File: Formula.cpp

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/* Formula.cpp
 *
 * Copyright (C) 1992-2011 Paul Boersma
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 * See the GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#include <ctype.h>
#include <time.h>
#if defined (UNIX)
	#include <sys/stat.h>
#endif
#include "NUM.h"
#include "NUM2.h"
#include "regularExp.h"
#include "Formula.h"
#include "Interpreter.h"
#include "Ui.h"
#include "praatP.h"
#include "UnicodeData.h"
#include "UiPause.h"
#include "DemoEditor.h"

#undef our
#define our ((Data_Table) my methods) ->
#undef your
#define your ((Data_Table) thy methods) ->

static Interpreter theInterpreter, theLocalInterpreter;
static Data theSource;
static const wchar_t *theExpression;
static int theExpressionType, theOptimize;

static struct Formula_NumericArray theZeroNumericArray = { 0, 0, NULL };

typedef struct structFormulaInstruction {
	int symbol;
	int position;
	union {
		double number;
		int label;
		wchar_t *string;
		//struct Formula_NumericArray numericArray;
		Data object;
		InterpreterVariable variable;
	} content;
} *FormulaInstruction;

static FormulaInstruction lexan, parse;
static int ilabel, ilexan, iparse, numberOfInstructions, numberOfStringConstants;

enum { GEENSYMBOOL_,

/* First, all symbols after which "-" is unary. */
/* The list ends with "MINUS_" itself. */

	/* Haakjes-openen. */
	IF_, THEN_, ELSE_, HAAKJEOPENEN_, RECHTEHAAKOPENEN_, KOMMA_, FROM_, TO_,
	/* Operatoren met boolean resultaat. */
	OR_, AND_, NOT_, EQ_, NE_, LE_, LT_, GE_, GT_,
	/* Operatoren met reeel resultaat. */
	ADD_, SUB_, MUL_, RDIV_, IDIV_, MOD_, POWER_, CALL_, MINUS_,

/* Then, the symbols after which "-" is binary. */

	/* Haakjes-sluiten. */
	ENDIF_, FI_, HAAKJESLUITEN_, RECHTEHAAKSLUITEN_,
	/* Dingen met een waarde. */
	#define LOW_VALUE  NUMBER_
		NUMBER_, NUMBER_PI_, NUMBER_E_, NUMBER_UNDEFINED_,
		/* Attributes of objects. */
		#define LOW_ATTRIBUTE  XMIN_
			XMIN_, XMAX_, YMIN_, YMAX_, NX_, NY_, DX_, DY_,
			ROW_, COL_, NROW_, NCOL_, ROWSTR_, COLSTR_, Y_, X_,
		#define HIGH_ATTRIBUTE  X_
	#define HIGH_VALUE  HIGH_ATTRIBUTE

	SELF_, SELFSTR_, OBJECT_, OBJECTSTR_, MATRIKS_, MATRIKSSTR_,
	STOPWATCH_,

/* The following symbols can be followed by "-" only if they are a variable. */

	/* Functions of 1 variable; if you add, update the #defines. */
	#define LOW_FUNCTION_1  ABS_
		ABS_, ROUND_, FLOOR_, CEILING_, SQRT_, SIN_, COS_, TAN_, ARCSIN_, ARCCOS_, ARCTAN_, SINC_, SINCPI_,
		EXP_, SINH_, COSH_, TANH_, ARCSINH_, ARCCOSH_, ARCTANH_,
		SIGMOID_, INV_SIGMOID_, ERF_, ERFC_, GAUSS_P_, GAUSS_Q_, INV_GAUSS_Q_,
		RANDOM_POISSON_, LOG2_, LN_, LOG10_, LN_GAMMA_,
		HERTZ_TO_BARK_, BARK_TO_HERTZ_, PHON_TO_DIFFERENCE_LIMENS_, DIFFERENCE_LIMENS_TO_PHON_,
		HERTZ_TO_MEL_, MEL_TO_HERTZ_, HERTZ_TO_SEMITONES_, SEMITONES_TO_HERTZ_,
		ERB_, HERTZ_TO_ERB_, ERB_TO_HERTZ_,
	#define HIGH_FUNCTION_1  ERB_TO_HERTZ_

	/* Functions of 2 variables; if you add, update the #defines. */
	#define LOW_FUNCTION_2  ARCTAN2_
		ARCTAN2_, RANDOM_UNIFORM_, RANDOM_INTEGER_, RANDOM_GAUSS_,
		CHI_SQUARE_P_, CHI_SQUARE_Q_, INCOMPLETE_GAMMAP_,
		INV_CHI_SQUARE_Q_, STUDENT_P_, STUDENT_Q_, INV_STUDENT_Q_,
		BETA_, BETA2_, BESSEL_I_, BESSEL_K_, LN_BETA_,
		SOUND_PRESSURE_TO_PHON_, OBJECTS_ARE_IDENTICAL_,
	#define HIGH_FUNCTION_2  OBJECTS_ARE_IDENTICAL_

	/* Functions of 3 variables; if you add, update the #defines. */
	#define LOW_FUNCTION_3  FISHER_P_
		FISHER_P_, FISHER_Q_, INV_FISHER_Q_,
		BINOMIAL_P_, BINOMIAL_Q_, INCOMPLETE_BETA_, INV_BINOMIAL_P_, INV_BINOMIAL_Q_,
	#define HIGH_FUNCTION_3  INV_BINOMIAL_Q_

	/* Functions of a variable number of variables; if you add, update the #defines. */
	#define LOW_FUNCTION_N  MIN_
		MIN_, MAX_, IMIN_, IMAX_,
		LEFTSTR_, RIGHTSTR_, MIDSTR_,
		SELECTED_, SELECTEDSTR_, NUMBER_OF_SELECTED_,
		BEGIN_PAUSE_FORM_, PAUSE_FORM_ADD_REAL_, PAUSE_FORM_ADD_POSITIVE_, PAUSE_FORM_ADD_INTEGER_, PAUSE_FORM_ADD_NATURAL_,
		PAUSE_FORM_ADD_WORD_, PAUSE_FORM_ADD_SENTENCE_, PAUSE_FORM_ADD_TEXT_, PAUSE_FORM_ADD_BOOLEAN_,
		PAUSE_FORM_ADD_CHOICE_, PAUSE_FORM_ADD_OPTION_MENU_, PAUSE_FORM_ADD_OPTION_,
		PAUSE_FORM_ADD_COMMENT_, END_PAUSE_FORM_,
		CHOOSE_READ_FILESTR_, CHOOSE_WRITE_FILESTR_, CHOOSE_DIRECTORYSTR_,
		DEMO_WINDOW_TITLE_, DEMO_SHOW_, DEMO_WAIT_FOR_INPUT_, DEMO_INPUT_, DEMO_CLICKED_IN_,
		DEMO_CLICKED_, DEMO_X_, DEMO_Y_, DEMO_KEY_PRESSED_, DEMO_KEY_,
		DEMO_SHIFT_KEY_PRESSED_, DEMO_COMMAND_KEY_PRESSED_, DEMO_OPTION_KEY_PRESSED_, DEMO_EXTRA_CONTROL_KEY_PRESSED_,
		ZERO_NUMAR_, LINEAR_NUMAR_, RANDOM_UNIFORM_NUMAR_, RANDOM_INTEGER_NUMAR_, RANDOM_GAUSS_NUMAR_,
		NUMBER_OF_ROWS_, NUMBER_OF_COLUMNS_,
	#define HIGH_FUNCTION_N  NUMBER_OF_COLUMNS_

	/* String functions. */
	#define LOW_STRING_FUNCTION  LOW_FUNCTION_STRNUM
	#define LOW_FUNCTION_STRNUM  LENGTH_
		LENGTH_, FILE_READABLE_, DELETE_FILE_, CREATE_DIRECTORY_, VARIABLE_EXISTS_,
	#define HIGH_FUNCTION_STRNUM  VARIABLE_EXISTS_
		DATESTR_,
		ENVIRONMENTSTR_, INDEX_, RINDEX_,
		STARTS_WITH_, ENDS_WITH_, REPLACESTR_, INDEX_REGEX_, RINDEX_REGEX_, REPLACE_REGEXSTR_,
		EXTRACT_NUMBER_, EXTRACT_WORDSTR_, EXTRACT_LINESTR_,
		FIXEDSTR_, PERCENTSTR_,
	#define HIGH_STRING_FUNCTION  PERCENTSTR_

	/* Range functions. */
	#define LOW_RANGE_FUNCTION  SUM_
		SUM_,
	#define HIGH_RANGE_FUNCTION  SUM_

	#define LOW_FUNCTION  LOW_FUNCTION_1
	#define HIGH_FUNCTION  HIGH_RANGE_FUNCTION

	/* Membership operator. */
	PERIOD_,
	#define hoogsteInvoersymbool  PERIOD_

/* Symbols introduced by the parser. */

	TRUE_, FALSE_,
	GOTO_, IFTRUE_, IFFALSE_, INCREMENT_GREATER_GOTO_,
	LABEL_,
	DECREMENT_AND_ASSIGN_, ADD_3DOWN_, POP_2_,
	NUMERIC_ARRAY_ELEMENT_, VARIABLE_REFERENCE_,
	SELF0_, SELFSTR0_,
	OBJECTCELL0_, OBJECTCELLSTR0_, OBJECTCELL1_, OBJECTCELLSTR1_, OBJECTCELL2_, OBJECTCELLSTR2_,
	OBJECTLOCATION0_, OBJECTLOCATIONSTR0_, OBJECTLOCATION1_, OBJECTLOCATIONSTR1_, OBJECTLOCATION2_, OBJECTLOCATIONSTR2_,
	SELFMATRIKS1_, SELFMATRIKSSTR1_, SELFMATRIKS2_, SELFMATRIKSSTR2_,
	SELFFUNKTIE1_, SELFFUNKTIESTR1_, SELFFUNKTIE2_, SELFFUNKTIESTR2_,
	MATRIKS0_, MATRIKSSTR0_, MATRIKS1_, MATRIKSSTR1_, MATRIKS2_, MATRIKSSTR2_,
	FUNKTIE0_, FUNKTIESTR0_, FUNKTIE1_, FUNKTIESTR1_, FUNKTIE2_, FUNKTIESTR2_,
	SQR_,

/* Symbols introduced by lexical analysis. */

	STRING_,
	NUMERIC_VARIABLE_, STRING_VARIABLE_, NUMERIC_ARRAY_VARIABLE_, STRING_ARRAY_VARIABLE_,
	VARIABLE_NAME_, INDEXED_NUMERIC_VARIABLE_, INDEXED_STRING_VARIABLE_,
	END_
	#define hoogsteSymbool END_
};

/* The names that start with an underscore (_) do not occur in the formula text: */
/* they are used in error messages and in debugging (see Formula_print). */

static const wchar_t *Formula_instructionNames [1 + hoogsteSymbool] = { L"",
	L"if", L"then", L"else", L"(", L"[", L",", L"from", L"to",
	L"or", L"and", L"not", L"=", L"<>", L"<=", L"<", L">=", L">",
	L"+", L"-", L"*", L"/", L"div", L"mod", L"^", L"_call", L"_neg",
	L"endif", L"fi", L")", L"]",
	L"a number", L"pi", L"e", L"undefined",
	L"xmin", L"xmax", L"ymin", L"ymax", L"nx", L"ny", L"dx", L"dy",
	L"row", L"col", L"nrow", L"ncol", L"row$", L"col$", L"y", L"x",
	L"self", L"self$", L"object", L"object$", L"_matriks", L"_matriks$",
	L"stopwatch",
	L"abs", L"round", L"floor", L"ceiling", L"sqrt", L"sin", L"cos", L"tan", L"arcsin", L"arccos", L"arctan", L"sinc", L"sincpi",
	L"exp", L"sinh", L"cosh", L"tanh", L"arcsinh", L"arccosh", L"arctanh",
	L"sigmoid", L"invSigmoid", L"erf", L"erfc", L"gaussP", L"gaussQ", L"invGaussQ",
	L"randomPoisson", L"log2", L"ln", L"log10", L"lnGamma",
	L"hertzToBark", L"barkToHertz", L"phonToDifferenceLimens", L"differenceLimensToPhon",
	L"hertzToMel", L"melToHertz", L"hertzToSemitones", L"semitonesToHertz",
	L"erb", L"hertzToErb", L"erbToHertz",
	L"arctan2", L"randomUniform", L"randomInteger", L"randomGauss",
	L"chiSquareP", L"chiSquareQ", L"incompleteGammaP", L"invChiSquareQ", L"studentP", L"studentQ", L"invStudentQ",
	L"beta", L"beta2", L"besselI", L"besselK", L"lnBeta",
	L"soundPressureToPhon", L"objectsAreIdentical",
	L"fisherP", L"fisherQ", L"invFisherQ",
	L"binomialP", L"binomialQ", L"incompleteBeta", L"invBinomialP", L"invBinomialQ",

	L"min", L"max", L"imin", L"imax",
	L"left$", L"right$", L"mid$",
	L"selected", L"selected$", L"numberOfSelected",
	L"beginPause", L"real", L"positive", L"integer", L"natural",
	L"word", L"sentence", L"text", L"boolean",
	L"choice", L"optionMenu", L"option",
	L"comment", L"endPause",
	L"chooseReadFile$", L"chooseWriteFile$", L"chooseDirectory$",
	L"demoWindowTitle", L"demoShow", L"demoWaitForInput", L"demoInput", L"demoClickedIn",
	L"demoClicked", L"demoX", L"demoY", L"demoKeyPressed", L"demoKey$",
	L"demoShiftKeyPressed", L"demoCommandKeyPressed", L"demoOptionKeyPressed", L"demoExtraControlKeyPressed",
	L"zero#", L"linear#", L"randomUniform#", L"randomInteger#", L"randomGauss#",
	L"numberOfRows", L"numberOfColumns",

	L"length", L"fileReadable",	L"deleteFile", L"createDirectory", L"variableExists",
	L"date$",
	L"environment$", L"index", L"rindex",
	L"startsWith", L"endsWith", L"replace$", L"index_regex", L"rindex_regex", L"replace_regex$",
	L"extractNumber", L"extractWord$", L"extractLine$",
	L"fixed$", L"percent$",
	L"sum",
	L".",
	L"_true", L"_false",
	L"_goto", L"_iftrue", L"_iffalse", L"_incrementGreaterGoto",
	L"_label",
	L"_decrementAndAssign", L"_add3Down", L"_pop2",
	L"_numericArrayElement", L"_variableReference",
	L"_self0", L"_self0$",
	L"_objectcell0", L"_objectcell0$", L"_objectcell1", L"_objectcell1$", L"_objectcell2", L"_objectcell2$",
	L"_objectlocation0", L"_objectlocation0$", L"_objectlocation1", L"_objectlocation1$", L"_objectlocation2", L"_objectlocation2$",
	L"_selfmatriks1", L"_selfmatriks1$", L"_selfmatriks2", L"_selfmatriks2$",
	L"_selffunktie1", L"_selffunktie1$", L"_selffunktie2", L"_selffunktie2$",
	L"_matriks0", L"_matriks0$", L"_matriks1", L"_matriks1$", L"_matriks2", L"_matriks2$",
	L"_funktie0", L"_funktie0$", L"_funktie1", L"_funktie1$", L"_funktie2", L"_funktie2$",
	L"_square",
	L"_string",
	L"a numeric variable", L"a string variable", L"a numeric array variable", L"a string array variable",
	L"a variable name", L"an indexed numeric variable", L"an indexed string variable",
	L"the end of the formula"
};

#define nieuwlabel (-- ilabel)
#define nieuwlees (lexan [++ ilexan]. symbol)
#define oudlees  (-- ilexan)

static void formulefout (const wchar *message, int position) {
	static MelderString truncatedExpression = { 0 };
	MelderString_ncopy (& truncatedExpression, theExpression, position + 1);
	Melder_throw (message, L":\n" L_LEFT_GUILLEMET L" ", truncatedExpression.string);
}

static const wchar *languageNameCompare_searchString;

static int languageNameCompare (const void *first, const void *second) {
	int i = * (int *) first, j = * (int *) second;
	return wcscmp (i == 0 ? languageNameCompare_searchString : Formula_instructionNames [i],
		j == 0 ? languageNameCompare_searchString : Formula_instructionNames [j]);
}

static int Formula_hasLanguageName (const wchar *f) {
	static int *index;
	if (index == NULL) {
		index = NUMvector <int> (1, hoogsteInvoersymbool);
		for (int tok = 1; tok <= hoogsteInvoersymbool; tok ++) {
			index [tok] = tok;
		}
		qsort (& index [1], hoogsteInvoersymbool, sizeof (int), languageNameCompare);
	}
	if (index == NULL) {   /* Linear search. */
		for (int tok = 1; tok <= hoogsteInvoersymbool; tok ++) {
			if (wcsequ (f, Formula_instructionNames [tok])) return tok;
		}
	} else {   /* Binary search. */
		int dummy = 0, *found;
		languageNameCompare_searchString = f;
		found = (int *) bsearch (& dummy, & index [1], hoogsteInvoersymbool, sizeof (int), languageNameCompare);
		if (found != NULL) return *found;
	}
	return 0;
}

static void Formula_lexan (void) {
/*
	Purpose:
		translate the formula text into a series of symbols.
	Return:
		0 in case of error, otherwise 1.
	Postcondition:
		if result != 0, then the last symbol is L"END_".
	Example:
		the text L"x*7" yields 5 symbols:
			lexan [0] is empty;
			lexan [1]. symbol = X_;
			lexan [2]. symbol = MUL_;
			lexan [3]. symbol = NUMBER_;
			lexan [3]. number = 7.00000000e+00;
			lexan [4]. symbol = END_;
*/
	int kar;   /* The character most recently read from theExpression. */
	int ikar = -1;   /* The position of that character in theExpression. */
#define nieuwkar kar = theExpression [++ ikar]
#define oudkar -- ikar

	int itok = 0;   /* Position of most recent symbol in "lexan". */
#define nieuwtok(s)  { lexan [++ itok]. symbol = s; lexan [itok]. position = ikar; }
#define tokgetal(g)  lexan [itok]. content.number = (g)
#define tokmatriks(m)  lexan [itok]. content.object = (m)

	static MelderString token = { 0 };   /* String to collect a symbol name in. */
#define stokaan MelderString_empty (& token);
#define stokkar { MelderString_appendCharacter (& token, kar); nieuwkar; }
#define stokuit (void) 0

