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Commons Math is an Apache library which includes a variety of mathematical tools, including 1st and 2nd-order ODE solvers.  In order to familiarize myself with the ODE solvers, I wrote a simple program to solve an RC charging circuit.

The circuit has these parameters:

• R (ohms), the resistance of the resistor
• C (farads), the capacitance of the capacitor
• V (volts), the voltage of the supply current

Differential equation solvers need initial conditions, so I've supplied the voltage across the capacitor as zero.  That is, the capacitor starts uncharged.

Commons Math requires that all equations are provided in the form

y' = f(y, t)

That is, the equation must provide the differential in terms of time, and the current state: y.   Note that both y' and y can be vectors.

In my case, the equation I've supplied is:

Vc' = - (Vc-Vin)/RC;

Where

• Vc' is the derivative with respect to time of the capacitor charge
• Vc is the current capacitor charge
• Vin is the supply voltage

This equation is coded as an implementation of FirstOrderDifferentialEquations.  Note that I could have supplied an multiple equations using this interface, and I could have done something more complex using SecondOrderDifferentialEquations.  My implementation is here.

Once I've defined equations, there are multiple implementations of ODE solvers.   For simplicity I chose ClassicalRungeKuttaIntegrator, however any of the implementations of AdaptiveStepsizeIntegrator might be faster.  My code to invoke the integrator with a step size of 1e-6 seconds is here.

The output of the test using

• R = 100KOhm
• V = 12V
• C = 10 nF
• Vc(0) = 0 V
• step size 1e-6 seconds
• T (0) = 0 seconds
• T (N) = .1 seconds

Starts like this:

1.0E-6,0.0011999400019999497
2.0E-6,0.0023997600159991993
3.0E-6,0.0035994600539959497
4.0E-6,0.0047990401279872
4.9999999999999996E-6,0.005998500249968752
5.999999999999999E-6,0.007197840431935207
6.999999999999999E-6,0.008397060685879965
8.0E-6,0.009596161023795232
9.0E-6,0.010795141457672009
1.0E-5,0.0119940019995001
1.1000000000000001E-5,0.01319274266126811
1.2000000000000002E-5,0.014391363454963448
1.3000000000000003E-5,0.01558986439257232
1.4000000000000003E-5,0.016788245486079736
1.5000000000000004E-5,0.017986506747469506
1.6000000000000003E-5,0.019184648188724243
1.7000000000000003E-5,0.020382669821825364
1.8000000000000004E-5,0.021580571658753083
1.9000000000000004E-5,0.02277835371148642
2.0000000000000005E-5,0.02397601599200319
2.1000000000000006E-5,0.025173558512280026

and ends like this:

0.09998900000007933,11.99945460123407
0.09999000000007933,11.99945465577122
0.09999100000007934,11.999454710302917
0.09999200000007934,11.99945476482916
0.09999300000007934,11.999454819349952
0.09999400000007934,11.999454873865291
0.09999500000007934,11.99945492837518
0.09999600000007934,11.999454982879616
0.09999700000007934,11.999455037378603
0.09999800000007934,11.99945509187214
0.09999900000007934,11.999455146360228

Pretty much exactly what you'd expect; the capacitor charges to ~12V, exponentially.

I've recently becoming interested in porting legacy PHP sites to JSPs.   It seemed to me that one of the hardest parts of this problem was parsing the PHP code.  Once a parse tree was created, the next step would be to emit equivalent JSP code.

I went looking for an ANTL4 grammar for PHP, but could only find an ANTLR3 grammar, so I went to work updating the ANTLR3 grammar to ANTLR4 and writing a very simple validation suite.  The github project is here, and the resulting grammar is here.

I've always had a fascination with compilers.  As a Java geek, I'm also quite interested in the JVM.  In order to learn a little more about both, and as a way to contribute to the open source world, I decided to implement a compiler for BASIC.   So, jvmBasic consumes BASIC code and emits .class files.

The first step was to build a parser and lexer for BASIC.  I decided to define an ANTLR4 grammar and use it to generate the lexer and parser.  BASIC is a fairly simple language, so the grammar was not difficult to define.  However, there are numerous BASIC dialects, so I had to pick a simple dialect.  jvmBASIC syntax looks much like Integer BASIC, but could easily be extended to parse GW-Basic, or maybe VB.  The resulting grammar is here.

Once ANTLR has generated a parser and lexer, it's possible to generate a parse tree for any BASIC input and then walk the tree emitting bytecode.  I used ASM to emit the bytecode.  An example BAS input file looks like this:

100 PRINT "Hello world"

The generated parse tree from jvmBASIC debug output looks like

- [1 line]
-  [3 linenumber]
-   [120 NUMBER] 100
-  [4 amprstmt]
-   [5 statement]
-    [7 printstmt1]
-     [4 'PRINT'] PRINT
-     [8 printlist]
-      [66 expression]
-       [60 func]
-        [118 STRINGLITERAL] "Hello world"
-  [122 CR]

Because there is no concept of functions, methods or classes in BASIC, I chose to enclose the generated code in a single method, of a single class.  The classname is the name of the BASIC input file, and the single method is:

public static void main(String[] args)

The class has two fields:

public InputStream inputStream;
public OutputStream outputStream;

The default values of inputStream and outputStream are System.in and System.out respectively.  However, in the case of jvmbasicwww, I replace them with HTTP input and output streams.

BASIC doesn't have new, delete, malloc, or free, or really any analogue of those.  Additionally, methods such as MID$ or perhaps VAL have certain semantics and behaviour.  In order to as closely as possible emulate BASIC, I implement jvmbasicrt.  Inside jvmbasicrt are implementation of each BASIC function, as well as a class called ExecutionContext. ExecutionContext includes the "guts" of a BASIC runtime:

• A stack.  Similar to many programming languages, BASIC needs a stack.
• All variables.  This is simple a hashtable of Values, keyed on the Variable name.

Additionally there is Value which implements a variable with BASIC semantics.

There is a maven mojo which wraps jvmbasicc.  The mojo jvmbasicmojo, compiles all BASIC files in "/src/main/bas" and produces a .class file for each one.  This mojo can be used to incorporate BASIC files into any normal maven project and then link them into a .jar file.

An additional example BASIC file is:

10 REM this is a comment
20 PRINT "13"
30 PRINT "hi"
40 PRINT 10
50 PRINT 15.55
60 LET x = 12
70 PRINT "hihi"
80 PRINT x
90 LET y = 1+2
100 LET z = 3*6
110 LET d= y+z
120 PRINT d

The maven pom file that uses jvmbasicmojo is here.

The javap output for the generated .class file is:

public class EXAMPLE1 {
 public com.khubla.jvmbasic.jvmbasicrt.ExecutionContext executionContext;
 public java.io.InputStream inputStream;
 public java.io.PrintStream outputStream;
 public EXAMPLE1();
 public static void main(java.lang.String[]);
 public void program() throws java.lang.Exception;
}

There isn't a big demand, that I'm aware of, for bytecode compilers for BASIC.  Two potential applications that come to mind are:

• Running VB code on the JVM.  Theoretically it would be possible to extend the grammar to include VB, and then to emit bytecode for VB programs.  This would form the foundation of technology to run .asp applications on the JVM.  The VB standard library would have to be implemented too.
• Cross-compilation.  Again, theoretically, it should be possible to use the grammar file to implement a cross compiler which consumes VB code and emits JSP code, or even PHP code.