`erfc` inaccurate results in non-constant batches

[petiaccja]

I ran into an issue with xsimd::erfc. For batches that have the same value in all their elements, the results look correct, however, for batches that have different values in their elements, the erfc function may be calculated inaccurately for some elements. The error can be large, above 100 ULP.

Repro

Version: xsimd/11.1.0 (conan)
ISA: SSE2, x86-64, AMD Ryzen

xsimd::batch<float, xsimd::sse2> v_ = { 0.5f, 0.6f, 0.7f, 0.8f };
xsimd::batch<float, xsimd::sse2> c1 = { 0.5f, 0.5f, 0.5f, 0.5f };
xsimd::batch<float, xsimd::sse2> c2 = { 0.6f, 0.6f, 0.6f, 0.6f };
xsimd::batch<float, xsimd::sse2> c3 = { 0.7f, 0.7f, 0.7f, 0.7f };
xsimd::batch<float, xsimd::sse2> c4 = { 0.8f, 0.8f, 0.8f, 0.8f };
std::cout << xsimd::erfc(v_) << std::endl;
std::cout << xsimd::erfc(c1) << std::endl;
std::cout << xsimd::erfc(c2) << std::endl;
std::cout << xsimd::erfc(c3) << std::endl;
std::cout << xsimd::erfc(c4) << std::endl;

Observed vs. expected behaviour:

The code above produces the following output:

(0.4795, 0.396144, 0.3222, 0.257916)
(0.4795, 0.4795, 0.4795, 0.4795)
(0.396144, 0.396144, 0.396144, 0.396144)
(0.322199, 0.322199, 0.322199, 0.322199)
(0.257899, 0.257899, 0.257899, 0.257899)

The last element of erfc(v_) should be equal to all elements of erfc(c4), however 0.257916 != 0.257899. The accurate value of Erfc[0.8] equals 0.2578990352923395... according to Wolfram Mathematica, so the heterogeneous batch is not calculated correctly.