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Implement FixedPoint trait. (#5877)
* Implement Fixed trait. * Fix tests * Fix tests * Fix tests 2 * Address review comment regarding from_i129. * Remove precision by using log10() as suggested in review. * Add small comments. * Use checked versions + panic for ops::*. * Remove repeated test. * Uncomment test. * Remove casts. * Add more comments. * Add tests. * Panic on saturating_div_int * More tests. * More docs. * Saturating renames. * Fix to_bound doc. * Move some impl to trait. * Add range * Add macro pre. * More round() tests. * Delete confusion. * More impl to trait * Add doc for fixedpoint op. * Remove trailing spaces. * Suggested docs changes. * More tests and comments for roundings. * Some quickcheck tests. * Add missing panic, more test/comments. * Nits. * Rename. * Remove primitives-types import. * Apply review suggestions * Fix long lines and add some fuzz. * fix long line * Update fuzzer * Bump impl * fix warnings Co-authored-by: Gavin Wood <gavin@parity.io> Co-authored-by: Shawn Tabrizi <shawntabrizi@gmail.com>
This commit is contained in:
Marcio Diaz
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// This file is part of Substrate.
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// Copyright (C) 2020 Parity Technologies (UK) Ltd.
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// SPDX-License-Identifier: Apache-2.0
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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use codec::{Decode, Encode};
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use primitive_types::U256;
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use crate::{
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traits::{Bounded, Saturating, UniqueSaturatedInto, SaturatedConversion},
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PerThing, Perquintill,
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};
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use sp_std::{
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convert::{Into, TryFrom, TryInto},
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fmt, ops,
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num::NonZeroI128,
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};
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#[cfg(feature = "std")]
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use serde::{de, Deserialize, Deserializer, Serialize, Serializer};
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/// A signed fixed-point number.
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/// Can hold any value in the range [-170_141_183_460_469_231_731, 170_141_183_460_469_231_731]
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/// with fixed-point accuracy of 10 ** 18.
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#[derive(Encode, Decode, Default, Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
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pub struct Fixed128(i128);
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const DIV: i128 = 1_000_000_000_000_000_000;
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impl Fixed128 {
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/// Create self from a natural number.
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///
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/// Note that this might be lossy.
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pub fn from_natural(int: i128) -> Self {
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Self(int.saturating_mul(DIV))
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}
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/// Accuracy of `Fixed128`.
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pub const fn accuracy() -> i128 {
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DIV
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}
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/// Raw constructor. Equal to `parts / DIV`.
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pub const fn from_parts(parts: i128) -> Self {
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Self(parts)
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}
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/// Creates self from a rational number. Equal to `n/d`.
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///
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/// Note that this might be lossy. Only use this if you are sure that `n * DIV` can fit into an
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/// i128.
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pub fn from_rational<N: UniqueSaturatedInto<i128>>(n: N, d: NonZeroI128) -> Self {
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let n = n.unique_saturated_into();
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Self(n.saturating_mul(DIV.into()) / d.get())
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}
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/// Consume self and return the inner raw `i128` value.
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///
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/// Note this is a low level function, as the returned value is represented with accuracy.
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pub fn deconstruct(self) -> i128 {
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self.0
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}
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/// Takes the reciprocal(inverse) of Fixed128, 1/x
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pub fn recip(&self) -> Option<Self> {
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Self::from_natural(1i128).checked_div(self)
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}
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/// Checked add. Same semantic to `num_traits::CheckedAdd`.
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pub fn checked_add(&self, rhs: &Self) -> Option<Self> {
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self.0.checked_add(rhs.0).map(Self)
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}
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/// Checked sub. Same semantic to `num_traits::CheckedSub`.
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pub fn checked_sub(&self, rhs: &Self) -> Option<Self> {
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self.0.checked_sub(rhs.0).map(Self)
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}
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/// Checked mul. Same semantic to `num_traits::CheckedMul`.
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pub fn checked_mul(&self, rhs: &Self) -> Option<Self> {
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let signum = self.0.signum() * rhs.0.signum();
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let mut lhs = self.0;
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if lhs.is_negative() {
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lhs = lhs.saturating_mul(-1);
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}
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let mut rhs: i128 = rhs.0.saturated_into();
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if rhs.is_negative() {
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rhs = rhs.saturating_mul(-1);
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}
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U256::from(lhs)
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.checked_mul(U256::from(rhs))
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.and_then(|n| n.checked_div(U256::from(DIV)))
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.and_then(|n| TryInto::<i128>::try_into(n).ok())
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.map(|n| Self(n * signum))
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}
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/// Checked div. Same semantic to `num_traits::CheckedDiv`.
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pub fn checked_div(&self, rhs: &Self) -> Option<Self> {
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if rhs.0.signum() == 0 {
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return None;
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}
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if self.0 == 0 {
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return Some(*self);
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}
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let signum = self.0.signum() / rhs.0.signum();
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let mut lhs: i128 = self.0;
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if lhs.is_negative() {
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lhs = lhs.saturating_mul(-1);
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}
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let mut rhs: i128 = rhs.0.saturated_into();
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if rhs.is_negative() {
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rhs = rhs.saturating_mul(-1);
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}
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U256::from(lhs)
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.checked_mul(U256::from(DIV))
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.and_then(|n| n.checked_div(U256::from(rhs)))
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.and_then(|n| TryInto::<i128>::try_into(n).ok())
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.map(|n| Self(n * signum))
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}
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/// Checked mul for int type `N`.
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pub fn checked_mul_int<N>(&self, other: &N) -> Option<N>
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where
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N: Copy + TryFrom<i128> + TryInto<i128>,
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{
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N::try_into(*other).ok().and_then(|rhs| {
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let mut lhs = self.0;
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if lhs.is_negative() {
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lhs = lhs.saturating_mul(-1);
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}
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let mut rhs: i128 = rhs.saturated_into();
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let signum = self.0.signum() * rhs.signum();
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if rhs.is_negative() {
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rhs = rhs.saturating_mul(-1);
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}
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U256::from(lhs)
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.checked_mul(U256::from(rhs))
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.and_then(|n| n.checked_div(U256::from(DIV)))
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.and_then(|n| TryInto::<i128>::try_into(n).ok())
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.and_then(|n| TryInto::<N>::try_into(n * signum).ok())
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})
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}
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/// Checked mul for int type `N`.
