protected override SyntaxToken VisitFunction(FunctionSyntaxToken token)
{
SyntaxToken arg = token.Arguments[0];
SyntaxToken diff = this.Visit(arg);
SyntaxToken one = SyntaxToken.Constant(1);
SyntaxToken two = SyntaxToken.Constant(2);
SyntaxToken result;
switch (token.Type)
{
case FunctionType.Sin:
result = SyntaxToken.Cos(arg);
break;
case FunctionType.Cos:
result = SyntaxToken.Negate(SyntaxToken.Sin(arg));
break;
case FunctionType.Tan:
result = SyntaxToken.Add(one, SyntaxToken.Pow(SyntaxToken.Tan(arg), two));
break;
case FunctionType.Cot:
result = SyntaxToken.Negate(SyntaxToken.Add(one, SyntaxToken.Pow(SyntaxToken.Cot(arg), two)));
break;
case FunctionType.Asin:
result = SyntaxToken.Divide(one, SyntaxToken.Root(SyntaxToken.Subtract(one, SyntaxToken.Pow(arg, two)), two));
break;
case FunctionType.Acos:
result = -(one / SyntaxToken.Root(one - SyntaxToken.Pow(arg, two), two));
break;
case FunctionType.Atan:
result = one / (one + SyntaxToken.Pow(arg, two));
break;
case FunctionType.Acot:
result = -(one / (one + SyntaxToken.Pow(arg, two)));
break;
case FunctionType.Log:
SyntaxToken b = token.Arguments[1];
result = one / (arg * SyntaxToken.Ln(b));
break;
case FunctionType.Ln:
result = one / arg;
break;
case FunctionType.Abs:
result = arg / SyntaxToken.Abs(arg);
break;
case FunctionType.Unsupported:
default: throw new NotSupportedException();
}
return(result * diff);
}
protected override SyntaxToken VisitBinary(BinarySyntaxToken token)
{
SyntaxToken leftDiff = this.Visit(token.Left);
SyntaxToken rightDiff = this.Visit(token.Right);
switch (token.Type)
{
case BinaryOperationType.Add: return(leftDiff + rightDiff);
case BinaryOperationType.Subtract: return(leftDiff - rightDiff);
case BinaryOperationType.Multiply: return(leftDiff * token.Right + token.Left * rightDiff);
case BinaryOperationType.Divide: return((leftDiff * token.Right - token.Left * rightDiff) / SyntaxToken.Pow(token.Right, SyntaxToken.Constant(2)));
// TODO: implement
case BinaryOperationType.Modulus: return(token);
case BinaryOperationType.Power:
if (!this.VarDetector.HasVariable(token.Right))
{
return(token.Right * SyntaxToken.Pow(token.Left, token.Right - SyntaxToken.Constant(1)));
}
return(token * (leftDiff * token.Right / token.Left + rightDiff * SyntaxToken.Ln(token.Left)));
default: throw new NotSupportedException();
}
}
private SyntaxToken EvalUnary(ConstantSyntaxToken value, UnaryOperationType type)
{
switch (type)
{
case UnaryOperationType.Factorial: return SyntaxToken.Constant(MathEx.Factorial(value.Value));
default: throw new NotSupportedException();
}
}
protected override SyntaxToken VisitVariable(VariableSyntaxToken token)
{
if (SyntaxToken.Equals(this.Variable, token))
{
return(SyntaxToken.Constant(1));
}
return(SyntaxToken.Constant(0));
}
public EvaluationContext CreateEvaluationContext()
{
EvaluationContext context = new EvaluationContext();
foreach (var item in this.Constants)
{
context.SetVariable(item.Key, SyntaxToken.Constant(item.Value));
}
return(context);
}
private SyntaxToken EvalBinary(ConstantSyntaxToken left, ConstantSyntaxToken right, BinaryOperationType type)
{
double lval = left.Value;
double rval = right.Value;
switch (type)
{
case BinaryOperationType.Add: return SyntaxToken.Constant(lval + rval);
case BinaryOperationType.Subtract: return SyntaxToken.Constant(lval - rval);
case BinaryOperationType.Multiply: return SyntaxToken.Constant(lval * rval);
case BinaryOperationType.Divide: return SyntaxToken.Constant(lval / rval);
case BinaryOperationType.Modulus: return SyntaxToken.Constant(lval % rval);
case BinaryOperationType.Power: return SyntaxToken.Constant(Math.Pow(lval, rval));
