Trait malachite_base::num::arithmetic::traits::XXXXAddYYYYToZZZZ

pub trait XXXXAddYYYYToZZZZ: Sized {
    // Required method
    fn xxxx_add_yyyy_to_zzzz(
        x_3: Self,
        x_2: Self,
        x_1: Self,
        x_0: Self,
        y_3: Self,
        y_2: Self,
        y_1: Self,
        y_0: Self,
    ) -> (Self, Self, Self, Self);
}

Adds two numbers, each composed of four Self values, returning the sum as a quadruple of Self values.

The more significant number always comes first. Addition is wrapping, and overflow is not indicated.

Required Methods

fn xxxx_add_yyyy_to_zzzz( x_3: Self, x_2: Self, x_1: Self, x_0: Self, y_3: Self, y_2: Self, y_1: Self, y_0: Self, ) -> (Self, Self, Self, Self)

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl XXXXAddYYYYToZZZZ for u8

fn xxxx_add_yyyy_to_zzzz( x_3: u8, x_2: u8, x_1: u8, x_0: u8, y_3: u8, y_2: u8, y_1: u8, y_0: u8, ) -> (u8, u8, u8, u8)

Adds two numbers, each composed of four Self values, returning the sum as a quadruple of Self values.

The more significant value always comes first. Addition is wrapping, and overflow is not indicated.

$$ f(x_3, x_2, x_1, x_0, y_2, y_2, y_1, y_0) = (z_3, z_2, z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_3, x_2, x_1, x_0, y_3, y_2, y_1, y_0, z_3, z_2, z_1, z_0 < 2^W$, and $$ (2^{3W}x_3 + 2^{2W}x_2 + 2^Wx_1 + x_0) + (2^{3W}y_3 + 2^{2W}y_2 + 2^Wy_1 + y_0) \equiv 2^{3W}z_3 + 2^{2W}z_2 + 2^Wz_1 + z_0 \mod 2^{4W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssssaaaaaaaa from longlong.h, FLINT 2.7.1, where (s3, s2, s1, s0) is returned.

impl XXXXAddYYYYToZZZZ for u16

fn xxxx_add_yyyy_to_zzzz( x_3: u16, x_2: u16, x_1: u16, x_0: u16, y_3: u16, y_2: u16, y_1: u16, y_0: u16, ) -> (u16, u16, u16, u16)

Adds two numbers, each composed of four Self values, returning the sum as a quadruple of Self values.

The more significant value always comes first. Addition is wrapping, and overflow is not indicated.

$$ f(x_3, x_2, x_1, x_0, y_2, y_2, y_1, y_0) = (z_3, z_2, z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_3, x_2, x_1, x_0, y_3, y_2, y_1, y_0, z_3, z_2, z_1, z_0 < 2^W$, and $$ (2^{3W}x_3 + 2^{2W}x_2 + 2^Wx_1 + x_0) + (2^{3W}y_3 + 2^{2W}y_2 + 2^Wy_1 + y_0) \equiv 2^{3W}z_3 + 2^{2W}z_2 + 2^Wz_1 + z_0 \mod 2^{4W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssssaaaaaaaa from longlong.h, FLINT 2.7.1, where (s3, s2, s1, s0) is returned.

impl XXXXAddYYYYToZZZZ for u32

fn xxxx_add_yyyy_to_zzzz( x_3: u32, x_2: u32, x_1: u32, x_0: u32, y_3: u32, y_2: u32, y_1: u32, y_0: u32, ) -> (u32, u32, u32, u32)

Adds two numbers, each composed of four Self values, returning the sum as a quadruple of Self values.