	ilexan = iparse = ilabel = numberOfStringConstants = 0;
	do {
		nieuwkar;
		if (kar == ' ' || kar == '\t') {
			;   /* Ignore spaces and tabs. */
		} else if (kar == '\0') {
			nieuwtok (END_)
		} else if (kar >= '0' && kar <= '9') {
			stokaan;
			do stokkar while (kar >= '0' && kar <= '9');
			if (kar == '.') do stokkar while (kar >= '0' && kar <= '9');
			if (kar == 'e' || kar == 'E') {
				kar = 'e'; stokkar
				if (kar == '-') stokkar
				else if (kar == '+') nieuwkar;
				if (! (kar >= '0' && kar <= '9'))
					formulefout (L"Missing exponent", ikar);
				do stokkar while (kar >= '0' && kar <= '9');
			}
			if (kar == '%') stokkar
			stokuit;
			oudkar;
			nieuwtok (NUMBER_)
			tokgetal (Melder_atof (token.string));
		} else if ((kar >= 'a' && kar <= 'z') || kar >= 192 || (kar == '.' &&
				((theExpression [ikar + 1] >= 'a' && theExpression [ikar + 1] <= 'z') || theExpression [ikar + 1] >= 192)
				&& (itok == 0 || (lexan [itok]. symbol != MATRIKS_ && lexan [itok]. symbol != MATRIKSSTR_)))) {
			int tok;
			bool isString = false, isArray = false;
			stokaan;
			do stokkar while ((kar >= 'A' && kar <= 'Z') || (kar >= 'a' && kar <= 'z') || kar >= 192 || (kar >= '0' && kar <= '9') || kar == '_' || kar == '.');
			if (kar == '$') {
				stokkar
				isString = true;
			}
			if (kar == '#') {
				stokkar
				isArray = true;
			}
			stokuit;
			oudkar;
			/*
			 * 'token' now contains a word, possibly ending in a dollar or number sign;
			 * it could be a variable name, a function name, both, or a procedure name.
			 * Try a language or function name first.
			 */
			tok = Formula_hasLanguageName (token.string);
			if (tok) {
				/*
				 * We have a language name or function name. It MIGHT be meant to be a variable name, though,
				 * regarding the large and expanding number of language names.
				 */
				/*
				 * First the constants. They are reserved words and can never be variable names.
				 */
				if (tok == NUMBER_PI_) {
					nieuwtok (NUMBER_)
					tokgetal (NUMpi);
				} else if (tok == NUMBER_E_) {
					nieuwtok (NUMBER_)
					tokgetal (NUMe);
				} else if (tok == NUMBER_UNDEFINED_) {
					nieuwtok (NUMBER_)
					tokgetal (NUMundefined);
				/*
				 * One very common language name must be converted to a synonym.
				 */
				} else if (tok == FI_) {
					nieuwtok (ENDIF_)
				/*
				 * Is it a function name? These may be ambiguous.
				 */
				} else if (tok >= LOW_FUNCTION && tok <= HIGH_FUNCTION) {
					/*
					 * Look ahead to find out whether the next token is a left parenthesis.
					 */
					int jkar;
					jkar = ikar + 1;
					while (theExpression [jkar] == ' ' || theExpression [jkar] == '\t') jkar ++;
					if (theExpression [jkar] == '(') {
						nieuwtok (tok)   /* This must be a function name. */
					} else {
						/*
						 * This could be a variable with the same name as a function.
						 */
						InterpreterVariable var = Interpreter_hasVariable (theInterpreter, token.string);
						if (var == NULL) {
							nieuwtok (VARIABLE_NAME_)
							lexan [itok]. content.string = Melder_wcsdup_f (token.string);
							numberOfStringConstants ++;
						} else {
							if (isArray) {
								if (isString) {
									nieuwtok (STRING_ARRAY_VARIABLE_)
								} else {
									nieuwtok (NUMERIC_ARRAY_VARIABLE_)
								}
							} else {
								if (isString) {
									nieuwtok (STRING_VARIABLE_)
								} else {
									nieuwtok (NUMERIC_VARIABLE_)
								}
							}
							lexan [itok]. content.variable = var;
						}
					}
				/*
				 * Not a function name.
				 * Must be a language name (if, then, else, endif, or, and, not, div, mod, x, ncol, stopwatch).
				 * Some can be used as variable names (x, ncol...).
				 */
				} else if (tok >= LOW_ATTRIBUTE && tok <= HIGH_ATTRIBUTE) {
					/*
					 * Look back to find out whether this is an attribute.
					 */
					if (itok > 0 && lexan [itok]. symbol == PERIOD_) {
						/*
						 * This must be an attribute that follows a period.
						 */
						nieuwtok (tok)
					} else if (theSource) {
						/*
						 * Look for ambiguity.
						 */
						if (Interpreter_hasVariable (theInterpreter, token.string))
							Melder_throw (
								L_LEFT_GUILLEMET, token.string,
								L_RIGHT_GUILLEMET " is ambiguous: a variable or an attribute of the current object. "
								"Please change variable name.");
						if (tok == ROW_ || tok == COL_ || tok == X_ || tok == Y_) {
							nieuwtok (tok)
						} else {
							nieuwtok (MATRIKS_)
							tokmatriks (theSource);
							nieuwtok (PERIOD_)
							nieuwtok (tok)
						}
					} else {
						/*
						 * This must be a variable, since there is no "current object" here.
						 */
						InterpreterVariable var = Interpreter_hasVariable (theInterpreter, token.string);
						if (var == NULL) {
							nieuwtok (VARIABLE_NAME_)
							lexan [itok]. content.string = Melder_wcsdup_f (token.string);
							numberOfStringConstants ++;
						} else {
							if (isArray) {
								if (isString) {
									nieuwtok (STRING_ARRAY_VARIABLE_)
								} else {
									nieuwtok (NUMERIC_ARRAY_VARIABLE_)
								}
							} else {
								if (isString) {
									nieuwtok (STRING_VARIABLE_)
								} else {
									nieuwtok (NUMERIC_VARIABLE_)
								}
							}
							lexan [itok]. content.variable = var;
						}
					}
				} else {
					nieuwtok (tok)   /* This must be a language name. */
				}
			} else {
				/*
				 * token.string is not a language name
				 */
				int jkar = ikar + 1;
				while (theExpression [jkar] == ' ' || theExpression [jkar] == '\t') jkar ++;
				if (theExpression [jkar] == '(') {
					Melder_throw (
						"Unknown function " L_LEFT_GUILLEMET, token.string, L_RIGHT_GUILLEMET " in formula.");
				} else if (theExpression [jkar] == '[' && ! isArray) {
					if (isString) {
						nieuwtok (INDEXED_STRING_VARIABLE_)
					} else {
						nieuwtok (INDEXED_NUMERIC_VARIABLE_)
					}
					lexan [itok]. content.string = Melder_wcsdup_f (token.string);
					numberOfStringConstants ++;
				} else {
					InterpreterVariable var = Interpreter_hasVariable (theInterpreter, token.string);
					if (var == NULL) {
						nieuwtok (VARIABLE_NAME_)
						lexan [itok]. content.string = Melder_wcsdup_f (token.string);
						numberOfStringConstants ++;
					} else {
						if (isArray) {
							if (isString) {
								nieuwtok (STRING_ARRAY_VARIABLE_)
							} else {
								nieuwtok (NUMERIC_ARRAY_VARIABLE_)
							}
						} else {
							if (isString) {
								nieuwtok (STRING_VARIABLE_)
							} else {
								nieuwtok (NUMERIC_VARIABLE_)
							}
						}
						lexan [itok]. content.variable = var;
					}
				}
			}
		} else if (kar >= 'A' && kar <= 'Z') {
			int endsInDollarSign = FALSE;
			wchar_t *underscore;
			stokaan;
			do stokkar while (isalnum (kar) || kar == '_');
			if (kar == '$') { stokkar endsInDollarSign = TRUE; }
			stokuit;
			oudkar;
			/*
			 * 'token' now contains a word that could be an object name.
			 */
			underscore = wcschr (token.string, '_');
			if (wcsequ (token.string, L"Self")) {
				if (theSource == NULL)
					formulefout (L"Cannot use \"Self\" if there is no current object.", ikar);
				nieuwtok (MATRIKS_)
				tokmatriks (theSource);
			} else if (wcsequ (token.string, L"Self$")) {
				if (theSource == NULL)
					formulefout (L"Cannot use \"Self$\" if there is no current object.", ikar);
				nieuwtok (MATRIKSSTR_)
				tokmatriks (theSource);
			} else if (underscore == NULL) {
				Melder_throw (
					"Unknown symbol " L_LEFT_GUILLEMET , token.string,
					L_RIGHT_GUILLEMET " in formula "
					"(variables start with lower case; object names contain an underscore).");
			} else if (wcsnequ (token.string, L"Object_", 7)) {
				long uniqueID = wcstol (token.string + 7, NULL, 10);
				int i = theCurrentPraatObjects -> n;
				while (i > 0 && uniqueID != theCurrentPraatObjects -> list [i]. id)
					i --;
				if (i == 0)
					formulefout (L"No such object (note: variables start with lower case)", ikar);
				nieuwtok (endsInDollarSign ? MATRIKSSTR_ : MATRIKS_)
				tokmatriks ((Data) theCurrentPraatObjects -> list [i]. object);
			} else {
				int i = theCurrentPraatObjects -> n;
				*underscore = ' ';
				if (endsInDollarSign) token.string [-- token.length] = '\0';
				while (i > 0 && ! wcsequ (token.string, theCurrentPraatObjects -> list [i]. name))
					i --;
				if (i == 0)
					formulefout (L"No such object (note: variables start with lower case)", ikar);
				nieuwtok (endsInDollarSign ? MATRIKSSTR_ : MATRIKS_)
				tokmatriks ((Data) theCurrentPraatObjects -> list [i]. object);
			}
		} else if (kar == '(') {
			nieuwtok (HAAKJEOPENEN_)
		} else if (kar == ')') {
			nieuwtok (HAAKJESLUITEN_)
		} else if (kar == '+') {
			nieuwtok (ADD_)
		} else if (kar == '-') {
			if (itok == 0 || lexan [itok]. symbol <= MINUS_) {
				nieuwtok (MINUS_)
			} else {
				nieuwtok (SUB_)
			}
		} else if (kar == '*') {
			nieuwkar;
			if (kar == '*') {
				nieuwtok (POWER_)   /* "**" = "^" */
			} else {
				oudkar;
				nieuwtok (MUL_)
			}
		} else if (kar == '/') {
			nieuwkar;
			if (kar == '=') {
				nieuwtok (NE_)   /* "/=" = "<>" */
			} else {
				oudkar;
				nieuwtok (RDIV_)
			}
		} else if (kar == '=') {
			nieuwtok (EQ_)   /* "=" */
			nieuwkar;
			if (kar != '=') {
				oudkar;   /* "==" = "=" */
			}
		} else if (kar == '>') {
			nieuwkar;
			if (kar == '=') {
				nieuwtok (GE_)
			} else {
				oudkar;
				nieuwtok (GT_)
			}
		} else if (kar == '<') {
			nieuwkar;
			if (kar == '=') {
				nieuwtok (LE_)
			} else if (kar == '>') {
				nieuwtok (NE_)
			} else {
				oudkar;
				nieuwtok (LT_)
			}
		} else if (kar == '!') {
			nieuwkar;
			if (kar == '=') {
				nieuwtok (NE_)   /* "!=" = "<>" */
			} else {
				oudkar;
				nieuwtok (NOT_)
			}
		} else if (kar == ',') {
			nieuwtok (KOMMA_)
		} else if (kar == ';') {
			nieuwtok (END_)
		} else if (kar == '^') {
			nieuwtok (POWER_)
		} else if (kar == '@') {
			do {
				nieuwkar;
			} while (kar == ' ' || kar == '\t');
			stokaan;
			do stokkar while ((kar >= 'A' && kar <= 'Z') || (kar >= 'a' && kar <= 'z') || kar >= 192 || (kar >= '0' && kar <= '9') || kar == '_' || kar == '.');
			stokuit;
			oudkar;
			nieuwtok (CALL_)
			lexan [itok]. content.string = Melder_wcsdup_f (token.string);
			numberOfStringConstants ++;
		} else if (kar == '\"') {
			/*
			 * String constant.
			 */
			nieuwkar;
			stokaan;
			for (;;) {
				if (kar == '\0')
					formulefout (L"No closing quote in string constant", ikar);
				if (kar == '\"') {
					nieuwkar;
					if (kar == '\"') stokkar
					else break;
				} else {
					stokkar
				}
			}
			stokuit;
			oudkar;
			nieuwtok (STRING_)
			lexan [itok]. content.string = Melder_wcsdup_f (token.string);
			numberOfStringConstants ++;
		} else if (kar == '|') {
			nieuwtok (OR_)   /* "|" = "or" */
			nieuwkar;
			if (kar != '|') {
				oudkar;   /* "||" = "or" */
			}
		} else if (kar == '&') {
			nieuwtok (AND_)   /* "&" = "and" */
			nieuwkar;
			if (kar != '&') {
				oudkar;   /* "&&" = "and" */
			}
		} else if (kar == '[') {
			nieuwtok (RECHTEHAAKOPENEN_)
		} else if (kar == ']') {
			nieuwtok (RECHTEHAAKSLUITEN_)
		} else if (kar == '.') {
			nieuwtok (PERIOD_)
		} else {
			formulefout (L"Unknown symbol", ikar);
		}
	} while (lexan [itok]. symbol != END_);
}

static void pas (int symbol) {
	if (symbol == nieuwlees) {
		return;   // success
	} else {
		static MelderString melding = { 0 };
		MelderString_empty (& melding);
		const wchar *symbolName1 = Formula_instructionNames [symbol];
		const wchar *symbolName2 = Formula_instructionNames [lexan [ilexan]. symbol];
		bool needQuotes1 = wcschr (symbolName1, ' ') == NULL;
		bool needQuotes2 = wcschr (symbolName2, ' ') == NULL;
		MelderString_append (& melding,
			L"Expected ", needQuotes1 ? L"\"" : NULL, symbolName1, needQuotes1 ? L"\"" : NULL,
			L", but found ", needQuotes2 ? L"\"" : NULL, symbolName2, needQuotes2 ? L"\"" : NULL);
		formulefout (melding.string, lexan [ilexan]. position);
	}
}

#define nieuwontleed(s)  parse [++ iparse]. symbol = (s)
#define parsenumber(g)  parse [iparse]. content.number = (g)
#define ontleedlabel(l)  parse [iparse]. content.label = (l)

static void parseExpression (void);

static void parsePowerFactor (void) {
	int symbol = nieuwlees;

	if (symbol >= LOW_VALUE && symbol <= HIGH_VALUE) {
		nieuwontleed (symbol);
		if (symbol == NUMBER_) parsenumber (lexan [ilexan]. content.number);
		return;
	}

	if (symbol == STRING_) {
		nieuwontleed (symbol);
		parse [iparse]. content.string = lexan [ilexan]. content.string;   // reference copy!
		return;
	}

	if (symbol == NUMERIC_VARIABLE_ || symbol == STRING_VARIABLE_) {
		nieuwontleed (symbol);
		parse [iparse]. content.variable = lexan [ilexan]. content.variable;
		return;
	}

	if (symbol == INDEXED_NUMERIC_VARIABLE_ || symbol == INDEXED_STRING_VARIABLE_) {
		wchar_t *var = lexan [ilexan]. content.string;   // Save before incrementing ilexan.
		if (nieuwlees == RECHTEHAAKOPENEN_) {
			int n = 0;
			if (nieuwlees != RECHTEHAAKSLUITEN_) {
				oudlees;
				parseExpression ();
				n ++;
				while (nieuwlees == KOMMA_) {
					parseExpression ();
					n ++;
				}
				oudlees;
				pas (RECHTEHAAKSLUITEN_);
			}
			nieuwontleed (NUMBER_); parsenumber (n);
			nieuwontleed (symbol);
		} else {
			Melder_fatal ("Formula:parsePowerFactor (indexed variable): No '['; cannot happen.");
		}
		parse [iparse]. content.string = var;
		return;
	}

	if (symbol == NUMERIC_ARRAY_VARIABLE_) {
		InterpreterVariable var = lexan [ilexan]. content.variable;   // Save before incrementing ilexan.
		if (nieuwlees == RECHTEHAAKOPENEN_) {
			int n = 0;
			if (nieuwlees != RECHTEHAAKSLUITEN_) {
				oudlees;
				parseExpression ();
				n ++;
				while (nieuwlees == KOMMA_) {
					parseExpression ();
					n ++;
				}
				oudlees;
				pas (RECHTEHAAKSLUITEN_);
			}
			nieuwontleed (NUMBER_); parsenumber (n);
			nieuwontleed (NUMERIC_ARRAY_ELEMENT_);
		} else {
			oudlees;
			nieuwontleed (NUMERIC_ARRAY_VARIABLE_);
		}
		parse [iparse]. content.variable = var;
		return;
	}

	if (symbol == VARIABLE_NAME_) {
		InterpreterVariable var = Interpreter_hasVariable (theInterpreter, lexan [ilexan]. content.string);
		if (var == NULL)
			formulefout (L"Unknown variable", lexan [ilexan]. position);
		nieuwontleed (NUMERIC_VARIABLE_);
		parse [iparse]. content.variable = var;
		return;
	}

	if (symbol == SELF_) {
		symbol = nieuwlees;
		if (symbol == RECHTEHAAKOPENEN_) {
			parseExpression ();
			if (nieuwlees == KOMMA_) {
				parseExpression ();
				nieuwontleed (SELFMATRIKS2_);
				pas (RECHTEHAAKSLUITEN_);
				return;
			}
			oudlees;
			nieuwontleed (SELFMATRIKS1_);
			pas (RECHTEHAAKSLUITEN_);
			return;
		}
		if (symbol == HAAKJEOPENEN_) {
			parseExpression ();
			if (nieuwlees == KOMMA_) {
				parseExpression ();
				nieuwontleed (SELFFUNKTIE2_);
				pas (HAAKJESLUITEN_);
				return;
			}
			oudlees;
			nieuwontleed (SELFFUNKTIE1_);
			pas (HAAKJESLUITEN_);
			return;
		}
		oudlees;
		nieuwontleed (SELF0_);
		return;
	}

	if (symbol == SELFSTR_) {
		symbol = nieuwlees;
		if (symbol == RECHTEHAAKOPENEN_) {
			parseExpression ();
			if (nieuwlees == KOMMA_) {
				parseExpression ();
				nieuwontleed (SELFMATRIKSSTR2_);
				pas (RECHTEHAAKSLUITEN_);
				return;
			}
			oudlees;
			nieuwontleed (SELFMATRIKSSTR1_);
			pas (RECHTEHAAKSLUITEN_);
			return;
		}
		if (symbol == HAAKJEOPENEN_) {
			parseExpression ();
			if (nieuwlees == KOMMA_) {
				parseExpression ();
				nieuwontleed (SELFFUNKTIESTR2_);
				pas (HAAKJESLUITEN_);
				return;
			}
			oudlees;
			nieuwontleed (SELFFUNKTIESTR1_);
			pas (HAAKJESLUITEN_);
			return;
		}
		oudlees;
		nieuwontleed (SELFSTR0_);
		return;
	}

	if (symbol == OBJECT_) {
		symbol = nieuwlees;
		if (symbol == RECHTEHAAKOPENEN_) {
			parseExpression ();   // the object's name or ID
			if (nieuwlees == RECHTEHAAKSLUITEN_) {
				nieuwontleed (OBJECTCELL0_);
			} else {
				oudlees;
				pas (KOMMA_);
				parseExpression ();
				if (nieuwlees == KOMMA_) {
					parseExpression ();
					nieuwontleed (OBJECTCELL2_);
					pas (RECHTEHAAKSLUITEN_);
				} else {
					oudlees;
					nieuwontleed (OBJECTCELL1_);
					pas (RECHTEHAAKSLUITEN_);
				}
			}
		} else if (symbol == HAAKJEOPENEN_) {   // the object's name or ID
			parseExpression ();
			if (nieuwlees == HAAKJESLUITEN_) {
				nieuwontleed (OBJECTLOCATION0_);
			} else {
				oudlees;
				pas (KOMMA_);
				parseExpression ();
				if (nieuwlees == KOMMA_) {
					parseExpression ();
					nieuwontleed (OBJECTLOCATION2_);
					pas (HAAKJESLUITEN_);
				} else {
					oudlees;
					nieuwontleed (OBJECTLOCATION1_);
					pas (HAAKJESLUITEN_);
				}
			}
		} else {
			formulefout (L"After \"object\" there should be \"(\" or \"[\"", lexan [ilexan]. position);
		}
		return;
	}

	if (symbol == OBJECTSTR_) {
		symbol = nieuwlees;
		if (symbol == RECHTEHAAKOPENEN_) {
			parseExpression ();   // the object's name or ID
			if (nieuwlees == RECHTEHAAKSLUITEN_) {
				nieuwontleed (OBJECTCELLSTR0_);
			} else {
				oudlees;
				pas (KOMMA_);
				parseExpression ();
				if (nieuwlees == KOMMA_) {
					parseExpression ();
					nieuwontleed (OBJECTCELLSTR2_);
					pas (RECHTEHAAKSLUITEN_);
				} else {
					oudlees;
					nieuwontleed (OBJECTCELLSTR1_);
					pas (RECHTEHAAKSLUITEN_);
				}
			}
		} else if (symbol == HAAKJEOPENEN_) {   // the object's name or ID
			parseExpression ();
			if (nieuwlees == HAAKJESLUITEN_) {
				nieuwontleed (OBJECTLOCATIONSTR0_);
			} else {
				oudlees;
				pas (KOMMA_);
				parseExpression ();
				if (nieuwlees == KOMMA_) {
					parseExpression ();
					nieuwontleed (OBJECTLOCATIONSTR2_);
					pas (HAAKJESLUITEN_);
				} else {
					oudlees;
					nieuwontleed (OBJECTLOCATIONSTR1_);
					pas (HAAKJESLUITEN_);
				}
			}
		} else {
			formulefout (L"After \"object$\" there should be \"(\" or \"[\"", lexan [ilexan]. position);
		}
		return;
	}

	if (symbol == HAAKJEOPENEN_) {
		parseExpression ();
		pas (HAAKJESLUITEN_);
		return;
	}

	if (symbol == IF_) {
		int elseLabel = nieuwlabel;   // has to be local,
		int endifLabel = nieuwlabel;   // because of recursion
		parseExpression ();
		nieuwontleed (IFFALSE_);  ontleedlabel (elseLabel);
		pas (THEN_);
		parseExpression ();
		nieuwontleed (GOTO_);     ontleedlabel (endifLabel);
		pas (ELSE_);
		nieuwontleed (LABEL_);    ontleedlabel (elseLabel);
		parseExpression ();
		pas (ENDIF_);
		nieuwontleed (LABEL_);    ontleedlabel (endifLabel);
		return;
	}

	if (symbol == MATRIKS_) {
		Data thee = lexan [ilexan]. content.object;
		Melder_assert (thee != NULL);
		symbol = nieuwlees;
		if (symbol == RECHTEHAAKOPENEN_) {
			if (nieuwlees == RECHTEHAAKSLUITEN_) {
				nieuwontleed (MATRIKS0_);
				parse [iparse]. content.object = thee;
			} else {
				oudlees;
				parseExpression ();
				if (nieuwlees == KOMMA_) {
					parseExpression ();
					nieuwontleed (MATRIKS2_);
					parse [iparse]. content.object = thee;
					pas (RECHTEHAAKSLUITEN_);
				} else {
					oudlees;
					nieuwontleed (MATRIKS1_);
					parse [iparse]. content.object = thee;
					pas (RECHTEHAAKSLUITEN_);
				}
			}
		} else if (symbol == HAAKJEOPENEN_) {
			if (nieuwlees == HAAKJESLUITEN_) {
				nieuwontleed (FUNKTIE0_);
				parse [iparse]. content.object = thee;
			} else {
				oudlees;
				parseExpression ();
				if (nieuwlees == KOMMA_) {
					parseExpression ();
					nieuwontleed (FUNKTIE2_);
					parse [iparse]. content.object = thee;
					pas (HAAKJESLUITEN_);
				} else {
					oudlees;
					nieuwontleed (FUNKTIE1_);
					parse [iparse]. content.object = thee;
					pas (HAAKJESLUITEN_);
				}
			}
		} else if (symbol == PERIOD_) {
			switch (nieuwlees) {
				case XMIN_:
					if (! thy v_hasGetXmin ()) {
						formulefout (L"Attribute \"xmin\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getXmin ());
						return;
					}
				case XMAX_:
					if (! thy v_hasGetXmax ()) {
						formulefout (L"Attribute \"xmax\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getXmax ());
						return;
					}
				case YMIN_:
					if (! thy v_hasGetYmin ()) {
						formulefout (L"Attribute \"ymin\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getYmin ());
						return;
					}
				case YMAX_:
					if (! thy v_hasGetYmax ()) {
						formulefout (L"Attribute \"ymax\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getYmax ());
						return;
					}
				case NX_:
					if (! thy v_hasGetNx ()) {
						formulefout (L"Attribute \"nx\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getNx ());
						return;
					}
				case NY_:
					if (! thy v_hasGetNy ()) {
						formulefout (L"Attribute \"ny\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getNy ());
						return;
					}
				case DX_:
					if (! thy v_hasGetDx ()) {
						formulefout (L"Attribute \"dx\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getDx ());
						return;
					}
				case DY_:
					if (! thy v_hasGetDy ()) {
						formulefout (L"Attribute \"dy\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getDy ());
						return;
					}
				case NCOL_:
					if (! thy v_hasGetNcol ()) {
						formulefout (L"Attribute \"ncol\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getNcol ());
						return;
					}
				case NROW_:
					if (! thy v_hasGetNrow ()) {
						formulefout (L"Attribute \"nrow\" not defined for this object", lexan [ilexan]. position);
					} else {
						nieuwontleed (NUMBER_);
						parsenumber (thy v_getNrow ());
						return;
					}
				case ROWSTR_:
					if (! thy v_hasGetRowStr ()) {
						formulefout (L"Attribute \"row$\" not defined for this object", lexan [ilexan]. position);
					} else {
						pas (RECHTEHAAKOPENEN_);
						parseExpression ();
						nieuwontleed (ROWSTR_);
						parse [iparse]. content.object = thee;
						pas (RECHTEHAAKSLUITEN_);
						return;
					}
				case COLSTR_:
					if (! thy v_hasGetColStr ()) {
						formulefout (L"Attribute \"col$\" not defined for this object", lexan [ilexan]. position);
					} else {
						pas (RECHTEHAAKOPENEN_);
						parseExpression ();
						nieuwontleed (COLSTR_);
						parse [iparse]. content.object = thee;
						pas (RECHTEHAAKSLUITEN_);
						return;
					}
				default: formulefout (L"Unknown attribute.", lexan [ilexan]. position);
			}
		} else {
			formulefout (L"After a name of a matrix there should be \"(\", \"[\", or \".\"", lexan [ilexan]. position);
		}
		return;
	}

