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use crate::natural::arithmetic::add::{
limbs_add_greater, limbs_slice_add_greater_in_place_left, limbs_slice_add_limb_in_place,
};
use crate::natural::arithmetic::mul::limb::{limbs_mul_limb_to_out, limbs_slice_mul_limb_in_place};
use crate::natural::arithmetic::mul::limbs_mul_to_out;
use crate::natural::InnerNatural::{Large, Small};
use crate::natural::Natural;
use crate::platform::{DoubleLimb, Limb};
use malachite_base::num::arithmetic::traits::{AddMul, AddMulAssign};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::conversion::traits::{ExactFrom, SplitInHalf};
use std::mem::swap;
// Given the limbs of two `Natural`s x and y, and a limb `z`, returns the limbs of x + y * z. `xs`
// and `ys` should be nonempty and have no trailing zeros, and `z` should be nonzero. The result
// will have no trailing zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `max(xs.len(), ys.len())`.
//
// This is equivalent to `mpz_aorsmul_1` from `mpz/aorsmul_i.c`, GMP 6.2.1, where `w` and `x` are
// positive, `sub` is positive, and `w` is returned instead of overwriting the first input.
pub_test! {limbs_add_mul_limb(xs: &[Limb], ys: &[Limb], limb: Limb) -> Vec<Limb> {
let mut out;
if xs.len() >= ys.len() {
out = xs.to_vec();
limbs_vec_add_mul_limb_greater_in_place_left(&mut out, ys, limb);
} else {
out = ys.to_vec();
limbs_vec_add_mul_limb_smaller_in_place_right(xs, &mut out, limb);
}
out
}}
// Given the equal-length limbs of two `Natural`s x and y, and a limb `z`, computes x + y * z. The
// lowest `xs.len()` limbs of the result are written to `xs`, and the highest limb of y * z, plus
// the carry-out from the addition, is returned.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// # Panics
// Panics if `xs` and `ys` have different lengths.
//
// This is equivalent to `mpn_addmul_1` from `mpn/generic/addmul_1.c`, GMP 6.2.1.
pub_crate_test! {limbs_slice_add_mul_limb_same_length_in_place_left(
xs: &mut [Limb],
ys: &[Limb],
z: Limb,
) -> Limb {
let len = xs.len();
assert_eq!(ys.len(), len);
let mut carry = 0;
let dz = DoubleLimb::from(z);
for (x, &y) in xs.iter_mut().zip(ys.iter()) {
let out = DoubleLimb::from(*x) + DoubleLimb::from(y) * dz + carry;
*x = out.lower_half();
carry = out >> Limb::WIDTH;
}
Limb::exact_from(carry)
}}
// Given the limbs of two `Natural`s x and y, and a limb `z`, computes x + y * z. The lowest limbs
// of the result are written to `ys` and the highest limb is returned. `xs` must have the same
// length as `ys`.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// # Panics
// Panics if `xs` and `ys` have different lengths.
//
// This is equivalent to `mpz_aorsmul_1` from `mpz/aorsmul_i.c`, GMP 6.2.1, where `w` and `x` are
// positive and have the same lengths, `sub` is positive, the lowest limbs of the result are
// written to the second input rather than the first, and the highest limb is returned.
pub_test! {limbs_slice_add_mul_limb_same_length_in_place_right(
xs: &[Limb],
ys: &mut [Limb],
z: Limb,
) -> Limb {
let xs_len = xs.len();
assert_eq!(ys.len(), xs_len);
let mut carry = 0;
let dz = DoubleLimb::from(z);
for (&x, y) in xs.iter().zip(ys.iter_mut()) {
let out = DoubleLimb::from(x) + DoubleLimb::from(*y) * dz + carry;
*y = out.lower_half();
carry = out >> Limb::WIDTH;
}
Limb::exact_from(carry)
}}
// Given the limbs of two `Natural`s a and b, and a limb c, writes the limbs of a + b * c to the
// first (left) input, corresponding to the limbs of a. `xs` and `ys` should be nonempty and have
// no trailing zeros, and `z` should be nonzero. The result will have no trailing zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(m) = O(m)$
//
// where $T$ is time, $M$ is additional memory, $n$ is `max(xs.len(), ys.len())` and $m$ is
// `max(1, ys.len() - xs.len())`.
