mirror of
https://github.com/pezkuwichain/pezkuwi-subxt.git
synced 2026-04-26 20:27:58 +00:00
Xiliang Chen
d1261d3482
* add fixed128 * fix build * re-export * fix test * saturating_pow * Update primitives/arithmetic/src/fixed128.rs Co-Authored-By: Shawn Tabrizi <shawntabrizi@gmail.com> Co-authored-by: Shawn Tabrizi <shawntabrizi@gmail.com>
1181 lines
36 KiB
Rust
1181 lines
36 KiB
Rust
// Copyright 2019-2020 Parity Technologies (UK) Ltd.
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// This file is part of Substrate.
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// Substrate is free software: you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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// Substrate is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU General Public License
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// along with Substrate. If not, see <http://www.gnu.org/licenses/>.
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#[cfg(feature = "std")]
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use serde::{Serialize, Deserialize};
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use sp_std::{ops, fmt, prelude::*, convert::TryInto};
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use codec::{Encode, CompactAs};
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use crate::traits::{
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SaturatedConversion, UniqueSaturatedInto, Saturating, BaseArithmetic, Bounded, Zero,
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};
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use sp_debug_derive::RuntimeDebug;
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/// Something that implements a fixed point ration with an arbitrary granularity `X`, as _parts per
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/// `X`_.
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pub trait PerThing:
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Sized + Saturating + Copy + Default + Eq + PartialEq + Ord + PartialOrd + Bounded + fmt::Debug
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{
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/// The data type used to build this per-thingy.
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type Inner: BaseArithmetic + Copy + fmt::Debug;
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/// A data type larger than `Self::Inner`, used to avoid overflow in some computations.
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/// It must be able to compute `ACCURACY^2`.
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type Upper: BaseArithmetic + Copy + From<Self::Inner> + TryInto<Self::Inner> + fmt::Debug;
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/// The accuracy of this type.
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const ACCURACY: Self::Inner;
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/// Equivalent to `Self::from_parts(0)`.
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fn zero() -> Self { Self::from_parts(Self::Inner::zero()) }
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/// Return `true` if this is nothing.
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fn is_zero(&self) -> bool { self.deconstruct() == Self::Inner::zero() }
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/// Equivalent to `Self::from_parts(Self::ACCURACY)`.
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fn one() -> Self { Self::from_parts(Self::ACCURACY) }
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/// Return `true` if this is one.
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fn is_one(&self) -> bool { self.deconstruct() == Self::ACCURACY }
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/// Build this type from a percent. Equivalent to `Self::from_parts(x * Self::ACCURACY / 100)`
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/// but more accurate.
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fn from_percent(x: Self::Inner) -> Self {
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let a = x.min(100.into());
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let b = Self::ACCURACY;
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// if Self::ACCURACY % 100 > 0 then we need the correction for accuracy
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let c = rational_mul_correction::<Self::Inner, Self>(b, a, 100.into(), Rounding::Nearest);
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Self::from_parts(a / 100.into() * b + c)
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}
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/// Return the product of multiplication of this value by itself.
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fn square(self) -> Self {
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let p = Self::Upper::from(self.deconstruct());
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let q = Self::Upper::from(Self::ACCURACY);
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Self::from_rational_approximation(p * p, q * q)
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}
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/// Multiplication that always rounds down to a whole number. The standard `Mul` rounds to the
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/// nearest whole number.
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///
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/// ```rust
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/// # use sp_arithmetic::{Percent, PerThing};
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/// # fn main () {
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/// // round to nearest
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/// assert_eq!(Percent::from_percent(34) * 10u64, 3);
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/// assert_eq!(Percent::from_percent(36) * 10u64, 4);
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///
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/// // round down
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/// assert_eq!(Percent::from_percent(34).mul_floor(10u64), 3);
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/// assert_eq!(Percent::from_percent(36).mul_floor(10u64), 3);
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/// # }
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/// ```
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fn mul_floor<N>(self, b: N) -> N
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where N: Clone + From<Self::Inner> + UniqueSaturatedInto<Self::Inner> + ops::Rem<N, Output=N> +
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ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N>
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{
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overflow_prune_mul::<N, Self>(b, self.deconstruct(), Rounding::Down)
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}
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/// Multiplication that always rounds the result up to a whole number. The standard `Mul`
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/// rounds to the nearest whole number.
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///
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/// ```rust
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/// # use sp_arithmetic::{Percent, PerThing};
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/// # fn main () {
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/// // round to nearest
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/// assert_eq!(Percent::from_percent(34) * 10u64, 3);
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/// assert_eq!(Percent::from_percent(36) * 10u64, 4);
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///
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/// // round up
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/// assert_eq!(Percent::from_percent(34).mul_ceil(10u64), 4);
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/// assert_eq!(Percent::from_percent(36).mul_ceil(10u64), 4);
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/// # }
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/// ```
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fn mul_ceil<N>(self, b: N) -> N
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where N: Clone + From<Self::Inner> + UniqueSaturatedInto<Self::Inner> + ops::Rem<N, Output=N> +
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ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N>
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{
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overflow_prune_mul::<N, Self>(b, self.deconstruct(), Rounding::Up)
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}
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/// Saturating multiplication by the reciprocal of `self`. The result is rounded to the
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/// nearest whole number and saturates at the numeric bounds instead of overflowing.
