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| author | Adhemerval Zanella <adhemerval.zanella@linaro.org> | 2021-04-05 23:55:55 -0300 |
|---|---|---|
| committer | Adhemerval Zanella <adhemerval.zanella@linaro.org> | 2021-12-13 09:02:34 -0300 |
| commit | c212d6397e05d0ce65405706ea0b427a418ce5ef (patch) | |
| tree | 0ce65616f2207eca9aad2814f3b079de41d896e5 /libof-iterator.mk | |
| parent | aa9c28cde3966064bf2b05ca8d25c62b3e463688 (diff) | |
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math: Use an improved algorithm for hypotl (ldbl-128)
This implementation is based on '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 subnormal results.
The main advantage of the new algorithm is its precision. With a
random 1e9 input pairs in the range of [LDBL_MIN, LDBL_MAX], glibc
current implementation shows around 0.05% results with an error of
1 ulp (453266 results) while the new implementation only shows
0.0001% of total (1280).
Checked on aarch64-linux-gnu and x86_64-linux-gnu.
[1] https://arxiv.org/pdf/1904.09481.pdf
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