private bool EmitFunc(FuncNode funcNode, bool negExpAbs = false)
{
switch (funcNode.FunctionType)
{
case KnownFuncType.Add:
return(EmitAddFunc(funcNode));
case KnownFuncType.Sub:
return(EmitSubFunc(funcNode));
case KnownFuncType.Mult:
return(EmitMultFunc(funcNode));
case KnownFuncType.Div:
return(EmitDivFunc(funcNode));
case KnownFuncType.Neg:
return(EmitNegFunc(funcNode, negExpAbs));
case KnownFuncType.Pow:
return(EmitExpFunc(funcNode, negExpAbs));
case KnownFuncType.Diff:
return(EmitDiffFunc(funcNode));
}
if (!EmitKnownFunc(funcNode)) // Unknown function (from input args).
{
EmitUnknownFunc(funcNode);
}
return(true);
}
private MathFuncNode MakeSubstitution(MathFuncNode left, MathFuncNode right, FuncNode currentFunc)
{
LeftNode = left;
RightNode = right;
_currentFunc = currentFunc;
return(MakeSubstitution(right));
}
protected string ToString(FuncNode parent,
KnownFuncType funcType,
IList <KnownFuncType> types)
{
var builder = new StringBuilder();
if (parent == null || parent.Name == null || parent.Children.Count <= 1)
{
AppendMathFunctionNode(builder, funcType);
return(builder.ToString());
}
var funcNodeParent = parent as FuncNode;
if (funcNodeParent != null && funcNodeParent.IsKnown)
{
if (types.Contains((KnownFuncType)funcNodeParent.FunctionType))
{
AppendMathFunctionNode(builder, funcType);
return(builder.ToString());
}
}
builder.Append("(");
AppendMathFunctionNode(builder, funcType);
builder.Append(")");
return(builder.ToString());
}
private bool EmitDiffFunc(FuncNode funcNode)
{
var diffFunc = funcNode.Childs[0];
var arg = diffFunc.Childs[0];
bool isUnknownFunc = diffFunc.Type == MathNodeType.Function && !((FuncNode)diffFunc).IsKnown;
var diff = FuncNodes[(FuncNode)diffFunc];
// f(x + dx)
if (isUnknownFunc)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldarg, diffFunc.ArgNumber));
}
EmitNode(arg);
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, DerivativeDelta));
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
if (isUnknownFunc)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Callvirt, MathFuncAssembly.InvokeFuncRef));
}
else
{
EmitNode(diffFunc);
}
// f(x)
EmitNode(diffFunc);
IlInstructions.Add(new OpCodeArg(OpCodes.Sub));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0 / DerivativeDelta));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
return(true);
}
private void BuildMultichildTree(FuncNode beginNode)
{
var newChilds = new List <MathFuncNode>();
BuildMultichildTree(beginNode, beginNode, newChilds, false);
beginNode.Childs = newChilds;
}
private MathFuncNode ExpValue(FuncNode funcNode)
{
var bValue = funcNode.Children[1] as ValueNode;
if (bValue != null)
{
if (bValue.Value == 0)
{
return(new ValueNode(1));
}
else if (bValue.Value == 1)
{
return(funcNode.Children[0]);
}
/*else if (funcNode.Children[0].Type == MathNodeType.Value)
* {
* double a = funcNode.Children[0].Value.ToDouble();
* double b = bValue.Value.ToDouble();
* double r = b == 0.5 ? Math.Sqrt(a) : Math.Pow(a, b);
* Rational<long> result;
* Rational<long>.FromDecimal((decimal)r, out result);
* return new ValueNode(result);
* }*/
else if (bValue.Value.IsInteger && funcNode.Children[0] is FuncNode childFuncNode &&
childFuncNode.FunctionType == KnownFuncType.Neg)
{
if (bValue.Value.Numerator % 2 == 0)
{
return(new FuncNode(KnownFuncType.Pow, funcNode.Children[0].Children[0], new ValueNode(bValue.Value)));
}
else
{
return(new FuncNode(KnownFuncType.Neg, new FuncNode(KnownFuncType.Pow, funcNode.Children[0].Children[0], new ValueNode(bValue.Value))));
}
}
}
if (funcNode.Children[0] is ValueNode aValue)
{
if (aValue.Value == 0)
{
return(new ValueNode(0));
}
else if (aValue.Value == 1)
{
return(new ValueNode(1));
}
else if (bValue != null)
{
return((MathFuncNode)SimplifyValues(KnownFuncType.Pow, new List <ValueNode>()
{
aValue, bValue
})
?? (MathFuncNode)funcNode);
}
}
return(funcNode);
}
private FuncNode PrecompileExpFunc(MathFuncNode parent, FuncNode funcNode)
{
if ((parent == null ||
((FuncNode)parent).FunctionType != KnownFuncType.Mult) &&
funcNode.Childs[1].LessThenZero())
{
if (!funcNode.Childs[1].IsValueOrCalculated || funcNode.Childs[1].DoubleValue != -1.0)
{
FuncNode second;
if (!funcNode.Childs[1].IsValueOrCalculated)
{
second = new FuncNode(KnownFuncType.Pow, funcNode.Childs[0], funcNode.Childs[1].Abs());
}
else
{
second = Math.Abs(funcNode.Childs[1].DoubleValue) != 0.5 ?