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///
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/// ```rust
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/// # use sp_arithmetic::{Percent, PerThing};
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/// # fn main () {
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/// assert_eq!(Percent::from_percent(50).saturating_reciprocal_mul(10u64), 20);
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/// # }
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/// ```
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fn saturating_reciprocal_mul<N>(self, b: N) -> N
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where N: Clone + From<Self::Inner> + UniqueSaturatedInto<Self::Inner> + ops::Rem<N, Output=N> +
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ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N> + Saturating
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{
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saturating_reciprocal_mul::<N, Self>(b, self.deconstruct(), Rounding::Nearest)
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}
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/// Saturating multiplication by the reciprocal of `self`. The result is rounded down to the
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/// nearest whole number and saturates at the numeric bounds instead of overflowing.
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///
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/// ```rust
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/// # use sp_arithmetic::{Percent, PerThing};
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/// # fn main () {
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/// // round to nearest
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/// assert_eq!(Percent::from_percent(60).saturating_reciprocal_mul(10u64), 17);
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/// // round down
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/// assert_eq!(Percent::from_percent(60).saturating_reciprocal_mul_floor(10u64), 16);
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/// # }
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/// ```
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fn saturating_reciprocal_mul_floor<N>(self, b: N) -> N
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where N: Clone + From<Self::Inner> + UniqueSaturatedInto<Self::Inner> + ops::Rem<N, Output=N> +
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ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N> + Saturating
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{
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saturating_reciprocal_mul::<N, Self>(b, self.deconstruct(), Rounding::Down)
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}
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/// Saturating multiplication by the reciprocal of `self`. The result is rounded up to the
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/// nearest whole number and saturates at the numeric bounds instead of overflowing.
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///
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/// ```rust
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/// # use sp_arithmetic::{Percent, PerThing};
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/// # fn main () {
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/// // round to nearest
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/// assert_eq!(Percent::from_percent(61).saturating_reciprocal_mul(10u64), 16);
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/// // round up
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/// assert_eq!(Percent::from_percent(61).saturating_reciprocal_mul_ceil(10u64), 17);
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/// # }
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/// ```
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fn saturating_reciprocal_mul_ceil<N>(self, b: N) -> N
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where N: Clone + From<Self::Inner> + UniqueSaturatedInto<Self::Inner> + ops::Rem<N, Output=N> +
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ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N> + Saturating
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{
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saturating_reciprocal_mul::<N, Self>(b, self.deconstruct(), Rounding::Up)
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}
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/// Consume self and return the number of parts per thing.
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fn deconstruct(self) -> Self::Inner;
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/// Build this type from a number of parts per thing.
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fn from_parts(parts: Self::Inner) -> Self;
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/// Converts a fraction into `Self`.
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#[cfg(feature = "std")]
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fn from_fraction(x: f64) -> Self;
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/// Approximate the fraction `p/q` into a per-thing fraction. This will never overflow.
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///
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/// The computation of this approximation is performed in the generic type `N`. Given
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/// `M` as the data type that can hold the maximum value of this per-thing (e.g. u32 for
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/// perbill), this can only work if `N == M` or `N: From<M> + TryInto<M>`.
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///
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/// Note that this always rounds _down_, i.e.
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///
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/// ```rust
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/// # use sp_arithmetic::{Percent, PerThing};
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/// # fn main () {
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/// // 989/100 is technically closer to 99%.
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/// assert_eq!(
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/// Percent::from_rational_approximation(989, 1000),
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/// Percent::from_parts(98),
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/// );
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/// # }
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/// ```
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fn from_rational_approximation<N>(p: N, q: N) -> Self
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where N: Clone + Ord + From<Self::Inner> + TryInto<Self::Inner> + TryInto<Self::Upper> +
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ops::Div<N, Output=N> + ops::Rem<N, Output=N> + ops::Add<N, Output=N>;
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}
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/// The rounding method to use.
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///
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/// `PerThing`s are unsigned so `Up` means towards infinity and `Down` means towards zero.
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/// `Nearest` will round an exact half down.
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enum Rounding {
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Up,
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Down,
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Nearest,
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}
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/// Saturating reciprocal multiplication. Compute `x / self`, saturating at the numeric
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/// bounds instead of overflowing.
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fn saturating_reciprocal_mul<N, P>(
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x: N,
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part: P::Inner,
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rounding: Rounding,
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) -> N
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where
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N: Clone + From<P::Inner> + UniqueSaturatedInto<P::Inner> + ops::Div<N, Output=N> + ops::Mul<N,
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Output=N> + ops::Add<N, Output=N> + ops::Rem<N, Output=N> + Saturating,
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P: PerThing,
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{
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let maximum: N = P::ACCURACY.into();
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let c = rational_mul_correction::<N, P>(
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x.clone(),
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P::ACCURACY,
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part,
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rounding,
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);
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(x / part.into()).saturating_mul(maximum).saturating_add(c)
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}
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/// Overflow-prune multiplication. Accurately multiply a value by `self` without overflowing.
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fn overflow_prune_mul<N, P>(
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x: N,
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part: P::Inner,
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rounding: Rounding,
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) -> N
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where
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N: Clone + From<P::Inner> + UniqueSaturatedInto<P::Inner> + ops::Div<N, Output=N> + ops::Mul<N,
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Output=N> + ops::Add<N, Output=N> + ops::Rem<N, Output=N>,
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P: PerThing,
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{
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let maximum: N = P::ACCURACY.into();
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let part_n: N = part.into();
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let c = rational_mul_correction::<N, P>(
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x.clone(),
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part,
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P::ACCURACY,
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rounding,
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);
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(x / maximum) * part_n + c
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}
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/// Compute the error due to integer division in the expression `x / denom * numer`.
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///
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/// Take the remainder of `x / denom` and multiply by `numer / denom`. The result can be added
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/// to `x / denom * numer` for an accurate result.