//
// This is equivalent to `mpz_aorsmul_1` from `mpz/aorsmul_i.c`, GMP 6.2.1, where `w` and `x` are
// positive and sub is positive.
pub_test! {limbs_vec_add_mul_limb_in_place_left(xs: &mut Vec<Limb>, ys: &[Limb], z: Limb) {
let xs_len = xs.len();
if xs_len >= ys.len() {
limbs_vec_add_mul_limb_greater_in_place_left(xs, ys, z);
} else {
xs.resize(ys.len(), 0);
let (xs_lo, xs_hi) = xs.split_at_mut(xs_len);
let (ys_lo, ys_hi) = ys.split_at(xs_len);
let mut carry = limbs_mul_limb_to_out(xs_hi, ys_hi, z);
let inner_carry = limbs_slice_add_mul_limb_same_length_in_place_left(xs_lo, ys_lo, z);
if inner_carry != 0 && limbs_slice_add_limb_in_place(xs_hi, inner_carry) {
carry += 1;
}
if carry != 0 {
xs.push(carry);
}
}
}}
// ys.len() > 0, xs.len() >= ys.len(), z != 0
fn limbs_vec_add_mul_limb_greater_in_place_left(xs: &mut Vec<Limb>, ys: &[Limb], z: Limb) {
let ys_len = ys.len();
let carry = limbs_slice_add_mul_limb_same_length_in_place_left(&mut xs[..ys_len], ys, z);
if carry != 0 {
if xs.len() == ys_len {
xs.push(carry);
} else if limbs_slice_add_limb_in_place(&mut xs[ys_len..], carry) {
xs.push(1);
}
}
}
// Given the limbs of two `Natural`s x and y, and a limb `z`, writes the limbs of x + y * z to the
// second (right) input, corresponding to the limbs of y. `xs` and `ys` should be nonempty and have
// no trailing zeros, and `z` should be nonzero. The result will have no trailing zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(m) = O(m)$
//
// where $T$ is time, $M$ is additional memory, $n$ is `max(xs.len(), ys.len())` and $m$ is
// `max(1, ys.len() - xs.len())`.
//
// This is equivalent to `mpz_aorsmul_1` from `mpz/aorsmul_i.c`, GMP 6.2.1, where `w` and `x` are
// positive, `sub` is positive, and the result is written to the second input rather than the first.
pub_test! {limbs_vec_add_mul_limb_in_place_right(xs: &[Limb], ys: &mut Vec<Limb>, z: Limb) {
let ys_len = ys.len();
if xs.len() >= ys_len {
let carry = limbs_slice_add_mul_limb_same_length_in_place_right(&xs[..ys_len], ys, z);
ys.extend_from_slice(&xs[ys_len..]);
if carry != 0 {
if xs.len() == ys_len {
ys.push(carry);
} else if limbs_slice_add_limb_in_place(&mut ys[ys_len..], carry) {
ys.push(1);
}
}
} else {
limbs_vec_add_mul_limb_smaller_in_place_right(xs, ys, z);
}
}}
// xs.len() > 0, xs.len() < ys.len(), z != 0
fn limbs_vec_add_mul_limb_smaller_in_place_right(xs: &[Limb], ys: &mut Vec<Limb>, z: Limb) {
let (ys_lo, ys_hi) = ys.split_at_mut(xs.len());
let mut carry = limbs_slice_mul_limb_in_place(ys_hi, z);
let inner_carry = limbs_slice_add_mul_limb_same_length_in_place_right(xs, ys_lo, z);
if inner_carry != 0 && limbs_slice_add_limb_in_place(ys_hi, inner_carry) {
carry += 1;
}
if carry != 0 {
ys.push(carry);
}
}
// Given the limbs of two `Natural`s x and y, and a limb `z`, writes the limbs of x + y * z to
// whichever input is longer. If the result is written to the first input, `false` is returned; if
// to the second, `true` is returned. `xs` and `ys` should be nonempty and have no trailing zeros,
// and `z` should be nonzero. The result will have no trailing zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory and $n$ is `max(xs.len(), ys.len())`.
//
// This is equivalent to `mpz_aorsmul_1` from `mpz/aorsmul_i.c`, GMP 6.2.1, where `w` and `x` are
// positive, `sub` is positive, and the result is written to the longer input.
pub_test! {limbs_vec_add_mul_limb_in_place_either(
xs: &mut Vec<Limb>,
ys: &mut Vec<Limb>,
z: Limb,
) -> bool {
if xs.len() >= ys.len() {
limbs_vec_add_mul_limb_greater_in_place_left(xs, ys, z);
false
} else {
limbs_vec_add_mul_limb_smaller_in_place_right(xs, ys, z);
true
}
}}
// Given the limbs `xs`, `ys` and `zs` of three `Natural`s x, y, and z, returns the limbs of
// x + y * z. `xs` should be nonempty and `ys` and `zs` should have length at least 2. None of the
// slices should have any trailing zeros. The result will have no trailing zeros.
