Raymond Hettinger <raymond.hettin...@gmail.com> added the comment:
> While we're doing this, any chance we could special-case
> the two-argument hypot to use the libm hypot directly?
Yes, that is an easy amendment (see below).
I just tried it out on the macOs build but didn't see a change in accuracy from
the current PR which uses lossless power-of-two-scaling and Neumaier summation.
In GCC's libquadmath implementation, the comments say that the error is less
than 1 ulp, falling short of being correctly rounded within ±½ ulp.
If the platform hypots have the nearly the same accuracy as the current PR, it
may make sense to skip the special case and opt for consistent cross-platform
results.
==================================================================
$ git diff
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index d0621f59df..3a42ea5318 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2457,6 +2457,10 @@ vector_norm(Py_ssize_t n, double *vec, double max, int
found_nan)
if (max == 0.0 || n <= 1) {
return max;
}
+ if (n == 2) {
+ /* C library hypot() implementations tend to be very accurate */
+ return hypot(vec[0], vec[1]);
+ }
frexp(max, &max_e);
if (max_e >= -1023) {
scale = ldexp(1.0, -max_e)
$ gcc --version
Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr
--with-gxx-include-dir=/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX.sdk/usr/include/c++/4.2.1
Apple clang version 11.0.3 (clang-1103.0.32.62)
Target: x86_64-apple-darwin19.6.0
Thread model: posix
InstalledDir:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin
$ ./python.exe test_hypot.py
======== 2 dimensions ========
platform hypot(): [(-1.0, 8398), (0.0, 83152), (1.0, 8450)]
scaled-by-2 : [(-1.0, 8412), (0.0, 83166), (1.0, 8422)]
----------
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<https://bugs.python.org/issue41513>
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