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fn rational_mul_correction<N, P>(
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x: N,
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numer: P::Inner,
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denom: P::Inner,
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rounding: Rounding,
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) -> N
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where
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N: From<P::Inner> + UniqueSaturatedInto<P::Inner> + ops::Div<N, Output=N> + ops::Mul<N,
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Output=N> + ops::Add<N, Output=N> + ops::Rem<N, Output=N>,
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P: PerThing,
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{
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let numer_upper = P::Upper::from(numer);
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let denom_n = N::from(denom);
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let denom_upper = P::Upper::from(denom);
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let rem = x.rem(denom_n);
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// `rem` is less than `denom`, which fits in `P::Inner`.
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let rem_inner = rem.saturated_into::<P::Inner>();
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// `P::Upper` always fits `P::Inner::max_value().pow(2)`, thus it fits `rem * numer`.
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let rem_mul_upper = P::Upper::from(rem_inner) * numer_upper;
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// `rem` is less than `denom`, so `rem * numer / denom` is less than `numer`, which fits in
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// `P::Inner`.
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let mut rem_mul_div_inner = (rem_mul_upper / denom_upper).saturated_into::<P::Inner>();
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match rounding {
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// Already rounded down
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Rounding::Down => {},
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// Round up if the fractional part of the result is non-zero.
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Rounding::Up => if rem_mul_upper % denom_upper > 0.into() {
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// `rem * numer / denom` is less than `numer`, so this will not overflow.
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rem_mul_div_inner = rem_mul_div_inner + 1.into();
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},
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// Round up if the fractional part of the result is greater than a half. An exact half is
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// rounded down.
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Rounding::Nearest => if rem_mul_upper % denom_upper > denom_upper / 2.into() {
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// `rem * numer / denom` is less than `numer`, so this will not overflow.
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rem_mul_div_inner = rem_mul_div_inner + 1.into();
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},
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}
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rem_mul_div_inner.into()
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}
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macro_rules! implement_per_thing {
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(
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$name:ident,
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$test_mod:ident,
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[$($test_units:tt),+],
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$max:tt,
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$type:ty,
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$upper_type:ty,
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$title:expr $(,)?
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) => {
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/// A fixed point representation of a number in the range [0, 1].
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///
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#[doc = $title]
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#[cfg_attr(feature = "std", derive(Serialize, Deserialize))]
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#[derive(Encode, Copy, Clone, Default, PartialEq, Eq, PartialOrd, Ord,
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RuntimeDebug, CompactAs)]
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pub struct $name($type);
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impl PerThing for $name {
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type Inner = $type;
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type Upper = $upper_type;
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const ACCURACY: Self::Inner = $max;
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/// Consume self and return the number of parts per thing.
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fn deconstruct(self) -> Self::Inner { self.0 }
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/// Build this type from a number of parts per thing.
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fn from_parts(parts: Self::Inner) -> Self { Self(parts.min($max)) }
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#[cfg(feature = "std")]
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fn from_fraction(x: f64) -> Self {
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Self::from_parts((x * $max as f64) as Self::Inner)
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}
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fn from_rational_approximation<N>(p: N, q: N) -> Self
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where N: Clone + Ord + From<Self::Inner> + TryInto<Self::Inner> + TryInto<Self::Upper>
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+ ops::Div<N, Output=N> + ops::Rem<N, Output=N> + ops::Add<N, Output=N>
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{
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let div_ceil = |x: N, f: N| -> N {
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let mut o = x.clone() / f.clone();
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let r = x.rem(f.clone());
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if r > N::from(0) {
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o = o + N::from(1);
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}
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o
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};
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// q cannot be zero.
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let q: N = q.max((1 as Self::Inner).into());
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// p should not be bigger than q.
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let p: N = p.min(q.clone());
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let factor: N = div_ceil(q.clone(), $max.into()).max((1 as Self::Inner).into());
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// q cannot overflow: (q / (q/$max)) < $max. p < q hence p also cannot overflow.
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let q_reduce: $type = (q.clone() / factor.clone())
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.try_into()
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.map_err(|_| "Failed to convert")
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.expect(
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"q / ceil(q/$max) < $max. Macro prevents any type being created that \
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does not satisfy this; qed"
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);
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let p_reduce: $type = (p / factor)
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.try_into()
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.map_err(|_| "Failed to convert")
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.expect(
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"q / ceil(q/$max) < $max. Macro prevents any type being created that \
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does not satisfy this; qed"
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);
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// `p_reduced` and `q_reduced` are withing Self::Inner. Mul by another $max will
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// always fit in $upper_type. This is guaranteed by the macro tests.
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let part =
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p_reduce as $upper_type
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* <$upper_type>::from($max)
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/ q_reduce as $upper_type;
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$name(part as Self::Inner)
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}
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}
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impl $name {
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/// From an explicitly defined number of parts per maximum of the type.
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///
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/// This can be called at compile time.
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// needed only for peru16. Since peru16 is the only type in which $max ==
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// $type::max_value(), rustc is being a smart-a** here by warning that the comparison
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// is not needed.
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#[allow(unused_comparisons)]
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pub const fn from_parts(parts: $type) -> Self {
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Self([parts, $max][(parts > $max) as usize])
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}
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/// Converts a percent into `Self`. Equal to `x / 100`.
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///
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/// This can be created at compile time.
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pub const fn from_percent(x: $type) -> Self {
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Self(([x, 100][(x > 100) as usize] as $upper_type * $max as $upper_type / 100) as $type)
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}
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/// See [`PerThing::one`].
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pub fn one() -> Self {
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<Self as PerThing>::one()
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}
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/// See [`PerThing::is_one`].
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pub fn is_one(&self) -> bool {
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PerThing::is_one(self)
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}
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/// See [`PerThing::zero`].
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pub fn zero() -> Self {
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<Self as PerThing>::zero()
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}
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/// See [`PerThing::is_zero`].
