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numeric_limits¶
View page sourceNumeric Limits For an AD and Base Types¶
Syntax¶
numeric_limits < Float >:: epsilon ()numeric_limits < Float >:: min ()numeric_limits < Float >:: max ()numeric_limits < Float >:: quiet_NaN ()numeric_limits < Float >:: infinity ()numeric_limits < Float >:: digits10numeric_limits < Float >:: max_digits10CppAD::numeric_limits¶
The functions above and have the prototype
staticFloatCppAD::numeric_limits<Float >:: fun ( void )
where fun is
epsilon , min , max , quiet_NaN , and infinity .
The values digits10 and max_digits10 are
member variable and not a functions.
std::numeric_limits¶
CppAD does not use a specialization of std::numeric_limits
because this would be to restrictive.
The C++ standard specifies that Non-fundamental standard
types, such as
std::complex<double>
shall not have specializations
of std::numeric_limits ; see Section 18.2 of
ISO/IEC 14882:1998(E).
In addition, since C++11, a only literal types can have a specialization
of std::numeric_limits .
Float¶
These functions are defined for all AD < Base > ,
and for all corresponding Base types;
see Base type base_limits .
epsilon¶
The result eps is equal to machine epsilon and has prototype
Float eps
The file num_limits.cpp tests the value eps by checking that the following are true
where all the values, and calculations, are done with the precision corresponding to Float .
min¶
The result min is equal to the minimum positive normalized value and has prototype
Float min
The file num_limits.cpp tests the value min by checking that the following are true
abs ( (( min / 100) * 100) / min - 1 ) > 3 * epsabs ( (( min * 100) / 100) / min - 1 ) < 3 * epswhere all the values, and calculations, are done with the precision corresponding to Float .
max¶
The result max is equal to the maximum finite value and has prototype
Float max
The file num_limits.cpp tests the value max by checking that the following are true
abs ( (( max * 100) / 100) / max - 1 ) > 3 * epsabs ( (( max / 100) * 100) / max - 1 ) < 3 * epswhere all the values, and calculations, are done with the precision corresponding to Float .
quiet_NaN¶
The result nan is not a number and has prototype
Float nan
The file num_limits.cpp tests the value nan by checking that the following is true
nan != nan
infinity¶
The result inf is equal to the positive infinite value and has prototype
Float inf
The file num_limits.cpp tests the value inf by checking that the following are true
isnan ( inf - inf )digits10¶
The member variable digits10 has prototype
static const int numeric_limits< Float >::digits10
It is the number of decimal digits that can be represented by a Float value. A number with this many decimal digits can be converted to Float and back to a string, without change due to rounding or overflow.
max_digits10¶
The member variable max_digits10 has prototype
static const int numeric_limits< Float >::max_digits10
is the number of decimal digits that are necessary to uniquely represent all distinct values of the type Float . For example, the number of digits necessary to convert to text and back and get the exact same result.
Example¶
The file num_limits.cpp contains an example and test of these functions.