private Variable ExecuteFunction(Variable func, List<Variable> arguments)
{
Kerbulator.DebugLine("Executing function: "+ func.id);
if(func.type == VarType.FUNCTION) {
if(arguments.Count != func.numArgs)
throw new Exception("Function "+ func.id +" takes "+ func.numArgs +" arguments, but "+ arguments.Count +" were supplied.");
double result = 0;
switch(func.id) {
case "abs":
return ApplyUnaryFunction(arguments[0], Math.Abs);
case "acos":
return ApplyUnaryFunction(arguments[0], Math.Acos);
case "asin":
return ApplyUnaryFunction(arguments[0], Math.Asin);
case "atan":
return ApplyUnaryFunction(arguments[0], Math.Atan);
case "ceil":
return ApplyUnaryFunction(arguments[0], Math.Ceiling);
case "cos":
return ApplyUnaryFunction(arguments[0], Math.Cos);
case "exp":
return ApplyUnaryFunction(arguments[0], Math.Exp);
case "floor":
return ApplyUnaryFunction(arguments[0], Math.Floor);
case "ln":
case "log":
return ApplyUnaryFunction(arguments[0], Math.Log);
case "log10":
return ApplyUnaryFunction(arguments[0], Math.Log10);
case "max":
return new Variable(VarType.NUMBER, Math.Max(arguments[0].val, arguments[1].val));
case "min":
return new Variable(VarType.NUMBER, Math.Min(arguments[0].val, arguments[1].val));
case "pow":
return new Variable(VarType.NUMBER, Math.Pow(arguments[0].val, arguments[1].val));
case "round":
if(arguments[1].type != VarType.NUMBER)
throw new Exception("Function round takes a number as second parameter.");
return ApplyUnaryFunction(arguments[0], delegate(double val) { return Math.Round(val, (int)arguments[1].val); });
case "sign":
return ApplyUnaryFunction(arguments[0], delegate(double val) { return (double)Math.Sign(val); });
case "sin":
return ApplyUnaryFunction(arguments[0], Math.Sin);
case "sqrt":
return ApplyUnaryFunction(arguments[0], Math.Sqrt);
case "tan":
return ApplyUnaryFunction(arguments[0], Math.Tan);
case "len":
if(arguments[0].type != VarType.LIST)
throw new Exception("Function len expects a list as input.");
return new Variable(VarType.NUMBER, (double)arguments[0].elements.Count);
case "norm":
if(arguments[0].type != VarType.LIST)
throw new Exception("Function norm expects a list as input.");
double length = 0;
foreach(Variable e in arguments[0].elements) {
if(e.type != VarType.NUMBER)
throw new Exception("Function norm cannot handle nested lists.");
length += e.val * e.val;
}
length = Math.Sqrt(length);
List<Variable> elements = new List<Variable>(arguments[0].elements.Count);
foreach(Variable e in arguments[0].elements)
elements.Add(new Variable(e.id, VarType.NUMBER, e.val/length));
return new Variable(VarType.LIST, elements);
case "dot":
if(arguments[0].type != VarType.LIST || arguments[1].type != VarType.LIST)
throw new Exception("Function dot expects two lists as input.");
if(arguments[0].elements.Count != arguments[1].elements.Count)
throw new Exception("Function dot requires two lists of the same size.");
result = 0;
for(int i=0; i<arguments[0].elements.Count; i++) {
Variable a = arguments[0].elements[i];
Variable b = arguments[1].elements[i];
if(a.type != VarType.NUMBER || b.type != VarType.NUMBER)
throw new Exception("Function dot cannot handle nested lists.");
result += a.val * b.val;
}
return new Variable(VarType.NUMBER, result);
case "cross":
if(arguments[0].type != VarType.LIST || arguments[1].type != VarType.LIST)
throw new Exception("Function cross expects two lists as input.");
if(arguments[0].elements.Count != 3 || arguments[1].elements.Count != 3)
throw new Exception("Function cross requires two lists of length 3.");
List<Variable> x = arguments[0].elements;
List<Variable> y = arguments[1].elements;
for(int i=0; i<x.Count; i++) {
if(x[i].type != VarType.NUMBER || y[i].type != VarType.NUMBER)
throw new Exception("Function cross cannot handle nested lists.");
}
List<Variable>z = new List<Variable>(new[]{
new Variable(VarType.NUMBER, x[1].val * y[2].val - x[2].val * y[1].val),
new Variable(VarType.NUMBER, x[2].val * y[0].val - x[0].val * y[2].val),
new Variable(VarType.NUMBER, x[0].val * y[1].val - x[1].val * y[0].val)
});
return new Variable(VarType.LIST, z);
default:
throw new Exception("unknown build-in function: "+ func.id);
}
} else {
// User function
Kerbulator.DebugLine("Executing "+ func.id);
Function f = functions[func.id];
List<Variable> result = f.Execute(arguments, operators, globals, functions);
if(f.InError)
throw new Exception(f.ErrorString);
