17 KiB
Fixed-point numbers
The 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.
This crate does not provide general analytic functions.
- No algebraic functions are provided, for example no
sqrt
orpow
. - No trigonometric functions are provided, for example no
sin
orcos
. - No other transcendental functions are provided: for example no
log
orexp
.
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.
What’s new
Version 0.4.4 news (unreleased)
- Bug fix: rounding could produce bad output for
Binary
,Octal
,LowerHex
andUpperHex
. - The following methods are now
const
functions:is_power_of_two
,abs
,wrapping_abs
,overflowing_abs
- The method
round_to_zero
was added. - The method
round_ties_to_even
and its checked versions were added.
Version 0.4.3 news (2019-08-20)
- The fixed crate now requires rustc version 1.34.0 or later.
- The precision argument is no longer ignored when formatting fixed-point numbers; precision should now be handled the same as for primitive floating-point numbers in the standard library.
- Parsing strings now rounds to the nearest with ties rounded to even.
- Checked versions of string parsing methods are now available as
inherent methods to all fixed-point numbers, and as methods in the
Fixed
trait. Wrapping
now has methods for parsing with wrapping, including an implementation ofFromStr
.- The following methods are now
const
functions:min_value
,max_value
,from_bits
,to_bits
count_ones
,count_zeros
,leading_zeros
,trailing_zeros
rotate_left
,rotate_right
wrapping_neg
,wrapping_add
,wrapping_sub
,wrapping_mul_int
,wrapping_shl
,wrapping_shr
overflowing_neg
,overflowing_add
,overflowing_sub
,overflowing_mul_int
,overflowing_shl
,overflowing_shr
is_positive
,is_negative
- The associated constants
INT_NBITS
andFRAC_NBITS
were added. - The reexports in the
frac
module and theLeEqU*
traits were moved into the newtypes::extra
module.
Version 0.4.2 news (2019-08-16)
- The new methods
from_num
andto_num
together with their checked versions were added to all fixed-point numbers. - The methods
from_fixed
,to_fixed
,from_int
,to_int
,from_float
, andto_float
, and their checked versions, were deprecated. - The new method
from_num
was added to theWrapping
wrapper. - Bug fix: parsing of decimal fractions was fixed to give correctly rounded results for long decimal fraction strings, for example with four fractional bits, 0.96874999… (just below 31⁄32) and 0.96875 (31⁄32) are now parsed correctly as 0.9375 (15⁄16) and 1.0.
Version 0.4.1 news (2019-08-12)
- All fixed-point types now implement
FromStr
. - The methods
from_str_binary
,from_str_octal
andfrom_str_hex
were added.
Version 0.4.0 news (2019-08-08)
- The fixed crate now requires rustc version 1.31.0 or later.
- The
traits
module was added, with its traitsFixed
,FixedSigned
,FixedUnsigned
,FromFixed
,ToFixed
,LossyFrom
andLossyInto
. - The
saturating_neg
method was added to all fixed-point numbers, and thesaturating_abs
method was added to signed fixed-point numbers. - The
consts
module was added. - The
signum
method now wraps instead of panics in release mode.
Incompatible changes
- The sealed traits
Int
andFloat
now have no provided methods; the methods in the old implementation are new provided byFromFixed
andToFixed
. - Deprecated methods were removed.
Contributors
Other releases
Details on other releases can be found in RELEASES.md.
Quick examples
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.
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.
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.