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pub fn saturating_mul_int<N>(&self, other: &N) -> N
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where
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N: Copy + TryFrom<i128> + TryInto<i128> + Bounded,
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{
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self.checked_mul_int(other).unwrap_or_else(|| {
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N::try_into(*other)
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.map(|n| n.signum())
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.map(|n| n * self.0.signum())
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.map(|signum| {
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if signum.is_negative() {
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Bounded::min_value()
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} else {
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Bounded::max_value()
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}
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})
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.unwrap_or(Bounded::max_value())
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})
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}
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/// Checked div for int type `N`.
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pub fn checked_div_int<N>(&self, other: &N) -> Option<N>
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where
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N: Copy + TryFrom<i128> + TryInto<i128>,
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{
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N::try_into(*other)
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.ok()
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.and_then(|n| self.0.checked_div(n))
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.and_then(|n| n.checked_div(DIV))
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.and_then(|n| TryInto::<N>::try_into(n).ok())
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}
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pub fn zero() -> Self {
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Self(0)
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}
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pub fn is_zero(&self) -> bool {
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self.0 == 0
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}
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/// Saturating absolute value. Returning MAX if `parts` == i128::MIN instead of overflowing.
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pub fn saturating_abs(&self) -> Self {
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if self.0 == i128::min_value() {
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return Fixed128::max_value();
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}
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if self.0.is_negative() {
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Fixed128::from_parts(self.0 * -1)
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} else {
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*self
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}
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}
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pub fn is_positive(&self) -> bool {
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self.0.is_positive()
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}
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pub fn is_negative(&self) -> bool {
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self.0.is_negative()
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}
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/// Performs a saturated multiply and accumulate by unsigned number.
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///
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/// Returns a saturated `int + (self * int)`.
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pub fn saturated_multiply_accumulate<N>(self, int: N) -> N
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where
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N: TryFrom<u128> + From<u64> + UniqueSaturatedInto<u64> + Bounded + Clone + Saturating +
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ops::Rem<N, Output=N> + ops::Div<N, Output=N> + ops::Mul<N, Output=N> +
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ops::Add<N, Output=N>,
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{
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let div = DIV as u128;
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let positive = self.0 > 0;
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// safe to convert as absolute value.
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let parts = self.0.checked_abs().map(|v| v as u128).unwrap_or(i128::max_value() as u128 + 1);
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// will always fit.
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let natural_parts = parts / div;
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// might saturate.
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let natural_parts: N = natural_parts.saturated_into();
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// fractional parts can always fit into u64.
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let perquintill_parts = (parts % div) as u64;
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let n = int.clone().saturating_mul(natural_parts);
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let p = Perquintill::from_parts(perquintill_parts) * int.clone();
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// everything that needs to be either added or subtracted from the original weight.
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let excess = n.saturating_add(p);
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if positive {
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int.saturating_add(excess)
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} else {
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int.saturating_sub(excess)
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}
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}
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}
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/// Note that this is a standard, _potentially-panicking_, implementation. Use `Saturating` trait
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/// for safe addition.
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impl ops::Add for Fixed128 {
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type Output = Self;
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fn add(self, rhs: Self) -> Self::Output {
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Self(self.0 + rhs.0)
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}
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}
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/// Note that this is a standard, _potentially-panicking_, implementation. Use `Saturating` trait
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/// for safe subtraction.
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impl ops::Sub for Fixed128 {
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type Output = Self;
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fn sub(self, rhs: Self) -> Self::Output {
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Self(self.0 - rhs.0)
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}
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}
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impl Saturating for Fixed128 {
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fn saturating_add(self, rhs: Self) -> Self {
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Self(self.0.saturating_add(rhs.0))
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}
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fn saturating_sub(self, rhs: Self) -> Self {
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Self(self.0.saturating_sub(rhs.0))
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}
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fn saturating_mul(self, rhs: Self) -> Self {
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self.checked_mul(&rhs).unwrap_or_else(|| {
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if (self.0.signum() * rhs.0.signum()).is_negative() {
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Bounded::min_value()
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} else {
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Bounded::max_value()
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}
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})
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}
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fn saturating_pow(self, exp: usize) -> Self {
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if exp == 0 {
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return Self::from_natural(1);
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}
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let exp = exp as u64;
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let msb_pos = 64 - exp.leading_zeros();
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let mut result = Self::from_natural(1);
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let mut pow_val = self;
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for i in 0..msb_pos {
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if ((1 << i) & exp) > 0 {
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result = result.saturating_mul(pow_val);
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}
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pow_val = pow_val.saturating_mul(pow_val);
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}
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result
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}
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}
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impl Bounded for Fixed128 {
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fn min_value() -> Self {
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Self(Bounded::min_value())
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}
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fn max_value() -> Self {
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Self(Bounded::max_value())
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}
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}
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impl fmt::Debug for Fixed128 {
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#[cfg(feature = "std")]
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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let integral = {
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let int = self.0 / DIV;
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let signum_for_zero = if int == 0 && self.is_negative() { "-" } else { "" };
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format!("{}{}", signum_for_zero, int)
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};
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let fractional = format!("{:0>18}", (self.0 % DIV).abs());
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write!(f, "Fixed128({}.{})", integral, fractional)
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}
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#[cfg(not(feature = "std"))]
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fn fmt(&self, _: &mut fmt::Formatter) -> fmt::Result {
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Ok(())
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}
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}
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impl<P: PerThing> From<P> for Fixed128 {
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fn from(val: P) -> Self {
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let accuracy = P::ACCURACY.saturated_into().max(1) as i128;
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let value = val.deconstruct().saturated_into() as i128;
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Fixed128::from_rational(value, NonZeroI128::new(accuracy).unwrap())
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}
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}
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#[cfg(feature = "std")]
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impl Fixed128 {
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fn i128_str(&self) -> String {
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format!("{}", &self.0)
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}
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fn try_from_i128_str(s: &str) -> Result<Self, &'static str> {
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let parts: i128 = s.parse().map_err(|_| "invalid string input")?;
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Ok(Self::from_parts(parts))
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}
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}
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// Manual impl `Serialize` as serde_json does not support i128.
