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<?php

namespace PhpOffice\PhpSpreadsheet\Calculation;

use 
PhpOffice\PhpSpreadsheet\Calculation\Engine\BranchPruner;
use 
PhpOffice\PhpSpreadsheet\Calculation\Engine\CyclicReferenceStack;
use 
PhpOffice\PhpSpreadsheet\Calculation\Engine\Logger;
use 
PhpOffice\PhpSpreadsheet\Calculation\Engine\Operands;
use 
PhpOffice\PhpSpreadsheet\Calculation\Token\Stack;
use 
PhpOffice\PhpSpreadsheet\Cell\AddressRange;
use 
PhpOffice\PhpSpreadsheet\Cell\Cell;
use 
PhpOffice\PhpSpreadsheet\Cell\Coordinate;
use 
PhpOffice\PhpSpreadsheet\Cell\DataType;
use 
PhpOffice\PhpSpreadsheet\DefinedName;
use 
PhpOffice\PhpSpreadsheet\ReferenceHelper;
use 
PhpOffice\PhpSpreadsheet\Shared;
use 
PhpOffice\PhpSpreadsheet\Spreadsheet;
use 
PhpOffice\PhpSpreadsheet\Worksheet\Worksheet;
use 
ReflectionClassConstant;
use 
ReflectionMethod;
use 
ReflectionParameter;

class 
Calculation
{
    
/** Constants                */
    /** Regular Expressions        */
    //    Numeric operand
    
const CALCULATION_REGEXP_NUMBER '[-+]?\d*\.?\d+(e[-+]?\d+)?';
    
//    String operand
    
const CALCULATION_REGEXP_STRING '"(?:[^"]|"")*"';
    
//    Opening bracket
    
const CALCULATION_REGEXP_OPENBRACE '\(';
    
//    Function (allow for the old @ symbol that could be used to prefix a function, but we'll ignore it)
    
const CALCULATION_REGEXP_FUNCTION '@?(?:_xlfn\.)?(?:_xlws\.)?([\p{L}][\p{L}\p{N}\.]*)[\s]*\(';
    
//    Cell reference (cell or range of cells, with or without a sheet reference)
    
const CALCULATION_REGEXP_CELLREF '((([^\s,!&%^\/\*\+<>=:`-]*)|(\'(?:[^\']|\'[^!])+?\')|(\"(?:[^\"]|\"[^!])+?\"))!)?\$?\b([a-z]{1,3})\$?(\d{1,7})(?![\w.])';
    
//    Cell reference (with or without a sheet reference) ensuring absolute/relative
    
const CALCULATION_REGEXP_CELLREF_RELATIVE '((([^\s\(,!&%^\/\*\+<>=:`-]*)|(\'(?:[^\']|\'[^!])+?\')|(\"(?:[^\"]|\"[^!])+?\"))!)?(\$?\b[a-z]{1,3})(\$?\d{1,7})(?![\w.])';
    const 
CALCULATION_REGEXP_COLUMN_RANGE '(((([^\s\(,!&%^\/\*\+<>=:`-]*)|(\'(?:[^\']|\'[^!])+?\')|(\".(?:[^\"]|\"[^!])?\"))!)?(\$?[a-z]{1,3})):(?![.*])';
    const 
CALCULATION_REGEXP_ROW_RANGE '(((([^\s\(,!&%^\/\*\+<>=:`-]*)|(\'(?:[^\']|\'[^!])+?\')|(\"(?:[^\"]|\"[^!])+?\"))!)?(\$?[1-9][0-9]{0,6})):(?![.*])';
    
//    Cell reference (with or without a sheet reference) ensuring absolute/relative
    //    Cell ranges ensuring absolute/relative
    
const CALCULATION_REGEXP_COLUMNRANGE_RELATIVE '(\$?[a-z]{1,3}):(\$?[a-z]{1,3})';
    const 
CALCULATION_REGEXP_ROWRANGE_RELATIVE '(\$?\d{1,7}):(\$?\d{1,7})';
    
//    Defined Names: Named Range of cells, or Named Formulae
    
const CALCULATION_REGEXP_DEFINEDNAME '((([^\s,!&%^\/\*\+<>=-]*)|(\'(?:[^\']|\'[^!])+?\')|(\"(?:[^\"]|\"[^!])+?\"))!)?([_\p{L}][_\p{L}\p{N}\.]*)';
    
// Structured Reference (Fully Qualified and Unqualified)
    
const CALCULATION_REGEXP_STRUCTURED_REFERENCE '([\p{L}_\\\\][\p{L}\p{N}\._]+)?(\[(?:[^\d\]+-])?)';
    
//    Error
    
const CALCULATION_REGEXP_ERROR '\#[A-Z][A-Z0_\/]*[!\?]?';

    
/** constants */
    
const RETURN_ARRAY_AS_ERROR 'error';
    const 
RETURN_ARRAY_AS_VALUE 'value';
    const 
RETURN_ARRAY_AS_ARRAY 'array';

    const 
FORMULA_OPEN_FUNCTION_BRACE '(';
    const 
FORMULA_CLOSE_FUNCTION_BRACE ')';
    const 
FORMULA_OPEN_MATRIX_BRACE '{';
    const 
FORMULA_CLOSE_MATRIX_BRACE '}';
    const 
FORMULA_STRING_QUOTE '"';

    
/** @var string */
    
private static $returnArrayAsType self::RETURN_ARRAY_AS_VALUE;

    
/**
     * Instance of this class.
     *
     * @var ?Calculation
     */
    
private static $instance;

    
/**
     * Instance of the spreadsheet this Calculation Engine is using.
     *
     * @var ?Spreadsheet
     */
    
private $spreadsheet;

    
/**
     * Calculation cache.
     *
     * @var array
     */
    
private $calculationCache = [];

    
/**
     * Calculation cache enabled.
     *
     * @var bool
     */
    
private $calculationCacheEnabled true;

    
/**
     * @var BranchPruner
     */
    
private $branchPruner;

    
/**
     * @var bool
     */
    
private $branchPruningEnabled true;

    
/**
     * List of operators that can be used within formulae
     * The true/false value indicates whether it is a binary operator or a unary operator.
     */
    
private const CALCULATION_OPERATORS = [
        
'+' => true'-' => true'*' => true'/' => true,
        
'^' => true'&' => true'%' => false'~' => false,
        
'>' => true'<' => true'=' => true'>=' => true,
        
'<=' => true'<>' => true'∩' => true'∪' => true,
        
':' => true,
    ];

    
/**
     * List of binary operators (those that expect two operands).
     */
    
private const BINARY_OPERATORS = [
        
'+' => true'-' => true'*' => true'/' => true,
        
'^' => true'&' => true'>' => true'<' => true,
        
'=' => true'>=' => true'<=' => true'<>' => true,
        
'∩' => true'∪' => true':' => true,
    ];

    
/**
     * The debug log generated by the calculation engine.
     *
     * @var Logger
     */
    
private $debugLog;

    
/**
     * Flag to determine how formula errors should be handled
     *        If true, then a user error will be triggered
     *        If false, then an exception will be thrown.
     *
     * @var ?bool
     *
     * @deprecated 1.25.2 use setSuppressFormulaErrors() instead
     */
    
public $suppressFormulaErrors;

    
/** @var bool */
    
private $suppressFormulaErrorsNew false;

    
/**
     * Error message for any error that was raised/thrown by the calculation engine.
     *
     * @var null|string
     */
    
public $formulaError;

    
/**
     * Reference Helper.
     *
     * @var ReferenceHelper
     */
    
private static $referenceHelper;

    
/**
     * An array of the nested cell references accessed by the calculation engine, used for the debug log.
     *
     * @var CyclicReferenceStack
     */
    
private $cyclicReferenceStack;

    
/** @var array */
    
private $cellStack = [];

    
/**
     * Current iteration counter for cyclic formulae
     * If the value is 0 (or less) then cyclic formulae will throw an exception,
     * otherwise they will iterate to the limit defined here before returning a result.
     *
     * @var int
     */
    
private $cyclicFormulaCounter 1;

    
/** @var string */
    
private $cyclicFormulaCell '';

    
/**
     * Number of iterations for cyclic formulae.
     *
     * @var int
     */
    
public $cyclicFormulaCount 1;

    
/**
     * The current locale setting.
     *
     * @var string
     */
    
private static $localeLanguage 'en_us'//    US English    (default locale)

    /**
     * List of available locale settings
     * Note that this is read for the locale subdirectory only when requested.
     *
     * @var string[]
     */
    
private static $validLocaleLanguages = [
        
'en'//    English        (default language)
    
];

    
/**
     * Locale-specific argument separator for function arguments.
     *
     * @var string
     */
    
private static $localeArgumentSeparator ',';

    
/** @var array */
    
private static $localeFunctions = [];

    
/**
     * Locale-specific translations for Excel constants (True, False and Null).
     *
     * @var array<string, string>
     */
    
private static $localeBoolean = [
        
'TRUE' => 'TRUE',
        
'FALSE' => 'FALSE',
        
'NULL' => 'NULL',
    ];

    public static function 
getLocaleBoolean(string $index): string
    
{
        return 
self::$localeBoolean[$index];
    }

    
/**
     * Excel constant string translations to their PHP equivalents
     * Constant conversion from text name/value to actual (datatyped) value.
     *
     * @var array<string, mixed>
     */
    
private static $excelConstants = [
        
'TRUE' => true,
        
'FALSE' => false,
        
'NULL' => null,
    ];

    public static function 
keyInExcelConstants(string $key): bool
    
{
        return 
array_key_exists($keyself::$excelConstants);
    }

    
/** @return mixed */
    
public static function getExcelConstants(string $key)
    {
        return 
self::$excelConstants[$key];
    }

    
/**
     * Array of functions usable on Spreadsheet.
     * In theory, this could be const rather than static;
     *   however, Phpstan breaks trying to analyze it when attempted.
     *
     *@var array
     */
    
private static $phpSpreadsheetFunctions = [
        
'ABS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Absolute::class, 'evaluate'],
            
'argumentCount' => '1',
        ],
        
'ACCRINT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\AccruedInterest::class, 'periodic'],
            
'argumentCount' => '4-8',
        ],
        
'ACCRINTM' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\AccruedInterest::class, 'atMaturity'],
            
'argumentCount' => '3-5',
        ],
        
'ACOS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cosine::class, 'acos'],
            
'argumentCount' => '1',
        ],
        
'ACOSH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cosine::class, 'acosh'],
            
'argumentCount' => '1',
        ],
        
'ACOT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cotangent::class, 'acot'],
            
'argumentCount' => '1',
        ],
        
'ACOTH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cotangent::class, 'acoth'],
            
'argumentCount' => '1',
        ],
        
'ADDRESS' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Address::class, 'cell'],
            
'argumentCount' => '2-5',
        ],
        
'AGGREGATE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3+',
        ],
        
'AMORDEGRC' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Amortization::class, 'AMORDEGRC'],
            
'argumentCount' => '6,7',
        ],
        
'AMORLINC' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Amortization::class, 'AMORLINC'],
            
'argumentCount' => '6,7',
        ],
        
'ANCHORARRAY' => [
            
'category' => Category::CATEGORY_UNCATEGORISED,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'AND' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Operations::class, 'logicalAnd'],
            
'argumentCount' => '1+',
        ],
        
'ARABIC' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Arabic::class, 'evaluate'],
            
'argumentCount' => '1',
        ],
        
'AREAS' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'ARRAYTOTEXT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Text::class, 'fromArray'],
            
'argumentCount' => '1,2',
        ],
        
'ASC' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'ASIN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Sine::class, 'asin'],
            
'argumentCount' => '1',
        ],
        
'ASINH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Sine::class, 'asinh'],
            
'argumentCount' => '1',
        ],
        
'ATAN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Tangent::class, 'atan'],
            
'argumentCount' => '1',
        ],
        
'ATAN2' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Tangent::class, 'atan2'],
            
'argumentCount' => '2',
        ],
        
'ATANH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Tangent::class, 'atanh'],
            
'argumentCount' => '1',
        ],
        
'AVEDEV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages::class, 'averageDeviations'],
            
'argumentCount' => '1+',
        ],
        
'AVERAGE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages::class, 'average'],
            
'argumentCount' => '1+',
        ],
        
'AVERAGEA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages::class, 'averageA'],
            
'argumentCount' => '1+',
        ],
        
'AVERAGEIF' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Conditional::class, 'AVERAGEIF'],
            
'argumentCount' => '2,3',
        ],
        
'AVERAGEIFS' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Conditional::class, 'AVERAGEIFS'],
            
'argumentCount' => '3+',
        ],
        
'BAHTTEXT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'BASE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Base::class, 'evaluate'],
            
'argumentCount' => '2,3',
        ],
        
'BESSELI' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BesselI::class, 'BESSELI'],
            
'argumentCount' => '2',
        ],
        
'BESSELJ' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BesselJ::class, 'BESSELJ'],
            
'argumentCount' => '2',
        ],
        
'BESSELK' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BesselK::class, 'BESSELK'],
            
'argumentCount' => '2',
        ],
        
'BESSELY' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BesselY::class, 'BESSELY'],
            
'argumentCount' => '2',
        ],
        
'BETADIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Beta::class, 'distribution'],
            
'argumentCount' => '3-5',
        ],
        
'BETA.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '4-6',
        ],
        
'BETAINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Beta::class, 'inverse'],
            
'argumentCount' => '3-5',
        ],
        
'BETA.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Beta::class, 'inverse'],
            
'argumentCount' => '3-5',
        ],
        
'BIN2DEC' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertBinary::class, 'toDecimal'],
            
'argumentCount' => '1',
        ],
        
'BIN2HEX' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertBinary::class, 'toHex'],
            
'argumentCount' => '1,2',
        ],
        
'BIN2OCT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertBinary::class, 'toOctal'],
            
'argumentCount' => '1,2',
        ],
        
'BINOMDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Binomial::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'BINOM.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Binomial::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'BINOM.DIST.RANGE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Binomial::class, 'range'],
            
'argumentCount' => '3,4',
        ],
        
'BINOM.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Binomial::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'BITAND' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BitWise::class, 'BITAND'],
            
'argumentCount' => '2',
        ],
        
'BITOR' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BitWise::class, 'BITOR'],
            
'argumentCount' => '2',
        ],
        
'BITXOR' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BitWise::class, 'BITXOR'],
            
'argumentCount' => '2',
        ],
        
'BITLSHIFT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BitWise::class, 'BITLSHIFT'],
            
'argumentCount' => '2',
        ],
        
'BITRSHIFT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\BitWise::class, 'BITRSHIFT'],
            
'argumentCount' => '2',
        ],
        
'BYCOL' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'BYROW' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'CEILING' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Ceiling::class, 'ceiling'],
            
'argumentCount' => '1-2'// 2 for Excel, 1-2 for Ods/Gnumeric
        
],
        
'CEILING.MATH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Ceiling::class, 'math'],
            
'argumentCount' => '1-3',
        ],
        
'CEILING.PRECISE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Ceiling::class, 'precise'],
            
'argumentCount' => '1,2',
        ],
        
'CELL' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1,2',
        ],
        
'CHAR' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\CharacterConvert::class, 'character'],
            
'argumentCount' => '1',
        ],
        
'CHIDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'distributionRightTail'],
            
'argumentCount' => '2',
        ],
        
'CHISQ.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'distributionLeftTail'],
            
'argumentCount' => '3',
        ],
        
'CHISQ.DIST.RT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'distributionRightTail'],
            
'argumentCount' => '2',
        ],
        
'CHIINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'inverseRightTail'],
            
'argumentCount' => '2',
        ],
        
'CHISQ.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'inverseLeftTail'],
            
'argumentCount' => '2',
        ],
        
'CHISQ.INV.RT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'inverseRightTail'],
            
'argumentCount' => '2',
        ],
        
'CHITEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'test'],
            
'argumentCount' => '2',
        ],
        
'CHISQ.TEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\ChiSquared::class, 'test'],
            
'argumentCount' => '2',
        ],
        
'CHOOSE' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Selection::class, 'CHOOSE'],
            
'argumentCount' => '2+',
        ],
        
'CHOOSECOLS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2+',
        ],
        
'CHOOSEROWS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2+',
        ],
        
'CLEAN' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Trim::class, 'nonPrintable'],
            
'argumentCount' => '1',
        ],
        
'CODE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\CharacterConvert::class, 'code'],
            
'argumentCount' => '1',
        ],
        
'COLUMN' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\RowColumnInformation::class, 'COLUMN'],
            
'argumentCount' => '-1',
            
'passCellReference' => true,
            
'passByReference' => [true],
        ],
        
'COLUMNS' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\RowColumnInformation::class, 'COLUMNS'],
            
'argumentCount' => '1',
        ],
        
'COMBIN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Combinations::class, 'withoutRepetition'],
            
'argumentCount' => '2',
        ],
        
'COMBINA' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Combinations::class, 'withRepetition'],
            
'argumentCount' => '2',
        ],
        
'COMPLEX' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\Complex::class, 'COMPLEX'],
            
'argumentCount' => '2,3',
        ],
        
'CONCAT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Concatenate::class, 'CONCATENATE'],
            
'argumentCount' => '1+',
        ],
        
'CONCATENATE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Concatenate::class, 'CONCATENATE'],
            
'argumentCount' => '1+',
        ],
        
'CONFIDENCE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Confidence::class, 'CONFIDENCE'],
            
'argumentCount' => '3',
        ],
        
'CONFIDENCE.NORM' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Confidence::class, 'CONFIDENCE'],
            
'argumentCount' => '3',
        ],
        
'CONFIDENCE.T' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3',
        ],
        
'CONVERT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertUOM::class, 'CONVERT'],
            
'argumentCount' => '3',
        ],
        
'CORREL' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'CORREL'],
            
'argumentCount' => '2',
        ],
        
'COS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cosine::class, 'cos'],
            
'argumentCount' => '1',
        ],
        
'COSH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cosine::class, 'cosh'],
            
'argumentCount' => '1',
        ],
        
'COT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cotangent::class, 'cot'],
            
'argumentCount' => '1',
        ],
        
'COTH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cotangent::class, 'coth'],
            
'argumentCount' => '1',
        ],
        
'COUNT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Counts::class, 'COUNT'],
            
'argumentCount' => '1+',
        ],
        
'COUNTA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Counts::class, 'COUNTA'],
            
'argumentCount' => '1+',
        ],
        
'COUNTBLANK' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Counts::class, 'COUNTBLANK'],
            
'argumentCount' => '1',
        ],
        
'COUNTIF' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Conditional::class, 'COUNTIF'],
            
'argumentCount' => '2',
        ],
        
'COUNTIFS' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Conditional::class, 'COUNTIFS'],
            
'argumentCount' => '2+',
        ],
        
'COUPDAYBS' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Coupons::class, 'COUPDAYBS'],
            
'argumentCount' => '3,4',
        ],
        
'COUPDAYS' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Coupons::class, 'COUPDAYS'],
            
'argumentCount' => '3,4',
        ],
        
'COUPDAYSNC' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Coupons::class, 'COUPDAYSNC'],
            
'argumentCount' => '3,4',
        ],
        
'COUPNCD' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Coupons::class, 'COUPNCD'],
            
'argumentCount' => '3,4',
        ],
        
'COUPNUM' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Coupons::class, 'COUPNUM'],
            
'argumentCount' => '3,4',
        ],
        
'COUPPCD' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Coupons::class, 'COUPPCD'],
            
'argumentCount' => '3,4',
        ],
        
'COVAR' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'COVAR'],
            
'argumentCount' => '2',
        ],
        
'COVARIANCE.P' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'COVAR'],
            
'argumentCount' => '2',
        ],
        
'COVARIANCE.S' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'CRITBINOM' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Binomial::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'CSC' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cosecant::class, 'csc'],
            
'argumentCount' => '1',
        ],
        
'CSCH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Cosecant::class, 'csch'],
            
'argumentCount' => '1',
        ],
        
'CUBEKPIMEMBER' => [
            
'category' => Category::CATEGORY_CUBE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'CUBEMEMBER' => [
            
'category' => Category::CATEGORY_CUBE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'CUBEMEMBERPROPERTY' => [
            
'category' => Category::CATEGORY_CUBE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'CUBERANKEDMEMBER' => [
            
'category' => Category::CATEGORY_CUBE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'CUBESET' => [
            
'category' => Category::CATEGORY_CUBE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'CUBESETCOUNT' => [
            
'category' => Category::CATEGORY_CUBE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'CUBEVALUE' => [
            
'category' => Category::CATEGORY_CUBE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'CUMIPMT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic\Cumulative::class, 'interest'],
            
'argumentCount' => '6',
        ],
        
'CUMPRINC' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic\Cumulative::class, 'principal'],
            
'argumentCount' => '6',
        ],
        
'DATE' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Date::class, 'fromYMD'],
            
'argumentCount' => '3',
        ],
        
'DATEDIF' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Difference::class, 'interval'],
            
'argumentCount' => '2,3',
        ],
        
'DATESTRING' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'DATEVALUE' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\DateValue::class, 'fromString'],
            
'argumentCount' => '1',
        ],
        
'DAVERAGE' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DAverage::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DAY' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\DateParts::class, 'day'],
            
'argumentCount' => '1',
        ],
        
'DAYS' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Days::class, 'between'],
            
'argumentCount' => '2',
        ],
        
'DAYS360' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Days360::class, 'between'],
            
'argumentCount' => '2,3',
        ],
        
'DB' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Depreciation::class, 'DB'],
            
'argumentCount' => '4,5',
        ],
        
'DBCS' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'DCOUNT' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DCount::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DCOUNTA' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DCountA::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DDB' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Depreciation::class, 'DDB'],
            