	if (symbol == MATRIKSSTR_) {
		Data thee = lexan [ilexan]. content.object;
		Melder_assert (thee != NULL);
		symbol = nieuwlees;
		if (symbol == RECHTEHAAKOPENEN_) {
			if (nieuwlees == RECHTEHAAKSLUITEN_) {
				nieuwontleed (MATRIKSSTR0_);
				parse [iparse]. content.object = thee;
			} else {
				oudlees;
				parseExpression ();
				if (nieuwlees == KOMMA_) {
					parseExpression ();
					nieuwontleed (MATRIKSSTR2_);
					parse [iparse]. content.object = thee;
					pas (RECHTEHAAKSLUITEN_);
				} else {
					oudlees;
					nieuwontleed (MATRIKSSTR1_);
					parse [iparse]. content.object = thee;
					pas (RECHTEHAAKSLUITEN_);
				}
			}
		} else {
			formulefout (L"After a name of a matrix$ there should be \"[\"", lexan [ilexan]. position);
		}
		return;
	}

	if (symbol >= LOW_FUNCTION_1 && symbol <= HIGH_FUNCTION_1) {
		pas (HAAKJEOPENEN_);
		parseExpression ();
		pas (HAAKJESLUITEN_);
		nieuwontleed (symbol);
		return;
	}

	if (symbol >= LOW_FUNCTION_2 && symbol <= HIGH_FUNCTION_2) {
		pas (HAAKJEOPENEN_);
		parseExpression ();
		pas (KOMMA_);
		parseExpression ();
		pas (HAAKJESLUITEN_);
		nieuwontleed (symbol);
		return;
	}

	if (symbol >= LOW_FUNCTION_3 && symbol <= HIGH_FUNCTION_3) {
		pas (HAAKJEOPENEN_);
		parseExpression ();
		pas (KOMMA_);
		parseExpression ();
		pas (KOMMA_);
		parseExpression ();
		pas (HAAKJESLUITEN_);
		nieuwontleed (symbol);
		return;
	}

	if (symbol >= LOW_FUNCTION_N && symbol <= HIGH_FUNCTION_N) {
		int n = 0;
		pas (HAAKJEOPENEN_);
		if (nieuwlees != HAAKJESLUITEN_) {
			oudlees;
			parseExpression ();
			n ++;
			while (nieuwlees == KOMMA_) {
				parseExpression ();
				n ++;
			}
			oudlees;
			pas (HAAKJESLUITEN_);
		}
		nieuwontleed (NUMBER_); parsenumber (n);
		nieuwontleed (symbol);
		return;
	}

	if (symbol == CALL_) {
		wchar *procedureName = lexan [ilexan]. content.string;   // reference copy!
		int n = 0;
		pas (HAAKJEOPENEN_);
		if (nieuwlees != HAAKJESLUITEN_) {
			oudlees;
			parseExpression ();
			n ++;
			while (nieuwlees == KOMMA_) {
				parseExpression ();
				n ++;
			}
			oudlees;
			pas (HAAKJESLUITEN_);
		}
		nieuwontleed (NUMBER_); parsenumber (n);
		nieuwontleed (CALL_);
		parse [iparse]. content.string = procedureName;
		return;
	}

	if (symbol >= LOW_STRING_FUNCTION && symbol <= HIGH_STRING_FUNCTION) {
		if (symbol >= LOW_FUNCTION_STRNUM && symbol <= HIGH_FUNCTION_STRNUM) {
			pas (HAAKJEOPENEN_);
			parseExpression ();
			pas (HAAKJESLUITEN_);
		} else if (symbol == INDEX_ || symbol == RINDEX_ ||
			symbol == STARTS_WITH_ || symbol == ENDS_WITH_ ||
			symbol == INDEX_REGEX_ || symbol == RINDEX_REGEX_ || symbol == EXTRACT_NUMBER_)
		{
			pas (HAAKJEOPENEN_);
			parseExpression ();
			pas (KOMMA_);
			parseExpression ();
			pas (HAAKJESLUITEN_);
		} else if (symbol == DATESTR_) {
			pas (HAAKJEOPENEN_);
			pas (HAAKJESLUITEN_);
		} else if (symbol == EXTRACT_WORDSTR_ || symbol == EXTRACT_LINESTR_) {
			pas (HAAKJEOPENEN_);
			parseExpression ();
			pas (KOMMA_);
			parseExpression ();
			pas (HAAKJESLUITEN_);
		} else if (symbol == ENVIRONMENTSTR_) {
			pas (HAAKJEOPENEN_);
			parseExpression ();
			pas (HAAKJESLUITEN_);
		} else if (symbol == FIXEDSTR_ || symbol == PERCENTSTR_) {
			pas (HAAKJEOPENEN_);
			parseExpression ();
			pas (KOMMA_);
			parseExpression ();
			pas (HAAKJESLUITEN_);
		} else if (symbol == REPLACESTR_ || symbol == REPLACE_REGEXSTR_) {
			pas (HAAKJEOPENEN_);
			parseExpression ();
			pas (KOMMA_);
			parseExpression ();
			pas (KOMMA_);
			parseExpression ();
			pas (KOMMA_);
			parseExpression ();
			pas (HAAKJESLUITEN_);
		} else {
			oudlees;   // needed for retry if we are going to be in a string comparison?
			formulefout (L"Function expected", lexan [ilexan + 1]. position);
		}
		nieuwontleed (symbol);
		return;
	}

	if (symbol >= LOW_RANGE_FUNCTION && symbol <= HIGH_RANGE_FUNCTION) {
		if (symbol == SUM_) {
			//theOptimize = 1;
			nieuwontleed (NUMBER_); parsenumber (0.0);   // initialize the sum
			pas (HAAKJEOPENEN_);
			int symbol2 = nieuwlees;
			if (symbol2 == NUMERIC_VARIABLE_) {   // an existing variable
				nieuwontleed (VARIABLE_REFERENCE_);
				InterpreterVariable loopVariable = lexan [ilexan]. content.variable;
				parse [iparse]. content.variable = loopVariable;
			} else if (symbol2 == VARIABLE_NAME_) {   // a new variable
				InterpreterVariable loopVariable = Interpreter_lookUpVariable (theInterpreter, lexan [ilexan]. content.string);
				nieuwontleed (VARIABLE_REFERENCE_);
				parse [iparse]. content.variable = loopVariable;
			} else {
				formulefout (L"Numeric variable expected", lexan [ilexan]. position);
			}
			// now on stack: sum, loop variable
			if (nieuwlees == FROM_) {
				parseExpression ();
			} else {
				oudlees;
				nieuwontleed (NUMBER_); parsenumber (1.0);
			}
			nieuwontleed (DECREMENT_AND_ASSIGN_);   // this pushes the variable back on the stack
			// now on stack: sum, loop variable
			pas (TO_);
			parseExpression ();
			// now on stack: sum, loop variable, end value
			int startLabel = nieuwlabel;
			int endLabel = nieuwlabel;
			nieuwontleed (LABEL_); ontleedlabel (startLabel);
			nieuwontleed (INCREMENT_GREATER_GOTO_); ontleedlabel (endLabel);
			pas (KOMMA_);
			parseExpression ();
			pas (HAAKJESLUITEN_);
			// now on stack: sum, loop variable, end value, value to add
			nieuwontleed (ADD_3DOWN_);
			// now on stack: sum, loop variable, end value
			nieuwontleed (GOTO_); ontleedlabel (startLabel);
			nieuwontleed (LABEL_); ontleedlabel (endLabel);
			nieuwontleed (POP_2_);
			// now on stack: sum
			return;
		}
	}

	if (symbol == STOPWATCH_) {
		nieuwontleed (symbol);
		return;
	}

	oudlees;   // needed for retry if we are going to be in a string comparison
	formulefout (L"Symbol misplaced", lexan [ilexan + 1]. position);
}

static void parseFactor (void);

static void parsePowerFactors (void) {
	if (nieuwlees == POWER_) {
		if (ilexan > 2 && lexan [ilexan - 2]. symbol == MINUS_ && lexan [ilexan - 1]. symbol == NUMBER_) {
			oudlees;
			formulefout (L"Expressions like -3^4 are ambiguous; use (-3)^4 or -(3^4) or -(3)^4", lexan [ilexan + 1]. position);
		}
		parseFactor ();   // like a^-b
		nieuwontleed (POWER_);
	}
	else
		oudlees;
}

static void parseMinus (void) {
	parsePowerFactor ();
	parsePowerFactors ();
}

static void parseFactor (void) {
	if (nieuwlees == MINUS_) {
		parseFactor ();   // there can be multiple consecutive minuses
		nieuwontleed (MINUS_);
		return;
	}
	oudlees;
	parseMinus ();   // like -a^b
}

static void parseFactors (void) {
	int sym = nieuwlees;   // has to be local, because of recursion
	if (sym == MUL_ || sym == RDIV_ || sym == IDIV_ || sym == MOD_) {
		parseFactor ();
		nieuwontleed (sym);
		parseFactors ();
	}
	else oudlees;
}

static void parseTerm (void) {
	parseFactor ();
	parseFactors ();
}

static void parseTerms (void) {
	int symbol = nieuwlees;
	if (symbol == ADD_ || symbol == SUB_) {
		parseTerm ();
		nieuwontleed (symbol);
		parseTerms ();
	}
	else oudlees;
}

static void parseNot (void) {
	int symbol;
	parseTerm ();
	parseTerms ();
	symbol = nieuwlees;
	if (symbol >= EQ_ && symbol <= GT_) {
		parseTerm ();
		parseTerms ();
		nieuwontleed (symbol);
	}
	else oudlees;
}

static void parseAnd (void) {
	if (nieuwlees == NOT_) {
		parseAnd ();   // like not not not
		nieuwontleed (NOT_);
		return;
	}
	oudlees;
	parseNot ();
}

static void parseOr (void) {
	parseAnd ();
	if (nieuwlees == AND_) {
		int falseLabel = nieuwlabel;
		int andLabel = nieuwlabel;
		do {
			nieuwontleed (IFFALSE_); ontleedlabel (falseLabel);
			parseAnd ();
		} while (nieuwlees == AND_);
		nieuwontleed (IFFALSE_); ontleedlabel (falseLabel);
		nieuwontleed (TRUE_);
		nieuwontleed (GOTO_); ontleedlabel (andLabel);
		nieuwontleed (LABEL_); ontleedlabel (falseLabel);
		nieuwontleed (FALSE_);
		nieuwontleed (LABEL_); ontleedlabel (andLabel);
	}
	oudlees;
}

static void parseExpression (void) {
	parseOr ();
	if (nieuwlees == OR_) {
		int trueLabel = nieuwlabel;
		int orLabel = nieuwlabel;
		do {
			nieuwontleed (IFTRUE_); ontleedlabel (trueLabel);
			parseOr ();
		} while (nieuwlees == OR_);
		nieuwontleed (IFTRUE_); ontleedlabel (trueLabel);
		nieuwontleed (FALSE_);
		nieuwontleed (GOTO_); ontleedlabel (orLabel);
		nieuwontleed (LABEL_); ontleedlabel (trueLabel);
		nieuwontleed (TRUE_);
		nieuwontleed (LABEL_); ontleedlabel (orLabel);
	}
	oudlees;
}

/*
	Translate the infix expression "my lexan" into the postfix expression "my parse":
	remove parentheses and brackets, commas, FROM_, TO_,
	IF_ THEN_ ELSE_ ENDIF_ OR_ AND_;
	introduce LABEL_ GOTO_ IFTRUE_ IFFALSE_ TRUE_ FALSE_
	SELF0_ SELF1_ SELF2_ MATRIKS0_ MATRIKS1_ MATRIKS2_
	Return:
		0 if error, otherwise 1.
	Precondition:
		"my lexan" contains an END_ symbol.
	Postconditions:
		*my lexan not changed.
		result == 0 || my parse [my numberOfInstructions]. symbol == END_
*/

static void Formula_parseExpression (void) {
	ilabel = ilexan = iparse = 0;
	if (lexan [1]. symbol == END_) Melder_throw ("Empty formula.");
	parseExpression ();
	pas (END_);
	nieuwontleed (END_);
	numberOfInstructions = iparse;
}

static void schuif (int begin, int afstand) {
	int j;
	numberOfInstructions -= afstand;
	for (j = begin; j <= numberOfInstructions; j ++)
		parse [j] = parse [j + afstand];
}

static int vindLabel (int label) {
	int result = numberOfInstructions;
	while (parse [result]. symbol != LABEL_ ||
			 parse [result]. content.label != label)
		result --;
	return result;
}

static void Formula_optimizeFlow (void)
/* Vereenvoudig boolse uitdrukkingen.					*/
/* Nadien:								*/
/*    de stroom volgt het kortste pad;					*/
/*    als de rekenkundige waarden van boolse uitdrukkingen		*/
/*    in de formule niet voorkomen, zijn alle TRUE_s en FALSE_s weg;	*/
/*    als in de formule geen NOT_s voorkwamen op rekenkundige		*/
/*    uitdrukkingen, zijn alle NOT_s weg;				*/
/*    onbereikbare kode is weg;						*/
{
	int i, j, volg;
	for (;;) {
		int verbeterd = 0;
		for (i = 1; i <= numberOfInstructions; i ++)
		{

/* Optimalisatie 1: */
/*    true   goto x  ->  goto y  /  __  ...  label x  iftrue y    */
/*    false  goto x  ->  goto y  /  __  ...  label x  iffalse y   */

			if ((parse [i]. symbol == TRUE_ &&
				 parse [i + 1]. symbol == GOTO_ &&
				 parse [volg = vindLabel (parse [i + 1]. content.label) + 1]
							. symbol == IFTRUE_)
				 ||
				 (parse [i]. symbol == FALSE_ &&
				  parse [i + 1]. symbol == GOTO_ &&
				  parse [volg = vindLabel (parse [i + 1]. content.label) + 1]
							. symbol == IFFALSE_))
			{
				 verbeterd = 1;
				 parse [i]. symbol = GOTO_;
				 parse [i]. content.label = parse [volg]. content.label;
				 schuif (i + 1, 1);
			}

/* Optimalisatie 2: */
/*    true  goto x  ...  label x  iffalse y  ->        */
/*          goto z  ...  label x  iffalse y  label z   */
/*    en analoog met false en iftrue. */

			if ((parse [i]. symbol == TRUE_ &&
				 parse [i + 1]. symbol == GOTO_ &&
				 parse [volg = vindLabel (parse [i + 1]. content.label) + 1]
							. symbol == IFFALSE_)
				 ||
				 (parse [i]. symbol == FALSE_ &&
				  parse [i + 1]. symbol == GOTO_ &&
				  parse [volg = vindLabel (parse [i + 1]. content.label) + 1]
							. symbol == IFTRUE_))
			{
				verbeterd = 1;
				parse [i]. symbol = GOTO_;
				parse [i]. content.label = nieuwlabel;
				for (j = i + 1; j < volg; j ++)
					parse [j] = parse [j + 1];
				parse [volg]. symbol = LABEL_;
				parse [volg]. content.label = ilabel;
			}

/* Optimalisatie 3a: */
/*    iftrue x  goto y  label x  ->  iffalse y  label x   */

			if (parse [i]. symbol == IFTRUE_ &&
				 parse [i + 1]. symbol == GOTO_ &&
				 parse [i + 2]. symbol == LABEL_ &&
				 parse [i]. content.label == parse [i + 2]. content.label)
			{
				verbeterd = 1;
				parse [i]. symbol = IFFALSE_;
				parse [i]. content.label = parse [i + 1]. content.label;
				schuif (i + 1, 1);
			}

/* Optimalisatie 3b: */
/*    iffalse x  goto y  label x  ->  iftrue y  label x   */

			if (parse [i]. symbol == IFFALSE_ &&
				 parse [i + 1]. symbol == GOTO_ &&
				 parse [i + 2]. symbol == LABEL_ &&
				 parse [i]. content.label == parse [i + 2]. content.label)
			{
				verbeterd = 1;
				parse [i]. symbol = IFTRUE_;
				parse [i]. content.label = parse [i + 1]. content.label;
				schuif (i + 1, 1);
			}

/* Optimalisatie 4: */
/*    verwijder onbereikbare kode: na een GOTO_ hoort een LABEL_. */

			if (parse [i]. symbol == GOTO_ &&
				 parse [i + 1]. symbol != LABEL_)
			{
				verbeterd = 1;
				j = i + 2;
				while (parse [j]. symbol != LABEL_) j ++;
				schuif (i + 1, j - i - 1);
			}

/* Optimalisatie 5: */
/*    goto x  ->  0  /  __  label x   */

			if (parse [i]. symbol == GOTO_ &&
				 parse [i]. symbol == LABEL_ &&
				 parse [i]. content.label == parse [i + 1]. content.label)
			{
				verbeterd = 1;
				schuif (i, 1);
			}

/* Optimalisatie 6: */
/*    true   iffalse x  ->  0  */
/*    false  iftrue x   ->  0  */

			if ((parse [i]. symbol == TRUE_ && parse [i + 1]. symbol == IFFALSE_)
				|| (parse [i]. symbol == FALSE_ && parse [i + 1]. symbol == IFTRUE_))
			{
				verbeterd = 1;
				schuif (i, 2);
			}

/* Optimalisatie 7: */
/*    true   iftrue x   ->  goto x    */
/*    false  iffalse x  ->  goto x    */
			
			if ((parse [i]. symbol == TRUE_ && parse [i + 1]. symbol == IFTRUE_)
				|| (parse [i]. symbol == FALSE_ && parse [i + 1]. symbol == IFFALSE_))
			{
				verbeterd = 1;
				parse [i]. symbol = GOTO_;
				parse [i]. content.label = parse [i + 1]. content.label;
				schuif (i + 1, 1);
			}

/* Optimalisatie 8: */
/*    iftrue x   ->  iftrue y   /  __  ...  label x  goto y   */
/*    iffalse x  ->  iffalse y  /  __  ...  label x  goto y   */

			if ((parse [i]. symbol == IFTRUE_ || parse [i]. symbol == IFFALSE_)
				&& parse [volg = vindLabel (parse [i]. content.label) + 1]. symbol == GOTO_)
			{
				verbeterd = 1;
				parse [i]. content.label = parse [volg]. content.label;
			}

/* Optimalisatie 9a: */
/*    not  iftrue x  ->  iffalse x   */

			if (parse [i]. symbol == NOT_ && parse [i + 1]. symbol == IFTRUE_)
			{
				verbeterd = 1;
				parse [i]. symbol = IFFALSE_;
				parse [i]. content.label = parse [i + 1]. content.label;
				schuif (i + 1, 1);
			}

/* Optimalisatie 9b: */
/*    not  iffalse x  ->  iftrue x   */

			if (parse [i]. symbol == NOT_ && parse [i + 1]. symbol == IFFALSE_)
			{
				verbeterd = 1;
				parse [i]. symbol = IFTRUE_;
				parse [i]. content.label = parse [i + 1]. content.label;
				schuif (i + 1, 1);
			}

/* De volgende optimalisaties ontbreken want zijn hier overbodig: */
/*    goto x  ->  goto y  /  __  ... label x  goto y   */
/*    trek twee opeenvolgende labels samen             */

		} /* for i */

		/* Verwijder labels waar niet naar verwezen wordt. */

		for (i = 1; i <= numberOfInstructions; i ++)
			if (parse [i]. symbol == LABEL_)
			{
				int gevonden = 0;
				for (j = 1; j <= numberOfInstructions; j ++)
					if ((parse [j]. symbol == GOTO_ || parse [j]. symbol == IFFALSE_ || parse [j]. symbol == IFTRUE_
						|| parse [j]. symbol == INCREMENT_GREATER_GOTO_)
						&& parse [i]. content.label == parse [j]. content.label)
						gevonden = 1;
				if (! gevonden)
				{
					verbeterd = 1;
					schuif (i, 1);
				}
			}
		if (! verbeterd) break;
	}
}

static void Formula_evaluateConstants (void) {
	for (;;) {
		bool improved = 0;
		for (int i = 1; i <= numberOfInstructions; i ++) {
			int gain = 0;
			if (parse [i]. symbol == NUMBER_) {
				if (parse [i]. content.number == 2.0 && parse [i + 1]. symbol == POWER_)
					{ gain = 1; parse [i]. symbol = SQR_; }
				else if (parse [i + 1]. symbol == MINUS_)
					{ gain = 1; parse [i]. content.number = - parse [i]. content.number; } 
				else if (parse [i + 1]. symbol == SQR_)
					{ gain = 1; parse [i]. content.number *= parse [i]. content.number; }
				else if (parse [i + 1]. symbol == NUMBER_) {
					if (parse [i + 2]. symbol == ADD_)
						{ gain = 2; parse [i]. content.number += parse [i + 1]. content.number; }
					else if (parse [i + 2]. symbol == SUB_)
						{ gain = 2; parse [i]. content.number -= parse [i + 1]. content.number; }
					else if (parse [i + 2]. symbol == MUL_)
						{ gain = 2; parse [i]. content.number *= parse [i + 1]. content.number; }
					else if (parse [i + 2]. symbol == RDIV_)
						{ gain = 2; parse [i]. content.number /= parse [i + 1]. content.number; }
				}
			}
			if (gain) { improved = true; schuif (i + 1, gain); }
		}
		if (! improved) break;
	}
}

static void Formula_removeLabels (void) {
	/*
	 * First translate symbolic labels (< 0) into instructions locations (> 0).
	 */
	for (int i = 1; i <= numberOfInstructions; i ++) {
		int symboli = parse [i]. symbol;
		if (symboli == GOTO_ || symboli == IFTRUE_ || symboli == IFFALSE_ || symboli == INCREMENT_GREATER_GOTO_) {
			int label = parse [i]. content.label;
			for (int j = 1; j <= numberOfInstructions; j ++) {
				if (parse [j]. symbol == LABEL_ && parse [j]. content.label == label) {
					parse [i]. content.label = j;
				}
			}
		}
	}
	/*
	 * Then remove the labels, which have become superfluous.
	 */
	if (theOptimize) {
		int i = 1;
		while (i <= numberOfInstructions) {
			int symboli = parse [i]. symbol;
			if (symboli == LABEL_) {
				schuif (i, 1);   // remove one label
				for (int j = 1; j <= numberOfInstructions; j ++) {
					int symbolj = parse [j]. symbol;
					if ((symbolj == GOTO_ || symbolj == IFTRUE_ || symbolj == IFFALSE_ || symbolj == INCREMENT_GREATER_GOTO_) && parse [j]. content.label > i)
						parse [j]. content.label --;  /* Pas een label aan. */
				}
				i --;   /* Voorkom ophogen i (overbodig?). */
			}
			i ++;
		}
	}
	numberOfInstructions --;   /* Het END_-symbol hoeft niet geinterpreteerd. */
}