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// TODO: remove impl if issue https://github.com/serde-rs/json/issues/548 fixed.
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#[cfg(feature = "std")]
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impl Serialize for Fixed128 {
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fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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where
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S: Serializer,
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{
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serializer.serialize_str(&self.i128_str())
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}
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}
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// Manual impl `Serialize` as serde_json does not support i128.
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// TODO: remove impl if issue https://github.com/serde-rs/json/issues/548 fixed.
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#[cfg(feature = "std")]
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impl<'de> Deserialize<'de> for Fixed128 {
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fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
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where
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D: Deserializer<'de>,
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{
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let s = String::deserialize(deserializer)?;
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Fixed128::try_from_i128_str(&s).map_err(|err_str| de::Error::custom(err_str))
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use crate::{Perbill, Percent, Permill, Perquintill};
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fn max() -> Fixed128 {
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Fixed128::max_value()
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}
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fn min() -> Fixed128 {
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Fixed128::min_value()
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}
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#[test]
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fn fixed128_semantics() {
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let a = Fixed128::from_rational(5, NonZeroI128::new(2).unwrap());
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let b = Fixed128::from_rational(10, NonZeroI128::new(4).unwrap());
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assert_eq!(a.0, 5 * DIV / 2);
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assert_eq!(a, b);
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let a = Fixed128::from_rational(-5, NonZeroI128::new(1).unwrap());
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assert_eq!(a, Fixed128::from_natural(-5));
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let a = Fixed128::from_rational(5, NonZeroI128::new(-1).unwrap());
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assert_eq!(a, Fixed128::from_natural(-5));
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// biggest value that can be created.
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assert_ne!(max(), Fixed128::from_natural(170_141_183_460_469_231_731));
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assert_eq!(max(), Fixed128::from_natural(170_141_183_460_469_231_732));
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// the smallest value that can be created.
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assert_ne!(min(), Fixed128::from_natural(-170_141_183_460_469_231_731));
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assert_eq!(min(), Fixed128::from_natural(-170_141_183_460_469_231_732));
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}
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#[test]
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fn fixed128_operation() {
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let a = Fixed128::from_natural(2);
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let b = Fixed128::from_natural(1);
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assert_eq!(a.checked_add(&b), Some(Fixed128::from_natural(1 + 2)));
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assert_eq!(a.checked_sub(&b), Some(Fixed128::from_natural(2 - 1)));
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assert_eq!(a.checked_mul(&b), Some(Fixed128::from_natural(1 * 2)));
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assert_eq!(
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a.checked_div(&b),
|
||||
Some(Fixed128::from_rational(2, NonZeroI128::new(1).unwrap()))
|
||||
);
|
||||
|
||||
let a = Fixed128::from_rational(5, NonZeroI128::new(2).unwrap());
|
||||
let b = Fixed128::from_rational(3, NonZeroI128::new(2).unwrap());
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assert_eq!(
|
||||
a.checked_add(&b),
|
||||
Some(Fixed128::from_rational(8, NonZeroI128::new(2).unwrap()))
|
||||
);
|
||||
assert_eq!(
|
||||
a.checked_sub(&b),
|
||||
Some(Fixed128::from_rational(2, NonZeroI128::new(2).unwrap()))
|
||||
);
|
||||
assert_eq!(
|
||||
a.checked_mul(&b),
|
||||
Some(Fixed128::from_rational(15, NonZeroI128::new(4).unwrap()))
|
||||
);
|
||||
assert_eq!(
|
||||
a.checked_div(&b),
|
||||
Some(Fixed128::from_rational(10, NonZeroI128::new(6).unwrap()))
|
||||
);
|
||||
|
||||
let a = Fixed128::from_natural(120);
|
||||
assert_eq!(a.checked_div_int(&2i32), Some(60));
|
||||
|
||||
let a = Fixed128::from_rational(20, NonZeroI128::new(1).unwrap());
|
||||
assert_eq!(a.checked_div_int(&2i32), Some(10));
