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bpo-41513: Improve speed and accuracy of math.hypot() #21803

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Merged
rhettinger merged 10 commits into from
Aug 16, 2020
+44 −6
Merged

bpo-41513: Improve speed and accuracy of math.hypot() #21803

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e2b1b38
frexp/ldexp variant
rhettinger Aug 8, 2020
7cb895d
Multiply by power of two variant
rhettinger Aug 8, 2020
2d586b1
Strengthen assertions
rhettinger Aug 9, 2020
c15ce79
Added notes and commented out assertions to reach a stable resting point
rhettinger Aug 9, 2020
c853597
Two code paths. All tests pass.
rhettinger Aug 9, 2020
03ec58b
Clean-up comments and ranges
rhettinger Aug 10, 2020
ebf6a31
Remove debugging code
rhettinger Aug 10, 2020
4742ef8
Clean-up comments and over-specified tests
rhettinger Aug 10, 2020
5e9f1a9
Add blurb
rhettinger Aug 10, 2020
5c6478f
Improve the comments.
rhettinger Aug 15, 2020
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Clean-up comments and over-specified tests
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@rhettinger
rhettinger committed Aug 10, 2020
commit 4742ef8aaac225f52e682e04a30882716cad14a9
3 changes: 2 additions & 1 deletion Lib/test/test_math.py
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Expand Up @@ -795,7 +795,8 @@ def testHypot(self):
# Verify scaling for extremely large values
fourthmax = FLOAT_MAX / 4.0
for n in range(32):
self.assertEqual(hypot(*([fourthmax]*n)), fourthmax * math.sqrt(n))
self.assertTrue(math.isclose(hypot(*([fourthmax]*n)),
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fourthmax * math.sqrt(n)))

# Verify scaling for extremely small values
for exp in range(32):
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12 changes: 5 additions & 7 deletions Modules/mathmodule.c
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Expand Up @@ -2458,12 +2458,7 @@ vector_norm(Py_ssize_t n, double *vec, double max, int found_nan)
return max;
}
frexp(max, &max_e);
if (-1020 <= max_e && max_e <= 1020) {
/* Stay away from extreme values.
ldexp(1.0, -1075) returns zero.
ldexp(1.0, -1023) is subnormal.
ldexp(1.0, 1024) gives Inf.
*/
if (max_e >= -1023) {
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scale = ldexp(1.0, -max_e);
assert(max * scale >= 0.5);
assert(max * scale < 1.0);
Expand All @@ -2480,7 +2475,10 @@ vector_norm(Py_ssize_t n, double *vec, double max, int found_nan)
}
return sqrt(csum - 1.0 + frac) / scale;
}
/* Near extreme values, just divide by *max*. */
/* When max_e < -1023, a scale computed given by ldexp(1.0, -max_e)
would be subnormal and break range invariants for max*scale.
Instead, we just divide by *max*.
*/
for (i=0 ; i < n ; i++) {
x = vec[i];
assert(Py_IS_FINITE(x) && fabs(x) <= max);
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