def round(x, ndigits=0):
"""
round(number[, ndigits]) - double-precision real number
Round a number to a given precision in decimal digits (default 0
digits). If no precision is specified this just calls the element's
.round() method.
EXAMPLES::
sage: round(sqrt(2),2)
1.41
sage: q = round(sqrt(2),5); q
1.41421
sage: type(q)
<type 'sage.rings.real_double.RealDoubleElement'>
sage: q = round(sqrt(2)); q
1
sage: type(q)
<type 'sage.rings.integer.Integer'>
sage: round(pi)
3
sage: b = 5.4999999999999999
sage: round(b)
5
Since we use floating-point with a limited range, some roundings can't
be performed::
sage: round(sqrt(Integer('1'*1000)),2)
+infinity
IMPLEMENTATION: If ndigits is specified, it calls Python's builtin
round function, and converts the result to a real double field
element. Otherwise, it tries the argument's .round() method; if
that fails, it reverts to the builtin round function, converted to
a real double field element.
.. note::
This is currently slower than the builtin round function, since
it does more work - i.e., allocating an RDF element and
initializing it. To access the builtin version do
``from six.moves import builtins; builtins.round``.
"""
try:
if ndigits:
return RealDoubleElement(builtins.round(x, ndigits))
else:
try:
return x.round()
except AttributeError:
return RealDoubleElement(builtins.round(x, 0))
except ArithmeticError:
if not isinstance(x, RealDoubleElement):
return round(RDF(x), ndigits)
else:
raise
def round(x, ndigits=0):
"""
round(number[, ndigits]) - double-precision real number
Round a number to a given precision in decimal digits (default 0
digits). If no precision is specified this just calls the element's
.round() method.
EXAMPLES::
sage: round(sqrt(2),2)
1.41
sage: q = round(sqrt(2),5); q
1.41421
sage: type(q)
<type 'sage.rings.real_double.RealDoubleElement'>
sage: q = round(sqrt(2)); q
1
sage: type(q)
<type 'sage.rings.integer.Integer'>
sage: round(pi)
3
sage: b = 5.4999999999999999
sage: round(b)
5
Since we use floating-point with a limited range, some roundings can't
be performed::
sage: round(sqrt(Integer('1'*1000)),2)
+infinity
IMPLEMENTATION: If ndigits is specified, it calls Python's builtin
round function, and converts the result to a real double field
element. Otherwise, it tries the argument's .round() method; if
that fails, it reverts to the builtin round function, converted to
a real double field element.
.. note::
This is currently slower than the builtin round function, since
it does more work - i.e., allocating an RDF element and
initializing it. To access the builtin version do
``from six.moves import builtins; builtins.round``.
"""
try:
if ndigits:
return RealDoubleElement(builtins.round(x, ndigits))
else:
try:
return x.round()
except AttributeError:
return RealDoubleElement(builtins.round(x, 0))
except ArithmeticError:
if not isinstance(x, RealDoubleElement):
return round(RDF(x), ndigits)
else:
raise