[I globally edited the question to be more "useful" and clear]
Hello all,
I was wondering about the complexity of the implementation of the function exp
in cmath.
By complexity, I mean algorithmic complexity if possible. Otherwise cost compared to a floating point operation (addition for example)
The following lines :
double x = 3;
double y = std::exp(x);
compile to :
...
19,23d16
movq %rax, -40(%rbp)
movsd -40(%rbp), %xmm0
call exp
movsd %xmm0, -40(%rbp)
movq -40(%rbp), %rax
...
exp
has to be dynamically loaded at runtime but I can't find many information on the implementation algorithmic complexity. It seems there's no call to a special processor instruction (at least on my x86_64 platform with gcc) so there must be an implementation somewhere that I can't find.
On my mind, the algorithm is likely to use the binary representation of the input to have a very weak complexity but I haven't been able to find a valuable reference on this topic.
Maybe speaking of algorithmical complexity is not really possible in this case and all what we can do is testing (cf. answers below) but I don't know how we can quantify objectively the difference between a floating point operation and a call to exp ?