Super fast expression evaluator/parser written in Java.
Paralithic is a library for parsing and evaluating mathematical expressions. It uses ASM to dynamically
generate implementations of the Expression interface representing the expression, with expressions converted directly
into Java bytecode for maximum performance, and maximum room for JIT optimization. Paralithic also uses several AOT
optimization techniques, such as:
- Evaluating stateless functions with constant arguments at parse time, replacing them with constants.
- Evaluating binary operations with constant operands at parse time, replacing them with constants.
- Combining constants in nested commutative binary operations.
By directly generating bytecode to be executed by the JVM, and with the above optimizations, Paralithic expressions are able to achieve about the same speed as hard-coded ones.
Paralithic uses Seismic as it's backing math library, which provides many of the math functions built into Paralithic, and provides more optimized versions for many functions built into Java's Math class.
Parser parser = new Parser(); // Create parser instance.
Scope scope = new Scope(); // Create variable scope. This scope can hold both constants and invocation variables scope.
addInvocationVariable("x"); // Register variable to be used in calls to #evaluate. Values are passed in the order they are registered scope.
create("y",3); // Create named constant y with value 3
Expression expression = parser.parse("x * 4 + pow(2, y)", scope); // expression.
evaluate(3); // 20 (3*4 + 2^3 = 20)The expression (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) was evaluated in
3 different
expression libraries.
The test was run for 3 iterations of 1 second each to allow the JIT to warmup and optimize as much as possible, the next 3 iterations of 1 second each were timed and averaged. This was then repeated 3 times, with a new JVM each time, and the results were averaged.
The native, native (simplified), native (optimized) tests each tested a hard-coded method containing the expanded,
simplified, and
optimized expression, respectively.
| Benchmark | Score |
|---|---|
| exp4J | 332.326 ± 15.629 ns/op |
| parsii | 97.120 ± 3.215 ns/op |
| native | 33.003 ± 0.699 ns/op |
| native (simplified) | 23.084 ± 0.299 ns/op |
| Paralithic | 5.541 ± 0.166 ns/op |
| native (optimized) | 5.306 ± 0.114 ns/op |
Results are from tests run on an Intel i7-1165G7.
Full Benchmark Results
Benchmark (input) (testExpression) Mode Cnt Score Error Units
PerformanceTest.exp4JPerformance 1 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 336.341 ± 46.461 ns/op
PerformanceTest.exp4JPerformance 1000 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 321.425 ± 9.348 ns/op
PerformanceTest.exp4JPerformance 23422 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 332.326 ± 15.629 ns/op
PerformanceTest.nativePerformance 1 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 33.102 ± 0.384 ns/op
PerformanceTest.nativePerformance 1000 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 33.286 ± 1.389 ns/op
PerformanceTest.nativePerformance 23422 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 33.003 ± 0.699 ns/op
PerformanceTest.nativePerformanceOptimized 1 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 5.301 ± 0.185 ns/op
PerformanceTest.nativePerformanceOptimized 1000 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 5.257 ± 0.043 ns/op
PerformanceTest.nativePerformanceOptimized 23422 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 5.306 ± 0.114 ns/op
PerformanceTest.nativePerformanceSimplified 1 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 23.112 ± 0.243 ns/op
PerformanceTest.nativePerformanceSimplified 1000 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 22.905 ± 0.610 ns/op
PerformanceTest.nativePerformanceSimplified 23422 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 23.084 ± 0.299 ns/op
PerformanceTest.paralithicPerformance 1 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 5.442 ± 0.079 ns/op
PerformanceTest.paralithicPerformance 1000 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 5.432 ± 0.115 ns/op
PerformanceTest.paralithicPerformance 23422 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 5.541 ± 0.166 ns/op
PerformanceTest.parsiiPerformance 1 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 97.353 ± 3.488 ns/op
PerformanceTest.parsiiPerformance 1000 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 96.237 ± 2.216 ns/op
PerformanceTest.parsiiPerformance 23422 (sin(x) + 2 + ((7-5) * (3.14159 * x^(14-10)) + sin(-3.141) + (0%x)) * x/3 * 3/sqrt(x)) avgt 9 97.120 ± 3.215 ns/op
Paralithic generated the following class from the input function (decompiled with Vineflower, a fork of FernFlower):
public class ExpressionIMPL_0 implements Expression {
public ExpressionIMPL_0() {
}
public double evaluate(Context var1, double[] var2) {
return TrigonometryFunctions.sin(var2[0]) + Math.fma(Math.fma(6.28318, IntegerFunctions.iPow(var2[0], 4.0), -7.669050828553736E-4) * var2[0], AlgebraFunctions.invSqrt(var2[0]), 2.0);
}
}Paralithic is licensed under the MIT License.
Paralithic is a "fork" of a modified version of Parsii, licensed under the MIT license.