[−][src]Crate fixed
Fixed-point numbers
The fixed crate provides fixed-point numbers. Currently it uses the typenum crate for the fractional bit count; it is planned to move to const generics when they are implemented by the Rust compiler.
The crate provides the following types:
FixedI8
is a signed eight-bit fixed-point number,FixedI16
is a signed 16-bit fixed-point number,FixedI32
is a signed 32-bit fixed-point number,FixedI64
is a signed 64-bit fixed-point number,FixedI128
is a signed 128-bit fixed-point number,FixedU8
is an unsigned eight-bit fixed-point number,FixedU16
is an unsigned 16-bit fixed-point number,FixedU32
is an unsigned 32-bit fixed-point number,FixedU64
is an unsigned 64-bit fixed-point number, andFixedU128
is an unsigned 128-bit fixed-point number.
All fixed-point numbers can have Frac
fractional bits, where Frac
can have any value from 0 up to and including the size of the number
in bits. When Frac
is 0, the fixed-point number behaves like an
integer. When Frac
is equal to the number of bits, the value of the
fixed-point number lies in the range −0.5 ≤ x < 0.5 for signed
fixed-point numbers, and in the range 0 ≤ x < 1 for unsigned
fixed-point numbers.
Various conversion methods are available:
- All lossless infallible conversions between fixed-point numbers
and numeric primitives are implemented. You can use
From
orInto
for conversions that always work without losing any bits. - For lossy infallible conversions between fixed-point numbers and
numeric primitives, where the source type may have more fractional
bits than the destination type, the
LossyFrom
andLossyInto
traits can be used. Excess fractional bits are truncated. - Checked conversions are provided between fixed-point numbers and
numeric primitives using the
FromFixed
andToFixed
traits, or using thefrom_num
andto_num
methods and their checked versions. - Fixed-point numbers can be parsed from decimal strings using
FromStr
, or from binary, octal or hexadecimal using thefrom_str_binary
,from_str_octal
orfrom_str_hex
methods. The result is rounded to the nearest, with ties rounded to even. - Fixed-point numbers can be converted to strings using
Display
,Binary
,Octal
,LowerHex
andUpperHex
. The output is rounded to the nearest, with ties rounded to even.
Quick examples
// 20 integer bits, 12 fractional bits use fixed::types::I20F12; // 19/3 = 6 1/3 let six_and_third = I20F12::from_num(19) / 3; // four decimal digits for 12 binary digits assert_eq!(six_and_third.to_string(), "6.3333"); // find the ceil and convert to i32 assert_eq!(six_and_third.ceil().to_num::<i32>(), 7); // we can also compare directly to integers assert_eq!(six_and_third.ceil(), 7);
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<U12>
.
The unsigned counterpart would be 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.
// −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06) use fixed::types::I4F4; let a = I4F4::from_num(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) assert_eq!(ans1, I4F4::from_bits((3 << 4) + 3)); assert_eq!(ans1.to_string(), "3.2"); // −8 ≤ I4F12 < 8 with steps of 1/4096 (~0.0002) use fixed::types::I4F12; let wider_a = I4F12::from(a); let wider_ans = wider_a / 5 * 17; let ans2 = I4F4::from_num(wider_ans); // now the answer is the much closer 3 6/16 (~3.4) assert_eq!(ans2, I4F4::from_bits((3 << 4) + 6)); assert_eq!(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.
Using the fixed crate
The fixed crate is available on crates.io. To use it in your crate, add it as a dependency inside Cargo.toml:
[dependencies]
fixed = "0.4.3"
The fixed crate requires rustc version 1.34.0 or later.
Optional features
The fixed crate has two optional feature:
f16
, disabled by default. This provides conversion to/fromf16
. 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.
To enable features, you can add the dependency like this to Cargo.toml:
[dependencies.fixed]
version = "0.4.3"
features = ["f16", "serde"]
License
This crate is free software: you can redistribute it and/or modify it under the terms of either
- the Apache License, Version 2.0 or
- the MIT License
at your option.
Contribution
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.
Modules
consts | This module contains constants. |
frac | Deprecated This module reexports items from the typenum crate. |
prelude | A prelude for users of the fixed crate. |
sealed | Deprecated This module contains sealed traits. |
traits | This module contains traits. |
types | This module provides type aliases for all supported fixed-point numbers. |
Structs
FixedI8 | An eight-bit fixed-point signed number with |
FixedI16 | A 16-bit fixed-point signed number with |
FixedI32 | A 32-bit fixed-point signed number with |
FixedI64 | A 64-bit fixed-point signed number with |
FixedI128 | A 128-bit fixed-point signed number with |
FixedU8 | An eight-bit fixed-point unsigned number with |
FixedU16 | A 16-bit fixed-point unsigned number with |
FixedU32 | A 32-bit fixed-point unsigned number with |
FixedU64 | A 64-bit fixed-point unsigned number with |
FixedU128 | A 128-bit fixed-point unsigned number with |
ParseFixedError | An error which can be returned when parsing a fixed-point number. |
Wrapping | Provides intentionally wrapped arithmetic on fixed-point numbers. |