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Implement checked arithmetic #152

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88 changes: 87 additions & 1 deletion src/lib.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -30,7 +30,10 @@ use core::str::FromStr;
#[cfg(feature = "std")]
use std::error::Error;

use num_traits::{ConstOne, ConstZero, Inv, MulAdd, Num, One, Pow, Signed, Zero};
use num_traits::{
CheckedAdd, CheckedDiv, CheckedMul, CheckedRem, CheckedSub, ConstOne, ConstZero, Inv, MulAdd,
Num, One, Pow, Signed, Zero,
};

use num_traits::float::FloatCore;
#[cfg(any(feature = "std", feature = "libm"))]
Expand Down Expand Up @@ -761,6 +764,16 @@ impl<T: Clone + Num> Add<Complex<T>> for Complex<T> {
}
}

impl<T: Clone + Num + CheckedAdd> CheckedAdd for Complex<T> {
#[inline]
fn checked_add(&self, other: &Self) -> Option<Self> {
Some(Self::new(
self.re.checked_add(&other.re)?,
self.im.checked_add(&other.im)?,
))
}
}

forward_all_binop!(impl Sub, sub);

// (a + i b) - (c + i d) == (a - c) + i (b - d)
Expand All @@ -773,6 +786,16 @@ impl<T: Clone + Num> Sub<Complex<T>> for Complex<T> {
}
}

impl<T: Clone + Num + CheckedSub> CheckedSub for Complex<T> {
#[inline]
fn checked_sub(&self, other: &Self) -> Option<Self> {
Some(Self::new(
self.re.checked_sub(&other.re)?,
self.im.checked_sub(&other.im)?,
))
}
}

forward_all_binop!(impl Mul, mul);

// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c)
Expand All @@ -787,6 +810,23 @@ impl<T: Clone + Num> Mul<Complex<T>> for Complex<T> {
}
}

impl<T: Clone + Num + CheckedMul + CheckedAdd + CheckedSub> CheckedMul for Complex<T> {
#[inline]
fn checked_mul(&self, other: &Self) -> Option<Self> {
let re = self
.re
.checked_mul(&other.re)?
.checked_sub(&self.im.checked_mul(&other.im)?)?;

let im = self
.re
.checked_mul(&other.im)?
.checked_add(&self.im.checked_mul(&other.re)?)?;

Some(Self::new(re, im))
}
}

// (a + i b) * (c + i d) + (e + i f) == ((a*c + e) - b*d) + i (a*d + (b*c + f))
impl<T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> for Complex<T> {
type Output = Complex<T>;
Expand All @@ -799,6 +839,7 @@ impl<T: Clone + Num + MulAdd<Output = T>> MulAdd<Complex<T>> for Complex<T> {
Complex::new(re, im)
}
}

impl<'a, 'b, T: Clone + Num + MulAdd<Output = T>> MulAdd<&'b Complex<T>> for &'a Complex<T> {
type Output = Complex<T>;

Expand All @@ -824,6 +865,30 @@ impl<T: Clone + Num> Div<Complex<T>> for Complex<T> {
}
}

impl<T: Clone + Num + CheckedAdd + CheckedSub + CheckedMul + CheckedDiv> CheckedDiv for Complex<T> {
#[inline]
fn checked_div(&self, other: &Self) -> Option<Self> {
let norm_sqr = other
.re
.checked_mul(&other.re)?
.checked_add(&other.im.checked_mul(&other.im)?)?;

let re = self
.re
.checked_mul(&other.re)?
.checked_add(&self.im.checked_mul(&other.im)?)?;

let im = self
.im
.checked_mul(&other.re)?
.checked_sub(&self.re.checked_mul(&other.im)?)?;
Some(Self::new(
re.checked_div(&norm_sqr)?,
im.checked_div(&norm_sqr)?,
))
}
}

Comment on lines +868 to +891
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IMHO I find it far easier to read if one uses aliases for the real/imag parts as in the formula of the documentation block above, e.g.

let (a, b) = (&self.re, &self.im);
let (c, d) = (&other.re, &other.im);
let norm_sqr = c.checked_mul(c)?.checked_add(&d.checked_mul(d)?)?;
...

Inconsistency to other code sections needs to be weighted in though...

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Nowhere else in the arithmetic code does this as far as I can tell.

forward_all_binop!(impl Rem, rem);

impl<T: Clone + Num> Complex<T> {
Expand All @@ -834,6 +899,16 @@ impl<T: Clone + Num> Complex<T> {
}
}

impl<T: Clone + Num + CheckedAdd + CheckedSub + CheckedMul + CheckedDiv + CheckedRem> Complex<T> {
fn checked_div_trunc(&self, divisor: &Self) -> Option<Self> {
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Could be added to the mr description.

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It parallels the implementation for Rem, which has its own private method div_trunc which is right above it and right beside the Rem impl. I don't believe it's specifically noteworthy to merit being added to the PR description.

let Complex { re, im } = self.checked_div(divisor)?;
let re = re.checked_sub(&re.checked_rem(&T::one())?)?;
let im = im.checked_sub(&im.checked_rem(&T::one())?)?;

Some(Self::new(re, im))
}
}

impl<T: Clone + Num> Rem<Complex<T>> for Complex<T> {
type Output = Self;

Expand All @@ -844,6 +919,17 @@ impl<T: Clone + Num> Rem<Complex<T>> for Complex<T> {
}
}

impl<T: Clone + Num + CheckedAdd + CheckedSub + CheckedMul + CheckedDiv + CheckedRem> CheckedRem
for Complex<T>
{
#[inline]
fn checked_rem(&self, modulus: &Self) -> Option<Self> {
let gaussian = self.checked_div_trunc(modulus)?;

self.checked_sub(&modulus.checked_mul(&gaussian)?)
}
}

// Op Assign

mod opassign {
Expand Down