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6c848d7038
This implementation is based on the 'An Improved Algorithm for
hypot(a,b)' by Carlos F. Borges [1] using the MyHypot3 with the
following changes:
- Handle qNaN and sNaN.
- Tune the 'widely varying operands' to avoid spurious underflow
due the multiplication and fix the return value for upwards
rounding mode.
- Handle required underflow exception for denormal results.
The main advantage of the new algorithm is its precision: with a
random 1e9 input pairs in the range of [DBL_MIN, DBL_MAX], glibc
current implementation shows around 0.34% results with an error of
1 ulp (3424869 results) while the new implementation only shows
0.002% of total (18851).
The performance result are also only slight worse than current
implementation. On x86_64 (Ryzen 5900X) with gcc 12:
Before:
"hypot": {
"workload-random": {
"duration": 3.73319e+09,
"iterations": 1.12e+08,
"reciprocal-throughput": 22.8737,
"latency": 43.7904,
"max-throughput": 4.37184e+07,
"min-throughput": 2.28361e+07
}
}
After:
"hypot": {
"workload-random": {
"duration": 3.7597e+09,
"iterations": 9.8e+07,
"reciprocal-throughput": 23.7547,
"latency": 52.9739,
"max-throughput": 4.2097e+07,
"min-throughput": 1.88772e+07
}
}
Co-Authored-By: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Checked on x86_64-linux-gnu and aarch64-linux-gnu.
[1] https://arxiv.org/pdf/1904.09481.pdf
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