IntelPython / dpnp / 28585342286

78%

push

github

Improve handling of large values by inverse hyperbolic and trigonometric functions (#2928)

The `dpnp.tensor.acosh` function was returning incorrect results
(infinity) for complex numbers with large negative real parts (see
#2924, #2896).

The issue was caused by the threshold used `1/epsilon` to decide when to
switch from acos in SYCL's experimental complex extension
(`exprm_ns::acos()`) to a log-based formula.
The SYCL `exprm_ns::acos()` returns incorrect results for large negative
real parts, due to used formula `z + sqrt(z² - 1)`, which leads to
`log(0) = -infinity`.

The PR proposes to change the threshold from `1/epsilon` to
`sqrt(1/epsilon)/2` for all inverse trig/hyperbolic functions. This is
the precision loss point where `sqrt(z² ± 1)` calculations become
unstable.

Also the PR reduces code duplication by creating shared `casinh()`,
`casin()`, `catanh()`, `catan()` functions in new `complex_math.hpp`
header.

1532 of 2854 branches covered (53.68%)

Branch coverage included in aggregate %.

25994 of 32386 relevant lines covered (80.26%)

8013.58 hits per line