    "An IEEE 754 64-bit [floating point number][]. A `Float` is
     capable of approximately representing numeric values
     between:

     - 2<sup>-1022</sup>, approximately
       1.79769\{#00D7}10<sup>308</sup>, and
     - (2-2<sup>-52</sup>)\{#00D7}2<sup>1023</sup>,
       approximately 5\{#00D7}10<sup>-324</sup>.

     Zero is represented by distinct instances `+0.0`, `-0.0`,
     but these instances are equal. `-0.0` can be distinguished
     from `+0.0` using `f == 0.0 && f.strictlyNegative`.

     In addition, the following special values exist:

     - [[infinity]] and `-infinity`, and
     - [[undefined values|undefined]], denoted [NaN][] by the
       IEEE standard.

     As required by the IEEE standard no undefined value is
     equal to any other value, nor even to itself. Thus, the
     definition of [[equals]] for `Float` violates the general
     contract defined by [[Object.equals]].

     A floating point value with a zero [[fractionalPart]] is
     considered equal to its [[integer]] part.

     Literal floating point values are written with a decimal
     point and, optionally, a magnitude or exponent:

         1.0
         1.0E6
         1.0M
         1.0E-6
         1.0u

     In the case of a fractional magnitude, the decimal point is
     optional. Underscores may be used to group digits into
     groups of three.

     [floating point number]: http://www.validlab.com/goldberg/paper.pdf
     [NaN]: http://en.wikipedia.org/wiki/NaN"
    see (`function parseFloat`)
    tagged("Basic types", "Numbers")
    shared native final class Float(Float float)
            extends Object()
            satisfies Number<Float> &
                      Exponentiable<Float,Float> {

        "Determines whether this value is undefined. The IEEE
         standard denotes undefined values [NaN][] (an
         abbreviation of Not a Number). Undefined values include:

         - _indeterminate forms_ including `0.0/0.0`,
           `infinity/infinity`, `0.0*infinity`, and
           `infinity-infinity`, along with
         - _complex numbers_ like `sqrt(-1.0)` and `log(-1.0)`.

         An undefined value has the property that it is not
         [[equal|Object.equals]] (`==`) to itself, and as a
         consequence the undefined value cannot sensibly be used
         in most collections.

         If `x` is an undefined `Float`, then:

         - `x==x` evaluates to `false`
         - `x!=x` evaluates to `true`, and
         - `x>x`, `x<x`, `x>=x`, `x<=x` all evaluate to `false`.

         [NaN]: http://en.wikipedia.org/wiki/NaN"
        see (`function compare`)
        aliased("notANumber")
        shared Boolean undefined => this!=this;

        "Determines whether this value is infinite in magnitude.
         Produces `true` for `infinity` and `-infinity`.
         Produces `false` for a finite number, `+0.0`, `-0.0`,
         or undefined."
        see (`value infinity`, `value finite`)
        shared Boolean infinite
                => this==infinity || this==-infinity;

        "Determines whether this value is finite. Produces
         `false` for `infinity`, `-infinity`, and undefined."
        see (`value infinite`, `value infinity`)
        shared Boolean finite
                => this!=infinity && this!=-infinity
                        && !this.undefined;

        "The sign of this value. Produces `1` for a positive
         number or `infinity`. Produces `-1` for a negative
         number or `-infinity`. Produces `0.0` for `+0.0`,
         `-0.0`, or undefined."
        shared actual native Integer sign
                =>   if (this < 0.0) then -1
                else if (this > 0.0) then 1
                else 0;

        "Determines if this value is a positive number or
         `infinity`. Produces `false` for a negative number,
         `+0.0`, `-0.0`, or undefined."
        shared actual native Boolean positive => this > 0.0;

        "Determines if this value is a negative number or
         `-infinity`. Produces `false` for a positive number,
         `+0.0`, `-0.0`, or undefined."
        shared actual native Boolean negative => this < 0.0;

        "Determines if this value is a positive number, `+0.0`,
         or `infinity`. Produces `false` for a negative number,
         `-0.0`, or undefined."
        shared native Boolean strictlyPositive
                => this > 0.0 || 1.0/this > 0.0;

        "Determines if this value is a negative number, `-0.0`,
         or `-infinity`. Produces `false` for a positive number,
         `+0.0`, or undefined."
        shared native Boolean strictlyNegative
                => this < 0.0 || 1.0/this < 0.0;

        "Determines if the given object is equal to this `Float`,
         that is, if:

         - the given object is also a `Float`,
         - neither this value nor the given value is
           [[undefined]], and either
         - both values are [[infinite]] and have the same
           [[sign]], or both represent the same finite floating
           point value as defined by the IEEE specification.