'argumentCount' => '4,5',
        ],
        
'DEC2BIN' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertDecimal::class, 'toBinary'],
            
'argumentCount' => '1,2',
        ],
        
'DEC2HEX' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertDecimal::class, 'toHex'],
            
'argumentCount' => '1,2',
        ],
        
'DEC2OCT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertDecimal::class, 'toOctal'],
            
'argumentCount' => '1,2',
        ],
        
'DECIMAL' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'DEGREES' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Angle::class, 'toDegrees'],
            
'argumentCount' => '1',
        ],
        
'DELTA' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\Compare::class, 'DELTA'],
            
'argumentCount' => '1,2',
        ],
        
'DEVSQ' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Deviations::class, 'sumSquares'],
            
'argumentCount' => '1+',
        ],
        
'DGET' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DGet::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DISC' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Rates::class, 'discount'],
            
'argumentCount' => '4,5',
        ],
        
'DMAX' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DMax::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DMIN' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DMin::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DOLLAR' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Format::class, 'DOLLAR'],
            
'argumentCount' => '1,2',
        ],
        
'DOLLARDE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Dollar::class, 'decimal'],
            
'argumentCount' => '2',
        ],
        
'DOLLARFR' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Dollar::class, 'fractional'],
            
'argumentCount' => '2',
        ],
        
'DPRODUCT' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DProduct::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DROP' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-3',
        ],
        
'DSTDEV' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DStDev::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DSTDEVP' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DStDevP::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DSUM' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DSum::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DURATION' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '5,6',
        ],
        
'DVAR' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DVar::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'DVARP' => [
            
'category' => Category::CATEGORY_DATABASE,
            
'functionCall' => [Database\DVarP::class, 'evaluate'],
            
'argumentCount' => '3',
        ],
        
'ECMA.CEILING' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1,2',
        ],
        
'EDATE' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Month::class, 'adjust'],
            
'argumentCount' => '2',
        ],
        
'EFFECT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\InterestRate::class, 'effective'],
            
'argumentCount' => '2',
        ],
        
'ENCODEURL' => [
            
'category' => Category::CATEGORY_WEB,
            
'functionCall' => [Web\Service::class, 'urlEncode'],
            
'argumentCount' => '1',
        ],
        
'EOMONTH' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Month::class, 'lastDay'],
            
'argumentCount' => '2',
        ],
        
'ERF' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\Erf::class, 'ERF'],
            
'argumentCount' => '1,2',
        ],
        
'ERF.PRECISE' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\Erf::class, 'ERFPRECISE'],
            
'argumentCount' => '1',
        ],
        
'ERFC' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ErfC::class, 'ERFC'],
            
'argumentCount' => '1',
        ],
        
'ERFC.PRECISE' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ErfC::class, 'ERFC'],
            
'argumentCount' => '1',
        ],
        
'ERROR.TYPE' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\ExcelError::class, 'type'],
            
'argumentCount' => '1',
        ],
        
'EVEN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Round::class, 'even'],
            
'argumentCount' => '1',
        ],
        
'EXACT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Text::class, 'exact'],
            
'argumentCount' => '2',
        ],
        
'EXP' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Exp::class, 'evaluate'],
            
'argumentCount' => '1',
        ],
        
'EXPAND' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-4',
        ],
        
'EXPONDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Exponential::class, 'distribution'],
            
'argumentCount' => '3',
        ],
        
'EXPON.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Exponential::class, 'distribution'],
            
'argumentCount' => '3',
        ],
        
'FACT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Factorial::class, 'fact'],
            
'argumentCount' => '1',
        ],
        
'FACTDOUBLE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Factorial::class, 'factDouble'],
            
'argumentCount' => '1',
        ],
        
'FALSE' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Boolean::class, 'FALSE'],
            
'argumentCount' => '0',
        ],
        
'FDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3',
        ],
        
'F.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\F::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'F.DIST.RT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3',
        ],
        
'FILTER' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Filter::class, 'filter'],
            
'argumentCount' => '2-3',
        ],
        
'FILTERXML' => [
            
'category' => Category::CATEGORY_WEB,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'FIND' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Search::class, 'sensitive'],
            
'argumentCount' => '2,3',
        ],
        
'FINDB' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Search::class, 'sensitive'],
            
'argumentCount' => '2,3',
        ],
        
'FINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3',
        ],
        
'F.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3',
        ],
        
'F.INV.RT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3',
        ],
        
'FISHER' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Fisher::class, 'distribution'],
            
'argumentCount' => '1',
        ],
        
'FISHERINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Fisher::class, 'inverse'],
            
'argumentCount' => '1',
        ],
        
'FIXED' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Format::class, 'FIXEDFORMAT'],
            
'argumentCount' => '1-3',
        ],
        
'FLOOR' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Floor::class, 'floor'],
            
'argumentCount' => '1-2'// Excel requries 2, Ods/Gnumeric 1-2
        
],
        
'FLOOR.MATH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Floor::class, 'math'],
            
'argumentCount' => '1-3',
        ],
        
'FLOOR.PRECISE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Floor::class, 'precise'],
            
'argumentCount' => '1-2',
        ],
        
'FORECAST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'FORECAST'],
            
'argumentCount' => '3',
        ],
        
'FORECAST.ETS' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3-6',
        ],
        
'FORECAST.ETS.CONFINT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3-6',
        ],
        
'FORECAST.ETS.SEASONALITY' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-4',
        ],
        
'FORECAST.ETS.STAT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3-6',
        ],
        
'FORECAST.LINEAR' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'FORECAST'],
            
'argumentCount' => '3',
        ],
        
'FORMULATEXT' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Formula::class, 'text'],
            
'argumentCount' => '1',
            
'passCellReference' => true,
            
'passByReference' => [true],
        ],
        
'FREQUENCY' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'FTEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'F.TEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'FV' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic::class, 'futureValue'],
            
'argumentCount' => '3-5',
        ],
        
'FVSCHEDULE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Single::class, 'futureValue'],
            
'argumentCount' => '2',
        ],
        
'GAMMA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Gamma::class, 'gamma'],
            
'argumentCount' => '1',
        ],
        
'GAMMADIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Gamma::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'GAMMA.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Gamma::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'GAMMAINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Gamma::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'GAMMA.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Gamma::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'GAMMALN' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Gamma::class, 'ln'],
            
'argumentCount' => '1',
        ],
        
'GAMMALN.PRECISE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Gamma::class, 'ln'],
            
'argumentCount' => '1',
        ],
        
'GAUSS' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StandardNormal::class, 'gauss'],
            
'argumentCount' => '1',
        ],
        
'GCD' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Gcd::class, 'evaluate'],
            
'argumentCount' => '1+',
        ],
        
'GEOMEAN' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages\Mean::class, 'geometric'],
            
'argumentCount' => '1+',
        ],
        
'GESTEP' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\Compare::class, 'GESTEP'],
            
'argumentCount' => '1,2',
        ],
        
'GETPIVOTDATA' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2+',
        ],
        
'GROWTH' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'GROWTH'],
            
'argumentCount' => '1-4',
        ],
        
'HARMEAN' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages\Mean::class, 'harmonic'],
            
'argumentCount' => '1+',
        ],
        
'HEX2BIN' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertHex::class, 'toBinary'],
            
'argumentCount' => '1,2',
        ],
        
'HEX2DEC' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertHex::class, 'toDecimal'],
            
'argumentCount' => '1',
        ],
        
'HEX2OCT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertHex::class, 'toOctal'],
            
'argumentCount' => '1,2',
        ],
        
'HLOOKUP' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\HLookup::class, 'lookup'],
            
'argumentCount' => '3,4',
        ],
        
'HOUR' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\TimeParts::class, 'hour'],
            
'argumentCount' => '1',
        ],
        
'HSTACK' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1+',
        ],
        
'HYPERLINK' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Hyperlink::class, 'set'],
            
'argumentCount' => '1,2',
            
'passCellReference' => true,
        ],
        
'HYPGEOMDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\HyperGeometric::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'HYPGEOM.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '5',
        ],
        
'IF' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Conditional::class, 'statementIf'],
            
'argumentCount' => '1-3',
        ],
        
'IFERROR' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Conditional::class, 'IFERROR'],
            
'argumentCount' => '2',
        ],
        
'IFNA' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Conditional::class, 'IFNA'],
            
'argumentCount' => '2',
        ],
        
'IFS' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Conditional::class, 'IFS'],
            
'argumentCount' => '2+',
        ],
        
'IMABS' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMABS'],
            
'argumentCount' => '1',
        ],
        
'IMAGINARY' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\Complex::class, 'IMAGINARY'],
            
'argumentCount' => '1',
        ],
        
'IMARGUMENT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMARGUMENT'],
            
'argumentCount' => '1',
        ],
        
'IMCONJUGATE' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMCONJUGATE'],
            
'argumentCount' => '1',
        ],
        
'IMCOS' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMCOS'],
            
'argumentCount' => '1',
        ],
        
'IMCOSH' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMCOSH'],
            
'argumentCount' => '1',
        ],
        
'IMCOT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMCOT'],
            
'argumentCount' => '1',
        ],
        
'IMCSC' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMCSC'],
            
'argumentCount' => '1',
        ],
        
'IMCSCH' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMCSCH'],
            
'argumentCount' => '1',
        ],
        
'IMDIV' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexOperations::class, 'IMDIV'],
            
'argumentCount' => '2',
        ],
        
'IMEXP' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMEXP'],
            
'argumentCount' => '1',
        ],
        
'IMLN' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMLN'],
            
'argumentCount' => '1',
        ],
        
'IMLOG10' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMLOG10'],
            
'argumentCount' => '1',
        ],
        
'IMLOG2' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMLOG2'],
            
'argumentCount' => '1',
        ],
        
'IMPOWER' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMPOWER'],
            
'argumentCount' => '2',
        ],
        
'IMPRODUCT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexOperations::class, 'IMPRODUCT'],
            
'argumentCount' => '1+',
        ],
        
'IMREAL' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\Complex::class, 'IMREAL'],
            
'argumentCount' => '1',
        ],
        
'IMSEC' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMSEC'],
            
'argumentCount' => '1',
        ],
        
'IMSECH' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMSECH'],
            
'argumentCount' => '1',
        ],
        
'IMSIN' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMSIN'],
            
'argumentCount' => '1',
        ],
        
'IMSINH' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMSINH'],
            
'argumentCount' => '1',
        ],
        
'IMSQRT' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMSQRT'],
            
'argumentCount' => '1',
        ],
        
'IMSUB' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexOperations::class, 'IMSUB'],
            
'argumentCount' => '2',
        ],
        
'IMSUM' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexOperations::class, 'IMSUM'],
            
'argumentCount' => '1+',
        ],
        
'IMTAN' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ComplexFunctions::class, 'IMTAN'],
            
'argumentCount' => '1',
        ],
        
'INDEX' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Matrix::class, 'index'],
            
'argumentCount' => '2-4',
        ],
        
'INDIRECT' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Indirect::class, 'INDIRECT'],
            
'argumentCount' => '1,2',
            
'passCellReference' => true,
        ],
        
'INFO' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'INT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\IntClass::class, 'evaluate'],
            
'argumentCount' => '1',
        ],
        
'INTERCEPT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'INTERCEPT'],
            
'argumentCount' => '2',
        ],
        
'INTRATE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Rates::class, 'interest'],
            
'argumentCount' => '4,5',
        ],
        
'IPMT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic\Interest::class, 'payment'],
            
'argumentCount' => '4-6',
        ],
        
'IRR' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Variable\Periodic::class, 'rate'],
            
'argumentCount' => '1,2',
        ],
        
'ISBLANK' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isBlank'],
            
'argumentCount' => '1',
        ],
        
'ISERR' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\ErrorValue::class, 'isErr'],
            
'argumentCount' => '1',
        ],
        
'ISERROR' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\ErrorValue::class, 'isError'],
            
'argumentCount' => '1',
        ],
        
'ISEVEN' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isEven'],
            
'argumentCount' => '1',
        ],
        
'ISFORMULA' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isFormula'],
            
'argumentCount' => '1',
            
'passCellReference' => true,
            
'passByReference' => [true],
        ],
        
'ISLOGICAL' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isLogical'],
            
'argumentCount' => '1',
        ],
        
'ISNA' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\ErrorValue::class, 'isNa'],
            
'argumentCount' => '1',
        ],
        
'ISNONTEXT' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isNonText'],
            
'argumentCount' => '1',
        ],
        
'ISNUMBER' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isNumber'],
            
'argumentCount' => '1',
        ],
        
'ISO.CEILING' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1,2',
        ],
        
'ISODD' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isOdd'],
            
'argumentCount' => '1',
        ],
        
'ISOMITTED' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'ISOWEEKNUM' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Week::class, 'isoWeekNumber'],
            
'argumentCount' => '1',
        ],
        
'ISPMT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic\Interest::class, 'schedulePayment'],
            
'argumentCount' => '4',
        ],
        
'ISREF' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isRef'],
            
'argumentCount' => '1',
            
'passCellReference' => true,
            
'passByReference' => [true],
        ],
        
'ISTEXT' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'isText'],
            
'argumentCount' => '1',
        ],
        
'ISTHAIDIGIT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'JIS' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'KURT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Deviations::class, 'kurtosis'],
            
'argumentCount' => '1+',
        ],
        
'LAMBDA' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'LARGE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Size::class, 'large'],
            
'argumentCount' => '2',
        ],
        
'LCM' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Lcm::class, 'evaluate'],
            
'argumentCount' => '1+',
        ],
        
'LEFT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'left'],
            
'argumentCount' => '1,2',
        ],
        
'LEFTB' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'left'],
            
'argumentCount' => '1,2',
        ],
        
'LEN' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Text::class, 'length'],
            
'argumentCount' => '1',
        ],
        
'LENB' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Text::class, 'length'],
            
'argumentCount' => '1',
        ],
        
'LET' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'LINEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'LINEST'],
            
'argumentCount' => '1-4',
        ],
        
'LN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Logarithms::class, 'natural'],
            
'argumentCount' => '1',
        ],
        
'LOG' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Logarithms::class, 'withBase'],
            
'argumentCount' => '1,2',
        ],
        
'LOG10' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Logarithms::class, 'base10'],
            
'argumentCount' => '1',
        ],
        
'LOGEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'LOGEST'],
            
'argumentCount' => '1-4',
        ],
        
'LOGINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\LogNormal::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'LOGNORMDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\LogNormal::class, 'cumulative'],
            
'argumentCount' => '3',
        ],
        
'LOGNORM.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\LogNormal::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'LOGNORM.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\LogNormal::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'LOOKUP' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Lookup::class, 'lookup'],
            
'argumentCount' => '2,3',
        ],
        
'LOWER' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\CaseConvert::class, 'lower'],
            
'argumentCount' => '1',
        ],
        
'MAKEARRAY' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'MAP' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'MATCH' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\ExcelMatch::class, 'MATCH'],
            
'argumentCount' => '2,3',
        ],
        
'MAX' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Maximum::class, 'max'],
            
'argumentCount' => '1+',
        ],
        
'MAXA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Maximum::class, 'maxA'],
            
'argumentCount' => '1+',
        ],
        
'MAXIFS' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Conditional::class, 'MAXIFS'],
            
'argumentCount' => '3+',
        ],
        
'MDETERM' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\MatrixFunctions::class, 'determinant'],
            
'argumentCount' => '1',
        ],
        
'MDURATION' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '5,6',
        ],
        
'MEDIAN' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages::class, 'median'],
            
'argumentCount' => '1+',
        ],
        
'MEDIANIF' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2+',
        ],
        
'MID' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'mid'],
            
'argumentCount' => '3',
        ],
        
'MIDB' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'mid'],
            
'argumentCount' => '3',
        ],
        
'MIN' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Minimum::class, 'min'],
            
'argumentCount' => '1+',
        ],
        
'MINA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Minimum::class, 'minA'],
            
'argumentCount' => '1+',
        ],
        
'MINIFS' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Conditional::class, 'MINIFS'],
            
'argumentCount' => '3+',
        ],
        
'MINUTE' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\TimeParts::class, 'minute'],
            
'argumentCount' => '1',
        ],
        
'MINVERSE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\MatrixFunctions::class, 'inverse'],
            
'argumentCount' => '1',
        ],
        
'MIRR' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Variable\Periodic::class, 'modifiedRate'],
            
'argumentCount' => '3',
        ],
        
'MMULT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\MatrixFunctions::class, 'multiply'],
            
'argumentCount' => '2',
        ],
        
'MOD' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Operations::class, 'mod'],
            
'argumentCount' => '2',
        ],
        
'MODE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages::class, 'mode'],
            
'argumentCount' => '1+',
        ],
        
'MODE.MULT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1+',
        ],
        
'MODE.SNGL' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages::class, 'mode'],
            
'argumentCount' => '1+',
        ],
        
'MONTH' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\DateParts::class, 'month'],
            
'argumentCount' => '1',
        ],
        
'MROUND' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Round::class, 'multiple'],
            
'argumentCount' => '2',
        ],
        
'MULTINOMIAL' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Factorial::class, 'multinomial'],
            
'argumentCount' => '1+',
        ],
        
'MUNIT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\MatrixFunctions::class, 'identity'],
            
'argumentCount' => '1',
        ],
        
'N' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'asNumber'],
            
'argumentCount' => '1',
        ],
        
'NA' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\ExcelError::class, 'NA'],
            
'argumentCount' => '0',
        ],
        
'NEGBINOMDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Binomial::class, 'negative'],
            
'argumentCount' => '3',
        ],
        
'NEGBINOM.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '4',
        ],
        
'NETWORKDAYS' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\NetworkDays::class, 'count'],
            
'argumentCount' => '2-3',
        ],
        
'NETWORKDAYS.INTL' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-4',
        ],
        
'NOMINAL' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\InterestRate::class, 'nominal'],
            
'argumentCount' => '2',
        ],
        
'NORMDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Normal::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'NORM.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Normal::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'NORMINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Normal::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'NORM.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Normal::class, 'inverse'],
            
'argumentCount' => '3',
        ],
        
'NORMSDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StandardNormal::class, 'cumulative'],
            
'argumentCount' => '1',
        ],
        
'NORM.S.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StandardNormal::class, 'distribution'],
            
'argumentCount' => '1,2',
        ],
        
'NORMSINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StandardNormal::class, 'inverse'],
            
'argumentCount' => '1',
        ],
        
'NORM.S.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StandardNormal::class, 'inverse'],
            
'argumentCount' => '1',
        ],
        
'NOT' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Operations::class, 'NOT'],
            
'argumentCount' => '1',
        ],
        
'NOW' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Current::class, 'now'],
            
'argumentCount' => '0',
        ],
        
'NPER' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic::class, 'periods'],
            
'argumentCount' => '3-5',
        ],
        
'NPV' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Variable\Periodic::class, 'presentValue'],
            
'argumentCount' => '2+',
        ],
        
'NUMBERSTRING' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'NUMBERVALUE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Format::class, 'NUMBERVALUE'],
            
'argumentCount' => '1+',
        ],
        
'OCT2BIN' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertOctal::class, 'toBinary'],
            
'argumentCount' => '1,2',
        ],
        
'OCT2DEC' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertOctal::class, 'toDecimal'],
            
'argumentCount' => '1',
        ],
        
'OCT2HEX' => [
            
'category' => Category::CATEGORY_ENGINEERING,
            
'functionCall' => [Engineering\ConvertOctal::class, 'toHex'],
            
'argumentCount' => '1,2',
        ],
        
'ODD' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Round::class, 'odd'],
            
'argumentCount' => '1',
        ],
        
'ODDFPRICE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '8,9',
        ],
        
'ODDFYIELD' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '8,9',
        ],
        
'ODDLPRICE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '7,8',
        ],
        
'ODDLYIELD' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '7,8',
        ],
        
'OFFSET' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Offset::class, 'OFFSET'],
            
'argumentCount' => '3-5',
            
'passCellReference' => true,
            
'passByReference' => [true],
        ],
        
'OR' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Operations::class, 'logicalOr'],
            
'argumentCount' => '1+',
        ],
        
'PDURATION' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Single::class, 'periods'],
            
'argumentCount' => '3',
        ],
        
'PEARSON' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'CORREL'],
            
'argumentCount' => '2',
        ],
        
'PERCENTILE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'PERCENTILE'],
            
'argumentCount' => '2',
        ],
        
'PERCENTILE.EXC' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'PERCENTILE.INC' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'PERCENTILE'],
            
'argumentCount' => '2',
        ],
        
'PERCENTRANK' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'PERCENTRANK'],
            
'argumentCount' => '2,3',
        ],
        
'PERCENTRANK.EXC' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2,3',
        ],
        
'PERCENTRANK.INC' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'PERCENTRANK'],
            
'argumentCount' => '2,3',
        ],
        
'PERMUT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Permutations::class, 'PERMUT'],
            
'argumentCount' => '2',
        ],
        
'PERMUTATIONA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Permutations::class, 'PERMUTATIONA'],
            
'argumentCount' => '2',
        ],
        
'PHONETIC' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'PHI' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1',
        ],
        
'PI' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => 'pi',
            
'argumentCount' => '0',
        ],
        
'PMT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic\Payments::class, 'annuity'],
            
'argumentCount' => '3-5',
        ],
        
'POISSON' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Poisson::class, 'distribution'],
            
'argumentCount' => '3',
        ],
        
'POISSON.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Poisson::class, 'distribution'],
            
'argumentCount' => '3',
        ],
        
'POWER' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Operations::class, 'power'],
            
