1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | *
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5 | * This file is part of HeuristicLab.
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6 | *
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7 | * HeuristicLab is free software: you can redistribute it and/or modify
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8 | * it under the terms of the GNU General Public License as published by
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9 | * the Free Software Foundation, either version 3 of the License, or
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10 | * (at your option) any later version.
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11 | *
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12 | * HeuristicLab is distributed in the hope that it will be useful,
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 | * GNU General Public License for more details.
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16 | *
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17 | * You should have received a copy of the GNU General Public License
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18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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19 | */
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20 | #endregion
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21 |
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22 | using System;
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23 | using System.Collections.Generic;
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24 | using System.Linq;
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25 | using System.Reflection;
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26 | using System.Reflection.Emit;
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27 | using HeuristicLab.Common;
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28 | using HeuristicLab.Core;
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29 | using HeuristicLab.Data;
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30 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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31 | using HeuristicLab.Parameters;
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32 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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33 |
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34 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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35 | [StorableClass]
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36 | [Item("SymbolicDataAnalysisExpressionTreeILEmittingInterpreter", "Interpreter for symbolic expression trees.")]
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37 | public sealed class SymbolicDataAnalysisExpressionTreeILEmittingInterpreter : ParameterizedNamedItem, ISymbolicDataAnalysisExpressionTreeInterpreter {
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38 | private static readonly Type thisType = typeof(SymbolicDataAnalysisExpressionTreeILEmittingInterpreter);
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39 | internal delegate double CompiledFunction(int sampleIndex, IList<double>[] columns);
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40 |
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41 | #region method infos
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42 | private static MethodInfo listGetValue = typeof(IList<double>).GetProperty("Item", new Type[] { typeof(int) }).GetGetMethod();
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43 |
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44 | private static MethodInfo cos = typeof(Math).GetMethod("Cos", new Type[] { typeof(double) });
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45 | private static MethodInfo sin = typeof(Math).GetMethod("Sin", new Type[] { typeof(double) });
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46 | private static MethodInfo tan = typeof(Math).GetMethod("Tan", new Type[] { typeof(double) });
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47 | private static MethodInfo exp = typeof(Math).GetMethod("Exp", new Type[] { typeof(double) });
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48 | private static MethodInfo log = typeof(Math).GetMethod("Log", new Type[] { typeof(double) });
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49 | private static MethodInfo power = typeof(Math).GetMethod("Pow", new Type[] { typeof(double), typeof(double) });
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50 | private static MethodInfo round = typeof(Math).GetMethod("Round", new Type[] { typeof(double) });
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51 | private static MethodInfo sqrt = typeof(Math).GetMethod("Sqrt", new Type[] { typeof(double) });
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52 | private static MethodInfo abs = typeof(Math).GetMethod("Abs", new Type[] { typeof(double) });
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53 |
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54 | private static MethodInfo airyA = thisType.GetMethod("AiryA", new Type[] { typeof(double) });
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55 | private static MethodInfo airyB = thisType.GetMethod("AiryB", new Type[] { typeof(double) });
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56 | private static MethodInfo gamma = thisType.GetMethod("Gamma", new Type[] { typeof(double) });
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57 | private static MethodInfo psi = thisType.GetMethod("Psi", new Type[] { typeof(double) });
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58 | private static MethodInfo dawson = thisType.GetMethod("Dawson", new Type[] { typeof(double) });
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59 | private static MethodInfo expIntegralEi = thisType.GetMethod("ExpIntegralEi", new Type[] { typeof(double) });
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60 | private static MethodInfo sinIntegral = thisType.GetMethod("SinIntegral", new Type[] { typeof(double) });
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61 | private static MethodInfo cosIntegral = thisType.GetMethod("CosIntegral", new Type[] { typeof(double) });
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62 | private static MethodInfo hypSinIntegral = thisType.GetMethod("HypSinIntegral", new Type[] { typeof(double) });
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63 | private static MethodInfo hypCosIntegral = thisType.GetMethod("HypCosIntegral", new Type[] { typeof(double) });
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64 | private static MethodInfo fresnelCosIntegral = thisType.GetMethod("FresnelCosIntegral", new Type[] { typeof(double) });
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65 | private static MethodInfo fresnelSinIntegral = thisType.GetMethod("FresnelSinIntegral", new Type[] { typeof(double) });
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66 | private static MethodInfo norm = thisType.GetMethod("Norm", new Type[] { typeof(double) });
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67 | private static MethodInfo erf = thisType.GetMethod("Erf", new Type[] { typeof(double) });
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68 | private static MethodInfo bessel = thisType.GetMethod("Bessel", new Type[] { typeof(double) });
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69 | private static MethodInfo string_eq = typeof(string).GetMethod("Equals", new Type[] { typeof(string) });
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70 | #endregion
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71 |
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72 | private const string CheckExpressionsWithIntervalArithmeticParameterName = "CheckExpressionsWithIntervalArithmetic";
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73 | private const string CheckExpressionsWithIntervalArithmeticParameterDescription = "Switch that determines if the interpreter checks the validity of expressions with interval arithmetic before evaluating the expression.";
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74 | private const string EvaluatedSolutionsParameterName = "EvaluatedSolutions";
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75 |
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76 | public override bool CanChangeName {
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77 | get { return false; }
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78 | }
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79 |
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80 | public override bool CanChangeDescription {
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81 | get { return false; }
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82 | }
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83 |
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84 | #region parameter properties
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85 | public IFixedValueParameter<BoolValue> CheckExpressionsWithIntervalArithmeticParameter {
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86 | get { return (IFixedValueParameter<BoolValue>)Parameters[CheckExpressionsWithIntervalArithmeticParameterName]; }
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87 | }
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88 |
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89 | public IFixedValueParameter<IntValue> EvaluatedSolutionsParameter {
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90 | get { return (IFixedValueParameter<IntValue>)Parameters[EvaluatedSolutionsParameterName]; }
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91 | }
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92 | #endregion