/*
 * For debugging.
 */
static void Formula_print (FormulaInstruction f) {
	int i = 0, symbol;
	do {
		const wchar *instructionName;
		symbol = f [++ i]. symbol;
		instructionName = Formula_instructionNames [symbol];
		if (symbol == NUMBER_)
			Melder_casual ("%d %ls %.17g", i, instructionName, f [i]. content.number);
		else if (symbol == GOTO_ || symbol == IFFALSE_ || symbol == IFTRUE_ || symbol == LABEL_ || symbol == INCREMENT_GREATER_GOTO_)
			Melder_casual ("%d %ls %d", i, instructionName, f [i]. content.label);
		else if (symbol == NUMERIC_VARIABLE_)
			Melder_casual ("%d %ls %ls %ls", i, instructionName, f [i]. content.variable -> string, Melder_double (f [i]. content.variable -> numericValue));
		else if (symbol == STRING_VARIABLE_)
			Melder_casual ("%d %ls %ls %ls", i, instructionName, f [i]. content.variable -> string, f [i]. content.variable -> stringValue);
		else if (symbol == STRING_ || symbol == VARIABLE_NAME_ || symbol == INDEXED_NUMERIC_VARIABLE_ || symbol == INDEXED_STRING_VARIABLE_)
			Melder_casual ("%d %ls \"%ls\"", i, instructionName, f [i]. content.string);
		else if (symbol == MATRIKS_ || symbol == MATRIKSSTR_ || symbol == MATRIKS1_ || symbol == MATRIKSSTR1_ ||
		         symbol == MATRIKS2_ || symbol == MATRIKSSTR2_ || symbol == ROWSTR_ || symbol == COLSTR_)
		{
			Thing object = (Thing) f [i]. content.object;
			if (object) {
				Melder_casual ("%d %ls %s %s", i, instructionName,
					Melder_peekWcsToUtf8 (Thing_className (object)),
					Melder_peekWcsToUtf8 (object -> name));
			} else {
				Melder_casual ("%d %ls", i, instructionName);
			}
		}
		else if (symbol == CALL_)
			Melder_casual ("%d %ls %ls", i, instructionName, f [i]. content.string);
		else
			Melder_casual ("%d %ls", i, instructionName);
	} while (symbol != END_);
}

void Formula_compile (Any interpreter, Any data, const wchar *expression, int expressionType, int optimize) {
	theInterpreter = (Interpreter) interpreter;
	if (theInterpreter == NULL) {
		if (theLocalInterpreter == NULL) {
			theLocalInterpreter = Interpreter_create (NULL, NULL);
		}
		theInterpreter = theLocalInterpreter;
		Collection_removeAllItems (theInterpreter -> variables);
	}
	theSource = (Data) data;
	theExpression = expression;
	theExpressionType = expressionType;
	theOptimize = optimize;
	if (! lexan) {
		lexan = Melder_calloc_f (struct structFormulaInstruction, 3000);
		lexan [3000 - 1]. symbol = END_;   /* Make sure that string cleaning always terminates. */
	}
	if (! parse) parse = Melder_calloc_f (struct structFormulaInstruction, 3000);

	/*
		Clean up strings from the previous call.
		These strings are in a union, that's why this cannot be done later, when a new string is created.
	*/
	if (numberOfStringConstants) {
		ilexan = 1;
		for (;;) {
			int symbol = lexan [ilexan]. symbol;
			if (symbol == STRING_ || symbol == VARIABLE_NAME_ || symbol == INDEXED_NUMERIC_VARIABLE_ || symbol == INDEXED_STRING_VARIABLE_ || symbol == CALL_) Melder_free (lexan [ilexan]. content.string);
			else if (symbol == END_) break;   /* Either the end of a formula, or the end of lexan. */
			ilexan ++;
		}
		numberOfStringConstants = 0;
	}

	Formula_lexan (); therror
	if (Melder_debug == 17) Formula_print (lexan);
	Formula_parseExpression (); therror
	if (Melder_debug == 17) Formula_print (parse);
	if (theOptimize) {
		Formula_optimizeFlow ();
		if (Melder_debug == 17) Formula_print (parse);
		Formula_evaluateConstants ();
		if (Melder_debug == 17) Formula_print (parse);
	}
	Formula_removeLabels ();
	if (Melder_debug == 17) Formula_print (parse);
}

/*
 * Running.
 */

static int programPointer;

typedef struct structStackel {
	#define Stackel_NUMBER  0
	#define Stackel_STRING  1
	#define Stackel_NUMERIC_ARRAY  2
	#define Stackel_STRING_ARRAY  3
	#define Stackel_VARIABLE  -1
	int which;   /* 0 or negative = no clean-up required, positive = requires clean-up */
	union {
		double number;
		wchar_t *string;
		struct Formula_NumericArray numericArray;
		InterpreterVariable variable;
	} content;
} *Stackel;

static void Stackel_cleanUp (Stackel me) {
	if (my which == Stackel_STRING) {
		Melder_free (my content.string);
	} else if (my which == Stackel_NUMERIC_ARRAY) {
		NUMmatrix_free (my content.numericArray.data, 1, 1);
		my content.numericArray = theZeroNumericArray;
	}
}
static Stackel theStack;
static int w, wmax;   /* w = stack pointer; */
#define pop  & theStack [w --]
static inline void pushNumber (double x) {
	/* inline runs 10 to 20 percent faster on i386; here's the test script:
		stopwatch
		Create Sound from formula... test mono 0 100 44100 1/2 * (2*pi*377*x)
		t = stopwatch
		echo 't'
	 * Mac: 0.75 -> 0.67 seconds
	 * Win: 1.10 -> 0.90 seconds (20100107)
	 */
	Stackel stackel = & theStack [++ w];
	if (stackel -> which > Stackel_NUMBER) Stackel_cleanUp (stackel);
	if (w > wmax) wmax ++;
	stackel -> which = Stackel_NUMBER;
	stackel -> content.number = x;
}
static void pushString (wchar_t *x) {
	Stackel stackel = & theStack [++ w];
	if (stackel -> which > Stackel_NUMBER) Stackel_cleanUp (stackel);
	if (w > wmax) wmax ++;
	stackel -> which = Stackel_STRING;
	stackel -> content.string = x;
}
static void pushNumericArray (long numberOfRows, long numberOfColumns, double **x) {
	Stackel stackel = & theStack [++ w];
	if (stackel -> which > Stackel_NUMBER) Stackel_cleanUp (stackel);
	if (w > wmax) wmax ++;
	stackel -> which = Stackel_NUMERIC_ARRAY;
	stackel -> content.numericArray.numberOfRows = numberOfRows;
	stackel -> content.numericArray.numberOfColumns = numberOfColumns;
	stackel -> content.numericArray.data = x;
}
static void pushVariable (InterpreterVariable var) {
	Stackel stackel = & theStack [++ w];
	if (stackel -> which > Stackel_NUMBER) Stackel_cleanUp (stackel);
	if (w > wmax) wmax ++;
	stackel -> which = Stackel_VARIABLE;
	stackel -> content.variable = var;
}
static const wchar *Stackel_whichText (Stackel me) {
	return
		my which == Stackel_NUMBER ? L"a number" :
		my which == Stackel_STRING ? L"a string" :
		my which == Stackel_NUMERIC_ARRAY ? L"a numeric array" :
		my which == Stackel_STRING_ARRAY ? L"a string array" :
		L"???";
}

