This crate provides an implementation of octuple-precision binary
floating-point arithmetics.

### From Wikipedia:

"In its 2008 revision, the IEEE 754 standard specifies a `binary256` format
among the interchange formats (it is not a basic format), as having:

```text
    Sign bit: 1 bit
    Exponent width: 19 bits
    Significand precision: 237 bits (236 explicitly stored)
```

The format is written with an implicit lead bit with value 1 unless the
exponent is all zeros. Thus only 236 bits of the significand appear in the
memory format, but the total precision is 237 bits (approximately 71 decimal
digits: log₁₀(2²³⁷) ≈ 71.344). The bits are laid out as follows:

![Layout of octuple-precision floating-point format](https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Octuple_precision_visual_demonstration.svg/2560px-Octuple_precision_visual_demonstration.svg.png)

##### Exponent encoding

The octuple-precision binary floating-point exponent is encoded using an
offset binary representation, with the zero offset being 262143; also known as
exponent bias in the IEEE 754 standard.

```text
    Eₘᵢₙ = −262142
    Eₘₐₓ = 262143
    Exponent bias = 3FFFF₁₆ = 262143
```

Thus, as defined by the offset binary representation, in order to get the true
exponent the offset of 262143 has to be subtracted from the stored exponent.

The stored exponents 00000₁₆ and 7FFFF₁₆ are interpreted specially.

| Exponent          | Significand zero | Significand non-zero    | Equation                                                                 |
|-------------------|------------------|-------------------------|--------------------------------------------------------------------------|
| 00000₁₆           | 0, −0            | subnormal numbers       | (-1)<sup>signbit</sup> × 2⁻²⁶²¹⁴² × 0.significandbits₂                   |
| 00001₁₆ … 7FFFE₁₆ | normalized value | normalized value        | (-1)<sup>signbit</sup> × 2<sup>exponent bits₂</sup> × 1.significandbits₂ |
| 7FFFF₁₆           | ±∞               | NaN (quiet, signalling) |

The minimum strictly positive (subnormal) value is 2⁻²⁶²³⁷⁸ ≈ 10⁻⁷⁸⁹⁸⁴ and has
a precision of only one bit. The minimum positive normal value is 2⁻²⁶²¹⁴² ≈
2.4824 × 10⁻⁷⁸⁹¹³. The maximum representable value is 2²⁶²¹⁴⁴ − 2²⁶¹⁹⁰⁷ ≈
1.6113 × 10⁷⁸⁹¹³.

The type `f256` will provide the same stable API as the built-in `f64`
(besides differences caused by the increased precision).

### Getting started

Add `f256` to your `Cargo.toml`:

```toml
[dependencies]
f256 = "0.3"
```

### Crate features

By default, only the feature `std` is enabled.

#### Ecosystem

* **std** - Printing and some tests depend on this feature. Besides that, support
  for conversion to string and formatting is provided by using crate `alloc` so
  that this functionality is also available in non-standard environments.

#### Optional dependencies

* **num-traits** - When enabled, the trait `num-traits::Num` is implemented
  for `f256`.