'argumentCount' => '2',
        ],
        
'PPMT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic\Payments::class, 'interestPayment'],
            
'argumentCount' => '4-6',
        ],
        
'PRICE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Price::class, 'price'],
            
'argumentCount' => '6,7',
        ],
        
'PRICEDISC' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Price::class, 'priceDiscounted'],
            
'argumentCount' => '4,5',
        ],
        
'PRICEMAT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Price::class, 'priceAtMaturity'],
            
'argumentCount' => '5,6',
        ],
        
'PROB' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3,4',
        ],
        
'PRODUCT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Operations::class, 'product'],
            
'argumentCount' => '1+',
        ],
        
'PROPER' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\CaseConvert::class, 'proper'],
            
'argumentCount' => '1',
        ],
        
'PV' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic::class, 'presentValue'],
            
'argumentCount' => '3-5',
        ],
        
'QUARTILE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'QUARTILE'],
            
'argumentCount' => '2',
        ],
        
'QUARTILE.EXC' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'QUARTILE.INC' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'QUARTILE'],
            
'argumentCount' => '2',
        ],
        
'QUOTIENT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Operations::class, 'quotient'],
            
'argumentCount' => '2',
        ],
        
'RADIANS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Angle::class, 'toRadians'],
            
'argumentCount' => '1',
        ],
        
'RAND' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Random::class, 'rand'],
            
'argumentCount' => '0',
        ],
        
'RANDARRAY' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Random::class, 'randArray'],
            
'argumentCount' => '0-5',
        ],
        
'RANDBETWEEN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Random::class, 'randBetween'],
            
'argumentCount' => '2',
        ],
        
'RANK' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'RANK'],
            
'argumentCount' => '2,3',
        ],
        
'RANK.AVG' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2,3',
        ],
        
'RANK.EQ' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Percentiles::class, 'RANK'],
            
'argumentCount' => '2,3',
        ],
        
'RATE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Constant\Periodic\Interest::class, 'rate'],
            
'argumentCount' => '3-6',
        ],
        
'RECEIVED' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Price::class, 'received'],
            
'argumentCount' => '4-5',
        ],
        
'REDUCE' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'REPLACE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Replace::class, 'replace'],
            
'argumentCount' => '4',
        ],
        
'REPLACEB' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Replace::class, 'replace'],
            
'argumentCount' => '4',
        ],
        
'REPT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Concatenate::class, 'builtinREPT'],
            
'argumentCount' => '2',
        ],
        
'RIGHT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'right'],
            
'argumentCount' => '1,2',
        ],
        
'RIGHTB' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'right'],
            
'argumentCount' => '1,2',
        ],
        
'ROMAN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Roman::class, 'evaluate'],
            
'argumentCount' => '1,2',
        ],
        
'ROUND' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Round::class, 'round'],
            
'argumentCount' => '2',
        ],
        
'ROUNDBAHTDOWN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'ROUNDBAHTUP' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'ROUNDDOWN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Round::class, 'down'],
            
'argumentCount' => '2',
        ],
        
'ROUNDUP' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Round::class, 'up'],
            
'argumentCount' => '2',
        ],
        
'ROW' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\RowColumnInformation::class, 'ROW'],
            
'argumentCount' => '-1',
            
'passCellReference' => true,
            
'passByReference' => [true],
        ],
        
'ROWS' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\RowColumnInformation::class, 'ROWS'],
            
'argumentCount' => '1',
        ],
        
'RRI' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Single::class, 'interestRate'],
            
'argumentCount' => '3',
        ],
        
'RSQ' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'RSQ'],
            
'argumentCount' => '2',
        ],
        
'RTD' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1+',
        ],
        
'SEARCH' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Search::class, 'insensitive'],
            
'argumentCount' => '2,3',
        ],
        
'SCAN' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'SEARCHB' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Search::class, 'insensitive'],
            
'argumentCount' => '2,3',
        ],
        
'SEC' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Secant::class, 'sec'],
            
'argumentCount' => '1',
        ],
        
'SECH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Secant::class, 'sech'],
            
'argumentCount' => '1',
        ],
        
'SECOND' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\TimeParts::class, 'second'],
            
'argumentCount' => '1',
        ],
        
'SEQUENCE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\MatrixFunctions::class, 'sequence'],
            
'argumentCount' => '1-4',
        ],
        
'SERIESSUM' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\SeriesSum::class, 'evaluate'],
            
'argumentCount' => '4',
        ],
        
'SHEET' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '0,1',
        ],
        
'SHEETS' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '0,1',
        ],
        
'SIGN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Sign::class, 'evaluate'],
            
'argumentCount' => '1',
        ],
        
'SIN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Sine::class, 'sin'],
            
'argumentCount' => '1',
        ],
        
'SINGLE' => [
            
'category' => Category::CATEGORY_UNCATEGORISED,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '*',
        ],
        
'SINH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Sine::class, 'sinh'],
            
'argumentCount' => '1',
        ],
        
'SKEW' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Deviations::class, 'skew'],
            
'argumentCount' => '1+',
        ],
        
'SKEW.P' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1+',
        ],
        
'SLN' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Depreciation::class, 'SLN'],
            
'argumentCount' => '3',
        ],
        
'SLOPE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'SLOPE'],
            
'argumentCount' => '2',
        ],
        
'SMALL' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Size::class, 'small'],
            
'argumentCount' => '2',
        ],
        
'SORT' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Sort::class, 'sort'],
            
'argumentCount' => '1-4',
        ],
        
'SORTBY' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Sort::class, 'sortBy'],
            
'argumentCount' => '2+',
        ],
        
'SQRT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Sqrt::class, 'sqrt'],
            
'argumentCount' => '1',
        ],
        
'SQRTPI' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Sqrt::class, 'pi'],
            
'argumentCount' => '1',
        ],
        
'STANDARDIZE' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Standardize::class, 'execute'],
            
'argumentCount' => '3',
        ],
        
'STDEV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\StandardDeviations::class, 'STDEV'],
            
'argumentCount' => '1+',
        ],
        
'STDEV.S' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\StandardDeviations::class, 'STDEV'],
            
'argumentCount' => '1+',
        ],
        
'STDEV.P' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\StandardDeviations::class, 'STDEVP'],
            
'argumentCount' => '1+',
        ],
        
'STDEVA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\StandardDeviations::class, 'STDEVA'],
            
'argumentCount' => '1+',
        ],
        
'STDEVP' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\StandardDeviations::class, 'STDEVP'],
            
'argumentCount' => '1+',
        ],
        
'STDEVPA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\StandardDeviations::class, 'STDEVPA'],
            
'argumentCount' => '1+',
        ],
        
'STEYX' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'STEYX'],
            
'argumentCount' => '2',
        ],
        
'SUBSTITUTE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Replace::class, 'substitute'],
            
'argumentCount' => '3,4',
        ],
        
'SUBTOTAL' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Subtotal::class, 'evaluate'],
            
'argumentCount' => '2+',
            
'passCellReference' => true,
        ],
        
'SUM' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Sum::class, 'sumErroringStrings'],
            
'argumentCount' => '1+',
        ],
        
'SUMIF' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Statistical\Conditional::class, 'SUMIF'],
            
'argumentCount' => '2,3',
        ],
        
'SUMIFS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Statistical\Conditional::class, 'SUMIFS'],
            
'argumentCount' => '3+',
        ],
        
'SUMPRODUCT' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Sum::class, 'product'],
            
'argumentCount' => '1+',
        ],
        
'SUMSQ' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\SumSquares::class, 'sumSquare'],
            
'argumentCount' => '1+',
        ],
        
'SUMX2MY2' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\SumSquares::class, 'sumXSquaredMinusYSquared'],
            
'argumentCount' => '2',
        ],
        
'SUMX2PY2' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\SumSquares::class, 'sumXSquaredPlusYSquared'],
            
'argumentCount' => '2',
        ],
        
'SUMXMY2' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\SumSquares::class, 'sumXMinusYSquared'],
            
'argumentCount' => '2',
        ],
        
'SWITCH' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Conditional::class, 'statementSwitch'],
            
'argumentCount' => '3+',
        ],
        
'SYD' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Depreciation::class, 'SYD'],
            
'argumentCount' => '4',
        ],
        
'T' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Text::class, 'test'],
            
'argumentCount' => '1',
        ],
        
'TAKE' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-3',
        ],
        
'TAN' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Tangent::class, 'tan'],
            
'argumentCount' => '1',
        ],
        
'TANH' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trig\Tangent::class, 'tanh'],
            
'argumentCount' => '1',
        ],
        
'TBILLEQ' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\TreasuryBill::class, 'bondEquivalentYield'],
            
'argumentCount' => '3',
        ],
        
'TBILLPRICE' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\TreasuryBill::class, 'price'],
            
'argumentCount' => '3',
        ],
        
'TBILLYIELD' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\TreasuryBill::class, 'yield'],
            
'argumentCount' => '3',
        ],
        
'TDIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StudentT::class, 'distribution'],
            
'argumentCount' => '3',
        ],
        
'T.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3',
        ],
        
'T.DIST.2T' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'T.DIST.RT' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'TEXT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Format::class, 'TEXTFORMAT'],
            
'argumentCount' => '2',
        ],
        
'TEXTAFTER' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'after'],
            
'argumentCount' => '2-6',
        ],
        
'TEXTBEFORE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Extract::class, 'before'],
            
'argumentCount' => '2-6',
        ],
        
'TEXTJOIN' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Concatenate::class, 'TEXTJOIN'],
            
'argumentCount' => '3+',
        ],
        
'TEXTSPLIT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Text::class, 'split'],
            
'argumentCount' => '2-6',
        ],
        
'THAIDAYOFWEEK' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'THAIDIGIT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'THAIMONTHOFYEAR' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'THAINUMSOUND' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'THAINUMSTRING' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'THAISTRINGLENGTH' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'THAIYEAR' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '?',
        ],
        
'TIME' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Time::class, 'fromHMS'],
            
'argumentCount' => '3',
        ],
        
'TIMEVALUE' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\TimeValue::class, 'fromString'],
            
'argumentCount' => '1',
        ],
        
'TINV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StudentT::class, 'inverse'],
            
'argumentCount' => '2',
        ],
        
'T.INV' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StudentT::class, 'inverse'],
            
'argumentCount' => '2',
        ],
        
'T.INV.2T' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2',
        ],
        
'TODAY' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Current::class, 'today'],
            
'argumentCount' => '0',
        ],
        
'TOCOL' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1-3',
        ],
        
'TOROW' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1-3',
        ],
        
'TRANSPOSE' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Matrix::class, 'transpose'],
            
'argumentCount' => '1',
        ],
        
'TREND' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Trends::class, 'TREND'],
            
'argumentCount' => '1-4',
        ],
        
'TRIM' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Trim::class, 'spaces'],
            
'argumentCount' => '1',
        ],
        
'TRIMMEAN' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Averages\Mean::class, 'trim'],
            
'argumentCount' => '2',
        ],
        
'TRUE' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Boolean::class, 'TRUE'],
            
'argumentCount' => '0',
        ],
        
'TRUNC' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [MathTrig\Trunc::class, 'evaluate'],
            
'argumentCount' => '1,2',
        ],
        
'TTEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '4',
        ],
        
'T.TEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '4',
        ],
        
'TYPE' => [
            
'category' => Category::CATEGORY_INFORMATION,
            
'functionCall' => [Information\Value::class, 'type'],
            
'argumentCount' => '1',
        ],
        
'UNICHAR' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\CharacterConvert::class, 'character'],
            
'argumentCount' => '1',
        ],
        
'UNICODE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\CharacterConvert::class, 'code'],
            
'argumentCount' => '1',
        ],
        
'UNIQUE' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\Unique::class, 'unique'],
            
'argumentCount' => '1+',
        ],
        
'UPPER' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\CaseConvert::class, 'upper'],
            
'argumentCount' => '1',
        ],
        
'USDOLLAR' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Dollar::class, 'format'],
            
'argumentCount' => '2',
        ],
        
'VALUE' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Format::class, 'VALUE'],
            
'argumentCount' => '1',
        ],
        
'VALUETOTEXT' => [
            
'category' => Category::CATEGORY_TEXT_AND_DATA,
            
'functionCall' => [TextData\Format::class, 'valueToText'],
            
'argumentCount' => '1,2',
        ],
        
'VAR' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Variances::class, 'VAR'],
            
'argumentCount' => '1+',
        ],
        
'VAR.P' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Variances::class, 'VARP'],
            
'argumentCount' => '1+',
        ],
        
'VAR.S' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Variances::class, 'VAR'],
            
'argumentCount' => '1+',
        ],
        
'VARA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Variances::class, 'VARA'],
            
'argumentCount' => '1+',
        ],
        
'VARP' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Variances::class, 'VARP'],
            
'argumentCount' => '1+',
        ],
        
'VARPA' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Variances::class, 'VARPA'],
            
'argumentCount' => '1+',
        ],
        
'VDB' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '5-7',
        ],
        
'VLOOKUP' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [LookupRef\VLookup::class, 'lookup'],
            
'argumentCount' => '3,4',
        ],
        
'VSTACK' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '1+',
        ],
        
'WEBSERVICE' => [
            
'category' => Category::CATEGORY_WEB,
            
'functionCall' => [Web\Service::class, 'webService'],
            
'argumentCount' => '1',
        ],
        
'WEEKDAY' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Week::class, 'day'],
            
'argumentCount' => '1,2',
        ],
        
'WEEKNUM' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\Week::class, 'number'],
            
'argumentCount' => '1,2',
        ],
        
'WEIBULL' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Weibull::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'WEIBULL.DIST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\Weibull::class, 'distribution'],
            
'argumentCount' => '4',
        ],
        
'WORKDAY' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\WorkDay::class, 'date'],
            
'argumentCount' => '2-3',
        ],
        
'WORKDAY.INTL' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-4',
        ],
        
'WRAPCOLS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-3',
        ],
        
'WRAPROWS' => [
            
'category' => Category::CATEGORY_MATH_AND_TRIG,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2-3',
        ],
        
'XIRR' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Variable\NonPeriodic::class, 'rate'],
            
'argumentCount' => '2,3',
        ],
        
'XLOOKUP' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '3-6',
        ],
        
'XNPV' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\CashFlow\Variable\NonPeriodic::class, 'presentValue'],
            
'argumentCount' => '3',
        ],
        
'XMATCH' => [
            
'category' => Category::CATEGORY_LOOKUP_AND_REFERENCE,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '2,3',
        ],
        
'XOR' => [
            
'category' => Category::CATEGORY_LOGICAL,
            
'functionCall' => [Logical\Operations::class, 'logicalXor'],
            
'argumentCount' => '1+',
        ],
        
'YEAR' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\DateParts::class, 'year'],
            
'argumentCount' => '1',
        ],
        
'YEARFRAC' => [
            
'category' => Category::CATEGORY_DATE_AND_TIME,
            
'functionCall' => [DateTimeExcel\YearFrac::class, 'fraction'],
            
'argumentCount' => '2,3',
        ],
        
'YIELD' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Functions::class, 'DUMMY'],
            
'argumentCount' => '6,7',
        ],
        
'YIELDDISC' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Yields::class, 'yieldDiscounted'],
            
'argumentCount' => '4,5',
        ],
        
'YIELDMAT' => [
            
'category' => Category::CATEGORY_FINANCIAL,
            
'functionCall' => [Financial\Securities\Yields::class, 'yieldAtMaturity'],
            
'argumentCount' => '5,6',
        ],
        
'ZTEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StandardNormal::class, 'zTest'],
            
'argumentCount' => '2-3',
        ],
        
'Z.TEST' => [
            
'category' => Category::CATEGORY_STATISTICAL,
            
'functionCall' => [Statistical\Distributions\StandardNormal::class, 'zTest'],
            
'argumentCount' => '2-3',
        ],
    ];

    
/**
     *    Internal functions used for special control purposes.
     *
     * @var array
     */
    
private static $controlFunctions = [
        
'MKMATRIX' => [
            
'argumentCount' => '*',
            
'functionCall' => [Internal\MakeMatrix::class, 'make'],
        ],
        
'NAME.ERROR' => [
            
'argumentCount' => '*',
            
'functionCall' => [Functions::class, 'NAME'],
        ],
        
'WILDCARDMATCH' => [
            
'argumentCount' => '2',
            
'functionCall' => [Internal\WildcardMatch::class, 'compare'],
        ],
    ];

    public function 
__construct(?Spreadsheet $spreadsheet null)
    {
        
$this->spreadsheet $spreadsheet;
        
$this->cyclicReferenceStack = new CyclicReferenceStack();
        
$this->debugLog = new Logger($this->cyclicReferenceStack);
        
$this->branchPruner = new BranchPruner($this->branchPruningEnabled);
        
self::$referenceHelper ReferenceHelper::getInstance();
    }

    private static function 
loadLocales(): void
    
{
        
$localeFileDirectory __DIR__ '/locale/';
        
$localeFileNames glob($localeFileDirectory '*'GLOB_ONLYDIR) ?: [];
        foreach (
$localeFileNames as $filename) {
            
$filename substr($filenamestrlen($localeFileDirectory));
            if (
$filename != 'en') {
                
self::$validLocaleLanguages[] = $filename;
            }
        }
    }

    
/**
     * Get an instance of this class.
     *
     * @param ?Spreadsheet $spreadsheet Injected spreadsheet for working with a PhpSpreadsheet Spreadsheet object,
     *                                    or NULL to create a standalone calculation engine
     */
    
public static function getInstance(?Spreadsheet $spreadsheet null): self
    
{
        if (
$spreadsheet !== null) {
            
$instance $spreadsheet->getCalculationEngine();
            if (isset(
$instance)) {
                return 
$instance;
            }
        }

        if (!isset(
self::$instance) || (self::$instance === null)) {
            
self::$instance = new self();
        }

        return 
self::$instance;
    }

    
/**
     * Flush the calculation cache for any existing instance of this class
     *        but only if a Calculation instance exists.
     */
    
public function flushInstance(): void
    
{
        
$this->clearCalculationCache();
        
$this->branchPruner->clearBranchStore();
    }

    
/**
     * Get the Logger for this calculation engine instance.
     *
     * @return Logger
     */
    
public function getDebugLog()
    {
        return 
$this->debugLog;
    }

    
/**
     * __clone implementation. Cloning should not be allowed in a Singleton!
     */
    
final public function __clone()
    {
        throw new 
Exception('Cloning the calculation engine is not allowed!');
    }

    
/**
     * Return the locale-specific translation of TRUE.
     *
     * @return string locale-specific translation of TRUE
     */
    
public static function getTRUE(): string
    
{
        return 
self::$localeBoolean['TRUE'];
    }

    
/**
     * Return the locale-specific translation of FALSE.
     *
     * @return string locale-specific translation of FALSE
     */
    
public static function getFALSE(): string
    
{
        return 
self::$localeBoolean['FALSE'];
    }

    
/**
     * Set the Array Return Type (Array or Value of first element in the array).
     *
     * @param string $returnType Array return type
     *
     * @return bool Success or failure
     */
    
public static function setArrayReturnType($returnType)
    {
        if (
            (
$returnType == self::RETURN_ARRAY_AS_VALUE) ||
            (
$returnType == self::RETURN_ARRAY_AS_ERROR) ||
            (
$returnType == self::RETURN_ARRAY_AS_ARRAY)
        ) {
            
self::$returnArrayAsType $returnType;

            return 
true;
        }

        return 
false;
    }

    
/**
     * Return the Array Return Type (Array or Value of first element in the array).
     *
     * @return string $returnType Array return type
     */
    
public static function getArrayReturnType()
    {
        return 
self::$returnArrayAsType;
    }

    
/**
     * Is calculation caching enabled?
     *
     * @return bool
     */
    
public function getCalculationCacheEnabled()
    {
        return 
$this->calculationCacheEnabled;
    }

    
/**
     * Enable/disable calculation cache.
     *
     * @param bool $calculationCacheEnabled
     */
    
public function setCalculationCacheEnabled($calculationCacheEnabled): void
    
{
        
$this->calculationCacheEnabled $calculationCacheEnabled;
        
$this->clearCalculationCache();
    }

    
/**
     * Enable calculation cache.
     */
    
public function enableCalculationCache(): void
    
{
        
$this->setCalculationCacheEnabled(true);
    }

    
/**
     * Disable calculation cache.
     */
    
public function disableCalculationCache(): void
    
{
        
$this->setCalculationCacheEnabled(false);
    }

    
/**
     * Clear calculation cache.
     */
    
public function clearCalculationCache(): void
    
{
        
$this->calculationCache = [];
    }

    
/**
     * Clear calculation cache for a specified worksheet.
     *
     * @param string $worksheetName
     */
    
public function clearCalculationCacheForWorksheet($worksheetName): void
    
{
        if (isset(
$this->calculationCache[$worksheetName])) {
            unset(
$this->calculationCache[$worksheetName]);
        }
    }

    
/**
     * Rename calculation cache for a specified worksheet.
     *
     * @param string $fromWorksheetName
     * @param string $toWorksheetName
     */
    
public function renameCalculationCacheForWorksheet($fromWorksheetName$toWorksheetName): void
    
{
        if (isset(
$this->calculationCache[$fromWorksheetName])) {
            
$this->calculationCache[$toWorksheetName] = &$this->calculationCache[$fromWorksheetName];
            unset(
$this->calculationCache[$fromWorksheetName]);
        }
    }

    
/**
     * Enable/disable calculation cache.
     *
     * @param mixed $enabled
     */
    
public function setBranchPruningEnabled($enabled): void
    
{
        
$this->branchPruningEnabled $enabled;
        
$this->branchPruner = new BranchPruner($this->branchPruningEnabled);
    }

    public function 
enableBranchPruning(): void
    
{
        
$this->setBranchPruningEnabled(true);
    }

    public function 
disableBranchPruning(): void
    
{
        
$this->setBranchPruningEnabled(false);
    }

    
/**
     * Get the currently defined locale code.
     *
     * @return string
     */
    
public function getLocale()
    {
        return 
self::$localeLanguage;
    }

    private function 
getLocaleFile(string $localeDirstring $localestring $languagestring $file): string
    
{
        
$localeFileName $localeDir str_replace('_'DIRECTORY_SEPARATOR$locale) .
            