new FuncNode(KnownFuncType.Pow, funcNode.Childs[0], funcNode.Childs[1].Abs()) :
new FuncNode(KnownFuncType.Sqrt, funcNode.Childs[0]);
}
return(new FuncNode(KnownFuncType.Div, new CalculatedNode(1.0), second));
}
else
{
return(new FuncNode(KnownFuncType.Div, new CalculatedNode(1.0), funcNode.Childs[0]));
}
}
if (funcNode.Childs[1].IsValueOrCalculated && funcNode.Childs[1].DoubleValue == 0.5)
{
return(new FuncNode(KnownFuncType.Sqrt, funcNode.Childs[0]));
}
return(funcNode);
}
private MathFuncNode BreakOnAddNodes(FuncNode funcNode)
{
var addNodes = funcNode.Childs.Where(child =>
child.Type == MathNodeType.Function &&
((FuncNode)child).FunctionType == KnownFuncType.Add).ToList();
if (addNodes.Count != 0)
{
var funcNodesExceptAddNodes = funcNode.Childs.Except(addNodes);
var ar = new int[addNodes.Count];
var lengthAr = addNodes.Select(addNode => addNode.Childs.Count).ToArray();
var newAddChilds = new List <MathFuncNode>();
var newChilds = new List <MathFuncNode>();
do
{
newAddChilds.Clear();
newAddChilds.AddRange(funcNodesExceptAddNodes);
for (int j = 0; j < ar.Length; j++)
{
newAddChilds.Add(addNodes[j].Childs[ar[j]]);
}
newChilds.Add(Simplify(new FuncNode(KnownFuncType.Mult, newAddChilds)));
}while (IncArray(ar, lengthAr));
return(Simplify(new FuncNode(KnownFuncType.Add, newChilds)));
}
else
{
return(null);
}
}
private MathFuncNode PrecompileAddFunc(FuncNode funcNode)
{
MathFuncNode firstItem;
MathFuncNode result = null;
var funcNode2 = FoldCalculatedSummands(funcNode);
firstItem = funcNode2.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return !(func != null && func.LessThenZero());
});
if (firstItem == null)
firstItem = funcNode2.Childs[0];
result = firstItem;
for (int i = 0; i < funcNode2.Childs.Count; i++)
{
if (funcNode2.Childs[i] == firstItem)
continue;
if (funcNode2.Childs[i].LessThenZero())
result = new FuncNode(KnownFuncType.Sub, result, funcNode2.Childs[i].Abs());
else
result = new FuncNode(KnownFuncType.Add, result, funcNode2.Childs[i]);
}
return result;
}
public MathFuncNode VisitBinaryExpression(BinaryExpressionContext context)
{
MathFuncNode arg1 = Visit(context.expression(0));
MathFuncNode arg2 = Visit(context.expression(1));
KnownFuncType funcType;
if (context.Plus() != null)
{
funcType = KnownFuncType.Add;
}
else if (context.Minus() != null)
{
funcType = KnownFuncType.Sub;
var second = new FuncNode(KnownFuncType.Neg, new MathFuncNode[] { arg2 });
var result = new FuncNode(KnownFuncType.Add, new MathFuncNode[] { arg1, second });
return(result);
}
else if (context.Mult() != null)
{
funcType = KnownFuncType.Mult;
}
else if (context.Div() != null)
{
var second = new FuncNode(KnownFuncType.Pow, new MathFuncNode[] { arg2, new ValueNode(-1) });
var result = new FuncNode(KnownFuncType.Mult, new MathFuncNode[] { arg1, second });
return(result);
}
else
{
funcType = KnownFuncType.Pow;
}
return(new FuncNode(funcType, new MathFuncNode[] { arg1, arg2 }));
}
public override string ToString(FuncNode parent)
{
if (IsKnown)
{
var funcType = (KnownFuncType)FunctionType;
switch ((KnownFuncType)FunctionType)
{
case KnownFuncType.Add:
case KnownFuncType.Sub:
return(ToString(parent, funcType, KnownFunc.AddKnownFuncs));
case KnownFuncType.Mult:
case KnownFuncType.Div:
return(ToString(parent, funcType, KnownFunc.MultKnownFuncs));
case KnownFuncType.Pow:
return(ToString(parent, funcType, KnownFunc.ExpKnownFuncs));
case KnownFuncType.Neg:
if (Childs[0].Type == MathNodeType.Function)
{
var func = (FuncNode)Childs[0];
if (KnownFunc.NegKnownFuncs.Contains((KnownFuncType)func.FunctionType))
{
return("-(" + Childs[0].ToString(this) + ")");
}
else
{
return("-" + Childs[0].ToString(this));
}
}
else
{
return("-" + Childs[0].ToString(this));
}
case KnownFuncType.Diff:
return(Childs[0].Type == MathNodeType.Function && ((FuncNode)Childs[0]).FunctionType != KnownFuncType.Diff ?
Childs[0].ToString(this) + "'" : "(" +
Childs[0].ToString(this) + ")'");
case KnownFuncType.Abs:
return(string.Format("|{0}|", Childs[0].ToString(this)));
}
}
var builder = new StringBuilder((FunctionType == KnownFuncType.Sqrt ? "√" : Name) + "(");
foreach (var arg in Childs)
{
builder.AppendFormat("{0}, ", arg.ToString(this));
}
if (Childs.Count != 0)
{
builder.Remove(builder.Length - 2, 2);
}
builder.Append(')');
return(builder.ToString());
}
public MathFuncNode VisitParenthesisExpression(ParenthesisExpressionContext context)
{
var result = Visit(context.expression());
if (context.Quote() != null)
{
result = new FuncNode(KnownFuncType.Diff, result);
}
return(result);
}
public MathFuncNode VisitAbsoluteExpression(AbsoluteExpressionContext context)
{
var result = new FuncNode(KnownFuncType.Abs, Visit(context.expression()));
if (context.Quote() != null)
{
result = new FuncNode(KnownFuncType.Diff, result);
}
return(result);
}
private bool EmitNegFunc(FuncNode funcNode, bool negExpAbs)
{
EmitNode(funcNode.Childs[0]);
if (!negExpAbs)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Neg));
}
return(true);
}
private bool EmitDivFunc(FuncNode funcNode)
{
EmitNode(funcNode.Childs[0]);
for (int i = 1; i < funcNode.Childs.Count; i++)
{
EmitNode(funcNode.Childs[i]);
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
}
return(true);
}
private bool EmitUnknownFunc(FuncNode funcNode)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldarg, funcNode.ArgNumber));
foreach (var child in funcNode.Childs)
{
EmitNode(child);
}
IlInstructions.Add(new OpCodeArg(OpCodes.Callvirt, MathFuncAssembly.InvokeFuncRef));
return(true);
}
public MathFuncNode VisitFuncExpression(FuncExpressionContext context)
{
IEnumerable <MathFuncNode> expressions = context.expressionList().expression()
.Select(e => Visit(e));
var result = new FuncNode(context.Id().GetText(), expressions);
if (context.Quote() != null)
{
result = new FuncNode(KnownFuncType.Diff, result);
}
return(result);
}
private bool EmitMultFunc(FuncNode funcNode)
{
MathFuncNode firstItem = null;
