The [fixed crate] provides fixed-point numbers.
FixedI8] and [FixedU8] are eight-bit fixed-point numbers.FixedI16] and [FixedU16] are 16-bit fixed-point numbers.FixedI32] and [FixedU32] are 32-bit fixed-point numbers.FixedI64] and [FixedU64] are 64-bit fixed-point numbers.FixedI128] and [FixedU128] are 128-bit fixed-point numbers.These types can have Frac fractional bits, where
0 ≤ Frac ≤ n and n is the total number of bits. When
Frac = 0, the fixed-point number behaves like an n-bit
integer. When Frac = n, the value x lies in the range
−0.5 ≤ x < 0.5 for signed numbers, and in the range
0 ≤ x < 1 for unsigned numbers.
In version 1 the [typenum crate] is used for the fractional bit
count Frac; the plan is to to have a major version 2 with [const
generics] instead when the Rust compiler support for them is powerful
enough.
The main features are
This crate does not provide general analytic functions.
sqrt or
pow.sin or
cos.log or exp.These functions are not provided because different implementations can have different trade-offs, for example trading some correctness for speed. Implementations can be provided in other crates.
The conversions supported cover the following cases.
From] and [Into]. These
never fail (infallible) and do not lose any bits (lossless).LossyFrom] and
[LossyInto] traits. The source can have more fractional bits
than the destination.LosslessTryFrom] and
[LosslessTryInto] traits. The source cannot have more fractional
bits than the destination.FromFixed] and [ToFixed]
traits, or using the [from_num] and [to_num] methods and
[their checked versions][checked_from_num].FromStr], and from binary, octal and hexadecimal strings using
the [from_str_binary], [from_str_octal] and [from_str_hex]
methods. The result is rounded to the nearest, with ties rounded
to even.Display],
[Binary], [Octal], [LowerHex] and [UpperHex]. The output
is rounded to the nearest, with ties rounded to even.unsigned_abs method was added to all signed
fixed-point types and to the FixedSigned trait.const functions:
unwrapped_to_fixed method was added to the
ToFixed trait.unwrapped_from_fixed method was added to the
FromFixed trait.Details on other releases can be found in [RELEASES.md].
```rust use fixed::types::I20F12;
// 19/3 = 6 1/3
let sixandthird = I20F12::fromnum(19) / 3;
// four decimal digits for 12 binary digits
asserteq!(sixandthird.tostring(), "6.3333");
// find the ceil and convert to i32
asserteq!(sixandthird.ceil().tonum::
The type [I20F12] is a 32-bit fixed-point signed number with 20
integer bits and 12 fractional bits. It is an alias to
[FixedI32][. The unsigned
counterpart would be [FixedI32]<[U12][U12]>U20F12]. Aliases are provided for all
combinations of integer and fractional bits adding up to a total of
eight, 16, 32, 64 or 128 bits.
```rust use fixed::types::{I4F4, I4F12};
// −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06) let a = I4F4::fromnum(1); // multiplication and division by integers are possible let ans1 = a / 5 * 17; // 1 / 5 × 17 = 3 2/5 (3.4), but we get 3 3/16 (~3.2) asserteq!(ans1, I4F4::frombits((3 << 4) + 3)); asserteq!(ans1.to_string(), "3.2");
// −8 ≤ I4F12 < 8 with steps of 1/4096 (~0.0002) let widera = I4F12::from(a); let widerans = widera / 5 * 17; let ans2 = I4F4::fromnum(widerans); // now the answer is the much closer 3 6/16 (~3.4) asserteq!(ans2, I4F4::frombits((3 << 4) + 6)); asserteq!(ans2.to_string(), "3.4"); ```
The second example shows some precision and conversion issues. The low
precision of a means that a / 5 is 3⁄16 instead of 1⁄5, leading to
an inaccurate result ans1 = 3 3⁄16 (~3.2). With a higher precision,
we get wider_a / 5 equal to 819⁄4096, leading to a more accurate
intermediate result wider_ans = 3 1635⁄4096. When we convert back to
four fractional bits, we get ans2 = 3 6⁄16 (~3.4).
Note that we can convert from [I4F4] to [I4F12] using [From], as
the target type has the same number of integer bits and a larger
number of fractional bits. Converting from [I4F12] to [I4F4]
cannot use [From] as we have less fractional bits, so we use
[from_num] instead.
The [fixed-macro crate] provides a convenient macro to write down fixed-point constants literally in the code.
```rust use fixed::types::I16F16; use fixed_macro::fixed;
const NUM1: I16F16 = fixed!(12.75: I16F16); let num2 = NUM1 + fixed!(13.125: I16F16); assert_eq!(num2, 25.875); ```
The fixed crate is available on crates.io. To use it in your crate, add it as a dependency inside [Cargo.toml]:
toml
[dependencies]
fixed = "1.6"
The fixed crate requires rustc version 1.47.0 or later.
The fixed crate has these optional feature:
az, disabled by default. This implements the cast traits
provided by the [az crate].f16, disabled by default. This provides conversion to/from
[f16] and [bf16]. This features requires the [half crate].serde, disabled by default. This provides serialization support
for the fixed-point types. This feature requires the
[serde crate].std, disabled by default. This is for features that are not
possible under no_std: currently the implementation of the
[Error] trait for [ParseFixedError].serde-str, disabled by default. Fixed-point numbers are
serialized as strings showing the value when using human-readable
formats. This feature requires the serde and the std optional
features. Warning: numbers serialized when this feature is
enabled cannot be deserialized when this feature is disabled, and
vice versa.To enable features, you can add the dependency like this to [Cargo.toml]:
toml
[dependencies.fixed]
version = "1.6"
features = ["f16", "serde"]
It is not considered a breaking change if experimental features are removed. The removal of experimental features would however require a minor version bump. Similarly, on a minor version bump, optional dependencies can be updated to an incompatible newer version.
There is one experimental feature:
num-traits, disabled by default. This implements some traits
from the [num-traits crate]. (The plan is to upgrade this to an
optional feature once the [num-traits crate] reaches version
1.0.0.)This crate is free software: you can redistribute it and/or modify it under the terms of either
at your option.
Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache License, Version 2.0, shall be dual licensed as above, without any additional terms or conditions.