# Fixed-point numbers 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. An n-bit fixed-point number has f = `Frac` fractional bits where 0 ≤ f ≤ n, and n − f integer bits. For example, [FixedI32]\<[U24]> is a 32-bit signed fixed-point number with n = 32 total bits, f = 24 fractional bits, and n − f = 8 integer bits. [FixedI32]\<[U0]> behaves like [`i32`], and [FixedU32]\<[U0]> behaves like [`u32`]. The difference between any two successive representable numbers is constant throughout the possible range for a fixed-point number: Δ = 1/2^f. When f = 0, like in [FixedI32]\<[U0]>, Δ = 1 because representable numbers are integers, and the difference between two successive integers is 1. When f = n, Δ = 1/2ⁿ and the value lies in the range −0.5 ≤ x < 0.5 for signed numbers like [FixedI32]\<[U32]>, and in the range 0 ≤ x < 1 for unsigned numbers like [FixedU32]\<[U32]>. 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 * 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. This crate does *not* provide general analytic functions. * No algebraic functions are provided, for example no `sqrt` or `pow`. * No trigonometric functions are provided, for example no `sin` or `cos`. * No other transcendental functions are provided, for example no `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 [*fixed-sqrt* crate] provides the square root operation. * The [*cordic* crate] provides various functions implemented using the [CORDIC] algorithm. 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 lossless conversions between fixed-point numbers and numeric primitives are provided using the [`LosslessTryFrom`] and [`LosslessTryInto`] traits. The source cannot 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][`checked_from_num`]. * Additionally, checked casts from the [*az* crate] are implemented for conversion between fixed-point nubmers and numeric primitives. * 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. * All fixed-point numbers are plain old data, so bit casting conversions from the [*bytemuck* crate] can be used. ## What’s new ### Version 1.9.0 news (unreleased) * Fixed-point numbers can now be formatted as hexadecimal with [`Debug`] similarly to primitive integers, for example formatting with `{:X?}` will produce upper-case hexadecimal fixed-point numbers. * The following methods were added to all fixed-point numbers, to the [`Fixed`][tf-1-9] trait, and to the [`Wrapping`][w-1-9] and [`Unwrapped`][u-1-9] wrappers: * [`is_zero`][f-iz-1-9] * [`distance`][f-d-1-9] * The following methods were added to all fixed-point numbers and to the [`Fixed`][tf-1-9] trait: * [`checked_distance`][f-cd-1-9], [`saturating_distance`][f-sd-1-9], [`wrapping_distance`][f-wd-1-9], [`unwrapped_distance`][f-ud-1-9], [`overflowing_distance`][f-od-1-9] * The [`unsigned_distance`][f-unsd-1-9] method was added to all signed fixed-point types and to the [`FixedSigned`][tfs-1-9] trait. * The following associated types and provided methods were added to the [`Fixed`][tf-1-9] trait: * [`Signed`][tf-s-1-9], [`Unsigned`][tf-u-1-9] * [`get_signed`][tf-gs-1-9], [`get_unsigned`][tf-gu-1-9] * [`get_signed_mut`][tf-gsm-1-9], [`get_unsigned_mut`][tf-gum-1-9] * The following traits from the [*bytemuck* crate] were implemented for all fixed-point numbers, added as supertraits to the [`Fixed`][tf-1-9] trait, and implemented for the [`Wrapping`][w-1-9] and [`Unwrapped`][u-1-9] wrappers. * [`Zeroable`][bm-z-1], [`Pod`][bm-p-1] * [`TransparentWrapper`][bm-tw-1] #### Compatibility notes * Now the [`Debug`] implementation for [`Wrapping`][w-1-9] outputs the value only without `"Wrapping()"`, and the [`Debug`] implementation for [`Unwrapped`][u-1-9] outputs the value only without `"Unwrapped()"`. * The [`LeEqU8`][leu8-1-9], [`LeEqU16`][leu16-1-9], [`LeEqU32`][leu32-1-9], [`LeEqU64`][leu64-1-9] and [`LeEqU128`][leu128-1-9] traits now have a `'static` constraint. This should have no practical side effects, since these traits are a convenience feature and already have the [`Unsigned`][uns-1-9] marker trait as a supertrait, and the types that implement [`Unsigned`][uns-1-9] are `'static`. * The [`FixedOptionalFeatures`][fof-1-9] trait was not sealed, which was as an oversight. Now it is sealed, and the documentation explicitly states that the trait should not be used directly. [`Debug`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html [bm-p-1]: https://docs.rs/bytemuck/^1/bytemuck/trait.Pod.html [bm-tw-1]: https://docs.rs/bytemuck/^1/bytemuck/trait.TransparentWrapper.html [bm-z-1]: https://docs.rs/bytemuck/^1/bytemuck/trait.Zeroable.html [f-cd-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.checked_distance [f-d-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.distance [f-iz-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.is_zero [f-od-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.overflowing_distance [f-sd-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.saturating_distance [f-ud-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.unwrapped_distance [f-unsd-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.unsigned_distance [f-wd-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.FixedI32.html#method.wrapping_distance [fof-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.FixedOptionalFeatures.html [leu128-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU128.html [leu16-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU16.html [leu32-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU32.html [leu64-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU64.html [leu8-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.LeEqU8.html [tf-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html [tf-gs-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html#method.get_signed [tf-gsm-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html#method.get_signed_mut [tf-gu-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html#method.get_unsigned [tf-gum-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html#method.get_unsigned_mut [tf-s-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html#associatedtype.Signed [tf-u-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.Fixed.html#associatedtype.Unsigned [tfs-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/traits/trait.FixedSigned.html [u-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.Unwrapped.html [uns-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/types/extra/trait.Unsigned.html [w-1-9]: https://tspiteri.gitlab.io/fixed/dev/fixed/struct.Wrapping.html ### Version 1.8.0 news (2021-04-20) * The following constants and method were added to all fixed-point numbers, to the [`Fixed`][tf-1-8] trait, and to the [`Wrapping`][w-1-8] and [`Unwrapped`][u-1-8] wrappers: * [`ZERO`][f-z-1-8], [`DELTA`][f-d-1-8] * [`mul_acc`][f-ma-1-8] * The [`ONE`][f-o-1-8] constant was added to all fixed-point numbers that can represent the value 1. * The following methods were added to all fixed-point numbers and to the [`Fixed`][tf-1-8] trait: * [`checked_mul_acc`][f-cma-1-8], [`saturating_mul_acc`][f-sma-1-8], [`wrapping_mul_acc`][f-wma-1-8], [`unwrapped_mul_acc`][f-uma-1-8], [`overflowing_mul_acc`][f-oma-1-8] * [`saturating_div_euclid_int`][f-sdei-1-8], [`saturating_rem_euclid_int`][f-srei-1-8] * [`unwrapped_rem`][f-ur-1-8], [`unwrapped_rem_euclid`][f-ure-1-8] * [`unwrapped_rem_int`][f-uri-1-8] * The following methods are now `const` functions: * [`checked_rem`][f-cr-1-8] * [`rem_euclid`][f-re-1-8], [`checked_rem_euclid`][f-cre-1-8] * [`checked_div_int`][f-cdi-1-8], [`wrapping_div_int`][f-wdi-1-8], [`unwrapped_div_int`][f-udi-1-8], [`overflowing_div_int`][f-odi-1-8] * The following methods were added to all fixed-point numbers: * [`const_not`][f-cn-1-8] * [`const_bitand`][f-cba-1-8], [`const_bitor`][f-cbo-1-8], [`const_bitxor`][f-cbx-1-8] * Many methods were marked with the `must_use` attribute. [f-cba-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.const_bitand [f-cbo-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.const_bitor [f-cbx-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.const_bitxor [f-cdi-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.checked_div_int [f-cma-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.checked_mul_acc [f-cn-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.const_not [f-cr-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.checked_rem [f-cre-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.checked_rem_euclid [f-d-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#associatedconstant.DELTA [f-ma-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.mul_acc [f-o-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#associatedconstant.ONE [f-odi-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.overflowing_div_int [f-oma-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.overflowing_mul_acc [f-re-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.rem_euclid [f-sdei-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.saturating_div_euclid_int [f-sma-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.saturating_mul_acc [f-srei-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.saturating_rem_euclid_int [f-udi-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.unwrapped_div_int [f-uma-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.unwrapped_mul_acc [f-ur-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.unwrapped_rem [f-ure-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.unwrapped_rem_euclid [f-uri-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.unwrapped_rem_int [f-wdi-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.wrapping_div_int [f-wma-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.wrapping_mul_acc [f-z-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#associatedconstant.ZERO [tf-1-8]: https://docs.rs/fixed/~1.8/fixed/traits/trait.Fixed.html [u-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.Unwrapped.html [w-1-8]: https://docs.rs/fixed/~1.8/fixed/struct.Wrapping.html ### Other releases Details on other releases can be found in [*RELEASES.md*]. [*RELEASES.md*]: https://gitlab.com/tspiteri/fixed/blob/master/RELEASES.md ## Quick examples ```rust 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::(), 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. ```rust use 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. ## Writing fixed-point constants and values literally 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); ``` ## Using the *fixed* crate The *fixed* crate is available on [crates.io][*fixed* crate]. To use it in your crate, add it as a dependency inside [*Cargo.toml*]: ```toml [dependencies] fixed = "1.8" ``` The *fixed* crate requires rustc version 1.50.0 or later. ## Optional features The *fixed* crate has these optional feature: 1. `serde`, disabled by default. This provides serialization support for the fixed-point types. This feature requires the [*serde* crate]. 