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pub fn is_zero(&self) -> bool {
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PerThing::is_zero(self)
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}
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/// See [`PerThing::deconstruct`].
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pub fn deconstruct(self) -> $type {
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PerThing::deconstruct(self)
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}
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/// See [`PerThing::square`].
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pub fn square(self) -> Self {
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PerThing::square(self)
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}
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/// See [`PerThing::from_fraction`].
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#[cfg(feature = "std")]
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pub fn from_fraction(x: f64) -> Self {
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<Self as PerThing>::from_fraction(x)
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}
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/// See [`PerThing::from_rational_approximation`].
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pub fn from_rational_approximation<N>(p: N, q: N) -> Self
|
|
where N: Clone + Ord + From<$type> + TryInto<$type> +
|
|
TryInto<$upper_type> + ops::Div<N, Output=N> + ops::Rem<N, Output=N> +
|
|
ops::Add<N, Output=N> {
|
|
<Self as PerThing>::from_rational_approximation(p, q)
|
|
}
|
|
|
|
/// See [`PerThing::mul_floor`].
|
|
pub fn mul_floor<N>(self, b: N) -> N
|
|
where N: Clone + From<$type> + UniqueSaturatedInto<$type> +
|
|
ops::Rem<N, Output=N> + ops::Div<N, Output=N> + ops::Mul<N, Output=N> +
|
|
ops::Add<N, Output=N> {
|
|
PerThing::mul_floor(self, b)
|
|
}
|
|
|
|
/// See [`PerThing::mul_ceil`].
|
|
pub fn mul_ceil<N>(self, b: N) -> N
|
|
where N: Clone + From<$type> + UniqueSaturatedInto<$type> +
|
|
ops::Rem<N, Output=N> + ops::Div<N, Output=N> + ops::Mul<N, Output=N> +
|
|
ops::Add<N, Output=N> {
|
|
PerThing::mul_ceil(self, b)
|
|
}
|
|
|
|
/// See [`PerThing::saturating_reciprocal_mul`].
|
|
pub fn saturating_reciprocal_mul<N>(self, b: N) -> N
|
|
where N: Clone + From<$type> + UniqueSaturatedInto<$type> + ops::Rem<N, Output=N> +
|
|
ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N> +
|
|
Saturating {
|
|
PerThing::saturating_reciprocal_mul(self, b)
|
|
}
|
|
|
|
/// See [`PerThing::saturating_reciprocal_mul_floor`].
|
|
pub fn saturating_reciprocal_mul_floor<N>(self, b: N) -> N
|
|
where N: Clone + From<$type> + UniqueSaturatedInto<$type> + ops::Rem<N, Output=N> +
|
|
ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N> +
|
|
Saturating {
|
|
PerThing::saturating_reciprocal_mul_floor(self, b)
|
|
}
|
|
|
|
/// See [`PerThing::saturating_reciprocal_mul_ceil`].
|
|
pub fn saturating_reciprocal_mul_ceil<N>(self, b: N) -> N
|
|
where N: Clone + From<$type> + UniqueSaturatedInto<$type> + ops::Rem<N, Output=N> +
|
|
ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N> +
|
|
Saturating {
|
|
PerThing::saturating_reciprocal_mul_ceil(self, b)
|
|
}
|
|
}
|
|
|
|
impl Saturating for $name {
|
|
/// Saturating addition. Compute `self + rhs`, saturating at the numeric bounds instead of
|
|
/// overflowing. This operation is lossless if it does not saturate.
|
|
fn saturating_add(self, rhs: Self) -> Self {
|
|
// defensive-only: since `$max * 2 < $type::max_value()`, this can never overflow.
|
|
Self::from_parts(self.0.saturating_add(rhs.0))
|
|
}
|
|
|
|
/// Saturating subtraction. Compute `self - rhs`, saturating at the numeric bounds instead of
|
|
/// overflowing. This operation is lossless if it does not saturate.
|
|
fn saturating_sub(self, rhs: Self) -> Self {
|
|
Self::from_parts(self.0.saturating_sub(rhs.0))
|
|
}
|
|
|
|
/// Saturating multiply. Compute `self * rhs`, saturating at the numeric bounds instead of
|
|
/// overflowing. This operation is lossy.
|
|
fn saturating_mul(self, rhs: Self) -> Self {
|
|
let a = self.0 as $upper_type;
|
|
let b = rhs.0 as $upper_type;
|
|
let m = <$upper_type>::from($max);
|
|
let parts = a * b / m;
|
|
// This will always fit into $type.
|
|
Self::from_parts(parts as $type)
|
|
}
|
|
|
|
/// Saturating exponentiation. Computes `self.pow(exp)`, saturating at the numeric
|
|
/// bounds instead of overflowing. This operation is lossy.
|
|
fn saturating_pow(self, exp: usize) -> Self {
|
|
if self.is_zero() || self.is_one() {
|
|
self
|
|
} else {
|
|
let p = <$name as PerThing>::Upper::from(self.deconstruct());
|
|
let q = <$name as PerThing>::Upper::from(Self::ACCURACY);
|
|
let mut s = Self::one();
|
|
for _ in 0..exp {
|
|
if s.is_zero() {
|
|
break;
|
|
} else {
|
|
// x^2 always fits in Self::Upper if x fits in Self::Inner.
|
|
// Verified by a test.