DIRECTORY_SEPARATOR $file;
        if (!
file_exists($localeFileName)) {
            
//    If there isn't a locale specific file, look for a language specific file
            
$localeFileName $localeDir $language DIRECTORY_SEPARATOR $file;
            if (!
file_exists($localeFileName)) {
                throw new 
Exception('Locale file not found');
            }
        }

        return 
$localeFileName;
    }

    
/**
     * Set the locale code.
     *
     * @param string $locale The locale to use for formula translation, eg: 'en_us'
     *
     * @return bool
     */
    
public function setLocale(string $locale)
    {
        
//    Identify our locale and language
        
$language $locale strtolower($locale);
        if (
strpos($locale'_') !== false) {
            [
$language] = explode('_'$locale);
        }
        if (
count(self::$validLocaleLanguages) == 1) {
            
self::loadLocales();
        }

        
//    Test whether we have any language data for this language (any locale)
        
if (in_array($languageself::$validLocaleLanguagestrue)) {
            
//    initialise language/locale settings
            
self::$localeFunctions = [];
            
self::$localeArgumentSeparator ',';
            
self::$localeBoolean = ['TRUE' => 'TRUE''FALSE' => 'FALSE''NULL' => 'NULL'];

            
//    Default is US English, if user isn't requesting US english, then read the necessary data from the locale files
            
if ($locale !== 'en_us') {
                
$localeDir implode(DIRECTORY_SEPARATOR, [__DIR__'locale'null]);
                
//    Search for a file with a list of function names for locale
                
try {
                    
$functionNamesFile $this->getLocaleFile($localeDir$locale$language'functions');
                } catch (
Exception $e) {
                    return 
false;
                }

                
//    Retrieve the list of locale or language specific function names
                
$localeFunctions file($functionNamesFileFILE_IGNORE_NEW_LINES FILE_SKIP_EMPTY_LINES) ?: [];
                foreach (
$localeFunctions as $localeFunction) {
                    [
$localeFunction] = explode('##'$localeFunction); //    Strip out comments
                    
if (strpos($localeFunction'=') !== false) {
                        [
$fName$lfName] = array_map('trim'explode('='$localeFunction));
                        if ((
substr($fName01) === '*' || isset(self::$phpSpreadsheetFunctions[$fName])) && ($lfName != '') && ($fName != $lfName)) {
                            
self::$localeFunctions[$fName] = $lfName;
                        }
                    }
                }
                
//    Default the TRUE and FALSE constants to the locale names of the TRUE() and FALSE() functions
                
if (isset(self::$localeFunctions['TRUE'])) {
                    
self::$localeBoolean['TRUE'] = self::$localeFunctions['TRUE'];
                }
                if (isset(
self::$localeFunctions['FALSE'])) {
                    
self::$localeBoolean['FALSE'] = self::$localeFunctions['FALSE'];
                }

                try {
                    
$configFile $this->getLocaleFile($localeDir$locale$language'config');
                } catch (
Exception $e) {
                    return 
false;
                }

                
$localeSettings file($configFileFILE_IGNORE_NEW_LINES FILE_SKIP_EMPTY_LINES) ?: [];
                foreach (
$localeSettings as $localeSetting) {
                    [
$localeSetting] = explode('##'$localeSetting); //    Strip out comments
                    
if (strpos($localeSetting'=') !== false) {
                        [
$settingName$settingValue] = array_map('trim'explode('='$localeSetting));
                        
$settingName strtoupper($settingName);
                        if (
$settingValue !== '') {
                            switch (
$settingName) {
                                case 
'ARGUMENTSEPARATOR':
                                    
self::$localeArgumentSeparator $settingValue;

                                    break;
                            }
                        }
                    }
                }
            }

            
self::$functionReplaceFromExcel self::$functionReplaceToExcel =
            
self::$functionReplaceFromLocale self::$functionReplaceToLocale null;
            
self::$localeLanguage $locale;

            return 
true;
        }

        return 
false;
    }

    public static function 
translateSeparator(
        
string $fromSeparator,
        
string $toSeparator,
        
string $formula,
        
int &$inBracesLevel,
        
string $openBrace self::FORMULA_OPEN_FUNCTION_BRACE,
        
string $closeBrace self::FORMULA_CLOSE_FUNCTION_BRACE
    
): string {
        
$strlen mb_strlen($formula);
        for (
$i 0$i $strlen; ++$i) {
            
$chr mb_substr($formula$i1);
            switch (
$chr) {
                case 
$openBrace:
                    ++
$inBracesLevel;

                    break;
                case 
$closeBrace:
                    --
$inBracesLevel;

                    break;
                case 
$fromSeparator:
                    if (
$inBracesLevel 0) {
                        
$formula mb_substr($formula0$i) . $toSeparator mb_substr($formula$i 1);
                    }
            }
        }

        return 
$formula;
    }

    private static function 
translateFormulaBlock(
        array 
$from,
        array 
$to,
        
string $formula,
        
int &$inFunctionBracesLevel,
        
int &$inMatrixBracesLevel,
        
string $fromSeparator,
        
string $toSeparator
    
): string {
        
// Function Names
        
$formula = (string) preg_replace($from$to$formula);

        
// Temporarily adjust matrix separators so that they won't be confused with function arguments
        
$formula self::translateSeparator(';''|'$formula$inMatrixBracesLevelself::FORMULA_OPEN_MATRIX_BRACEself::FORMULA_CLOSE_MATRIX_BRACE);
        
$formula self::translateSeparator(',''!'$formula$inMatrixBracesLevelself::FORMULA_OPEN_MATRIX_BRACEself::FORMULA_CLOSE_MATRIX_BRACE);
        
// Function Argument Separators
        
$formula self::translateSeparator($fromSeparator$toSeparator$formula$inFunctionBracesLevel);
        
// Restore matrix separators
        
$formula self::translateSeparator('|'';'$formula$inMatrixBracesLevelself::FORMULA_OPEN_MATRIX_BRACEself::FORMULA_CLOSE_MATRIX_BRACE);
        
$formula self::translateSeparator('!'','$formula$inMatrixBracesLevelself::FORMULA_OPEN_MATRIX_BRACEself::FORMULA_CLOSE_MATRIX_BRACE);

        return 
$formula;
    }

    private static function 
translateFormula(array $from, array $tostring $formulastring $fromSeparatorstring $toSeparator): string
    
{
        
// Convert any Excel function names and constant names to the required language;
        //     and adjust function argument separators
        
if (self::$localeLanguage !== 'en_us') {
            
$inFunctionBracesLevel 0;
            
$inMatrixBracesLevel 0;
            
//    If there is the possibility of separators within a quoted string, then we treat them as literals
            
if (strpos($formulaself::FORMULA_STRING_QUOTE) !== false) {
                
//    So instead we skip replacing in any quoted strings by only replacing in every other array element
                //       after we've exploded the formula
                
$temp explode(self::FORMULA_STRING_QUOTE$formula);
                
$notWithinQuotes false;
                foreach (
$temp as &$value) {
                    
//    Only adjust in alternating array entries
                    
$notWithinQuotes $notWithinQuotes === false;
                    if (
$notWithinQuotes === true) {
                        
$value self::translateFormulaBlock($from$to$value$inFunctionBracesLevel$inMatrixBracesLevel$fromSeparator$toSeparator);
                    }
                }
                unset(
$value);
                
//    Then rebuild the formula string
                
$formula implode(self::FORMULA_STRING_QUOTE$temp);
            } else {
                
//    If there's no quoted strings, then we do a simple count/replace
                
$formula self::translateFormulaBlock($from$to$formula$inFunctionBracesLevel$inMatrixBracesLevel$fromSeparator$toSeparator);
            }
        }

        return 
$formula;
    }

    
/** @var ?array */
    
private static $functionReplaceFromExcel;

    
/** @var ?array */
    
private static $functionReplaceToLocale;

    
/**
     * @param string $formula
     *
     * @return string
     */
    
public function _translateFormulaToLocale($formula)
    {
        
// Build list of function names and constants for translation
        
if (self::$functionReplaceFromExcel === null) {
            
self::$functionReplaceFromExcel = [];
            foreach (
array_keys(self::$localeFunctions) as $excelFunctionName) {
                
self::$functionReplaceFromExcel[] = '/(@?[^\w\.])' preg_quote($excelFunctionName'/') . '([\s]*\()/ui';
            }
            foreach (
array_keys(self::$localeBoolean) as $excelBoolean) {
                
self::$functionReplaceFromExcel[] = '/(@?[^\w\.])' preg_quote($excelBoolean'/') . '([^\w\.])/ui';
            }
        }

        if (
self::$functionReplaceToLocale === null) {
            
self::$functionReplaceToLocale = [];
            foreach (
self::$localeFunctions as $localeFunctionName) {
                
self::$functionReplaceToLocale[] = '$1' trim($localeFunctionName) . '$2';
            }
            foreach (
self::$localeBoolean as $localeBoolean) {
                
self::$functionReplaceToLocale[] = '$1' trim($localeBoolean) . '$2';
            }
        }

        return 
self::translateFormula(
            
self::$functionReplaceFromExcel,
            
self::$functionReplaceToLocale,
            
$formula,
            
',',
            
self::$localeArgumentSeparator
        
);
    }

    
/** @var ?array */
    
private static $functionReplaceFromLocale;

    
/** @var ?array */
    
private static $functionReplaceToExcel;

    
/**
     * @param string $formula
     *
     * @return string
     */
    
public function _translateFormulaToEnglish($formula)
    {
        if (
self::$functionReplaceFromLocale === null) {
            
self::$functionReplaceFromLocale = [];
            foreach (
self::$localeFunctions as $localeFunctionName) {
                
self::$functionReplaceFromLocale[] = '/(@?[^\w\.])' preg_quote($localeFunctionName'/') . '([\s]*\()/ui';
            }
            foreach (
self::$localeBoolean as $excelBoolean) {
                
self::$functionReplaceFromLocale[] = '/(@?[^\w\.])' preg_quote($excelBoolean'/') . '([^\w\.])/ui';
            }
        }

        if (
self::$functionReplaceToExcel === null) {
            
self::$functionReplaceToExcel = [];
            foreach (
array_keys(self::$localeFunctions) as $excelFunctionName) {
                
self::$functionReplaceToExcel[] = '$1' trim($excelFunctionName) . '$2';
            }
            foreach (
array_keys(self::$localeBoolean) as $excelBoolean) {
                
self::$functionReplaceToExcel[] = '$1' trim($excelBoolean) . '$2';
            }
        }

        return 
self::translateFormula(self::$functionReplaceFromLocaleself::$functionReplaceToExcel$formulaself::$localeArgumentSeparator',');
    }

    
/**
     * @param string $function
     *
     * @return string
     */
    
public static function localeFunc($function)
    {
        if (
self::$localeLanguage !== 'en_us') {
            
$functionName trim($function'(');
            if (isset(
self::$localeFunctions[$functionName])) {
                
$brace = ($functionName != $function);
                
$function self::$localeFunctions[$functionName];
                if (
$brace) {
                    
$function .= '(';
                }
            }
        }

        return 
$function;
    }

    
/**
     * Wrap string values in quotes.
     *
     * @param mixed $value
     *
     * @return mixed
     */
    
public static function wrapResult($value)
    {
        if (
is_string($value)) {
            
//    Error values cannot be "wrapped"
            
if (preg_match('/^' self::CALCULATION_REGEXP_ERROR '$/i'$value$match)) {
                
//    Return Excel errors "as is"
                
return $value;
            }

            
//    Return strings wrapped in quotes
            
return self::FORMULA_STRING_QUOTE $value self::FORMULA_STRING_QUOTE;
        } elseif ((
is_float($value)) && ((is_nan($value)) || (is_infinite($value)))) {
            
//    Convert numeric errors to NaN error
            
return Information\ExcelError::NAN();
        }

        return 
$value;
    }

    
/**
     * Remove quotes used as a wrapper to identify string values.
     *
     * @param mixed $value
     *
     * @return mixed
     */
    
public static function unwrapResult($value)
    {
        if (
is_string($value)) {
            if ((isset(
$value[0])) && ($value[0] == self::FORMULA_STRING_QUOTE) && (substr($value, -1) == self::FORMULA_STRING_QUOTE)) {
                return 
substr($value1, -1);
            }
            
//    Convert numeric errors to NAN error
        
} elseif ((is_float($value)) && ((is_nan($value)) || (is_infinite($value)))) {
            return 
Information\ExcelError::NAN();
        }

        return 
$value;
    }

    
/**
     * Calculate cell value (using formula from a cell ID)
     * Retained for backward compatibility.
     *
     * @param Cell $cell Cell to calculate
     *
     * @return mixed
     */
    
public function calculate(?Cell $cell null)
    {
        try {
            return 
$this->calculateCellValue($cell);
        } catch (
\Exception $e) {
            throw new 
Exception($e->getMessage());
        }
    }

    
/**
     * Calculate the value of a cell formula.
     *
     * @param Cell $cell Cell to calculate
     * @param bool $resetLog Flag indicating whether the debug log should be reset or not
     *
     * @return mixed
     */
    
public function calculateCellValue(?Cell $cell null$resetLog true)
    {
        if (
$cell === null) {
            return 
null;
        }

        
$returnArrayAsType self::$returnArrayAsType;
        if (
$resetLog) {
            
//    Initialise the logging settings if requested
            
$this->formulaError null;
            
$this->debugLog->clearLog();
            
$this->cyclicReferenceStack->clear();
            
$this->cyclicFormulaCounter 1;

            
self::$returnArrayAsType self::RETURN_ARRAY_AS_ARRAY;
        }

        
//    Execute the calculation for the cell formula
        
$this->cellStack[] = [
            
'sheet' => $cell->getWorksheet()->getTitle(),
            
'cell' => $cell->getCoordinate(),
        ];

        
$cellAddressAttempted false;
        
$cellAddress null;

        try {
            
$result self::unwrapResult($this->_calculateFormulaValue($cell->getValue(), $cell->getCoordinate(), $cell));
            if (
$this->spreadsheet === null) {
                throw new 
Exception('null spreadsheet in calculateCellValue');
            }
            
$cellAddressAttempted true;
            
$cellAddress array_pop($this->cellStack);
            if (
$cellAddress === null) {
                throw new 
Exception('null cellAddress in calculateCellValue');
            }
            
$testSheet $this->spreadsheet->getSheetByName($cellAddress['sheet']);
            if (
$testSheet === null) {
                throw new 
Exception('worksheet not found in calculateCellValue');
            }
            
$testSheet->getCell($cellAddress['cell']);
        } catch (
\Exception $e) {
            if (!
$cellAddressAttempted) {
                
$cellAddress array_pop($this->cellStack);
            }
            if (
$this->spreadsheet !== null && is_array($cellAddress) && array_key_exists('sheet'$cellAddress)) {
                
$testSheet $this->spreadsheet->getSheetByName($cellAddress['sheet']);
                if (
$testSheet !== null && array_key_exists('cell'$cellAddress)) {
                    
$testSheet->getCell($cellAddress['cell']);
                }
            }

            throw new 
Exception($e->getMessage());
        }

        if ((
is_array($result)) && (self::$returnArrayAsType != self::RETURN_ARRAY_AS_ARRAY)) {
            
self::$returnArrayAsType $returnArrayAsType;
            
$testResult Functions::flattenArray($result);
            if (
self::$returnArrayAsType == self::RETURN_ARRAY_AS_ERROR) {
                return 
Information\ExcelError::VALUE();
            }
            
//    If there's only a single cell in the array, then we allow it
            
if (count($testResult) != 1) {
                
//    If keys are numeric, then it's a matrix result rather than a cell range result, so we permit it
                
$r array_keys($result);
                
$r array_shift($r);
                if (!
is_numeric($r)) {
                    return 
Information\ExcelError::VALUE();
                }
                if (
is_array($result[$r])) {
                    
$c array_keys($result[$r]);
                    
$c array_shift($c);
                    if (!
is_numeric($c)) {
                        return 
Information\ExcelError::VALUE();
                    }
                }
            }
            
$result array_shift($testResult);
        }
        
self::$returnArrayAsType $returnArrayAsType;

        if (
$result === null && $cell->getWorksheet()->getSheetView()->getShowZeros()) {
            return 
0;
        } elseif ((
is_float($result)) && ((is_nan($result)) || (is_infinite($result)))) {
            return 
Information\ExcelError::NAN();
        }

        return 
$result;
    }

    
/**
     * Validate and parse a formula string.
     *
     * @param string $formula Formula to parse
     *
     * @return array|bool
     */
    
public function parseFormula($formula)
    {
        
//    Basic validation that this is indeed a formula
        //    We return an empty array if not
        
$formula trim($formula);
        if ((!isset(
$formula[0])) || ($formula[0] != '=')) {
            return [];
        }
        
$formula ltrim(substr($formula1));
        if (!isset(
$formula[0])) {
            return [];
        }

        
//    Parse the formula and return the token stack
        
return $this->internalParseFormula($formula);
    }

    
/**
     * Calculate the value of a formula.
     *
     * @param string $formula Formula to parse
     * @param string $cellID Address of the cell to calculate
     * @param Cell $cell Cell to calculate
     *
     * @return mixed
     */
    
public function calculateFormula($formula$cellID null, ?Cell $cell null)
    {
        
//    Initialise the logging settings
        
$this->formulaError null;
        
$this->debugLog->clearLog();
        
$this->cyclicReferenceStack->clear();

        
$resetCache $this->getCalculationCacheEnabled();
        if (
$this->spreadsheet !== null && $cellID === null && $cell === null) {
            
$cellID 'A1';
            
$cell $this->spreadsheet->getActiveSheet()->getCell($cellID);
        } else {
            
//    Disable calculation cacheing because it only applies to cell calculations, not straight formulae
            //    But don't actually flush any cache
            
$this->calculationCacheEnabled false;
        }

        
//    Execute the calculation
        
try {
            
$result self::unwrapResult($this->_calculateFormulaValue($formula$cellID$cell));
        } catch (
\Exception $e) {
            throw new 
Exception($e->getMessage());
        }

        if (
$this->spreadsheet === null) {
            
//    Reset calculation cacheing to its previous state
            
$this->calculationCacheEnabled $resetCache;
        }

        return 
$result;
    }

    
/**
     * @param mixed $cellValue
     */
    
public function getValueFromCache(string $cellReference, &$cellValue): bool
    
{
        
$this->debugLog->writeDebugLog('Testing cache value for cell %s'$cellReference);
        
// Is calculation cacheing enabled?
        // If so, is the required value present in calculation cache?
        
if (($this->calculationCacheEnabled) && (isset($this->calculationCache[$cellReference]))) {
            
$this->debugLog->writeDebugLog('Retrieving value for cell %s from cache'$cellReference);
            
// Return the cached result

            
$cellValue $this->calculationCache[$cellReference];

            return 
true;
        }

        return 
false;
    }

    
/**
     * @param string $cellReference
     * @param mixed $cellValue
     */
    
public function saveValueToCache($cellReference$cellValue): void
    
{
        if (
$this->calculationCacheEnabled) {
            
$this->calculationCache[$cellReference] = $cellValue;
        }
    }

    
/**
     * Parse a cell formula and calculate its value.
     *
     * @param string $formula The formula to parse and calculate
     * @param string $cellID The ID (e.g. A3) of the cell that we are calculating
     * @param Cell $cell Cell to calculate
     * @param bool $ignoreQuotePrefix If set to true, evaluate the formyla even if the referenced cell is quote prefixed
     *
     * @return mixed
     */
    
public function _calculateFormulaValue($formula$cellID null, ?Cell $cell nullbool $ignoreQuotePrefix false)
    {
        
$cellValue null;

        
//  Quote-Prefixed cell values cannot be formulae, but are treated as strings
        
if ($cell !== null && $ignoreQuotePrefix === false && $cell->getStyle()->getQuotePrefix() === true) {
            return 
self::wrapResult((string) $formula);
        }

        if (
preg_match('/^=\s*cmd\s*\|/miu'$formula) !== 0) {
            return 
self::wrapResult($formula);
        }

        
//    Basic validation that this is indeed a formula
        //    We simply return the cell value if not
        
$formula trim($formula);
        if (
$formula[0] != '=') {
            return 
self::wrapResult($formula);
        }
        
$formula ltrim(substr($formula1));
        if (!isset(
$formula[0])) {
            return 
self::wrapResult($formula);
        }

        
$pCellParent = ($cell !== null) ? $cell->getWorksheet() : null;
        
$wsTitle = ($pCellParent !== null) ? $pCellParent->getTitle() : "\x00Wrk";
        
$wsCellReference $wsTitle '!' $cellID;

        if ((
$cellID !== null) && ($this->getValueFromCache($wsCellReference$cellValue))) {
            return 
$cellValue;
        }
        
$this->debugLog->writeDebugLog('Evaluating formula for cell %s'$wsCellReference);

        if ((
$wsTitle[0] !== "\x00") && ($this->cyclicReferenceStack->onStack($wsCellReference))) {
            if (
$this->cyclicFormulaCount <= 0) {
                
