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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::num::arithmetic::traits::{SaturatingSubMul, SaturatingSubMulAssign, UnsignedAbs};
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::WrappingFrom;
fn saturating_sub_mul_unsigned<T: PrimitiveUnsigned>(x: T, y: T, z: T) -> T {
x.saturating_sub(y.saturating_mul(z))
}
fn saturating_sub_mul_assign_unsigned<T: PrimitiveUnsigned>(x: &mut T, y: T, z: T) {
x.saturating_sub_assign(y.saturating_mul(z));
}
macro_rules! impl_saturating_sub_mul_unsigned {
($t:ident) => {
impl SaturatingSubMul<$t> for $t {
type Output = $t;
/// Subtracts a number by the product of two other numbers, saturating at the numeric
/// bounds instead of overflowing.
///
/// $$
/// f(x, y, z) = \\begin{cases}
/// x - yz & \text{if} \\quad m \leq x - yz \leq M, \\\\
/// M & \text{if} \\quad x - yz > M, \\\\
/// m & \text{if} \\quad x - yz < m,
/// \\end{cases}
/// $$
/// where $m$ is `Self::MIN` and $M$ is `Self::MAX`.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::saturating_sub_mul#saturating_sub_mul_assign).
#[inline]
fn saturating_sub_mul(self, y: $t, z: $t) -> $t {
saturating_sub_mul_unsigned(self, y, z)
}
}
impl SaturatingSubMulAssign<$t> for $t {
/// Subtracts a number by the product of two other numbers in place, saturating at the
/// numeric bounds instead of overflowing.
///
/// $$
/// x \gets \\begin{cases}
/// x - yz & \text{if} \\quad m \leq x - yz \leq M, \\\\
/// M & \text{if} \\quad x - yz > M, \\\\
/// m & \text{if} \\quad x - yz < m,
/// \\end{cases}
/// $$
/// where $m$ is `Self::MIN` and $M$ is `Self::MAX`.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::saturating_sub_mul#saturating_sub_mul_assign).
#[inline]
fn saturating_sub_mul_assign(&mut self, y: $t, z: $t) {
saturating_sub_mul_assign_unsigned(self, y, z);
}
}
};
}
apply_to_unsigneds!(impl_saturating_sub_mul_unsigned);
fn saturating_sub_mul_signed<
U: PrimitiveUnsigned,
S: PrimitiveSigned + UnsignedAbs<Output = U> + WrappingFrom<U>,
>(
x: S,
y: S,
z: S,
) -> S {
if y == S::ZERO || z == S::ZERO {
return x;
}
let x_sign = x >= S::ZERO;
if x_sign == ((y >= S::ZERO) != (z >= S::ZERO)) {
x.saturating_sub(y.saturating_mul(z))
} else {
let x = x.unsigned_abs();
let product = if let Some(product) = y.unsigned_abs().checked_mul(z.unsigned_abs()) {
product
} else {
return if x_sign { S::MIN } else { S::MAX };
};
let result = S::wrapping_from(if x_sign {
x.wrapping_sub(product)
} else {
product.wrapping_sub(x)
});
if x >= product || (x_sign == (result < S::ZERO)) {
result
} else if x_sign {
S::MIN
} else {
S::MAX
}
}
}
macro_rules! impl_saturating_sub_mul_signed {
($t:ident) => {
impl SaturatingSubMul<$t> for $t {
type Output = $t;
/// Subtracts a number by the product of two other numbers, saturating at the numeric
/// bounds instead of overflowing.
///
/// $$
/// f(x, y, z) = \\begin{cases}
/// x - yz & \text{if} \\quad m \leq x - yz \leq M, \\\\
/// M & \text{if} \\quad x - yz > M, \\\\
/// m & \text{if} \\quad x - yz < m,
/// \\end{cases}
/// $$
/// where $m$ is `Self::MIN` and $M$ is `Self::MAX`.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::saturating_sub_mul#saturating_sub_mul).
#[inline]
fn saturating_sub_mul(self, y: $t, z: $t) -> $t {
saturating_sub_mul_signed(self, y, z)
}
}
impl SaturatingSubMulAssign<$t> for $t {
/// Subtracts a number by the product of two other numbers in place, saturating at the
/// numeric bounds instead of overflowing.
///
/// $$
/// x \gets \\begin{cases}
/// x - yz & \text{if} \\quad m \leq x - yz \leq M, \\\\
/// M & \text{if} \\quad x - yz > M, \\\\
/// m & \text{if} \\quad x - yz < m,
/// \\end{cases}
/// $$
/// where $m$ is `Self::MIN` and $M$ is `Self::MAX`.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::saturating_sub_mul#saturating_sub_mul_assign).
#[inline]
fn saturating_sub_mul_assign(&mut self, y: $t, z: $t) {
*self = self.saturating_sub_mul(y, z);
}
}
};
}
apply_to_signeds!(impl_saturating_sub_mul_signed);