/**
* Evaluates the given mathematical expression and returns the result.
* Angles may be expressed in degrees (default), rad (#r), gon (#g)
* or as surveyors angles (N#d#'#"E).
*/
double RMath::eval(const QString& expression, bool* ok) {
lastError = "";
if (expression.isEmpty()) {
if (ok!=NULL) {
*ok = false;
}
lastError = "Expression is empty";
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
if (ok!=NULL) {
*ok = true;
}
QString expr = expression;
// 'correct' commas to points:
if (RSettings::getNumberLocale().decimalPoint()==',') {
expr.replace(',', '.');
}
if (expr.contains(',') || expr.contains(';')) {
if (ok!=NULL) {
*ok = false;
}
lastError = "Multiple expressions";
return RNANDOUBLE;
}
int idx = -1;
// convert surveyor type angles (e.g. N10d30'12.5"E) to degrees:
if (expr.contains(QRegExp("[NESW]", Qt::CaseInsensitive))) {
// \b(?:(?:([NS])(?:([+-]?)(?:(?:(\d*\.?\d*)[d°])?(?:(\d*\.?\d*)')?(?:(\d*\.?\d*)")?|(\d*))([EW]))?)|([EW]))\b
QRegExp re(
"\\b" // a word
"(?:"
"(?:"
"([NS])" // expression starts with nord or south
"(?:"
"([+-]?)" // sign
"(?:"
"(?:(\\d*\\.?\\d*)[d°])?" // degrees with d
"(?:(\\d*\\.?\\d*)')?" // minutes with '
"(?:(\\d*\\.?\\d*)\")?" // seconds with "
"|" // or...
"(\\d*)" // degrees without d
")"
"([EW])" // east or west
")?"
")"
"|" // or...
"([EW])" // only east (0d) or west (180d)
")"
"\\b",
Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
double angle = 0.0;
QString sign;
// "E" or "W":
if (!re.cap(8).isEmpty()) {
if (re.cap(8).toUpper()=="E") {
angle = 0.0;
}
else if (re.cap(8).toUpper()=="W") {
angle = 180.0;
}
else {
if (ok!=NULL) {
*ok = false;
}
lastError = "Invalid cardinal direction found (valid values are: N,E,S,W)";
return RNANDOUBLE;
}
}
// "[NS]...[EW]":
else {
bool north = re.cap(1).toUpper()=="N";
bool south = re.cap(1).toUpper()=="S";
sign = re.cap(2);
double degrees = 0.0;
double minutes = 0.0;
double seconds = 0.0;
if (!re.cap(6).isEmpty()) {
degrees = re.cap(6).toDouble(ok);
}
else {
degrees = re.cap(3).toDouble(ok);
minutes = re.cap(4).toDouble(ok);
seconds = re.cap(5).toDouble(ok);
}
bool east = re.cap(7).toUpper()=="E";
bool west = re.cap(7).toUpper()=="W";
double base = (north ? 90.0 : 270.0);
int dir = ((north && west) || (south && east) ? 1 : -1);
angle = base + dir * (degrees + minutes/60.0 + seconds/3600.0);
}
expr.replace(
re.cap(),
QString("%1%2").arg(sign).arg(angle, 0, 'g', 16)
);
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression 001 is: " << expr;
// convert radiant angles (e.g. "1.2r") to degrees:
{
QRegExp re("((?:\\.\\d+)|(?:\\d+\\.\\d*)|(?:\\d+))r\\b", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString match = re.cap(1);
//qDebug() << "RMath::eval: match 001a is: " << match;
expr.replace(
re,
QString("%1").arg(rad2deg(match.toDouble(ok)), 0, 'g', 16)
);
//qDebug() << "RMath::eval: expression 001a is: " << expr;
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression 002 is: " << expr;
// convert grad angles (e.g. "100g") to degrees:
{
QRegExp re("((?:\\.\\d+)|(?:\\d+\\.\\d*)|(?:\\d+))g\\b", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString match = re.cap(1);
expr.replace(
re,
QString("%1").arg(gra2deg(match.toDouble(ok)), 0, 'g', 16)
);
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression 003 is: " << expr;
// convert explicitely indicated degree angles (e.g. "90d") to degrees:
{
QRegExp re("((?:\\.\\d+)|(?:\\d+\\.\\d*)|(?:\\d+))d\\b", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString match = re.cap(1);
