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Date: Tue, 28 May 2024 16:48:23 -0400
From: Nikolaos Chatzikonstantinou <>
Subject: Re: Implementing csqrtl()

On Mon, Jul 4, 2022 at 5:35 AM Nikolaos Chatzikonstantinou
<> wrote:
> Hello list,
> I wanted to implement some function from
> <>
> which is an open issue in the wiki.
> One of the missing complex functions is csqrtl(), the long double
> version of complex square root. I was able to find a 1987 article from
> W. Kahan, titled "Branch cuts for complex elementary functions." that
> contained an implementation for complex square root for arbitrary
> floating-point numbers. In this e-mail you'll find an attached git
> patch with the implementation.
> As a very basic test, I wrote a program that produces random
> complex numbers in the square [0, N] x [0, N] for N=1,100 and
> calculates csqrt{,f,l}() with my implementation, glibc and the
> arbitrary precision mpc_sqrt() from MPC,
> <>.
> Glibc stays almost within 1 ulp in float and double, but my
> implementation wasn't so good with float. The double
> implementation seems to get the exact same results as glibc does.
> I was not able to even test the long double version with this
> method, because I did not write the code that produces random
> long double complex numbers yet.
> There's a few things that I don't quite understand here. One is, I'm
> not sure why Kahan's implementation is accurate. For another, I don't
> know how to do any sort of speed tests; I've read online that
> microbenchmarking is not reproducible for math functions, and so
> google's benchmark <> does not seem
> to help. Of course I'm aware that the C implementation would not be
> the one used in most systems, as the assembly implementations are
> usually better. Finally, I don't know what the right way to test an
> implementation for accuracy is: whether by using automation or writing
> proofs. It seems the state of the art has evolved quite a bit from
> 1987, and yet I don't know where to look for information on this
> topic, as it seems very specific to chips & the C std lib.
> Feel free to provide any sort of criticism. I'm e-mailing this
> implementation for the purpose of starting a discussion, but I'm
> hoping to be able to contribute something in the near future.

Hello, I want to revive the discussion on this message. Last time I
attached the patch I was ignored, apart from some nitpicks on the C
source in the patch, which was a draft anyway. Missing complex math
functions are still an open issue. I can't help but think that last
time I was ignored apart from some nitpick on some signed/unsigned
type, as if getting schooled on C is the purpose of the mailing list
-- bizarre! the patch was a draft to start a discussion on resolving
the complex math issue. What I concluded from the responses I received
is that the musl project does not have a maintainer who is capable of
understanding the underlying issues with the complex math algorithms
in libc. Is that still the case and is there any interest in resolving
it perhaps by finding a maintainer who can work on this issue?

Nikolaos Chatzikonstantinou

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