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93 |
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94 | #region properties
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95 | public bool CheckExpressionsWithIntervalArithmetic {
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96 | get { return CheckExpressionsWithIntervalArithmeticParameter.Value.Value; }
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97 | set { CheckExpressionsWithIntervalArithmeticParameter.Value.Value = value; }
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98 | }
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99 | public int EvaluatedSolutions {
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100 | get { return EvaluatedSolutionsParameter.Value.Value; }
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101 | set { EvaluatedSolutionsParameter.Value.Value = value; }
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102 | }
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103 | #endregion
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104 |
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105 | [StorableConstructor]
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106 | private SymbolicDataAnalysisExpressionTreeILEmittingInterpreter(bool deserializing) : base(deserializing) { }
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107 |
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108 | private SymbolicDataAnalysisExpressionTreeILEmittingInterpreter(SymbolicDataAnalysisExpressionTreeILEmittingInterpreter original, Cloner cloner) : base(original, cloner) { }
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109 | public override IDeepCloneable Clone(Cloner cloner) {
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110 | return new SymbolicDataAnalysisExpressionTreeILEmittingInterpreter(this, cloner);
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111 | }
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112 |
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113 | public SymbolicDataAnalysisExpressionTreeILEmittingInterpreter()
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114 | : base("SymbolicDataAnalysisExpressionTreeILEmittingInterpreter", "Interpreter for symbolic expression trees.") {
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115 | Parameters.Add(new FixedValueParameter<BoolValue>(CheckExpressionsWithIntervalArithmeticParameterName,
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116 | "Switch that determines if the interpreter checks the validity of expressions with interval arithmetic before evaluating the expression.", new BoolValue(false)));
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117 | Parameters.Add(new FixedValueParameter<IntValue>(EvaluatedSolutionsParameterName, "A counter for the total number of solutions the interpreter has evaluated", new IntValue(0)));
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118 | }
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119 |
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120 | public SymbolicDataAnalysisExpressionTreeILEmittingInterpreter(string name, string description)
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121 | : base(name, description) {
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122 | Parameters.Add(new FixedValueParameter<BoolValue>(CheckExpressionsWithIntervalArithmeticParameterName,
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123 | "Switch that determines if the interpreter checks the validity of expressions with interval arithmetic before evaluating the expression.", new BoolValue(false)));
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124 | Parameters.Add(new FixedValueParameter<IntValue>(EvaluatedSolutionsParameterName, "A counter for the total number of solutions the interpreter has evaluated", new IntValue(0)));
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125 | }
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126 |
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127 | [StorableHook(HookType.AfterDeserialization)]
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128 | private void AfterDeserialization() {
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129 | var evaluatedSolutions = new IntValue(0);
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130 | var checkExpressionsWithIntervalArithmetic = new BoolValue(false);
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131 | if (Parameters.ContainsKey(EvaluatedSolutionsParameterName)) {
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132 | var evaluatedSolutionsParameter = (IValueParameter<IntValue>)Parameters[EvaluatedSolutionsParameterName];
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133 | evaluatedSolutions = evaluatedSolutionsParameter.Value;
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134 | Parameters.Remove(EvaluatedSolutionsParameterName);
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135 | }
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136 | Parameters.Add(new FixedValueParameter<IntValue>(EvaluatedSolutionsParameterName, "A counter for the total number of solutions the interpreter has evaluated", evaluatedSolutions));
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137 | if (Parameters.ContainsKey(CheckExpressionsWithIntervalArithmeticParameterName)) {
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138 | var checkExpressionsWithIntervalArithmeticParameter = (IValueParameter<BoolValue>)Parameters[CheckExpressionsWithIntervalArithmeticParameterName];
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139 | Parameters.Remove(CheckExpressionsWithIntervalArithmeticParameterName);
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140 | checkExpressionsWithIntervalArithmetic = checkExpressionsWithIntervalArithmeticParameter.Value;
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141 | }
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142 | Parameters.Add(new FixedValueParameter<BoolValue>(CheckExpressionsWithIntervalArithmeticParameterName, CheckExpressionsWithIntervalArithmeticParameterDescription, checkExpressionsWithIntervalArithmetic));
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143 | }
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144 |
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145 | #region IStatefulItem
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146 | public void InitializeState() {
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147 | EvaluatedSolutions = 0;
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148 | }
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149 |
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150 | public void ClearState() {
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151 | }
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152 | #endregion
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153 |
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154 | private readonly object syncRoot = new object();
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155 | public IEnumerable<double> GetSymbolicExpressionTreeValues(ISymbolicExpressionTree tree, IDataset dataset, IEnumerable<int> rows) {
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156 | if (CheckExpressionsWithIntervalArithmetic)
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157 | throw new NotSupportedException("Interval arithmetic is not yet supported in the symbolic data analysis interpreter.");
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158 |
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159 | lock (syncRoot) {
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160 | EvaluatedSolutions++; // increment the evaluated solutions counter
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161 | }
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162 | var state = PrepareInterpreterState(tree, dataset);
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163 |
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164 | Type[] methodArgs = { typeof(int), typeof(IList<double>[]) };
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165 | DynamicMethod testFun = new DynamicMethod("TestFun", typeof(double), methodArgs, typeof(SymbolicDataAnalysisExpressionTreeILEmittingInterpreter).Module);
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166 |
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167 | ILGenerator il = testFun.GetILGenerator();
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168 | CompileInstructions(il, state, dataset);
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169 | il.Emit(System.Reflection.Emit.OpCodes.Conv_R8);
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170 | il.Emit(System.Reflection.Emit.OpCodes.Ret);
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171 | var function = (CompiledFunction)testFun.CreateDelegate(typeof(CompiledFunction));
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172 |
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173 | IList<double>[] columns = dataset.DoubleVariables.Select(v => dataset.GetReadOnlyDoubleValues(v)).ToArray();
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174 |
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175 | foreach (var row in rows) {
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176 | yield return function(row, columns);
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177 | }
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178 | }
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179 |
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180 | private InterpreterState PrepareInterpreterState(ISymbolicExpressionTree tree, IDataset dataset) {
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181 | Instruction[] code = SymbolicExpressionTreeCompiler.Compile(tree, OpCodes.MapSymbolToOpCode);
