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// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
// Copyright © 1991, 1992, 1993, 1994, 1996, 1997, 1999, 2000, 2001, 2002, 2003, 2004, 2005
// Free Software Foundation, Inc.
//
// Copyright © 2009, 2015, 2016 William Hart
//
// Copyright © 2011 Fredrik Johansson
//
// 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::XXDivModYToQR;
use crate::num::basic::integers::USIZE_IS_U32;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::half::{wide_join_halves, wide_split_in_half};
use crate::num::conversion::traits::WrappingFrom;
use crate::num::conversion::traits::{HasHalf, JoinHalves, SplitInHalf};
use crate::num::logic::traits::LeadingZeros;
fn implicit_xx_div_mod_y_to_qr<
T: PrimitiveUnsigned,
DT: From<T> + HasHalf<Half = T> + JoinHalves + PrimitiveUnsigned + SplitInHalf,
>(
x_1: T,
x_0: T,
y: T,
) -> (T, T) {
assert!(x_1 < y);
let (q, r) = DT::join_halves(x_1, x_0).div_mod(DT::from(y));
(q.lower_half(), r.lower_half())
}
// This is equivalent to `udiv_qrnnd_int` from `longlong.h`, FLINT 2.7.1, where `(q, r)` is
// returned.
fn explicit_xx_div_mod_y_to_qr_normalized<T: PrimitiveUnsigned>(x_1: T, x_0: T, y: T) -> (T, T) {
let (d_1, d_0) = wide_split_in_half(y);
let (x_0_1, x_0_0) = wide_split_in_half(x_0);
let mut q_1 = x_1 / d_1;
let mut r_1 = x_1.wrapping_sub(q_1.wrapping_mul(d_1));
let product = q_1.wrapping_mul(d_0);
r_1 = wide_join_halves(r_1, x_0_1);
if r_1 < product {
q_1.wrapping_sub_assign(T::ONE);
if !r_1.overflowing_add_assign(y) && r_1 < product {
q_1.wrapping_sub_assign(T::ONE);
r_1.wrapping_add_assign(y);
}
}
r_1.wrapping_sub_assign(product);
let mut q_0 = r_1 / d_1;
let mut r_0 = r_1.wrapping_sub(q_0.wrapping_mul(d_1));
let product = q_0.wrapping_mul(d_0);
r_0 = wide_join_halves(r_0, x_0_0);
if r_0 < product {
q_0.wrapping_sub_assign(T::ONE);
if !r_0.overflowing_add_assign(y) && r_0 < product {
q_0.wrapping_sub_assign(T::ONE);
r_0.wrapping_add_assign(y);
}
}
r_0.wrapping_sub_assign(product);
(wide_join_halves(q_1, q_0), r_0)
}
// This is udiv_qrnnd from longlong.h, FLINT 2.7.1, where (q, r) is returned.
pub_test! {explicit_xx_div_mod_y_to_qr<T: PrimitiveUnsigned>(x_1: T, x_0: T, y: T) -> (T, T) {
assert!(x_1 < y);
let shift = LeadingZeros::leading_zeros(y);
if shift == 0 {
explicit_xx_div_mod_y_to_qr_normalized(x_1, x_0, y)
} else {
let (q, r) = explicit_xx_div_mod_y_to_qr_normalized(
(x_1 << shift) | (x_0 >> (T::WIDTH - shift)),
x_0 << shift,
y << shift,
);
(q, r >> shift)
}
}}
macro_rules! implicit_xx_div_mod_to_qr {
($t:ident, $dt:ident) => {
impl XXDivModYToQR for $t {
/// Computes the quotient and remainder of two numbers. The first is composed of two
/// `Self` values, and the second of a single one.
///
/// `x_1` must be less than `y`.
///
/// $$
/// f(x_1, x_0, y) = (q, r),
/// $$
/// where $W$ is `Self::WIDTH`,
///
/// $x_1, x_0, y, q, r < 2^W$,
///
/// $x_1, r < y$, and
/// $$
/// qy + r = 2^Wx_1 + x_0.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::xx_div_mod_y_to_qr#xx_div_mod_y_to_qr).
///
/// This is equivalent to `udiv_qrnnd` from `longlong.h`, FLINT 2.7.1, where `(q, r)` is
/// returned.
#[inline]
fn xx_div_mod_y_to_qr(x_1: $t, x_0: $t, y: $t) -> ($t, $t) {
implicit_xx_div_mod_y_to_qr::<$t, $dt>(x_1, x_0, y)
}
}
};
}
implicit_xx_div_mod_to_qr!(u8, u16);
implicit_xx_div_mod_to_qr!(u16, u32);
implicit_xx_div_mod_to_qr!(u32, u64);
implicit_xx_div_mod_to_qr!(u64, u128);
impl XXDivModYToQR for usize {
/// Computes the quotient and remainder of two numbers. The first is composed of two [`usize`]
/// values, and the second of a single one.
///
/// `x_1` must be less than `y`.
///
/// $$
/// f(x_1, x_0, y) = (q, r),
/// $$
/// where $W$ is `Self::WIDTH`,
///
/// $x_1, x_0, y, q, r < 2^W$,
///
/// $x_1, r < y$, and
/// $$
/// qy + r = 2^Wx_1 + x_0.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::xx_div_mod_y_to_qr#xx_div_mod_y_to_qr).
///
/// This is `udiv_qrnnd` from `longlong.h`, FLINT 2.7.1, where `(q, r)` is returned.
fn xx_div_mod_y_to_qr(x_1: Self, x_0: Self, y: Self) -> (Self, Self) {
if USIZE_IS_U32 {
let (q, r) = u32::xx_div_mod_y_to_qr(
u32::wrapping_from(x_1),
u32::wrapping_from(x_0),
u32::wrapping_from(y),
);
(Self::wrapping_from(q), Self::wrapping_from(r))
} else {
let (q, r) = u64::xx_div_mod_y_to_qr(
u64::wrapping_from(x_1),
u64::wrapping_from(x_0),
u64::wrapping_from(y),
);
(Self::wrapping_from(q), Self::wrapping_from(r))
}
}
}
impl XXDivModYToQR for u128 {
/// Computes the quotient and remainder of two numbers. The first is composed of two [`u128`]
/// values, and the second of a single one.
///
/// `x_1` must be less than `y`.
///
/// $$
/// f(x_1, x_0, y) = (q, r),
/// $$
/// where $W$ is `Self::WIDTH`,
///
/// $x_1, x_0, y, q, r < 2^W$,
///
/// $x_1, r < y$, and
/// $$
/// qy + r = 2^Wx_1 + x_0.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::xx_div_mod_y_to_qr#xx_div_mod_y_to_qr).
///
/// This is equivalent to `udiv_qrnnd` from `longlong.h`, FLINT 2.7.1, where `(q, r)` is
/// returned.
#[inline]
fn xx_div_mod_y_to_qr(x_1: Self, x_0: Self, y: Self) -> (Self, Self) {
explicit_xx_div_mod_y_to_qr(x_1, x_0, y)
}
}