|
||
---|---|---|
.. | ||
docs | ||
reference | ||
src | ||
build.gradle.kts | ||
README.md |
Module kmath-ast
Extensions to MST API: transformations, dynamic compilation and visualization.
- expression-language : Expression language and its parser
- mst-jvm-codegen : Dynamic MST to JVM bytecode compiler
- mst-js-codegen : Dynamic MST to JS compiler
- rendering : Extendable MST rendering
Artifact:
The Maven coordinates of this project are space.kscience:kmath-ast:0.4.0-dev-1
.
Gradle Groovy:
repositories {
maven { url 'https://repo.kotlin.link' }
mavenCentral()
}
dependencies {
implementation 'space.kscience:kmath-ast:0.4.0-dev-1'
}
Gradle Kotlin DSL:
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:
- Constants and variables (consist of latin letters, digits and underscores, can't start with digit):
x
,_Abc2
. - Numbers:
123
,1.02
,1e10
,1e-10
,1.0e+3
—all parsed either askotlin.Long
orkotlin.Double
.
Supported binary operators (from the highest precedence to the lowest one):
^
*
,/
+
,-
Supported unary operator:
-
, 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:
sin(x)
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:
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:
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:
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.
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:
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.
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:
(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:
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):
<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>×</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).