Trait malachite_base::num::arithmetic::traits::XXXAddYYYToZZZ

pub trait XXXAddYYYToZZZ: Sized {
    fn xxx_add_yyy_to_zzz(
        x_2: Self,
        x_1: Self,
        x_0: Self,
        y_2: Self,
        y_1: Self,
        y_0: Self
    ) -> (Self, Self, Self);
}

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

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

Required Methods

fn xxx_add_yyy_to_zzz(
    x_2: Self,
    x_1: Self,
    x_0: Self,
    y_2: Self,
    y_1: Self,
    y_0: Self
) -> (Self, Self, Self)

Implementations on Foreign Types

impl XXXAddYYYToZZZ for u8

fn xxx_add_yyy_to_zzz(
    x_2: u8,
    x_1: u8,
    x_0: u8,
    y_2: u8,
    y_1: u8,
    y_0: u8
) -> (u8, u8, u8)

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

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

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

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

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_sssaaaaaa from longlong.h, FLINT 2.7.1, where (sh, sm, sl) is returned.

impl XXXAddYYYToZZZ for u16

fn xxx_add_yyy_to_zzz(
    x_2: u16,
    x_1: u16,
    x_0: u16,
    y_2: u16,
    y_1: u16,
    y_0: u16
) -> (u16, u16, u16)

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

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

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

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

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_sssaaaaaa from longlong.h, FLINT 2.7.1, where (sh, sm, sl) is returned.

impl XXXAddYYYToZZZ for u32

fn xxx_add_yyy_to_zzz(
    x_2: u32,
    x_1: u32,
    x_0: u32,
    y_2: u32,
    y_1: u32,
    y_0: u32
) -> (u32, u32, u32)

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

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

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

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

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_sssaaaaaa from longlong.h, FLINT 2.7.1, where (sh, sm, sl) is returned.

impl XXXAddYYYToZZZ for u64

fn xxx_add_yyy_to_zzz(
    x_2: u64,
    x_1: u64,
    x_0: u64,
    y_2: u64,
    y_1: u64,
    y_0: u64
) -> (u64, u64, u64)

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

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

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

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

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_sssaaaaaa from longlong.h, FLINT 2.7.1, where (sh, sm, sl) is returned.

impl XXXAddYYYToZZZ for u128

fn xxx_add_yyy_to_zzz(
    x_2: u128,
    x_1: u128,
    x_0: u128,
    y_2: u128,
    y_1: u128,
    y_0: u128
) -> (u128, u128, u128)

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

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

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

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

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_sssaaaaaa from longlong.h, FLINT 2.7.1, where (sh, sm, sl) is returned.

impl XXXAddYYYToZZZ for usize

fn xxx_add_yyy_to_zzz(
    x_2: usize,
    x_1: usize,
    x_0: usize,
    y_2: usize,
    y_1: usize,
    y_0: usize
) -> (usize, usize, usize)

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

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

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

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

Worst-case complexity

Constant time and additional memory.

Examples

See here.

This is equivalent to add_sssaaaaaa from longlong.h, FLINT 2.7.1, where (sh, sm, sl) is returned.

Implementors