expr.replace(
re,
QString("%1").arg(match.toDouble(ok), 0, 'g', 16)
);
} while(idx!=-1);
}
// convert fraction notation to formula:
// e.g. 7 3/32 to 7+3/32
{
QRegExp re("(\\d+)[ ]+(\\d+/\\d+)", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString numberString = re.cap(1);
QString fractionString = re.cap(2);
expr.replace(
re,
QString("%1+%2").arg(numberString).arg(fractionString)
);
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression is: " << expr;
QScriptEngine e;
// add common functions of Math to global scope for use in math input fields:
QStringList mathProp;
mathProp << "PI" << "LN2" << "LN10" << "LOG2E" << "LOG10E" << "SQRT1_2" << "SQRT2"
<< "abs"
//<< "cos" << "sin" << "tan"
//<< "acos" << "asin" << "atan" << "atan2"
<< "ceil" << "floor"
<< "exp" << "log"
<< "max" << "min"
<< "pow" << "sqrt"
<< "random"
<< "round";
for (int i=0; i<mathProp.length(); i++) {
e.evaluate(mathProp[i] + " = Math." + mathProp[i]);
}
e.evaluate("rad2deg = function(a) { return a / (2.0 * Math.PI) * 360.0; }");
e.evaluate("deg2rad = function(a) { return (a / 360.0) * (2.0 * Math.PI); }");
e.evaluate("sin = function(v) { return Math.sin(deg2rad(v)); }");
e.evaluate("cos = function(v) { return Math.cos(deg2rad(v)); }");
e.evaluate("tan = function(v) { return Math.tan(deg2rad(v)); }");
e.evaluate("asin = function(v) { return rad2deg(Math.asin(v)); }");
e.evaluate("acos = function(v) { return rad2deg(Math.acos(v)); }");
e.evaluate("atan = function(v) { return rad2deg(Math.atan(v)); }");
//e.evaluate("atan2 = function(y,x) { return rad2deg(Math.atan2(y,x)); }");
QScriptValue res = e.evaluate(expr);
if (res.isError()) {
if (ok!=NULL) {
*ok = false;
}
lastError = res.toString();
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
if (!res.isNumber()) {
if (ok != NULL) {
*ok = false;
}
lastError = expr + " is not a number";
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
//qDebug() << "res.toNumber(): " << res.toNumber();
//qDebug() << "fpclassify: " << std::fpclassify(res.toNumber());
if (!isNormal(res.toNumber())) {
if (ok != NULL) {
*ok = false;
}
lastError = expr + " is not a normal number";
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
return res.toNumber();
}
/**
* Evaluates the given mathematical expression and returns the result.
* Angles may be expressed in degrees (default), rad (#r), gon (#g)
* or as surveyors angles (N#d#'#"E).
*/
double RMath::eval(const QString& expression, bool* ok) {
lastError = "";
if (expression.isEmpty()) {
if (ok!=NULL) {
*ok = false;
}
lastError = "Expression is empty";
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
if (ok!=NULL) {
*ok = true;
}
QString expr = expression;
// 'correct' commas in numbers to points:
if (RSettings::getNumberLocale().decimalPoint()==',') {
expr.replace(QRegExp("(\\d*),(\\d+)"), "\\1.\\2");
}
int idx = -1;
// convert surveyor type angles (e.g. N10d30'12.5"E) to degrees:
if (expr.contains(QRegExp("[NESW]", Qt::CaseInsensitive))) {
// \b(?:(?:([NS])(?:([+-]?)(?:(?:(\d*\.?\d*)[d°])?(?:(\d*\.?\d*)')?(?:(\d*\.?\d*)")?|(\d*))([EW]))?)|([EW]))\b
QRegExp re(
"\\b" // a word
"(?:"
"(?:"
"([NS])" // expression starts with nord or south
"(?:"
"([+-]?)" // sign
"(?:"
"(?:(\\d*\\.?\\d*)[d°])?" // degrees with d
"(?:(\\d*\\.?\\d*)')?" // minutes with '
"(?:(\\d*\\.?\\d*)\")?" // seconds with "
"|" // or...
"(\\d*)" // degrees without d
")"
"([EW])" // east or west
")?"
")"
"|" // or...