$this->cyclicFormulaCell '';

                return 
$this->raiseFormulaError('Cyclic Reference in Formula');
            } elseif (
$this->cyclicFormulaCell === $wsCellReference) {
                ++
$this->cyclicFormulaCounter;
                if (
$this->cyclicFormulaCounter >= $this->cyclicFormulaCount) {
                    
$this->cyclicFormulaCell '';

                    return 
$cellValue;
                }
            } elseif (
$this->cyclicFormulaCell == '') {
                if (
$this->cyclicFormulaCounter >= $this->cyclicFormulaCount) {
                    return 
$cellValue;
                }
                
$this->cyclicFormulaCell $wsCellReference;
            }
        }

        
$this->debugLog->writeDebugLog('Formula for cell %s is %s'$wsCellReference$formula);
        
//    Parse the formula onto the token stack and calculate the value
        
$this->cyclicReferenceStack->push($wsCellReference);

        
$cellValue $this->processTokenStack($this->internalParseFormula($formula$cell), $cellID$cell);
        
$this->cyclicReferenceStack->pop();

        
// Save to calculation cache
        
if ($cellID !== null) {
            
$this->saveValueToCache($wsCellReference$cellValue);
        }

        
//    Return the calculated value
        
return $cellValue;
    }

    
/**
     * Ensure that paired matrix operands are both matrices and of the same size.
     *
     * @param mixed $operand1 First matrix operand
     * @param mixed $operand2 Second matrix operand
     * @param int $resize Flag indicating whether the matrices should be resized to match
     *                                        and (if so), whether the smaller dimension should grow or the
     *                                        larger should shrink.
     *                                            0 = no resize
     *                                            1 = shrink to fit
     *                                            2 = extend to fit
     *
     * @return array
     */
    
private static function checkMatrixOperands(&$operand1, &$operand2$resize 1)
    {
        
//    Examine each of the two operands, and turn them into an array if they aren't one already
        //    Note that this function should only be called if one or both of the operand is already an array
        
if (!is_array($operand1)) {
            [
$matrixRows$matrixColumns] = self::getMatrixDimensions($operand2);
            
$operand1 array_fill(0$matrixRowsarray_fill(0$matrixColumns$operand1));
            
$resize 0;
        } elseif (!
is_array($operand2)) {
            [
$matrixRows$matrixColumns] = self::getMatrixDimensions($operand1);
            
$operand2 array_fill(0$matrixRowsarray_fill(0$matrixColumns$operand2));
            
$resize 0;
        }

        [
$matrix1Rows$matrix1Columns] = self::getMatrixDimensions($operand1);
        [
$matrix2Rows$matrix2Columns] = self::getMatrixDimensions($operand2);
        if ((
$matrix1Rows == $matrix2Columns) && ($matrix2Rows == $matrix1Columns)) {
            
$resize 1;
        }

        if (
$resize == 2) {
            
//    Given two matrices of (potentially) unequal size, convert the smaller in each dimension to match the larger
            
self::resizeMatricesExtend($operand1$operand2$matrix1Rows$matrix1Columns$matrix2Rows$matrix2Columns);
        } elseif (
$resize == 1) {
            
//    Given two matrices of (potentially) unequal size, convert the larger in each dimension to match the smaller
            
self::resizeMatricesShrink($operand1$operand2$matrix1Rows$matrix1Columns$matrix2Rows$matrix2Columns);
        }

        return [
$matrix1Rows$matrix1Columns$matrix2Rows$matrix2Columns];
    }

    
/**
     * Read the dimensions of a matrix, and re-index it with straight numeric keys starting from row 0, column 0.
     *
     * @param array $matrix matrix operand
     *
     * @return int[] An array comprising the number of rows, and number of columns
     */
    
public static function getMatrixDimensions(array &$matrix)
    {
        
$matrixRows count($matrix);
        
$matrixColumns 0;
        foreach (
$matrix as $rowKey => $rowValue) {
            if (!
is_array($rowValue)) {
                
$matrix[$rowKey] = [$rowValue];
                
$matrixColumns max(1$matrixColumns);
            } else {
                
$matrix[$rowKey] = array_values($rowValue);
                
$matrixColumns max(count($rowValue), $matrixColumns);
            }
        }
        
$matrix array_values($matrix);

        return [
$matrixRows$matrixColumns];
    }

    
/**
     * Ensure that paired matrix operands are both matrices of the same size.
     *
     * @param mixed $matrix1 First matrix operand
     * @param mixed $matrix2 Second matrix operand
     * @param int $matrix1Rows Row size of first matrix operand
     * @param int $matrix1Columns Column size of first matrix operand
     * @param int $matrix2Rows Row size of second matrix operand
     * @param int $matrix2Columns Column size of second matrix operand
     */
    
private static function resizeMatricesShrink(&$matrix1, &$matrix2$matrix1Rows$matrix1Columns$matrix2Rows$matrix2Columns): void
    
{
        if ((
$matrix2Columns $matrix1Columns) || ($matrix2Rows $matrix1Rows)) {
            if (
$matrix2Rows $matrix1Rows) {
                for (
$i $matrix2Rows$i $matrix1Rows; ++$i) {
                    unset(
$matrix1[$i]);
                }
            }
            if (
$matrix2Columns $matrix1Columns) {
                for (
$i 0$i $matrix1Rows; ++$i) {
                    for (
$j $matrix2Columns$j $matrix1Columns; ++$j) {
                        unset(
$matrix1[$i][$j]);
                    }
                }
            }
        }

        if ((
$matrix1Columns $matrix2Columns) || ($matrix1Rows $matrix2Rows)) {
            if (
$matrix1Rows $matrix2Rows) {
                for (
$i $matrix1Rows$i $matrix2Rows; ++$i) {
                    unset(
$matrix2[$i]);
                }
            }
            if (
$matrix1Columns $matrix2Columns) {
                for (
$i 0$i $matrix2Rows; ++$i) {
                    for (
$j $matrix1Columns$j $matrix2Columns; ++$j) {
                        unset(
$matrix2[$i][$j]);
                    }
                }
            }
        }
    }

    
/**
     * Ensure that paired matrix operands are both matrices of the same size.
     *
     * @param mixed $matrix1 First matrix operand
     * @param mixed $matrix2 Second matrix operand
     * @param int $matrix1Rows Row size of first matrix operand
     * @param int $matrix1Columns Column size of first matrix operand
     * @param int $matrix2Rows Row size of second matrix operand
     * @param int $matrix2Columns Column size of second matrix operand
     */
    
private static function resizeMatricesExtend(&$matrix1, &$matrix2$matrix1Rows$matrix1Columns$matrix2Rows$matrix2Columns): void
    
{
        if ((
$matrix2Columns $matrix1Columns) || ($matrix2Rows $matrix1Rows)) {
            if (
$matrix2Columns $matrix1Columns) {
                for (
$i 0$i $matrix2Rows; ++$i) {
                    
$x $matrix2[$i][$matrix2Columns 1];
                    for (
$j $matrix2Columns$j $matrix1Columns; ++$j) {
                        
$matrix2[$i][$j] = $x;
                    }
                }
            }
            if (
$matrix2Rows $matrix1Rows) {
                
$x $matrix2[$matrix2Rows 1];
                for (
$i 0$i $matrix1Rows; ++$i) {
                    
$matrix2[$i] = $x;
                }
            }
        }

        if ((
$matrix1Columns $matrix2Columns) || ($matrix1Rows $matrix2Rows)) {
            if (
$matrix1Columns $matrix2Columns) {
                for (
$i 0$i $matrix1Rows; ++$i) {
                    
$x $matrix1[$i][$matrix1Columns 1];
                    for (
$j $matrix1Columns$j $matrix2Columns; ++$j) {
                        
$matrix1[$i][$j] = $x;
                    }
                }
            }
            if (
$matrix1Rows $matrix2Rows) {
                
$x $matrix1[$matrix1Rows 1];
                for (
$i 0$i $matrix2Rows; ++$i) {
                    
$matrix1[$i] = $x;
                }
            }
        }
    }

    
/**
     * Format details of an operand for display in the log (based on operand type).
     *
     * @param mixed $value First matrix operand
     *
     * @return mixed
     */
    
private function showValue($value)
    {
        if (
$this->debugLog->getWriteDebugLog()) {
            
$testArray Functions::flattenArray($value);
            if (
count($testArray) == 1) {
                
$value array_pop($testArray);
            }

            if (
is_array($value)) {
                
$returnMatrix = [];
                
$pad $rpad ', ';
                foreach (
$value as $row) {
                    if (
is_array($row)) {
                        
$returnMatrix[] = implode($padarray_map([$this'showValue'], $row));
                        
$rpad '; ';
                    } else {
                        
$returnMatrix[] = $this->showValue($row);
                    }
                }

                return 
'{ ' implode($rpad$returnMatrix) . ' }';
            } elseif (
is_string($value) && (trim($valueself::FORMULA_STRING_QUOTE) == $value)) {
                return 
self::FORMULA_STRING_QUOTE $value self::FORMULA_STRING_QUOTE;
            } elseif (
is_bool($value)) {
                return (
$value) ? self::$localeBoolean['TRUE'] : self::$localeBoolean['FALSE'];
            } elseif (
$value === null) {
                return 
self::$localeBoolean['NULL'];
            }
        }

        return 
Functions::flattenSingleValue($value);
    }

    
/**
     * Format type and details of an operand for display in the log (based on operand type).
     *
     * @param mixed $value First matrix operand
     *
     * @return null|string
     */
    
private function showTypeDetails($value)
    {
        if (
$this->debugLog->getWriteDebugLog()) {
            
$testArray Functions::flattenArray($value);
            if (
count($testArray) == 1) {
                
$value array_pop($testArray);
            }

            if (
$value === null) {
                return 
'a NULL value';
            } elseif (
is_float($value)) {
                
$typeString 'a floating point number';
            } elseif (
is_int($value)) {
                
$typeString 'an integer number';
            } elseif (
is_bool($value)) {
                
$typeString 'a boolean';
            } elseif (
is_array($value)) {
                
$typeString 'a matrix';
            } else {
                if (
$value == '') {
                    return 
'an empty string';
                } elseif (
$value[0] == '#') {
                    return 
'a ' $value ' error';
                }
                
$typeString 'a string';
            }

            return 
$typeString ' with a value of ' $this->showValue($value);
        }

        return 
null;
    }

    
/**
     * @param string $formula
     *
     * @return false|string False indicates an error
     */
    
private function convertMatrixReferences($formula)
    {
        static 
$matrixReplaceFrom = [self::FORMULA_OPEN_MATRIX_BRACE';'self::FORMULA_CLOSE_MATRIX_BRACE];
        static 
$matrixReplaceTo = ['MKMATRIX(MKMATRIX(''),MKMATRIX(''))'];

        
//    Convert any Excel matrix references to the MKMATRIX() function
        
if (strpos($formulaself::FORMULA_OPEN_MATRIX_BRACE) !== false) {
            
//    If there is the possibility of braces within a quoted string, then we don't treat those as matrix indicators
            
if (strpos($formulaself::FORMULA_STRING_QUOTE) !== false) {
                
//    So instead we skip replacing in any quoted strings by only replacing in every other array element after we've exploded
                //        the formula
                
$temp explode(self::FORMULA_STRING_QUOTE$formula);
                
//    Open and Closed counts used for trapping mismatched braces in the formula
                
$openCount $closeCount 0;
                
$notWithinQuotes false;
                foreach (
$temp as &$value) {
                    
//    Only count/replace in alternating array entries
                    
$notWithinQuotes $notWithinQuotes === false;
                    if (
$notWithinQuotes === true) {
                        
$openCount += substr_count($valueself::FORMULA_OPEN_MATRIX_BRACE);
                        
$closeCount += substr_count($valueself::FORMULA_CLOSE_MATRIX_BRACE);
                        
$value str_replace($matrixReplaceFrom$matrixReplaceTo$value);
                    }
                }
                unset(
$value);
                
//    Then rebuild the formula string
                
$formula implode(self::FORMULA_STRING_QUOTE$temp);
            } else {
                
//    If there's no quoted strings, then we do a simple count/replace
                
$openCount substr_count($formulaself::FORMULA_OPEN_MATRIX_BRACE);
                
$closeCount substr_count($formulaself::FORMULA_CLOSE_MATRIX_BRACE);
                
$formula str_replace($matrixReplaceFrom$matrixReplaceTo$formula);
            }
            
//    Trap for mismatched braces and trigger an appropriate error
            
if ($openCount $closeCount) {
                if (
$openCount 0) {
                    return 
$this->raiseFormulaError("Formula Error: Mismatched matrix braces '}'");
                }

                return 
$this->raiseFormulaError("Formula Error: Unexpected '}' encountered");
            } elseif (
$openCount $closeCount) {
                if (
$closeCount 0) {
                    return 
$this->raiseFormulaError("Formula Error: Mismatched matrix braces '{'");
                }

                return 
$this->raiseFormulaError("Formula Error: Unexpected '{' encountered");
            }
        }

        return 
$formula;
    }

    
/**
     *    Binary Operators.
     *    These operators always work on two values.
     *    Array key is the operator, the value indicates whether this is a left or right associative operator.
     *
     * @var array
     */
    
private static $operatorAssociativity = [
        
'^' => 0//    Exponentiation
        
'*' => 0'/' => 0//    Multiplication and Division
        
'+' => 0'-' => 0//    Addition and Subtraction
        
'&' => 0//    Concatenation
        
'∪' => 0'∩' => 0':' => 0//    Union, Intersect and Range
        
'>' => 0'<' => 0'=' => 0'>=' => 0'<=' => 0'<>' => 0//    Comparison
    
];

    
/**
     *    Comparison (Boolean) Operators.
     *    These operators work on two values, but always return a boolean result.
     *
     * @var array
     */
    
private static $comparisonOperators = ['>' => true'<' => true'=' => true'>=' => true'<=' => true'<>' => true];

    
/**
     *    Operator Precedence.
     *    This list includes all valid operators, whether binary (including boolean) or unary (such as %).
     *    Array key is the operator, the value is its precedence.
     *
     * @var array
     */
    
private static $operatorPrecedence = [
        
':' => 9//    Range
        
'∩' => 8//    Intersect
        
'∪' => 7//    Union
        
'~' => 6//    Negation
        
'%' => 5//    Percentage
        
'^' => 4//    Exponentiation
        
'*' => 3'/' => 3//    Multiplication and Division
        
'+' => 2'-' => 2//    Addition and Subtraction
        
'&' => 1//    Concatenation
        
'>' => 0'<' => 0'=' => 0'>=' => 0'<=' => 0'<>' => 0//    Comparison
    
];

    
// Convert infix to postfix notation

    /**
     * @param string $formula
     *
     * @return array<int, mixed>|false
     */
    
private function internalParseFormula($formula, ?Cell $cell null)
    {
        if ((
$formula $this->convertMatrixReferences(trim($formula))) === false) {
            return 
false;
        }

        
//    If we're using cell caching, then $pCell may well be flushed back to the cache (which detaches the parent worksheet),
        //        so we store the parent worksheet so that we can re-attach it when necessary
        
$pCellParent = ($cell !== null) ? $cell->getWorksheet() : null;

        
$regexpMatchString '/^((?<string>' self::CALCULATION_REGEXP_STRING .
                                
')|(?<function>' self::CALCULATION_REGEXP_FUNCTION .
                                
')|(?<cellRef>' self::CALCULATION_REGEXP_CELLREF .
                                
')|(?<colRange>' self::CALCULATION_REGEXP_COLUMN_RANGE .
                                
')|(?<rowRange>' self::CALCULATION_REGEXP_ROW_RANGE .
                                
')|(?<number>' self::CALCULATION_REGEXP_NUMBER .
                                
')|(?<openBrace>' self::CALCULATION_REGEXP_OPENBRACE .
                                
')|(?<structuredReference>' self::CALCULATION_REGEXP_STRUCTURED_REFERENCE .
                                
')|(?<definedName>' self::CALCULATION_REGEXP_DEFINEDNAME .
                                
')|(?<error>' self::CALCULATION_REGEXP_ERROR .
                                
'))/sui';

        
//    Start with initialisation
        
$index 0;
        
$stack = new Stack($this->branchPruner);
        
$output = [];
        
$expectingOperator false//    We use this test in syntax-checking the expression to determine when a
        //        - is a negation or + is a positive operator rather than an operation
        
$expectingOperand false//    We use this test in syntax-checking the expression to determine whether an operand
        //        should be null in a function call

        //    The guts of the lexical parser
        //    Loop through the formula extracting each operator and operand in turn
        
while (true) {
            
// Branch pruning: we adapt the output item to the context (it will
            // be used to limit its computation)
            
$this->branchPruner->initialiseForLoop();

            
$opCharacter $formula[$index]; //    Get the first character of the value at the current index position

            // Check for two-character operators (e.g. >=, <=, <>)
            
if ((isset(self::$comparisonOperators[$opCharacter])) && (strlen($formula) > $index) && (isset(self::$comparisonOperators[$formula[$index 1]]))) {
                
$opCharacter .= $formula[++$index];
            }
            
//    Find out if we're currently at the beginning of a number, variable, cell/row/column reference,
            //         function, defined name, structured reference, parenthesis, error or operand
            
$isOperandOrFunction = (bool) preg_match($regexpMatchStringsubstr($formula$index), $match);

            
$expectingOperatorCopy $expectingOperator;
            if (
$opCharacter === '-' && !$expectingOperator) {                //    Is it a negation instead of a minus?
                //    Put a negation on the stack
                
$stack->push('Unary Operator''~');
                ++
$index//        and drop the negation symbol
            
} elseif ($opCharacter === '%' && $expectingOperator) {
                
//    Put a percentage on the stack
                
$stack->push('Unary Operator''%');
                ++
$index;
            } elseif (
$opCharacter === '+' && !$expectingOperator) {            //    Positive (unary plus rather than binary operator plus) can be discarded?
                
++$index//    Drop the redundant plus symbol
            
} elseif ((($opCharacter === '~') || ($opCharacter === '∩') || ($opCharacter === '∪')) && (!$isOperandOrFunction)) {
                
//    We have to explicitly deny a tilde, union or intersect because they are legal
                
return $this->raiseFormulaError("Formula Error: Illegal character '~'"); //        on the stack but not in the input expression
            
} elseif ((isset(self::CALCULATION_OPERATORS[$opCharacter]) || $isOperandOrFunction) && $expectingOperator) {    //    Are we putting an operator on the stack?
                
while (
                    
$stack->count() > &&
                    (
$o2 $stack->last()) &&
                    isset(
self::CALCULATION_OPERATORS[$o2['value']]) &&
                    @(
self::$operatorAssociativity[$opCharacter] ? self::$operatorPrecedence[$opCharacter] < self::$operatorPrecedence[$o2['value']] : self::$operatorPrecedence[$opCharacter] <= self::$operatorPrecedence[$o2['value']])
                ) {
                    
$output[] = $stack->pop(); //    Swap operands and higher precedence operators from the stack to the output
                
}

                
//    Finally put our current operator onto the stack
                
$stack->push('Binary Operator'$opCharacter);

                ++
$index;
                
$expectingOperator false;
            } elseif (
$opCharacter === ')' && $expectingOperator) { //    Are we expecting to close a parenthesis?
                
$expectingOperand false;
                while ((
$o2 $stack->pop()) && $o2['value'] !== '(') { //    Pop off the stack back to the last (
                    
$output[] = $o2;
                }
                
$d $stack->last(2);

                
// Branch pruning we decrease the depth whether is it a function
                // call or a parenthesis
                
$this->branchPruner->decrementDepth();

                if (
is_array($d) && preg_match('/^' self::CALCULATION_REGEXP_FUNCTION '$/miu'$d['value'], $matches)) {
                    
//    Did this parenthesis just close a function?
                    
try {
                        
$this->branchPruner->closingBrace($d['value']);
                    } catch (
Exception $e) {
                        return 
$this->raiseFormulaError($e->getMessage());
                    }

                    
$functionName $matches[1]; //    Get the function name
                    
$d $stack->pop();
                    
$argumentCount $d['value'] ?? 0//    See how many arguments there were (argument count is the next value stored on the stack)
                    
$output[] = $d//    Dump the argument count on the output
                    
$output[] = $stack->pop(); //    Pop the function and push onto the output
                    
if (isset(self::$controlFunctions[$functionName])) {
                        
$expectedArgumentCount self::$controlFunctions[$functionName]['argumentCount'];
                        
// Scrutinizer says functionCall is unused after this assignment.
                        // It might be right, but I'm too lazy to confirm.
                        
