Calculate log (x - y) given by log (x) and log (y) without overflow?

The following function calculates log(x + y)

, taking into account the values log(x)

and log(y)

, avoiding overflows or overflows, if x

either y

very large or very small:

double log_add(double logx, double logy)
    return max(logx, logy) + log1p(exp(-fabs(logx - logy)));


There log(x - y)

must be a similar function for the calculation log_sub

. What is it?

More generally, I need to compute log(x - y - z)

given log(x)

, log(y)

and log(z)

. From log_add

and log_sub

I can calculate log(x - y - z)

in two steps, but maybe there is an optimal way?


source to share

1 answer

Why not just go straight from identities :

double log_add(double logx, double logy) {
    return logx + log1p(exp(logy - logx));

double log_sub(double logx, double logy) {
    return logx + log1p(-exp(logy - logx));


In your specific case:

// log(x - y - z) given the three logs
double log_xyz(double logx, double logy, double logz) {
    return logx + log1p(-exp(logy - logx) - exp(logz - logx));




All Articles