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182 | Dictionary<string, int> doubleVariableNames = dataset.DoubleVariables.Select((x, i) => new { x, i }).ToDictionary(e => e.x, e => e.i);
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183 | int necessaryArgStackSize = 0;
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184 | foreach (Instruction instr in code) {
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185 | if (instr.opCode == OpCodes.Variable) {
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186 | var variableTreeNode = (VariableTreeNode)instr.dynamicNode;
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187 | instr.data = doubleVariableNames[variableTreeNode.VariableName];
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188 | } else if (instr.opCode == OpCodes.LagVariable) {
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189 | var laggedVariableTreeNode = (LaggedVariableTreeNode)instr.dynamicNode;
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190 | instr.data = doubleVariableNames[laggedVariableTreeNode.VariableName];
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191 | } else if (instr.opCode == OpCodes.VariableCondition) {
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192 | var variableConditionTreeNode = (VariableConditionTreeNode)instr.dynamicNode;
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193 | instr.data = doubleVariableNames[variableConditionTreeNode.VariableName];
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194 | } else if (instr.opCode == OpCodes.Call) {
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195 | necessaryArgStackSize += instr.nArguments + 1;
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196 | }
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197 | }
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198 | return new InterpreterState(code, necessaryArgStackSize);
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199 | }
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200 |
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201 | private void CompileInstructions(ILGenerator il, InterpreterState state, IDataset ds) {
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202 | Instruction currentInstr = state.NextInstruction();
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203 | int nArgs = currentInstr.nArguments;
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204 |
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205 | switch (currentInstr.opCode) {
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206 | case OpCodes.Add: {
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207 | if (nArgs > 0) {
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208 | CompileInstructions(il, state, ds);
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209 | }
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210 | for (int i = 1; i < nArgs; i++) {
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211 | CompileInstructions(il, state, ds);
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212 | il.Emit(System.Reflection.Emit.OpCodes.Add);
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213 | }
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214 | return;
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215 | }
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216 | case OpCodes.Sub: {
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217 | if (nArgs == 1) {
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218 | CompileInstructions(il, state, ds);
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219 | il.Emit(System.Reflection.Emit.OpCodes.Neg);
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220 | return;
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221 | }
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222 | if (nArgs > 0) {
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223 | CompileInstructions(il, state, ds);
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224 | }
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225 | for (int i = 1; i < nArgs; i++) {
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226 | CompileInstructions(il, state, ds);
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227 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
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228 | }
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229 | return;
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230 | }
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231 | case OpCodes.Mul: {
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232 | if (nArgs > 0) {
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233 | CompileInstructions(il, state, ds);
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234 | }
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235 | for (int i = 1; i < nArgs; i++) {
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236 | CompileInstructions(il, state, ds);
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237 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
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238 | }
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239 | return;
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240 | }
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241 | case OpCodes.Div: {
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242 | if (nArgs == 1) {
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243 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0);
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244 | CompileInstructions(il, state, ds);
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245 | il.Emit(System.Reflection.Emit.OpCodes.Div);
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246 | return;
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247 | }
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248 | if (nArgs > 0) {
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249 | CompileInstructions(il, state, ds);
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250 | }
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251 | for (int i = 1; i < nArgs; i++) {
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252 | CompileInstructions(il, state, ds);
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253 | il.Emit(System.Reflection.Emit.OpCodes.Div);
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254 | }
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255 | return;
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256 | }
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257 | case OpCodes.Average: {
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258 | CompileInstructions(il, state, ds);
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259 | for (int i = 1; i < nArgs; i++) {
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260 | CompileInstructions(il, state, ds);
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261 | il.Emit(System.Reflection.Emit.OpCodes.Add);
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262 | }
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263 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, (double)nArgs);
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264 | il.Emit(System.Reflection.Emit.OpCodes.Div);
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265 | return;
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266 | }
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267 | case OpCodes.Absolute: {
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268 | CompileInstructions(il, state, ds);
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269 | il.Emit(System.Reflection.Emit.OpCodes.Call, abs);
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270 | return;
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271 | }
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272 | case OpCodes.Cos: {
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273 | CompileInstructions(il, state, ds);
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274 | il.Emit(System.Reflection.Emit.OpCodes.Call, cos);
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275 | return;
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276 | }
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277 | case OpCodes.Sin: {
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278 | CompileInstructions(il, state, ds);
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279 | il.Emit(System.Reflection.Emit.OpCodes.Call, sin);
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280 | return;
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281 | }
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282 | case OpCodes.Tan: {
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283 | CompileInstructions(il, state, ds);
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284 | il.Emit(System.Reflection.Emit.OpCodes.Call, tan);
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285 | return;
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286 | }
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287 | case OpCodes.Power: {
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288 | CompileInstructions(il, state, ds);
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289 | CompileInstructions(il, state, ds);
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290 | il.Emit(System.Reflection.Emit.OpCodes.Call, round);
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291 | il.Emit(System.Reflection.Emit.OpCodes.Call, power);
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292 | return;
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293 | }
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294 | case OpCodes.Root: {
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295 | CompileInstructions(il, state, ds);
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296 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // 1 / round(...)