firstItem = funcNode.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return(!(func != null && FuncNodes[func].Count == 1 && func.FunctionType == KnownFuncType.Pow && func.Childs[1].LessThenZero()));
});
if (firstItem == null)
{
firstItem = funcNode.Childs[0];
}
EmitNode(firstItem);
for (int i = 0; i < funcNode.Childs.Count; i++)
{
if (funcNode.Childs[i] == firstItem)
{
continue;
}
var func = funcNode.Childs[i] as FuncNode;
if (func != null && FuncNodes[func].Count == 1 && func.FunctionType == KnownFuncType.Pow && func.Childs[1].LessThenZero())
{
EmitNode(funcNode.Childs[i], true);
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
}
else
{
EmitNode(funcNode.Childs[i]);
if (IlInstructions[IlInstructions.Count - 1].OpCode == OpCodes.Ldc_R8 && (double)IlInstructions[IlInstructions.Count - 1].Arg == 1.0)
{
IlInstructions.RemoveAt(IlInstructions.Count - 1);
}
else
{
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
}
}
}
return(true);
}
public override string ToString(FuncNode parent)
{
if (Value.Denominator == 1 || !parent.IsKnown)
{
return(Name);
}
if (parent.FunctionType == KnownFuncType.Mult || parent.FunctionType == KnownFuncType.Div ||
parent.FunctionType == KnownFuncType.Pow || parent.FunctionType == KnownFuncType.Neg)
{
return('(' + Name + ')');
}
else
{
return(Name);
}
}
public MathFuncNode VisitUnaryExpression(UnaryExpressionContext context)
{
var result = Visit(context.expression());
if (context.Minus() != null)
{
if (result is ValueNode valueNode)
{
result = new ValueNode(-valueNode.Value);
}
else
{
result = new FuncNode(KnownFuncType.Neg, result);
}
}
return(result);
}
private MathFuncNode Precompile(MathFuncNode parent, MathFuncNode node)
{
if (node.Type == MathNodeType.Value)
{
return(new CalculatedNode(((ValueNode)node).Value));
}
else if (node.Type == MathNodeType.Function)
{
for (int i = 0; i < node.Childs.Count; i++)
{
node.Childs[i] = Precompile(node, node.Childs[i]);
}
FuncNode func = (FuncNode)node;
switch (func.FunctionType)
{
case KnownFuncType.Add:
node = PrecompileAddFunc(func);
break;
case KnownFuncType.Mult:
node = PrecompileMultFunc(func);
break;
case KnownFuncType.Pow:
node = PrecompileExpFunc(parent, func);
break;
}
if (node.Childs.Count > 0 && node.Childs.All(child => child.Type == MathNodeType.Value || child.Type == MathNodeType.Calculated))
{
return((MathFuncNode)CalculateValues(((FuncNode)node).FunctionType, node.Childs) ?? (MathFuncNode)node);
}
else
{
return(node);
}
}
else
{
return(node);
}
}
private FuncNode MultCalculatedFactors(FuncNode mult)
{
var result = mult.Childs
.Where(child => child.Type == MathNodeType.Calculated || child.Type == MathNodeType.Value)
.Select(factor => factor.DoubleValue)
.Aggregate(1.0, (t, factor) => t *= factor);
if (result != 1.0)
{
var newChilds = new List <MathFuncNode>()
{
new CalculatedNode(result)
};
newChilds.AddRange(mult.Childs.Where(c => c.Type != MathNodeType.Calculated && c.Type != MathNodeType.Value));
return(new FuncNode(KnownFuncType.Mult, newChilds));
}
else
{
return(mult);
}
}
private bool EmitAddFunc(FuncNode funcNode)
{
MathFuncNode firstItem = null;
firstItem = funcNode.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return(!(func != null && FuncNodes[func].Count == 1 && func.LessThenZero()));
});
if (firstItem == null)
{
firstItem = funcNode.Childs[0];
}
EmitNode(firstItem);
for (int i = 0; i < funcNode.Childs.Count; i++)
{
if (funcNode.Childs[i] == firstItem)
{
continue;
}
var func = funcNode.Childs[i] as FuncNode;
if (func != null && FuncNodes[func].Count == 1 && func.LessThenZero())
{
EmitNode(func.Childs[0], true);
IlInstructions.Add(new OpCodeArg(OpCodes.Sub));
}
else
{
EmitNode(funcNode.Childs[i]);
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
}
}
return(true);
}
private FuncNode FoldCalculatedSummands(FuncNode sum)
{
var result = sum.Childs
.Where(child => child.Type == MathNodeType.Calculated || child.Type == MathNodeType.Value)
.Select(summand => summand.DoubleValue)
.Aggregate(0.0, (t, factor) => t += factor);
if (result != 0.0)
{
var newChilds = new List <MathFuncNode>()
{
new CalculatedNode(result)
};
newChilds.AddRange(sum.Childs.Where(c => c.Type != MathNodeType.Calculated && c.Type != MathNodeType.Value));
return(new FuncNode(KnownFuncType.Sub, newChilds));
}
else
{
return(sum);
}
}
private MathFuncNode PrecompileAddFunc(FuncNode funcNode)
{
MathFuncNode firstItem;
MathFuncNode result = null;
var funcNode2 = FoldCalculatedSummands(funcNode);
firstItem = funcNode2.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return(!(func != null && func.LessThenZero()));
});
if (firstItem == null)
{
firstItem = funcNode2.Childs[0];
}
result = firstItem;
for (int i = 0; i < funcNode2.Childs.Count; i++)
{
if (funcNode2.Childs[i] == firstItem)
{
continue;
}
if (funcNode2.Childs[i].LessThenZero())
{
result = new FuncNode(KnownFuncType.Sub, result, funcNode2.Childs[i].Abs());
}
else
{
result = new FuncNode(KnownFuncType.Add, result, funcNode2.Childs[i]);
}
}
return(result);
}
private void ReduceSummands(FuncNode funcNode)
{
int i = 0;
while (i < funcNode.Childs.Count)
{
int j = i + 1;
while (j < funcNode.Childs.Count)
{
var newNode = ReduceAddition(funcNode.Childs[i], funcNode.Childs[j]);
if (newNode != null)
{
funcNode.Childs[i] = newNode;
funcNode.Childs.RemoveAt(j);
}
else
{
j++;
}
}
i++;
}
}
private void BuildMultichildTree(FuncNode beginNode, FuncNode funcNode, List <MathFuncNode> newChilds, bool neg)
{
foreach (var child in funcNode.Childs)
{
var childFuncNode = child as FuncNode;
if (childFuncNode != null)
{
if (childFuncNode.FunctionType == beginNode.FunctionType)
{
BuildMultichildTree(beginNode, childFuncNode, newChilds, neg);
continue;
}
else if (childFuncNode.FunctionType == KnownFuncType.Neg)
{
BuildMultichildTree(beginNode, childFuncNode, newChilds, !neg);
continue;
}
}
if (neg && (beginNode.FunctionType == KnownFuncType.Add ||
(beginNode.FunctionType == KnownFuncType.Mult && child == funcNode.Childs.First())))
