Fast transcendent / trigonometric functions for Java

Question

Since the trigonometric functions in java.lang.Math are quite slow: is there a library that does a quick and good approximation? It seems possible to do a calculation severa

Answer 1

In the sin/cos test I was performing for integers zero to one million. I assume that 144 ns is not fast enough for you.

Do you have a specific requirement for the speed you need?

Can you qualify your requirement in terms of time per operation which is satisfactory?

Answer 2

That might make it : http://sourceforge.net/projects/jafama/

Answer 3

I haven't heard of any libs, probably because it's rare enough to see trig heavy Java apps. It's also easy enough to roll your own with JNI (same precision, better performance), numerical methods (variable precision / performance ) or a simple approximation table.

As with any optimization, best to test that these functions are actually a bottleneck before bothering to reinvent the wheel.

Answer 4

I'm surprised that the built-in Java functions would be so slow. Surely the JVM is calling the native trig functions on your CPU, not implementing the algorithms in Java. Are you certain your bottleneck is calls to trig functions and not some surrounding code? Maybe some memory allocations?

Could you rewrite in C++ the part of your code that does the math? Just calling C++ code to compute trig functions probably wouldn't speed things up, but moving some context too, like an outer loop, to C++ might speed things up.

If you must roll your own trig functions, don't use Taylor series alone. The CORDIC algorithms are much faster unless your argument is very small. You could use CORDIC to get started, then polish the result with a short Taylor series. See this StackOverflow question on how to implement trig functions.

Answer 5

On the x86 the java.lang.Math sin and cos functions do not directly call the hardware functions because Intel didn't always do such a good job implimenting them. There is a nice explanation in bug #4857011.

http://bugs.sun.com/bugdatabase/view_bug.do?bug_id=4857011

You might want to think hard about an inexact result. It's amusing how often I spend time finding this in others code.

"But the comment says Sin..."

Answer 6

Computer Approximations by Hart. Tabulates Chebyshev-economized approximate formulas for a bunch of functions at different precisions.

Edit: Getting my copy off the shelf, it turned out to be a different book that just sounds very similar. Here's a sin function using its tables. (Tested in C since that's handier for me.) I don't know if this will be faster than the Java built-in, but it's guaranteed to be less accurate, at least. :) You may need to range-reduce the argument first; see John Cook's suggestions. The book also has arcsin and arctan.

#include <math.h>
#include <stdio.h>

// Return an approx to sin(pi/2 * x) where -1 <= x <= 1.
// In that range it has a max absolute error of 5e-9
// according to Hastings, Approximations For Digital Computers.
static double xsin (double x) {
  double x2 = x * x;
  return ((((.00015148419 * x2
             - .00467376557) * x2
            + .07968967928) * x2
           - .64596371106) * x2
          + 1.57079631847) * x;
}

int main () {
  double pi = 4 * atan (1);
  printf ("%.10f\n", xsin (0.77));
  printf ("%.10f\n", sin (0.77 * (pi/2)));
  return 0;
}