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297 | CompileInstructions(il, state, ds);
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298 | il.Emit(System.Reflection.Emit.OpCodes.Call, round);
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299 | il.Emit(System.Reflection.Emit.OpCodes.Div);
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300 | il.Emit(System.Reflection.Emit.OpCodes.Call, power);
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301 | return;
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302 | }
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303 | case OpCodes.Exp: {
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304 | CompileInstructions(il, state, ds);
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305 | il.Emit(System.Reflection.Emit.OpCodes.Call, exp);
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306 | return;
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307 | }
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308 | case OpCodes.Log: {
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309 | CompileInstructions(il, state, ds);
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310 | il.Emit(System.Reflection.Emit.OpCodes.Call, log);
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311 | return;
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312 | }
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313 | case OpCodes.Square: {
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314 | CompileInstructions(il, state, ds);
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315 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 2.0);
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316 | il.Emit(System.Reflection.Emit.OpCodes.Call, power);
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317 | return;
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318 | }
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319 | case OpCodes.Cube: {
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320 | CompileInstructions(il, state, ds);
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321 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 3.0);
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322 | il.Emit(System.Reflection.Emit.OpCodes.Call, power);
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323 | return;
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324 | }
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325 | case OpCodes.SquareRoot: {
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326 | CompileInstructions(il, state, ds);
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327 | il.Emit(System.Reflection.Emit.OpCodes.Call, sqrt);
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328 | return;
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329 | }
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330 | case OpCodes.CubeRoot: {
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331 | CompileInstructions(il, state, ds);
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332 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0 / 3.0);
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333 | il.Emit(System.Reflection.Emit.OpCodes.Call, power);
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334 | return;
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335 | }
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336 | case OpCodes.AiryA: {
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337 | CompileInstructions(il, state, ds);
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338 | il.Emit(System.Reflection.Emit.OpCodes.Call, airyA);
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339 | return;
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340 | }
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341 | case OpCodes.AiryB: {
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342 | CompileInstructions(il, state, ds);
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343 | il.Emit(System.Reflection.Emit.OpCodes.Call, airyB);
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344 | return;
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345 | }
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346 | case OpCodes.Bessel: {
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347 | CompileInstructions(il, state, ds);
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348 | il.Emit(System.Reflection.Emit.OpCodes.Call, bessel);
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349 | return;
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350 | }
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351 | case OpCodes.CosineIntegral: {
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352 | CompileInstructions(il, state, ds);
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353 | il.Emit(System.Reflection.Emit.OpCodes.Call, cosIntegral);
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354 | return;
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355 | }
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356 | case OpCodes.Dawson: {
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357 | CompileInstructions(il, state, ds);
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358 | il.Emit(System.Reflection.Emit.OpCodes.Call, dawson);
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359 | return;
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360 | }
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361 | case OpCodes.Erf: {
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362 | CompileInstructions(il, state, ds);