static void do_not (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : x->content.number == 0.0 ? 1.0 : 0.0);
	} else {
		Melder_throw ("Cannot negate (\"not\") ", Stackel_whichText (x), ".");
	}
}
static void do_eq (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == y->content.number ? 1.0 : 0.0);   /* Even if undefined. */
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		double result = wcsequ (x->content.string, y->content.string) ? 1.0 : 0.0;
		pushNumber (result);
	} else {
		Melder_throw ("Cannot compare (=) ", Stackel_whichText (x), " to ", Stackel_whichText (y), ".");
	}
}
static void do_ne (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number != y->content.number ? 1.0 : 0.0);   /* Even if undefined. */
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		double result = wcsequ (x->content.string, y->content.string) ? 0.0 : 1.0;
		pushNumber (result);
	} else {
		Melder_throw ("Cannot compare (<>) ", Stackel_whichText (x), " to ", Stackel_whichText (y), ".");
	}
}
static void do_le (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			x->content.number <= y->content.number ? 1.0 : 0.0);
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		double result = wcscmp (x->content.string, y->content.string) <= 0 ? 1.0 : 0.0;
		pushNumber (result);
	} else {
		Melder_throw ("Cannot compare (<=) ", Stackel_whichText (x), " to ", Stackel_whichText (y), ".");
	}
}
static void do_lt (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			x->content.number < y->content.number ? 1.0 : 0.0);
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		double result = wcscmp (x->content.string, y->content.string) < 0 ? 1.0 : 0.0;
		pushNumber (result);
	} else {
		Melder_throw ("Cannot compare (<) ", Stackel_whichText (x), " to ", Stackel_whichText (y), ".");
	}
}
static void do_ge (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			x->content.number >= y->content.number ? 1.0 : 0.0);
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		double result = wcscmp (x->content.string, y->content.string) >= 0 ? 1.0 : 0.0;
		pushNumber (result);
	} else {
		Melder_throw ("Cannot compare (>=) ", Stackel_whichText (x), " to ", Stackel_whichText (y), ".");
	}
}
static void do_gt (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			x->content.number > y->content.number ? 1.0 : 0.0);
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		double result = wcscmp (x->content.string, y->content.string) > 0 ? 1.0 : 0.0;
		pushNumber (result);
	} else {
		Melder_throw ("Cannot compare (>) ", Stackel_whichText (x), " to ", Stackel_whichText (y), ".");
	}
}
static void do_add (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			x->content.number + y->content.number);
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		long length1 = wcslen (x->content.string), length2 = wcslen (y->content.string);
		wchar_t *result = Melder_malloc (wchar_t, length1 + length2 + 1);
		wcscpy (result, x->content.string);
		wcscpy (result + length1, y->content.string);
		pushString (result);
	} else {
		Melder_throw ("Cannot add ", Stackel_whichText (y), " to ", Stackel_whichText (x), ".");
	}
}
static void do_sub (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			x->content.number - y->content.number);
	} else if (x->which == Stackel_STRING && y->which == Stackel_STRING) {
		long length1 = wcslen (x->content.string), length2 = wcslen (y->content.string), newlength = length1 - length2;
		wchar_t *result;
		if (newlength >= 0 && wcsnequ (x->content.string + newlength, y->content.string, length2)) {
			result = Melder_malloc (wchar_t, newlength + 1);
			wcsncpy (result, x->content.string, newlength);
			result [newlength] = '\0';
		} else {
			result = Melder_wcsdup (x->content.string);
		}
		pushString (result);
	} else {
		Melder_throw ("Cannot subtract (-) ", Stackel_whichText (y), " from ", Stackel_whichText (x), ".");
	}
}
static void do_mul (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			x->content.number * y->content.number);
	} else {
		Melder_throw ("Cannot multiply (*) ", Stackel_whichText (x), " by ", Stackel_whichText (y), ".");
	}
}
static void do_rdiv (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			y->content.number == 0.0 ? NUMundefined :
			x->content.number / y->content.number);
	} else {
		Melder_throw ("Cannot divide (/) ", Stackel_whichText (x), " by ", Stackel_whichText (y), ".");
	}
}
static void do_idiv (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			y->content.number == 0.0 ? NUMundefined :
			floor (x->content.number / y->content.number));
	} else {
		Melder_throw ("Cannot divide (\"div\") ", Stackel_whichText (x), " by ", Stackel_whichText (y), ".");
	}
}
static void do_mod (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			y->content.number == 0.0 ? NUMundefined :
			x->content.number - floor (x->content.number / y->content.number) * y->content.number);
	} else {
		Melder_throw ("Cannot divide (\"mod\") ", Stackel_whichText (x), " by ", Stackel_whichText (y), ".");
	}
}
static void do_minus (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : - x->content.number);
	} else {
		Melder_throw ("Cannot take the opposite (-) of ", Stackel_whichText (x), ".");
	}
}
static void do_power (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			pow (x->content.number, y->content.number));
	} else {
		Melder_throw ("Cannot exponentiate (^) ", Stackel_whichText (x), " to ", Stackel_whichText (y), ".");
	}
}
static void do_sqr (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : x->content.number * x->content.number);
	} else {
		Melder_throw ("Cannot take the square (^ 2) of ", Stackel_whichText (x), ".");
	}
}
static void do_function_n_n (double (*f) (double)) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : f (x->content.number));
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires a numeric argument, not ", Stackel_whichText (x), ".");
	}
}
static void do_abs (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : fabs (x->content.number));
	} else {
		Melder_throw ("Cannot take the absolute value (abs) of ", Stackel_whichText (x), ".");
	}
}
static void do_round (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : floor (x->content.number + 0.5));
	} else {
		Melder_throw ("Cannot round ", Stackel_whichText (x), ".");
	}
}
static void do_floor (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : floor (x->content.number));
	} else {
		Melder_throw ("Cannot round down (floor) ", Stackel_whichText (x), ".");
	}
}
static void do_ceiling (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : ceil (x->content.number));
	} else {
		Melder_throw ("Cannot round up (ceiling) ", Stackel_whichText (x), ".");
	}
}
static void do_sqrt (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined :
			x->content.number < 0.0 ? NUMundefined : sqrt (x->content.number));
	} else {
		Melder_throw ("Cannot take the square root (sqrt) of ", Stackel_whichText (x), ".");
	}
}
static void do_sin (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : sin (x->content.number));
	} else {
		Melder_throw ("Cannot take the sine (sin) of ", Stackel_whichText (x), ".");
	}
}
static void do_cos (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : cos (x->content.number));
	} else {
		Melder_throw ("Cannot take the cosine (cos) of ", Stackel_whichText (x), ".");
	}
}
static void do_tan (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : tan (x->content.number));
	} else {
		Melder_throw ("Cannot take the tangent (tan) of ", Stackel_whichText (x), ".");
	}
}
static void do_arcsin (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined :
			fabs (x->content.number) > 1.0 ? NUMundefined : asin (x->content.number));
	} else {
		Melder_throw ("Cannot take the arcsine (arcsin) of ", Stackel_whichText (x), ".");
	}
}
static void do_arccos (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined :
			fabs (x->content.number) > 1.0 ? NUMundefined : acos (x->content.number));
	} else {
		Melder_throw ("Cannot take the arccosine (arccos) of ", Stackel_whichText (x), ".");
	}
}
static void do_arctan (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : atan (x->content.number));
	} else {
		Melder_throw ("Cannot take the arctangent (arctan) of ", Stackel_whichText (x), ".");
	}
}
static void do_exp (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : exp (x->content.number));
	} else {
		Melder_throw ("Cannot exponentiate (exp) ", Stackel_whichText (x), ".");
	}
}
static void do_sinh (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : sinh (x->content.number));
	} else {
		Melder_throw ("Cannot take the hyperbolic sine (sinh) of ", Stackel_whichText (x), ".");
	}
}
static void do_cosh (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : cosh (x->content.number));
	} else {
		Melder_throw ("Cannot take the hyperbolic cosine (cosh) of ", Stackel_whichText (x), ".");
	}
}
static void do_tanh (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined : tanh (x->content.number));
	} else {
		Melder_throw ("Cannot take the hyperbolic tangent (tanh) of ", Stackel_whichText (x), ".");
	}
}
static void do_log2 (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined :
			x->content.number <= 0.0 ? NUMundefined : log (x->content.number) * NUMlog2e);
	} else {
		Melder_throw ("Cannot take the base-2 logarithm (log2) of ", Stackel_whichText (x), ".");
	}
}
static void do_ln (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined :
			x->content.number <= 0.0 ? NUMundefined : log (x->content.number));
	} else {
		Melder_throw ("Cannot take the natural logarithm (ln) of ", Stackel_whichText (x), ".");
	}
}
static void do_log10 (void) {
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined ? NUMundefined :
			x->content.number <= 0.0 ? NUMundefined : log10 (x->content.number));
	} else {
		Melder_throw ("Cannot take the base-10 logarithm (log10) of ", Stackel_whichText (x), ".");
	}
}
static void do_function_dd_d (double (*f) (double, double)) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			f (x->content.number, y->content.number));
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires two numeric arguments, not ",
			Stackel_whichText (x), " and ", Stackel_whichText (y), ".");
	}
}
static void do_function_dd_d_numar (double (*f) (double, double)) {
	Stackel n = pop;
	Melder_assert (n -> which == Stackel_NUMBER);
	if (n -> content.number != 3)
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol], " requires three arguments.");
	Stackel y = pop, x = pop, a = pop;
	if (a->which == Stackel_NUMERIC_ARRAY && x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		long numberOfRows = a->content.numericArray.numberOfRows;
		long numberOfColumns = a->content.numericArray.numberOfColumns;
		double **newData = NUMmatrix <double> (1, numberOfRows, 1, numberOfColumns); therror
		for (long irow = 1; irow <= numberOfRows; irow ++) {
			for (long icol = 1; icol <= numberOfColumns; icol ++) {
				newData [irow] [icol] = f (x->content.number, y->content.number);
			}
		}
		pushNumericArray (numberOfRows, numberOfColumns, newData);
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires one array argument and two numeric arguments, not ",
			Stackel_whichText (a), ", ", Stackel_whichText (x), " and ", Stackel_whichText (y), ".");
	}
}
static void do_function_ll_l_numar (long (*f) (long, long)) {
	Stackel n = pop;
	Melder_assert (n -> which == Stackel_NUMBER);
	if (n -> content.number != 3)
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol], " requires three arguments.");
	Stackel y = pop, x = pop, a = pop;
	if (a->which == Stackel_NUMERIC_ARRAY && x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		long numberOfRows = a->content.numericArray.numberOfRows;
		long numberOfColumns = a->content.numericArray.numberOfColumns;
		double **newData = NUMmatrix <double> (1, numberOfRows, 1, numberOfColumns); therror
		for (long irow = 1; irow <= numberOfRows; irow ++) {
			for (long icol = 1; icol <= numberOfColumns; icol ++) {
				newData [irow] [icol] = f (x->content.number, y->content.number);
			}
		}
		pushNumericArray (numberOfRows, numberOfColumns, newData);
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires one array argument and two numeric arguments, not ",
			Stackel_whichText (a), ", ", Stackel_whichText (x), " and ", Stackel_whichText (y), ".");
	}
}
static void do_function_dl_d (double (*f) (double, long)) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			f (x->content.number, y->content.number));
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires two numeric arguments, not ",
			Stackel_whichText (x), " and ", Stackel_whichText (y), ".");
	}
}
static void do_function_ld_d (double (*f) (long, double)) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			f (x->content.number, y->content.number));
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires two numeric arguments, not ",
			Stackel_whichText (x), " and ", Stackel_whichText (y), ".");
	}
}
static void do_function_ll_l (long (*f) (long, long)) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined :
			f (x->content.number, y->content.number));
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires two numeric arguments, not ",
			Stackel_whichText (x), " and ", Stackel_whichText (y), ".");
	}
}
static void do_objects_are_identical (void) {
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		int id1 = x->content.number, id2 = y->content.number;
		int i = theCurrentPraatObjects -> n;
		while (i > 0 && id1 != theCurrentPraatObjects -> list [i]. id) i --;
		if (i == 0) Melder_throw ("Object #", id1, " does not exist in function objectsAreIdentical.");
		Data object1 = (Data) theCurrentPraatObjects -> list [i]. object;
		i = theCurrentPraatObjects -> n;
		while (i > 0 && id2 != theCurrentPraatObjects -> list [i]. id) i --;
		if (i == 0) Melder_throw ("Object #", id2, " does not exist in function objectsAreIdentical.");
		Data object2 = (Data) theCurrentPraatObjects -> list [i]. object;
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined ? NUMundefined : Data_equal (object1, object2));
	} else {
		Melder_throw ("The function objectsAreIdentical requires two numeric arguments (object IDs), not ",
			Stackel_whichText (x), " and ", Stackel_whichText (y), ".");
	}
}
static void do_function_ddd_d (double (*f) (double, double, double)) {
	Stackel z = pop, y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER && z->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined || z->content.number == NUMundefined ? NUMundefined :
			f (x->content.number, y->content.number, z->content.number));
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires three numeric arguments, not ", Stackel_whichText (x), ", ",
			Stackel_whichText (y), ", and ", Stackel_whichText (z), ".");
	}
}
static void do_function_dll_d (double (*f) (double, long, long)) {
	Stackel z = pop, y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER && z->which == Stackel_NUMBER) {
		pushNumber (x->content.number == NUMundefined || y->content.number == NUMundefined || z->content.number == NUMundefined ? NUMundefined :
			f (x->content.number, y->content.number, z->content.number));
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires three numeric arguments, not ", Stackel_whichText (x), ", ",
			Stackel_whichText (y), ", and ", Stackel_whichText (z), ".");
	}
}
static void do_min (void) {
	Stackel n = pop, last;
	double result;
	Melder_assert (n->which == Stackel_NUMBER);
	if (n->content.number < 1)
		Melder_throw ("The function \"min\" requires at least one argument.");
	last = pop;
	if (last->which != Stackel_NUMBER)
		Melder_throw ("The function \"min\" can only have numeric arguments, not ", Stackel_whichText (last), ".");
	result = last->content.number;
	for (int j = n->content.number - 1; j > 0; j --) {
		Stackel previous = pop;
		if (previous->which != Stackel_NUMBER)
			Melder_throw ("The function \"min\" can only have numeric arguments, not ", Stackel_whichText (previous), ".");
		result = result == NUMundefined || previous->content.number == NUMundefined ? NUMundefined :
			result < previous->content.number ? result : previous->content.number;
	}
	pushNumber (result);
}
static void do_max (void) {
	Stackel n = pop, last;
	double result;
	Melder_assert (n->which == Stackel_NUMBER);
	if (n->content.number < 1)
		Melder_throw ("The function \"max\" requires at least one argument.");
	last = pop;
	if (last->which != Stackel_NUMBER)
		Melder_throw ("The function \"max\" can only have numeric arguments, not ", Stackel_whichText (last), ".");
	result = last->content.number;
	for (int j = n->content.number - 1; j > 0; j --) {
		Stackel previous = pop;
		if (previous->which != Stackel_NUMBER)
			Melder_throw ("The function \"max\" can only have numeric arguments, not ", Stackel_whichText (previous), ".");
		result = result == NUMundefined || previous->content.number == NUMundefined ? NUMundefined :
			result > previous->content.number ? result : previous->content.number;
	}
	pushNumber (result);
}
static void do_imin (void) {
	Stackel n = pop, last;
	double minimum, result;
	Melder_assert (n->which == Stackel_NUMBER);
	if (n->content.number < 1)
		Melder_throw ("The function \"imin\" requires at least one argument.");
	last = pop;
	if (last->which != Stackel_NUMBER)
		Melder_throw ("The function \"imin\" can only have numeric arguments, not ", Stackel_whichText (last), ".");
	minimum = last->content.number;
	result = n->content.number;
	for (int j = n->content.number - 1; j > 0; j --) {
		Stackel previous = pop;
		if (previous->which != Stackel_NUMBER)
			Melder_throw ("The function \"imin\" can only have numeric arguments, not ", Stackel_whichText (previous), ".");
		if (minimum == NUMundefined || previous->content.number == NUMundefined) {
			minimum = NUMundefined;
			result = NUMundefined;
		} else if (previous->content.number < minimum) {
			minimum = previous->content.number;
			result = j;
		}
	}
	pushNumber (result);
}
static void do_imax (void) {
	Stackel n = pop, last;
	double maximum, result;
	Melder_assert (n->which == Stackel_NUMBER);
	if (n->content.number < 1)
		Melder_throw ("The function \"imax\" requires at least one argument.");
	last = pop;
	if (last->which != Stackel_NUMBER)
		Melder_throw ("The function \"imax\" can only have numeric arguments, not ", Stackel_whichText (last), ".");
	maximum = last->content.number;
	result = n->content.number;
	for (int j = n->content.number - 1; j > 0; j --) {
		Stackel previous = pop;
		if (previous->which != Stackel_NUMBER)
			Melder_throw ("The function \"imax\" can only have numeric arguments, not ", Stackel_whichText (previous), ".");
		if (maximum == NUMundefined || previous->content.number == NUMundefined) {
			maximum = NUMundefined;
			result = NUMundefined;
		} else if (previous->content.number > maximum) {
			maximum = previous->content.number;
			result = j;
		}
	}
	pushNumber (result);
}
static void do_zeroNumar (void) {
	Stackel n = pop;
	Melder_assert (n -> which == Stackel_NUMBER);
	int rank = n -> content.number;
	if (rank < 1)
		Melder_throw ("The function \"zero#\" requires arguments.");
	long numberOfRows = 1, numberOfColumns = 1;
	if (rank > 1) {
		if (rank > 2)
			Melder_throw ("The function \"zero#\" cannot have more than two arguments.");
		Stackel ncol = pop;
		if (ncol -> which != Stackel_NUMBER)
			Melder_throw ("In the function \"zero#\", the number of columns has to be a number, not ", Stackel_whichText (ncol), ".");
		numberOfColumns = ncol -> content.number;
	}
	Stackel nrow = pop;
	if (nrow -> which != Stackel_NUMBER)
		Melder_throw ("In the function \"zero#\", the number of rows has to be a number, not ", Stackel_whichText (nrow), ".");
	numberOfRows = nrow -> content.number;
	if (numberOfRows == NUMundefined)
		Melder_throw ("In the function \"zero#\", the number of rows is undefined.");
	if (numberOfColumns == NUMundefined)
		Melder_throw ("In the function \"zero#\", the number of columns is undefined.");
	if (numberOfRows <= 0)
		Melder_throw ("In the function \"zero#\", the number of rows has to be positive.");
	if (numberOfColumns <= 0)
		Melder_throw ("In the function \"zero#\", the number of columns has to be positive.");
	autoNUMmatrix <double> data (1, numberOfRows, 1, numberOfColumns);
	pushNumericArray (numberOfRows, numberOfColumns, data.transfer());
}
static void do_linearNumar (void) {
	Stackel stackel_narg = pop;
	Melder_assert (stackel_narg -> which == Stackel_NUMBER);
	int narg = stackel_narg -> content.number;
	if (narg < 3 || narg > 4)
		Melder_throw ("The function \"linear#\" requires three or four arguments.");
	bool excludeEdges = false;   // default
	if (narg == 4) {
		Stackel stack_excludeEdges = pop;
		if (stack_excludeEdges -> which != Stackel_NUMBER)
			Melder_throw ("In the function \"linear#\", the edge exclusion flag (fourth argument) has to be a number, not ", Stackel_whichText (stack_excludeEdges), ".");
		excludeEdges = stack_excludeEdges -> content.number;
	}
	Stackel stack_numberOfSteps = pop, stack_maximum = pop, stack_minimum = pop;
	if (stack_minimum -> which != Stackel_NUMBER)
		Melder_throw ("In the function \"linear#\", the minimum (first argument) has to be a number, not ", Stackel_whichText (stack_minimum), ".");
	double minimum = stack_minimum -> content.number;
	if (minimum == NUMundefined)
		Melder_throw ("Undefined minimum in the function \"linear#\" (first argument).");
	if (stack_maximum -> which != Stackel_NUMBER)
		Melder_throw ("In the function \"linear#\", the maximum (second argument) has to be a number, not ", Stackel_whichText (stack_maximum), ".");
	double maximum = stack_maximum -> content.number;
	if (maximum == NUMundefined)
		Melder_throw ("Undefined maximum in the function \"linear#\" (second argument).");
	if (maximum < minimum)
		Melder_throw ("Maximum (", maximum, L") smaller than minimum (", minimum, ") in function \"linear#\".");
	if (stack_numberOfSteps -> which != Stackel_NUMBER)
		Melder_throw ("In the function \"linear#\", the number of steps (third argument) has to be a number, not ", Stackel_whichText (stack_numberOfSteps), ".");
	if (stack_numberOfSteps -> content.number == NUMundefined)
		Melder_throw ("Undefined number of steps in the function \"linear#\" (third argument).");
	long numberOfSteps = floor (stack_numberOfSteps -> content.number + 0.5);
	if (numberOfSteps <= 0)
		Melder_throw ("In the function \"linear#\", the number of steps (third argument) has to be positive, not ", numberOfSteps, ".");
	autoNUMmatrix <double> data (1, numberOfSteps, 1, 1);
	for (long irow = 1; irow <= numberOfSteps; irow ++) {
		data [irow] [1] = excludeEdges ?
			minimum + (irow - 0.5) * (maximum - minimum) / numberOfSteps :
			minimum + (irow - 1) * (maximum - minimum) / (numberOfSteps - 1);
	}
	if (! excludeEdges) data [numberOfSteps] [1] = maximum;   // remove rounding problems
	pushNumericArray (numberOfSteps, 1, data.transfer());
}
static void do_numberOfRows (void) {
	Stackel n = pop;
	Melder_assert (n->which == Stackel_NUMBER);
	if (n->content.number != 1)
		Melder_throw ("The function \"numberOfRows\" requires one argument.");
	Stackel array = pop;
	if (array->which == Stackel_NUMERIC_ARRAY) {
		pushNumber (array->content.numericArray.numberOfRows);
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires a numeric argument, not ", Stackel_whichText (array), ".");
	}
}
static void do_numberOfColumns (void) {
	Stackel n = pop;
	Melder_assert (n->which == Stackel_NUMBER);
	if (n->content.number != 1)
		Melder_throw ("The function \"numberOfColumns\" requires one argument.");
	Stackel array = pop;
	if (array->which == Stackel_NUMERIC_ARRAY) {
		pushNumber (array->content.numericArray.numberOfColumns);
	} else {
		Melder_throw ("The function ", Formula_instructionNames [parse [programPointer]. symbol],
			" requires a numeric argument, not ", Stackel_whichText (array), ".");
	}
}
static void do_numericArrayElement (void) {
	Stackel n = pop;
	Melder_assert (n -> which == Stackel_NUMBER);
	int narg = n -> content.number;
	if (narg < 1 || narg > 2)
		Melder_throw ("Array indexing requires one or two arguments.");
	InterpreterVariable array = parse [programPointer]. content.variable;
	long row = 1, column = 1;   // default
	if (narg > 1) {
		Stackel c = pop;
		if (c -> which != Stackel_NUMBER)
			Melder_throw ("In array indexing, the column index has to be a number, not ", Stackel_whichText (c), ".");
		if (c -> content.number == NUMundefined)
			Melder_throw ("The column index is undefined.");
		column = floor (c -> content.number + 0.5);
		if (column <= 0)
			Melder_throw ("In array indexing, the column index has to be positive.");
		if (column > array -> numericArrayValue. numberOfColumns)
			Melder_throw ("Column index out of bounds.");
	}
	Stackel r = pop;
	if (r -> which != Stackel_NUMBER)
		Melder_throw ("In array indexing, the row index has to be a number, not ", Stackel_whichText (r), ".");
	if (r -> content.number == NUMundefined)
		Melder_throw ("The row index is undefined.");
	row = floor (r -> content.number + 0.5);
	if (row <= 0)
		Melder_throw ("In array indexing, the row index has to be positive.");
	if (row > array -> numericArrayValue. numberOfRows)
		Melder_throw ("Row index out of bounds.");
	pushNumber (array -> numericArrayValue. data [row] [column]);
}
static void do_indexedNumericVariable (void) {
	Stackel n = pop;
	Melder_assert (n -> which == Stackel_NUMBER);
	int nindex = n -> content.number;
	if (nindex < 1)
		Melder_throw ("Indexed variables require at least one index.");
	wchar_t *indexedVariableName = parse [programPointer]. content.string;
	static MelderString totalVariableName = { 0 };
	MelderString_copy (& totalVariableName, indexedVariableName);
	MelderString_append (& totalVariableName, L"[");
	w -= nindex;
	for (int iindex = 1; iindex <= nindex; iindex ++) {
		Stackel index = & theStack [w + iindex];
		if (index -> which != Stackel_NUMBER)
			Melder_throw ("In indexed variables, the index has to be a number, not ", Stackel_whichText (index), ".");
		MelderString_append (& totalVariableName, Melder_double (index -> content.number), iindex == nindex ? L"]" : L",");
	}
	InterpreterVariable var = Interpreter_hasVariable (theInterpreter, totalVariableName.string);
	if (var == NULL)
		Melder_throw ("Undefined indexed variable " L_LEFT_GUILLEMET, totalVariableName.string, L_RIGHT_GUILLEMET ".");
	pushNumber (var -> numericValue);
}
static void do_indexedStringVariable (void) {
	Stackel n = pop;
	Melder_assert (n -> which == Stackel_NUMBER);
	int nindex = n -> content.number;
	if (nindex < 1)
		Melder_throw ("Indexed variables require at least one index.");
	wchar_t *indexedVariableName = parse [programPointer]. content.string;
	static MelderString totalVariableName = { 0 };
	MelderString_copy (& totalVariableName, indexedVariableName);
	MelderString_append (& totalVariableName, L"[");
	w -= nindex;
	for (int iindex = 1; iindex <= nindex; iindex ++) {
		Stackel index = & theStack [w + iindex];
		if (index -> which != Stackel_NUMBER)
			Melder_throw ("In indexed variables, the index has to be a number, not ", Stackel_whichText (index), ".");
		MelderString_append (& totalVariableName, Melder_double (index -> content.number), iindex == nindex ? L"]" : L",");
	}
	InterpreterVariable var = Interpreter_hasVariable (theInterpreter, totalVariableName.string);
	if (var == NULL)
		Melder_throw ("Undefined indexed variable " L_LEFT_GUILLEMET, totalVariableName.string, L_RIGHT_GUILLEMET ".");
