def frexp(x):
"""
Version of frexp that works for numbers with uncertainty, and also
for regular numbers.
"""
# The code below is inspired by uncert_core.wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
aff_func = to_affine_scalar(x)
if aff_func._linear_part:
(mantissa, exponent) = math.frexp(aff_func.nominal_value)
return (
AffineScalarFunc(
mantissa,
# With frexp(x) = (m, e), x = m*2**e, so m = x*2**-e
# and therefore dm/dx = 2**-e (as e in an integer that
# does not vary when x changes):
LinearCombination([2**-exponent, aff_func._linear_part])),
# The exponent is an integer and is supposed to be
# continuous (errors must be small):
exponent)
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
return math.frexp(x)
def frexp(x):
"""
Version of frexp that works for numbers with uncertainty, and also
for regular numbers.
"""
# The code below is inspired by uncert_core.wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
aff_func = to_affine_scalar(x)
if aff_func.derivatives:
result = math.frexp(aff_func.nominal_value)
# With frexp(x) = (m, e), dm/dx = 1/(2**e):
factor = 1 / (2**result[1])
return (
AffineScalarFunc(
result[0],
# Chain rule:
dict([(var, factor * deriv)
for (var, deriv) in aff_func.derivatives.iteritems()])),
# The exponent is an integer and is supposed to be
# continuous (small errors):
result[1])
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
return math.frexp(x)
def ldexp(x, y):
# The code below is inspired by uncert_core.wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
# Another approach would be to add an additional argument to
# uncert_core.wrap() so that some arguments are automatically
# considered as constants.
aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
if aff_func.derivatives:
factor = 2**y
return AffineScalarFunc(
math.ldexp(aff_func.nominal_value, y),
# Chain rule:
dict([(var, factor * deriv)
for (var, deriv) in aff_func.derivatives.iteritems()]))
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
# aff_func.nominal_value is not passed instead of x, because
# we do not have to care about the type of the return value of
# math.ldexp, this way (aff_func.nominal_value might be the
# value of x coerced to a difference type [int->float, for
# instance]):
return math.ldexp(x, y)
def ldexp(x, i):
# Another approach would be to add an additional argument to
# uncert_core.wrap() so that some arguments are automatically
# considered as constants.
aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
if aff_func._linear_part:
return AffineScalarFunc(
math.ldexp(aff_func.nominal_value, i),
LinearCombination([(2**i, aff_func._linear_part)]))
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
# aff_func.nominal_value is not passed instead of x, because
# we do not have to care about the type of the return value of
# math.ldexp, this way (aff_func.nominal_value might be the
# value of x coerced to a difference type [int->float, for
# instance]):
return math.ldexp(x, i)
def modf(x):
"""
Version of modf that works for numbers with uncertainty, and also
for regular numbers.
"""
# The code below is inspired by uncert_core.wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
aff_func = to_affine_scalar(x) # Uniform treatment of all numbers
(frac_part, int_part) = math.modf(aff_func.nominal_value)
if aff_func._linear_part: # If not a constant
# The derivative of the fractional part is simply 1: the
# linear part of modf(x)[0] is the linear part of x:
return (AffineScalarFunc(frac_part, aff_func._linear_part), int_part)
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
return (frac_part, int_part)