$functionCall self::$controlFunctions[$functionName]['functionCall'];
                        
self::doNothing($functionCall);
                    } elseif (isset(
self::$phpSpreadsheetFunctions[$functionName])) {
                        
$expectedArgumentCount self::$phpSpreadsheetFunctions[$functionName]['argumentCount'];
                        
$functionCall self::$phpSpreadsheetFunctions[$functionName]['functionCall'];
                        
self::doNothing($functionCall);
                    } else {    
// did we somehow push a non-function on the stack? this should never happen
                        
return $this->raiseFormulaError('Formula Error: Internal error, non-function on stack');
                    }
                    
//    Check the argument count
                    
$argumentCountError false;
                    
$expectedArgumentCountString null;
                    if (
is_numeric($expectedArgumentCount)) {
                        if (
$expectedArgumentCount 0) {
                            if (
$argumentCount abs($expectedArgumentCount)) {
                                
$argumentCountError true;
                                
$expectedArgumentCountString 'no more than ' abs($expectedArgumentCount);
                            }
                        } else {
                            if (
$argumentCount != $expectedArgumentCount) {
                                
$argumentCountError true;
                                
$expectedArgumentCountString $expectedArgumentCount;
                            }
                        }
                    } elseif (
$expectedArgumentCount != '*') {
                        
$isOperandOrFunction preg_match('/(\d*)([-+,])(\d*)/'$expectedArgumentCount$argMatch);
                        
self::doNothing($isOperandOrFunction);
                        switch (
$argMatch[2]) {
                            case 
'+':
                                if (
$argumentCount $argMatch[1]) {
                                    
$argumentCountError true;
                                    
$expectedArgumentCountString $argMatch[1] . ' or more ';
                                }

                                break;
                            case 
'-':
                                if ((
$argumentCount $argMatch[1]) || ($argumentCount $argMatch[3])) {
                                    
$argumentCountError true;
                                    
$expectedArgumentCountString 'between ' $argMatch[1] . ' and ' $argMatch[3];
                                }

                                break;
                            case 
',':
                                if ((
$argumentCount != $argMatch[1]) && ($argumentCount != $argMatch[3])) {
                                    
$argumentCountError true;
                                    
$expectedArgumentCountString 'either ' $argMatch[1] . ' or ' $argMatch[3];
                                }

                                break;
                        }
                    }
                    if (
$argumentCountError) {
                        return 
$this->raiseFormulaError("Formula Error: Wrong number of arguments for $functionName() function: $argumentCount given, " $expectedArgumentCountString ' expected');
                    }
                }
                ++
$index;
            } elseif (
$opCharacter === ',') { // Is this the separator for function arguments?
                
try {
                    
$this->branchPruner->argumentSeparator();
                } catch (
Exception $e) {
                    return 
$this->raiseFormulaError($e->getMessage());
                }

                while ((
$o2 $stack->pop()) && $o2['value'] !== '(') {        //    Pop off the stack back to the last (
                    
$output[] = $o2// pop the argument expression stuff and push onto the output
                
}
                
//    If we've a comma when we're expecting an operand, then what we actually have is a null operand;
                //        so push a null onto the stack
                
if (($expectingOperand) || (!$expectingOperator)) {
                    
$output[] = ['type' => 'Empty Argument''value' => self::$excelConstants['NULL'], 'reference' => 'NULL'];
                }
                
// make sure there was a function
                
$d $stack->last(2);
                if (!
preg_match('/^' self::CALCULATION_REGEXP_FUNCTION '$/miu'$d['value'] ?? ''$matches)) {
                    
// Can we inject a dummy function at this point so that the braces at least have some context
                    //     because at least the braces are paired up (at this stage in the formula)
                    // MS Excel allows this if the content is cell references; but doesn't allow actual values,
                    //    but at this point, we can't differentiate (so allow both)
                    
return $this->raiseFormulaError('Formula Error: Unexpected ,');
                }

                
/** @var array $d */
                
$d $stack->pop();
                ++
$d['value']; // increment the argument count

                
$stack->pushStackItem($d);
                
$stack->push('Brace''('); // put the ( back on, we'll need to pop back to it again

                
$expectingOperator false;
                
$expectingOperand true;
                ++
$index;
            } elseif (
$opCharacter === '(' && !$expectingOperator) {
                
// Branch pruning: we go deeper
                
$this->branchPruner->incrementDepth();
                
$stack->push('Brace''('null);
                ++
$index;
            } elseif (
$isOperandOrFunction && !$expectingOperatorCopy) {
                
// do we now have a function/variable/number?
                
$expectingOperator true;
                
$expectingOperand false;
                
$val $match[1];
                
$length strlen($val);

                if (
preg_match('/^' self::CALCULATION_REGEXP_FUNCTION '$/miu'$val$matches)) {
                    
$val = (string) preg_replace('/\s/u'''$val);
                    if (isset(
self::$phpSpreadsheetFunctions[strtoupper($matches[1])]) || isset(self::$controlFunctions[strtoupper($matches[1])])) {    // it's a function
                        
$valToUpper strtoupper($val);
                    } else {
                        
$valToUpper 'NAME.ERROR(';
                    }
                    
// here $matches[1] will contain values like "IF"
                    // and $val "IF("

                    
$this->branchPruner->functionCall($valToUpper);

                    
$stack->push('Function'$valToUpper);
                    
// tests if the function is closed right after opening
                    
$ax preg_match('/^\s*\)/u'substr($formula$index $length));
                    if (
$ax) {
                        
$stack->push('Operand Count for Function ' $valToUpper ')'0);
                        
$expectingOperator true;
                    } else {
                        
$stack->push('Operand Count for Function ' $valToUpper ')'1);
                        
$expectingOperator false;
                    }
                    
$stack->push('Brace''(');
                } elseif (
preg_match('/^' self::CALCULATION_REGEXP_CELLREF '$/miu'$val$matches)) {
                    
//    Watch for this case-change when modifying to allow cell references in different worksheets...
                    //    Should only be applied to the actual cell column, not the worksheet name
                    //    If the last entry on the stack was a : operator, then we have a cell range reference
                    
$testPrevOp $stack->last(1);
                    if (
$testPrevOp !== null && $testPrevOp['value'] === ':') {
                        
//    If we have a worksheet reference, then we're playing with a 3D reference
                        
if ($matches[2] === '') {
                            
//    Otherwise, we 'inherit' the worksheet reference from the start cell reference
                            //    The start of the cell range reference should be the last entry in $output
                            
$rangeStartCellRef $output[count($output) - 1]['value'] ?? '';
                            if (
$rangeStartCellRef === ':') {
                                
// Do we have chained range operators?
                                
$rangeStartCellRef $output[count($output) - 2]['value'] ?? '';
                            }
                            
preg_match('/^' self::CALCULATION_REGEXP_CELLREF '$/miu'$rangeStartCellRef$rangeStartMatches);
                            if (
$rangeStartMatches[2] > '') {
                                
$val $rangeStartMatches[2] . '!' $val;
                            }
                        } else {
                            
$rangeStartCellRef $output[count($output) - 1]['value'] ?? '';
                            if (
$rangeStartCellRef === ':') {
                                
// Do we have chained range operators?
                                
$rangeStartCellRef $output[count($output) - 2]['value'] ?? '';
                            }
                            
preg_match('/^' self::CALCULATION_REGEXP_CELLREF '$/miu'$rangeStartCellRef$rangeStartMatches);
                            if (
$rangeStartMatches[2] !== $matches[2]) {
                                return 
$this->raiseFormulaError('3D Range references are not yet supported');
                            }
                        }
                    } elseif (
strpos($val'!') === false && $pCellParent !== null) {
                        
$worksheet $pCellParent->getTitle();
                        
$val "'{$worksheet}'!{$val}";
                    }
                    
// unescape any apostrophes or double quotes in worksheet name
                    
$val str_replace(["''"'""'], ["'"'"'], $val);
                    
$outputItem $stack->getStackItem('Cell Reference'$val$val);

                    
$output[] = $outputItem;
                } elseif (
preg_match('/^' self::CALCULATION_REGEXP_STRUCTURED_REFERENCE '$/miu'$val$matches)) {
                    try {
                        
$structuredReference Operands\StructuredReference::fromParser($formula$index$matches);
                    } catch (
Exception $e) {
                        return 
$this->raiseFormulaError($e->getMessage());
                    }

                    
$val $structuredReference->value();
                    
$length strlen($val);
                    
$outputItem $stack->getStackItem(Operands\StructuredReference::NAME$structuredReferencenull);

                    
$output[] = $outputItem;
                    
$expectingOperator true;
                } else {
                    
// it's a variable, constant, string, number or boolean
                    
$localeConstant false;
                    
$stackItemType 'Value';
                    
$stackItemReference null;

                    
//    If the last entry on the stack was a : operator, then we may have a row or column range reference
                    
$testPrevOp $stack->last(1);
                    if (
$testPrevOp !== null && $testPrevOp['value'] === ':') {
                        
$stackItemType 'Cell Reference';

                        if (
                            !
is_numeric($val) &&
                            ((
ctype_alpha($val) === false || strlen($val) > 3)) &&
                            (
preg_match('/^' self::CALCULATION_REGEXP_DEFINEDNAME '$/mui'$val) !== false) &&
                            (
$this->spreadsheet === null || $this->spreadsheet->getNamedRange($val) !== null)
                        ) {
                            
$namedRange = ($this->spreadsheet === null) ? null $this->spreadsheet->getNamedRange($val);
                            if (
$namedRange !== null) {
                                
$stackItemType 'Defined Name';
                                
$address str_replace('$'''$namedRange->getValue());
                                
$stackItemReference $val;
                                if (
strpos($address':') !== false) {
                                    
// We'll need to manipulate the stack for an actual named range rather than a named cell
                                    
$fromTo explode(':'$address);
                                    
$to array_pop($fromTo);
                                    foreach (
$fromTo as $from) {
                                        
$output[] = $stack->getStackItem($stackItemType$from$stackItemReference);
                                        
$output[] = $stack->getStackItem('Binary Operator'':');
                                    }
                                    
$address $to;
                                }
                                
$val $address;
                            }
                        } else {
                            
$startRowColRef $output[count($output) - 1]['value'] ?? '';
                            [
$rangeWS1$startRowColRef] = Worksheet::extractSheetTitle($startRowColReftrue);
                            
$rangeSheetRef $rangeWS1;
                            if (
$rangeWS1 !== '') {
                                
$rangeWS1 .= '!';
                            }
                            
$rangeSheetRef trim($rangeSheetRef"'");
                            [
$rangeWS2$val] = Worksheet::extractSheetTitle($valtrue);
                            if (
$rangeWS2 !== '') {
                                
$rangeWS2 .= '!';
                            } else {
                                
$rangeWS2 $rangeWS1;
                            }

                            
$refSheet $pCellParent;
                            if (
$pCellParent !== null && $rangeSheetRef !== '' && $rangeSheetRef !== $pCellParent->getTitle()) {
                                
$refSheet $pCellParent->getParentOrThrow()->getSheetByName($rangeSheetRef);
                            }

                            if (
ctype_digit($val) && $val <= 1048576) {
                                
//    Row range
                                
$stackItemType 'Row Reference';
                                
/** @var int $valx */
                                
$valx $val;
                                
$endRowColRef = ($refSheet !== null) ? $refSheet->getHighestDataColumn($valx) : AddressRange::MAX_COLUMN//    Max 16,384 columns for Excel2007
                                
$val "{$rangeWS2}{$endRowColRef}{$val}";
                            } elseif (
ctype_alpha($val) && strlen($val) <= 3) {
                                
//    Column range
                                
$stackItemType 'Column Reference';
                                
$endRowColRef = ($refSheet !== null) ? $refSheet->getHighestDataRow($val) : AddressRange::MAX_ROW//    Max 1,048,576 rows for Excel2007
                                
$val "{$rangeWS2}{$val}{$endRowColRef}";
                            }
                            
$stackItemReference $val;
                        }
                    } elseif (
$opCharacter === self::FORMULA_STRING_QUOTE) {
                        
//    UnEscape any quotes within the string
                        
$val self::wrapResult(str_replace('""'self::FORMULA_STRING_QUOTEself::unwrapResult($val)));
                    } elseif (isset(
self::$excelConstants[trim(strtoupper($val))])) {
                        
$stackItemType 'Constant';
                        
$excelConstant trim(strtoupper($val));
                        
$val self::$excelConstants[$excelConstant];
                        
$stackItemReference $excelConstant;
                    } elseif ((
$localeConstant array_search(trim(strtoupper($val)), self::$localeBoolean)) !== false) {
                        
$stackItemType 'Constant';
                        
$val self::$excelConstants[$localeConstant];
                        
$stackItemReference $localeConstant;
                    } elseif (
                        
preg_match('/^' self::CALCULATION_REGEXP_ROW_RANGE '/miu'substr($formula$index), $rowRangeReference)
                    ) {
                        
$val $rowRangeReference[1];
                        
$length strlen($rowRangeReference[1]);
                        
$stackItemType 'Row Reference';
                        
// unescape any apostrophes or double quotes in worksheet name
                        
$val str_replace(["''"'""'], ["'"'"'], $val);
                        
$column 'A';
                        if ((
$testPrevOp !== null && $testPrevOp['value'] === ':') && $pCellParent !== null) {
                            
$column $pCellParent->getHighestDataColumn($val);
                        }
                        
$val "{$rowRangeReference[2]}{$column}{$rowRangeReference[7]}";
                        
$stackItemReference $val;
                    } elseif (
                        
preg_match('/^' self::CALCULATION_REGEXP_COLUMN_RANGE '/miu'substr($formula$index), $columnRangeReference)
                    ) {
                        
$val $columnRangeReference[1];
                        
$length strlen($val);
                        
$stackItemType 'Column Reference';
                        
// unescape any apostrophes or double quotes in worksheet name
                        
$val str_replace(["''"'""'], ["'"'"'], $val);
                        
$row '1';
                        if ((
$testPrevOp !== null && $testPrevOp['value'] === ':') && $pCellParent !== null) {
                            
$row $pCellParent->getHighestDataRow($val);
                        }
                        
$val "{$val}{$row}";
                        
$stackItemReference $val;
                    } elseif (
preg_match('/^' self::CALCULATION_REGEXP_DEFINEDNAME '.*/miu'$val$match)) {
                        
$stackItemType 'Defined Name';
                        
$stackItemReference $val;
                    } elseif (
is_numeric($val)) {
                        if ((
strpos((string) $val'.') !== false) || (stripos((string) $val'e') !== false) || ($val PHP_INT_MAX) || ($val < -PHP_INT_MAX)) {
                            
$val = (float) $val;
                        } else {
                            
$val = (int) $val;
                        }
                    }

                    
$details $stack->getStackItem($stackItemType$val$stackItemReference);
                    if (
$localeConstant) {
                        
$details['localeValue'] = $localeConstant;
                    }
                    
$output[] = $details;
                }
                
$index += $length;
            } elseif (
$opCharacter === '$') { // absolute row or column range
                
++$index;
            } elseif (
$opCharacter === ')') { // miscellaneous error checking
                
if ($expectingOperand) {
                    
$output[] = ['type' => 'Empty Argument''value' => self::$excelConstants['NULL'], 'reference' => 'NULL'];
                    
$expectingOperand false;
                    
$expectingOperator true;
                } else {
                    return 
$this->raiseFormulaError("Formula Error: Unexpected ')'");
                }
            } elseif (isset(
self::CALCULATION_OPERATORS[$opCharacter]) && !$expectingOperator) {
                return 
$this->raiseFormulaError("Formula Error: Unexpected operator '$opCharacter'");
            } else {    
// I don't even want to know what you did to get here
                
return $this->raiseFormulaError('Formula Error: An unexpected error occurred');
            }
            
//    Test for end of formula string
            
if ($index == strlen($formula)) {
                
//    Did we end with an operator?.
                //    Only valid for the % unary operator
                
if ((isset(self::CALCULATION_OPERATORS[$opCharacter])) && ($opCharacter != '%')) {
                    return 
$this->raiseFormulaError("Formula Error: Operator '$opCharacter' has no operands");
                }

                break;
            }
            
//    Ignore white space
            
while (($formula[$index] === "\n") || ($formula[$index] === "\r")) {
                ++
$index;
            }

            if (
$formula[$index] === ' ') {
                while (
$formula[$index] === ' ') {
                    ++
$index;
                }

                
//    If we're expecting an operator, but only have a space between the previous and next operands (and both are
                //        Cell References, Defined Names or Structured References) then we have an INTERSECTION operator
                
$countOutputMinus1 count($output) - 1;
                if (
                    (
$expectingOperator) &&
                    
array_key_exists($countOutputMinus1$output) &&
                    
is_array($output[$countOutputMinus1]) &&
                    
array_key_exists('type'$output[$countOutputMinus1]) &&
                    (
                        (
preg_match('/^' self::CALCULATION_REGEXP_CELLREF '.*/miu'substr($formula$index), $match)) &&
                            (
$output[$countOutputMinus1]['type'] === 'Cell Reference') ||
                        (
preg_match('/^' self::CALCULATION_REGEXP_DEFINEDNAME '.*/miu'substr($formula$index), $match)) &&
                            (
$output[$countOutputMinus1]['type'] === 'Defined Name' || $output[$countOutputMinus1]['type'] === 'Value') ||
                        (
preg_match('/^' self::CALCULATION_REGEXP_STRUCTURED_REFERENCE '.*/miu'substr($formula$index), $match)) &&
                            (
$output[$countOutputMinus1]['type'] === Operands\StructuredReference::NAME || $output[$countOutputMinus1]['type'] === 'Value')
                    )
                ) {
                    while (
                        
$stack->count() > &&
                        (
$o2 $stack->last()) &&
                        isset(
self::CALCULATION_OPERATORS[$o2['value']]) &&
                        @(
self::$operatorAssociativity[$opCharacter] ? self::$operatorPrecedence[$opCharacter] < self::$operatorPrecedence[$o2['value']] : self::$operatorPrecedence[$opCharacter] <= self::$operatorPrecedence[$o2['value']])
                    ) {
                        
$output[] = $stack->pop(); //    Swap operands and higher precedence operators from the stack to the output
                    
}
                    
$stack->push('Binary Operator''∩'); //    Put an Intersect Operator on the stack
                    
$expectingOperator false;
                }
            }
        }

        while ((
$op $stack->pop()) !== null) {
            
// pop everything off the stack and push onto output
            
if ((is_array($op) && $op['value'] == '(')) {
                return 
$this->raiseFormulaError("Formula Error: Expecting ')'"); // if there are any opening braces on the stack, then braces were unbalanced
            
}
            
$output[] = $op;
        }

        return 
$output;
    }

    
/**
     * @param array $operandData
     *
     * @return mixed
     */
    
private static function dataTestReference(&$operandData)
    {
        
$operand $operandData['value'];
        if ((
$operandData['reference'] === null) && (is_array($operand))) {
            
$rKeys array_keys($operand);
            
$rowKey array_shift($rKeys);
            if (
is_array($operand[$rowKey]) === false) {
                
$operandData['value'] = $operand[$rowKey];

                return 
$operand[$rowKey];
            }

            
$cKeys array_keys(array_keys($operand[$rowKey]));
            
$colKey array_shift($cKeys);
            if (
ctype_upper("$colKey")) {
                
$operandData['reference'] = $colKey $rowKey;
            }
        }

        return 
$operand;
    }

    
/**
     * @param mixed $tokens
     * @param null|string $cellID
     *
     * @return array<int, mixed>|false
     */
    
private function processTokenStack($tokens$cellID null, ?Cell $cell null)
    {
        if (
$tokens === false) {
            return 
false;
        }

        
//    If we're using cell caching, then $pCell may well be flushed back to the cache (which detaches the parent cell collection),
        //        so we store the parent cell collection so that we can re-attach it when necessary
        
$pCellWorksheet = ($cell !== null) ? $cell->getWorksheet() : null;
        
$pCellParent = ($cell !== null) ? $cell->getParent() : null;
        
$stack = new Stack($this->branchPruner);

        
// Stores branches that have been pruned
        
$fakedForBranchPruning = [];
        
// help us to know when pruning ['branchTestId' => true/false]
        
$branchStore = [];
        
//    Loop through each token in turn
        
foreach ($tokens as $tokenData) {
            
$token $tokenData['value'];
            
// Branch pruning: skip useless resolutions
            
$storeKey $tokenData['storeKey'] ?? null;
            if (
$this->branchPruningEnabled && isset($tokenData['onlyIf'])) {
                
$onlyIfStoreKey $tokenData['onlyIf'];
                
$storeValue $branchStore[$onlyIfStoreKey] ?? null;
                
$storeValueAsBool = ($storeValue === null) ?
                    
true : (bool) Functions::flattenSingleValue($storeValue);
                if (
is_array($storeValue)) {
                    
$wrappedItem end($storeValue);
                    
$storeValue is_array($wrappedItem) ? end($wrappedItem) : $wrappedItem;
                }

                if (
                    (isset(
$storeValue) || $tokenData['reference'] === 'NULL')
                    && (!
$storeValueAsBool || Information\ErrorValue::isError($storeValue) || ($storeValue === 'Pruned branch'))
                ) {
                    
// If branching value is not true, we don't need to compute
                    
if (!isset($fakedForBranchPruning['onlyIf-' $onlyIfStoreKey])) {
                        
$stack->push('Value''Pruned branch (only if ' $onlyIfStoreKey ') ' $token);
                        
$fakedForBranchPruning['onlyIf-' $onlyIfStoreKey] = true;
                    }

                    if (isset(
$storeKey)) {
                        
// We are processing an if condition
                        // We cascade the pruning to the depending branches
                        
$branchStore[$storeKey] = 'Pruned branch';
                        
$fakedForBranchPruning['onlyIfNot-' $storeKey] = true;
                        
$fakedForBranchPruning['onlyIf-' $storeKey] = true;
                    }

                    continue;
                }
            }

            if (
$this->branchPruningEnabled && isset($tokenData['onlyIfNot'])) {
                
$onlyIfNotStoreKey $tokenData['onlyIfNot'];
                
$storeValue $branchStore[$onlyIfNotStoreKey] ?? null;
                
$storeValueAsBool = ($storeValue === null) ?
                    
true : (bool) Functions::flattenSingleValue($storeValue);
                if (
is_array($storeValue)) {
                    
$wrappedItem end($storeValue);
                    
$storeValue is_array($wrappedItem) ? end($wrappedItem) : $wrappedItem;
                }

                if (
                    (isset(
$storeValue) || $tokenData['reference'] === 'NULL')
                    && (
$storeValueAsBool || Information\ErrorValue::isError($storeValue) || ($storeValue === 'Pruned branch'))
                ) {
                    
