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use super::div_rem_euclid::DivRemEuclid;
pub trait CheckedRemEuclidInv<Divisor = Self> {
type Output;
/// Returns multiplicative inverse of checked euclidean division.
/// ```
/// use traiter::numbers::CheckedRemEuclidInv;
/// // signed integers
/// assert_eq!(
/// CheckedRemEuclidInv::checked_rem_euclid_inv(-3i8, 2i8), Some(1i8)
/// );
/// assert_eq!(
/// CheckedRemEuclidInv::checked_rem_euclid_inv(-3i8, 1i8), Some(0i8)
/// );
/// assert_eq!(
/// CheckedRemEuclidInv::checked_rem_euclid_inv(-3i8, 0i8), None
/// );
/// // unsigned integers
/// assert_eq!(
/// CheckedRemEuclidInv::checked_rem_euclid_inv(3u8, 2u8), Some(1u8)
/// );
/// assert_eq!(
/// CheckedRemEuclidInv::checked_rem_euclid_inv(3u8, 1u8), Some(0u8)
/// );
/// assert_eq!(
/// CheckedRemEuclidInv::checked_rem_euclid_inv(3u8, 0u8), None
/// );
/// ```
fn checked_rem_euclid_inv(self, divisor: Divisor) -> Self::Output;
}
macro_rules! signed_integer_checked_rem_euclid_inv_impl {
($($integer:ty)*) => ($(
impl CheckedRemEuclidInv for $integer {
type Output = Option<Self>;
#[inline(always)]
fn checked_rem_euclid_inv(self, divisor: Self) -> Self::Output {
let mut candidate = 0;
let mut result = 1;
let mut step_dividend = self;
let mut step_divisor = divisor;
while step_divisor != 0 {
let (quotient, remainder) =
step_dividend.div_rem_euclid(step_divisor);
step_dividend = step_divisor;
step_divisor = remainder;
(result, candidate) =
(candidate, result - quotient * candidate);
}
if step_dividend == 1 {
Some(if result.is_negative() {
divisor + result
} else {
result
})
} else {
None
}
}
}
)*)
}
signed_integer_checked_rem_euclid_inv_impl!(i8 i16 i32 i64 i128 isize);
macro_rules! unsigned_integer_checked_rem_euclid_inv_impl {
($($integer:ty)*) => ($(
impl CheckedRemEuclidInv for $integer {
type Output = Option<Self>;
#[inline(always)]
fn checked_rem_euclid_inv(self, divisor: Self) -> Self::Output {
let mut candidate_modulus = 0;
let mut result_modulus = 1;
let mut is_result_negative = false;
let mut is_candidate_negative = false;
let mut step_dividend = self;
let mut step_divisor = divisor;
while step_divisor != 0 {
let (quotient, remainder) =
step_dividend.div_rem_euclid(step_divisor);
step_dividend = step_divisor;
step_divisor = remainder;
let subtrahend_modulus = quotient * candidate_modulus;
(
is_result_negative,
result_modulus,
(is_candidate_negative, candidate_modulus),
) = (
is_candidate_negative,
candidate_modulus,
if is_result_negative {
if is_candidate_negative {
if result_modulus > subtrahend_modulus {
(true, result_modulus - subtrahend_modulus)
} else {
(
false,
subtrahend_modulus - result_modulus,
)
}
} else {
(true, subtrahend_modulus + result_modulus)
}
} else if is_candidate_negative {
(false, subtrahend_modulus + result_modulus)
} else if result_modulus > subtrahend_modulus {
(false, result_modulus - subtrahend_modulus)
} else {
(true, subtrahend_modulus - result_modulus)
},
);
}
if step_dividend == 1 {
Some(if is_result_negative {
divisor - result_modulus
} else {
result_modulus
})
} else {
None
}
}
}
)*)
}
unsigned_integer_checked_rem_euclid_inv_impl!(u8 u16 u32 u64 u128 usize);