Fixed-point numbers for substrate

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

• 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 and Into. 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 and LossyInto 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 and ToFixed traits, or using the from_num and to_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 the from_str_binary, from_str_octal and from_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 and UpperHex. The output is rounded to the nearest, with ties rounded to even.

Upstream releases

Details on other releases can be found in RELEASES.md.

Quick examples

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.

Using the substrate-fixed crate

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.

Optional features

The fixed crate has four optional feature:

1. az, disabled by default. This implements the cast traits provided by the az crate.
2. f16, disabled by default. This provides conversion to/from f16 and bf16. This features requires the half crate.
3. serde, disabled by default. This provides serialization support for the fixed-point types. This feature requires the serde crate.
4. 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"]

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.