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363 | il.Emit(System.Reflection.Emit.OpCodes.Call, erf);
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364 | return;
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365 | }
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366 | case OpCodes.ExponentialIntegralEi: {
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367 | CompileInstructions(il, state, ds);
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368 | il.Emit(System.Reflection.Emit.OpCodes.Call, expIntegralEi);
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369 | return;
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370 | }
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371 | case OpCodes.FresnelCosineIntegral: {
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372 | CompileInstructions(il, state, ds);
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373 | il.Emit(System.Reflection.Emit.OpCodes.Call, fresnelCosIntegral);
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374 | return;
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375 | }
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376 | case OpCodes.FresnelSineIntegral: {
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377 | CompileInstructions(il, state, ds);
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378 | il.Emit(System.Reflection.Emit.OpCodes.Call, fresnelSinIntegral);
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379 | return;
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380 | }
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381 | case OpCodes.Gamma: {
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382 | CompileInstructions(il, state, ds);
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383 | il.Emit(System.Reflection.Emit.OpCodes.Call, gamma);
|
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384 | return;
|
---|
385 | }
|
---|
386 | case OpCodes.HyperbolicCosineIntegral: {
|
---|
387 | CompileInstructions(il, state, ds);
|
---|
388 | il.Emit(System.Reflection.Emit.OpCodes.Call, hypCosIntegral);
|
---|
389 | return;
|
---|
390 | }
|
---|
391 | case OpCodes.HyperbolicSineIntegral: {
|
---|
392 | CompileInstructions(il, state, ds);
|
---|
393 | il.Emit(System.Reflection.Emit.OpCodes.Call, hypSinIntegral);
|
---|
394 | return;
|
---|
395 | }
|
---|
396 | case OpCodes.Norm: {
|
---|
397 | CompileInstructions(il, state, ds);
|
---|
398 | il.Emit(System.Reflection.Emit.OpCodes.Call, norm);
|
---|
399 | return;
|
---|
400 | }
|
---|
401 | case OpCodes.Psi: {
|
---|
402 | CompileInstructions(il, state, ds);
|
---|
403 | il.Emit(System.Reflection.Emit.OpCodes.Call, psi);
|
---|
404 | return;
|
---|
405 | }
|
---|
406 | case OpCodes.SineIntegral: {
|
---|
407 | CompileInstructions(il, state, ds);
|
---|
408 | il.Emit(System.Reflection.Emit.OpCodes.Call, sinIntegral);
|
---|
409 | return;
|
---|
410 | }
|
---|
411 | case OpCodes.AnalyticalQuotient: {
|
---|
412 | CompileInstructions(il, state, ds); // x1
|
---|
413 | CompileInstructions(il, state, ds); // x2
|
---|
414 |
|
---|
415 | il.Emit(System.Reflection.Emit.OpCodes.Dup);
|
---|
416 | il.Emit(System.Reflection.Emit.OpCodes.Mul); // x2*x2
|
---|
417 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0);
|
---|
418 | il.Emit(System.Reflection.Emit.OpCodes.Mul); // 1+x2*x2
|
---|
419 | il.Emit(System.Reflection.Emit.OpCodes.Call, sqrt);
|
---|
420 | il.Emit(System.Reflection.Emit.OpCodes.Div);
|
---|
421 | return;
|
---|
422 | }
|
---|
423 | case OpCodes.IfThenElse: {
|
---|
424 | Label end = il.DefineLabel();
|
---|
425 | Label c1 = il.DefineLabel();
|
---|
426 | CompileInstructions(il, state, ds);
|
---|
427 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0); // > 0
|
---|
428 | il.Emit(System.Reflection.Emit.OpCodes.Cgt);
|
---|
429 | il.Emit(System.Reflection.Emit.OpCodes.Brfalse, c1);
|
---|
430 | CompileInstructions(il, state, ds);
|
---|
431 | il.Emit(System.Reflection.Emit.OpCodes.Br, end);
|
---|
432 | il.MarkLabel(c1);
|
---|
433 | CompileInstructions(il, state, ds);
|
---|
434 | il.MarkLabel(end);
|
---|
435 | return;
|
---|
436 | }
|
---|
437 | case OpCodes.AND: {
|
---|
438 | Label falseBranch = il.DefineLabel();
|
---|
439 | Label end = il.DefineLabel();
|
---|
440 | CompileInstructions(il, state, ds);
|
---|
441 | for (int i = 1; i < nArgs; i++) {
|
---|
442 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0); // > 0
|
---|
443 | il.Emit(System.Reflection.Emit.OpCodes.Cgt);
|
---|
444 | il.Emit(System.Reflection.Emit.OpCodes.Brfalse, falseBranch);
|
---|
445 | CompileInstructions(il, state, ds);
|
---|
446 | }
|
---|
447 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0); // > 0
|
---|
448 | il.Emit(System.Reflection.Emit.OpCodes.Cgt);
|
---|
449 | il.Emit(System.Reflection.Emit.OpCodes.Brfalse, falseBranch);
|
---|
450 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // 1
|
---|
451 | il.Emit(System.Reflection.Emit.OpCodes.Br, end);
|
---|
452 | il.MarkLabel(falseBranch);
|
---|
453 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // -1
|
---|
454 | il.Emit(System.Reflection.Emit.OpCodes.Neg);
|
---|
455 | il.MarkLabel(end);
|
---|
456 | return;
|
---|
457 | }
|
---|
458 | case OpCodes.OR: {
|
---|
459 | Label trueBranch = il.DefineLabel();
|
---|
460 | Label end = il.DefineLabel();
|
---|
461 | Label resultBranch = il.DefineLabel();
|
---|
462 | CompileInstructions(il, state, ds);
|
---|
463 | for (int i = 1; i < nArgs; i++) {
|
---|
464 | Label nextArgBranch = il.DefineLabel();
|
---|
465 | // complex definition because of special properties of NaN
|
---|
466 | il.Emit(System.Reflection.Emit.OpCodes.Dup);
|
---|
467 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0); // <= 0
|
---|
