arb4j Overview

What is arb4j?

arb4j is a robust Java API designed to efficiently represent mathematical structures in their most general forms, prioritizing high performance. It seamlessly integrates with the arblib library via an interface generated by SWIG, enabling arbitrary precision real and complex ball arithmetic operations.

Features and Usage Patterns

Fluent Interface Pattern

• arb4j employs a fluent pattern wherever possible, enhancing the way functions receive and return values.
• Typically, the last argument in a function call becomes the return value, defaulting to 'this' if not specified.

Example:

Real x = new Real("25", 128); // 128 bits of precision

// Both lines achieve the same result:
Real five = x.sqrt(128);
Real five = x.sqrt(128, x); // Using 'this' as the result variable explicitly

• To prevent overwriting the input variable:

Real five = x.sqrt(128, new Real());

• Chain function calls in an object-oriented way:

Real y = new Real("25", 128)
            .add(RealConstants.one, 128)
            .log(128)
            .tanh(128);

Resource Management with AutoCloseable

• The AutoCloseable interface is used for memory management.
• This implementation ensures that objects can and should be used within try-with-resources blocks for optimal resource handling, especially important for managing native resources.

Example:

try (Real x = new Real("25", 128)) {
    doSomething(x);
} // x is automatically closed, ensuring proper resource management

Advanced Tools

Expression Compiler

• The arb.expressions package in arb4j includes tools for compiling mathematical expressions directly into Java bytecode, saving milleniums of development time, reducing the need to laborously and tediously write new code for each different formula to be evaluated whilst also ensuring efficiency and correctness; it would be challenging to write code manually that would significantly outperform the generated code

Error Messages Produced By Expression Parser

Example: unmatched paranthesis

arb.exceptions.CompilerException: unexpected ')'(0x29) character at position=11 in expression '(1/2)-(z/2))^n' of length 14, remaining=)^n

	at arb4j/arb.expressions.Expression.throwNewUnexpectedCharacterException(Expression.java:1933)
	at arb4j/arb.expressions.Expression.parseRoot(Expression.java:1586)
	at arb4j/arb.functions.Function.parse(Function.java:381)
	at arb4j/arb.expressions.Compiler.compile(Compiler.java:161)
	at arb4j/arb.expressions.Compiler.express(Compiler.java:246)
	at arb4j/arb.expressions.Compiler.express(Compiler.java:222)
	at arb4j/arb.expressions.Compiler.compile(Compiler.java:127)
	at arb4j/arb.functions.Function.instantiate(Function.java:413)
	at arb4j/arb.functions.Function.express(Function.java:159)
	at arb4j/arb.functions.sequences.RationalFunctionSequence.express(RationalFunctionSequence.java:35)
	at arb4j/arb.functions.sequences.RationalFunctionSequence.express(RationalFunctionSequence.java:25)
	at arb4j/arb.RationalFunctionTest.testPowers(RationalFunctionTest.java:49)

which was generated because of the buggy test

  public void testPowers()
  {
    try ( Integer n = Integer.named("n").set(0))
    {
      Context          context            = new Context(n);
      var              rationalFunctional = RationalFunctionSequence.express("(1/2)-(z/2))^n", context);
      RationalFunction expressed          = rationalFunctional.evaluate(n, 128, new RationalFunction());
      assertEquals("x", expressed.toString());
    }
  }

Easily Decompilable Code

Example: Chebyshev Polynomials of the First Kind

The unmodified decompiled code generated by the Type1ChebyshevPolynomial class

import arb.Integer;
import arb.RealPolynomial;
import arb.functions.Function;

public class T implements Function<Integer, RealPolynomial> {
   private boolean isInitialized;
   Integer c1 = new Integer("0");
   Integer c2 = new Integer("1");
   Integer c3 = new Integer("2");
   public RealPolynomial r̅1 = new RealPolynomial();
   public Integer ℤ1 = new Integer();
   public RealPolynomial r̅2 = new RealPolynomial();
   public RealPolynomial r̅3 = new RealPolynomial();
   public Integer ℤ2 = new Integer();
   public RealPolynomial r̅4 = new RealPolynomial();
   public T T;

   public RealPolynomial evaluate(Integer in, int order, int bits, RealPolynomial result) {
      if (!isInitialized) {
         initialize();
      }
      return switch(in.getSignedValue()) {
         case 0 -> result.set(c2);
         case 1 -> result.set(result.identity());
         default -> c3
         .mul(result.identity(), bits, r̅1)
         .mul(T.evaluate(in.sub(c2, bits, ℤ1), order, bits, r̅2), bits, r̅3)
         .sub(T.evaluate(in.sub(c3, bits, ℤ2), order, bits, r̅4), bits, result);
      };
   }

   public void initialize() {
      if (isInitialized) {
         throw new AssertionError("Already initialized");
      } else {
         T = new T();
         isInitialized = true;
      }
   }

   public void close() {
      c1.close();
      c2.close();
      c3.close();
      r̅1.close();
      ℤ1.close();
      r̅2.close();
      r̅3.close();
      ℤ2.close();
      r̅4.close();
      T.close();
   }
}

Automatic Differentiation of Expressions (Upcoming)

• A symbolic parser and compiler for automatic differentiation is in development.
• Current progress can be tracked at: GitHub Issue #253.

Forked modularized version of jlatexmath

See this for a version of jlatexmath without the unnamed module warnings

Licensing

arb4j is made available under the terms of the Business Source License™ v1.1 which can be found in the root directory of this project in a file named License.pdf, License.txt, or License.tm which are the pdf, text, and TeXmacs format of the same document respectively.