68 lines
2.4 KiB
Python
68 lines
2.4 KiB
Python
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# This file is part of Hypothesis, which may be found at
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# https://github.com/HypothesisWorks/hypothesis/
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#
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# Most of this work is copyright (C) 2013-2021 David R. MacIver
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# (david@drmaciver.com), but it contains contributions by others. See
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# CONTRIBUTING.rst for a full list of people who may hold copyright, and
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# consult the git log if you need to determine who owns an individual
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# contribution.
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#
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# This Source Code Form is subject to the terms of the Mozilla Public License,
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# v. 2.0. If a copy of the MPL was not distributed with this file, You can
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# obtain one at https://mozilla.org/MPL/2.0/.
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#
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# END HEADER
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from math import fabs, inf, isinf, isnan, nan, sqrt
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from sys import float_info
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def cathetus(h, a):
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"""Given the lengths of the hypotenuse and a side of a right triangle,
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return the length of the other side.
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A companion to the C99 hypot() function. Some care is needed to avoid
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underflow in the case of small arguments, and overflow in the case of
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large arguments as would occur for the naive implementation as
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sqrt(h*h - a*a). The behaviour with respect the non-finite arguments
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(NaNs and infinities) is designed to be as consistent as possible with
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the C99 hypot() specifications.
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This function relies on the system ``sqrt`` function and so, like it,
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may be inaccurate up to a relative error of (around) floating-point
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epsilon.
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Based on the C99 implementation https://github.com/jjgreen/cathetus
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"""
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if isnan(h):
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return nan
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if isinf(h):
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if isinf(a):
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return nan
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else:
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# Deliberately includes the case when isnan(a), because the
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# C99 standard mandates that hypot(inf, nan) == inf
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return inf
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h = fabs(h)
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a = fabs(a)
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if h < a:
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return nan
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# Thanks to floating-point precision issues when performing multiple
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# operations on extremely large or small values, we may rarely calculate
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# a side length that is longer than the hypotenuse. This is clearly an
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# error, so we clip to the hypotenuse as the best available estimate.
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if h > sqrt(float_info.max):
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if h > float_info.max / 2:
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b = sqrt(h - a) * sqrt(h / 2 + a / 2) * sqrt(2)
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else:
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b = sqrt(h - a) * sqrt(h + a)
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elif h < sqrt(float_info.min):
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b = sqrt(h - a) * sqrt(h + a)
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else:
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b = sqrt((h - a) * (h + a))
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return min(b, h)
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