// If branching value is true, we don't need to compute
                    
if (!isset($fakedForBranchPruning['onlyIfNot-' $onlyIfNotStoreKey])) {
                        
$stack->push('Value''Pruned branch (only if not ' $onlyIfNotStoreKey ') ' $token);
                        
$fakedForBranchPruning['onlyIfNot-' $onlyIfNotStoreKey] = true;
                    }

                    if (isset(
$storeKey)) {
                        
// We are processing an if condition
                        // We cascade the pruning to the depending branches
                        
$branchStore[$storeKey] = 'Pruned branch';
                        
$fakedForBranchPruning['onlyIfNot-' $storeKey] = true;
                        
$fakedForBranchPruning['onlyIf-' $storeKey] = true;
                    }

                    continue;
                }
            }

            if (
$token instanceof Operands\StructuredReference) {
                if (
$cell === null) {
                    return 
$this->raiseFormulaError('Structured References must exist in a Cell context');
                }

                try {
                    
$cellRange $token->parse($cell);
                    if (
strpos($cellRange':') !== false) {
                        
$this->debugLog->writeDebugLog('Evaluating Structured Reference %s as Cell Range %s'$token->value(), $cellRange);
                        
$rangeValue self::getInstance($cell->getWorksheet()->getParent())->_calculateFormulaValue("={$cellRange}"$token->value(), $cell);
                        
$stack->push('Value'$rangeValue);
                        
$this->debugLog->writeDebugLog('Evaluated Structured Reference %s as value %s'$token->value(), $this->showValue($rangeValue));
                    } else {
                        
$this->debugLog->writeDebugLog('Evaluating Structured Reference %s as Cell %s'$token->value(), $cellRange);
                        
$cellValue $cell->getWorksheet()->getCell($cellRange)->getCalculatedValue(false);
                        
$stack->push('Cell Reference'$cellValue$cellRange);
                        
$this->debugLog->writeDebugLog('Evaluated Structured Reference %s as value %s'$token->value(), $this->showValue($cellValue));
                    }
                } catch (
Exception $e) {
                    if (
$e->getCode() === Exception::CALCULATION_ENGINE_PUSH_TO_STACK) {
                        
$stack->push('Error'Information\ExcelError::REF(), null);
                        
$this->debugLog->writeDebugLog('Evaluated Structured Reference %s as error value %s'$token->value(), Information\ExcelError::REF());
                    } else {
                        return 
$this->raiseFormulaError($e->getMessage());
                    }
                }
            } elseif (!
is_numeric($token) && !is_object($token) && isset(self::BINARY_OPERATORS[$token])) {
                
// if the token is a binary operator, pop the top two values off the stack, do the operation, and push the result back on the stack
                //    We must have two operands, error if we don't
                
if (($operand2Data $stack->pop()) === null) {
                    return 
$this->raiseFormulaError('Internal error - Operand value missing from stack');
                }
                if ((
$operand1Data $stack->pop()) === null) {
                    return 
$this->raiseFormulaError('Internal error - Operand value missing from stack');
                }

                
$operand1 self::dataTestReference($operand1Data);
                
$operand2 self::dataTestReference($operand2Data);

                
//    Log what we're doing
                
if ($token == ':') {
                    
$this->debugLog->writeDebugLog('Evaluating Range %s %s %s'$this->showValue($operand1Data['reference']), $token$this->showValue($operand2Data['reference']));
                } else {
                    
$this->debugLog->writeDebugLog('Evaluating %s %s %s'$this->showValue($operand1), $token$this->showValue($operand2));
                }

                
//    Process the operation in the appropriate manner
                
switch ($token) {
                    
// Comparison (Boolean) Operators
                    
case '>'// Greater than
                    
case '<'// Less than
                    
case '>='// Greater than or Equal to
                    
case '<='// Less than or Equal to
                    
case '='// Equality
                    
case '<>'// Inequality
                        
$result $this->executeBinaryComparisonOperation($operand1$operand2, (string) $token$stack);
                        if (isset(
$storeKey)) {
                            
$branchStore[$storeKey] = $result;
                        }

                        break;
                    
// Binary Operators
                    
case ':'// Range
                        
if ($operand1Data['type'] === 'Defined Name') {
                            if (
preg_match('/$' self::CALCULATION_REGEXP_DEFINEDNAME '^/mui'$operand1Data['reference']) !== false && $this->spreadsheet !== null) {
                                
$definedName $this->spreadsheet->getNamedRange($operand1Data['reference']);
                                if (
$definedName !== null) {
                                    
$operand1Data['reference'] = $operand1Data['value'] = str_replace('$'''$definedName->getValue());
                                }
                            }
                        }
                        if (
strpos($operand1Data['reference'], '!') !== false) {
                            [
$sheet1$operand1Data['reference']] = Worksheet::extractSheetTitle($operand1Data['reference'], true);
                        } else {
                            
$sheet1 = ($pCellWorksheet !== null) ? $pCellWorksheet->getTitle() : '';
                        }

                        [
$sheet2$operand2Data['reference']] = Worksheet::extractSheetTitle($operand2Data['reference'], true);
                        if (empty(
$sheet2)) {
                            
$sheet2 $sheet1;
                        }

                        if (
trim($sheet1"'") === trim($sheet2"'")) {
                            if (
$operand1Data['reference'] === null && $cell !== null) {
                                if (
is_array($operand1Data['value'])) {
                                    
$operand1Data['reference'] = $cell->getCoordinate();
                                } elseif ((
trim($operand1Data['value']) != '') && (is_numeric($operand1Data['value']))) {
                                    
$operand1Data['reference'] = $cell->getColumn() . $operand1Data['value'];
                                } elseif (
trim($operand1Data['value']) == '') {
                                    
$operand1Data['reference'] = $cell->getCoordinate();
                                } else {
                                    
$operand1Data['reference'] = $operand1Data['value'] . $cell->getRow();
                                }
                            }
                            if (
$operand2Data['reference'] === null && $cell !== null) {
                                if (
is_array($operand2Data['value'])) {
                                    
$operand2Data['reference'] = $cell->getCoordinate();
                                } elseif ((
trim($operand2Data['value']) != '') && (is_numeric($operand2Data['value']))) {
                                    
$operand2Data['reference'] = $cell->getColumn() . $operand2Data['value'];
                                } elseif (
trim($operand2Data['value']) == '') {
                                    
$operand2Data['reference'] = $cell->getCoordinate();
                                } else {
                                    
$operand2Data['reference'] = $operand2Data['value'] . $cell->getRow();
                                }
                            }

                            
$oData array_merge(explode(':'$operand1Data['reference']), explode(':'$operand2Data['reference']));
                            
$oCol $oRow = [];
                            foreach (
$oData as $oDatum) {
                                
$oCR Coordinate::coordinateFromString($oDatum);
                                
$oCol[] = Coordinate::columnIndexFromString($oCR[0]) - 1;
                                
$oRow[] = $oCR[1];
                            }
                            
$cellRef Coordinate::stringFromColumnIndex(min($oCol) + 1) . min($oRow) . ':' Coordinate::stringFromColumnIndex(max($oCol) + 1) . max($oRow);
                            if (
$pCellParent !== null && $this->spreadsheet !== null) {
                                
$cellValue $this->extractCellRange($cellRef$this->spreadsheet->getSheetByName($sheet1), false);
                            } else {
                                return 
$this->raiseFormulaError('Unable to access Cell Reference');
                            }

                            
$stack->push('Cell Reference'$cellValue$cellRef);
                        } else {
                            
$stack->push('Error'Information\ExcelError::REF(), null);
                        }

                        break;
                    case 
'+':            //    Addition
                    
case '-':            //    Subtraction
                    
case '*':            //    Multiplication
                    
case '/':            //    Division
                    
case '^':            //    Exponential
                        
$result $this->executeNumericBinaryOperation($operand1$operand2$token$stack);
                        if (isset(
$storeKey)) {
                            
$branchStore[$storeKey] = $result;
                        }

                        break;
                    case 
'&':            //    Concatenation
                        //    If either of the operands is a matrix, we need to treat them both as matrices
                        //        (converting the other operand to a matrix if need be); then perform the required
                        //        matrix operation
                        
$operand1 self::boolToString($operand1);
                        
$operand2 self::boolToString($operand2);
                        if (
is_array($operand1) || is_array($operand2)) {
                            if (
is_string($operand1)) {
                                
$operand1 self::unwrapResult($operand1);
                            }
                            if (
is_string($operand2)) {
                                
$operand2 self::unwrapResult($operand2);
                            }
                            
//    Ensure that both operands are arrays/matrices
                            
[$rows$columns] = self::checkMatrixOperands($operand1$operand22);

                            for (
$row 0$row $rows; ++$row) {
                                for (
$column 0$column $columns; ++$column) {
                                    
$operand1[$row][$column] =
                                        
Shared\StringHelper::substring(
                                            
self::boolToString($operand1[$row][$column])
                                            . 
self::boolToString($operand2[$row][$column]),
                                            
0,
                                            
DataType::MAX_STRING_LENGTH
                                        
);
                                }
                            }
                            
$result $operand1;
                        } else {
                            
// In theory, we should truncate here.
                            // But I can't figure out a formula
                            // using the concatenation operator
                            // with literals that fits in 32K,
                            // so I don't think we can overflow here.
                            
$result self::FORMULA_STRING_QUOTE str_replace('""'self::FORMULA_STRING_QUOTEself::unwrapResult($operand1) . self::unwrapResult($operand2)) . self::FORMULA_STRING_QUOTE;
                        }
                        
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails($result));
                        
$stack->push('Value'$result);

                        if (isset(
$storeKey)) {
                            
$branchStore[$storeKey] = $result;
                        }

                        break;
                    case 
'∩':            //    Intersect
                        
$rowIntersect array_intersect_key($operand1$operand2);
                        
$cellIntersect $oCol $oRow = [];
                        foreach (
array_keys($rowIntersect) as $row) {
                            
$oRow[] = $row;
                            foreach (
$rowIntersect[$row] as $col => $data) {
                                
$oCol[] = Coordinate::columnIndexFromString($col) - 1;
                                
$cellIntersect[$row] = array_intersect_key($operand1[$row], $operand2[$row]);
                            }
                        }
                        if (
count(Functions::flattenArray($cellIntersect)) === 0) {
                            
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails($cellIntersect));
                            
$stack->push('Error'Information\ExcelError::null(), null);
                        } else {
                            
$cellRef Coordinate::stringFromColumnIndex(min($oCol) + 1) . min($oRow) . ':' .
                                
Coordinate::stringFromColumnIndex(max($oCol) + 1) . max($oRow);
                            
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails($cellIntersect));
                            
$stack->push('Value'$cellIntersect$cellRef);
                        }

                        break;
                }
            } elseif ((
$token === '~') || ($token === '%')) {
                
// if the token is a unary operator, pop one value off the stack, do the operation, and push it back on
                
if (($arg $stack->pop()) === null) {
                    return 
$this->raiseFormulaError('Internal error - Operand value missing from stack');
                }
                
$arg $arg['value'];
                if (
$token === '~') {
                    
$this->debugLog->writeDebugLog('Evaluating Negation of %s'$this->showValue($arg));
                    
$multiplier = -1;
                } else {
                    
$this->debugLog->writeDebugLog('Evaluating Percentile of %s'$this->showValue($arg));
                    
$multiplier 0.01;
                }
                if (
is_array($arg)) {
                    
$operand2 $multiplier;
                    
$result $arg;
                    [
$rows$columns] = self::checkMatrixOperands($result$operand20);
                    for (
$row 0$row $rows; ++$row) {
                        for (
$column 0$column $columns; ++$column) {
                            if (
self::isNumericOrBool($result[$row][$column])) {
                                
$result[$row][$column] *= $multiplier;
                            } else {
                                
$result[$row][$column] = self::makeError($result[$row][$column]);
                            }
                        }
                    }

                    
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails($result));
                    
$stack->push('Value'$result);
                    if (isset(
$storeKey)) {
                        
$branchStore[$storeKey] = $result;
                    }
                } else {
                    
$this->executeNumericBinaryOperation($multiplier$arg'*'$stack);
                }
            } elseif (
preg_match('/^' self::CALCULATION_REGEXP_CELLREF '$/i'$token ?? ''$matches)) {
                
$cellRef null;

                if (isset(
$matches[8])) {
                    if (
$cell === null) {
                        
// We can't access the range, so return a REF error
                        
$cellValue Information\ExcelError::REF();
                    } else {
                        
$cellRef $matches[6] . $matches[7] . ':' $matches[9] . $matches[10];
                        if (
$matches[2] > '') {
                            
$matches[2] = trim($matches[2], "\"'");
                            if ((
strpos($matches[2], '[') !== false) || (strpos($matches[2], ']') !== false)) {
                                
//    It's a Reference to an external spreadsheet (not currently supported)
                                
return $this->raiseFormulaError('Unable to access External Workbook');
                            }
                            
$matches[2] = trim($matches[2], "\"'");
                            
$this->debugLog->writeDebugLog('Evaluating Cell Range %s in worksheet %s'$cellRef$matches[2]);
                            if (
$pCellParent !== null && $this->spreadsheet !== null) {
                                
$cellValue $this->extractCellRange($cellRef$this->spreadsheet->getSheetByName($matches[2]), false);
                            } else {
                                return 
$this->raiseFormulaError('Unable to access Cell Reference');
                            }
                            
$this->debugLog->writeDebugLog('Evaluation Result for cells %s in worksheet %s is %s'$cellRef$matches[2], $this->showTypeDetails($cellValue));
                        } else {
                            
$this->debugLog->writeDebugLog('Evaluating Cell Range %s in current worksheet'$cellRef);
                            if (
$pCellParent !== null) {
                                
$cellValue $this->extractCellRange($cellRef$pCellWorksheetfalse);
                            } else {
                                return 
$this->raiseFormulaError('Unable to access Cell Reference');
                            }
                            
$this->debugLog->writeDebugLog('Evaluation Result for cells %s is %s'$cellRef$this->showTypeDetails($cellValue));
                        }
                    }
                } else {
                    if (
$cell === null) {
                        
// We can't access the cell, so return a REF error
                        
$cellValue Information\ExcelError::REF();
                    } else {
                        
$cellRef $matches[6] . $matches[7];
                        if (
$matches[2] > '') {
                            
$matches[2] = trim($matches[2], "\"'");
                            if ((
strpos($matches[2], '[') !== false) || (strpos($matches[2], ']') !== false)) {
                                
//    It's a Reference to an external spreadsheet (not currently supported)
                                
return $this->raiseFormulaError('Unable to access External Workbook');
                            }
                            
$this->debugLog->writeDebugLog('Evaluating Cell %s in worksheet %s'$cellRef$matches[2]);
                            if (
$pCellParent !== null && $this->spreadsheet !== null) {
                                
$cellSheet $this->spreadsheet->getSheetByName($matches[2]);
                                if (
$cellSheet && $cellSheet->cellExists($cellRef)) {
                                    
$cellValue $this->extractCellRange($cellRef$this->spreadsheet->getSheetByName($matches[2]), false);
                                    
$cell->attach($pCellParent);
                                } else {
                                    
$cellRef = ($cellSheet !== null) ? "'{$matches[2]}'!{$cellRef}$cellRef;
                                    
$cellValue = ($cellSheet !== null) ? null Information\ExcelError::REF();
                                }
                            } else {
                                return 
$this->raiseFormulaError('Unable to access Cell Reference');
                            }
                            
$this->debugLog->writeDebugLog('Evaluation Result for cell %s in worksheet %s is %s'$cellRef$matches[2], $this->showTypeDetails($cellValue));
                        } else {
                            
$this->debugLog->writeDebugLog('Evaluating Cell %s in current worksheet'$cellRef);
                            if (
$pCellParent !== null && $pCellParent->has($cellRef)) {
                                
$cellValue $this->extractCellRange($cellRef$pCellWorksheetfalse);
                                
$cell->attach($pCellParent);
                            } else {
                                
$cellValue null;
                            }
                            
$this->debugLog->writeDebugLog('Evaluation Result for cell %s is %s'$cellRef$this->showTypeDetails($cellValue));
                        }
                    }
                }

                
$stack->push('Cell Value'$cellValue$cellRef);
                if (isset(
$storeKey)) {
                    
$branchStore[$storeKey] = $cellValue;
                }
            } elseif (
preg_match('/^' self::CALCULATION_REGEXP_FUNCTION '$/miu'$token ?? ''$matches)) {
                
// if the token is a function, pop arguments off the stack, hand them to the function, and push the result back on
                
if ($cell !== null && $pCellParent !== null) {
                    
$cell->attach($pCellParent);
                }

                
$functionName $matches[1];
                
$argCount $stack->pop();
                
$argCount $argCount['value'];
                if (
$functionName !== 'MKMATRIX') {
                    
$this->debugLog->writeDebugLog('Evaluating Function %s() with %s argument%s'self::localeFunc($functionName), (($argCount == 0) ? 'no' $argCount), (($argCount == 1) ? '' 's'));
                }
                if ((isset(
self::$phpSpreadsheetFunctions[$functionName])) || (isset(self::$controlFunctions[$functionName]))) {    // function
                    
$passByReference false;
                    
$passCellReference false;
                    
$functionCall null;
                    if (isset(
self::$phpSpreadsheetFunctions[$functionName])) {
                        
$functionCall self::$phpSpreadsheetFunctions[$functionName]['functionCall'];
                        
$passByReference = isset(self::$phpSpreadsheetFunctions[$functionName]['passByReference']);
                        
$passCellReference = isset(self::$phpSpreadsheetFunctions[$functionName]['passCellReference']);
                    } elseif (isset(
self::$controlFunctions[$functionName])) {
                        
$functionCall self::$controlFunctions[$functionName]['functionCall'];
                        
$passByReference = isset(self::$controlFunctions[$functionName]['passByReference']);
                        
$passCellReference = isset(self::$controlFunctions[$functionName]['passCellReference']);
                    }

                    
// get the arguments for this function
                    
$args $argArrayVals = [];
                    
$emptyArguments = [];
                    for (
$i 0$i $argCount; ++$i) {
                        
$arg $stack->pop();
                        
$a $argCount $i 1;
                        if (
                            (
$passByReference) &&
                            (isset(
self::$phpSpreadsheetFunctions[$functionName]['passByReference'][$a])) &&
                            (
self::$phpSpreadsheetFunctions[$functionName]['passByReference'][$a])
                        ) {
                            if (
$arg['reference'] === null) {
                                
$args[] = $cellID;
                                if (
$functionName !== 'MKMATRIX') {
                                    
$argArrayVals[] = $this->showValue($cellID);
                                }
                            } else {
                                
$args[] = $arg['reference'];
                                if (
$functionName !== 'MKMATRIX') {
                                    
$argArrayVals[] = $this->showValue($arg['reference']);
                                }
                            }
                        } else {
                            
$emptyArguments[] = ($arg['type'] === 'Empty Argument');
                            
$args[] = self::unwrapResult($arg['value']);
                            if (
$functionName !== 'MKMATRIX') {
                                
$argArrayVals[] = $this->showValue($arg['value']);
                            }
                        }
                    }

                    
//    Reverse the order of the arguments
                    
krsort($args);
                    
krsort($emptyArguments);

                    if (
$argCount 0) {
                        
$args $this->addDefaultArgumentValues($functionCall$args$emptyArguments);
                    }

                    if ((
$passByReference) && ($argCount == 0)) {
                        
$args[] = $cellID;
                        
$argArrayVals[] = $this->showValue($cellID);
                    }

                    if (
$functionName !== 'MKMATRIX') {
                        if (
$this->debugLog->getWriteDebugLog()) {
                            
krsort($argArrayVals);
                            
$this->debugLog->writeDebugLog('Evaluating %s ( %s )'self::localeFunc($functionName), implode(self::$localeArgumentSeparator ' 'Functions::flattenArray($argArrayVals)));
                        }
                    }

                    
//    Process the argument with the appropriate function call
                    
$args $this->addCellReference($args$passCellReference$functionCall$cell);

                    if (!
is_array($functionCall)) {
                        foreach (
$args as &$arg) {
                            
$arg Functions::flattenSingleValue($arg);
                        }
                        unset(
$arg);
                    }

                    
$result call_user_func_array($functionCall$args);

                    if (
$functionName !== 'MKMATRIX') {
                        
$this->debugLog->writeDebugLog('Evaluation Result for %s() function call is %s'self::localeFunc($functionName), $this->showTypeDetails($result));
                    }
                    
$stack->push('Value'self::wrapResult($result));
                    if (isset(
$storeKey)) {
                        
$branchStore[$storeKey] = $result;
                    }
                }
            } else {
                
// if the token is a number, boolean, string or an Excel error, push it onto the stack
                
if (isset(self::$excelConstants[strtoupper($token ?? '')])) {
                    
$excelConstant strtoupper($token);
                    
$stack->push('Constant Value'self::$excelConstants[$excelConstant]);
                    if (isset(
$storeKey)) {
                        
$branchStore[$storeKey] = self::$excelConstants[$excelConstant];
                    }
                    
$this->debugLog->writeDebugLog('Evaluating Constant %s as %s'$excelConstant$this->showTypeDetails(self::$excelConstants[$excelConstant]));
                } elseif ((
is_numeric($token)) || ($token === null) || (is_bool($token)) || ($token == '') || ($token[0] == self::FORMULA_STRING_QUOTE) || ($token[0] == '#')) {
                    
$stack->push($tokenData['type'], $token$tokenData['reference']);
                    if (isset(
$storeKey)) {
                        