         Or if:

         - the given object is an [[Integer]],
         - this value is neither [[undefined]], nor [[infinite]],
         - the [[fractionalPart]] of this value equals `0.0`,
         - the [[integer]] part of this value equals the given
           integer, and
         - the given integer is between -2<sup>53</sup> and
           2<sup>53</sup> (exclusive)."
        shared actual native Boolean equals(Object that);

        "A platform-dependent hash code for this `Float`."
        shared actual native Integer hash;

        "Compare this value to the given value, where
         [[infinity]] is considered greater than every defined,
         finite value, and `-infinity` is considered smaller
         than every defined, finite value, and [[undefined]]
         values are considered incomparable.

         Note that if `x` is an undefined `Float` and `y` is any
         `Float` that is not undefined, then:

         - `x<=>y` produces an exception when evaluated, but
         - `x>y`, `x<y`, `x>=y`, `x<=y`, and `x==y` all evaluate
           to `false`."
        throws (`class Exception`,
                "if either this value, the given value, or both
                 are [[undefined]]")
        shared actual native Comparison compare(Float other)
                =>   if (this < other) then smaller
                else if (this > other) then larger
                else equal;

        shared actual native Float negated;

        shared actual native Float plus(Float other);
        shared actual native Float minus(Float other);
        shared actual native Float times(Float other);
        shared actual native Float divided(Float other);

        "The result of raising this number to the given floating
         point power, where, following the definition of the
         IEEE `pow()` function, the following indeterminate
         forms all evaluate to `1.0`:

         - `0.0^0.0`,
         - `infinity^0.0` and `(-infinity)^0.0`,
         - `1.0^infinity` and `(-1.0)^infinity`.

         Furthermore:

          - `0.0^infinity` evaluates to `0.0`, and
          - `0.0^(-infinity)` evaluates to `infinity`.

         If this is a [[negative]] number, and the given
         [[power|other]] has a nonzero [[fractionalPart]], the
         result is [[undefined]].

         For any negative power `y<0.0`:

         - `0.0^y` evaluates to `infinity`,
         - `(-0.0)^y` evaluates to `-infinity`, and
         - for any nonzero floating point number `x`, `x^y`
           evaluates to `1.0/x^(-y)`."
        shared actual native Float power(Float other);

        shared actual native Float wholePart;
        shared actual native Float fractionalPart;

        aliased("absolute")
        shared actual native Float magnitude
                => this <= 0.0 then 0.0-this else this;

        "This value, represented as an [[Integer]], after
         truncation of its fractional part, if such a
         representation is possible."
        throws (`class OverflowException`,
            "if the the [[wholePart]] of this value is too large
             or too small to be represented as an `Integer`")
        since("1.1.0")
        shared native Integer integer;

        shared actual native Float timesInteger(Integer integer)
                => times(integer.nearestFloat);

        shared actual native Float plusInteger(Integer integer)
                => plus(integer.nearestFloat);

        "The result of raising this number to the given integer
         power, where the following indeterminate forms evaluate
         to `1.0`:

         - `0.0^0`,
         - `infinity^0` and `(-infinity)^0`.

         For any negative integer power `n<0`:

         - `0.0^n` evaluates to `infinity`,
         - `(-0.0)^n` evaluates to `-infinity`, and
         - for any nonzero floating point number `x`, `x^n`
           evaluates to `1.0/x^(-n)`."
        shared actual native Float powerOfInteger(Integer integer);

        "A string representing this floating point number.

         - `\"NaN\"`, for any [[undefined value|undefined]]
         - `\"Infinity\"`, for [[infinity]],
         - `\"-Infinity\"`, for [[-infinity]], or,
         - a Ceylon floating point literal that evaluates to
           this floating point number, for example, `\"1.0\"`,
           `\"-0.0\"`, or `\"1.5E10\"`."
        see (`function formatFloat`)
        shared actual native String string;

        "Determines if this value is strictly larger than the
         given value, where [[infinity]] is considered greater
         than every defined, finite value, and `-infinity` is
         considered smaller than every defined, finite value.
         Evaluates to `false` if this value, the given value, or
         both are [[undefined]]."
        shared actual native Boolean largerThan(Float other);

        "Determines if this value is strictly smaller than the
         given value, where [[infinity]] is considered greater
         than every defined, finite value, and `-infinity` is
         considered smaller than every defined, finite value.
         Evaluates to `false` if this value, the given value, or
         both are [[undefined]]."
        shared actual native Boolean smallerThan(Float other);

        "Determines if this value is larger than or equal to the
         given value, where [[infinity]] is considered greater
         than every defined, finite value, and `-infinity` is
         considered smaller than every defined, finite value.
         Evaluates to `false` if this value, the given value, or
         both are [[undefined]]."
        shared actual native Boolean notSmallerThan(Float other);

        "Determines if this value is smaller than or equal to the
         given value, where [[infinity]] is considered greater
         than every defined, finite value, and `-infinity` is
         considered smaller than every defined, finite value.
         Evaluates to `false` if this value, the given value, or
         both are [[undefined]]."
        shared actual native Boolean notLargerThan(Float other);
    }