|
||||
|
||||
let a = Fixed128::from_natural(120);
|
||||
assert_eq!(a.checked_mul_int(&2i32), Some(240));
|
||||
|
||||
let a = Fixed128::from_rational(1, NonZeroI128::new(2).unwrap());
|
||||
assert_eq!(a.checked_mul_int(&20i32), Some(10));
|
||||
|
||||
let a = Fixed128::from_rational(-1, NonZeroI128::new(2).unwrap());
|
||||
assert_eq!(a.checked_mul_int(&20i32), Some(-10));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn saturating_mul_should_work() {
|
||||
let a = Fixed128::from_natural(-1);
|
||||
assert_eq!(min().saturating_mul(a), max());
|
||||
|
||||
assert_eq!(Fixed128::from_natural(125).saturating_mul(a).deconstruct(), -125 * DIV);
|
||||
|
||||
let a = Fixed128::from_rational(1, NonZeroI128::new(5).unwrap());
|
||||
assert_eq!(Fixed128::from_natural(125).saturating_mul(a).deconstruct(), 25 * DIV);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn saturating_mul_int_works() {
|
||||
let a = Fixed128::from_rational(10, NonZeroI128::new(1).unwrap());
|
||||
assert_eq!(a.saturating_mul_int(&i32::max_value()), i32::max_value());
|
||||
|
||||
let a = Fixed128::from_rational(-10, NonZeroI128::new(1).unwrap());
|
||||
assert_eq!(a.saturating_mul_int(&i32::max_value()), i32::min_value());
|
||||
|
||||
let a = Fixed128::from_rational(3, NonZeroI128::new(1).unwrap());
|
||||
assert_eq!(a.saturating_mul_int(&100i8), i8::max_value());
|
||||
|
||||
let a = Fixed128::from_rational(10, NonZeroI128::new(1).unwrap());
|
||||
assert_eq!(a.saturating_mul_int(&123i128), 1230);
|
||||
|
||||
let a = Fixed128::from_rational(-10, NonZeroI128::new(1).unwrap());
|
||||
assert_eq!(a.saturating_mul_int(&123i128), -1230);
|
||||
|
||||
assert_eq!(max().saturating_mul_int(&2i128), 340_282_366_920_938_463_463);
|
||||
|
||||
assert_eq!(max().saturating_mul_int(&i128::min_value()), i128::min_value());
|
||||
|
||||
assert_eq!(min().saturating_mul_int(&i128::max_value()), i128::min_value());
|
||||
|
||||
assert_eq!(min().saturating_mul_int(&i128::min_value()), i128::max_value());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn zero_works() {
|
||||
assert_eq!(Fixed128::zero(), Fixed128::from_natural(0));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn is_zero_works() {
|
||||
assert!(Fixed128::zero().is_zero());
|
||||
assert!(!Fixed128::from_natural(1).is_zero());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn checked_div_with_zero_should_be_none() {
|
||||
let a = Fixed128::from_natural(1);
|
||||
let b = Fixed128::from_natural(0);
|
||||
assert_eq!(a.checked_div(&b), None);
|
||||
assert_eq!(b.checked_div(&a), Some(b));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn checked_div_int_with_zero_should_be_none() {
|
||||
let a = Fixed128::from_natural(1);
|
||||
assert_eq!(a.checked_div_int(&0i32), None);
|
||||
let a = Fixed128::from_natural(0);
|
||||
assert_eq!(a.checked_div_int(&1i32), Some(0));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn checked_div_with_zero_dividend_should_be_zero() {
|
||||
let a = Fixed128::zero();
|
||||
let b = Fixed128::from_parts(1);
|
||||
|
||||
assert_eq!(a.checked_div(&b), Some(Fixed128::zero()));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn under_flow_should_be_none() {
|
||||
let b = Fixed128::from_natural(1);
|
||||
assert_eq!(min().checked_sub(&b), None);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn over_flow_should_be_none() {
|
||||
let a = Fixed128::from_parts(i128::max_value() - 1);
|
||||
let b = Fixed128::from_parts(2);
|
||||
assert_eq!(a.checked_add(&b), None);
|
||||
|
||||
let a = Fixed128::max_value();
|
||||
let b = Fixed128::from_rational(2, NonZeroI128::new(1).unwrap());
|
||||
assert_eq!(a.checked_mul(&b), None);
|
||||
|
||||
let a = Fixed128::from_natural(255);
|
||||
let b = 2u8;
|
||||
assert_eq!(a.checked_mul_int(&b), None);
|
||||
|
||||
let a = Fixed128::from_natural(256);
|
||||
let b = 1u8;
|
||||
assert_eq!(a.checked_div_int(&b), None);
|
||||
|
||||
let a = Fixed128::from_natural(256);
|
||||
let b = -1i8;
|
||||
assert_eq!(a.checked_div_int(&b), None);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn checked_div_int_should_work() {
|
||||
// 256 / 10 = 25 (25.6 as int = 25)
|
||||
let a = Fixed128::from_natural(256);
|
||||
let result = a.checked_div_int(&10i128).unwrap();
|
||||
assert_eq!(result, 25);
|
||||
|
||||
// 256 / 100 = 2 (2.56 as int = 2)
|
||||
let a = Fixed128::from_natural(256);
|
||||
let result = a.checked_div_int(&100i128).unwrap();
|
||||
assert_eq!(result, 2);
|
||||
|
||||
// 256 / 1000 = 0 (0.256 as int = 0)
|
||||
let a = Fixed128::from_natural(256);
|
||||
let result = a.checked_div_int(&1000i128).unwrap();
|
||||
assert_eq!(result, 0);
|
||||
|
||||
// 256 / -1 = -256
|
||||
let a = Fixed128::from_natural(256);
|
||||
let result = a.checked_div_int(&-1i128).unwrap();
|
||||
assert_eq!(result, -256);
|
||||
|
||||
// -256 / -1 = 256
|
||||
let a = Fixed128::from_natural(-256);
|
||||
let result = a.checked_div_int(&-1i128).unwrap();
|
||||
assert_eq!(result, 256);
|
||||
|
||||
// 10 / -5 = -2
|
||||
let a = Fixed128::from_rational(20, NonZeroI128::new(2).unwrap());
|
||||
let result = a.checked_div_int(&-5i128).unwrap();
|
||||
assert_eq!(result, -2);
|
||||
|
||||
// -170_141_183_460_469_231_731 / -2 = 85_070_591_730_234_615_865
|
||||
let result = min().checked_div_int(&-2i128).unwrap();
|
||||
assert_eq!(result, 85_070_591_730_234_615_865);
|
||||
|
||||
// 85_070_591_730_234_615_865 * -2 = -170_141_183_460_469_231_730
|
||||
let result = Fixed128::from_natural(result).checked_mul_int(&-2i128).unwrap();
|
||||
assert_eq!(result, -170_141_183_460_469_231_730);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn perthing_into_fixed_i128() {
|
||||
let ten_percent_percent: Fixed128 = Percent::from_percent(10).into();
|
||||