default: throw new NotSupportedException();
}
}
private SyntaxToken EvalFunction(ConstantSyntaxToken[] values, FunctionType type)
{
switch (type)
{
case FunctionType.Sin: return SyntaxToken.Constant(Math.Sin(values[0].Value));
case FunctionType.Cos: return SyntaxToken.Constant(Math.Cos(values[0].Value));
case FunctionType.Tan: return SyntaxToken.Constant(Math.Tan(values[0].Value));
case FunctionType.Cot: return SyntaxToken.Constant(MathEx.Cot(values[0].Value));
case FunctionType.Asin: return SyntaxToken.Constant(Math.Asin(values[0].Value));
case FunctionType.Acos: return SyntaxToken.Constant(Math.Acos(values[0].Value));
case FunctionType.Atan: return SyntaxToken.Constant(Math.Atan(values[0].Value));
case FunctionType.Acot: return SyntaxToken.Constant(MathEx.Acot(values[0].Value));
case FunctionType.Log: return SyntaxToken.Constant(Math.Log(values[0].Value, values[1].Value));
case FunctionType.Ln: return SyntaxToken.Constant(Math.Log(values[0].Value));
case FunctionType.Abs: return SyntaxToken.Constant(Math.Abs(values[0].Value));
default: throw new NotSupportedException();
}
}
protected override SyntaxToken VisitConstant(ConstantSyntaxToken token)
{
return(SyntaxToken.Constant(0));
}
protected override SyntaxToken VisitNamedConstant(NamedConstantSyntaxToken token)
{
return SyntaxToken.Constant(token.Value);
}
protected override SyntaxToken VisitBinary(BinarySyntaxToken token)
{
SyntaxToken left = this.Visit(token.Left);
SyntaxToken right = this.Visit(token.Right);
BinaryOperationType type = token.Type;
if (left.TokenType == SyntaxTokenType.Constant && right.TokenType == SyntaxTokenType.Constant)
{
return this.EvalBinary((ConstantSyntaxToken)left, (ConstantSyntaxToken)right, type);
}
// swap constant to the right
if ((type == BinaryOperationType.Add || type == BinaryOperationType.Multiply) && (left.TokenType == SyntaxTokenType.Constant))
{
SyntaxToken temp = right;
right = left;
left = temp;
}
// add
if (type == BinaryOperationType.Add)
{
if (right.HasValue(0))
{
return left;
}
}
// subtract
else if (type == BinaryOperationType.Subtract)
{
if (right.HasValue(0))
{
return left;
}
if (SyntaxToken.Equals(left, right))
{
return SyntaxToken.Constant(0);
}
}
// multiply
else if (type == BinaryOperationType.Multiply)
{
if (right.HasValue(0))
{
return SyntaxToken.Constant(0);
}
if (right.HasValue(1))
{
return left;
}
if (left.TokenType == SyntaxTokenType.Binary && right.TokenType == SyntaxTokenType.Binary)
{
BinarySyntaxToken bl = (BinarySyntaxToken)left;
BinarySyntaxToken br = (BinarySyntaxToken)right;
if (bl.Type == BinaryOperationType.Power && br.Type == BinaryOperationType.Power && SyntaxToken.Equals(bl.Left, br.Left))
{
return this.Visit(SyntaxToken.Pow(bl.Left, SyntaxToken.Add(bl.Right, br.Right)));
}
}
}
// divide
else if (type == BinaryOperationType.Divide)
{
if (left.HasValue(0))
{
return SyntaxToken.Constant(0);
}
if (SyntaxToken.Equals(left, right))
{
return SyntaxToken.Constant(1);
}
}
// modulus
else if (type == BinaryOperationType.Modulus)
{
if (left.HasValue(0))
{
return SyntaxToken.Constant(0);
}
if (SyntaxToken.Equals(left, right))
{
return SyntaxToken.Constant(0);
}
}
// pow
else if (type == BinaryOperationType.Power)
{
if (right.HasValue(0))
{
return SyntaxToken.Constant(1);
}
if (right.HasValue(1))
{
return left;
}
if (left.HasValue(0))
{
return SyntaxToken.Constant(1);
}
if (left.TokenType == SyntaxTokenType.Binary)
{
BinarySyntaxToken bl = (BinarySyntaxToken)left;
if (bl.Type == BinaryOperationType.Power)
{
return this.Visit(SyntaxToken.Pow(bl.Left, SyntaxToken.Multiply(bl.Right, right)));
}
}
}
return SyntaxToken.Binary(left, right, type);
}