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] 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.
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
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.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.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][. 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.
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 crate isn't available on [crates.io] yet. To use it in your crate, add it as a git dependency inside Cargo.toml:
[dependencies.fixed]
default-features = false
git = "https://github.com/encointer/substrate-fixed"
package = "substrate-fixed"
The substrate-fixed crate requires rustc version 1.39.0 or later.
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/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].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
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.
$ claude mcp add substrate-fixed \
-- python -m otcore.mcp_server <graph>