assert_eq!(ten_percent_percent.deconstruct(), DIV / 10);
|
||||
|
||||
let ten_percent_permill: Fixed128 = Permill::from_percent(10).into();
|
||||
assert_eq!(ten_percent_permill.deconstruct(), DIV / 10);
|
||||
|
||||
let ten_percent_perbill: Fixed128 = Perbill::from_percent(10).into();
|
||||
assert_eq!(ten_percent_perbill.deconstruct(), DIV / 10);
|
||||
|
||||
let ten_percent_perquintill: Fixed128 = Perquintill::from_percent(10).into();
|
||||
assert_eq!(ten_percent_perquintill.deconstruct(), DIV / 10);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn recip_should_work() {
|
||||
let a = Fixed128::from_natural(2);
|
||||
assert_eq!(
|
||||
a.recip(),
|
||||
Some(Fixed128::from_rational(1, NonZeroI128::new(2).unwrap()))
|
||||
);
|
||||
|
||||
let a = Fixed128::from_natural(2);
|
||||
assert_eq!(a.recip().unwrap().checked_mul_int(&4i32), Some(2i32));
|
||||
|
||||
let a = Fixed128::from_rational(100, NonZeroI128::new(121).unwrap());
|
||||
assert_eq!(
|
||||
a.recip(),
|
||||
Some(Fixed128::from_rational(121, NonZeroI128::new(100).unwrap()))
|
||||
);
|
||||
|
||||
let a = Fixed128::from_rational(1, NonZeroI128::new(2).unwrap());
|
||||
assert_eq!(a.recip().unwrap().checked_mul(&a), Some(Fixed128::from_natural(1)));
|
||||
|
||||
let a = Fixed128::from_natural(0);
|
||||
assert_eq!(a.recip(), None);
|
||||
|
||||
let a = Fixed128::from_rational(-1, NonZeroI128::new(2).unwrap());
|
||||
assert_eq!(a.recip(), Some(Fixed128::from_natural(-2)));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn serialize_deserialize_should_work() {
|
||||
let two_point_five = Fixed128::from_rational(5, NonZeroI128::new(2).unwrap());
|
||||
let serialized = serde_json::to_string(&two_point_five).unwrap();
|
||||
assert_eq!(serialized, "\"2500000000000000000\"");
|
||||
let deserialized: Fixed128 = serde_json::from_str(&serialized).unwrap();
|
||||
assert_eq!(deserialized, two_point_five);
|
||||
|
||||
let minus_two_point_five = Fixed128::from_rational(-5, NonZeroI128::new(2).unwrap());
|
||||
let serialized = serde_json::to_string(&minus_two_point_five).unwrap();
|
||||
assert_eq!(serialized, "\"-2500000000000000000\"");
|
||||
let deserialized: Fixed128 = serde_json::from_str(&serialized).unwrap();
|
||||
assert_eq!(deserialized, minus_two_point_five);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn saturating_abs_should_work() {
|
||||
// normal
|
||||
assert_eq!(Fixed128::from_parts(1).saturating_abs(), Fixed128::from_parts(1));
|
||||
assert_eq!(Fixed128::from_parts(-1).saturating_abs(), Fixed128::from_parts(1));
|
||||
|
||||
// saturating
|
||||
assert_eq!(Fixed128::min_value().saturating_abs(), Fixed128::max_value());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn is_positive_negative_should_work() {
|
||||
let positive = Fixed128::from_parts(1);
|
||||
assert!(positive.is_positive());
|
||||
assert!(!positive.is_negative());
|
||||
|
||||
let negative = Fixed128::from_parts(-1);
|
||||
assert!(!negative.is_positive());
|
||||
assert!(negative.is_negative());
|
||||
|
||||
let zero = Fixed128::zero();
|
||||
assert!(!zero.is_positive());
|
||||
assert!(!zero.is_negative());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn fmt_should_work() {
|
||||
let positive = Fixed128::from_parts(1000000000000000001);
|
||||
assert_eq!(format!("{:?}", positive), "Fixed128(1.000000000000000001)");
|
||||
let negative = Fixed128::from_parts(-1000000000000000001);
|
||||
assert_eq!(format!("{:?}", negative), "Fixed128(-1.000000000000000001)");
|
||||
|
||||
let positive_fractional = Fixed128::from_parts(1);
|
||||
assert_eq!(format!("{:?}", positive_fractional), "Fixed128(0.000000000000000001)");
|
||||
let negative_fractional = Fixed128::from_parts(-1);
|
||||
assert_eq!(format!("{:?}", negative_fractional), "Fixed128(-0.000000000000000001)");
|
||||
|
||||
let zero = Fixed128::zero();
|
||||
assert_eq!(format!("{:?}", zero), "Fixed128(0.000000000000000000)");
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn saturating_pow_should_work() {
|
||||
assert_eq!(Fixed128::from_natural(2).saturating_pow(0), Fixed128::from_natural(1));
|
||||
assert_eq!(Fixed128::from_natural(2).saturating_pow(1), Fixed128::from_natural(2));
|
||||
assert_eq!(Fixed128::from_natural(2).saturating_pow(2), Fixed128::from_natural(4));
|
||||
assert_eq!(Fixed128::from_natural(2).saturating_pow(3), Fixed128::from_natural(8));
|
||||
assert_eq!(Fixed128::from_natural(2).saturating_pow(50), Fixed128::from_natural(1125899906842624));
|
||||
|
||||
assert_eq!(Fixed128::from_natural(1).saturating_pow(1000), Fixed128::from_natural(1));
|
||||
assert_eq!(Fixed128::from_natural(-1).saturating_pow(1000), Fixed128::from_natural(1));
|
||||
assert_eq!(Fixed128::from_natural(-1).saturating_pow(1001), Fixed128::from_natural(-1));
|
||||
assert_eq!(Fixed128::from_natural(1).saturating_pow(usize::max_value()), Fixed128::from_natural(1));
|
||||
assert_eq!(Fixed128::from_natural(-1).saturating_pow(usize::max_value()), Fixed128::from_natural(-1));
|
||||
assert_eq!(Fixed128::from_natural(-1).saturating_pow(usize::max_value() - 1), Fixed128::from_natural(1));
|
||||
|
||||
assert_eq!(Fixed128::from_natural(114209).saturating_pow(4), Fixed128::from_natural(170137997018538053761));
|
||||
assert_eq!(Fixed128::from_natural(114209).saturating_pow(5), Fixed128::max_value());
|
||||
|
||||
assert_eq!(Fixed128::from_natural(1).saturating_pow(usize::max_value()), Fixed128::from_natural(1));
|
||||
assert_eq!(Fixed128::from_natural(0).saturating_pow(usize::max_value()), Fixed128::from_natural(0));
|
||||
assert_eq!(Fixed128::from_natural(2).saturating_pow(usize::max_value()), Fixed128::max_value());
|
||||
}
|
||||
}
|
||||
@@ -1,382 +0,0 @@
|
||||
// This file is part of Substrate.
|
||||
|
||||
// Copyright (C) 2019-2020 Parity Technologies (UK) Ltd.