//
// # Worst-case complexity
// $T(n, m) = O(m + n \log n \log\log n)$
//
// $M(n, m) = O(m + n \log n)$
//
// where $T$ is time, $M$ is additional memory, $n$ is `max(ys.len(), zs.len())`, and $m$ is
// `xs.len()`.
//
// # Panics
// Panics if `ys` or `zs` are empty.
//
// This is equivalent to `mpz_aorsmul` from `mpz/aorsmul.c`, GMP 6.2.1, where `w`, `x`, and `y` are
// positive, `sub` is positive, and `w` is returned instead of overwriting the first input.
pub_test! {limbs_add_mul(xs: &[Limb], ys: &[Limb], zs: &[Limb]) -> Vec<Limb> {
let xs_len = xs.len();
let mut out_len = ys.len() + zs.len();
let mut out = vec![0; out_len];
if limbs_mul_to_out(&mut out, ys, zs) == 0 {
out_len -= 1;
out.pop();
}
assert_ne!(*out.last().unwrap(), 0);
if xs_len >= out_len {
limbs_add_greater(xs, &out)
} else {
if limbs_slice_add_greater_in_place_left(&mut out, xs) {
out.push(1);
}
out
}
}}
// Given the limbs `xs`, `ys` and `zs` of three `Natural`s x, y, and z, computes x + y * z. The
// limbs of the result are written to `xs`. `xs` should be nonempty and `ys` and `zs` should have
// length at least 2. None of the slices should have any trailing zeros. The result will have no
// trailing zeros.
//
// # Worst-case complexity
// $T(n, m) = O(m + n \log n \log\log n)$
//
// $M(n) = O(n \log n)$
//
// where $T$ is time, $M$ is additional memory, $n$ is `max(ys.len(), zs.len())`, and $m$ is
// `xs.len()`.
//
// # Panics
// Panics if `ys` or `zs` are empty.
//
// This is equivalent to `mpz_aorsmul` from `mpz/aorsmul.c`, GMP 6.2.1, where `w`, `x`, and `y` are
// positive and `sub` is positive.
pub_test! {limbs_add_mul_in_place_left(xs: &mut Vec<Limb>, ys: &[Limb], zs: &[Limb]) {
let xs_len = xs.len();
let mut out_len = ys.len() + zs.len();
let mut out = vec![0; out_len];
if limbs_mul_to_out(&mut out, ys, zs) == 0 {
out_len -= 1;
out.pop();
}
assert_ne!(*out.last().unwrap(), 0);
if xs_len < out_len {
swap(xs, &mut out);
}
if limbs_slice_add_greater_in_place_left(xs, &out) {
xs.push(1);
}
}}
impl Natural {
fn add_mul_limb_ref_ref(&self, y: &Natural, z: Limb) -> Natural {
match (self, y, z) {
(x, _, 0) | (x, natural_zero!(), _) => x.clone(),
(x, y, 1) => x + y,
(x, natural_one!(), z) => x + Natural::from(z),
(Natural(Large(ref xs)), Natural(Large(ref ys)), z) => {
Natural(Large(limbs_add_mul_limb(xs, ys, z)))
}
(x, y, z) => x + y * Natural::from(z),
}
}
fn add_mul_assign_limb(&mut self, mut y: Natural, z: Limb) {
match (&mut *self, &mut y, z) {
(_, _, 0) | (_, natural_zero!(), _) => {}
(x, _, 1) => *x += y,
(x, natural_one!(), z) => *x += Natural::from(z),
(Natural(Large(ref mut xs)), Natural(Large(ref mut ys)), z) => {
if limbs_vec_add_mul_limb_in_place_either(xs, ys, z) {
*self = y;
}
}
(x, _, z) => *x += y * Natural::from(z),
}
}
fn add_mul_assign_limb_ref(&mut self, y: &Natural, z: Limb) {
match (&mut *self, y, z) {
(_, _, 0) | (_, natural_zero!(), _) => {}
(x, y, 1) => *x += y,
(x, natural_one!(), z) => *x += Natural::from(z),
(Natural(Large(ref mut xs)), Natural(Large(ref ys)), z) => {
limbs_vec_add_mul_limb_in_place_left(xs, ys, z);
}
(x, y, z) => *x += y * Natural::from(z),
}
}
}
impl AddMul<Natural, Natural> for Natural {
type Output = Natural;
/// Adds a [`Natural`] and the product of two other [`Natural`]s, taking all three by value.
