Trait 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)

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so 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