|
||||
// SPDX-License-Identifier: Apache-2.0
|
||||
|
||||
// Licensed under the Apache License, Version 2.0 (the "License");
|
||||
// you may not use this file except in compliance with the License.
|
||||
// You may obtain a copy of the License at
|
||||
//
|
||||
// http://www.apache.org/licenses/LICENSE-2.0
|
||||
//
|
||||
// Unless required by applicable law or agreed to in writing, software
|
||||
// distributed under the License is distributed on an "AS IS" BASIS,
|
||||
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||||
// See the License for the specific language governing permissions and
|
||||
// limitations under the License.
|
||||
|
||||
use sp_std::{
|
||||
ops, prelude::*,
|
||||
convert::{TryFrom, TryInto},
|
||||
};
|
||||
use codec::{Encode, Decode};
|
||||
use crate::{
|
||||
Perbill,
|
||||
traits::{
|
||||
SaturatedConversion, CheckedSub, CheckedAdd, CheckedDiv, Bounded, UniqueSaturatedInto, Saturating
|
||||
}
|
||||
};
|
||||
|
||||
/// An unsigned fixed point number. Can hold any value in the range [-9_223_372_036, 9_223_372_036]
|
||||
/// with fixed point accuracy of one billion.
|
||||
#[derive(Encode, Decode, Default, Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
|
||||
pub struct Fixed64(i64);
|
||||
|
||||
/// The accuracy of the `Fixed64` type.
|
||||
const DIV: i64 = 1_000_000_000;
|
||||
|
||||
impl Fixed64 {
|
||||
/// creates self from a natural number.
|
||||
///
|
||||
/// Note that this might be lossy.
|
||||
pub fn from_natural(int: i64) -> Self {
|
||||
Self(int.saturating_mul(DIV))
|
||||
}
|
||||
|
||||
/// Return the accuracy of the type. Given that this function returns the value `X`, it means
|
||||
/// that an instance composed of `X` parts (`Fixed64::from_parts(X)`) is equal to `1`.
|
||||
pub fn accuracy() -> i64 {
|
||||
DIV
|
||||
}
|
||||
|
||||
/// Consume self and return the inner value.
|
||||
pub fn into_inner(self) -> i64 { self.0 }
|
||||
|
||||
/// Raw constructor. Equal to `parts / 1_000_000_000`.
|
||||
pub fn from_parts(parts: i64) -> Self {
|
||||
Self(parts)
|
||||
}
|
||||
|
||||
/// creates self from a rational number. Equal to `n/d`.
|
||||
///
|
||||
/// Note that this might be lossy.
|
||||
pub fn from_rational(n: i64, d: u64) -> Self {
|
||||
Self(
|
||||
(i128::from(n).saturating_mul(i128::from(DIV)) / i128::from(d).max(1))
|
||||
.try_into()
|
||||
.unwrap_or_else(|_| Bounded::max_value())
|
||||
)
|
||||
}
|
||||
|
||||
/// Performs a saturated multiply and accumulate by unsigned number.
|
||||
///
|
||||
/// Returns a saturated `int + (self * int)`.
|
||||
pub fn saturated_multiply_accumulate<N>(self, int: N) -> N
|
||||
where
|
||||
N: TryFrom<u64> + From<u32> + UniqueSaturatedInto<u32> + Bounded + Clone + Saturating +
|
||||
ops::Rem<N, Output=N> + ops::Div<N, Output=N> + ops::Mul<N, Output=N> +
|
||||
ops::Add<N, Output=N>,
|
||||
{
|
||||
let div = DIV as u64;
|
||||
let positive = self.0 > 0;
|
||||
// safe to convert as absolute value.
|
||||
let parts = self.0.checked_abs().map(|v| v as u64).unwrap_or(i64::max_value() as u64 + 1);
|
||||
|
||||
|
||||
// will always fit.
|
||||
let natural_parts = parts / div;
|
||||
// might saturate.
|
||||
let natural_parts: N = natural_parts.saturated_into();
|
||||
// fractional parts can always fit into u32.
|
||||
let perbill_parts = (parts % div) as u32;
|
||||
|
||||
let n = int.clone().saturating_mul(natural_parts);
|
||||
let p = Perbill::from_parts(perbill_parts) * int.clone();
|
||||
|
||||
// everything that needs to be either added or subtracted from the original weight.
|
||||
let excess = n.saturating_add(p);
|
||||
|
||||
if positive {
|
||||
int.saturating_add(excess)
|
||||
} else {
|
||||
int.saturating_sub(excess)
|
||||
}
|
||||
}
|
||||
|
||||
pub fn is_negative(&self) -> bool {
|
||||
self.0.is_negative()
|
||||
}
|
||||
}
|
||||
|
||||
impl Saturating for Fixed64 {
|
||||
fn saturating_add(self, rhs: Self) -> Self {
|
||||
Self(self.0.saturating_add(rhs.0))
|
||||
}
|
||||
|
||||
fn saturating_mul(self, rhs: Self) -> Self {
|
||||
let a = self.0 as i128;
|
||||
let b = rhs.0 as i128;
|
||||
let res = a * b / DIV as i128;
|
||||
Self(res.saturated_into())
|
||||
}
|
||||
|
||||
fn saturating_sub(self, rhs: Self) -> Self {
|
||||
Self(self.0.saturating_sub(rhs.0))
|
||||
}
|
||||
|
||||
fn saturating_pow(self, exp: usize) -> Self {
|
||||
if exp == 0 {
|
||||
return Self::from_natural(1);
|
||||
}
|
||||
|
||||
let exp = exp as u64;
|
||||
let msb_pos = 64 - exp.leading_zeros();
|
||||
|
||||
let mut result = Self::from_natural(1);
|
||||
let mut pow_val = self;
|
||||
for i in 0..msb_pos {
|
||||
if ((1 << i) & exp) > 0 {
|
||||
result = result.saturating_mul(pow_val);
|
||||
}
|
||||
pow_val = pow_val.saturating_mul(pow_val);
|
||||
}
|
||||
result
|
||||
}
|
||||
}
|
||||
|
||||
/// Use `Saturating` trait for safe addition.