///
/// $f(x, y, z) = x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMul, Pow};
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(10u32).add_mul(Natural::from(3u32), Natural::from(4u32)), 22);
/// assert_eq!(
/// Natural::from(10u32).pow(12)
/// .add_mul(Natural::from(0x10000u32), Natural::from(10u32).pow(12)),
/// 65537000000000000u64
/// );
/// ```
#[inline]
fn add_mul(mut self, y: Natural, z: Natural) -> Natural {
self.add_mul_assign(y, z);
self
}
}
impl<'a> AddMul<Natural, &'a Natural> for Natural {
type Output = Natural;
/// Adds a [`Natural`] and the product of two other [`Natural`]s, taking the first two by value
/// and the third by reference.
///
/// $f(x, y, z) = x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMul, Pow};
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(10u32).add_mul(Natural::from(3u32), &Natural::from(4u32)), 22);
/// assert_eq!(
/// Natural::from(10u32).pow(12)
/// .add_mul(Natural::from(0x10000u32), &Natural::from(10u32).pow(12)),
/// 65537000000000000u64
/// );
/// ```
#[inline]
fn add_mul(mut self, y: Natural, z: &'a Natural) -> Natural {
self.add_mul_assign(y, z);
self
}
}
impl<'a> AddMul<&'a Natural, Natural> for Natural {
type Output = Natural;
/// Adds a [`Natural`] and the product of two other [`Natural`]s, taking the first and third by
/// value and the second by reference.
///
/// $f(x, y, z) = x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMul, Pow};
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(10u32).add_mul(&Natural::from(3u32), Natural::from(4u32)), 22);
/// assert_eq!(
/// Natural::from(10u32).pow(12)
/// .add_mul(&Natural::from(0x10000u32), Natural::from(10u32).pow(12)),
/// 65537000000000000u64
/// );
/// ```
#[inline]
fn add_mul(mut self, y: &'a Natural, z: Natural) -> Natural {
self.add_mul_assign(y, z);
self
}
}
impl<'a, 'b> AddMul<&'a Natural, &'b Natural> for Natural {
type Output = Natural;
/// Adds a [`Natural`] and the product of two other [`Natural`]s, taking the first by value and
/// the second and third by reference.
///
/// $f(x, y, z) = x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMul, Pow};
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(10u32).add_mul(&Natural::from(3u32), &Natural::from(4u32)), 22);
/// assert_eq!(
/// Natural::from(10u32).pow(12)
/// .add_mul(&Natural::from(0x10000u32), &Natural::from(10u32).pow(12)),
/// 65537000000000000u64
/// );
/// ```
#[inline]
fn add_mul(mut self, y: &'a Natural, z: &'b Natural) -> Natural {
self.add_mul_assign(y, z);
self
}
}
impl<'a, 'b, 'c> AddMul<&'a Natural, &'b Natural> for &'c Natural {
type Output = Natural;
/// Adds a [`Natural`] and the product of two other [`Natural`]s, taking all three by
/// reference.
///
/// $f(x, y, z) = x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n, m) = O(m + n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMul, Pow};
/// use malachite_nz::natural::Natural;
///
/// assert_eq!((&Natural::from(10u32)).add_mul(&Natural::from(3u32), &Natural::from(4u32)), 22);
/// assert_eq!(
/// (&Natural::from(10u32).pow(12))
/// .add_mul(&Natural::from(0x10000u32), &Natural::from(10u32).pow(12)),
/// 65537000000000000u64
/// );
/// ```
fn add_mul(self, y: &'a Natural, z: &'b Natural) -> Natural {
match (self, y, z) {
(Natural(Small(x)), y, z) => (y * z).add_limb(*x),
(x, Natural(Small(y)), z) => x.add_mul_limb_ref_ref(z, *y),
(x, y, Natural(Small(z))) => x.add_mul_limb_ref_ref(y, *z),
(Natural(Large(ref xs)), Natural(Large(ref ys)), Natural(Large(ref zs))) => {
Natural(Large(limbs_add_mul(xs, ys, zs)))
}
}
}
}
impl AddMulAssign<Natural, Natural> for Natural {
/// Adds the product of two other [`Natural`]s to a [`Natural`] in place, taking both
/// [`Natural`]s on the right-hand side by value.
