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Module kmath-ast

Extensions to MST API: transformations, dynamic compilation and visualization.

Artifact:

The Maven coordinates of this project are space.kscience:kmath-ast:0.4.0-dev-1.

Gradle Groovy: 

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repositories {
    maven { url 'https://repo.kotlin.link' }
    mavenCentral()
}

dependencies {
    implementation 'space.kscience:kmath-ast:0.4.0-dev-1'
}
Gradle Kotlin DSL: 
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repositories {
    maven("https://repo.kotlin.link")
    mavenCentral()
}

dependencies {
    implementation("space.kscience:kmath-ast:0.4.0-dev-1")
}

Parsing expressions

In this module there is a parser from human-readable strings like "x^3-x+3" (in the more specific grammar) to MST instances.

Supported literals: 1. Constants and variables (consist of latin letters, digits and underscores, can't start with digit): x, _Abc2. 2. Numbers: 123, 1.02, 1e10, 1e-10, 1.0e+3—all parsed either as kotlin.Long or kotlin.Double.

Supported binary operators (from the highest precedence to the lowest one): 1. ^ 2. *, / 3. +, -

Supported unary operator: 1. -, e. g. -x

Arbitrary unary and binary functions are also supported: names consist of latin letters, digits and underscores, can't start with digit. Examples: 1. sin(x) 2. add(x, y)

Dynamic expression code generation

On JVM

kmath-ast JVM module supports runtime code generation to eliminate overhead of tree traversal. Code generator builds a special implementation of Expression<T> with implemented invoke function.

For example, the following code:

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import space.kscience.kmath.asm.compileToExpression
import space.kscience.kmath.operations.DoubleField

"x^3-x+3".parseMath().compileToExpression(DoubleField)

… leads to generation of bytecode, which can be decompiled to the following Java class:

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import java.util.*;
import kotlin.jvm.functions.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.complex.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_45045_0 implements Expression<Complex> {
    private final Object[] constants;

    public Complex invoke(Map<Symbol, ? extends Complex> arguments) {
        Complex var2 = (Complex)MapIntrinsics.getOrFail(arguments, "x");
        return (Complex)((Function2)this.constants[0]).invoke(var2, (Complex)this.constants[1]);
    }
}

For LongRing, IntRing, and DoubleField specialization is supported for better performance:

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import java.util.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_-386104628_0 implements DoubleExpression {
    private final SymbolIndexer indexer;

    public SymbolIndexer getIndexer() {
        return this.indexer;
    }

    public double invoke(double[] arguments) {
        double var2 = arguments[0];
        return Math.pow(var2, 3.0D) - var2 + 3.0D;
    }

    public final Double invoke(Map<Symbol, ? extends Double> arguments) {
        double var2 = ((Double)MapIntrinsics.getOrFail(arguments, "x")).doubleValue();
        return Math.pow(var2, 3.0D) - var2 + 3.0D;
    }
}

Setting JVM system property space.kscience.kmath.ast.dump.generated.classes to 1 makes the translator dump class files to program's working directory, so they can be reviewed manually.

Limitations

  • The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class loading overhead.
  • This API is not supported by non-dynamic JVM implementations like TeaVM or GraalVM Native Image because they may not support class loaders.

On JS

A similar feature is also available on JS.

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import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.estree.*

MstField { x + 2 }.compileToExpression(DoubleField)

The code above returns expression implemented with such a JS function:

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var executable = function (constants, arguments) {
    return constants[1](constants[0](arguments, "x"), 2);
};

JS also supports experimental expression optimization with WebAssembly IR generation. Currently, only expressions inside DoubleField and IntRing are supported.

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import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.wasm.*

MstField { x + 2 }.compileToExpression(DoubleField)

An example of emitted Wasm IR in the form of WAT:

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(func \$executable (param \$0 f64) (result f64)
  (f64.add
    (local.get \$0)
    (f64.const 2)
  )
)

Limitations

  • ESTree expression compilation uses eval which can be unavailable in several environments.
  • WebAssembly isn't supported by old versions of browsers (see https://webassembly.org/roadmap/).

Rendering expressions

kmath-ast also includes an extensible engine to display expressions in LaTeX or MathML syntax.

Example usage:

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import space.kscience.kmath.ast.*
import space.kscience.kmath.ast.rendering.*
import space.kscience.kmath.misc.*

@OptIn(UnstableKMathAPI::class)
public fun main() {
    val mst = "exp(sqrt(x))-asin(2*x)/(2e10+x^3)/(12)+x^(2/3)".parseMath()
    val syntax = FeaturedMathRendererWithPostProcess.Default.render(mst)
    val latex = LatexSyntaxRenderer.renderWithStringBuilder(syntax)
    println("LaTeX:")
    println(latex)
    println()
    val mathML = MathMLSyntaxRenderer.renderWithStringBuilder(syntax)
    println("MathML:")
    println(mathML)
}

Result LaTeX:

\[\operatorname{exp}\\,\left(\sqrt{x}\right)-\frac{\frac{\operatorname{arcsin}\\,\left(2\\,x\right)}{2\times10^{10}+x^{3}}}{12}+x^{2/3}\]

Result MathML (can be used with MathJax or other renderers):

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<math xmlns="https://www.w3.org/1998/Math/MathML">
    <mrow>
        <mo>exp</mo>
        <mspace width="0.167em"></mspace>
        <mfenced open="(" close=")" separators="">
            <msqrt>
                <mi>x</mi>
            </msqrt>
        </mfenced>
        <mo>-</mo>
        <mfrac>
            <mrow>
                <mfrac>
                    <mrow>
                        <mo>arcsin</mo>
                        <mspace width="0.167em"></mspace>
                        <mfenced open="(" close=")" separators="">
                            <mn>2</mn>
                            <mspace width="0.167em"></mspace>
                            <mi>x</mi>
                        </mfenced>
                    </mrow>
                    <mrow>
                        <mn>2</mn>
                        <mo>&times;</mo>
                        <msup>
                            <mrow>
                                <mn>10</mn>
                            </mrow>
                            <mrow>
                                <mn>10</mn>
                            </mrow>
                        </msup>
                        <mo>+</mo>
                        <msup>
                            <mrow>
                                <mi>x</mi>
                            </mrow>
                            <mrow>
                                <mn>3</mn>
                            </mrow>
                        </msup>
                    </mrow>
                </mfrac>
            </mrow>
            <mrow>
                <mn>12</mn>
            </mrow>
        </mfrac>
        <mo>+</mo>
        <msup>
            <mrow>
                <mi>x</mi>
            </mrow>
            <mrow>
                <mn>2</mn>
                <mo>/</mo>
                <mn>3</mn>
            </mrow>
        </msup>
    </mrow>
</math>

It is also possible to create custom algorithms of render, and even add support of other markup languages (see API reference).