The new release 1.11 is faster (use it) and much more uniformly accurate (accuracy is quite stable throughout function domains, even at the more tricky regions). Yes, faster and more accurate.
The results in comparisons with BigFloat are great!
However, at first the name of the package is a big strange, because in many programming language double is mainly 64 bits, while Double64 in your package is the double of Float64, so it has more decimal numbers than I was expecting.
However, it is a great work! I will note it to use it when I want a more precision than Float64, because clearly it is a lot more performance than BigFloat.
How does it compare now to Multifloats.jl?
Good question. Had not looked.
It is slower by too much. Working on that now,
Now, (v1.11.1) both exp and log are faster than MultiFloats.jl. Their accuracies are quite similar to MultiFloats. They exhibit better stability over difficult intervals.
DoubleFloats exp and log are ~50% faster.
N.B.: The current implementations of exp, log in DoubleFloats began with adapting MultiFloats.jl (David K. Zhang) algorithms for exp, log, Additional modifications and minor restructurings combine to enhance performance.
How did you get log that much faster?
There are two paths available to compute log, I choose the appropriate path very early. This lets me do less work than an alternative implementation.
How is the GPU implementation now?
I have a GPU version in development. Contact me to get at it.
Running Double32 on a GPU for matrix multiplication is much slower than running the matrix multiplication using Float64s on the CPU. The DoubleDouble structure does not appear to lend itself to GPU fastness. If you know better .. tell me.