{
if (child.Type == MathNodeType.Value)
{
newChilds.Add(new ValueNode(-((ValueNode)child).Value));
}
else
{
newChilds.Add(new FuncNode(KnownFuncType.Neg, child));
}
}
else
{
newChilds.Add(child);
}
}
}
public FuncNode(FuncNode node)
{
FunctionType = node.FunctionType;
Name = node.Name;
Number = node.Number;
for (int i = 0; i < node.Childs.Count; i++)
{
switch (node.Childs[i].Type)
{
case MathNodeType.Value:
Childs.Add(new ValueNode(((ValueNode)node.Childs[i]).Value));
break;
case MathNodeType.Constant:
case MathNodeType.Variable:
Childs.Add(node.Childs[i]);
break;
case MathNodeType.Function:
Childs.Add(new FuncNode((FuncNode)node.Childs[i]));
break;
}
}
}
public FuncNode(FuncNode node)
{
FunctionType = node.FunctionType;
Name = node.Name;
Number = node.Number;
for (int i = 0; i < node.Children.Count; i++)
{
switch (node.Children[i])
{
case ValueNode valueNode:
Children.Add(new ValueNode(valueNode.Value));
break;
case ConstNode constNode:
case VarNode varNode:
Children.Add(node.Children[i]);
break;
case FuncNode funcNode:
Children.Add(new FuncNode(funcNode));
break;
}
}
}
private MathFuncNode FoldValues(FuncNode funcNode)
{
var values = funcNode.Childs
.Where(child => child.Type == MathNodeType.Value)
.Select(valueChild => ((ValueNode)valueChild).Value);
Rational <long> result = 0;
foreach (var value in values)
{
result += value;
}
var notValuesNodes = funcNode.Childs
.Where(child => child.Type != MathNodeType.Value).ToList();
if (result == 0)
{
return
(notValuesNodes.Count == 0 ? new ValueNode(0) :
notValuesNodes.Count == 1 ? notValuesNodes.First() :
new FuncNode(KnownFuncType.Add, notValuesNodes.ToList()));
}
else
{
if (notValuesNodes.Count == 0)
{
return(new ValueNode(result));
}
else
{
notValuesNodes.Add(new ValueNode(result));
return(new FuncNode(KnownFuncType.Add, notValuesNodes));
}
}
}
private bool EmitDivFunc(FuncNode funcNode)
{
EmitNode(funcNode.Childs[0]);
for (int i = 1; i < funcNode.Childs.Count; i++)
{
EmitNode(funcNode.Childs[i]);
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
}
return true;
}
public FuncNode(FuncNode node)
{
FunctionType = node.FunctionType;
Name = node.Name;
Number = node.Number;
for (int i = 0; i < node.Childs.Count; i++)
switch (node.Childs[i].Type)
{
case MathNodeType.Value:
Childs.Add(new ValueNode(((ValueNode)node.Childs[i]).Value));
break;
case MathNodeType.Constant:
case MathNodeType.Variable:
Childs.Add(node.Childs[i]);
break;
case MathNodeType.Function:
Childs.Add(new FuncNode((FuncNode)node.Childs[i]));
break;
}
}
private MathFuncNode FoldValues(FuncNode funcNode)
{
var values = funcNode.Childs
.Where(child => child.Type == MathNodeType.Value)
.Select(valueChild => ((ValueNode)valueChild).Value);
Rational<long> result = 0;
foreach (var value in values)
result += value;
var notValuesNodes = funcNode.Childs
.Where(child => child.Type != MathNodeType.Value).ToList();
if (result == 0)
return
notValuesNodes.Count == 0 ? new ValueNode(0) :
notValuesNodes.Count == 1 ? notValuesNodes.First() :
new FuncNode(KnownFuncType.Add, notValuesNodes.ToList());
else
{
if (notValuesNodes.Count == 0)
return new ValueNode(result);
else
{
notValuesNodes.Add(new ValueNode(result));
return new FuncNode(KnownFuncType.Add, notValuesNodes);
}
}
}
private MathFuncNode ExpValue(FuncNode funcNode)
{
var bValue = funcNode.Childs[1] as ValueNode;
if (bValue != null)
{
if (bValue.Value == 0)
return new ValueNode(1);
else if (bValue.Value == 1)
return funcNode.Childs[0];
/*else if (funcNode.Childs[0].Type == MathNodeType.Value)
{
double a = funcNode.Childs[0].Value.ToDouble();
double b = bValue.Value.ToDouble();
double r = b == 0.5 ? Math.Sqrt(a) : Math.Pow(a, b);
Rational<long> result;
Rational<long>.FromDecimal((decimal)r, out result);
return new ValueNode(result);
}*/
else if (bValue.Value.IsInteger && funcNode.Childs[0].Type == MathNodeType.Function &&
((FuncNode)funcNode.Childs[0]).FunctionType == KnownFuncType.Neg)
{
if (bValue.Value.Numerator % 2 == 0)
return new FuncNode(KnownFuncType.Exp, funcNode.Childs[0].Childs[0], new ValueNode(bValue.Value));
else
return new FuncNode(KnownFuncType.Neg, new FuncNode(KnownFuncType.Exp, funcNode.Childs[0].Childs[0], new ValueNode(bValue.Value)));
}
}
var aValue = funcNode.Childs[0] as ValueNode;
if (aValue != null)
{
if (aValue.Value == 0)
return new ValueNode(0);
else if (aValue.Value == 1)
return new ValueNode(1);
else if (bValue != null)
return (MathFuncNode)SimplifyValues(KnownFuncType.Exp, new List<ValueNode>() { aValue, bValue })
?? (MathFuncNode)funcNode;
}
return funcNode;
}
private MathFuncNode BreakOnAddNodes(FuncNode funcNode)
{
var addNodes = funcNode.Childs.Where(child =>
child.Type == MathNodeType.Function &&
((FuncNode)child).FunctionType == KnownFuncType.Add).ToList();
if (addNodes.Count != 0)
{
var funcNodesExceptAddNodes = funcNode.Childs.Except(addNodes);
var ar = new int[addNodes.Count];
var lengthAr = addNodes.Select(addNode => addNode.Childs.Count).ToArray();
var newAddChilds = new List<MathFuncNode>();
var newChilds = new List<MathFuncNode>();
do
{
newAddChilds.Clear();
newAddChilds.AddRange(funcNodesExceptAddNodes);
for (int j = 0; j < ar.Length; j++)
newAddChilds.Add(addNodes[j].Childs[ar[j]]);
newChilds.Add(Simplify(new FuncNode(KnownFuncType.Mult, newAddChilds)));
}
while (IncArray(ar, lengthAr));
return Simplify(new FuncNode(KnownFuncType.Add, newChilds));
}
else
return null;
}
private FuncNode PrecompileExpFunc(MathFuncNode parent, FuncNode funcNode)
{
if ((parent == null ||
((FuncNode)parent).FunctionType != KnownFuncType.Mult) &&
funcNode.Childs[1].LessThenZero())
{
if (!funcNode.Childs[1].IsValueOrCalculated || funcNode.Childs[1].DoubleValue != -1.0)
{
FuncNode second;
if (!funcNode.Childs[1].IsValueOrCalculated)
second = new FuncNode(KnownFuncType.Pow, funcNode.Childs[0], funcNode.Childs[1].Abs());
else
second = Math.Abs(funcNode.Childs[1].DoubleValue) != 0.5 ?
