def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
msg=None):
"""Fail if the two floating-point numbers are not almost equal.
Determine whether floating-point values a and b are equal to within
a (small) rounding error. The default values for rel_err and
abs_err are chosen to be suitable for platforms where a float is
represented by an IEEE 754 double. They allow an error of between
9 and 19 ulps.
"""
# special values testing
if math.isnan(a):
if math.isnan(b):
return
self.fail(msg or '{!r} should be nan'.format(b))
if math.isinf(a):
if a == b:
return
self.fail(msg or 'finite result where infinity expected: '
'expected {!r}, got {!r}'.format(a, b))
# if both a and b are zero, check whether they have the same sign
# (in theory there are examples where it would be legitimate for a
# and b to have opposite signs; in practice these hardly ever
# occur).
if not a and not b:
if math.copysign(1., a) != math.copysign(1., b):
self.fail(msg or 'zero has wrong sign: expected {!r}, '
'got {!r}'.format(a, b))
# if a-b overflows, or b is infinite, return False. Again, in
# theory there are examples where a is within a few ulps of the
# max representable float, and then b could legitimately be
# infinite. In practice these examples are rare.
try:
absolute_error = abs(b-a)
except OverflowError:
pass
else:
# test passes if either the absolute error or the relative
# error is sufficiently small. The defaults amount to an
# error of between 9 ulps and 19 ulps on an IEEE-754 compliant
# machine.
if absolute_error <= max(abs_err, rel_err * abs(a)):
return
self.fail(msg or
'{!r} and {!r} are not sufficiently close'.format(a, b))
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