	autostring result = Melder_wcsdup (var -> stringValue);
	pushString (result.transfer());
}
static void do_length (void) {
	Stackel s = pop;
	if (s->which == Stackel_STRING) {
		double result = wcslen (s->content.string);
		pushNumber (result);
	} else {
		Melder_throw ("The function \"length\" requires a string, not ", Stackel_whichText (s), ".");
	}
}
static void do_fileReadable (void) {
	Stackel s = pop;
	if (s->which == Stackel_STRING) {
		structMelderFile file = { 0 };
		Melder_relativePathToFile (s->content.string, & file);
		pushNumber (MelderFile_readable (& file));
	} else {
		Melder_throw ("The function \"fileReadable\" requires a string, not ", Stackel_whichText (s), ".");
	}
}
static void do_dateStr (void) {
	time_t today = time (NULL);
	wchar_t *date, *newline;
	date = Melder_utf8ToWcs (ctime (& today));
	newline = wcschr (date, '\n');
	if (newline) *newline = '\0';
	pushString (date);
}
static void do_leftStr (void) {
//Melder_casual ("entering left$");
	Stackel narg = pop;
	if (narg->content.number == 1 || narg->content.number == 2) {
		Stackel x = ( narg->content.number == 2 ? pop : NULL ), s = pop;
		if (s->which == Stackel_STRING && (x == NULL || x->which == Stackel_NUMBER)) {
			long newlength = x ? x->content.number : 1;
			long length = wcslen (s->content.string);
			if (newlength < 0) newlength = 0;
			if (newlength > length) newlength = length;
			#if 0
				autostring s1;
				autostring s2 = s1;   // copy constructor disabled
				s1 = s2;
			#endif
			autostring result = Melder_malloc (wchar, newlength + 1);
			wcsncpy (result.peek(), s->content.string, newlength);
			result [newlength] = '\0';
			pushString (result.transfer());
		} else {
			Melder_throw ("The function \"left$\" requires a string, or a string and a number.");
		}
	} else {
		Melder_throw ("The function \"left$\" requires one or two arguments.");
	}
//Melder_casual ("leaving left$");
}
static void do_rightStr (void) {
	Stackel narg = pop;
	if (narg->content.number == 1 || narg->content.number == 2) {
		Stackel x = ( narg->content.number == 2 ? pop : NULL ), s = pop;
		if (s->which == Stackel_STRING && (x == NULL || x->which == Stackel_NUMBER)) {
			long newlength = x ? x->content.number : 1;
			long length = wcslen (s->content.string);
			if (newlength < 0) newlength = 0;
			if (newlength > length) newlength = length;
			pushString (Melder_wcsdup (s->content.string + length - newlength));
		} else {
			Melder_throw ("The function \"right$\" requires a string, or a string and a number.");
		}
	} else {
		Melder_throw ("The function \"right$\" requires one or two arguments.");
	}
}
static void do_midStr (void) {
	Stackel narg = pop;
	if (narg->content.number == 2 || narg->content.number == 3) {
		Stackel y = ( narg->content.number == 3 ? pop : NULL ), x = pop, s = pop;
		if (s->which == Stackel_STRING && x->which == Stackel_NUMBER && (y == NULL || y->which == Stackel_NUMBER)) {
			long newlength = y ? y->content.number : 1;
			long start = x->content.number;
			long length = wcslen (s->content.string), finish = start + newlength - 1;
			autostring result;
			if (start < 1) start = 1;
			if (finish > length) finish = length;
			newlength = finish - start + 1;
			if (newlength > 0) {
				result.reset (Melder_malloc (wchar, newlength + 1));
				wcsncpy (result.peek(), s->content.string + start - 1, newlength);
				result [newlength] = '\0';
			} else {
				result.reset (Melder_wcsdup (L""));
			}
			pushString (result.transfer());
		} else {
			Melder_throw ("The function \"mid$\" requires a string and one or two numbers.");
		}
	} else {
		Melder_throw ("The function \"mid$\" requires two or three arguments.");
	}
}
static void do_environmentStr (void) {
	Stackel s = pop;
	if (s->which == Stackel_STRING) {
		wchar_t *value = Melder_getenv (s->content.string);
		autostring result = Melder_wcsdup (value != NULL ? value : L"");
		pushString (result.transfer());
	} else {
		Melder_throw ("The function \"environment$\" requires a string, not ", Stackel_whichText (s), ".");
	}
}
static void do_index (void) {
	Stackel t = pop, s = pop;
	if (s->which == Stackel_STRING && t->which == Stackel_STRING) {
		wchar_t *substring = wcsstr (s->content.string, t->content.string);
		long result = substring ? substring - s->content.string + 1 : 0;
		pushNumber (result);
	} else {
		Melder_throw ("The function \"index\" requires two strings, not ",
			Stackel_whichText (s), " and ", Stackel_whichText (t), ".");
	}
}
static void do_rindex (void) {
	Stackel part = pop, whole = pop;
	if (whole->which == Stackel_STRING && part->which == Stackel_STRING) {
		wchar_t *lastSubstring = wcsstr (whole->content.string, part->content.string);
		if (part->content.string [0] == '\0') {
			long result = wcslen (whole->content.string);
			pushNumber (result);
		} else if (lastSubstring) {
			for (;;) {
				wchar_t *substring = wcsstr (lastSubstring + 1, part->content.string);
				if (substring == NULL) break;
				lastSubstring = substring;
			}
			pushNumber (lastSubstring - whole->content.string + 1);
		} else {
			pushNumber (0);
		}
	} else {
		Melder_throw ("The function \"rindex\" requires two strings, not ",
			Stackel_whichText (whole), " and ", Stackel_whichText (part), ".");
	}
}
static void do_stringMatchesCriterion (int criterion) {
	Stackel t = pop, s = pop;
	if (s->which == Stackel_STRING && t->which == Stackel_STRING) {
		int result = Melder_stringMatchesCriterion (s->content.string, criterion, t->content.string);
		pushNumber (result);
	} else {
		Melder_throw ("The function \"", Formula_instructionNames [parse [programPointer]. symbol],
			"\" requires two strings, not ", Stackel_whichText (s), " and ", Stackel_whichText (t), ".");
	}
}
static void do_index_regex (int backward) {
	Stackel t = pop, s = pop;
	if (s->which == Stackel_STRING && t->which == Stackel_STRING) {
		const wchar_t *errorMessage;
		regexp *compiled_regexp = CompileRE ((const regularExp_CHAR *) t->content.string, & errorMessage, 0);
		if (compiled_regexp == NULL) {
			pushNumber (NUMundefined);
		} else if (ExecRE (compiled_regexp, NULL, (const regularExp_CHAR *) s->content.string, NULL, backward, '\0', '\0', NULL, NULL, NULL)) {
			wchar_t *place = (wchar *) compiled_regexp -> startp [0];
			pushNumber (place - s->content.string + 1);
			free (compiled_regexp);
		} else {
			pushNumber (FALSE);
		}
	} else {
		Melder_throw ("The function \"", Formula_instructionNames [parse [programPointer]. symbol],
			"\" requires two strings, not ", Stackel_whichText (s), " and ", Stackel_whichText (t), ".");
	}
}
static void do_replaceStr (void) {
	Stackel x = pop, u = pop, t = pop, s = pop;
	if (s->which == Stackel_STRING && t->which == Stackel_STRING && u->which == Stackel_STRING && x->which == Stackel_NUMBER) {
		long numberOfMatches;
		autostring result = str_replace_literal (s->content.string, t->content.string, u->content.string, x->content.number, & numberOfMatches);
		pushString (result.transfer());
	} else {
		Melder_throw ("The function \"replace$\" requires three strings and a number.");
	}
}
static void do_replace_regexStr (void) {
	Stackel x = pop, u = pop, t = pop, s = pop;
	if (s->which == Stackel_STRING && t->which == Stackel_STRING && u->which == Stackel_STRING && x->which == Stackel_NUMBER) {
		const wchar_t *errorMessage;
		regexp *compiled_regexp = CompileRE ((const regularExp_CHAR *) t->content.string, & errorMessage, 0);
		if (compiled_regexp == NULL) {
			autostring result = Melder_wcsdup (L"");
			pushString (result.transfer());
		} else {
			long numberOfMatches;
			autostring result = str_replace_regexp (s->content.string, compiled_regexp, u->content.string, x->content.number, & numberOfMatches);
			pushString (result.transfer());
		}
	} else {
		Melder_throw ("The function \"replace_regex$\" requires three strings and a number.");
	}
}
static void do_extractNumber (void) {
	Stackel t = pop, s = pop;
	if (s->which == Stackel_STRING && t->which == Stackel_STRING) {
		wchar_t *substring = wcsstr (s->content.string, t->content.string);
		if (substring == NULL) {
			pushNumber (NUMundefined);
		} else {
			/* Skip the prompt. */
			substring += wcslen (t->content.string);
			/* Skip white space. */
			while (*substring == ' ' || *substring == '\t' || *substring == '\n' || *substring == '\r') substring ++;
			if (substring [0] == '\0' || wcsnequ (substring, L"--undefined--", 13)) {
				pushNumber (NUMundefined);
			} else {
				wchar_t buffer [101], *slash;
				int i;
				for (i = 0; i < 100; i ++) {
					buffer [i] = *substring;
					substring ++;
					if (*substring == '\0' || *substring == ' ' || *substring == '\t' || *substring == '\n' || *substring == '\r') break;
				}
				if (i >= 100) {
					buffer [100] = '\0';
					pushNumber (Melder_atof (buffer));
				} else {
					buffer [i + 1] = '\0';
					slash = wcschr (buffer, '/');
					if (slash) {
						double numerator, denominator;
						*slash = '\0';
						numerator = Melder_atof (buffer), denominator = Melder_atof (slash + 1);
						pushNumber (numerator / denominator);
					} else {
						pushNumber (Melder_atof (buffer));
					}
				}
			}
		}
	} else {
		Melder_throw ("The function \"", Formula_instructionNames [parse [programPointer]. symbol],
			"\" requires two strings, not ", Stackel_whichText (s), " and ", Stackel_whichText (t), ".");
	}
}
static void do_extractTextStr (int singleWord) {
	Stackel t = pop, s = pop;
	if (s->which == Stackel_STRING && t->which == Stackel_STRING) {
		wchar_t *substring = wcsstr (s->content.string, t->content.string);
		autostring result;
		if (substring == NULL) {
			result.reset (Melder_wcsdup (L""));
		} else {
			long length;
			/* Skip the prompt. */
			substring += wcslen (t->content.string);
			if (singleWord) {
				/* Skip white space. */
				while (*substring == ' ' || *substring == '\t' || *substring == '\n' || *substring == '\r') substring ++;
			}
			wchar *p = substring;
			if (singleWord) {
				/* Proceed until next white space. */
				while (*p != '\0' && *p != ' ' && *p != '\t' && *p != '\n' && *p != '\r') p ++;
			} else {
				/* Proceed until end of line. */
				while (*p != '\0' && *p != '\n' && *p != '\r') p ++;
			}
			length = p - substring;
			result.reset (Melder_malloc (wchar, length + 1));
			wcsncpy (result.peek(), substring, length);
			result [length] = '\0';
		}
		pushString (result.transfer());
	} else {
		Melder_throw ("The function \"", Formula_instructionNames [parse [programPointer]. symbol],
			"\" requires two strings, not ", Stackel_whichText (s), " and ", Stackel_whichText (t), ".");
	}
}
static void do_selected (void) {
	Stackel n = pop;
	long result = 0;
	if (n->content.number == 0) {
		result = praat_getIdOfSelected (NULL, 0);
	} else if (n->content.number == 1) {
		Stackel a = pop;
		if (a->which == Stackel_STRING) {
			ClassInfo klas = Thing_classFromClassName (a->content.string); therror
			result = praat_getIdOfSelected (klas, 0);
		} else if (a->which == Stackel_NUMBER) {
			result = praat_getIdOfSelected (NULL, a->content.number);
		} else {
			Melder_throw ("The function \"selected\" requires a string (an object type name) and/or a number.");
		}
	} else if (n->content.number == 2) {
		Stackel x = pop, s = pop;
		if (s->which == Stackel_STRING && x->which == Stackel_NUMBER) {
			ClassInfo klas = Thing_classFromClassName (s->content.string); therror
			result = praat_getIdOfSelected (klas, x->content.number);
		} else {
			Melder_throw ("The function \"selected\" requires a string (an object type name) and/or a number.");
		}
	} else {
		Melder_throw ("The function \"selected\" requires 0, 1, or 2 arguments, not ", n->content.number, ".");
	}
	pushNumber (result);
}
static void do_selectedStr (void) {
	Stackel n = pop;
	wchar_t *name;
	autostring result;
	if (n->content.number == 0) {
		name = praat_getNameOfSelected (NULL, 0);
		result.reset (Melder_wcsdup (name));
	} else if (n->content.number == 1) {
		Stackel a = pop;
		if (a->which == Stackel_STRING) {
			ClassInfo klas = Thing_classFromClassName (a->content.string); therror
			name = praat_getNameOfSelected (klas, 0);
			result.reset (Melder_wcsdup (name));
		} else if (a->which == Stackel_NUMBER) {
			name = praat_getNameOfSelected (NULL, a->content.number);
			result.reset (Melder_wcsdup (name));
		} else {
			Melder_throw ("The function \"selected$\" requires a string (an object type name) and/or a number.");
		}
	} else if (n->content.number == 2) {
		Stackel x = pop, s = pop;
		if (s->which == Stackel_STRING && x->which == Stackel_NUMBER) {
			ClassInfo klas = Thing_classFromClassName (s->content.string); therror
			name = praat_getNameOfSelected (klas, x->content.number);
			result.reset (Melder_wcsdup (name));
		} else {
			Melder_throw ("The function \"selected$\" requires 0, 1, or 2 arguments, not ", n->content.number, ".");
		}
	}
	pushString (result.transfer());
}
static void do_numberOfSelected (void) {
	Stackel n = pop;
	long result = 0;
	if (n->content.number == 0) {
		result = praat_selection (NULL);
	} else if (n->content.number == 1) {
		Stackel s = pop;
		if (s->which == Stackel_STRING) {
			ClassInfo klas = Thing_classFromClassName (s->content.string); therror
			result = praat_selection (klas);
		} else {
			Melder_throw ("The function \"numberOfSelected\" requires a string (an object type name), not ", Stackel_whichText (s), ".");
		}
	} else {
		Melder_throw ("The function \"numberOfSelected\" requires 0 or 1 arguments, not ", n->content.number, ".");
	}
	pushNumber (result);
}
static void do_fixedStr (void) {
	Stackel precision = pop, value = pop;
	if (value->which == Stackel_NUMBER && precision->which == Stackel_NUMBER) {
		autostring result = Melder_wcsdup (Melder_fixed (value->content.number, precision->content.number));
		pushString (result.transfer());
	} else {
		Melder_throw ("The function \"fixed$\" requires two numbers (value and precision), not ", Stackel_whichText (value), " and ", Stackel_whichText (precision), ".");
	}
}
static void do_percentStr (void) {
	Stackel precision = pop, value = pop;
	if (value->which == Stackel_NUMBER && precision->which == Stackel_NUMBER) {
		autostring result = Melder_wcsdup (Melder_percent (value->content.number, precision->content.number));
		pushString (result.transfer());
	} else {
		Melder_throw ("The function \"percent$\" requires two numbers (value and precision), not ", Stackel_whichText (value), " and ", Stackel_whichText (precision), ".");
	}
}
static void do_deleteFile (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"deleteFile\" is not available inside manuals.");
	Stackel f = pop;
	if (f->which == Stackel_STRING) {
		structMelderFile file = { 0 };
		Melder_relativePathToFile (f->content.string, & file); therror
		MelderFile_delete (& file);
		pushNumber (1);
	} else {
		Melder_throw ("The function \"deleteFile\" requires a string, not ", Stackel_whichText (f), ".");
	}
}
static void do_createDirectory (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"createDirectory\" is not available inside manuals.");
	Stackel f = pop;
	if (f->which == Stackel_STRING) {
		structMelderDir currentDirectory = { { 0 } };
		Melder_getDefaultDir (& currentDirectory);
		#if defined (UNIX) || defined (macintosh)
			Melder_createDirectory (& currentDirectory, f->content.string, S_IRWXU | S_IRWXG | S_IROTH | S_IXOTH); therror
		#else
			Melder_createDirectory (& currentDirectory, f->content.string, 0); therror
		#endif
		pushNumber (1);
	} else {
		Melder_throw ("The function \"deleteFile\" requires a string, not ", Stackel_whichText (f), ".");
	}
}
static void do_variableExists (void) {
	Stackel f = pop;
	if (f->which == Stackel_STRING) {
		bool result = Interpreter_hasVariable (theInterpreter, f->content.string) != NULL;
		pushNumber (result);
	} else {
		Melder_throw ("The function \"variableExists\" requires a string, not ", Stackel_whichText (f), ".");
	}
}
static void do_beginPauseForm (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"beginPauseForm\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 1) {
		Stackel title = pop;
		if (title->which == Stackel_STRING) {
			UiPause_begin (theCurrentPraatApplication -> topShell, title->content.string, theInterpreter);
		} else {
			Melder_throw ("The function \"beginPauseForm\" requires a string (the title), not ", Stackel_whichText (title), ".");
		}
	} else {
		Melder_throw ("The function \"beginPauseForm\" requires 1 argument (a title), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddReal (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"real\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		const wchar *defaultString = NULL;
		if (defaultValue->which == Stackel_STRING) {
			defaultString = defaultValue->content.string;
		} else if (defaultValue->which == Stackel_NUMBER) {
			defaultString = Melder_double (defaultValue->content.number);
		} else {
			Melder_throw ("The second argument of \"real\" (the default value) must be a string or a number, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_real (label->content.string, defaultString);
		} else {
			Melder_throw ("The first argument of \"real\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"real\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddPositive (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"positive\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		const wchar *defaultString = NULL;
		if (defaultValue->which == Stackel_STRING) {
			defaultString = defaultValue->content.string;
		} else if (defaultValue->which == Stackel_NUMBER) {
			defaultString = Melder_double (defaultValue->content.number);
		} else {
			Melder_throw ("The second argument of \"positive\" (the default value) must be a string or a number, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_positive (label->content.string, defaultString);
		} else {
			Melder_throw ("The first argument of \"positive\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"positive\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddInteger (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"integer\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		const wchar *defaultString = NULL;
		if (defaultValue->which == Stackel_STRING) {
			defaultString = defaultValue->content.string;
		} else if (defaultValue->which == Stackel_NUMBER) {
			defaultString = Melder_double (defaultValue->content.number);
		} else {
			Melder_throw ("The second argument of \"integer\" (the default value) must be a string or a number, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_integer (label->content.string, defaultString);
		} else {
			Melder_throw ("The first argument of \"integer\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"integer\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddNatural (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"natural\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		const wchar *defaultString = NULL;
		if (defaultValue->which == Stackel_STRING) {
			defaultString = defaultValue->content.string;
		} else if (defaultValue->which == Stackel_NUMBER) {
			defaultString = Melder_double (defaultValue->content.number);
		} else {
			Melder_throw ("The second argument of \"natural\" (the default value) must be a string or a number, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_natural (label->content.string, defaultString);
		} else {
			Melder_throw ("The first argument of \"natural\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"natural\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddWord (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"word\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		if (defaultValue->which != Stackel_STRING) {
			Melder_throw ("The second argument of \"word\" (the default value) must be a string, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_word (label->content.string, defaultValue->content.string);
		} else {
			Melder_throw ("The first argument of \"word\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"word\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddSentence (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"sentence\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		if (defaultValue->which != Stackel_STRING) {
			Melder_throw ("The second argument of \"sentence\" (the default value) must be a string, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_sentence (label->content.string, defaultValue->content.string);
		} else {
			Melder_throw ("The first argument of \"sentence\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"sentence\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddText (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"text\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		if (defaultValue->which != Stackel_STRING) {
			Melder_throw ("The second argument of \"text\" (the default value) must be a string, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_text (label->content.string, defaultValue->content.string);
		} else {
			Melder_throw ("The first argument of \"text\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"text\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddBoolean (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"boolean\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		if (defaultValue->which != Stackel_NUMBER) {
			Melder_throw ("The second argument of \"boolean\" (the default value) must be a number (0 or 1), not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_boolean (label->content.string, defaultValue->content.number);
		} else {
			Melder_throw ("The first argument of \"boolean\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"boolean\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddChoice (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"choice\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		if (defaultValue->which != Stackel_NUMBER) {
			Melder_throw ("The second argument of \"choice\" (the default value) must be a whole number, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_choice (label->content.string, defaultValue->content.number);
		} else {
			Melder_throw ("The first argument of \"choice\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"choice\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddOptionMenu (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"optionMenu\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultValue = pop;
		if (defaultValue->which != Stackel_NUMBER) {
			Melder_throw ("The second argument of \"optionMenu\" (the default value) must be a whole number, not ", Stackel_whichText (defaultValue), ".");
		}
		Stackel label = pop;
		if (label->which == Stackel_STRING) {
			UiPause_optionMenu (label->content.string, defaultValue->content.number);
		} else {
			Melder_throw ("The first argument of \"optionMenu\" (the label) must be a string, not ", Stackel_whichText (label), ".");
		}
	} else {
		Melder_throw ("The function \"optionMenu\" requires 2 arguments (a label and a default value), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddOption (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"option\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 1) {
		Stackel text = pop;
		if (text->which == Stackel_STRING) {
			UiPause_option (text->content.string);
		} else {
			Melder_throw ("The argument of \"option\" must be a string (the text), not ", Stackel_whichText (text), ".");
		}
	} else {
		Melder_throw ("The function \"option\" requires 1 argument (a text), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_pauseFormAddComment (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"comment\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number == 1) {
		Stackel text = pop;
		if (text->which == Stackel_STRING) {
			UiPause_comment (text->content.string);
		} else {
			Melder_throw ("The argument of \"comment\" must be a string (the text), not ", Stackel_whichText (text), ".");
		}
	} else {
		Melder_throw ("The function \"comment\" requires 1 argument (a text), not ", n->content.number, ".");
	}
	pushNumber (1);
}
static void do_endPauseForm (void) {
	if (theCurrentPraatObjects != & theForegroundPraatObjects)
		Melder_throw ("The function \"endPause\" is not available inside manuals.");
	Stackel n = pop;
	if (n->content.number < 2 || n->content.number > 12)
		Melder_throw ("The function \"endPause\" requires 2 to 12 arguments, not ", n->content.number, ".");
	Stackel d = pop;
	if (d->which != Stackel_NUMBER)
		Melder_throw ("The last argument of \"endPause\" has to be a number (the default or cancel continue button), not ", Stackel_whichText (d), ".");
	int numberOfContinueButtons = n->content.number - 1;
	int cancelContinueButton = 0, defaultContinueButton = d->content.number;
	Stackel ca = pop;
	if (ca->which == Stackel_NUMBER) {
		cancelContinueButton = defaultContinueButton;
		defaultContinueButton = ca->content.number;
		numberOfContinueButtons --;
		if (cancelContinueButton < 1 || cancelContinueButton > numberOfContinueButtons)
			Melder_throw ("Your last argument of \"endPause\" is the number of the cancel button; it cannot be ", cancelContinueButton,
				" but has to lie between 1 and ", numberOfContinueButtons, ".");
	}
	Stackel co [1+10] = { 0 };
	for (int i = numberOfContinueButtons; i >= 1; i --) {
		co [i] = cancelContinueButton != 0 || i != numberOfContinueButtons ? pop : ca;
		if (co[i]->which != Stackel_STRING)
			Melder_throw ("Each of the first ", numberOfContinueButtons,
				" argument(s) of \"endPause\" has to be a string (a button text), not ", Stackel_whichText (co[i]), ".");
	}
	int buttonClicked = UiPause_end (numberOfContinueButtons, defaultContinueButton, cancelContinueButton,
		co [1] == NULL ? NULL : co[1]->content.string, co [2] == NULL ? NULL : co[2]->content.string,
		co [3] == NULL ? NULL : co[3]->content.string, co [4] == NULL ? NULL : co[4]->content.string,
		co [5] == NULL ? NULL : co[5]->content.string, co [6] == NULL ? NULL : co[6]->content.string,
		co [7] == NULL ? NULL : co[7]->content.string, co [8] == NULL ? NULL : co[8]->content.string,
		co [9] == NULL ? NULL : co[9]->content.string, co [10] == NULL ? NULL : co[10]->content.string,
		theInterpreter); therror
	//Melder_casual ("Button %d", buttonClicked);
	pushNumber (buttonClicked);
}
static void do_chooseReadFileStr (void) {
	Stackel n = pop;
	if (n->content.number == 1) {
		Stackel title = pop;
		if (title->which == Stackel_STRING) {
			autoSortedSetOfString fileNames = GuiFileSelect_getInfileNames (NULL, title->content.string, false);
			if (fileNames -> size == 0) {
				autostring result = Melder_wcsdup (L"");
				pushString (result.transfer());
			} else {
				SimpleString fileName = (SimpleString) fileNames -> item [1];
				autostring result = Melder_wcsdup (fileName -> string);
				pushString (result.transfer());
			}
		} else {
			Melder_throw ("The argument of \"chooseReadFile$\" must be a string (the title), not ", Stackel_whichText (title), ".");
		}
	} else {
		Melder_throw ("The function \"chooseReadFile$\" requires 1 argument (a title), not ", n->content.number, ".");
	}
}
static void do_chooseWriteFileStr (void) {
	Stackel n = pop;
	if (n->content.number == 2) {
		Stackel defaultName = pop, title = pop;
		if (title->which == Stackel_STRING && defaultName->which == Stackel_STRING) {
			autostring result = GuiFileSelect_getOutfileName (NULL, title->content.string, defaultName->content.string);