468 | il.Emit(System.Reflection.Emit.OpCodes.Ble, nextArgBranch);
|
---|
469 | il.Emit(System.Reflection.Emit.OpCodes.Br, resultBranch);
|
---|
470 | il.MarkLabel(nextArgBranch);
|
---|
471 | il.Emit(System.Reflection.Emit.OpCodes.Pop);
|
---|
472 | CompileInstructions(il, state, ds);
|
---|
473 | }
|
---|
474 | il.MarkLabel(resultBranch);
|
---|
475 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0); // > 0
|
---|
476 | il.Emit(System.Reflection.Emit.OpCodes.Cgt);
|
---|
477 | il.Emit(System.Reflection.Emit.OpCodes.Brtrue, trueBranch);
|
---|
478 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // -1
|
---|
479 | il.Emit(System.Reflection.Emit.OpCodes.Neg);
|
---|
480 | il.Emit(System.Reflection.Emit.OpCodes.Br, end);
|
---|
481 | il.MarkLabel(trueBranch);
|
---|
482 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // 1
|
---|
483 | il.MarkLabel(end);
|
---|
484 | return;
|
---|
485 | }
|
---|
486 | case OpCodes.NOT: {
|
---|
487 | CompileInstructions(il, state, ds);
|
---|
488 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0); // > 0
|
---|
489 | il.Emit(System.Reflection.Emit.OpCodes.Cgt);
|
---|
490 | il.Emit(System.Reflection.Emit.OpCodes.Conv_R8); // convert to float64
|
---|
491 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 2.0); // * 2
|
---|
492 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
493 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // - 1
|
---|
494 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
|
---|
495 | il.Emit(System.Reflection.Emit.OpCodes.Neg); // * -1
|
---|
496 | return;
|
---|
497 | }
|
---|
498 | case OpCodes.XOR: {
|
---|
499 | CompileInstructions(il, state, ds);
|
---|
500 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0);
|
---|
501 | il.Emit(System.Reflection.Emit.OpCodes.Cgt);// > 0
|
---|
502 |
|
---|
503 | for (int i = 1; i < nArgs; i++) {
|
---|
504 | CompileInstructions(il, state, ds);
|
---|
505 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0);
|
---|
506 | il.Emit(System.Reflection.Emit.OpCodes.Cgt);// > 0
|
---|
507 | il.Emit(System.Reflection.Emit.OpCodes.Xor);
|
---|
508 | }
|
---|
509 | il.Emit(System.Reflection.Emit.OpCodes.Conv_R8); // convert to float64
|
---|
510 |
|
---|
511 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 2.0); // * 2
|
---|
512 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
513 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // - 1
|
---|
514 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
|
---|
515 | return;
|
---|
516 | }
|
---|
517 | case OpCodes.GT: {
|
---|
518 | CompileInstructions(il, state, ds);
|
---|
519 | CompileInstructions(il, state, ds);
|
---|
520 |
|
---|
521 | il.Emit(System.Reflection.Emit.OpCodes.Cgt); // 1 (>) / 0 (otherwise)
|
---|
522 | il.Emit(System.Reflection.Emit.OpCodes.Conv_R8); // convert to float64
|
---|
523 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 2.0); // * 2
|
---|
524 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
525 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // - 1
|
---|
526 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
|
---|
527 | return;
|
---|
528 | }
|
---|
529 | case OpCodes.LT: {
|
---|
530 | CompileInstructions(il, state, ds);
|
---|
531 | CompileInstructions(il, state, ds);
|
---|
532 | il.Emit(System.Reflection.Emit.OpCodes.Clt);
|
---|
533 | il.Emit(System.Reflection.Emit.OpCodes.Conv_R8); // convert to float64
|
---|
534 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 2.0); // * 2
|
---|
535 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
536 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 1.0); // - 1
|
---|
537 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
|
---|
538 | return;
|
---|
539 | }
|
---|
540 | case OpCodes.TimeLag: {
|
---|
541 | LaggedTreeNode laggedTreeNode = (LaggedTreeNode)currentInstr.dynamicNode;
|
---|
542 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row -= lag
|
---|
543 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, laggedTreeNode.Lag);
|
---|
544 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
545 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
546 | var prevLaggedContext = state.InLaggedContext;
|
---|
547 | state.InLaggedContext = true;
|
---|
548 | CompileInstructions(il, state, ds);
|
---|
549 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row += lag
|
---|
550 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, laggedTreeNode.Lag);
|
---|
551 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
|
---|
552 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
553 | state.InLaggedContext = prevLaggedContext;
|
---|
554 | return;
|
---|
555 | }
|
---|
556 | case OpCodes.Integral: {
|
---|
557 | int savedPc = state.ProgramCounter;
|
---|
558 | LaggedTreeNode laggedTreeNode = (LaggedTreeNode)currentInstr.dynamicNode;
|
---|
559 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row -= lag
|
---|
560 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, laggedTreeNode.Lag);
|
---|
561 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
562 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
563 | var prevLaggedContext = state.InLaggedContext;
|
---|
564 | state.InLaggedContext = true;
|
---|
565 | CompileInstructions(il, state, ds);
|
---|
566 | for (int l = laggedTreeNode.Lag; l < 0; l++) {
|
---|
567 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row += lag
|
---|
568 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_1);
|
---|
569 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
570 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
571 | state.ProgramCounter = savedPc;
|
---|
572 | CompileInstructions(il, state, ds);
|
---|
573 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
