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backend/venv/Lib/site-packages/hypothesis/internal/cathetus.py

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+# This file is part of Hypothesis, which may be found at
+# https://github.com/HypothesisWorks/hypothesis/
+#
+# Copyright the Hypothesis Authors.
+# Individual contributors are listed in AUTHORS.rst and the git log.
+#
+# This Source Code Form is subject to the terms of the Mozilla Public License,
+# v. 2.0. If a copy of the MPL was not distributed with this file, You can
+# obtain one at https://mozilla.org/MPL/2.0/.
+
+from math import fabs, inf, isinf, isnan, nan, sqrt
+from sys import float_info
+
+
+def cathetus(h, a):
+    """Given the lengths of the hypotenuse and a side of a right triangle,
+    return the length of the other side.
+
+    A companion to the C99 hypot() function.  Some care is needed to avoid
+    underflow in the case of small arguments, and overflow in the case of
+    large arguments as would occur for the naive implementation as
+    sqrt(h*h - a*a).  The behaviour with respect the non-finite arguments
+    (NaNs and infinities) is designed to be as consistent as possible with
+    the C99 hypot() specifications.
+
+    This function relies on the system ``sqrt`` function and so, like it,
+    may be inaccurate up to a relative error of (around) floating-point
+    epsilon.
+
+    Based on the C99 implementation https://github.com/jjgreen/cathetus
+    """
+    if isnan(h):
+        return nan
+
+    if isinf(h):
+        if isinf(a):
+            return nan
+        else:
+            # Deliberately includes the case when isnan(a), because the
+            # C99 standard mandates that hypot(inf, nan) == inf
+            return inf
+
+    h = fabs(h)
+    a = fabs(a)
+
+    if h < a:
+        return nan
+
+    # Thanks to floating-point precision issues when performing multiple
+    # operations on extremely large or small values, we may rarely calculate
+    # a side length that is longer than the hypotenuse.  This is clearly an
+    # error, so we clip to the hypotenuse as the best available estimate.
+    if h > sqrt(float_info.max):
+        if h > float_info.max / 2:
+            b = sqrt(h - a) * sqrt(h / 2 + a / 2) * sqrt(2)
+        else:
+            b = sqrt(h - a) * sqrt(h + a)
+    elif h < sqrt(float_info.min):
+        b = sqrt(h - a) * sqrt(h + a)
+    else:
+        b = sqrt((h - a) * (h + a))
+    return min(b, h)