new FuncNode(KnownFuncType.Pow, funcNode.Childs[0], funcNode.Childs[1].Abs()) :
new FuncNode(KnownFuncType.Sqrt, funcNode.Childs[0]);
return new FuncNode(KnownFuncType.Div, new CalculatedNode(1.0), second);
}
else
return new FuncNode(KnownFuncType.Div, new CalculatedNode(1.0), funcNode.Childs[0]);
}
if (funcNode.Childs[1].IsValueOrCalculated && funcNode.Childs[1].DoubleValue == 0.5)
return new FuncNode(KnownFuncType.Sqrt, funcNode.Childs[0]);
return funcNode;
}
private bool EmitUnknownFunc(FuncNode funcNode)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldarg, funcNode.ArgNumber));
foreach (var child in funcNode.Childs)
EmitNode(child);
IlInstructions.Add(new OpCodeArg(OpCodes.Callvirt, MathFuncAssembly.InvokeFuncRef));
return true;
}
private bool EmitMultFunc(FuncNode funcNode)
{
MathFuncNode firstItem = null;
firstItem = funcNode.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return !(func != null && FuncNodes[func].Count == 1 && func.FunctionType == KnownFuncType.Pow && func.Childs[1].LessThenZero());
});
if (firstItem == null)
firstItem = funcNode.Childs[0];
EmitNode(firstItem);
for (int i = 0; i < funcNode.Childs.Count; i++)
{
if (funcNode.Childs[i] == firstItem)
continue;
var func = funcNode.Childs[i] as FuncNode;
if (func != null && FuncNodes[func].Count == 1 && func.FunctionType == KnownFuncType.Pow && func.Childs[1].LessThenZero())
{
EmitNode(funcNode.Childs[i], true);
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
}
else
{
EmitNode(funcNode.Childs[i]);
if (IlInstructions[IlInstructions.Count - 1].OpCode == OpCodes.Ldc_R8 && (double)IlInstructions[IlInstructions.Count - 1].Arg == 1.0)
IlInstructions.RemoveAt(IlInstructions.Count - 1);
else
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
}
}
return true;
}
private MathFuncNode PrecompileMultFunc(FuncNode funcNode)
{
MathFuncNode firstItem;
MathFuncNode result = null;
var funcNode2 = MultCalculatedFactors(funcNode);
//var funcNode2 = funcNode;
firstItem = funcNode2.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return(!(func != null && func.FunctionType == KnownFuncType.Pow && func.Childs[1].LessThenZero()));
});
if (firstItem == null)
{
firstItem = funcNode2.Childs[0];
result = PrecompileExpFunc(null, (FuncNode)funcNode2.Childs[0]);
}
else
{
result = firstItem;
}
for (int i = 0; i < funcNode2.Childs.Count; i++)
{
if (funcNode2.Childs[i] == firstItem)
{
continue;
}
FuncNode funcChildNode = funcNode2.Childs[i] as FuncNode;
if (funcChildNode != null && funcChildNode.FunctionType == KnownFuncType.Pow && funcChildNode.Childs[1].LessThenZero())
{
if (!funcChildNode.Childs[1].IsValueOrCalculated || funcChildNode.Childs[1].DoubleValue != -1.0)
{
FuncNode second;
if (!funcChildNode.Childs[1].IsValueOrCalculated)
{
second = new FuncNode(KnownFuncType.Pow, funcChildNode.Childs[0], funcChildNode.Childs[1].Abs());
}
else
{
second = Math.Abs(funcChildNode.Childs[1].DoubleValue) != 0.5 ?
new FuncNode(KnownFuncType.Pow, funcChildNode.Childs[0], funcChildNode.Childs[1].Abs()) :
new FuncNode(KnownFuncType.Sqrt, funcChildNode.Childs[0]);
}
result = new FuncNode(KnownFuncType.Div, result, second);
}
else
{
result = new FuncNode(KnownFuncType.Div, result, funcChildNode.Childs[0]);
}
}
else
{
result = new FuncNode(KnownFuncType.Mult, result, funcNode2.Childs[i]);
}
}
return(result);
}
private MathFuncNode PrecompileMultFunc(FuncNode funcNode)
{
MathFuncNode firstItem;
MathFuncNode result = null;
var funcNode2 = MultCalculatedFactors(funcNode);
//var funcNode2 = funcNode;
firstItem = funcNode2.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return !(func != null && func.FunctionType == KnownFuncType.Pow && func.Childs[1].LessThenZero());
});
if (firstItem == null)
{
firstItem = funcNode2.Childs[0];
result = PrecompileExpFunc(null, (FuncNode)funcNode2.Childs[0]);
}
else
result = firstItem;
for (int i = 0; i < funcNode2.Childs.Count; i++)
{
if (funcNode2.Childs[i] == firstItem)
continue;
FuncNode funcChildNode = funcNode2.Childs[i] as FuncNode;
if (funcChildNode != null && funcChildNode.FunctionType == KnownFuncType.Pow && funcChildNode.Childs[1].LessThenZero())
{
if (!funcChildNode.Childs[1].IsValueOrCalculated || funcChildNode.Childs[1].DoubleValue != -1.0)
{
FuncNode second;
if (!funcChildNode.Childs[1].IsValueOrCalculated)
second = new FuncNode(KnownFuncType.Pow, funcChildNode.Childs[0], funcChildNode.Childs[1].Abs());
else
second = Math.Abs(funcChildNode.Childs[1].DoubleValue) != 0.5 ?
