Are cmath exp() and log() functions always symmetrical?

问题

Are cmath exp() and log() functions always symmetrical?

Ergo if I do

double x;
double y = exp(log(x));
assert(x == y);

will the assert ever fail, and in that case: under what circumstances? We can assume that x is a rational number > 0.

回答1:

A floating-point log cannot be one-to-one. It needs to be monotone increasing and satisfy log(64) > 4.15 and log(128) < 4.86. There are 2⁵²doubles between 64 and 128, but there are fewer than 2⁵⁰doubles between 4.15 and 4.86. There are multiple doubles in that range with the same double-precision logarithm, so exp(log(x)) == x must fail for at least one of them.

回答2:

They are no more symmetrical than * and /. When dealing with floating point numbers there are rounding errors, so x and y may differ in the 15th (or so) digit.

来源：https://stackoverflow.com/questions/16913277/are-cmath-exp-and-log-functions-always-symmetrical