|
|
s = Self::from_rational_approximation(
|
|
<$name as PerThing>::Upper::from(s.deconstruct()) * p,
|
|
q * q,
|
|
);
|
|
}
|
|
}
|
|
s
|
|
}
|
|
}
|
|
}
|
|
|
|
impl codec::Decode for $name {
|
|
fn decode<I: codec::Input>(input: &mut I) -> Result<Self, codec::Error> {
|
|
let inner = <$type as codec::Decode>::decode(input)?;
|
|
|
|
if inner <= <Self as PerThing>::ACCURACY {
|
|
Ok(Self(inner))
|
|
} else {
|
|
Err("Value is greater than allowed maximum!".into())
|
|
}
|
|
}
|
|
}
|
|
|
|
impl crate::traits::Bounded for $name {
|
|
fn min_value() -> Self {
|
|
<Self as PerThing>::zero()
|
|
}
|
|
|
|
fn max_value() -> Self {
|
|
<Self as PerThing>::one()
|
|
}
|
|
}
|
|
|
|
impl ops::Div for $name {
|
|
type Output = Self;
|
|
|
|
fn div(self, rhs: Self) -> Self::Output {
|
|
let p = self.0;
|
|
let q = rhs.0;
|
|
Self::from_rational_approximation(p, q)
|
|
}
|
|
}
|
|
|
|
/// Non-overflow multiplication.
|
|
///
|
|
/// This is tailored to be used with a balance type.
|
|
impl<N> ops::Mul<N> for $name
|
|
where
|
|
N: Clone + From<$type> + UniqueSaturatedInto<$type> + ops::Rem<N, Output=N>
|
|
+ ops::Div<N, Output=N> + ops::Mul<N, Output=N> + ops::Add<N, Output=N>,
|
|
{
|
|
type Output = N;
|
|
fn mul(self, b: N) -> Self::Output {
|
|
overflow_prune_mul::<N, Self>(b, self.deconstruct(), Rounding::Nearest)
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod $test_mod {
|
|
use codec::{Encode, Decode};
|
|
use super::{$name, Saturating, RuntimeDebug, PerThing};
|
|
use crate::traits::Zero;
|
|
|
|
#[test]
|
|
fn macro_expanded_correctly() {
|
|
// needed for the `from_percent` to work. UPDATE: this is no longer needed; yet note
|
|
// that tests that use percentage or fractions such as $name::from_fraction(0.2) to
|
|
// create values will most likely be inaccurate when used with per_things that are
|
|
// not multiples of 100.
|
|
// assert!($max >= 100);
|
|
// assert!($max % 100 == 0);
|
|
|
|
// needed for `from_rational_approximation`
|
|
assert!(2 * ($max as $upper_type) < <$upper_type>::max_value());
|
|
assert!(<$upper_type>::from($max) < <$upper_type>::max_value());
|
|
|
|
// for something like percent they can be the same.
|
|
assert!((<$type>::max_value() as $upper_type) <= <$upper_type>::max_value());
|
|
assert!(<$upper_type>::from($max).checked_mul($max.into()).is_some());
|
|
|
|
// make sure saturating_pow won't overflow the upper type
|
|
assert!(<$upper_type>::from($max) * <$upper_type>::from($max) < <$upper_type>::max_value());
|
|
}
|
|
|
|
#[derive(Encode, Decode, PartialEq, Eq, RuntimeDebug)]
|
|
struct WithCompact<T: codec::HasCompact> {
|
|
data: T,
|
|
}
|
|
|
|
#[test]
|
|
fn has_compact() {
|
|
let data = WithCompact { data: $name(1) };
|
|
let encoded = data.encode();
|
|
assert_eq!(data, WithCompact::<$name>::decode(&mut &encoded[..]).unwrap());
|
|
}
|
|
|
|
#[test]
|
|
fn compact_encoding() {
|
|
let tests = [
|
|
// assume all per_things have the size u8 at least.
|
|
(0 as $type, 1usize),
|
|
(1 as $type, 1usize),
|
|
(63, 1),
|
|
(64, 2),
|
|
(65, 2),
|
|
// (<$type>::max_value(), <$type>::max_value().encode().len() + 1)
|
|
];
|
|
for &(n, l) in &tests {
|
|
let compact: codec::Compact<$name> = $name(n).into();
|
|
let encoded = compact.encode();
|
|
assert_eq!(encoded.len(), l);
|
|
let decoded = <codec::Compact<$name>>::decode(&mut & encoded[..])
