```"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);
}
```