The more significant value always comes first. Addition is wrapping, and overflow is not indicated.

$$ f(x_3, x_2, x_1, x_0, y_2, y_2, y_1, y_0) = (z_3, z_2, z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_3, x_2, x_1, x_0, y_3, y_2, y_1, y_0, z_3, z_2, z_1, z_0 < 2^W$, and $$ (2^{3W}x_3 + 2^{2W}x_2 + 2^Wx_1 + x_0) + (2^{3W}y_3 + 2^{2W}y_2 + 2^Wy_1 + y_0) \equiv 2^{3W}z_3 + 2^{2W}z_2 + 2^Wz_1 + z_0 \mod 2^{4W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssssaaaaaaaa from longlong.h, FLINT 2.7.1, where (s3, s2, s1, s0) is returned.

impl XXXXAddYYYYToZZZZ for u64

fn xxxx_add_yyyy_to_zzzz( x_3: u64, x_2: u64, x_1: u64, x_0: u64, y_3: u64, y_2: u64, y_1: u64, y_0: u64, ) -> (u64, u64, u64, u64)

Adds two numbers, each composed of four Self values, returning the sum as a quadruple of Self values.

The more significant value always comes first. Addition is wrapping, and overflow is not indicated.

$$ f(x_3, x_2, x_1, x_0, y_2, y_2, y_1, y_0) = (z_3, z_2, z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_3, x_2, x_1, x_0, y_3, y_2, y_1, y_0, z_3, z_2, z_1, z_0 < 2^W$, and $$ (2^{3W}x_3 + 2^{2W}x_2 + 2^Wx_1 + x_0) + (2^{3W}y_3 + 2^{2W}y_2 + 2^Wy_1 + y_0) \equiv 2^{3W}z_3 + 2^{2W}z_2 + 2^Wz_1 + z_0 \mod 2^{4W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssssaaaaaaaa from longlong.h, FLINT 2.7.1, where (s3, s2, s1, s0) is returned.

impl XXXXAddYYYYToZZZZ for u128

fn xxxx_add_yyyy_to_zzzz( x_3: u128, x_2: u128, x_1: u128, x_0: u128, y_3: u128, y_2: u128, y_1: u128, y_0: u128, ) -> (u128, u128, u128, u128)

Adds two numbers, each composed of four Self values, returning the sum as a quadruple of Self values.

The more significant value always comes first. Addition is wrapping, and overflow is not indicated.

$$ f(x_3, x_2, x_1, x_0, y_2, y_2, y_1, y_0) = (z_3, z_2, z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_3, x_2, x_1, x_0, y_3, y_2, y_1, y_0, z_3, z_2, z_1, z_0 < 2^W$, and $$ (2^{3W}x_3 + 2^{2W}x_2 + 2^Wx_1 + x_0) + (2^{3W}y_3 + 2^{2W}y_2 + 2^Wy_1 + y_0) \equiv 2^{3W}z_3 + 2^{2W}z_2 + 2^Wz_1 + z_0 \mod 2^{4W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssssaaaaaaaa from longlong.h, FLINT 2.7.1, where (s3, s2, s1, s0) is returned.

impl XXXXAddYYYYToZZZZ for usize

fn xxxx_add_yyyy_to_zzzz( x_3: usize, x_2: usize, x_1: usize, x_0: usize, y_3: usize, y_2: usize, y_1: usize, y_0: usize, ) -> (usize, usize, usize, usize)

Adds two numbers, each composed of four usize values, returning the sum as a quadruple of usize values.

The more significant value always comes first. Addition is wrapping, and overflow is not indicated.

$$ f(x_3, x_2, x_1, x_0, y_2, y_2, y_1, y_0) = (z_3, z_2, z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_3, x_2, x_1, x_0, y_3, y_2, y_1, y_0, z_3, z_2, z_1, z_0 < 2^W$, and $$ (2^{3W}x_3 + 2^{2W}x_2 + 2^Wx_1 + x_0) + (2^{3W}y_3 + 2^{2W}y_2 + 2^Wy_1 + y_0) \equiv 2^{3W}z_3 + 2^{2W}z_2 + 2^Wz_1 + z_0 \mod 2^{4W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssssaaaaaaaa from longlong.h, FLINT 2.7.1, where (s3, s2, s1, s0) is returned.

Implementors