|
|
.unwrap();
|
|
let per_thingy: $name = decoded.into();
|
|
assert_eq!(per_thingy, $name(n));
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn fail_on_invalid_encoded_value() {
|
|
let value = <$upper_type>::from($max) * 2;
|
|
let casted = value as $type;
|
|
let encoded = casted.encode();
|
|
|
|
// For types where `$max == $type::maximum()` we can not
|
|
if <$upper_type>::from(casted) == value {
|
|
assert_eq!(
|
|
$name::decode(&mut &encoded[..]),
|
|
Err("Value is greater than allowed maximum!".into()),
|
|
);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn per_thing_api_works() {
|
|
// some really basic stuff
|
|
assert_eq!($name::zero(), $name::from_parts(Zero::zero()));
|
|
assert_eq!($name::one(), $name::from_parts($max));
|
|
assert_eq!($name::ACCURACY, $max);
|
|
|
|
assert_eq!($name::from_percent(0), $name::from_parts(Zero::zero()));
|
|
assert_eq!($name::from_percent(10), $name::from_parts($max / 10));
|
|
assert_eq!($name::from_percent(100), $name::from_parts($max));
|
|
assert_eq!($name::from_percent(200), $name::from_parts($max));
|
|
|
|
assert_eq!($name::from_fraction(0.0), $name::from_parts(Zero::zero()));
|
|
assert_eq!($name::from_fraction(0.1), $name::from_parts($max / 10));
|
|
assert_eq!($name::from_fraction(1.0), $name::from_parts($max));
|
|
}
|
|
|
|
macro_rules! u256ify {
|
|
($val:expr) => {
|
|
Into::<U256>::into($val)
|
|
};
|
|
}
|
|
|
|
macro_rules! per_thing_mul_test {
|
|
($num_type:tt) => {
|
|
// multiplication from all sort of from_percent
|
|
assert_eq!(
|
|
$name::from_fraction(1.0) * $num_type::max_value(),
|
|
$num_type::max_value()
|
|
);
|
|
if $max % 100 == 0 {
|
|
assert_eq_error_rate!(
|
|
$name::from_percent(99) * $num_type::max_value(),
|
|
((Into::<U256>::into($num_type::max_value()) * 99u32) / 100u32).as_u128() as $num_type,
|
|
1,
|
|
);
|
|
assert_eq!(
|
|
$name::from_fraction(0.5) * $num_type::max_value(),
|
|
$num_type::max_value() / 2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
$name::from_percent(1) * $num_type::max_value(),
|
|
$num_type::max_value() / 100,
|
|
1,
|
|
);
|
|
} else {
|
|
assert_eq!(
|
|
$name::from_fraction(0.99) * <$num_type>::max_value(),
|
|
(
|
|
(
|
|
u256ify!($name::from_fraction(0.99).0) *
|
|
u256ify!(<$num_type>::max_value()) /
|
|
u256ify!($max)
|
|
).as_u128()
|
|
) as $num_type,
|
|
);
|
|
assert_eq!(
|
|
$name::from_fraction(0.50) * <$num_type>::max_value(),
|
|
(
|
|
(
|
|
u256ify!($name::from_fraction(0.50).0) *
|
|
u256ify!(<$num_type>::max_value()) /
|
|
u256ify!($max)
|
|
).as_u128()
|
|
) as $num_type,
|
|
);
|
|
assert_eq!(
|
|
$name::from_fraction(0.01) * <$num_type>::max_value(),
|
|
(
|
|
(
|
|
u256ify!($name::from_fraction(0.01).0) *
|
|
u256ify!(<$num_type>::max_value()) /
|
|
u256ify!($max)
|
|
).as_u128()
|
|
) as $num_type,
|
|
);
|
|
}
|
|
|
|
assert_eq!($name::from_fraction(0.0) * $num_type::max_value(), 0);
|
|
|
|
// // multiplication with bounds
|
|
assert_eq!($name::one() * $num_type::max_value(), $num_type::max_value());
|
|
assert_eq!($name::zero() * $num_type::max_value(), 0);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn per_thing_mul_works() {
|
|
use primitive_types::U256;
|
|
|
|
// accuracy test
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1 as $type, 3) * 30 as $type,
|
|
10,
|
|
);
|
|
|
|
$(per_thing_mul_test!($test_units);)*
|
|
}
|
|
|
|
#[test]
|
|
fn per_thing_mul_rounds_to_nearest_number() {
|
|
assert_eq!($name::from_fraction(0.33) * 10u64, 3);
|
|
assert_eq!($name::from_fraction(0.34) * 10u64, 3);
|
|
assert_eq!($name::from_fraction(0.35) * 10u64, 3);
|
|
assert_eq!($name::from_fraction(0.36) * 10u64, 4);
|
|
}
|
|
|
|
#[test]
|
|
fn per_thing_multiplication_with_large_number() {
|
|
use primitive_types::U256;
|
|
let max_minus_one = $max - 1;
|
|
assert_eq_error_rate!(
|
|
$name::from_parts(max_minus_one) * std::u128::MAX,
|
|
((Into::<U256>::into(std::u128::MAX) * max_minus_one) / $max).as_u128(),
|
|
1,
|
|
);
|
|
}
|
|
|
|
macro_rules! per_thing_from_rationale_approx_test {
|
|
($num_type:tt) => {
|
|
// within accuracy boundary
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1 as $num_type, 0),
|
|
$name::one(),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1 as $num_type, 1),
|
|
$name::one(),
|
|
);
|
|
assert_eq_error_rate!(
|
|
$name::from_rational_approximation(1 as $num_type, 3).0,
|
|
$name::from_parts($max / 3).0,
|
|
2
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1 as $num_type, 10),
|
|
$name::from_fraction(0.10),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1 as $num_type, 4),
|
|
$name::from_fraction(0.25),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1 as $num_type, 4),
|
|
$name::from_rational_approximation(2 as $num_type, 8),
|
|
);
|
|
// no accurate anymore but won't overflow.
|
|
assert_eq_error_rate!(
|
|
$name::from_rational_approximation(
|
|
$num_type::max_value() - 1,
|
|
$num_type::max_value()
|
|
).0 as $upper_type,
|
|
$name::one().0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
$name::from_rational_approximation(
|
|
$num_type::max_value() / 3,
|
|
$num_type::max_value()
|
|
).0 as $upper_type,
|
|
$name::from_parts($max / 3).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1, $num_type::max_value()),
|
|
$name::zero(),
|
|
);
|
|
};
|
|
}
|
|
|
|
#[test]
|
|
fn per_thing_from_rationale_approx_works() {
|
|
// This is just to make sure something like Percent which _might_ get built from a
|
|
// u8 does not overflow in the context of this test.