if(result.Count == 1)
return result[0];
else {
return new Variable(VarType.LIST, result);
}
}
}
public void AddGlobal(Variable v)
{
if(globals.ContainsKey(v.id))
globals[v.id] = v;
else
globals.Add(v.id, v);
}
private Variable ApplyBinaryFunction(Variable a, Variable b, BinaryFunction action)
{
if(a.type == VarType.NUMBER && b.type == VarType.NUMBER)
return new Variable("", VarType.NUMBER, action(a.val, b.val));
else if(a.type == VarType.NUMBER && b.type == VarType.LIST) {
List<Variable> newElements = new List<Variable>(b.elements.Count);
foreach(Variable e in b.elements)
newElements.Add(ApplyBinaryFunction(a, e, action));
return new Variable("", VarType.LIST, newElements);
}
else if(a.type == VarType.LIST && b.type == VarType.NUMBER) {
List<Variable> newElements = new List<Variable>(a.elements.Count);
foreach(Variable e in a.elements)
newElements.Add(ApplyBinaryFunction(e, b, action));
return new Variable("", VarType.LIST, newElements);
}
else if(a.type == VarType.LIST && b.type == VarType.LIST) {
if(a.elements.Count != b.elements.Count)
throw new Exception("Trying to perform a binary operation on lists of unequal size.");
List<Variable> newElements = new List<Variable>(a.elements.Count);
for(int i=0; i<a.elements.Count; i++)
newElements.Add(ApplyBinaryFunction(a.elements[i], b.elements[i], action));
return new Variable("", VarType.LIST, newElements);
}
throw new Exception("Trying to perform an operation on invalid types.");
}
private Variable ApplyUnaryFunction(Variable v, UnaryFunction action)
{
if(v.type == VarType.NUMBER)
return new Variable(v.id, v.type, action(v.val));
else if(v.type == VarType.LIST) {
List<Variable> newElements = new List<Variable>(v.elements.Count);
foreach(Variable e in v.elements)
newElements.Add(ApplyUnaryFunction(e, action));
return new Variable(v.id, v.type, newElements);
}
throw new Exception("Trying to perform an operation on invalid type.");
}
protected Variable ExecuteExpression()
{
Stack<Variable> expr = new Stack<Variable>();
Stack<Operator> ops = new Stack<Operator>();
Token t = null;
while(tokens.Count > 0 && tokens.Peek().type != TokenType.END) {
t = tokens.Peek();
Kerbulator.DebugLine("Token: "+ Enum.GetName(typeof(TokenType), t.type) +": "+ t.val);
if(t.type == TokenType.BRACE) {
// Determine whether it's a left or right brace
bool isLeft = false;
switch(t.val) {
case "(":
case "{":
case "⌊":
case "⌈":
isLeft = true;
break;
case "|":
isLeft = !PossiblyValidExpression(expr, ops);
if(isLeft)
Kerbulator.DebugLine("| is left brace");
else {
Kerbulator.DebugLine("| is right brace");
}
break;
}
// If it's a left brace, start a sub-expression
if(isLeft) {
Consume();
// Execute sub-expression
Kerbulator.DebugLine("Starting subexpression");
Variable subexpr = ExecuteExpression();
Kerbulator.DebugLine("Answer of subexpression: "+ subexpr.ToString());
expr.Push(subexpr);
// Consume right brace. Execute operation if any
switch(t.val) {
case "(":
Consume(")");
break;
case "{":
Consume("}");
break;
case "⌊":
Consume("⌋");
ops.Push(operators[t.val]);
break;
case "⌈":
Consume("⌉");
ops.Push(operators[t.val]);
break;
case "|":
Consume("|");
ops.Push(operators[t.val]);
break;
}
} else {
// It's a right brace, just end the sub-expression
break;
}
}
else if(t.type == TokenType.NUMBER) {
expr.Push( new Variable(VarType.NUMBER, Double.Parse(t.val, System.Globalization.CultureInfo.InvariantCulture)) );
Consume();
}
else if(t.type == TokenType.OPERATOR) {
Operator op = operators[t.val];
// Handle ambiguous cases of arity
if(op.arity == Arity.BOTH) {
if(PossiblyValidExpression(expr, ops) ) {
op = new Operator(op.id, op.precidence, Arity.BINARY);
Kerbulator.DebugLine(op.id +" is binary.");
} else {
op = new Operator(op.id, 3, Arity.UNARY);
Kerbulator.DebugLine(op.id +" is unary.");
}
}
// Handle operators with higher precidence
while(ops.Count > 0) {
Operator prevOp = ops.Peek();
if(op.arity == Arity.BINARY && prevOp.precidence >= op.precidence) {
try {
expr.Push( ExecuteOperator(ops.Pop(), expr, ops) );
} catch(Exception e) {
throw new Exception(t.pos + e.Message);
}
} else
break;
}
ops.Push(op);
Consume();
}
else if(t.type == TokenType.IDENTIFIER) {
Variable var;
if(locals.ContainsKey(t.val))
var = locals[t.val];
else if(functions.ContainsKey(t.val))
var = new Variable(t.val, VarType.USER_FUNCTION, null);
else if(globals.ContainsKey(t.val))
var = globals[t.val];
else
