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Safe Numerics

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interval<R>

Description
Template Parameters
Notation
Associated Types
Valid Expressions
Example of use
Header

Description

A closed arithmetic interval represented by a pair of elements of type R. In principle, one should be able to use Boost.Interval library for this. But the functions in this library are not constexpr. Also, this Boost.Interval is more complex and does not support certain operations such bit operations. Perhaps some time in the future, Boost.Interval will be used instead of this interval<R> type.

Template Parameters

R must model the type requirements of Numeric. Note this in principle includes any numeric type including floating point numbers and instances of checked_result<R>.

Notation

Symbol Description
I An interval type
i, j An instance of interval type
R Numeric types which can be used to make an interval
r An instance of type R
p An instance of std::pair<R, R>
l, u Lowermost and uppermost values in an interval
os std::basic_ostream<class CharT, class Traits = std::char_traits<CharT>>

Associated Types

checked_result holds either the result of an operation or information as to why it failed

Valid Expressions

Note that all expressions are constexpr.

Expression Return Type Semantics
interval<R>(l, u) interval<R> construct a new interval from a pair of limits
interval<R>(p) interval<R> construct a new interval from a pair of limits
interval<R>(i) interval<R> copy constructor
make_interval<R>() interval<R> return new interval with std::numric_limits<R>::min() and std::numric_limits<R>::max()
make_interval<R>(const R &r) interval<R> return new interval with std::numric_limits<R>::min() and std::numric_limits<R>::max()
i.l R lowermost value in the interval i
i.u R uppermost value in the interval i
i.includes(j) boost::logic::tribool return true if interval i includes interval j
i.excludes(j) boost::logic::tribool return true if interval i includes interval j
i.includes(t) bool return true if interval i includes value t
i.excludes(t) bool return true if interval i includes value t
i + j interval<R> add two intervals and return the result
i - j interval<R> subtract two intervals and return the result
i * j interval<R> multiply two intervals and return the result
i / j interval<R> divide one interval by another and return the result
i % j interval<R> calculate modulus of one interval by another and return the result
i << j interval<R> calculate the range that would result from shifting one interval by another
i >> j interval<R> calculate the range that would result from shifting one interval by another
i | j interval<R> range of values which can result from applying | to any pair of operands from I and j
i & j interval<R> range of values which can result from applying & to any pair of operands from I and j
i ^ j interval<R> range of values which can result from applying ^ to any pair of operands from I and j
t < u boost::logic::tribool true if every element in t is less than every element in u
t > u boost::logic::tribool true if every element in t is greater than every element in u
t <= u boost::logic::tribool true if every element in t is less than or equal to every element in u
t >= u boost::logic::tribool true if every element in t is greater than or equal to every element in u
t == u bool true if limits are equal
t != u bool true if limits are not equal
os << i os & print interval to output stream

Example of use

#include <iostream>
#include <cstdint>
#include <cassert>
#include <boost/numeric/safe_numerics/interval.hpp>

int main(){
    std::cout << "test1" << std::endl;
    interval<std::int16_t> x = {-64, 63};
    std::cout << "x = " << x << std::endl;
    interval<std::int16_t> y(-128, 126);
    std::cout << "y = " << y << std::endl;
    assert(static_cast<interval<std::int16_t>>(add<std::int16_t>(x,x)) == y);
    std::cout << "x + x =" << add<std::int16_t>(x, x) << std::endl;
    std::cout << "x - x = " << subtract<std::int16_t>(x, x) << std::endl;
    return 0;
}

Header

#include <boost/numeric/safe_numerics/interval.hpp>


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