|
|
let max_value = <$upper_type>::from($max);
|
|
|
|
// almost at the edge
|
|
assert_eq!(
|
|
$name::from_rational_approximation(max_value - 1, max_value + 1),
|
|
$name::from_parts($max - 2),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1, $max - 1),
|
|
$name::from_parts(1),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1, $max),
|
|
$name::from_parts(1),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(2, 2 * max_value - 1),
|
|
$name::from_parts(1),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(1, max_value + 1),
|
|
$name::zero(),
|
|
);
|
|
assert_eq!(
|
|
$name::from_rational_approximation(3 * max_value / 2, 3 * max_value),
|
|
$name::from_fraction(0.5),
|
|
);
|
|
|
|
$(per_thing_from_rationale_approx_test!($test_units);)*
|
|
}
|
|
|
|
#[test]
|
|
fn per_things_mul_operates_in_output_type() {
|
|
// assert_eq!($name::from_fraction(0.5) * 100u32, 50u32);
|
|
assert_eq!($name::from_fraction(0.5) * 100u64, 50u64);
|
|
assert_eq!($name::from_fraction(0.5) * 100u128, 50u128);
|
|
}
|
|
|
|
#[test]
|
|
fn per_thing_saturating_op_works() {
|
|
assert_eq_error_rate!(
|
|
$name::from_fraction(0.5).saturating_add($name::from_fraction(0.4)).0 as $upper_type,
|
|
$name::from_fraction(0.9).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
$name::from_fraction(0.5).saturating_add($name::from_fraction(0.5)).0 as $upper_type,
|
|
$name::one().0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq!(
|
|
$name::from_fraction(0.6).saturating_add($name::from_fraction(0.5)),
|
|
$name::one(),
|
|
);
|
|
|
|
assert_eq_error_rate!(
|
|
$name::from_fraction(0.6).saturating_sub($name::from_fraction(0.5)).0 as $upper_type,
|
|
$name::from_fraction(0.1).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq!(
|
|
$name::from_fraction(0.6).saturating_sub($name::from_fraction(0.6)),
|
|
$name::from_fraction(0.0),
|
|
);
|
|
assert_eq!(
|
|
$name::from_fraction(0.6).saturating_sub($name::from_fraction(0.7)),
|
|
$name::from_fraction(0.0),
|
|
);
|
|
|
|
assert_eq_error_rate!(
|
|
$name::from_fraction(0.5).saturating_mul($name::from_fraction(0.5)).0 as $upper_type,
|
|
$name::from_fraction(0.25).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
$name::from_fraction(0.2).saturating_mul($name::from_fraction(0.2)).0 as $upper_type,
|
|
$name::from_fraction(0.04).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
$name::from_fraction(0.1).saturating_mul($name::from_fraction(0.1)).0 as $upper_type,
|
|
$name::from_fraction(0.01).0 as $upper_type,
|
|
1,
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn per_thing_square_works() {
|
|
assert_eq!($name::from_fraction(1.0).square(), $name::from_fraction(1.0));
|
|
assert_eq!($name::from_fraction(0.5).square(), $name::from_fraction(0.25));
|
|
assert_eq!($name::from_fraction(0.1).square(), $name::from_fraction(0.01));
|
|
assert_eq!(
|
|
$name::from_fraction(0.02).square(),
|
|
$name::from_parts((4 * <$upper_type>::from($max) / 100 / 100) as $type)
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn per_things_div_works() {
|
|
// normal
|
|
assert_eq_error_rate!(
|
|
($name::from_fraction(0.1) / $name::from_fraction(0.20)).0 as $upper_type,
|
|
$name::from_fraction(0.50).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
($name::from_fraction(0.1) / $name::from_fraction(0.10)).0 as $upper_type,
|
|
$name::from_fraction(1.0).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
($name::from_fraction(0.1) / $name::from_fraction(0.0)).0 as $upper_type,
|
|
$name::from_fraction(1.0).0 as $upper_type,
|
|
2,
|
|
);
|
|
|
|
// will not overflow
|
|
assert_eq_error_rate!(
|
|
($name::from_fraction(0.10) / $name::from_fraction(0.05)).0 as $upper_type,
|
|
$name::from_fraction(1.0).0 as $upper_type,
|
|
2,
|
|
);
|
|
assert_eq_error_rate!(
|
|
($name::from_fraction(1.0) / $name::from_fraction(0.5)).0 as $upper_type,
|
|
$name::from_fraction(1.0).0 as $upper_type,
|
|
2,
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn saturating_pow_works() {
|
|
// x^0 == 1
|
|
assert_eq!(
|
|
$name::from_parts($max / 2).saturating_pow(0),
|
|
$name::from_parts($max),
|
|
);
|
|
|
|
// x^1 == x
|
|
assert_eq!(
|
|
$name::from_parts($max / 2).saturating_pow(1),
|
|
$name::from_parts($max / 2),
|
|
);
|
|
|
|
// x^2
|
|
assert_eq!(
|
|
$name::from_parts($max / 2).saturating_pow(2),
|
|
$name::from_parts($max / 2).square(),
|
|
);
|
|
|
|
// x^3
|
|
assert_eq!(
|
|
$name::from_parts($max / 2).saturating_pow(3),
|
|
$name::from_parts($max / 8),
|
|
);
|
|
|
|
// 0^n == 0
|
|
assert_eq!(
|
|
$name::from_parts(0).saturating_pow(3),
