fredrik-johansson / arbcmath Goto Github PK

Greetings, I'm interested in using your 2f1 methods in an academic publication. I see you released everything in the public domain (which I'm very grateful for), but I'm curious if you have any additional information you might like included (i.e., citation). Is this something that's been published in any journals or proceedings?

Thanks again for this.

SG

a@zelman:/arbcmath$ export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib/
a@zelman:/arbcmath$ gcc example.c -larb -lflint -lgmp -lmpfr -lpthread -Wall
In file included from example.c:1:0:
arbcmath.h: In function ‘_acb_init_set_c’:
arbcmath.h:21:1: warning: no return statement in function returning non-void [-Wreturn-type]
}

The output, if finite, is guaranteed to have a relative error that is at most a small multiple of 2^-53 (todo: specify an explicit multiple here), unless the function value is so small that this value underflows to zero.

If arbcmath keeps increasing the working precision until acb_rel_accuracy_bits(out1) >= 53 then doesn't this mean the relative error will be at most 2^-53? I don't understand the part about small multiples. Is it due to using complex numbers? Would a similar module for real-valued functions have the same caveat about small multiples?