This crate ist ported from fixed = 0.5.4
. It has been adapted to be usable within substrate runtimes. Additionally, transcendental functions have been added (log, exp, pow, trigonometry).
Please also have a look at our encointer-js libraries to learn how to parse fixpoint values for javascript UIs.
The [substrate-fixed crate] provides fixed-point numbers.
FixedI8
andFixedU8
are eight-bit fixed-point numbers.FixedI16
andFixedU16
are 16-bit fixed-point numbers.FixedI32
andFixedU32
are 32-bit fixed-point numbers.FixedI64
andFixedU64
are 64-bit fixed-point numbers.FixedI128
andFixedU128
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.
Currently the typenum crate is used for the fractional bit count
Frac
; it is planned to move to const generics when they are
supported by the Rust compiler.
The main features are
- Representation of fixed-point numbers up to 128 bits wide.
- Conversions between fixed-point numbers and numeric primitives.
- Comparisons between fixed-point numbers and numeric primitives.
- Parsing from strings in decimal, binary, octal and hexadecimal.
- Display as decimal, binary, octal and hexadecimal.
- Arithmetic and logic operations.
The conversions supported cover the following cases.
- Infallible lossless conversions between fixed-point numbers and
numeric primitives are provided using
From
andInto
. These never fail (infallible) and do not lose any bits (lossless). - Infallible lossy conversions between fixed-point numbers and
numeric primitives are provided using the
LossyFrom
andLossyInto
traits. The source can have more fractional bits than the destination. - Checked conversions between fixed-point numbers and numeric
primitives are provided 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
, and from binary, octal and hexadecimal strings using thefrom_str_binary
,from_str_octal
andfrom_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.
Details on other releases can be found in RELEASES.md.
use substrate_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.
use substrate_fixed::types::{I4F4, I4F12};
// −8 ≤ I4F4 < 8 with steps of 1/16 (~0.06)
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)
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.
The substrate-fixed is available on crates.io.
The fixed crate has four optional feature:
az
, disabled by default. This implements the cast traits provided by the az crate.f16
, disabled by default. This provides conversion to/fromf16
andbf16
. 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 underno_std
: currently the implementation of theError
trait forParseFixedError
.
To enable features, you can add the dependency like this to Cargo.toml:
[dependencies.fixed]
default-features = false
git = "https://github.com/encointer/substrate-fixed"
package = "substrate-fixed"
features = ["f16", "serde"]
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.
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.