|
||||
impl ops::Add for Fixed64 {
|
||||
type Output = Self;
|
||||
|
||||
fn add(self, rhs: Self) -> Self::Output {
|
||||
Self(self.0 + rhs.0)
|
||||
}
|
||||
}
|
||||
|
||||
/// Use `Saturating` trait for safe subtraction.
|
||||
impl ops::Sub for Fixed64 {
|
||||
type Output = Self;
|
||||
|
||||
fn sub(self, rhs: Self) -> Self::Output {
|
||||
Self(self.0 - rhs.0)
|
||||
}
|
||||
}
|
||||
|
||||
/// Use `CheckedDiv` trait for safe division.
|
||||
impl ops::Div for Fixed64 {
|
||||
type Output = Self;
|
||||
|
||||
fn div(self, rhs: Self) -> Self::Output {
|
||||
if rhs.0 == 0 {
|
||||
panic!("attempt to divide by zero");
|
||||
}
|
||||
let (n, d) = if rhs.0 < 0 {
|
||||
(-self.0, rhs.0.abs() as u64)
|
||||
} else {
|
||||
(self.0, rhs.0 as u64)
|
||||
};
|
||||
Fixed64::from_rational(n, d)
|
||||
}
|
||||
}
|
||||
|
||||
impl CheckedSub for Fixed64 {
|
||||
fn checked_sub(&self, rhs: &Self) -> Option<Self> {
|
||||
self.0.checked_sub(rhs.0).map(Self)
|
||||
}
|
||||
}
|
||||
|
||||
impl CheckedAdd for Fixed64 {
|
||||
fn checked_add(&self, rhs: &Self) -> Option<Self> {
|
||||
self.0.checked_add(rhs.0).map(Self)
|
||||
}
|
||||
}
|
||||
|
||||
impl CheckedDiv for Fixed64 {
|
||||
fn checked_div(&self, rhs: &Self) -> Option<Self> {
|
||||
if rhs.0 == 0 {
|
||||
None
|
||||
} else {
|
||||
Some(*self / *rhs)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl sp_std::fmt::Debug for Fixed64 {
|
||||
#[cfg(feature = "std")]
|
||||
fn fmt(&self, f: &mut sp_std::fmt::Formatter) -> sp_std::fmt::Result {
|
||||
let integral = {
|
||||
let int = self.0 / DIV;
|
||||
let signum_for_zero = if int == 0 && self.is_negative() { "-" } else { "" };
|
||||
format!("{}{}", signum_for_zero, int)
|
||||
};
|
||||
let fractional = format!("{:0>9}", (self.0 % DIV).abs());
|
||||
write!(f, "Fixed64({}.{})", integral, fractional)
|
||||
}
|
||||
|
||||
#[cfg(not(feature = "std"))]
|
||||
fn fmt(&self, _: &mut sp_std::fmt::Formatter) -> sp_std::fmt::Result {
|
||||
Ok(())
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
||||
fn max() -> Fixed64 {
|
||||
Fixed64::from_parts(i64::max_value())
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn fixed64_semantics() {
|
||||
assert_eq!(Fixed64::from_rational(5, 2).0, 5 * 1_000_000_000 / 2);
|
||||
assert_eq!(Fixed64::from_rational(5, 2), Fixed64::from_rational(10, 4));
|
||||
assert_eq!(Fixed64::from_rational(5, 0), Fixed64::from_rational(5, 1));
|
||||
|
||||
// biggest value that can be created.
|
||||
assert_ne!(max(), Fixed64::from_natural(9_223_372_036));
|
||||
assert_eq!(max(), Fixed64::from_natural(9_223_372_037));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn fixed_64_growth_decrease_curve() {
|
||||
let test_set = vec![0u32, 1, 10, 1000, 1_000_000_000];
|
||||
|
||||
// negative (1/2)
|
||||
let mut fm = Fixed64::from_rational(-1, 2);
|
||||
test_set.clone().into_iter().for_each(|i| {
|
||||
assert_eq!(fm.saturated_multiply_accumulate(i) as i32, i as i32 - i as i32 / 2);
|
||||
});
|
||||
|
||||
// unit (1) multiplier
|
||||
fm = Fixed64::from_parts(0);
|
||||
test_set.clone().into_iter().for_each(|i| {
|
||||
assert_eq!(fm.saturated_multiply_accumulate(i), i);
|
||||
});
|
||||
|
||||
// i.5 multiplier
|
||||
fm = Fixed64::from_rational(1, 2);
|
||||
test_set.clone().into_iter().for_each(|i| {
|
||||
assert_eq!(fm.saturated_multiply_accumulate(i), i * 3 / 2);
|
||||
});
|
||||
|
||||
// dual multiplier
|
||||
fm = Fixed64::from_rational(1, 1);
|
||||
test_set.clone().into_iter().for_each(|i| {
|
||||
assert_eq!(fm.saturated_multiply_accumulate(i), i * 2);
|
||||
});
|
||||
}
|
||||
|
||||
macro_rules! saturating_mul_acc_test {
|
||||
($num_type:tt) => {
|
||||
assert_eq!(
|
||||
Fixed64::from_rational(100, 1).saturated_multiply_accumulate(10 as $num_type),
|
||||
1010,
|
||||
);
|
||||
assert_eq!(
|
||||
Fixed64::from_rational(100, 2).saturated_multiply_accumulate(10 as $num_type),
|
||||
510,
|
||||
);
|
||||
assert_eq!(
|
||||
Fixed64::from_rational(100, 3).saturated_multiply_accumulate(0 as $num_type),
|
||||
0,
|
||||
);
|
||||
assert_eq!(
|
||||
Fixed64::from_rational(5, 1).saturated_multiply_accumulate($num_type::max_value()),
|
||||
$num_type::max_value()
|
||||
);
|
||||
assert_eq!(
|
||||
max().saturated_multiply_accumulate($num_type::max_value()),
|
||||
$num_type::max_value()
|
||||
);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn fixed64_multiply_accumulate_works() {
|
||||
saturating_mul_acc_test!(u32);
|
||||
saturating_mul_acc_test!(u64);
|
||||
saturating_mul_acc_test!(u128);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn div_works() {
|
||||
let a = Fixed64::from_rational(12, 10);
|
||||
let b = Fixed64::from_rational(10, 1);
|
||||