			if (result.peek() == NULL) {
				result.reset (Melder_wcsdup (L""));
			}
			pushString (result.transfer());
		} else {
			Melder_throw ("The arguments of \"chooseWriteFile$\" must be two strings (the title and the default name).");
		}
	} else {
		Melder_throw ("The function \"chooseWriteFile$\" requires 2 arguments (a title and a default name), not ", n->content.number, ".");
	}
}
static void do_chooseDirectoryStr (void) {
	Stackel n = pop;
	if (n->content.number == 1) {
		Stackel title = pop;
		if (title->which == Stackel_STRING) {
			autostring result = GuiFileSelect_getDirectoryName (NULL, title->content.string);
			if (result.peek() == NULL) {
				result.reset (Melder_wcsdup (L""));
			}
			pushString (result.transfer());
		} else {
			Melder_throw ("The argument of \"chooseDirectory$\" must be a string (the title).");
		}
	} else {
		Melder_throw ("The function \"chooseDirectory$\" requires 1 argument (a title), not ", n->content.number, ".");
	}
}
static void do_demoWindowTitle (void) {
	Stackel n = pop;
	if (n->content.number == 1) {
		Stackel title = pop;
		if (title->which == Stackel_STRING) {
			Demo_windowTitle (title->content.string); therror
		} else {
			Melder_throw ("The argument of \"demoWindowTitle\" must be a string (the title), not ", Stackel_whichText (title), ".");
		}
	} else {
		Melder_throw ("The function \"demoWindowTitle\" requires 1 argument (a title), not ", Melder_integer (n->content.number), ".");
	}
	pushNumber (1);
}
static void do_demoShow (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoShow\" requires 0 arguments, not ", n->content.number, ".");
	Demo_show (); therror
	pushNumber (1);
}
static void do_demoWaitForInput (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoWaitForInput\" requires 0 arguments, not ", n->content.number, ".");
	Demo_waitForInput (theInterpreter); therror
	pushNumber (1);
}
static void do_demoInput (void) {
	Stackel n = pop;
	if (n->content.number == 1) {
		Stackel keys = pop;
		if (keys->which == Stackel_STRING) {
			bool result = Demo_input (keys->content.string); therror
			pushNumber (result);
		} else {
			Melder_throw ("The argument of \"demoInput\" must be a string (the keys), not ", Stackel_whichText (keys), ".");
		}
	} else {
		Melder_throw ("The function \"demoInput\" requires 1 argument (keys), not ", n->content.number, ".");
	}
}
static void do_demoClickedIn (void) {
	Stackel n = pop;
	if (n->content.number == 4) {
		Stackel top = pop, bottom = pop, right = pop, left = pop;
		if (left->which == Stackel_NUMBER && right->which == Stackel_NUMBER && bottom->which == Stackel_NUMBER && top->which == Stackel_NUMBER) {
			bool result = Demo_clickedIn (left->content.number, right->content.number, bottom->content.number, top->content.number); therror
			pushNumber (result);
		} else {
			Melder_throw ("All arguments of \"demoClickedIn\" must be numbers (the x and y ranges).");
		}
	} else {
		Melder_throw ("The function \"demoClickedIn\" requires 4 arguments (x and y ranges), not ", n->content.number, ".");
	}
}
static void do_demoClicked (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoClicked\" requires 0 arguments, not ", n->content.number, ".");
	bool result = Demo_clicked (); therror
	pushNumber (result);
}
static void do_demoX (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoX\" requires 0 arguments, not ", n->content.number, ".");
	double result = Demo_x (); therror
	pushNumber (result);
}
static void do_demoY (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoY\" requires 0 arguments, not ", n->content.number, L".");
	double result = Demo_y (); therror
	pushNumber (result);
}
static void do_demoKeyPressed (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoKeyPressed\" requires 0 arguments, not ", n->content.number, ".");
	bool result = Demo_keyPressed (); therror
	pushNumber (result);
}
static void do_demoKey (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoKey\" requires 0 arguments, not ", n->content.number, ".");
	autostring key = Melder_malloc (wchar, 2);
	key [0] = Demo_key (); therror
	key [1] = '\0';
	pushString (key.transfer());
}
static void do_demoShiftKeyPressed (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoShiftKeyPressed\" requires 0 arguments, not ", n->content.number, ".");
	bool result = Demo_shiftKeyPressed (); therror
	pushNumber (result);
}
static void do_demoCommandKeyPressed (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoCommandKeyPressed\" requires 0 arguments, not ", n->content.number, ".");
	bool result = Demo_commandKeyPressed (); therror
	pushNumber (result);
}
static void do_demoOptionKeyPressed (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoOptionKeyPressed\" requires 0 arguments, not ", n->content.number, ".");
	bool result = Demo_optionKeyPressed (); therror
	pushNumber (result);
}
static void do_demoExtraControlKeyPressed (void) {
	Stackel n = pop;
	if (n->content.number != 0)
		Melder_throw ("The function \"demoControlKeyPressed\" requires 0 arguments, not ", n->content.number, ".");
	bool result = Demo_extraControlKeyPressed (); therror
	pushNumber (result);
}
static long Stackel_getRowNumber (Stackel row, Data thee) {
	long result = 0;
	if (row->which == Stackel_NUMBER) {
		result = floor (row->content.number + 0.5);   // round
	} else if (row->which == Stackel_STRING) {
		if (! thy v_hasGetRowIndex ())
			Melder_throw ("Objects of type ", Thing_className (thee), " do not have row labels, so row indexes have to be numbers.");
		result = thy v_getRowIndex (row->content.string);
		if (result == 0)
			Melder_throw ("Object \"", thy name, "\" has no row labelled \"", row->content.string, "\".");
	} else {
		Melder_throw ("A row index should be a number or a string, not ", Stackel_whichText (row), ".");
	}
	return result;
}
static long Stackel_getColumnNumber (Stackel column, Data thee) {
	long result = 0;
	if (column->which == Stackel_NUMBER) {
		result = floor (column->content.number + 0.5);   // round
	} else if (column->which == Stackel_STRING) {
		if (! thy v_hasGetColIndex ())
			Melder_throw ("Objects of type ", Thing_className (thee), " do not have column labels, so column indexes have to be numbers.");
		result = thy v_getColIndex (column->content.string);
		if (result == 0)
			Melder_throw ("Object \"", thy name, "\" has no column labelled \"", column->content.string, "\".");
	} else {
		Melder_throw ("A column index should be a number or a string, not ", Stackel_whichText (column), ".");
	}
	return result;
}
static void do_self0 (long irow, long icol) {
	Data me = theSource;
	if (me == NULL) Melder_throw ("The name \"self\" is restricted to formulas for objects.");
	if (my v_hasGetCell ()) {
		pushNumber (my v_getCell ());
	} else if (my v_hasGetVector ()) {
		if (icol == 0) {
			Melder_throw ("We are not in a loop, hence no implicit column index for the current ",
				Thing_className (me), " object (self).\nTry using the [column] index explicitly.");
		} else {
			pushNumber (my v_getVector (irow, icol));
		}
	} else if (my v_hasGetMatrix ()) {
		if (irow == 0) {
			if (icol == 0) {
				Melder_throw ("We are not in a loop over rows and columns,\n"
					"hence no implicit row and column indexing for the current ",
					Thing_className (me), " object (self).\n"
					"Try using both [row, column] indexes explicitly.");
			} else {
				Melder_throw ("We are not in a loop over columns only,\n"
					"hence no implicit row index for the current ",
					Thing_className (me), " object (self).\n"
					"Try using the [row] index explicitly.");
			}
		} else {
			pushNumber (my v_getMatrix (irow, icol));
		}
	} else {
		Melder_throw (Thing_className (me), " objects (like self) accept no [] indexing.");
	}
}
static void do_selfStr0 (long irow, long icol) {
	Data me = theSource;
	if (me == NULL) Melder_throw ("The name \"self$\" is restricted to formulas for objects.");
	if (my v_hasGetCellStr ()) {
		autostring result = Melder_wcsdup (my v_getCellStr ());
		pushString (result.transfer());
	} else if (my v_hasGetVectorStr ()) {
		if (icol == 0) {
			Melder_throw ("We are not in a loop, hence no implicit column index for the current ",
				Thing_className (me), " object (self).\nTry using the [column] index explicitly.");
		} else {
			autostring result = Melder_wcsdup (my v_getVectorStr (icol));
			pushString (result.transfer());
		}
	} else if (my v_hasGetMatrixStr ()) {
		if (irow == 0) {
			if (icol == 0) {
				Melder_throw ("We are not in a loop over rows and columns,\n"
					"hence no implicit row and column indexing for the current ",
					Thing_className (me), " object (self).\n"
					"Try using both [row, column] indexes explicitly.");
			} else {
				Melder_throw ("We are not in a loop over columns only,\n"
					"hence no implicit row index for the current ",
					Thing_className (me), " object (self).\n"
					"Try using the [row] index explicitly.");
			}
		} else {
			autostring result = Melder_wcsdup (my v_getMatrixStr (irow, icol));
			pushString (result.transfer());
		}
	} else {
		Melder_throw (Thing_className (me), " objects (like self) accept no [] indexing.");
	}
}
static Data getObjectFromUniqueID (Stackel object) {
	Data thee = NULL;
	if (object->which == Stackel_NUMBER) {
		int i = theCurrentPraatObjects -> n;
		while (i > 0 && object->content.number != theCurrentPraatObjects -> list [i]. id)
			i --;
		if (i == 0) {
			Melder_throw ("No such object: ", object->content.number);
		}
		thee = (Data) theCurrentPraatObjects -> list [i]. object;
	} else if (object->which == Stackel_STRING) {
		int i = theCurrentPraatObjects -> n;
		while (i > 0 && ! Melder_wcsequ (object->content.string, theCurrentPraatObjects -> list [i]. name))
			i --;
		if (i == 0) {
			Melder_throw ("No such object: ", object->content.string);
		}
		thee = (Data) theCurrentPraatObjects -> list [i]. object;
	} else {
		Melder_throw ("The first argument to \"object\" must be a number (unique ID) or a string (name), not ", Stackel_whichText (object), ".");
	}
	return thee;
}
static void do_objectCell0 (long irow, long icol) {
	Data thee = getObjectFromUniqueID (pop);
	if (thy v_hasGetCell ()) {
		pushNumber (thy v_getCell ());
	} else if (thy v_hasGetVector ()) {
		if (icol == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit column index for this ", Thing_className (thee), " object.\n"
				"Try using: object [id, column].");
		} else {
			pushNumber (thy v_getVector (irow, icol));
		}
	} else if (thy v_hasGetMatrix ()) {
		if (irow == 0) {
			if (icol == 0) {
				Melder_throw ("We are not in a loop over rows and columns,\n"
					"hence no implicit row and column indexing for this ", Thing_className (thee), " object.\n"
					"Try using: object [id, row, column].");
			} else {
				Melder_throw ("We are not in a loop over columns only,\n"
					"hence no implicit row index for this ", Thing_className (thee), " object.\n"
					"Try using: object [id, row].");
			}
		} else {
			pushNumber (thy v_getMatrix (irow, icol));
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept no [] indexing.");
	}
}
static void do_matriks0 (long irow, long icol) {
	Data thee = parse [programPointer]. content.object;
	if (thy v_hasGetCell ()) {
		pushNumber (thy v_getCell ());
	} else if (thy v_hasGetVector ()) {
		if (icol == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit column index for this ", Thing_className (thee), " object.\n"
				"Try using the [column] index explicitly.");
		} else {
			pushNumber (thy v_getVector (irow, icol));
		}
	} else if (thy v_hasGetMatrix ()) {
		if (irow == 0) {
			if (icol == 0) {
				Melder_throw ("We are not in a loop over rows and columns,\n"
					"hence no implicit row and column indexing for this ", Thing_className (thee), " object.\n"
					"Try using both [row, column] indexes explicitly.");
			} else {
				Melder_throw ("We are not in a loop over columns only,\n"
					"hence no implicit row index for this ", Thing_className (thee), " object.\n"
					"Try using the [row] index explicitly.");
			}
		} else {
			pushNumber (thy v_getMatrix (irow, icol));
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept no [] indexing.");
	}
}
static void do_selfMatriks1 (long irow) {
	Data me = theSource;
	Stackel column = pop;
	if (me == NULL) Melder_throw ("The name \"self\" is restricted to formulas for objects.");
	long icol = Stackel_getColumnNumber (column, me);
	if (my v_hasGetVector ()) {
		pushNumber (my v_getVector (irow, icol));
	} else if (my v_hasGetMatrix ()) {
		if (irow == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit row index for the current ", Thing_className (me), " object (self).\n"
				"Try using both [row, column] indexes instead.");
		} else {
			pushNumber (my v_getMatrix (irow, icol));
		}
	} else {
		Melder_throw (Thing_className (me), " objects (like self) accept no [column] indexes.");
	}
}
static void do_selfMatriksStr1 (long irow) {
	Data me = theSource;
	Stackel column = pop;
	if (me == NULL) Melder_throw ("The name \"self$\" is restricted to formulas for objects.");
	long icol = Stackel_getColumnNumber (column, me);
	if (my v_hasGetVectorStr ()) {
		autostring result = Melder_wcsdup (my v_getVectorStr (icol));
		pushString (result.transfer());
	} else if (my v_hasGetMatrixStr ()) {
		if (irow == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit row index for the current ", Thing_className (me), " object (self).\n"
				"Try using both [row, column] indexes instead.");
		} else {
			autostring result = Melder_wcsdup (my v_getMatrixStr (irow, icol));
			pushString (result.transfer());
		}
	} else {
		Melder_throw (Thing_className (me), " objects (like self) accept no [column] indexes.");
	}
}
static void do_objectCell1 (long irow) {
	Stackel column = pop;
	Data thee = getObjectFromUniqueID (pop);
	long icol = Stackel_getColumnNumber (column, thee);
	if (thy v_hasGetVector ()) {
		pushNumber (thy v_getVector (irow, icol));
	} else if (thy v_hasGetMatrix ()) {
		if (irow == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit row index for this ", Thing_className (thee), " object.\n"
				"Try using: object [id, row, column].");
		} else {
			pushNumber (thy v_getMatrix (irow, icol));
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept no [column] indexes.");
	}
}
static void do_matriks1 (long irow) {
	Data thee = parse [programPointer]. content.object;
	Stackel column = pop;
	long icol = Stackel_getColumnNumber (column, thee);
	if (thy v_hasGetVector ()) {
		pushNumber (thy v_getVector (irow, icol));
	} else if (thy v_hasGetMatrix ()) {
		if (irow == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit row index for this ", Thing_className (thee), " object.\n"
				"Try using both [row, column] indexes instead.");
		} else {
			pushNumber (thy v_getMatrix (irow, icol));
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept no [column] indexes.");
	}
}
static void do_objectCellStr1 (long irow) {
	Stackel column = pop;
	Data thee = getObjectFromUniqueID (pop);
	long icol = Stackel_getColumnNumber (column, thee);
	if (thy v_hasGetVectorStr ()) {
		autostring result = Melder_wcsdup (thy v_getVectorStr (icol));
		pushString (result.transfer());
	} else if (thy v_hasGetMatrixStr ()) {
		if (irow == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit row index for this ", Thing_className (thee), " object.\n"
				"Try using: object [id, row, column].");
		} else {
			autostring result = Melder_wcsdup (thy v_getMatrixStr (irow, icol));
			pushString (result.transfer());
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept no [column] indexes for string cells.");
	}
}
static void do_matrixStr1 (long irow) {
	Data thee = parse [programPointer]. content.object;
	Stackel column = pop;
	long icol = Stackel_getColumnNumber (column, thee);
	if (thy v_hasGetVectorStr ()) {
		autostring result = Melder_wcsdup (thy v_getVectorStr (icol));
		pushString (result.transfer());
	} else if (thy v_hasGetMatrixStr ()) {
		if (irow == 0) {
			Melder_throw ("We are not in a loop,\n"
				"hence no implicit row index for this ", Thing_className (thee), " object.\n"
				"Try using both [row, column] indexes instead.");
		} else {
			autostring result = Melder_wcsdup (thy v_getMatrixStr (irow, icol));
			pushString (result.transfer());
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept no [column] indexes for string cells.");
	}
}
static void do_selfMatriks2 (void) {
	Data me = theSource;
	Stackel column = pop, row = pop;
	if (me == NULL) Melder_throw ("The name \"self\" is restricted to formulas for objects.");
	long irow = Stackel_getRowNumber (row, me);
	long icol = Stackel_getColumnNumber (column, me);
	if (! my v_hasGetMatrix ())
		Melder_throw (Thing_className (me), " objects like \"self\" accept no [row, column] indexing.");
	pushNumber (my v_getMatrix (irow, icol));
}
static void do_selfMatriksStr2 (void) {
	Data me = theSource;
	Stackel column = pop, row = pop;
	if (me == NULL) Melder_throw ("The name \"self$\" is restricted to formulas for objects.");
	long irow = Stackel_getRowNumber (row, me);
	long icol = Stackel_getColumnNumber (column, me);
	if (! my v_hasGetMatrixStr ())
		Melder_throw (Thing_className (me), " objects like \"self$\" accept no [row, column] indexing for string cells.");
	autostring result = Melder_wcsdup (my v_getMatrixStr (irow, icol));
	pushString (result.transfer());
}
static void do_objectCell2 (void) {
	Stackel column = pop, row = pop;
	Data thee = getObjectFromUniqueID (pop);
	long irow = Stackel_getRowNumber (row, thee);
	long icol = Stackel_getColumnNumber (column, thee);
	if (! thy v_hasGetMatrix ())
		Melder_throw (Thing_className (thee), " objects accept no [id, row, column] indexing.");
	pushNumber (thy v_getMatrix (irow, icol));
}
static void do_matriks2 (void) {
	Data thee = parse [programPointer]. content.object;
	Stackel column = pop, row = pop;
	long irow = Stackel_getRowNumber (row, thee);
	long icol = Stackel_getColumnNumber (column, thee);
	if (! thy v_hasGetMatrix ())
		Melder_throw (Thing_className (thee), " objects accept no [row, column] indexing.");
	pushNumber (thy v_getMatrix (irow, icol));
}
static void do_objectCellStr2 (void) {
	Stackel column = pop, row = pop;
	Data thee = getObjectFromUniqueID (pop);
	long irow = Stackel_getRowNumber (row, thee);
	long icol = Stackel_getColumnNumber (column, thee);
	if (! thy v_hasGetMatrixStr ())
		Melder_throw (Thing_className (thee), " objects accept no [id, row, column] indexing for string cells.");
	autostring result = Melder_wcsdup (thy v_getMatrixStr (irow, icol));
	pushString (result.transfer());
}
static void do_matriksStr2 (void) {
	Data thee = parse [programPointer]. content.object;
	Stackel column = pop, row = pop;
	long irow = Stackel_getRowNumber (row, thee);
	long icol = Stackel_getColumnNumber (column, thee);
	if (! thy v_hasGetMatrixStr ())
		Melder_throw (Thing_className (thee), " objects accept no [row, column] indexing for string cells.");
	autostring result = Melder_wcsdup (thy v_getMatrixStr (irow, icol));
	pushString (result.transfer());
}
static void do_objectLocation0 (long irow, long icol) {
	Data thee = getObjectFromUniqueID (pop);
	if (thy v_hasGetFunction0 ()) {
		pushNumber (thy v_getFunction0 ());
	} else if (thy v_hasGetFunction1 ()) {
		Data me = theSource;
		if (me == NULL)
			Melder_throw ("No current object (we are not in a Formula command),\n"
				"hence no implicit x value for this ", Thing_className (thee), " object.\n"
				"Try using: object (id, x).");
		if (! my v_hasGetX ())
			Melder_throw ("The current ", Thing_className (me),
				" object gives no implicit x values,\nhence no implicit x value for this ",
				Thing_className (thee), " object.\n"
				"Try using: object (id, x).");
		double x = my v_getX (icol);
		pushNumber (thy v_getFunction1 (irow, x));
	} else if (thy v_hasGetFunction2 ()) {
		Data me = theSource;
		if (me == NULL)
			Melder_throw ("No current object (we are not in a Formula command),\n"
				"hence no implicit x or y values for this ", Thing_className (thee), " object.\n"
				"Try using: object (id, x, y).");
		if (! my v_hasGetX ())
			Melder_throw ("The current ", Thing_className (me), " object gives no implicit x values,\n"
				"hence no implicit x value for this ", Thing_className (thee), " object.\n"
				"Try using: object (id, x, y).");
		double x = my v_getX (icol);
		if (! my v_hasGetY ())
			Melder_throw ("The current ", Thing_className (me), L" object gives no implicit y values,\n"
					"hence no implicit y value for this ", Thing_className (thee), " object.\n"
					"Try using: object (id, y).");
		double y = my v_getY (irow);
		pushNumber (thy v_getFunction2 (x, y));
	} else {
		Melder_throw (Thing_className (thee), " objects accept no () values.");
	}
}
static void do_funktie0 (long irow, long icol) {
	Data thee = parse [programPointer]. content.object;
	if (thy v_hasGetFunction0 ()) {
		pushNumber (thy v_getFunction0 ());
	} else if (thy v_hasGetFunction1 ()) {
		Data me = theSource;
		if (me == NULL)
			Melder_throw ("No current object (we are not in a Formula command),\n"
				"hence no implicit x value for this ", Thing_className (thee), " object.\n"
				"Try using the (x) argument explicitly.");
		if (! my v_hasGetX ())
			Melder_throw ("The current ", Thing_className (me),
				" object gives no implicit x values,\nhence no implicit x value for this ",
				Thing_className (thee), " object.\n"
				"Try using the (x) argument explicitly.");
		double x = my v_getX (icol);
		pushNumber (thy v_getFunction1 (irow, x));
	} else if (thy v_hasGetFunction2 ()) {
		Data me = theSource;
		if (me == NULL)
			Melder_throw ("No current object (we are not in a Formula command),\n"
				"hence no implicit x or y values for this ", Thing_className (thee), " object.\n"
				"Try using both (x, y) arguments explicitly.");
		if (! my v_hasGetX ())
			Melder_throw ("The current ", Thing_className (me), " object gives no implicit x values,\n"
				"hence no implicit x value for this ", Thing_className (thee), " object.\n"
				"Try using both (x, y) arguments explicitly.");
		double x = my v_getX (icol);
		if (! my v_hasGetY ())
			Melder_throw ("The current ", Thing_className (me), " object gives no implicit y values,\n"
					"hence no implicit y value for this ", Thing_className (thee), " object.\n"
					"Try using the (y) argument explicitly.");
		double y = my v_getY (irow);
		pushNumber (thy v_getFunction2 (x, y));
	} else {
		Melder_throw (Thing_className (thee), " objects accept no () values.");
	}
}
static void do_selfFunktie1 (long irow) {
	Data me = theSource;
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		if (me == NULL) Melder_throw ("The name \"self\" is restricted to formulas for objects.");
		if (my v_hasGetFunction1 ()) {
			pushNumber (my v_getFunction1 (irow, x->content.number));
		} else if (my v_hasGetFunction2 ()) {
			if (! my v_hasGetY ())
				Melder_throw ("The current ", Thing_className (me), " object (self) accepts no implicit y values.\n"
					"Try using both (x, y) arguments instead.");
			double y = my v_getY (irow);
			pushNumber (my v_getFunction2 (x->content.number, y));
		} else {
			Melder_throw (Thing_className (me), " objects like \"self\" accept no (x) values.");
		}
	} else {
		Melder_throw (Thing_className (me), " objects like \"self\" accept only numeric x values.");
	}
}
static void do_objectLocation1 (long irow) {
	Stackel x = pop;
	Data thee = getObjectFromUniqueID (pop);
	if (x->which == Stackel_NUMBER) {
		if (thy v_hasGetFunction1 ()) {
			pushNumber (thy v_getFunction1 (irow, x->content.number));
		} else if (thy v_hasGetFunction2 ()) {
			Data me = theSource;
			if (me == NULL)
				Melder_throw ("No current object (we are not in a Formula command),\n"
					"hence no implicit y value for this ", Thing_className (thee), " object.\n"
					"Try using: object (id, x, y).");
			if (! my v_hasGetY ())
				Melder_throw ("The current ", Thing_className (me), " object gives no implicit y values,\n"
					"hence no implicit y value for this ", Thing_className (thee), " object.\n"
					"Try using: object (id, x, y).");
			double y = my v_getY (irow);
			pushNumber (thy v_getFunction2 (x->content.number, y));
		} else {
			Melder_throw (Thing_className (thee), " objects accept no (x) values.");
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept only numeric x values.");
	}
}
static void do_funktie1 (long irow) {
	Data thee = parse [programPointer]. content.object;
	Stackel x = pop;
	if (x->which == Stackel_NUMBER) {
		if (thy v_hasGetFunction1 ()) {
			pushNumber (thy v_getFunction1 (irow, x->content.number));
		} else if (thy v_hasGetFunction2 ()) {
			Data me = theSource;
			if (me == NULL)
				Melder_throw ("No current object (we are not in a Formula command),\n"
					"hence no implicit y value for this ", Thing_className (thee), " object.\n"
					"Try using both (x, y) arguments instead.");
			if (! my v_hasGetY ())
				Melder_throw ("The current ", Thing_className (me), " object gives no implicit y values,\n"
					"hence no implicit y value for this ", Thing_className (thee), " object.\n"
					"Try using both (x, y) arguments instead.");
			double y = my v_getY (irow);
			pushNumber (thy v_getFunction2 (x->content.number, y));
		} else {
			Melder_throw (Thing_className (thee), " objects accept no (x) values.");
		}
	} else {
		Melder_throw (Thing_className (thee), " objects accept only numeric x values.");
	}
}
static void do_selfFunktie2 (void) {
	Data me = theSource;
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		if (me == NULL) Melder_throw ("The name \"self\" is restricted to formulas for objects.");
		if (! my v_hasGetFunction2 ())
			Melder_throw (Thing_className (me), " objects like \"self\" accept no (x, y) values.");
		pushNumber (my v_getFunction2 (x->content.number, y->content.number));
	} else {
		Melder_throw (Thing_className (me), " objects accept only numeric x values.");
	}
}
static void do_objectLocation2 (void) {
	Stackel y = pop, x = pop;
	Data thee = getObjectFromUniqueID (pop);
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		if (! thy v_hasGetFunction2 ())
			Melder_throw (Thing_className (thee), " objects accept no (x, y) values.");
		pushNumber (thy v_getFunction2 (x->content.number, y->content.number));
	} else {
		Melder_throw (Thing_className (thee), " objects accept only numeric x values.");
	}
}
static void do_funktie2 (void) {
	Data thee = parse [programPointer]. content.object;
	Stackel y = pop, x = pop;
	if (x->which == Stackel_NUMBER && y->which == Stackel_NUMBER) {
		if (! thy v_hasGetFunction2 ())
			Melder_throw (Thing_className (thee), " objects accept no (x, y) values.");
		pushNumber (thy v_getFunction2 (x->content.number, y->content.number));
	} else {
		Melder_throw (Thing_className (thee), " objects accept only numeric x values.");
	}
}
static void do_rowStr (void) {
	Data thee = parse [programPointer]. content.object;
	Stackel row = pop;
	long irow = Stackel_getRowNumber (row, thee);
	autostring result = Melder_wcsdup (thy v_getRowStr (irow));
	if (result.peek() == NULL)
		Melder_throw ("Row index out of bounds.");
	pushString (result.transfer());
}
static void do_colStr (void) {
	Data thee = parse [programPointer]. content.object;
	Stackel col = pop;
	long icol = Stackel_getColumnNumber (col, thee);
	autostring result = Melder_wcsdup (thy v_getColStr (icol));
	if (result.peek() == NULL)
		Melder_throw ("Column index out of bounds.");
	pushString (result.transfer());
}

