Trait malachite_base::num::arithmetic::traits::XXAddYYToZZ

pub trait XXAddYYToZZ: Sized {
    // Required method
    fn xx_add_yy_to_zz(
        x_1: Self,
        x_0: Self,
        y_1: Self,
        y_0: Self,
    ) -> (Self, Self);
}

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

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

Required Methods

fn xx_add_yy_to_zz(x_1: Self, x_0: Self, y_1: Self, y_0: Self) -> (Self, Self)

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl XXAddYYToZZ for u8

fn xx_add_yy_to_zz(x_1: u8, x_0: u8, y_1: u8, y_0: u8) -> (u8, u8)

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

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

$$ f(x_1, x_0, y_1, y_0) = (z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_1, x_0, y_1, y_0, z_1, z_0 < 2^W$, and $$ (2^Wx_1 + x_0) + (2^Wy_1 + y_0) \equiv 2^Wz_1 + z_0 \mod 2^{2W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssaaaa from longlong.h, GMP 6.2.1, where (sh, sl) is returned.

impl XXAddYYToZZ for u16

fn xx_add_yy_to_zz(x_1: u16, x_0: u16, y_1: u16, y_0: u16) -> (u16, u16)

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

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

$$ f(x_1, x_0, y_1, y_0) = (z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_1, x_0, y_1, y_0, z_1, z_0 < 2^W$, and $$ (2^Wx_1 + x_0) + (2^Wy_1 + y_0) \equiv 2^Wz_1 + z_0 \mod 2^{2W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssaaaa from longlong.h, GMP 6.2.1, where (sh, sl) is returned.

impl XXAddYYToZZ for u32

fn xx_add_yy_to_zz(x_1: u32, x_0: u32, y_1: u32, y_0: u32) -> (u32, u32)

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

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

$$ f(x_1, x_0, y_1, y_0) = (z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_1, x_0, y_1, y_0, z_1, z_0 < 2^W$, and $$ (2^Wx_1 + x_0) + (2^Wy_1 + y_0) \equiv 2^Wz_1 + z_0 \mod 2^{2W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssaaaa from longlong.h, GMP 6.2.1, where (sh, sl) is returned.

impl XXAddYYToZZ for u64

fn xx_add_yy_to_zz(x_1: u64, x_0: u64, y_1: u64, y_0: u64) -> (u64, u64)

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

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

$$ f(x_1, x_0, y_1, y_0) = (z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_1, x_0, y_1, y_0, z_1, z_0 < 2^W$, and $$ (2^Wx_1 + x_0) + (2^Wy_1 + y_0) \equiv 2^Wz_1 + z_0 \mod 2^{2W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssaaaa from longlong.h, GMP 6.2.1, where (sh, sl) is returned.

impl XXAddYYToZZ for u128

fn xx_add_yy_to_zz(x_1: u128, x_0: u128, y_1: u128, y_0: u128) -> (u128, u128)

Adds two numbers, each composed of two u128 values, returning the sum as a pair of u128 values.

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

$$ f(x_1, x_0, y_1, y_0) = (z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_1, x_0, y_1, y_0, z_1, z_0 < 2^W$, and $$ (2^Wx_1 + x_0) + (2^Wy_1 + y_0) \equiv 2^Wz_1 + z_0 \mod 2^{2W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssaaaa from longlong.h, GMP 6.2.1, where (sh, sl) is returned.

impl XXAddYYToZZ for usize

fn xx_add_yy_to_zz( x_1: usize, x_0: usize, y_1: usize, y_0: usize, ) -> (usize, usize)

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

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

$$ f(x_1, x_0, y_1, y_0) = (z_1, z_0), $$ where $W$ is Self::WIDTH,

$x_1, x_0, y_1, y_0, z_1, z_0 < 2^W$, and $$ (2^Wx_1 + x_0) + (2^Wy_1 + y_0) \equiv 2^Wz_1 + z_0 \mod 2^{2W}. $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_ssaaaa from longlong.h, GMP 6.2.1, where (sh, sl) is returned.

Implementors