Complex arithmetic bug: creal(0+I*Inf) -> NaN

[jwuttke]

In C99, there is no constructor for complex numbers. We need to write z = a + I*b. When b is Inf, then z becomes NaN. In numeric code, however, it may make perfect sense to rely on Re(z) = a.

This problem is known at since 12 years [1]. Other compilers (gcc, MSVC) do it right.

[1] https://www.mail-archive.com/freebsd-toolchain@freebsd.org/msg00000.html

[llvmbot]

@llvm/issue-subscribers-clang-frontend

[AaronBallman]

From C2x Annex G.3p1: "A complex or imaginary value with at least one infinite part is regarded as an infinity (even if its other part is a quiet NaN). A complex or imaginary value is a finite number if each of its parts is a finite number (neither infinite nor NaN). A complex or imaginary value is a zero if each of its parts is a zero."

So I believe z should be inf rather than a.

[jwuttke]

You are refering to https://www.open-std.org/jtc1/sc22/wg14/www/docs/n3054.pdf, right?

Sect G3, which you quoted in full length, says that a+I*inf is to be regarded as infinity. This is important for function like isfinite or isnan. It has no implications whatsoever for addition.

The addition operator is treated in Sect G5.2, which however only states the obvious, and does not explicitly refer to infinities.

For our purpose most helpful is Sect G6, which specifies some function values for infinite arguments. Specfically, G6.1.1 says about the complex arccos function: "cacos(x + i∞) returns π2 − i∞, for finite x." From this it is absolutely clear that complex numbers with one finite and one infinite component should be supported as such.

[AaronBallman]

You are refering to https://www.open-std.org/jtc1/sc22/wg14/www/docs/n3054.pdf, right?

Correct

Sect G3, which you quoted in full length, says that a+I*inf is to be regarded as infinity. This is important for function like isfinite or isnan. It has no implications whatsoever for addition.

I may not be understanding the summary of the issue then. I was under the impression that z = a + I*b is currently resulting in z being NaN when it should be infinity when b is infinity, but that you were looking for z to be a instead of NaN or infinity.

I might be getting thrown off by having no idea what type z, a, or b are. Or the fact that my last use of complex math was decades ago...

The addition operator is treated in Sect G5.2, which however only states the obvious, and does not explicitly refer to infinities.

For our purpose most helpful is Sect G6, which specifies some function values for infinite arguments. Specfically, G6.1.1 says about the complex arccos function: "cacos(x + i∞) returns π2 − i∞, for finite x." From this it is absolutely clear that complex numbers with one finite and one infinite component should be supported as such.

I think I agree, but given my confidence level, I'm going to CC @jcranmer-intel for a second opinion that this issue should be confirmed.

[jwuttke]

I was under the impression that z = a + I*b is currently resulting in z being NaN when it should be infinity when b is infinity, but that you were looking for z to be a instead of NaN or infinity.

I might be getting thrown off by having no idea what type z, a, or b are. Or the fact that my last use of complex math was decades ago...

Say, a and b are of type double, and z is double complex. The internal representation of z is a pair of doubles. Say, z=(re_z,im_z). So, my request is that the code line z = a + I*b should result in re_z=a and im_z=b. Which can be tested by calling the function creal(z), which always should return a, but currently does not in case that b is infinite.