2. `std`, disabled by default. This is for features that are not possible under `no_std`: currently the implementation of the [`Error`] trait for [`ParseFixedError`]. 3. `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 = "1.8" features = ["serde"] ``` ## Experimental optional features It is not considered a breaking change if the following 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. 1. `num-traits`, disabled by default. This implements some traits from the [*num-traits* crate]. (The plan is to promote this to an optional feature once the [*num-traits* crate] reaches version 1.0.0.) ## Deprecated optional features The following optional features are deprecated and may be removed in the next major version of the crate. 1. `az`, has no effect. Previously required for the cast traits from the [*az* crate]. Now these cast traits are always provided. 2. `f16`, has no effect. Previously required for conversion to/from [`f16`] and [`bf16`]. Now these conversions are always provided. ## 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][LICENSE-APACHE] or * the [MIT License][LICENSE-MIT] 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. [*Cargo.toml*]: https://doc.rust-lang.org/cargo/guide/dependencies.html [*az* crate]: https://crates.io/crates/az [*bytemuck* crate]: https://crates.io/crates/bytemuck [*cordic* crate]: https://crates.io/crates/cordic [*fixed* crate]: https://crates.io/crates/fixed [*fixed-macro* crate]: https://crates.io/crates/fixed-macro [*fixed-sqrt* crate]: https://crates.io/crates/fixed-sqrt [*half* crate]: https://crates.io/crates/half [*num-traits* crate]: https://crates.io/crates/num-traits [*serde* crate]: https://crates.io/crates/serde [*typenum* crate]: https://crates.io/crates/typenum [CORDIC]: https://en.wikipedia.org/wiki/CORDIC [FixedI32]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html [FixedU32]: https://docs.rs/fixed/~1.8/fixed/struct.FixedU32.html [LICENSE-APACHE]: https://www.apache.org/licenses/LICENSE-2.0 [LICENSE-MIT]: https://opensource.org/licenses/MIT [U0]: https://docs.rs/fixed/~1.8/fixed/types/extra/type.U0.html [U12]: https://docs.rs/fixed/~1.8/fixed/types/extra/type.U12.html [U24]: https://docs.rs/fixed/~1.8/fixed/types/extra/type.U24.html [U32]: https://docs.rs/fixed/~1.8/fixed/types/extra/type.U32.html [`Binary`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Binary.html [`Display`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Display.html [`Error`]: https://doc.rust-lang.org/nightly/std/error/trait.Error.html [`FixedI128`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI128.html [`FixedI16`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI16.html [`FixedI32`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html [`FixedI64`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI64.html [`FixedI8`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI8.html [`FixedU128`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedU128.html [`FixedU16`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedU16.html [`FixedU32`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedU32.html [`FixedU64`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedU64.html [`FixedU8`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedU8.html [`FromFixed`]: https://docs.rs/fixed/~1.8/fixed/traits/trait.FromFixed.html [`FromStr`]: https://doc.rust-lang.org/nightly/core/str/trait.FromStr.html [`From`]: https://doc.rust-lang.org/nightly/core/convert/trait.From.html [`I20F12`]: https://docs.rs/fixed/~1.8/fixed/types/type.I20F12.html [`I4F12`]: https://docs.rs/fixed/~1.8/fixed/types/type.I4F12.html [`I4F4`]: https://docs.rs/fixed/~1.8/fixed/types/type.I4F4.html [`Into`]: https://doc.rust-lang.org/nightly/core/convert/trait.Into.html [`LosslessTryFrom`]: https://docs.rs/fixed/~1.8/fixed/traits/trait.LosslessTryFrom.html [`LosslessTryInto`]: https://docs.rs/fixed/~1.8/fixed/traits/trait.LosslessTryInto.html [`LossyFrom`]: https://docs.rs/fixed/~1.8/fixed/traits/trait.LossyFrom.html [`LossyInto`]: https://docs.rs/fixed/~1.8/fixed/traits/trait.LossyInto.html [`LowerHex`]: https://doc.rust-lang.org/nightly/core/fmt/trait.LowerHex.html [`Octal`]: https://doc.rust-lang.org/nightly/core/fmt/trait.Octal.html [`ParseFixedError`]: https://docs.rs/fixed/~1.8/fixed/struct.ParseFixedError.html [`ToFixed`]: https://docs.rs/fixed/~1.8/fixed/traits/trait.ToFixed.html [`U20F12`]: https://docs.rs/fixed/~1.8/fixed/types/type.U20F12.html [`UpperHex`]: https://doc.rust-lang.org/nightly/core/fmt/trait.UpperHex.html [`bf16`]: https://docs.rs/half/^1/half/struct.bf16.html [`checked_from_num`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.checked_from_num [`f16`]: https://docs.rs/half/^1/half/struct.f16.html [`from_num`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.from_num [`from_str_binary`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.from_str_binary [`from_str_hex`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.from_str_hex [`from_str_octal`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.from_str_octal [`i32`]: https://doc.rust-lang.org/nightly/std/primitive.i32.html [`to_num`]: https://docs.rs/fixed/~1.8/fixed/struct.FixedI32.html#method.to_num [`u32`]: https://doc.rust-lang.org/nightly/std/primitive.u32.html [const generics]: https://github.com/rust-lang/rust/issues/44580