new FuncNode(KnownFuncType.Pow, funcChildNode.Childs[0], funcChildNode.Childs[1].Abs()) :
new FuncNode(KnownFuncType.Sqrt, funcChildNode.Childs[0]);
result = new FuncNode(KnownFuncType.Div, result, second);
}
else
result = new FuncNode(KnownFuncType.Div, result, funcChildNode.Childs[0]);
}
else
result = new FuncNode(KnownFuncType.Mult, result, funcNode2.Childs[i]);
}
return result;
}
private bool EmitAddFunc(FuncNode funcNode)
{
MathFuncNode firstItem = null;
firstItem = funcNode.Childs.FirstOrDefault(node =>
{
var func = node as FuncNode;
return !(func != null && FuncNodes[func].Count == 1 && func.LessThenZero());
});
if (firstItem == null)
firstItem = funcNode.Childs[0];
EmitNode(firstItem);
for (int i = 0; i < funcNode.Childs.Count; i++)
{
if (funcNode.Childs[i] == firstItem)
continue;
var func = funcNode.Childs[i] as FuncNode;
if (func != null && FuncNodes[func].Count == 1 && func.LessThenZero())
{
EmitNode(func.Childs[0], true);
IlInstructions.Add(new OpCodeArg(OpCodes.Sub));
}
else
{
EmitNode(funcNode.Childs[i]);
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
}
}
return true;
}
private FuncNode FoldCalculatedSummands(FuncNode sum)
{
var result = sum.Childs
.Where(child => child.Type == MathNodeType.Calculated || child.Type == MathNodeType.Value)
.Select(summand => summand.DoubleValue)
.Aggregate(0.0, (t, factor) => t += factor);
if (result != 0.0)
{
var newChilds = new List<MathFuncNode>() { new CalculatedNode(result) };
newChilds.AddRange(sum.Childs.Where(c => c.Type != MathNodeType.Calculated && c.Type != MathNodeType.Value));
return new FuncNode(KnownFuncType.Sub, newChilds);
}
else
return sum;
}
private bool EmitExpFunc(FuncNode funcNode, bool negExpAbs)
{
if ((funcNode.Childs[1].Type == MathNodeType.Value && ((ValueNode)funcNode.Childs[1]).Value.IsInteger) ||
(funcNode.Childs[1].Type == MathNodeType.Calculated && ((CalculatedNode)funcNode.Childs[1]).Value % 1 == 0))
{
int powerValue = (int)funcNode.Childs[1].DoubleValue;
int power = Math.Abs(powerValue);
if (negExpAbs)
powerValue = power;
if (powerValue < 0)
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0));
EmitNode(funcNode.Childs[0]);
if (power == 1)
{
}
else
if (power <= 3)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Stloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number));
for (int i = 1; i < power; i++)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
}
}
else if (power == 4)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Stloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
IlInstructions.Add(new OpCodeArg(OpCodes.Stloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
}
else
{
// result: funcNode.Number
// x: funcNode.Number + 1
//int result = x;
IlInstructions.Add(new OpCodeArg(OpCodes.Stloc, funcNode.Number + 1));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number + 1));
power--;
do
{
if ((power & 1) == 1)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number + 1));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
}
if (power <= 1)
break;
//x = x * x;
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number + 1));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldloc, funcNode.Number + 1));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
IlInstructions.Add(new OpCodeArg(OpCodes.Stloc, funcNode.Number + 1));
power = power >> 1;
}
while (power != 0);
}
if (powerValue < 0)
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
}
else
{
var child1 = funcNode.Childs[1];
if ((child1.Type == MathNodeType.Value && ((ValueNode)child1).Value.Abs() == new Rational<long>(1, 2, false)) ||
(child1.Type == MathNodeType.Calculated && Math.Abs(((CalculatedNode)child1).Value) == 0.5))
{
if (!negExpAbs && ((child1.Type == MathNodeType.Value && ((ValueNode)child1).Value < 0) ||
(child1.Type == MathNodeType.Calculated && ((CalculatedNode)child1).Value < 0)))
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0));
EmitNode(funcNode.Childs[0]);
IlInstructions.Add(new OpCodeArg(OpCodes.Call, MathFuncAssembly.TypesReferences[KnownFuncType.Sqrt]));
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
}
else
{
EmitNode(funcNode.Childs[0]);
IlInstructions.Add(new OpCodeArg(OpCodes.Call, MathFuncAssembly.TypesReferences[KnownFuncType.Sqrt]));
}
}
else
{
EmitNode(funcNode.Childs[0]);
if (negExpAbs)
EmitNode(funcNode.Childs[1].Abs());
else
EmitNode(funcNode.Childs[1]);
IlInstructions.Add(new OpCodeArg(OpCodes.Call, MathFuncAssembly.TypesReferences[(KnownFuncType)funcNode.FunctionType]));
}
}
return true;
}
protected string ToString(FuncNode parent,
KnownFuncType funcType,
IList<KnownFuncType> types)
{
var builder = new StringBuilder();
if (parent == null || parent.Name == null || parent.Childs.Count <= 1)
{
AppendMathFunctionNode(builder, funcType);
return builder.ToString();
}
var funcNodeParent = parent as FuncNode;
if (funcNodeParent != null && funcNodeParent.IsKnown)
if (types.Contains((KnownFuncType)funcNodeParent.FunctionType))
{
AppendMathFunctionNode(builder, funcType);
return builder.ToString();
}
builder.Append("(");
AppendMathFunctionNode(builder, funcType);
builder.Append(")");
return builder.ToString();
}
private MathFuncNode GetFuncDerivative(FuncNode funcNode)
{
MathFunc value;
if (funcNode.IsKnown)
{
if (funcNode.FunctionType == KnownFuncType.Add ||
funcNode.FunctionType == KnownFuncType.Sub)
{
var newChilds = new List<MathFuncNode>(funcNode.Childs.Count);
for (int i = 0; i < funcNode.Childs.Count; i++)
newChilds.Add(GetDerivative(funcNode.Childs[i]));
return new FuncNode(KnownFuncType.Add, newChilds);
}
else if (funcNode.FunctionType == KnownFuncType.Mult)
{
var newChilds = new List<MathFuncNode>(funcNode.Childs.Count);
for (int i = 0; i < funcNode.Childs.Count; i++)
{
var addNode = new List<MathFuncNode>();
for (int j = 0; j < funcNode.Childs.Count; j++)
{
if (i == j)
addNode.Add(GetDerivative(funcNode.Childs[i]));
else
addNode.Add((MathFuncNode)funcNode.Childs[j].Clone());
}
newChilds.Add(new FuncNode(KnownFuncType.Mult, addNode));
}
return new FuncNode(KnownFuncType.Add, newChilds);
}
else if (funcNode.FunctionType == KnownFuncType.Pow)
{
if (funcNode.Childs[1].IsValueOrCalculated)
{
var node1 = funcNode.Childs[1].Type == MathNodeType.Value ? (MathFuncNode)
new ValueNode((ValueNode)funcNode.Childs[1]) :
new CalculatedNode((CalculatedNode)funcNode.Childs[1]);
var node2 = funcNode.Childs[1].Type == MathNodeType.Value ? (MathFuncNode)
new ValueNode(((ValueNode)funcNode.Childs[1]).Value - 1) :
new CalculatedNode(((CalculatedNode)funcNode.Childs[1]).Value - 1);
return new FuncNode(KnownFuncType.Mult,
node1,
new FuncNode(KnownFuncType.Pow, (MathFuncNode)funcNode.Childs[0].Clone(), node2),
GetDerivative(funcNode.Childs[0]));