574 | }
|
---|
575 | state.InLaggedContext = prevLaggedContext;
|
---|
576 | return;
|
---|
577 | }
|
---|
578 |
|
---|
579 | //mkommend: derivate calculation taken from:
|
---|
580 | //http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/
|
---|
581 | //one sided smooth differentiatior, N = 4
|
---|
582 | // y' = 1/8h (f_i + 2f_i-1, -2 f_i-3 - f_i-4)
|
---|
583 | case OpCodes.Derivative: {
|
---|
584 | int savedPc = state.ProgramCounter;
|
---|
585 | CompileInstructions(il, state, ds);
|
---|
586 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row --
|
---|
587 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_M1);
|
---|
588 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
589 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
590 | state.ProgramCounter = savedPc;
|
---|
591 | var prevLaggedContext = state.InLaggedContext;
|
---|
592 | state.InLaggedContext = true;
|
---|
593 | CompileInstructions(il, state, ds);
|
---|
594 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 2.0); // f_0 + 2 * f_1
|
---|
595 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
596 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
597 |
|
---|
598 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row -=2
|
---|
599 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_2);
|
---|
600 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
|
---|
601 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
602 | state.ProgramCounter = savedPc;
|
---|
603 | CompileInstructions(il, state, ds);
|
---|
604 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 2.0); // f_0 + 2 * f_1 - 2 * f_3
|
---|
605 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
606 | il.Emit(System.Reflection.Emit.OpCodes.Sub);
|
---|
607 |
|
---|
608 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row --
|
---|
609 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_M1);
|
---|
610 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
611 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
612 | state.ProgramCounter = savedPc;
|
---|
613 | CompileInstructions(il, state, ds);
|
---|
614 | il.Emit(System.Reflection.Emit.OpCodes.Sub); // f_0 + 2 * f_1 - 2 * f_3 - f_4
|
---|
615 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, 8.0); // / 8
|
---|
616 | il.Emit(System.Reflection.Emit.OpCodes.Div);
|
---|
617 |
|
---|
618 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // row +=4
|
---|
619 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_4);
|
---|
620 | il.Emit(System.Reflection.Emit.OpCodes.Add);
|
---|
621 | il.Emit(System.Reflection.Emit.OpCodes.Starg, 0);
|
---|
622 | state.InLaggedContext = prevLaggedContext;
|
---|
623 | return;
|
---|
624 | }
|
---|
625 | case OpCodes.Call: {
|
---|
626 | throw new NotSupportedException(
|
---|
627 | "Automatically defined functions are not supported by the SymbolicDataAnalysisTreeILEmittingInterpreter. Either turn of ADFs or change the interpeter.");
|
---|
628 | }
|
---|
629 | case OpCodes.Arg: {
|
---|
630 | throw new NotSupportedException(
|
---|
631 | "Automatically defined functions are not supported by the SymbolicDataAnalysisTreeILEmittingInterpreter. Either turn of ADFs or change the interpeter.");
|
---|
632 | }
|
---|
633 | case OpCodes.Variable: {
|
---|
634 | VariableTreeNode varNode = (VariableTreeNode)currentInstr.dynamicNode;
|
---|
635 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_1); // load columns array
|
---|
636 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, (int)currentInstr.data);
|
---|
637 | // load correct column of the current variable
|
---|
638 | il.Emit(System.Reflection.Emit.OpCodes.Ldelem_Ref);
|
---|
639 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // rowIndex
|
---|
640 | if (!state.InLaggedContext) {
|
---|
641 | il.Emit(System.Reflection.Emit.OpCodes.Call, listGetValue);
|
---|
642 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, varNode.Weight); // load weight
|
---|
643 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
644 | } else {
|
---|
645 | var nanResult = il.DefineLabel();
|
---|
646 | var normalResult = il.DefineLabel();
|
---|
647 | il.Emit(System.Reflection.Emit.OpCodes.Dup);
|
---|
648 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0);
|
---|
649 | il.Emit(System.Reflection.Emit.OpCodes.Blt, nanResult);
|
---|
650 | il.Emit(System.Reflection.Emit.OpCodes.Dup);
|
---|
651 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, ds.Rows);
|
---|
652 | il.Emit(System.Reflection.Emit.OpCodes.Bge, nanResult);
|
---|
653 | il.Emit(System.Reflection.Emit.OpCodes.Call, listGetValue);
|
---|
654 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, varNode.Weight); // load weight
|
---|
655 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
656 | il.Emit(System.Reflection.Emit.OpCodes.Br, normalResult);
|
---|
657 | il.MarkLabel(nanResult);
|
---|
658 | il.Emit(System.Reflection.Emit.OpCodes.Pop); // rowIndex
|
---|
659 | il.Emit(System.Reflection.Emit.OpCodes.Pop); // column reference
|
---|
660 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, double.NaN);
|
---|
661 | il.MarkLabel(normalResult);
|
---|
662 | }
|
---|
663 | return;
|
---|
664 | }
|
---|
665 | case OpCodes.LagVariable: {
|
---|
666 | var nanResult = il.DefineLabel();
|
---|
667 | var normalResult = il.DefineLabel();
|
---|
668 | LaggedVariableTreeNode varNode = (LaggedVariableTreeNode)currentInstr.dynamicNode;
|
---|
669 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_1); // load columns array
|
---|
670 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, (int)currentInstr.data);
|
---|
671 | // load correct column of the current variable
|
---|
672 | il.Emit(System.Reflection.Emit.OpCodes.Ldelem_Ref);
|
---|
