numeric_limits.hpp

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# ifndef CPPAD_CORE_NUMERIC_LIMITS_HPP
# define CPPAD_CORE_NUMERIC_LIMITS_HPP
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
------------------------------------------------------------------------------
$begin numeric_limits$$
$spell
     std
     eps
     CppAD
     namespace
     const
$$

$section Numeric Limits For an AD and Base Types$$

$head Syntax$$
$icode%eps% = numeric_limits<%Float%>::epsilon()
%$$
$icode%min% = numeric_limits<%Float%>::min()
%$$
$icode%max% = numeric_limits<%Float%>::max()
%$$
$icode%nan% = numeric_limits<%Float%>::quiet_NaN()
%$$
$codei%numeric_limits<%Float%>::digits10%$$

$head CppAD::numeric_limits$$
These functions and have the prototype
$codei%
     static %Float% CppAD::numeric_limits<%Float%>::%fun%(%void%)
%$$
where $icode fun$$ is
$code epsilon$$, $code min$$, $code max$$, and $code quiet_NaN$$.
(Note that $code digits10$$ is member variable and not a function.)

$head std::numeric_limits$$
CppAD does not use a specialization of $code std::numeric_limits$$
because this would be to restrictive.
The C++ standard specifies that Non-fundamental standard
types, such as
$cref/std::complex<double>/base_complex.hpp/$$ shall not have specializations
of $code std::numeric_limits$$; see Section 18.2 of
ISO/IEC 14882:1998(E).
In addition, since C++11, a only literal types can have a specialization
of $code std::numeric_limits$$.

$head Float$$
These functions are defined for all $codei%AD<%Base%>%$$,
and for all corresponding $icode Base$$ types;
see $icode Base$$ type $cref base_limits$$.

$head epsilon$$
The result $icode eps$$ is equal to machine epsilon and has prototype
$codei%
     %Float% %eps%
%$$
The file $cref num_limits.cpp$$
tests the value $icode eps$$ by checking that the following are true
$codei%
     1 != 1 + %eps%
     1 == 1 + %eps% / 2
%$$
where all the values, and calculations, are done with the precision
corresponding to $icode Float$$.

$head min$$
The result $icode min$$ is equal to
the minimum positive normalized value and has prototype
$codei%
     %Float% %min%
%$$
The file $cref num_limits.cpp$$
tests the value $icode min$$ by checking that the following are true
$codei%
     abs( ((%min% / 100) * 100) / %min% - 1 ) > 3 * %eps%
     abs( ((%min% * 100) / 100) / %min% - 1 ) < 3 * %eps%
%$$
where all the values, and calculations, are done with the precision
corresponding to $icode Float$$.

$head max$$
The result $icode max$$ is equal to
the maximum finite value and has prototype
$codei%
     %Float% %max%
%$$
The file $cref num_limits.cpp$$
tests the value $icode max$$ by checking that the following are true
$codei%
     abs( ((%max% * 100) / 100) / %max% - 1 ) > 3 * %eps%
     abs( ((%max% / 100) * 100) / %max% - 1 ) < 3 * %eps%
%$$
where all the values, and calculations, are done with the precision
corresponding to $icode Float$$.

$head quiet_NaN$$
The result $icode nan$$ is not a number and has prototype
$codei%
     %Float% %nan%
%$$
The file $cref num_limits.cpp$$
tests the value $icode nan$$ by checking that the following is true
$codei%
     %nan% != %nan%
%$$

$head digits10$$
The member variable $code digits10$$ has prototype
$codei%
     static const int numeric_limits<%Float%>::digits10
%$$
It is the number of decimal digits that can be represented by a
$icode Float$$ value.  A number with this many decimal digits can be
converted to $icode Float$$ and back to a string,
without change due to rounding or overflow.


$head Example$$
$children%
     example/general/num_limits.cpp
%$$
The file
$cref num_limits.cpp$$
contains an example and test of these functions.

$end
------------------------------------------------------------------------------
*/
# include <iostream>

# include <cppad/configure.hpp>
# include <cppad/core/define.hpp>
# include <cppad/core/cppad_assert.hpp>
# include <cppad/local/declare_ad.hpp>

namespace CppAD { // BEGIN_CPPAD_NAMESPACE
/*!
\file numeric_limits.hpp
File that defines CppAD numeric_limits for AD types
*/

/// All tthese defaults correspond to errors
template <class Float>
class numeric_limits {
public:
     /// machine epsilon
     static Float epsilon(void)
     {    CPPAD_ASSERT_KNOWN(
          false,
          "numeric_limits<Float>::epsilon() is not specialized for this Float"
          );
          return Float(0);
     }
     /// minimum positive normalized value
     static Float min(void)
     {    CPPAD_ASSERT_KNOWN(
          false,
          "numeric_limits<Float>::min() is not specialized for this Float"
          );
          return Float(0);
     }
     /// maximum finite value
     static Float max(void)
     {    CPPAD_ASSERT_KNOWN(
          false,
          "numeric_limits<Float>::max() is not specialized for this Float"
          );
          return Float(0);
     }
     /// not a number
     static Float quiet_NaN(void)
     {    CPPAD_ASSERT_KNOWN(
          false,
          "numeric_limits<Float>::quiet_NaN() is not specialized for this Float"
          );
          return Float(0);
     }
     /// number of decimal digits
     static const int digits10 = -1;
};

/// Partial specialization that defines limits for for all AD types
template <class Base>
class numeric_limits< AD<Base> > {
public:
     /// machine epsilon
     static AD<Base> epsilon(void)
     {    return AD<Base>( numeric_limits<Base>::epsilon() ); }
     /// minimum positive normalized value
     static AD<Base> min(void)
     {    return AD<Base>( numeric_limits<Base>::min() ); }
     /// maximum finite value
     static AD<Base> max(void)
     {    return AD<Base>( numeric_limits<Base>::max() ); }
     /// not a number
     static AD<Base> quiet_NaN(void)
     {    return AD<Base>( numeric_limits<Base>::quiet_NaN() ); }
     /// number of decimal digits
     static const int digits10 = numeric_limits<Base>::digits10;
};

} // END_CPPAD_NAMESPACE
# endif