faster Math.exp() via JNI?

Question

I need to calculate Math.exp() from java very frequently, is it possible to get a native version to run faster than java\'s Math.exp()

Answer 1

I run a fitting algorithm and the minimum error of the fitting result is way larger than the precision of the Math.exp().

Transcendental functions are always much more slower than addition or multiplication and a well-known bottleneck. If you know that your values are in a narrow range, you can simply build a lookup-table (Two sorted array ; one input, one output). Use Arrays.binarySearch to find the correct index and interpolate value with the elements at [index] and [index+1].

Another method is to split the number. Lets take e.g. 3.81 and split that in 3+0.81. Now you multiply e = 2.718 three times and get 20.08.

Now to 0.81. All values between 0 and 1 converge fast with the well-known exponential series

1+x+x^2/2+x^3/6+x^4/24.... etc.

Take as much terms as you need for precision; unfortunately it's slower if x approaches 1. Lets say you go to x^4, then you get 2.2445 instead of the correct 2.2448

Then multiply the result 2.781^3 = 20.08 with 2.781^0.81 = 2.2445 and you have the result 45.07 with an error of one part of two thousand (correct: 45.15).