The `atanhl` function is broken under Rosetta 2 with 80-bit long
doubles, which numpy uses to implement long double complex numbers. This
results in a test failure. Attempts were made to change the
implementation of things, but that just changed the breakage.
The following Swift program demonstrates the problem.
import Foundation
import Numerics
let x = Float80(1.00000000e-20)
let z = Complex(x)
print("X: \(x), Z: \(z)")
let x_atanh = Float80.atanh(x)
let z_atanh = Complex.atanh(z)
print("atanh:")
print("X: \(x_atanh), Z: \(z_atanh)")
let d = abs(x_atanh / z_atanh.real - 1)
print("d: \(d)")
On x86_64-darwin hardware, it prints the following:
X: 1e-20, Z: (1e-20, 0.0)
atanh:
X: 1e-20, Z: (1e-20, 0.0)
d: 0.0
On aarch64-darwin under Rosetta 2, it prints the following:
X: 1e-20, Z: (1e-20, 0.0)
atanh:
X: 1e-20, Z: (-1.0237493319595677839e-40, 0.0)
d: 9.7680161420558978584e+19
The latter is obviously incorrect. FB12656897 was submitted to Apple,
but even if this is fixed eventually, this derivation needs to build for
users (and Hydra) who aren’t on the latest version.