}
var constNode = funcNode.Childs[1] as ConstNode;
if (constNode != null)
return new FuncNode(KnownFuncType.Mult,
new ConstNode(constNode.Name),
new FuncNode(KnownFuncType.Pow,
(MathFuncNode)funcNode.Childs[0].Clone(),
new FuncNode(KnownFuncType.Add, new ConstNode(constNode.Name), new ValueNode(-1))
),
GetDerivative(funcNode.Childs[0])
);
}
else if (funcNode.FunctionType == KnownFuncType.Diff)
{
if (funcNode.Childs[0].Type == MathNodeType.Function)
{
if (((FuncNode)funcNode.Childs[0]).IsKnown)
{
var der = GetDerivative(funcNode.Childs[0]);
if (der.Childs[0].Type == MathNodeType.Function && ((FuncNode)der).FunctionType == KnownFuncType.Diff)
return new FuncNode(KnownFuncType.Diff, der, Variable);
else
return GetDerivative(der);
}
else
return new FuncNode(KnownFuncType.Diff, GetDerivative(funcNode.Childs[0]), Variable);
}
else
return new ValueNode(0);
}
else if (funcNode.FunctionType == KnownFuncType.Neg)
{
return new FuncNode(KnownFuncType.Neg, GetDerivative(funcNode.Childs[0]));
}
}
if (Helper.Derivatives.TryGetValue(funcNode.Name, out value))
{
var sub = value;
var subNode = MakeSubstitution(sub.LeftNode.Childs[0], sub.RightNode, funcNode);
GetDerivatives(subNode);
return subNode;
}
else
{
return new FuncNode(KnownFuncType.Mult,
new FuncNode(KnownFuncType.Diff, (MathFuncNode)funcNode.Clone(), Variable),
GetDerivative(funcNode.Childs[0]));
}
}
public override string ToString(FuncNode parent)
{
if (IsKnown)
{
var funcType = (KnownFuncType)FunctionType;
switch ((KnownFuncType)FunctionType)
{
case KnownFuncType.Add:
case KnownFuncType.Sub:
return ToString(parent, funcType, KnownFunc.AddKnownFuncs);
case KnownFuncType.Mult:
case KnownFuncType.Div:
return ToString(parent, funcType, KnownFunc.MultKnownFuncs);
case KnownFuncType.Exp:
return ToString(parent, funcType, KnownFunc.ExpKnownFuncs);
case KnownFuncType.Neg:
if (Childs[0].Type == MathNodeType.Function)
{
var func = (FuncNode)Childs[0];
if (KnownFunc.NegKnownFuncs.Contains((KnownFuncType)func.FunctionType))
return "-(" + Childs[0].ToString(this) + ")";
else
return "-" + Childs[0].ToString(this);
}
else
return "-" + Childs[0].ToString(this);
case KnownFuncType.Diff:
return Childs[0].Type == MathNodeType.Function && ((FuncNode)Childs[0]).FunctionType != KnownFuncType.Diff ?
Childs[0].ToString(this) + "'" : "(" +
Childs[0].ToString(this) + ")'";
case KnownFuncType.Abs:
return string.Format("|{0}|", Childs[0].ToString(this));
}
}
var builder = new StringBuilder((FunctionType == KnownFuncType.Sqrt ? "√" : Name) + "(");
foreach (var arg in Childs)
builder.AppendFormat("{0}, ", arg.ToString(this));
if (Childs.Count != 0)
builder.Remove(builder.Length - 2, 2);
builder.Append(')');
return builder.ToString();
}
private bool EmitDiffFunc(FuncNode funcNode)
{
var diffFunc = funcNode.Childs[0];
var arg = diffFunc.Childs[0];
bool isUnknownFunc = diffFunc.Type == MathNodeType.Function && !((FuncNode)diffFunc).IsKnown;
var diff = FuncNodes[(FuncNode)diffFunc];
// f(x + dx)
if (isUnknownFunc)
IlInstructions.Add(new OpCodeArg(OpCodes.Ldarg, diffFunc.ArgNumber));
EmitNode(arg);
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, DerivativeDelta));
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
if (isUnknownFunc)
IlInstructions.Add(new OpCodeArg(OpCodes.Callvirt, MathFuncAssembly.InvokeFuncRef));
else
EmitNode(diffFunc);
// f(x)
EmitNode(diffFunc);
IlInstructions.Add(new OpCodeArg(OpCodes.Sub));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0 / DerivativeDelta));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
return true;
}
public override string ToString(FuncNode parent)
{
if (Value.Denominator == 1 || !parent.IsKnown)
return Name;
if (parent.FunctionType == KnownFuncType.Mult || parent.FunctionType == KnownFuncType.Div ||
parent.FunctionType == KnownFuncType.Exp || parent.FunctionType == KnownFuncType.Neg)
{
return '(' + Name + ')';
}
else
return Name;
}
private bool EmitKnownFunc(FuncNode funcNode)
{
MethodReference value;
if (funcNode.FunctionType != null && MathFuncAssembly.TypesReferences.TryGetValue((KnownFuncType)funcNode.FunctionType, out value))
{
foreach (var child in funcNode.Childs)
EmitNode(child);
IlInstructions.Add(new OpCodeArg(OpCodes.Call, value));
return true;
}
else if (funcNode.FunctionType == KnownFuncType.Cot)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0));
EmitNode(funcNode.Childs[0]);
IlInstructions.Add(new OpCodeArg(OpCodes.Call, KnownFunc.TypesMethods[KnownFuncType.Tan]));
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
return true;
}
else if (funcNode.FunctionType == KnownFuncType.Arccot)
{
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0));
EmitNode(funcNode.Childs[0]);
IlInstructions.Add(new OpCodeArg(OpCodes.Div));
IlInstructions.Add(new OpCodeArg(OpCodes.Call, KnownFunc.TypesMethods[KnownFuncType.Arctan]));
return true;
}
else if (funcNode.FunctionType == KnownFuncType.Arcsinh)
{
EmitNode(funcNode.Childs[0]);
EmitNode(funcNode.Childs[0]);
EmitNode(funcNode.Childs[0]);
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0));
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
IlInstructions.Add(new OpCodeArg(OpCodes.Call, KnownFunc.TypesMethods[KnownFuncType.Sqrt]));
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
IlInstructions.Add(new OpCodeArg(OpCodes.Call, KnownFunc.TypesMethods[KnownFuncType.Log]));
return true;
}
else if (funcNode.FunctionType == KnownFuncType.Arcosh)
{
EmitNode(funcNode.Childs[0]);
EmitNode(funcNode.Childs[0]);
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0));
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
IlInstructions.Add(new OpCodeArg(OpCodes.Call, KnownFunc.TypesMethods[KnownFuncType.Sqrt]));
EmitNode(funcNode.Childs[0]);
IlInstructions.Add(new OpCodeArg(OpCodes.Ldc_R8, 1.0));
IlInstructions.Add(new OpCodeArg(OpCodes.Sub));
IlInstructions.Add(new OpCodeArg(OpCodes.Call, KnownFunc.TypesMethods[KnownFuncType.Sqrt]));
IlInstructions.Add(new OpCodeArg(OpCodes.Mul));
IlInstructions.Add(new OpCodeArg(OpCodes.Add));
IlInstructions.Add(new OpCodeArg(OpCodes.Call, KnownFunc.TypesMethods[KnownFuncType.Log]));
return true;
}
else
return false;
}
private bool EmitFunc(FuncNode funcNode, bool negExpAbs = false)
{
switch (funcNode.FunctionType)
{
case KnownFuncType.Add:
return EmitAddFunc(funcNode);
case KnownFuncType.Sub:
return EmitSubFunc(funcNode);
case KnownFuncType.Mult:
return EmitMultFunc(funcNode);
case KnownFuncType.Div:
return EmitDivFunc(funcNode);
case KnownFuncType.Neg:
return EmitNegFunc(funcNode, negExpAbs);
case KnownFuncType.Pow:
return EmitExpFunc(funcNode, negExpAbs);
case KnownFuncType.Diff:
return EmitDiffFunc(funcNode);
}
if (!EmitKnownFunc(funcNode)) // Unknown function (from input args).
