 ## CGAL::MP_Float

### Definition

An object of the class MP_Float is able to represent a floating point value with arbitrary precision. This number type has the property that additions, subtractions and multiplications are computed exactly, as well as the construction from float, double and long double.

Division and square root are not enabled by default since CGAL release 3.2, since they are computed approximately. We suggest that you use rationals like Quotient<MP_Float> when you need exact divisions.

Note on the implementation : although the mantissa length is basically only limited by the available memory, the exponent is currently represented by a (integral valued) double, which can overflow in some circumstances. We plan to also have a multiprecision exponent to fix this issue.

#include <CGAL/MP_Float.h>

EuclideanRing.

RealEmbeddable

### Creation

 MP_Float m; introduces an uninitialized variable m. MP_Float m ( MP_Float); copy constructor. MP_Float m ( int i); introduces the integral value i. MP_Float m ( float d); introduces the floating point value d (exact conversion). MP_Float m ( double d); introduces the floating point value d (exact conversion). MP_Float m ( long double d); introduces the floating point value d (exact conversion).

### Operations

 std::ostream& std::ostream& out << m writes a double approximation of m to the ostream out. std::istream& std::istream& in >> & m reads a double from in, then converts it to an MP_Float. MP_Float approximate_division ( a, b) computes an approximation of the division by converting the operands to double, performing the division on double, and converting back to MP_Float. MP_Float approximate_sqrt ( a) computes an approximation of the square root by converting the operand to double, performing the square root on double, and converting back to MP_Float.

### Implementation

The implementation of MP_Float is simple but provides a quadratic complexity for multiplications. This can be a problem for large operands. For faster implementations of the same functionality with large integral values, you may want to consider using GMP or LEDA instead.