"([EW])" // only east (0d) or west (180d)
")"
"\\b",
Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
double angle = 0.0;
QString sign;
// "E" or "W":
if (!re.cap(8).isEmpty()) {
if (re.cap(8).toUpper()=="E") {
angle = 0.0;
}
else if (re.cap(8).toUpper()=="W") {
angle = 180.0;
}
else {
if (ok!=NULL) {
*ok = false;
}
lastError = "Invalid cardinal direction found (valid values are: N,E,S,W)";
return RNANDOUBLE;
}
}
// "[NS]...[EW]":
else {
bool north = re.cap(1).toUpper()=="N";
bool south = re.cap(1).toUpper()=="S";
sign = re.cap(2);
double degrees = 0.0;
double minutes = 0.0;
double seconds = 0.0;
if (!re.cap(6).isEmpty()) {
degrees = re.cap(6).toDouble(ok);
}
else {
degrees = re.cap(3).toDouble(ok);
minutes = re.cap(4).toDouble(ok);
seconds = re.cap(5).toDouble(ok);
}
bool east = re.cap(7).toUpper()=="E";
bool west = re.cap(7).toUpper()=="W";
double base = (north ? 90.0 : 270.0);
int dir = ((north && west) || (south && east) ? 1 : -1);
angle = base + dir * (degrees + minutes/60.0 + seconds/3600.0);
}
expr.replace(
re.cap(),
QString("%1%2").arg(sign).arg(angle, 0, 'g', 16)
);
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression 001 is: " << expr;
// convert radiant angles (e.g. "1.2r") to degrees:
{
QRegExp re("((?:\\.\\d+)|(?:\\d+\\.\\d*)|(?:\\d+))r\\b", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString match = re.cap(1);
//qDebug() << "RMath::eval: match 001a is: " << match;
expr.replace(
re,
QString("%1").arg(rad2deg(match.toDouble(ok)), 0, 'g', 16)
);
//qDebug() << "RMath::eval: expression 001a is: " << expr;
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression 002 is: " << expr;
// convert grad angles (e.g. "100g") to degrees:
{
QRegExp re("((?:\\.\\d+)|(?:\\d+\\.\\d*)|(?:\\d+))g\\b", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString match = re.cap(1);
expr.replace(
re,
QString("%1").arg(gra2deg(match.toDouble(ok)), 0, 'g', 16)
);
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression 003 is: " << expr;
// convert explicitely indicated degree angles (e.g. "90d") to degrees:
{
QRegExp re("((?:\\.\\d+)|(?:\\d+\\.\\d*)|(?:\\d+))d\\b", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString match = re.cap(1);
expr.replace(
re,
QString("%1").arg(match.toDouble(ok), 0, 'g', 16)
);
} while(idx!=-1);
}
// convert fraction notation to formula:
// e.g. 7 3/32 to 7+3/32
{
QRegExp re("(\\d+)[ ]+(\\d+/\\d+)", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString numberString = re.cap(1);
QString fractionString = re.cap(2);
expr.replace(
re,
QString("%1+%2").arg(numberString).arg(fractionString)
);
} while(idx!=-1);
}
// convert foot indication to a factor of 12
// e.g. "10'" to 10*12 and "10' " to 10*12+
{
QRegExp re("(\\d+)'[ ]*(\\d*)", Qt::CaseInsensitive, QRegExp::RegExp2);
do {
idx = re.indexIn(expr);
if (idx==-1) {
break;
}
QString feetString = re.cap(1);
//QString spacesString = re.cap(2);
QString inchString = re.cap(2);
expr.replace(
re,
QString("%1*12%2%3")
.arg(feetString)
.arg(inchString.isEmpty() ? "" : "+")
.arg(inchString)
);
} while(idx!=-1);
}
//qDebug() << "RMath::eval: expression is: " << expr;
QScriptEngine e;
if (mathExt.isNull()) {
QString inputJs = "scripts/input.js";
QFile file(inputJs);
if (file.exists()) {
if (file.open(QIODevice::ReadOnly|QIODevice::Text)) {
mathExt = QString(file.readAll());
file.close();
}
}
else {
qDebug() << "file not found: input.js";
}
}
e.evaluate(mathExt);
QScriptValue res = e.evaluate(expr);
if (res.isError()) {
if (ok!=NULL) {
*ok = false;
}
lastError = res.toString();
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
if (!res.isNumber()) {
if (ok != NULL) {
*ok = false;
}
lastError = expr + " is not a number";
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
//qDebug() << "res.toNumber(): " << res.toNumber();
//qDebug() << "fpclassify: " << std::fpclassify(res.toNumber());
if (!isNormal(res.toNumber())) {
if (ok != NULL) {
*ok = false;
}
lastError = expr + " is not a normal number";
//qDebug() << "RMath::evel: error: " << lastError;
return RNANDOUBLE;
}
return res.toNumber();
}