throw new Exception(t.pos +"undefined variable or function: "+ t.val);
Consume();
if(var.type == VarType.FUNCTION || var.type == VarType.USER_FUNCTION) {
List<Variable> arguments = new List<Variable>();
// Check for argument list
if(tokens.Peek().val == "(") {
Consume();
Kerbulator.DebugLine("Arguments specified");
while(tokens.Peek().val != ")") {
Kerbulator.DebugLine("Starting subexpression");
Variable subexpr = ExecuteExpression();
Kerbulator.DebugLine("Answer of subexpression: "+ subexpr.ToString());
arguments.Add(subexpr);
if(tokens.Peek().val != ")")
Consume(TokenType.COMMA);
}
Consume(")");
// Execute function right now with the given argument list
try {
Variable result = ExecuteFunction(var, arguments);
Kerbulator.DebugLine("Result of function: "+ result.ToString());
expr.Push(result);
} catch(Exception e) {
throw new Exception(e.Message +" (called from "+ t.func +", line "+ t.line +")");
}
} else {
int numArgs = 0;
if(var.type == VarType.FUNCTION)
numArgs = globals[t.val].numArgs;
else
numArgs = functions[t.val].Ins.Count;
if(numArgs == 0) {
// Function doesn't take arguments, execute right now with empty argument list
try {
Variable result = ExecuteFunction(var, new List<Variable>());
Kerbulator.DebugLine("Result of function: "+ result.ToString());
expr.Push(result);
} catch(Exception e) {
throw new Exception(e.Message +" (called from "+ t.func +", line "+ t.line +")");
}
} else {
// Push the execution of the function onto the stack
Kerbulator.DebugLine("No arguments specified");
expr.Push(var);
ops.Push(operators["func"]);
}
}
} else {
expr.Push(var);
}
} else if(t.type == TokenType.LIST) {
if(t.val == "]")
break; // Right brace ends list
List<Variable> elements = new List<Variable>();
Consume();
while(tokens.Peek().val != "]") {
Kerbulator.DebugLine("Starting subexpression");
Variable subexpr = ExecuteExpression();
Kerbulator.DebugLine("Answer of subexpression: "+ subexpr.ToString());
elements.Add(subexpr);
if(tokens.Peek().val != "]")
Consume(TokenType.COMMA);
}
Consume("]");
expr.Push(new Variable("", VarType.LIST, elements));
} else
break;
}
// Handle remaining ops
while(ops.Count > 0) {
Operator op = ops.Pop();
try {
expr.Push( ExecuteOperator(op, expr, ops) );
} catch(Exception e) {
if(t == null)
throw new Exception(e.Message);
else
throw new Exception(t.pos + e.Message);
}
}
if(expr.Count > 1) {
if(t == null)
throw new Exception("malformed expression");
else
throw new Exception(t.pos + "malformed expression");
}
return expr.Pop();
}
public List<Variable> Execute(List<Variable> arguments, Dictionary<string, Operator> operators, Dictionary<string, Variable> globals, Dictionary<string, Function> functions)
{
List<Variable> result = new List<Variable>();
Queue<Token> oldTokens = new Queue<Token>(tokens);
try {
this.InError = false;
this.locals = new Dictionary<string, Variable>();
this.operators = operators;
this.globals = globals;
this.functions = functions;
if(ins.Count != arguments.Count)
throw new Exception("function "+ this.id +" takes "+ ins.Count +" arguments, but "+ arguments.Count +" were supplied");
for(int i=0; i<ins.Count; i++)
locals.Add(ins[i], arguments[i].Copy(ins[i]));
Variable lastVal = new Variable(VarType.NUMBER, 0.0);
while(tokens.Count > 0) {
Variable val = ExecuteStatement();
if(val != null)
lastVal = val;
Consume(TokenType.END);
}
if(outs.Count > 0) {
foreach(string id in outs) {
if(!locals.ContainsKey(id))
throw new Exception("output variable "+ id +" is not defined in the code of function "+ this.id);
result.Add(locals[id]);
}
} else
result.Add(lastVal);
} catch(Exception e) {
this.InError = true;
this.ErrorString = e.Message;
}
tokens = oldTokens;
return result;
}
public static void AddBool(Kerbulator kalc, string id, bool v)
{
double val = v ? 1.0 : 0.0;
Variable g = new Variable(id, VarType.NUMBER, val);
kalc.AddGlobal(g);
}
public static void AddVector3d(Kerbulator kalc, string id, Vector3d v)
{
Variable x = new Variable("x", VarType.NUMBER, v.x);
Variable y = new Variable("y", VarType.NUMBER, v.y);
Variable z = new Variable("z", VarType.NUMBER, v.z);
List<Variable> elements = new List<Variable>(3);
elements.Add(x);
elements.Add(y);
elements.Add(z);
Variable g = new Variable(id, VarType.LIST, elements);
kalc.AddGlobal(g);
}
public static void AddDouble(Kerbulator kalc, string id, double v)
{
Variable g = new Variable(id, VarType.NUMBER, v);
kalc.AddGlobal(g);
}