Log Domain Computations

code.java

/*
First off, logAdd() takes two arguments of type double in log space, logX and logY.
It returns a double value which closely approximates log(X + Y). Consequently, the inputs and output are in log space, and we need not convert in and out of log space to complete this operation.
*/
public static double logAdd(double logX, double logY) {
       // 1. make X the max
       if (logY > logX) {
           double temp = logX;
           logX = logY;
           logY = temp;
       }
       // 2. now X is bigger
       if (logX == Double.NEGATIVE_INFINITY) {
           return logX;
       }
       // 3. how far "down" (think decibels) is logY from logX?
       //    if it's really small (20 orders of magnitude smaller), then ignore
       double negDiff = logY - logX;
       if (negDiff < -20) {
           return logX;
       }
       // 4. otherwise use some nice algebra to stay in the log domain
       //    (except for negDiff)
       return logX + java.lang.Math.log(1.0 + java.lang.Math.exp(negDiff));
   }