assert_eq!(a / b, Fixed64::from_rational(12, 100));
|
||||
|
||||
let a = Fixed64::from_rational(12, 10);
|
||||
let b = Fixed64::from_rational(1, 100);
|
||||
assert_eq!(a / b, Fixed64::from_rational(120, 1));
|
||||
|
||||
let a = Fixed64::from_rational(12, 100);
|
||||
let b = Fixed64::from_rational(10, 1);
|
||||
assert_eq!(a / b, Fixed64::from_rational(12, 1000));
|
||||
|
||||
let a = Fixed64::from_rational(12, 100);
|
||||
let b = Fixed64::from_rational(1, 100);
|
||||
assert_eq!(a / b, Fixed64::from_rational(12, 1));
|
||||
|
||||
let a = Fixed64::from_rational(-12, 10);
|
||||
let b = Fixed64::from_rational(10, 1);
|
||||
assert_eq!(a / b, Fixed64::from_rational(-12, 100));
|
||||
|
||||
let a = Fixed64::from_rational(12, 10);
|
||||
let b = Fixed64::from_rational(-10, 1);
|
||||
assert_eq!(a / b, Fixed64::from_rational(-12, 100));
|
||||
|
||||
let a = Fixed64::from_rational(-12, 10);
|
||||
let b = Fixed64::from_rational(-10, 1);
|
||||
assert_eq!(a / b, Fixed64::from_rational(12, 100));
|
||||
}
|
||||
|
||||
#[test]
|
||||
#[should_panic(expected = "attempt to divide by zero")]
|
||||
fn div_zero() {
|
||||
let a = Fixed64::from_rational(12, 10);
|
||||
let b = Fixed64::from_natural(0);
|
||||
let _ = a / b;
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn checked_div_zero() {
|
||||
let a = Fixed64::from_rational(12, 10);
|
||||
let b = Fixed64::from_natural(0);
|
||||
assert_eq!(a.checked_div(&b), None);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn checked_div_non_zero() {
|
||||
let a = Fixed64::from_rational(12, 10);
|
||||
let b = Fixed64::from_rational(1, 100);
|
||||
assert_eq!(a.checked_div(&b), Some(Fixed64::from_rational(120, 1)));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn saturating_mul_should_work() {
|
||||
assert_eq!(Fixed64::from_natural(100).saturating_mul(Fixed64::from_natural(100)), Fixed64::from_natural(10000));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn saturating_pow_should_work() {
|
||||
assert_eq!(Fixed64::from_natural(2).saturating_pow(0), Fixed64::from_natural(1));
|
||||
assert_eq!(Fixed64::from_natural(2).saturating_pow(1), Fixed64::from_natural(2));
|
||||
assert_eq!(Fixed64::from_natural(2).saturating_pow(2), Fixed64::from_natural(4));
|
||||
assert_eq!(Fixed64::from_natural(2).saturating_pow(3), Fixed64::from_natural(8));
|
||||
assert_eq!(Fixed64::from_natural(2).saturating_pow(20), Fixed64::from_natural(1048576));
|
||||
|
||||
assert_eq!(Fixed64::from_natural(1).saturating_pow(1000), Fixed64::from_natural(1));
|
||||
assert_eq!(Fixed64::from_natural(-1).saturating_pow(1000), Fixed64::from_natural(1));
|
||||
assert_eq!(Fixed64::from_natural(-1).saturating_pow(1001), Fixed64::from_natural(-1));
|
||||
assert_eq!(Fixed64::from_natural(1).saturating_pow(usize::max_value()), Fixed64::from_natural(1));
|
||||
assert_eq!(Fixed64::from_natural(-1).saturating_pow(usize::max_value()), Fixed64::from_natural(-1));
|
||||
assert_eq!(Fixed64::from_natural(-1).saturating_pow(usize::max_value() - 1), Fixed64::from_natural(1));
|
||||
|
||||
assert_eq!(Fixed64::from_natural(309).saturating_pow(4), Fixed64::from_natural(9_116_621_361));
|
||||
assert_eq!(Fixed64::from_natural(309).saturating_pow(5), Fixed64::from_parts(i64::max_value()));
|
||||
|
||||
assert_eq!(Fixed64::from_natural(1).saturating_pow(usize::max_value()), Fixed64::from_natural(1));
|
||||
assert_eq!(Fixed64::from_natural(0).saturating_pow(usize::max_value()), Fixed64::from_natural(0));
|
||||
assert_eq!(Fixed64::from_natural(2).saturating_pow(usize::max_value()), Fixed64::from_parts(i64::max_value()));
|
||||
}
|
||||
}
|
||||
@@ -37,12 +37,10 @@ pub mod biguint;
|
||||
pub mod helpers_128bit;
|
||||
pub mod traits;
|
||||
mod per_things;
|
||||
mod fixed64;
|
||||
mod fixed128;
|
||||
mod fixed;
|
||||
mod rational128;
|
||||
|
||||
pub use fixed64::Fixed64;
|
||||
pub use fixed128::Fixed128;
|
||||
pub use fixed::{FixedPointNumber, Fixed64, Fixed128};
|
||||
pub use per_things::{PerThing, Percent, PerU16, Permill, Perbill, Perquintill};
|
||||
pub use rational128::Rational128;
|
||||
|
||||
|
||||
@@ -21,8 +21,8 @@ use sp_std::{self, convert::{TryFrom, TryInto}};
|
||||
use codec::HasCompact;
|
||||
pub use integer_sqrt::IntegerSquareRoot;
|
||||
pub use num_traits::{
|
||||
Zero, One, Bounded, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv,
|
||||
CheckedShl, CheckedShr, checked_pow
|
||||
Zero, One, Bounded, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, CheckedNeg,
|
||||
CheckedShl, CheckedShr, checked_pow, Signed
|
||||
};
|
||||
use sp_std::ops::{
|
||||
Add, Sub, Mul, Div, Rem, AddAssign, SubAssign, MulAssign, DivAssign,
|
||||
|
||||
Reference in New Issue
Block a user