
	 */
	public static function isTypeNumeric(string $type): bool {
		return $type == CellValue::TYPE_NUMBER ||
			$type == CellValue::TYPE_PERCENT ||
			$type == CellValue::TYPE_CURRENCY ||
			$type == CellValue::TYPE_BOOLEAN;
	}

	public function __toString(): string {
		return "<CellValue type={$this->type} value={$this->value} \"{$this->formattedValue}\">";
	}
}

/**
 * A rectangular grid of `SpreadsheetCell`s representing a spreadsheet.
 * Agnostic of presentation.
 */
class SpreadsheetGrid {
	/**
	 * Indexed by column then row.
	 * @type {SpreadsheetCell[][]}
	 */
	public array $cells;

	public int $columnCount;
	public int $rowCount;

	public function __construct(int $columnCount, int $rowCount) {
		$this->columnCount = $columnCount;
		$this->rowCount = $rowCount;
		$this->cells = [];
		for ($c = 0; $c < $columnCount; $c++) {
			$column = [];
			for ($r = 0; $r < $rowCount; $r++) {
				array_push($column, new SpreadsheetCell());
			}
			array_push($this->cells, $column);
		}
	}

	/**
	 * @param CellAddress $address
	 * @return SpreadsheetCell $cell
	 * @throws CellEvaluationException  if the address it out of bounds
	 */
	public function cellAt(CellAddress $address): SpreadsheetCell {
		$c = $address->columnIndex; $r = $address->rowIndex;
		if ($c < 0 || $c >= sizeof($this->cells)) throw new CellEvaluationException("Unresolved cell address {$address->name}", '#REF');
		$col = $this->cells[$c];
		if ($r < 0 || $r >= sizeof($col)) throw new CellEvaluationException("Unresolved cell address {$address->name}", '#REF');
		return $col[$r];
	}

	/**
	 * Returns the original value at the given address.
	 */
	public function valueAt(CellAddress $address): ?CellValue {
		return $this->cellAt($address)->originalValue;
	}

	/**
	 * Returns the computed value at the given address.
	 */
	public function outputValueAt(CellAddress $address): ?CellValue {
		return $this->cellAt($address)->outputValue;
	}
}

/**
 * One cell in a spreadsheet grid. Has an `originalValue` to start and an
 * evaluated `outputValue` after population by a `CellExpressionSet` computation.
 */
class SpreadsheetCell {
	public CellValue $originalValue;

	public ?CellValue $outputValue = null;

	/**
	 * Whether `outputValue` is the result of a formula evaluation.
	 */
	public bool $isCalculated = false;

	public ?CellExpression $parsedExpression = null;

	public function __construct() {
		$this->originalValue = new CellValue('', null, CellValue::TYPE_BLANK, 0);
	}

	public function resolvedValue(): CellValue { return $this->outputValue ?? $this->originalValue; }
}

/**
 * Integration with Markdown. Adding this block reader to a parser will run a
 * post-process step on any tables in the document tree. Must be used with
 * `MDTableReader`. Tables without at least one formula will not be altered.
 */
class MDSpreadsheetReader extends MDReader {
	public function postProcess(MDState $state, array &$nodes) {
		foreach ($nodes as $node) {
			if ($node instanceof MDTableNode) {
				$this->processTable($node, $state);
			}
		}
	}

	private function processTable(MDTableNode $tableNode, MDState $state) {
		// Measure table
		$rowCount = sizeof($tableNode->bodyRows());
		$columnCount = 0;
		foreach ($tableNode->bodyRows() as $row) {
			$columnCount = max($columnCount, sizeof($row->children));
		}

		// Create and populate grid
		$grid = new SpreadsheetGrid($columnCount, $rowCount);
		for ($c = 0; $c < $columnCount; $c++) {
			for ($r = 0; $r < $rowCount; $r++) {
				$cellNode = $tableNode->bodyRows()[$r]->children[$c];
				if ($cellNode === null) continue;
				$cellText = $cellNode->toPlaintext($state);
				$gridCell = $grid->cells[$c][$r];
				$gridCell->originalValue = CellValue::fromCellString($cellText);
			}
		}

		// Calculate
		$expressions = new CellExpressionSet($grid);
		$expressions->calculateCells();

		// See if anything was calculated. If not, don't mess with table.
		$isCalculated = false;
		for ($c = 0; $c < $columnCount && !$isCalculated; $c++) {
			for ($r = 0; $r < $rowCount; $r++) {
				if ($grid->cells[$c][$r]->isCalculated) {
					$isCalculated = true;
					break;
				}
			}
		}
		if (!$isCalculated) return;

		// Copy results back to table
		for ($c = 0; $c < $columnCount; $c++) {
			for ($r = 0; $r < $rowCount; $r++) {
				$cellNode = $tableNode->bodyRows[$r]->children[$c];
				if ($cellNode === null) continue;
				$gridCell = $grid->cells[$c][$r];
				$gridValue = $gridCell->outputValue;
				$cellText = $gridValue->formattedValue;
				$cellNode->children = [ new MDTextNode($cellText) ];
				if ($gridCell->isCalculated) {
					$cellNode->addClass('calculated');
				}
				$cellNode->addClass("spreadsheet-type-{$gridValue->type}");
				if ($gridValue->type == CellValue::TYPE_ERROR) {
					$cellNode->attributes['title'] = $gridValue->value;
				}
				$gridNumber = $gridValue->numericValue();
				if ($gridNumber !== null) {
					$cellNode->attributes['data-numeric-value'] = "{$gridNumber}";
				}
				$gridString = $gridValue->stringValue(false);
				if ($gridString !== null) {
					$cellNode->attributes['data-string-value'] = $gridString;
				}
			}
		}
	}
}
?>