673 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, varNode.Lag); // lag
|
---|
674 | il.Emit(System.Reflection.Emit.OpCodes.Ldarg_0); // rowIndex
|
---|
675 | il.Emit(System.Reflection.Emit.OpCodes.Add); // actualRowIndex = rowIndex + sampleOffset
|
---|
676 | il.Emit(System.Reflection.Emit.OpCodes.Dup);
|
---|
677 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4_0);
|
---|
678 | il.Emit(System.Reflection.Emit.OpCodes.Blt, nanResult);
|
---|
679 | il.Emit(System.Reflection.Emit.OpCodes.Dup);
|
---|
680 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_I4, ds.Rows);
|
---|
681 | il.Emit(System.Reflection.Emit.OpCodes.Bge, nanResult);
|
---|
682 | il.Emit(System.Reflection.Emit.OpCodes.Call, listGetValue);
|
---|
683 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, varNode.Weight); // load weight
|
---|
684 | il.Emit(System.Reflection.Emit.OpCodes.Mul);
|
---|
685 | il.Emit(System.Reflection.Emit.OpCodes.Br, normalResult);
|
---|
686 | il.MarkLabel(nanResult);
|
---|
687 | il.Emit(System.Reflection.Emit.OpCodes.Pop); // sample index
|
---|
688 | il.Emit(System.Reflection.Emit.OpCodes.Pop); // column reference
|
---|
689 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, double.NaN);
|
---|
690 | il.MarkLabel(normalResult);
|
---|
691 | return;
|
---|
692 | }
|
---|
693 | case OpCodes.Constant: {
|
---|
694 | ConstantTreeNode constNode = (ConstantTreeNode)currentInstr.dynamicNode;
|
---|
695 | il.Emit(System.Reflection.Emit.OpCodes.Ldc_R8, constNode.Value);
|
---|
696 | return;
|
---|
697 | }
|
---|
698 |
|
---|
699 | //mkommend: this symbol uses the logistic function f(x) = 1 / (1 + e^(-alpha * x) )
|
---|
700 | //to determine the relative amounts of the true and false branch see http://en.wikipedia.org/wiki/Logistic_function
|
---|
701 | case OpCodes.VariableCondition: {
|
---|
702 | throw new NotSupportedException("Interpretation of symbol " + currentInstr.dynamicNode.Symbol.Name +
|
---|
703 | " is not supported by the SymbolicDataAnalysisTreeILEmittingInterpreter");
|
---|
704 | }
|
---|
705 | default:
|
---|
706 | throw new NotSupportedException("Interpretation of symbol " + currentInstr.dynamicNode.Symbol.Name +
|
---|
707 | " is not supported by the SymbolicDataAnalysisTreeILEmittingInterpreter");
|
---|
708 | }
|
---|
709 | }
|
---|
710 |
|
---|
711 | public static double AiryA(double x) {
|
---|
712 | if (double.IsNaN(x)) return double.NaN;
|
---|
713 | double ai, aip, bi, bip;
|
---|
714 | alglib.airy(x, out ai, out aip, out bi, out bip);
|
---|
715 | return ai;
|
---|
716 | }
|
---|
717 |
|
---|
718 | public static double AiryB(double x) {
|
---|
719 | if (double.IsNaN(x)) return double.NaN;
|
---|
720 | double ai, aip, bi, bip;
|
---|
721 | alglib.airy(x, out ai, out aip, out bi, out bip);
|
---|
722 | return bi;
|
---|
723 | }
|
---|
724 | public static double Dawson(double x) {
|
---|
725 | if (double.IsNaN(x)) return double.NaN;
|
---|
726 | return alglib.dawsonintegral(x);
|
---|
727 | }
|
---|
728 |
|
---|
729 | public static double Gamma(double x) {
|
---|
730 | if (double.IsNaN(x)) return double.NaN;
|
---|
731 | return alglib.gammafunction(x);
|
---|
732 | }
|
---|
733 |
|
---|
734 | public static double Psi(double x) {
|
---|
735 | if (double.IsNaN(x)) return double.NaN;
|
---|
736 | else if (x <= 0 && (Math.Floor(x) - x).IsAlmost(0)) return double.NaN;
|
---|
737 | return alglib.psi(x);
|
---|
738 | }
|
---|
739 |
|
---|
740 | public static double ExpIntegralEi(double x) {
|
---|
741 | if (double.IsNaN(x)) return double.NaN;
|
---|
742 | return alglib.exponentialintegralei(x);
|
---|
743 | }
|
---|
744 |
|
---|
745 | public static double SinIntegral(double x) {
|
---|
746 | if (double.IsNaN(x)) return double.NaN;
|
---|
747 | double si, ci;
|
---|
748 | alglib.sinecosineintegrals(x, out si, out ci);
|
---|
749 | return si;
|
---|
750 | }
|
---|
751 |
|
---|
752 | public static double CosIntegral(double x) {
|
---|
753 | if (double.IsNaN(x)) return double.NaN;
|
---|
754 | double si, ci;
|
---|
755 | alglib.sinecosineintegrals(x, out si, out ci);
|
---|
756 | return ci;
|
---|
757 | }
|
---|
758 |
|
---|
759 | public static double HypSinIntegral(double x) {
|
---|
760 | if (double.IsNaN(x)) return double.NaN;
|
---|
761 | double shi, chi;
|
---|
762 | alglib.hyperbolicsinecosineintegrals(x, out shi, out chi);
|
---|
763 | return shi;
|
---|
764 | }
|
---|
765 |
|
---|
766 | public static double HypCosIntegral(double x) {
|
---|
767 | if (double.IsNaN(x)) return double.NaN;
|
---|
768 | double shi, chi;
|
---|
769 | alglib.hyperbolicsinecosineintegrals(x, out shi, out chi);
|
---|
770 | return chi;
|
---|
771 | }
|
---|
772 |
|
---|
773 | public static double FresnelCosIntegral(double x) {
|
---|
774 | if (double.IsNaN(x)) return double.NaN;
|
---|
775 | double c = 0, s = 0;
|
---|
776 | alglib.fresnelintegral(x, ref c, ref s);
|
---|
777 | return c;
|
---|
778 | }
|
---|
779 |
|
---|
780 | public static double FresnelSinIntegral(double x) {
|
---|
781 | if (double.IsNaN(x)) return double.NaN;
|
---|
782 | double c = 0, s = 0;
|
---|
783 | alglib.fresnelintegral(x, ref c, ref s);
|
---|
784 | return s;
|
---|
785 | }
|
---|
786 |
|
---|
787 | public static double Norm(double x) {
|
---|
788 | if (double.IsNaN(x)) return double.NaN;
|
---|
789 | return alglib.normaldistribution(x);
|
---|
790 | }
|
---|
791 |
|
---|
792 | public static double Erf(double x) {
|
---|
793 | if (double.IsNaN(x)) return double.NaN;
|
---|
794 | return alglib.errorfunction(x);
|
---|
795 | }
|
---|
796 |
|
---|
797 | public static double Bessel(double x) {
|
---|
798 | if (double.IsNaN(x)) return double.NaN;
|
---|
799 | return alglib.besseli0(x);
|
---|
800 | }
|
---|
801 | }
|
---|
802 | }
|
---|