|
|
$name::from_parts(0),
|
|
);
|
|
|
|
// 1^n == 1
|
|
assert_eq!(
|
|
$name::from_parts($max).saturating_pow(3),
|
|
$name::from_parts($max),
|
|
);
|
|
|
|
// (x < 1)^inf == 0 (where 2.pow(31) ~ inf)
|
|
assert_eq!(
|
|
$name::from_parts($max / 2).saturating_pow(2usize.pow(31)),
|
|
$name::from_parts(0),
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn saturating_reciprocal_mul_works() {
|
|
// divide by 1
|
|
assert_eq!(
|
|
$name::from_parts($max).saturating_reciprocal_mul(<$type>::from(10u8)),
|
|
10,
|
|
);
|
|
// divide by 1/2
|
|
assert_eq!(
|
|
$name::from_parts($max / 2).saturating_reciprocal_mul(<$type>::from(10u8)),
|
|
20,
|
|
);
|
|
// saturate
|
|
assert_eq!(
|
|
$name::from_parts(1).saturating_reciprocal_mul($max),
|
|
<$type>::max_value(),
|
|
);
|
|
// round to nearest
|
|
assert_eq!(
|
|
$name::from_percent(60).saturating_reciprocal_mul(<$type>::from(10u8)),
|
|
17,
|
|
);
|
|
// round down
|
|
assert_eq!(
|
|
$name::from_percent(60).saturating_reciprocal_mul_floor(<$type>::from(10u8)),
|
|
16,
|
|
);
|
|
// round to nearest
|
|
assert_eq!(
|
|
$name::from_percent(61).saturating_reciprocal_mul(<$type>::from(10u8)),
|
|
16,
|
|
);
|
|
// round up
|
|
assert_eq!(
|
|
$name::from_percent(61).saturating_reciprocal_mul_ceil(<$type>::from(10u8)),
|
|
17,
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn saturating_truncating_mul_works() {
|
|
assert_eq!(
|
|
$name::from_percent(49).mul_floor(10 as $type),
|
|
4,
|
|
);
|
|
let a: $upper_type = $name::from_percent(50).mul_floor(($max as $upper_type).pow(2));
|
|
let b: $upper_type = ($max as $upper_type).pow(2) / 2;
|
|
if $max % 2 == 0 {
|
|
assert_eq!(a, b);
|
|
} else {
|
|
// difference should be less that 1%, IE less than the error in `from_percent`
|
|
assert!(b - a < ($max as $upper_type).pow(2) / 100 as $upper_type);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn rational_mul_correction_works() {
|
|
assert_eq!(
|
|
super::rational_mul_correction::<$type, $name>(
|
|
<$type>::max_value(),
|
|
<$type>::max_value(),
|
|
<$type>::max_value(),
|
|
super::Rounding::Nearest,
|
|
),
|
|
0,
|
|
);
|
|
assert_eq!(
|
|
super::rational_mul_correction::<$type, $name>(
|
|
<$type>::max_value() - 1,
|
|
<$type>::max_value(),
|
|
<$type>::max_value(),
|
|
super::Rounding::Nearest,
|
|
),
|
|
<$type>::max_value() - 1,
|
|
);
|
|
assert_eq!(
|
|
super::rational_mul_correction::<$upper_type, $name>(
|
|
((<$type>::max_value() - 1) as $upper_type).pow(2),
|
|
<$type>::max_value(),
|
|
<$type>::max_value(),
|
|
super::Rounding::Nearest,
|
|
),
|
|
1,
|
|
);
|
|
// ((max^2 - 1) % max) * max / max == max - 1
|
|
assert_eq!(
|
|
super::rational_mul_correction::<$upper_type, $name>(
|
|
(<$type>::max_value() as $upper_type).pow(2) - 1,
|
|
<$type>::max_value(),
|
|
<$type>::max_value(),
|
|
super::Rounding::Nearest,
|
|
),
|
|
<$upper_type>::from((<$type>::max_value() - 1)),
|
|
);
|
|
// (max % 2) * max / 2 == max / 2
|
|
assert_eq!(
|
|
super::rational_mul_correction::<$upper_type, $name>(
|
|
(<$type>::max_value() as $upper_type).pow(2),
|
|
<$type>::max_value(),
|
|
2 as $type,
|
|
super::Rounding::Nearest,
|
|
),
|
|
<$type>::max_value() as $upper_type / 2,
|
|
);
|
|
// ((max^2 - 1) % max) * 2 / max == 2 (rounded up)
|
|
assert_eq!(
|
|
super::rational_mul_correction::<$upper_type, $name>(
|
|
(<$type>::max_value() as $upper_type).pow(2) - 1,
|
|
2 as $type,
|
|
<$type>::max_value(),
|
|
super::Rounding::Nearest,
|
|
),
|
|
2,
|
|
);
|
|
// ((max^2 - 1) % max) * 2 / max == 1 (rounded down)
|
|
assert_eq!(
|
|
super::rational_mul_correction::<$upper_type, $name>(
|
|
(<$type>::max_value() as $upper_type).pow(2) - 1,
|
|
2 as $type,
|
|
<$type>::max_value(),
|
|
super::Rounding::Down,
|
|
),
|
|
1,
|
|
);
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
implement_per_thing!(
|
|
Percent,
|
|
test_per_cent,
|
|
[u32, u64, u128],
|
|
100u8,
|
|
u8,
|
|
u16,
|
|
"_Percent_",
|
|
);
|
|
implement_per_thing!(
|
|
PerU16,
|
|
test_peru16,
|
|
[u32, u64, u128],
|
|
65535_u16,
|
|
u16,
|
|
u32,
|
|
"_Parts per 65535_",
|
|
);
|
|
implement_per_thing!(
|
|
Permill,
|
|
test_permill,
|
|
[u32, u64, u128],
|
|
1_000_000u32,
|
|
u32,
|
|
u64,
|
|
"_Parts per Million_",
|
|
);
|
|
implement_per_thing!(
|
|
Perbill,
|
|
test_perbill,
|
|
[u32, u64, u128],
|
|
1_000_000_000u32,
|
|
u32,
|
|
u64,
|
|
"_Parts per Billion_",
|
|
);
|
|
implement_per_thing!(
|
|
Perquintill,
|
|
test_perquintill,
|
|
[u64, u128],
|
|
1_000_000_000_000_000_000u64,
|
|
u64,
|
|
u128,
|
|
"_Parts per Quintillion_",
|
|
);
|