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bpo-41513: Second attempt to add accuracy tests for math.hypot() #22327

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Merged
merged 5 commits into from
Sep 21, 2020
Merged

bpo-41513: Second attempt to add accuracy tests for math.hypot() #22327

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58cbdbb
Revert "bpo-41513: Remove broken tests that fail on Gentoo (GH-22249)"
rhettinger Sep 19, 2020
5edc606
Add guards to bypass the test when double rounding can occur.
rhettinger Sep 19, 2020
9255115
Check Gentoo bot to determine which guard caused the tests to pass
rhettinger Sep 20, 2020
6da426d
Restore the requirement for IEEE_754
rhettinger Sep 21, 2020
1cd8b13
Generate more informative error messages
rhettinger Sep 21, 2020
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63 changes: 63 additions & 0 deletions Lib/test/test_math.py
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Original file line number Diff line number Diff line change
Expand Up @@ -803,6 +803,69 @@ def testHypot(self):
scale = FLOAT_MIN / 2.0 ** exp
self.assertEqual(math.hypot(4*scale, 3*scale), 5*scale)

@requires_IEEE_754
@unittest.skipIf(HAVE_DOUBLE_ROUNDING,
"hypot() loses accuracy on machines with double rounding")
def testHypotAccuracy(self):
# Verify improved accuracy in cases that were known to be inaccurate.
#
# The new algorithm's accuracy depends on IEEE 754 arithmetic
# guarantees, on having the usual ROUND HALF EVEN rounding mode, on
# the system not having double rounding due to extended precision,
# and on the compiler maintaining the specified order of operations.
#
# This test is known to succeed on most of our builds. If it fails
# some build, we either need to add another skipIf if the cause is
# identifiable; otherwise, we can remove this test entirely.

hypot = math.hypot
Decimal = decimal.Decimal
high_precision = decimal.Context(prec=500)

for hx, hy in [
# Cases with a 1 ulp error in Python 3.7 compiled with Clang
('0x1.10e89518dca48p+29', '0x1.1970f7565b7efp+30'),
('0x1.10106eb4b44a2p+29', '0x1.ef0596cdc97f8p+29'),
('0x1.459c058e20bb7p+30', '0x1.993ca009b9178p+29'),
('0x1.378371ae67c0cp+30', '0x1.fbe6619854b4cp+29'),
('0x1.f4cd0574fb97ap+29', '0x1.50fe31669340ep+30'),
('0x1.494b2cdd3d446p+29', '0x1.212a5367b4c7cp+29'),
('0x1.f84e649f1e46dp+29', '0x1.1fa56bef8eec4p+30'),
('0x1.2e817edd3d6fap+30', '0x1.eb0814f1e9602p+29'),
('0x1.0d3a6e3d04245p+29', '0x1.32a62fea52352p+30'),
('0x1.888e19611bfc5p+29', '0x1.52b8e70b24353p+29'),

# Cases with 2 ulp error in Python 3.8
('0x1.538816d48a13fp+29', '0x1.7967c5ca43e16p+29'),
('0x1.57b47b7234530p+29', '0x1.74e2c7040e772p+29'),
('0x1.821b685e9b168p+30', '0x1.677dc1c1e3dc6p+29'),
('0x1.9e8247f67097bp+29', '0x1.24bd2dc4f4baep+29'),
('0x1.b73b59e0cb5f9p+29', '0x1.da899ab784a97p+28'),
('0x1.94a8d2842a7cfp+30', '0x1.326a51d4d8d8ap+30'),
('0x1.e930b9cd99035p+29', '0x1.5a1030e18dff9p+30'),
('0x1.1592bbb0e4690p+29', '0x1.a9c337b33fb9ap+29'),
('0x1.1243a50751fd4p+29', '0x1.a5a10175622d9p+29'),
('0x1.57a8596e74722p+30', '0x1.42d1af9d04da9p+30'),

# Cases with 1 ulp error in version fff3c28052e6b0
('0x1.ee7dbd9565899p+29', '0x1.7ab4d6fc6e4b4p+29'),
('0x1.5c6bfbec5c4dcp+30', '0x1.02511184b4970p+30'),
('0x1.59dcebba995cap+30', '0x1.50ca7e7c38854p+29'),
('0x1.768cdd94cf5aap+29', '0x1.9cfdc5571d38ep+29'),
('0x1.dcf137d60262ep+29', '0x1.1101621990b3ep+30'),
('0x1.3a2d006e288b0p+30', '0x1.e9a240914326cp+29'),
('0x1.62a32f7f53c61p+29', '0x1.47eb6cd72684fp+29'),
('0x1.d3bcb60748ef2p+29', '0x1.3f13c4056312cp+30'),
('0x1.282bdb82f17f3p+30', '0x1.640ba4c4eed3ap+30'),
('0x1.89d8c423ea0c6p+29', '0x1.d35dcfe902bc3p+29'),
]:
x = float.fromhex(hx)
y = float.fromhex(hy)
with self.subTest(hx=hx, hy=hy, x=x, y=y):
with decimal.localcontext(high_precision):
z = float((Decimal(x)**2 + Decimal(y)**2).sqrt())
self.assertEqual(hypot(x, y), z)

def testDist(self):
from decimal import Decimal as D
from fractions import Fraction as F
Expand Down