EmitUnknownFunc(funcNode);
return true;
}
private void ReduceSummands(FuncNode funcNode)
{
int i = 0;
while (i < funcNode.Childs.Count)
{
int j = i + 1;
while (j < funcNode.Childs.Count)
{
var newNode = ReduceAddition(funcNode.Childs[i], funcNode.Childs[j]);
if (newNode != null)
{
funcNode.Childs[i] = newNode;
funcNode.Childs.RemoveAt(j);
}
else
j++;
}
i++;
}
}
private void BuildMultichildTree(FuncNode beginNode)
{
var newChilds = new List<MathFuncNode>();
BuildMultichildTree(beginNode, beginNode, newChilds, false);
beginNode.Childs = newChilds;
}
private bool EmitNegFunc(FuncNode funcNode, bool negExpAbs)
{
EmitNode(funcNode.Childs[0]);
if (!negExpAbs)
IlInstructions.Add(new OpCodeArg(OpCodes.Neg));
return true;
}
private void BuildMultichildTree(FuncNode beginNode, FuncNode funcNode, List<MathFuncNode> newChilds, bool neg)
{
foreach (var child in funcNode.Childs)
{
var childFuncNode = child as FuncNode;
if (childFuncNode != null)
{
if (childFuncNode.FunctionType == beginNode.FunctionType)
{
BuildMultichildTree(beginNode, childFuncNode, newChilds, neg);
continue;
}
else if (childFuncNode.FunctionType == KnownFuncType.Neg)
{
BuildMultichildTree(beginNode, childFuncNode, newChilds, !neg);
continue;
}
}
if (neg && (beginNode.FunctionType == KnownFuncType.Add ||
(beginNode.FunctionType == KnownFuncType.Mult && child == funcNode.Childs.First())))
{
if (child.Type == MathNodeType.Value)
newChilds.Add(new ValueNode(-((ValueNode)child).Value));
else
newChilds.Add(new FuncNode(KnownFuncType.Neg, child));
}
else
newChilds.Add(child);
}
}
private MathFuncNode ReduceAddition(MathFuncNode node1, MathFuncNode node2)
{
var node1neg = node1.Type == MathNodeType.Function && (node1 as FuncNode).FunctionType == KnownFuncType.Neg;
var node2neg = node2.Type == MathNodeType.Function && (node2 as FuncNode).FunctionType == KnownFuncType.Neg;
var node11 = node1neg ? node1.Childs[0] : node1;
var node21 = node2neg ? node2.Childs[0] : node2;
MathFuncNode valueNode1 = null;
if (node11.Type == MathNodeType.Function &&
(node11 as FuncNode).FunctionType == KnownFuncType.Mult)
valueNode1 = node11.Childs.Where(child => child.IsValueOrCalculated).FirstOrDefault();
if (valueNode1 == null)
valueNode1 = node11.IsValueOrCalculated ? node11 : new ValueNode(new Rational<long>(1, 1));
var value1 = ((ValueNode)valueNode1).Value;
if (node1neg)
value1 *= -1;
MathFuncNode valueNode2 = null;
if (node21.Type == MathNodeType.Function &&
(node21 as FuncNode).FunctionType == KnownFuncType.Mult)
valueNode2 = node21.Childs.Where(child => child.IsValueOrCalculated).FirstOrDefault();
if (valueNode2 == null)
valueNode2 = node21.IsValueOrCalculated ? node21 : new ValueNode(new Rational<long>(1, 1));
var value2 = ((ValueNode)valueNode2).Value;
if (node2neg)
value2 *= -1;
var notValueNodes1 = node11.Type == MathNodeType.Function &&
(node11 as FuncNode).FunctionType == KnownFuncType.Mult ?
node11.Childs.Where(child => !child.IsValueOrCalculated).ToList() :
node11.IsValueOrCalculated ?
new List<MathFuncNode>() { } :
new List<MathFuncNode>() { node11 };
var notValueNodes2 = node21.Type == MathNodeType.Function &&
(node21 as FuncNode).FunctionType == KnownFuncType.Mult ?
node21.Childs.Where(child => !child.IsValueOrCalculated).ToList() :
node21.IsValueOrCalculated ?
new List<MathFuncNode>() { } :
new List<MathFuncNode>() { node21 };
var mult1 = new FuncNode(KnownFuncType.Mult, notValueNodes1.ToList());
var mult2 = new FuncNode(KnownFuncType.Mult, notValueNodes2.ToList());
mult1.Sort();
mult2.Sort();
if (mult1.Equals(mult2))
{
var resultNodes = new List<MathFuncNode>();
resultNodes.Add(new ValueNode(value1 + value2));
resultNodes.AddRange(notValueNodes1);
return Simplify(new FuncNode(KnownFuncType.Mult, resultNodes));
}
else
return null;
}
private MathFuncNode MakeSubstitution(MathFuncNode left, MathFuncNode right, FuncNode currentFunc)
{
LeftNode = left;
RightNode = right;
_currentFunc = currentFunc;
return MakeSubstitution(right);
}
private FuncNode MultCalculatedFactors(FuncNode mult)
{
var result = mult.Childs
.Where(child => child.Type == MathNodeType.Calculated || child.Type == MathNodeType.Value)
.Select(factor => factor.DoubleValue)
.Aggregate(1.0, (t, factor) => t *= factor);
if (result != 1.0)
{
var newChilds = new List<MathFuncNode>() { new CalculatedNode(result) };
newChilds.AddRange(mult.Childs.Where(c => c.Type != MathNodeType.Calculated && c.Type != MathNodeType.Value));
return new FuncNode(KnownFuncType.Mult, newChilds);
}
else
return mult;
}
