Skip to content

Commit

Permalink
introduce checked_div for PerThings and checked_rational_mul_correction
Browse files Browse the repository at this point in the history
  • Loading branch information
@Gioyik
Gioyik committed Oct 19, 2023
1 parent 3e98021 commit 1bd75e2
Show file tree
Hide file tree
Showing 2 changed files with 175 additions and 9 deletions.
55 changes: 50 additions & 5 deletions substrate/primitives/arithmetic/src/helpers_128bit.rs
View file
Original file line number Diff line number Diff line change
Expand Up @@ -183,21 +183,35 @@ mod double128 {
}

/// Returns `a * b / c` (wrapping to 128 bits) or `None` in the case of
/// overflow.
/// overflow or div by zero.
pub const fn multiply_by_rational_with_rounding(
a: u128,
b: u128,
c: u128,
r: Rounding,
) -> Option<u128> {
match checked_multiply_by_rational_with_rounding(a, b, c, r) {
Ok(value) => Some(value),
Err(_) => None,
}
}

/// Returns `a * b / c` (wrapping to 128 bits) or `Err` if tries to div by zero or
/// overflow
pub const fn checked_multiply_by_rational_with_rounding(
a: u128,
b: u128,
c: u128,
r: Rounding,
) -> Result<u128, &'static str> {
use double128::Double128;
if c == 0 {
return None
return Err("Division by zero")
}
let (result, remainder) = Double128::product_of(a, b).div(c);
let mut result: u128 = match result.try_into_u128() {
Ok(v) => v,
Err(_) => return None,
Err(_) => return Err("Overflow"),
};
if match r {
Rounding::Up => remainder > 0,
Expand All @@ -208,10 +222,10 @@ pub const fn multiply_by_rational_with_rounding(
} {
result = match result.checked_add(1) {
Some(v) => v,
None => return None,
None => return Err("None"),
};
}
Some(result)
Ok(result)
}

pub const fn sqrt(mut n: u128) -> u128 {
Expand Down Expand Up @@ -244,6 +258,7 @@ pub const fn sqrt(mut n: u128) -> u128 {
#[cfg(test)]
mod tests {
use super::*;
use checked_multiply_by_rational_with_rounding as checked_mulrat;
use codec::{Decode, Encode};
use multiply_by_rational_with_rounding as mulrat;
use Rounding::*;
Expand Down Expand Up @@ -278,6 +293,36 @@ mod tests {
assert_eq!(mulrat(1, MAX / 2 + 1, MAX, NearestPrefUp), Some(1));
}

#[test]
fn rational_checked_multiply_basic_rounding_works() {
assert_eq!(checked_mulrat(1, 1, 1, Up), Ok(1));
assert_eq!(checked_mulrat(3, 1, 3, Up), Ok(1));
assert_eq!(checked_mulrat(1, 1, 3, Up), Ok(1));
assert_eq!(checked_mulrat(1, 2, 3, Down), Ok(0));
assert_eq!(checked_mulrat(1, 1, 3, NearestPrefDown), Ok(0));
assert_eq!(checked_mulrat(1, 1, 2, NearestPrefDown), Ok(0));
assert_eq!(checked_mulrat(1, 2, 3, NearestPrefDown), Ok(1));
assert_eq!(checked_mulrat(1, 1, 3, NearestPrefUp), Ok(0));
assert_eq!(checked_mulrat(1, 1, 2, NearestPrefUp), Ok(1));
assert_eq!(checked_mulrat(1, 2, 3, NearestPrefUp), Ok(1));
assert_eq!(checked_mulrat(3, 1, 0, Up), Err("Division by zero"));
}

#[test]
fn rational_checked_multiply_big_number_works() {
assert_eq!(checked_mulrat(MAX, MAX - 1, MAX, Down), Ok(MAX - 1));
assert_eq!(checked_mulrat(MAX, 1, MAX, Down), Ok(1));
assert_eq!(checked_mulrat(MAX, MAX - 1, MAX, Up), Ok(MAX - 1));
assert_eq!(checked_mulrat(MAX, 1, MAX, Up), Ok(1));
assert_eq!(checked_mulrat(1, MAX - 1, MAX, Down), Ok(0));
assert_eq!(checked_mulrat(1, 1, MAX, Up), Ok(1));
assert_eq!(checked_mulrat(1, MAX / 2, MAX, NearestPrefDown), Ok(0));
assert_eq!(checked_mulrat(1, MAX / 2 + 1, MAX, NearestPrefDown), Ok(1));
assert_eq!(checked_mulrat(1, MAX / 2, MAX, NearestPrefUp), Ok(0));
assert_eq!(checked_mulrat(1, MAX / 2 + 1, MAX, NearestPrefUp), Ok(1));
assert_eq!(checked_mulrat(1, MAX / 2 + 1, 0, NearestPrefUp), Err("Division by zero"));
}

#[test]
fn sqrt_works() {
for i in 0..100_000u32 {
Expand Down
129 changes: 125 additions & 4 deletions substrate/primitives/arithmetic/src/per_things.rs
View file
Original file line number Diff line number Diff line change
Expand Up @@ -19,8 +19,8 @@
use serde::{Deserialize, Serialize};

use crate::traits::{
BaseArithmetic, Bounded, CheckedAdd, CheckedMul, CheckedSub, One, SaturatedConversion,
Saturating, UniqueSaturatedInto, Unsigned, Zero,
BaseArithmetic, Bounded, CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, One,
SaturatedConversion, Saturating, UniqueSaturatedInto, Unsigned, Zero,
};
use codec::{CompactAs, Encode};
use num_traits::{Pow, SaturatingAdd, SaturatingSub};
Expand Down Expand Up @@ -496,16 +496,35 @@ where
(x / maximum) * part_n + c
}