static double NUMarcsinh (double x) {
	return log (x + sqrt (1.0 + x * x));
}
static double NUMarccosh (double x) {
	return x < 1.0 ? NUMundefined : log (x + sqrt (x * x - 1.0));
}
static double NUMarctanh (double x) {
	return x <= -1.0 || x >= 1.0 ? NUMundefined : 0.5 * log ((1.0 + x) / (1.0 - x));
}
static double NUMerf (double x) {
	return 1.0 - NUMerfcc (x);
}

void Formula_run (long row, long col, struct Formula_Result *result) {
	FormulaInstruction f = parse;
	programPointer = 1;   // first symbol of the program
	if (theStack == NULL) theStack = Melder_calloc_f (struct structStackel, 10000);
	if (theStack == NULL)
		Melder_throw ("Out of memory during formula computation.");
	w = 0, wmax = 0;   // start new stack
	try {
		while (programPointer <= numberOfInstructions) {
			int symbol;
				switch (symbol = f [programPointer]. symbol) {

case NUMBER_: { pushNumber (f [programPointer]. content.number);
} break; case STOPWATCH_: { pushNumber (Melder_stopwatch ());
} break; case ROW_: { pushNumber (row);
} break; case COL_: { pushNumber (col);
} break; case X_: {
	Data me = theSource;
	if (! my v_hasGetX ()) Melder_throw ("No values for \"x\" for this object.");
	pushNumber (my v_getX (col));
} break; case Y_: {
	Data me = theSource;
	if (! my v_hasGetY ()) Melder_throw ("No values for \"y\" for this object.");
	pushNumber (my v_getY (row));
} break; case NOT_: { do_not ();
} break; case EQ_: { do_eq ();
} break; case NE_: { do_ne ();
} break; case LE_: { do_le ();
} break; case LT_: { do_lt ();
} break; case GE_: { do_ge ();
} break; case GT_: { do_gt ();
} break; case ADD_: { do_add ();
} break; case SUB_: { do_sub ();
} break; case MUL_: { do_mul ();
} break; case RDIV_: { do_rdiv ();
} break; case IDIV_: { do_idiv ();
} break; case MOD_: { do_mod ();
} break; case MINUS_: { do_minus ();
} break; case POWER_: { do_power ();
/********** Functions of 1 numerical variable: **********/
} break; case ABS_: { do_abs ();
} break; case ROUND_: { do_round ();
} break; case FLOOR_: { do_floor ();
} break; case CEILING_: { do_ceiling ();
} break; case SQRT_: { do_sqrt ();
} break; case SIN_: { do_sin ();
} break; case COS_: { do_cos ();
} break; case TAN_: { do_tan ();
} break; case ARCSIN_: { do_arcsin ();
} break; case ARCCOS_: { do_arccos ();
} break; case ARCTAN_: { do_arctan ();
} break; case SINC_: { do_function_n_n (NUMsinc);
} break; case SINCPI_: { do_function_n_n (NUMsincpi);
} break; case EXP_: { do_exp ();
} break; case SINH_: { do_sinh ();
} break; case COSH_: { do_cosh ();
} break; case TANH_: { do_tanh ();
} break; case ARCSINH_: { do_function_n_n (NUMarcsinh);
} break; case ARCCOSH_: { do_function_n_n (NUMarccosh);
} break; case ARCTANH_: { do_function_n_n (NUMarctanh);
} break; case SIGMOID_: { do_function_n_n (NUMsigmoid);
} break; case INV_SIGMOID_: { do_function_n_n (NUMinvSigmoid);
} break; case ERF_: { do_function_n_n (NUMerf);
} break; case ERFC_: { do_function_n_n (NUMerfcc);
} break; case GAUSS_P_: { do_function_n_n (NUMgaussP);
} break; case GAUSS_Q_: { do_function_n_n (NUMgaussQ);
} break; case INV_GAUSS_Q_: { do_function_n_n (NUMinvGaussQ);
} break; case RANDOM_POISSON_: { do_function_n_n (NUMrandomPoisson);
} break; case LOG2_: { do_log2 ();
} break; case LN_: { do_ln ();
} break; case LOG10_: { do_log10 ();
} break; case LN_GAMMA_: { do_function_n_n (NUMlnGamma);
} break; case HERTZ_TO_BARK_: { do_function_n_n (NUMhertzToBark);
} break; case BARK_TO_HERTZ_: { do_function_n_n (NUMbarkToHertz);
} break; case PHON_TO_DIFFERENCE_LIMENS_: { do_function_n_n (NUMphonToDifferenceLimens);
} break; case DIFFERENCE_LIMENS_TO_PHON_: { do_function_n_n (NUMdifferenceLimensToPhon);
} break; case HERTZ_TO_MEL_: { do_function_n_n (NUMhertzToMel);
} break; case MEL_TO_HERTZ_: { do_function_n_n (NUMmelToHertz);
} break; case HERTZ_TO_SEMITONES_: { do_function_n_n (NUMhertzToSemitones);
} break; case SEMITONES_TO_HERTZ_: { do_function_n_n (NUMsemitonesToHertz);
} break; case ERB_: { do_function_n_n (NUMerb);
} break; case HERTZ_TO_ERB_: { do_function_n_n (NUMhertzToErb);
} break; case ERB_TO_HERTZ_: { do_function_n_n (NUMerbToHertz);
/********** Functions of 2 numerical variables: **********/
} break; case ARCTAN2_: { do_function_dd_d (atan2);
} break; case RANDOM_UNIFORM_: { do_function_dd_d (NUMrandomUniform);
} break; case RANDOM_INTEGER_: { do_function_ll_l (NUMrandomInteger);
} break; case RANDOM_GAUSS_: { do_function_dd_d (NUMrandomGauss);
} break; case CHI_SQUARE_P_: { do_function_dd_d (NUMchiSquareP);
} break; case CHI_SQUARE_Q_: { do_function_dd_d (NUMchiSquareQ);
} break; case INCOMPLETE_GAMMAP_: { do_function_dd_d (NUMincompleteGammaP);
} break; case INV_CHI_SQUARE_Q_: { do_function_dd_d (NUMinvChiSquareQ);
} break; case STUDENT_P_: { do_function_dd_d (NUMstudentP);
} break; case STUDENT_Q_: { do_function_dd_d (NUMstudentQ);
} break; case INV_STUDENT_Q_: { do_function_dd_d (NUMinvStudentQ);
} break; case BETA_: { do_function_dd_d (NUMbeta);
} break; case BETA2_: { do_function_dd_d (NUMbeta2);
} break; case BESSEL_I_: { do_function_ld_d (NUMbesselI);
} break; case BESSEL_K_: { do_function_ld_d (NUMbesselK);
} break; case LN_BETA_: { do_function_dd_d (NUMlnBeta);
} break; case SOUND_PRESSURE_TO_PHON_: { do_function_dd_d (NUMsoundPressureToPhon);
} break; case OBJECTS_ARE_IDENTICAL_: { do_objects_are_identical ();
/********** Functions of 3 numerical variables: **********/
} break; case FISHER_P_: { do_function_ddd_d (NUMfisherP);
} break; case FISHER_Q_: { do_function_ddd_d (NUMfisherQ);
} break; case INV_FISHER_Q_: { do_function_ddd_d (NUMinvFisherQ);
} break; case BINOMIAL_P_: { do_function_ddd_d (NUMbinomialP);
} break; case BINOMIAL_Q_: { do_function_ddd_d (NUMbinomialQ);
} break; case INCOMPLETE_BETA_: { do_function_ddd_d (NUMincompleteBeta);
} break; case INV_BINOMIAL_P_: { do_function_ddd_d (NUMinvBinomialP);
} break; case INV_BINOMIAL_Q_: { do_function_ddd_d (NUMinvBinomialQ);
/********** Functions of a variable number of variables: **********/
} break; case MIN_: { do_min ();
} break; case MAX_: { do_max ();
} break; case IMIN_: { do_imin ();
} break; case IMAX_: { do_imax ();
} break; case ZERO_NUMAR_: { do_zeroNumar ();
} break; case LINEAR_NUMAR_: { do_linearNumar ();
} break; case RANDOM_UNIFORM_NUMAR_: { do_function_dd_d_numar (NUMrandomUniform);
} break; case RANDOM_INTEGER_NUMAR_: { do_function_ll_l_numar (NUMrandomInteger);
} break; case RANDOM_GAUSS_NUMAR_: { do_function_dd_d_numar (NUMrandomGauss);
} break; case NUMBER_OF_ROWS_: { do_numberOfRows ();
} break; case NUMBER_OF_COLUMNS_: { do_numberOfColumns ();
/********** String functions: **********/
} break; case LENGTH_: { do_length ();
} break; case FILE_READABLE_: { do_fileReadable ();
} break; case DATESTR_: { do_dateStr ();
} break; case LEFTSTR_: { do_leftStr ();
} break; case RIGHTSTR_: { do_rightStr ();
} break; case MIDSTR_: { do_midStr ();
} break; case ENVIRONMENTSTR_: { do_environmentStr ();
} break; case INDEX_: { do_index ();
} break; case RINDEX_: { do_rindex ();
} break; case STARTS_WITH_: { do_stringMatchesCriterion (kMelder_string_STARTS_WITH);
} break; case ENDS_WITH_: { do_stringMatchesCriterion (kMelder_string_ENDS_WITH);
} break; case REPLACESTR_: { do_replaceStr ();
} break; case INDEX_REGEX_: { do_index_regex (FALSE);
} break; case RINDEX_REGEX_: { do_index_regex (TRUE);
} break; case REPLACE_REGEXSTR_: { do_replace_regexStr ();
} break; case EXTRACT_NUMBER_: { do_extractNumber ();
} break; case EXTRACT_WORDSTR_: { do_extractTextStr (TRUE);
} break; case EXTRACT_LINESTR_: { do_extractTextStr (FALSE);
} break; case SELECTED_: { do_selected ();
} break; case SELECTEDSTR_: { do_selectedStr ();
} break; case NUMBER_OF_SELECTED_: { do_numberOfSelected ();
} break; case FIXEDSTR_: { do_fixedStr ();
} break; case PERCENTSTR_: { do_percentStr ();
} break; case DELETE_FILE_: { do_deleteFile ();
} break; case CREATE_DIRECTORY_: { do_createDirectory ();
} break; case VARIABLE_EXISTS_: { do_variableExists ();
/********** Pause window functions: **********/
} break; case BEGIN_PAUSE_FORM_: { do_beginPauseForm ();
} break; case PAUSE_FORM_ADD_REAL_: { do_pauseFormAddReal ();
} break; case PAUSE_FORM_ADD_POSITIVE_: { do_pauseFormAddPositive ();
} break; case PAUSE_FORM_ADD_INTEGER_: { do_pauseFormAddInteger ();
} break; case PAUSE_FORM_ADD_NATURAL_: { do_pauseFormAddNatural ();
} break; case PAUSE_FORM_ADD_WORD_: { do_pauseFormAddWord ();
} break; case PAUSE_FORM_ADD_SENTENCE_: { do_pauseFormAddSentence ();
} break; case PAUSE_FORM_ADD_TEXT_: { do_pauseFormAddText ();
} break; case PAUSE_FORM_ADD_BOOLEAN_: { do_pauseFormAddBoolean ();
} break; case PAUSE_FORM_ADD_CHOICE_: { do_pauseFormAddChoice ();
} break; case PAUSE_FORM_ADD_OPTION_MENU_: { do_pauseFormAddOptionMenu ();
} break; case PAUSE_FORM_ADD_OPTION_: { do_pauseFormAddOption ();
} break; case PAUSE_FORM_ADD_COMMENT_: { do_pauseFormAddComment ();
} break; case END_PAUSE_FORM_: { do_endPauseForm ();
} break; case CHOOSE_READ_FILESTR_: { do_chooseReadFileStr ();
} break; case CHOOSE_WRITE_FILESTR_: { do_chooseWriteFileStr ();
} break; case CHOOSE_DIRECTORYSTR_: { do_chooseDirectoryStr ();
/********** Demo window functions: **********/
} break; case DEMO_WINDOW_TITLE_: { do_demoWindowTitle ();
} break; case DEMO_SHOW_: { do_demoShow ();
} break; case DEMO_WAIT_FOR_INPUT_: { do_demoWaitForInput ();
} break; case DEMO_INPUT_: { do_demoInput ();
} break; case DEMO_CLICKED_IN_: { do_demoClickedIn ();
} break; case DEMO_CLICKED_: { do_demoClicked ();
} break; case DEMO_X_: { do_demoX ();
} break; case DEMO_Y_: { do_demoY ();
} break; case DEMO_KEY_PRESSED_: { do_demoKeyPressed ();
} break; case DEMO_KEY_: { do_demoKey ();
} break; case DEMO_SHIFT_KEY_PRESSED_: { do_demoShiftKeyPressed ();
} break; case DEMO_COMMAND_KEY_PRESSED_: { do_demoCommandKeyPressed ();
} break; case DEMO_OPTION_KEY_PRESSED_: { do_demoOptionKeyPressed ();
} break; case DEMO_EXTRA_CONTROL_KEY_PRESSED_: { do_demoExtraControlKeyPressed ();
/********** **********/
} break; case TRUE_: {
	pushNumber (1.0);
} break; case FALSE_: {
	pushNumber (0.0);
/* Possible compiler BUG: many compilers cannot handle the following assignment. */
/* Those compilers have trouble with praat's AND and OR. */
} break; case IFTRUE_: {
	Stackel condition = pop;
	if (condition->which == Stackel_NUMBER) {
		if (condition->content.number != 0.0) {
			programPointer = f [programPointer]. content.label - theOptimize;
		}
	} else {
		Melder_throw ("A condition between \"if\" and \"then\" has to be a number, not ", Stackel_whichText (condition), ".");
	}
} break; case IFFALSE_: {
	Stackel condition = pop;
	if (condition->which == Stackel_NUMBER) {
		if (condition->content.number == 0.0) {
			programPointer = f [programPointer]. content.label - theOptimize;
		}
	} else {
		Melder_throw ("A condition between \"if\" and \"then\" has to be a number, not ", Stackel_whichText (condition), ".");
	}
} break; case GOTO_: {
	programPointer = f [programPointer]. content.label - theOptimize;
} break; case LABEL_: {
	;
} break; case DECREMENT_AND_ASSIGN_: {
	Stackel x = pop, v = pop;
	InterpreterVariable var = v->content.variable;
	var -> numericValue = x->content.number - 1.0;
	//Melder_casual ("starting value %f", var -> numericValue);
	pushVariable (var);
} break; case INCREMENT_GREATER_GOTO_: {
	//Melder_casual ("top of loop, stack depth %d", w);
	Stackel e = & theStack [w], v = & theStack [w - 1];
	Melder_assert (e->which == Stackel_NUMBER);
	Melder_assert (v->which == Stackel_VARIABLE);
	InterpreterVariable var = v->content.variable;
	//Melder_casual ("loop variable %f", var -> numericValue);
	var -> numericValue += 1.0;
	//Melder_casual ("loop variable %f", var -> numericValue);
	//Melder_casual ("end value %f", e->content.number);
	if (var -> numericValue > e->content.number) {
		programPointer = f [programPointer]. content.label - theOptimize;
	}
} break; case ADD_3DOWN_: {
	Stackel x = pop, s = & theStack [w - 2];
	Melder_assert (x->which == Stackel_NUMBER);
	Melder_assert (s->which == Stackel_NUMBER);
	//Melder_casual ("to add %f", x->content.number);
	s->content.number += x->content.number;
	//Melder_casual ("sum %f", s->content.number);
} break; case POP_2_: {
	w -= 2;
	//Melder_casual ("total %f", theStack[w].content.number);
} break; case NUMERIC_ARRAY_ELEMENT_: { do_numericArrayElement ();
} break; case INDEXED_NUMERIC_VARIABLE_: { do_indexedNumericVariable ();
} break; case INDEXED_STRING_VARIABLE_: { do_indexedStringVariable ();
} break; case VARIABLE_REFERENCE_: {
	InterpreterVariable var = f [programPointer]. content.variable;
	pushVariable (var);
} break; case SELF0_: { do_self0 (row, col);
} break; case SELFSTR0_: { do_selfStr0 (row, col);
} break; case SELFMATRIKS1_: { do_selfMatriks1 (row);
} break; case SELFMATRIKSSTR1_: { do_selfMatriksStr1 (row);
} break; case SELFMATRIKS2_: { do_selfMatriks2 ();
} break; case SELFMATRIKSSTR2_: { do_selfMatriksStr2 ();
} break; case SELFFUNKTIE1_: { do_selfFunktie1 (row);
} break; case SELFFUNKTIE2_: { do_selfFunktie2 ();
} break; case OBJECTCELL0_: { do_objectCell0 (row, col);
} break; case OBJECTCELL1_: { do_objectCell1 (row);
} break; case OBJECTCELLSTR1_: { do_objectCellStr1 (row);
} break; case OBJECTCELL2_: { do_objectCell2 ();
} break; case OBJECTCELLSTR2_: { do_objectCellStr2 ();
} break; case OBJECTLOCATION0_: { do_objectLocation0 (row, col);
} break; case OBJECTLOCATION1_: { do_objectLocation1 (row);
} break; case OBJECTLOCATION2_: { do_objectLocation2 ();
} break; case MATRIKS0_: { do_matriks0 (row, col);
} break; case MATRIKS1_: { do_matriks1 (row);
} break; case MATRIKSSTR1_: { do_matrixStr1 (row);
} break; case MATRIKS2_: { do_matriks2 ();
} break; case MATRIKSSTR2_: { do_matriksStr2 ();
} break; case FUNKTIE0_: { do_funktie0 (row, col);
} break; case FUNKTIE1_: { do_funktie1 (row);
} break; case FUNKTIE2_: { do_funktie2 ();
} break; case ROWSTR_: { do_rowStr ();
} break; case COLSTR_: { do_colStr ();
} break; case SQR_: { do_sqr ();
} break; case STRING_: {
	autostring string = Melder_wcsdup (f [programPointer]. content.string);
	pushString (string.transfer());
} break; case NUMERIC_VARIABLE_: {
	InterpreterVariable var = f [programPointer]. content.variable;
	pushNumber (var -> numericValue);
} break; case STRING_VARIABLE_: {
	InterpreterVariable var = f [programPointer]. content.variable;
	autostring string = Melder_wcsdup (var -> stringValue);
	pushString (string.transfer());
} break; case NUMERIC_ARRAY_VARIABLE_: {
	InterpreterVariable var = f [programPointer]. content.variable;
	double **data = NUMmatrix_copy (var -> numericArrayValue. data,
		1, var -> numericArrayValue. numberOfRows, 1, var -> numericArrayValue. numberOfColumns); therror
	pushNumericArray (var -> numericArrayValue. numberOfRows, var -> numericArrayValue. numberOfColumns, data);
} break; default: Melder_throw ("Symbol \"", Formula_instructionNames [parse [programPointer]. symbol], "\" without action.");
			} // endswitch
			programPointer ++;
		} // endwhile
		if (w != 1) Melder_fatal ("Formula: stackpointer ends at %ld instead of 1.", w);
		if (theExpressionType == kFormula_EXPRESSION_TYPE_NUMERIC) {
			if (theStack [1]. which == Stackel_STRING) Melder_throw ("Found a string expression instead of a numeric expression.");
			if (theStack [1]. which == Stackel_NUMERIC_ARRAY) Melder_throw ("Found a numeric array expression instead of a numeric expression.");
			if (result) {
				result -> expressionType = kFormula_EXPRESSION_TYPE_NUMERIC;
				result -> result.numericResult = theStack [1]. content.number;
			} else {
				Melder_information (Melder_double (theStack [1]. content.number));
			}
		} else if (theExpressionType == kFormula_EXPRESSION_TYPE_STRING) {
			if (theStack [1]. which == Stackel_NUMBER) Melder_throw ("Found a numeric expression instead of a string expression.");
			if (theStack [1]. which == Stackel_NUMERIC_ARRAY) Melder_throw ("Found a numeric array expression instead of a string expression.");
			if (result) {
				result -> expressionType = kFormula_EXPRESSION_TYPE_STRING;
				result -> result.stringResult = theStack [1]. content.string; theStack [1]. content.string = NULL;   /* Undangle. */
			} else {
				Melder_information (theStack [1]. content.string);
			}
		} else if (theExpressionType == kFormula_EXPRESSION_TYPE_NUMERIC_ARRAY) {
			if (theStack [1]. which == Stackel_NUMBER) Melder_throw ("Found a numeric expression instead of a numeric array expression.");
			if (theStack [1]. which == Stackel_STRING) Melder_throw ("Found a string expression instead of a numeric array expression.");
			if (result) {
				result -> expressionType = kFormula_EXPRESSION_TYPE_NUMERIC_ARRAY;
				result -> result.numericArrayResult = theStack [1]. content.numericArray; theStack [1]. content.numericArray = theZeroNumericArray;   /* Undangle. */
			} else {
				//Melder_information (theStack [1]. content.string);  // TODO: implement
			}
		} else {
			Melder_assert (theExpressionType == kFormula_EXPRESSION_TYPE_UNKNOWN);
			if (theStack [1]. which == Stackel_NUMBER) {
				if (result) {
					result -> expressionType = kFormula_EXPRESSION_TYPE_NUMERIC;
					result -> result.numericResult = theStack [1]. content.number;
				} else {
					Melder_information (Melder_double (theStack [1]. content.number));
				}
			} else {
				Melder_assert (theStack [1]. which == Stackel_STRING);
				if (result) {
					result -> expressionType = kFormula_EXPRESSION_TYPE_STRING;
					result -> result.stringResult = theStack [1]. content.string; theStack [1]. content.string = NULL;   /* Undangle. */
				} else {
					Melder_information (theStack [1]. content.string);
				}
			}
		}
		/*
			Clean up the stack (theStack [1] may have been disowned).
		*/
		for (w = wmax; w > 0; w --) {
			Stackel stackel = & theStack [w];
			if (stackel -> which > Stackel_NUMBER) Stackel_cleanUp (stackel);
		}
	} catch (MelderError) {
		/*
			Clean up the stack (theStack [1] may have been disowned).
		*/
		for (w = wmax; w > 0; w --) {
			Stackel stackel = & theStack [w];
			if (stackel -> which > Stackel_NUMBER) Stackel_cleanUp (stackel);
		}
		Melder_throw ("Formula not run.");
	}
}

/* End of file Formula.cpp */