$branchStore[$storeKey] = $token;
                    }
                } elseif (
preg_match('/^' self::CALCULATION_REGEXP_DEFINEDNAME '$/miu'$token$matches)) {
                    
// if the token is a named range or formula, evaluate it and push the result onto the stack
                    
$definedName $matches[6];
                    if (
$cell === null || $pCellWorksheet === null) {
                        return 
$this->raiseFormulaError("undefined name '$token'");
                    }

                    
$this->debugLog->writeDebugLog('Evaluating Defined Name %s'$definedName);
                    
$namedRange DefinedName::resolveName($definedName$pCellWorksheet);
                    if (
$namedRange === null) {
                        return 
$this->raiseFormulaError("undefined name '$definedName'");
                    }

                    
$result $this->evaluateDefinedName($cell$namedRange$pCellWorksheet$stack);
                    if (isset(
$storeKey)) {
                        
$branchStore[$storeKey] = $result;
                    }
                } else {
                    return 
$this->raiseFormulaError("undefined name '$token'");
                }
            }
        }
        
// when we're out of tokens, the stack should have a single element, the final result
        
if ($stack->count() != 1) {
            return 
$this->raiseFormulaError('internal error');
        }
        
$output $stack->pop();
        
$output $output['value'];

        return 
$output;
    }

    
/**
     * @param mixed $operand
     * @param mixed $stack
     *
     * @return bool
     */
    
private function validateBinaryOperand(&$operand, &$stack)
    {
        if (
is_array($operand)) {
            if ((
count($operandCOUNT_RECURSIVE) - count($operand)) == 1) {
                do {
                    
$operand array_pop($operand);
                } while (
is_array($operand));
            }
        }
        
//    Numbers, matrices and booleans can pass straight through, as they're already valid
        
if (is_string($operand)) {
            
//    We only need special validations for the operand if it is a string
            //    Start by stripping off the quotation marks we use to identify true excel string values internally
            
if ($operand '' && $operand[0] == self::FORMULA_STRING_QUOTE) {
                
$operand self::unwrapResult($operand);
            }
            
//    If the string is a numeric value, we treat it as a numeric, so no further testing
            
if (!is_numeric($operand)) {
                
//    If not a numeric, test to see if the value is an Excel error, and so can't be used in normal binary operations
                
if ($operand '' && $operand[0] == '#') {
                    
$stack->push('Value'$operand);
                    
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails($operand));

                    return 
false;
                } elseif (
Engine\FormattedNumber::convertToNumberIfFormatted($operand) === false) {
                    
//    If not a numeric, a fraction or a percentage, then it's a text string, and so can't be used in mathematical binary operations
                    
$stack->push('Error''#VALUE!');
                    
$this->debugLog->writeDebugLog('Evaluation Result is a %s'$this->showTypeDetails('#VALUE!'));

                    return 
false;
                }
            }
        }

        
//    return a true if the value of the operand is one that we can use in normal binary mathematical operations
        
return true;
    }

    
/**
     * @param mixed $operand1
     * @param mixed $operand2
     * @param string $operation
     *
     * @return array
     */
    
private function executeArrayComparison($operand1$operand2$operationStack &$stackbool $recursingArrays)
    {
        
$result = [];
        if (!
is_array($operand2)) {
            
// Operand 1 is an array, Operand 2 is a scalar
            
foreach ($operand1 as $x => $operandData) {
                
$this->debugLog->writeDebugLog('Evaluating Comparison %s %s %s'$this->showValue($operandData), $operation$this->showValue($operand2));
                
$this->executeBinaryComparisonOperation($operandData$operand2$operation$stack);
                
$r $stack->pop();
                
$result[$x] = $r['value'];
            }
        } elseif (!
is_array($operand1)) {
            
// Operand 1 is a scalar, Operand 2 is an array
            
foreach ($operand2 as $x => $operandData) {
                
$this->debugLog->writeDebugLog('Evaluating Comparison %s %s %s'$this->showValue($operand1), $operation$this->showValue($operandData));
                
$this->executeBinaryComparisonOperation($operand1$operandData$operation$stack);
                
$r $stack->pop();
                
$result[$x] = $r['value'];
            }
        } else {
            
// Operand 1 and Operand 2 are both arrays
            
if (!$recursingArrays) {
                
self::checkMatrixOperands($operand1$operand22);
            }
            foreach (
$operand1 as $x => $operandData) {
                
$this->debugLog->writeDebugLog('Evaluating Comparison %s %s %s'$this->showValue($operandData), $operation$this->showValue($operand2[$x]));
                
$this->executeBinaryComparisonOperation($operandData$operand2[$x], $operation$stacktrue);
                
$r $stack->pop();
                
$result[$x] = $r['value'];
            }
        }
        
//    Log the result details
        
$this->debugLog->writeDebugLog('Comparison Evaluation Result is %s'$this->showTypeDetails($result));
        
//    And push the result onto the stack
        
$stack->push('Array'$result);

        return 
$result;
    }

    
/**
     * @param mixed $operand1
     * @param mixed $operand2
     * @param string $operation
     * @param bool $recursingArrays
     *
     * @return mixed
     */
    
private function executeBinaryComparisonOperation($operand1$operand2$operationStack &$stack$recursingArrays false)
    {
        
//    If we're dealing with matrix operations, we want a matrix result
        
if ((is_array($operand1)) || (is_array($operand2))) {
            return 
$this->executeArrayComparison($operand1$operand2$operation$stack$recursingArrays);
        }

        
$result BinaryComparison::compare($operand1$operand2$operation);

        
//    Log the result details
        
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails($result));
        
//    And push the result onto the stack
        
$stack->push('Value'$result);

        return 
$result;
    }

    
/**
     * @param mixed $operand1
     * @param mixed $operand2
     * @param string $operation
     * @param Stack $stack
     *
     * @return bool|mixed
     */
    
private function executeNumericBinaryOperation($operand1$operand2$operation, &$stack)
    {
        
//    Validate the two operands
        
if (
            (
$this->validateBinaryOperand($operand1$stack) === false) ||
            (
$this->validateBinaryOperand($operand2$stack) === false)
        ) {
            return 
false;
        }

        if (
            (
Functions::getCompatibilityMode() != Functions::COMPATIBILITY_OPENOFFICE) &&
            ((
is_string($operand1) && !is_numeric($operand1) && strlen($operand1) > 0) ||
                (
is_string($operand2) && !is_numeric($operand2) && strlen($operand2) > 0))
        ) {
            
$result Information\ExcelError::VALUE();
        } elseif (
is_array($operand1) || is_array($operand2)) {
            
//    Ensure that both operands are arrays/matrices
            
if (is_array($operand1)) {
                foreach (
$operand1 as $key => $value) {
                    
$operand1[$key] = Functions::flattenArray($value);
                }
            }
            if (
is_array($operand2)) {
                foreach (
$operand2 as $key => $value) {
                    
$operand2[$key] = Functions::flattenArray($value);
                }
            }
            [
$rows$columns] = self::checkMatrixOperands($operand1$operand22);

            for (
$row 0$row $rows; ++$row) {
                for (
$column 0$column $columns; ++$column) {
                    if (
$operand1[$row][$column] === null) {
                        
$operand1[$row][$column] = 0;
                    } elseif (!
self::isNumericOrBool($operand1[$row][$column])) {
                        
$operand1[$row][$column] = self::makeError($operand1[$row][$column]);

                        continue;
                    }
                    if (
$operand2[$row][$column] === null) {
                        
$operand2[$row][$column] = 0;
                    } elseif (!
self::isNumericOrBool($operand2[$row][$column])) {
                        
$operand1[$row][$column] = self::makeError($operand2[$row][$column]);

                        continue;
                    }
                    switch (
$operation) {
                        case 
'+':
                            
$operand1[$row][$column] += $operand2[$row][$column];

                            break;
                        case 
'-':
                            
$operand1[$row][$column] -= $operand2[$row][$column];

                            break;
                        case 
'*':
                            
$operand1[$row][$column] *= $operand2[$row][$column];

                            break;
                        case 
'/':
                            if (
$operand2[$row][$column] == 0) {
                                
$operand1[$row][$column] = Information\ExcelError::DIV0();
                            } else {
                                
$operand1[$row][$column] /= $operand2[$row][$column];
                            }

                            break;
                        case 
'^':
                            
$operand1[$row][$column] = $operand1[$row][$column] ** $operand2[$row][$column];

                            break;

                        default:
                            throw new 
Exception('Unsupported numeric binary operation');
                    }
                }
            }
            
$result $operand1;
        } else {
            
//    If we're dealing with non-matrix operations, execute the necessary operation
            
switch ($operation) {
                
//    Addition
                
case '+':
                    
$result $operand1 $operand2;

                    break;
                
//    Subtraction
                
case '-':
                    
$result $operand1 $operand2;

                    break;
                
//    Multiplication
                
case '*':
                    
$result $operand1 $operand2;

                    break;
                
//    Division
                
case '/':
                    if (
$operand2 == 0) {
                        
//    Trap for Divide by Zero error
                        
$stack->push('Error'Information\ExcelError::DIV0());
                        
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails(Information\ExcelError::DIV0()));

                        return 
false;
                    }
                    
$result $operand1 $operand2;

                    break;
                
//    Power
                
case '^':
                    
$result $operand1 ** $operand2;

                    break;

                default:
                    throw new 
Exception('Unsupported numeric binary operation');
            }
        }

        
//    Log the result details
        
$this->debugLog->writeDebugLog('Evaluation Result is %s'$this->showTypeDetails($result));
        
//    And push the result onto the stack
        
$stack->push('Value'$result);

        return 
$result;
    }

    
/**
     * Trigger an error, but nicely, if need be.
     *
     * @return false
     */
    
protected function raiseFormulaError(string $errorMessage)
    {
        
$this->formulaError $errorMessage;
        
$this->cyclicReferenceStack->clear();
        
$suppress /** @scrutinizer ignore-deprecated */ $this->suppressFormulaErrors ?? $this->suppressFormulaErrorsNew;
        if (!
$suppress) {
            throw new 
Exception($errorMessage);
        }

        return 
false;
    }

    
/**
     * Extract range values.
     *
     * @param string $range String based range representation
     * @param Worksheet $worksheet Worksheet
     * @param bool $resetLog Flag indicating whether calculation log should be reset or not
     *
     * @return mixed Array of values in range if range contains more than one element. Otherwise, a single value is returned.
     */
    
public function extractCellRange(&$range 'A1', ?Worksheet $worksheet null$resetLog true)
    {
        
// Return value
        
$returnValue = [];

        if (
$worksheet !== null) {
            
$worksheetName $worksheet->getTitle();

            if (
strpos($range'!') !== false) {
                [
$worksheetName$range] = Worksheet::extractSheetTitle($rangetrue);
                
$worksheet = ($this->spreadsheet === null) ? null $this->spreadsheet->getSheetByName($worksheetName);
            }

            
// Extract range
            
$aReferences Coordinate::extractAllCellReferencesInRange($range);
            
$range "'" $worksheetName "'" '!' $range;
            
$currentCol '';
            
$currentRow 0;
            if (!isset(
$aReferences[1])) {
                
//    Single cell in range
                
sscanf($aReferences[0], '%[A-Z]%d'$currentCol$currentRow);
                if (
$worksheet !== null && $worksheet->cellExists($aReferences[0])) {
                    
$returnValue[$currentRow][$currentCol] = $worksheet->getCell($aReferences[0])->getCalculatedValue($resetLog);
                } else {
                    
$returnValue[$currentRow][$currentCol] = null;
                }
            } else {
                
// Extract cell data for all cells in the range
                
foreach ($aReferences as $reference) {
                    
// Extract range
                    
sscanf($reference'%[A-Z]%d'$currentCol$currentRow);
                    if (
$worksheet !== null && $worksheet->cellExists($reference)) {
                        
$returnValue[$currentRow][$currentCol] = $worksheet->getCell($reference)->getCalculatedValue($resetLog);
                    } else {
                        
$returnValue[$currentRow][$currentCol] = null;
                    }
                }
            }
        }

        return 
$returnValue;
    }

    
/**
     * Extract range values.
     *
     * @param string $range String based range representation
     * @param null|Worksheet $worksheet Worksheet
     * @param bool $resetLog Flag indicating whether calculation log should be reset or not
     *
     * @return mixed Array of values in range if range contains more than one element. Otherwise, a single value is returned.
     */
    
public function extractNamedRange(string &$range 'A1', ?Worksheet $worksheet null$resetLog true)
    {
        
// Return value
        
$returnValue = [];

        if (
$worksheet !== null) {
            if (
strpos($range'!') !== false) {
                [
$worksheetName$range] = Worksheet::extractSheetTitle($rangetrue);
                
$worksheet = ($this->spreadsheet === null) ? null $this->spreadsheet->getSheetByName($worksheetName);
            }

            
// Named range?
            
$namedRange = ($worksheet === null) ? null DefinedName::resolveName($range$worksheet);
            if (
$namedRange === null) {
                return 
Information\ExcelError::REF();
            }

            
$worksheet $namedRange->getWorksheet();
            
$range $namedRange->getValue();
            
$splitRange Coordinate::splitRange($range);
            
//    Convert row and column references
            
if ($worksheet !== null && ctype_alpha($splitRange[0][0])) {
                
$range $splitRange[0][0] . '1:' $splitRange[0][1] . $worksheet->getHighestRow();
            } elseif (
$worksheet !== null && ctype_digit($splitRange[0][0])) {
                
$range 'A' $splitRange[0][0] . ':' $worksheet->getHighestColumn() . $splitRange[0][1];
            }

            
// Extract range
            
$aReferences Coordinate::extractAllCellReferencesInRange($range);
            if (!isset(
$aReferences[1])) {
                
//    Single cell (or single column or row) in range
                
[$currentCol$currentRow] = Coordinate::coordinateFromString($aReferences[0]);
                if (
$worksheet !== null && $worksheet->cellExists($aReferences[0])) {
                    
$returnValue[$currentRow][$currentCol] = $worksheet->getCell($aReferences[0])->getCalculatedValue($resetLog);
                } else {
                    
$returnValue[$currentRow][$currentCol] = null;
                }
            } else {
                
// Extract cell data for all cells in the range
                
foreach ($aReferences as $reference) {
                    
// Extract range
                    
[$currentCol$currentRow] = Coordinate::coordinateFromString($reference);
                    if (
$worksheet !== null && $worksheet->cellExists($reference)) {
                        
$returnValue[$currentRow][$currentCol] = $worksheet->getCell($reference)->getCalculatedValue($resetLog);
                    } else {
                        
$returnValue[$currentRow][$currentCol] = null;
                    }
                }
            }
        }

        return 
$returnValue;
    }

    
/**
     * Is a specific function implemented?
     *
     * @param string $function Function Name
     *
     * @return bool
     */
    
public function isImplemented($function)
    {
        
$function strtoupper($function);
        
$notImplemented = !isset(self::$phpSpreadsheetFunctions[$function]) || (is_array(self::$phpSpreadsheetFunctions[$function]['functionCall']) && self::$phpSpreadsheetFunctions[$function]['functionCall'][1] === 'DUMMY');

        return !
$notImplemented;
    }

    
/**
     * Get a list of all implemented functions as an array of function objects.
     */
    
public static function getFunctions(): array
    {
        return 
self::$phpSpreadsheetFunctions;
    }

    
/**
     * Get a list of implemented Excel function names.
     *
     * @return array
     */
    
public function getImplementedFunctionNames()
    {
        
$returnValue = [];
        foreach (
self::$phpSpreadsheetFunctions as $functionName => $function) {
            if (
$this->isImplemented($functionName)) {
                
$returnValue[] = $functionName;
            }
        }

        return 
$returnValue;
    }

    private function 
addDefaultArgumentValues(array $functionCall, array $args, array $emptyArguments): array
    {
        
$reflector = new ReflectionMethod(implode('::'$functionCall));
        
$methodArguments $reflector->getParameters();

        if (
count($methodArguments) > 0) {
            
// Apply any defaults for empty argument values
            
foreach ($emptyArguments as $argumentId => $isArgumentEmpty) {
                if (
$isArgumentEmpty === true) {
                    
$reflectedArgumentId count($args) - (int) $argumentId 1;
                    if (
                        !
array_key_exists($reflectedArgumentId$methodArguments) ||
                        
$methodArguments[$reflectedArgumentId]->isVariadic()
                    ) {
                        break;
                    }

                    
$args[$argumentId] = $this->getArgumentDefaultValue($methodArguments[$reflectedArgumentId]);
                }
            }
        }

        return 
$args;
    }

    
/**
     * @return null|mixed
     */
    
private function getArgumentDefaultValue(ReflectionParameter $methodArgument)
    {
        
$defaultValue null;

        if (
$methodArgument->isDefaultValueAvailable()) {
            
$defaultValue $methodArgument->getDefaultValue();
            if (
$methodArgument->isDefaultValueConstant()) {
                
$constantName $methodArgument->getDefaultValueConstantName() ?? '';
                
// read constant value
                
if (strpos($constantName'::') !== false) {
                    [
$className$constantName] = explode('::'$constantName);
                    
$constantReflector = new ReflectionClassConstant($className$constantName);

                    return 
$constantReflector->getValue();
                }

                return 
constant($constantName);
            }
        }

        return 
$defaultValue;
    }

    
/**
     * Add cell reference if needed while making sure that it is the last argument.
     *
     * @param bool $passCellReference
     * @param array|string $functionCall
     *
     * @return array
     */
    
private function addCellReference(array $args$passCellReference$functionCall, ?Cell $cell null)
    {
        if (
$passCellReference) {
            if (
is_array($functionCall)) {
                
$className $functionCall[0];
                
$methodName $functionCall[1];

                
$reflectionMethod = new ReflectionMethod($className$methodName);
                
$argumentCount count($reflectionMethod->getParameters());
                while (
count($args) < $argumentCount 1) {
                    
$args[] = null;
                }
            }

            
$args[] = $cell;
        }

        return 
$args;
    }

    
/**
     * @return mixed|string
     */
    
private function evaluateDefinedName(Cell $cellDefinedName $namedRangeWorksheet $cellWorksheetStack $stack)
    {
        
$definedNameScope $namedRange->getScope();
        if (
$definedNameScope !== null && $definedNameScope !== $cellWorksheet) {
            
// The defined name isn't in our current scope, so #REF
            
$result Information\ExcelError::REF();
            
$stack->push('Error'$result$namedRange->getName());

            return 
$result;
        }

        
$definedNameValue $namedRange->getValue();
        
$definedNameType $namedRange->isFormula() ? 'Formula' 'Range';
        
$definedNameWorksheet $namedRange->getWorksheet();

        if (
$definedNameValue[0] !== '=') {
            
$definedNameValue '=' $definedNameValue;
        }

        
$this->debugLog->writeDebugLog('Defined Name is a %s with a value of %s'$definedNameType$definedNameValue);

        
$recursiveCalculationCell = ($definedNameWorksheet !== null && $definedNameWorksheet !== $cellWorksheet)
            ? 
$definedNameWorksheet->getCell('A1')
            : 
$cell;
        
$recursiveCalculationCellAddress $recursiveCalculationCell->getCoordinate();

        
// Adjust relative references in ranges and formulae so that we execute the calculation for the correct rows and columns
        
$definedNameValue self::$referenceHelper->updateFormulaReferencesAnyWorksheet(
            
$definedNameValue,
            
Coordinate::columnIndexFromString($cell->getColumn()) - 1,
            
$cell->getRow() - 1
        
);

        
$this->debugLog->writeDebugLog('Value adjusted for relative references is %s'$definedNameValue);

        
$recursiveCalculator = new self($this->spreadsheet);
        
$recursiveCalculator->getDebugLog()->setWriteDebugLog($this->getDebugLog()->getWriteDebugLog());
        
$recursiveCalculator->getDebugLog()->setEchoDebugLog($this->getDebugLog()->getEchoDebugLog());
        
$result $recursiveCalculator->_calculateFormulaValue($definedNameValue$recursiveCalculationCellAddress$recursiveCalculationCelltrue);

        if (
$this->getDebugLog()->getWriteDebugLog()) {
            
$this->debugLog->mergeDebugLog(array_slice($recursiveCalculator->getDebugLog()->getLog(), 3));
            
$this->debugLog->writeDebugLog('Evaluation Result for Named %s %s is %s'$definedNameType$namedRange->getName(), $this->showTypeDetails($result));
        }

        
$stack->push('Defined Name'$result$namedRange->getName());

        return 
$result;
    }

    public function 
setSuppressFormulaErrors(bool $suppressFormulaErrors): void
    
{
        
$this->suppressFormulaErrorsNew $suppressFormulaErrors;
    }

    public function 
getSuppressFormulaErrors(): bool
    
{
        return 
$this->suppressFormulaErrorsNew;
    }

    
/** @param mixed $arg */
    
private static function doNothing($arg): bool
    
{
        return (bool) 
$arg;
    }

    
/**
     * @param mixed $operand1
     *
     * @return mixed
     */
    
private static function boolToString($operand1)
    {
        if (
is_bool($operand1)) {
            
$operand1 = ($operand1) ? self::$localeBoolean['TRUE'] : self::$localeBoolean['FALSE'];
        } elseif (
$operand1 === null) {
            
$operand1 '';
        }

        return 
$operand1;
    }

    
/** @param mixed $operand */
    
private static function isNumericOrBool($operand): bool
    
{
        return 
is_numeric($operand) || is_bool($operand);
    }

    
/** @param mixed $operand */
    
private static function makeError($operand ''): string
    
{
        return 
Information\ErrorValue::isError($operand) ? $operand Information\ExcelError::VALUE();
    }
}

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