/// Checked compute of the error due to integer division in the expression `x / denom * numer`.
fn rational_mul_correction<N, P>(x: N, numer: P::Inner, denom: P::Inner, rounding: Rounding) -> N
where
N: MultiplyArg + UniqueSaturatedInto<P::Inner>,
P: PerThing,
P::Inner: Into<N>,
{
checked_rational_mul_correction::<N, P>(x, numer, denom, rounding).unwrap()
}

/// Compute the error due to integer division in the expression `x / denom * numer`.
///
/// Take the remainder of `x / denom` and multiply by `numer / denom`. The result can be added
/// to `x / denom * numer` for an accurate result.
fn rational_mul_correction<N, P>(x: N, numer: P::Inner, denom: P::Inner, rounding: Rounding) -> N
fn checked_rational_mul_correction<N, P>(
x: N,
numer: P::Inner,
denom: P::Inner,
rounding: Rounding,
) -> Result<N, &'static str>
where
N: MultiplyArg + UniqueSaturatedInto<P::Inner>,
P: PerThing,
P::Inner: Into<N>,
{
if P::Inner::is_zero(&denom) {
return Err("Division by zero")
}

let numer_upper = P::Upper::from(numer);
let denom_n: N = denom.into();
let denom_upper = P::Upper::from(denom);
Expand Down Expand Up @@ -540,7 +559,7 @@ where
}
},
}
rem_mul_div_inner.into()
Ok(rem_mul_div_inner.into())
}

macro_rules! implement_per_thing {
Expand Down Expand Up @@ -1021,6 +1040,17 @@ macro_rules! implement_per_thing {
}
}

impl CheckedDiv for $name {
#[inline]
fn checked_div(&self, rhs: &Self) -> Option<Self> {
if rhs.0.is_zero() {
return None
}

self.deconstruct().checked_div(rhs.deconstruct()).map($name::from_parts)
}
}

impl $crate::traits::Zero for $name {
fn zero() -> Self {
Self::zero()
Expand Down Expand Up @@ -1544,6 +1574,77 @@ macro_rules! implement_per_thing {
}
}

#[test]
fn checked_rational_mul_correction_works() {
assert_eq!(
super::checked_rational_mul_correction::<$type, $name>(
<$type>::max_value(),
<$type>::max_value(),
<$type>::max_value(),
super::Rounding::NearestPrefDown,
),
Ok(0),
);
assert_eq!(
super::checked_rational_mul_correction::<$type, $name>(
<$type>::max_value() - 1,
<$type>::max_value(),
<$type>::max_value(),
super::Rounding::NearestPrefDown,
),
Ok(<$type>::max_value() - 1),
);
assert_eq!(
super::checked_rational_mul_correction::<$upper_type, $name>(
((<$type>::max_value() - 1) as $upper_type).pow(2),
<$type>::max_value(),
<$type>::max_value(),
super::Rounding::NearestPrefDown,
),
Ok(1),
);
// ((max^2 - 1) % max) * max / max == max - 1
assert_eq!(
super::checked_rational_mul_correction::<$upper_type, $name>(
(<$type>::max_value() as $upper_type).pow(2) - 1,
<$type>::max_value(),
<$type>::max_value(),
super::Rounding::NearestPrefDown,
),
Ok(<$upper_type>::from((<$type>::max_value() - 1))),
);
// (max % 2) * max / 2 == max / 2
assert_eq!(
super::checked_rational_mul_correction::<$upper_type, $name>(
(<$type>::max_value() as $upper_type).pow(2),
<$type>::max_value(),
2 as $type,
super::Rounding::NearestPrefDown,
),
Ok(<$type>::max_value() as $upper_type / 2),
);
// ((max^2 - 1) % max) * 2 / max == 2 (rounded up)
assert_eq!(
super::checked_rational_mul_correction::<$upper_type, $name>(
(<$type>::max_value() as $upper_type).pow(2) - 1,
2 as $type,
<$type>::max_value(),
super::Rounding::NearestPrefDown,
),
Ok(2),
);
// ((max^2 - 1) % max) * 2 / max == 1 (rounded down)
assert_eq!(
super::checked_rational_mul_correction::<$upper_type, $name>(
(<$type>::max_value() as $upper_type).pow(2) - 1,
2 as $type,
<$type>::max_value(),
super::Rounding::Down,
),
Ok(1),
);
}

#[test]
fn rational_mul_correction_works() {
assert_eq!(
Expand Down Expand Up @@ -1737,6 +1838,26 @@ macro_rules! implement_per_thing {
Some($name::from_percent(0))
);
}

#[test]
fn test_basic_checked_div() {
assert_eq!(
$name::from_parts($max).checked_div(&$name::from_parts($max)),
Some($name::from_parts(1))
);
assert_eq!(
$name::from_percent(100).checked_div(&$name::from_parts(100)),
Some($name::from_percent(1))
);
assert_eq!(
$name::from_percent(0).checked_div(&$name::from_percent(0)),
None
);
assert_eq!(
$name::from_parts(0).checked_div(&$name::from_parts(0)),
None
);
}
}
};
}
Expand Down

0 comments on commit 1bd75e2

Please sign in to comment.