| ## Safe Numerics

### safe_signed_range<MIN, MAX, PP, EP> and safe_unsigned_range<MIN, MAX, PP, EP>

#### Description

This type holds a signed or unsigned integer in the closed range [MIN, MAX]. A `safe_signed_range<MIN, MAX, PP, EP>` or `safe_unsigned_range<MIN, MAX, PP, EP>` can be used anywhere an arithmetic type is permitted. Any expression which uses either of these types is guaranteed to return an arithmetically correct value or to trap in some way.

#### Notation

Symbol | Description
--- | ---
`MIN, MAX` | Minimum and maximum values that the range can represent.

#### Associated Types

`PP` | Promotion Policy. A type which specifies the result type of an expression using safe types.
`EP` | Exception Policy. A type containing members which are called when a correct result cannot be returned

#### Template Parameters

Parameter | Requirements | Description
--- | --- | ---
`T` | std::is_integer<T> | The underlying type. Currently only built-in integer types are supported
`MIN` | must be a non-negative literal | The minimum non-negative integer value that this type may hold
`MAX` | must be a non-negative literal | The maximum non-negative integer value that this type may hold
| MIN <= MAX | must be a valid closed range
`PP` | PromotionPolicy<PP> | Default value is `boost::numeric::native`
`EP` | Exception Policy<EP> | Default value is `boost::numeric::default_exception_policy`

#### Model of

Numeric

Integer

#### Valid Expressions

Implements all expressions and only those expressions supported by the base type T. Note that all these expressions are `constexpr`. The result type of such an expression will be another safe type. The actual type of the result of such an expression will depend upon the specific promotion policy template parameter.

When a binary operand is applied to two instances of A `safe_signed_range<MIN, MAX, PP, EP>` or `safe_unsigned_range<MIN, MAX, PP, EP>` one of the following must be true:

- The promotion policies of the two operands must be the same or one of them must be void

- The exception policies of the two operands must be the same or one of them must be void

If either of the above is not true, a compile error will result.

#### Example of use

    //  Copyright (c) 2018 Robert Ramey
    //
    // Distributed under the Boost Software License, Version 1.0. (See
    // accompanying file LICENSE_1_0.txt or copy at
    // http://www.boost.org/LICENSE_1_0.txt)

    #include <exception>
    #include <iostream>
    #include <type_traits>
    #include <boost/safe_numerics/safe_integer.hpp>
    #include <boost/safe_numerics/safe_integer_range.hpp>
    #include <boost/safe_numerics/safe_integer_literal.hpp>

    #include <boost/safe_numerics/utility.hpp>

    using namespace boost::safe_numerics;

    int main(){
        safe_unsigned_range<7, 24> i;

        // since the range is included in [0,255], the underlying type of i
        // will be an unsigned char.
        try{
            i = 0;  // throws out_of_range exception
            std::cout << "fails to detect erroneous assignment" << std::endl;
        }
        catch(std::exception & e){
            // should arrive here
        }
        try{
            i = 9;  // ok - no exception expected
        }
        catch(std::exception & e){
            std::cout << "erroneous error for legal assignment" << std::endl;
        }
        try{
            i *= 9; // fails to compile because result can't fin in range
            std::cout << "fails to out of range result" << std::endl;
        }
        catch(std::exception & e){
            // should arrive here
        }
        try{
            i = -1; // throws out_of_range exception
            std::cout << "fails to detect erroneous assignment" << std::endl;
        }
        catch(std::exception & e){
            // should arrive here
        }
        std::uint8_t j = 4;
        auto k = i + j;

        // if either or both types are safe types, the result is a safe type
        // determined by promotion policy.  In this instance
        // the range of i is [7, 24] and the range of j is [0,255].
        // so the type of k will be a safe type with a range of [7,279]
        static_assert(
            is_safe<decltype(k)>::value
            && std::numeric_limits<decltype(k)>::min() == 7
            && std::numeric_limits<decltype(k)>::max() == 279,
            "k is a safe range of [7,279]"
        );
        return 0;
    }

#### Header

`#include <boost/numeric/safe_numerics/safe_range.hpp>`