///
/// $x \gets x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMulAssign, Pow};
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(10u32);
/// x.add_mul_assign(Natural::from(3u32), Natural::from(4u32));
/// assert_eq!(x, 22);
///
/// let mut x = Natural::from(10u32).pow(12);
/// x.add_mul_assign(Natural::from(0x10000u32), Natural::from(10u32).pow(12));
/// assert_eq!(x, 65537000000000000u64);
/// ```
fn add_mul_assign(&mut self, mut y: Natural, mut z: Natural) {
match (&mut *self, &mut y, &mut z) {
(Natural(Small(x)), _, _) => *self = (y * z).add_limb(*x),
(_, Natural(Small(y)), _) => self.add_mul_assign_limb(z, *y),
(_, _, Natural(Small(z))) => self.add_mul_assign_limb(y, *z),
(Natural(Large(ref mut xs)), Natural(Large(ref ys)), Natural(Large(ref zs))) => {
limbs_add_mul_in_place_left(xs, ys, zs)
}
}
}
}
impl<'a> AddMulAssign<Natural, &'a Natural> for Natural {
/// Adds the product of two other [`Natural`]s to a [`Natural`] in place, taking the first
/// [`Natural`] on the right-hand side by value and the second by reference.
///
/// $x \gets x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMulAssign, Pow};
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(10u32);
/// x.add_mul_assign(Natural::from(3u32), &Natural::from(4u32));
/// assert_eq!(x, 22);
///
/// let mut x = Natural::from(10u32).pow(12);
/// x.add_mul_assign(Natural::from(0x10000u32), &Natural::from(10u32).pow(12));
/// assert_eq!(x, 65537000000000000u64);
/// ```
fn add_mul_assign(&mut self, mut y: Natural, z: &'a Natural) {
match (&mut *self, &mut y, z) {
(Natural(Small(x)), _, _) => *self = (y * z).add_limb(*x),
(_, Natural(Small(y)), _) => self.add_mul_assign_limb_ref(z, *y),
(_, _, Natural(Small(z))) => self.add_mul_assign_limb(y, *z),
(Natural(Large(ref mut xs)), Natural(Large(ref ys)), Natural(Large(ref zs))) => {
limbs_add_mul_in_place_left(xs, ys, zs)
}
}
}
}
impl<'a> AddMulAssign<&'a Natural, Natural> for Natural {
/// Adds the product of two other [`Natural`]s to a [`Natural`] in place, taking the first
/// [`Natural`] on the right-hand side by reference and the second by value.
///
/// $x \gets x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMulAssign, Pow};
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(10u32);
/// x.add_mul_assign(&Natural::from(3u32), Natural::from(4u32));
/// assert_eq!(x, 22);
///
/// let mut x = Natural::from(10u32).pow(12);
/// x.add_mul_assign(&Natural::from(0x10000u32), Natural::from(10u32).pow(12));
/// assert_eq!(x, 65537000000000000u64);
/// ```
fn add_mul_assign(&mut self, y: &'a Natural, mut z: Natural) {
match (&mut *self, y, &mut z) {
(Natural(Small(x)), _, _) => *self = (y * z).add_limb(*x),
(_, Natural(Small(y)), _) => self.add_mul_assign_limb(z, *y),
(_, _, Natural(Small(z))) => self.add_mul_assign_limb_ref(y, *z),
(Natural(Large(ref mut xs)), Natural(Large(ref ys)), Natural(Large(ref zs))) => {
limbs_add_mul_in_place_left(xs, ys, zs)
}
}
}
}
impl<'a, 'b> AddMulAssign<&'a Natural, &'b Natural> for Natural {
/// Adds the product of two other [`Natural`]s to a [`Natural`] in place, taking both
/// [`Natural`]s on the right-hand side by reference.
///
/// $x \gets x + yz$.
///
/// # Worst-case complexity
/// $T(n, m) = O(m + n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is
/// `max(y.significant_bits(), z.significant_bits())`, and $m$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::{AddMulAssign, Pow};
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(10u32);
/// x.add_mul_assign(&Natural::from(3u32), &Natural::from(4u32));
/// assert_eq!(x, 22);
///
/// let mut x = Natural::from(10u32).pow(12);
/// x.add_mul_assign(&Natural::from(0x10000u32), &Natural::from(10u32).pow(12));
/// assert_eq!(x, 65537000000000000u64);
/// ```
fn add_mul_assign(&mut self, y: &'a Natural, z: &'b Natural) {
match (&mut *self, y, z) {
(Natural(Small(x)), _, _) => *self = (y * z).add_limb(*x),
(_, Natural(Small(y)), _) => self.add_mul_assign_limb_ref(z, *y),
(_, _, Natural(Small(z))) => self.add_mul_assign_limb_ref(y, *z),
(Natural(Large(ref mut xs)), Natural(Large(ref ys)), Natural(Large(ref zs))) => {
limbs_add_mul_in_place_left(xs, ys, zs)
}
}
}
}