Trait XXXSubYYYToZZZ

pub trait XXXSubYYYToZZZ: Sized {
    // Required method
    fn xxx_sub_yyy_to_zzz(
        x_2: Self,
        x_1: Self,
        x_0: Self,
        y_2: Self,
        y_1: Self,
        y_0: Self,
    ) -> (Self, Self, Self);
}

Subtracts two numbers, each composed of three Self values, returing the difference as a triple of Self values.

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

Required Methods

fn xxx_sub_yyy_to_zzz( x_2: Self, x_1: Self, x_0: Self, y_2: Self, y_1: Self, y_0: 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 XXXSubYYYToZZZ for u8

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

Subtracts two numbers, each composed of three Self values, returning the difference as a triple of Self values.

The more significant value always comes first. Subtraction 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 sub_dddmmmsss from longlong.h, FLINT 2.7.1, where (dh, dm, dl) is returned.

impl XXXSubYYYToZZZ for u16

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

Subtracts two numbers, each composed of three Self values, returning the difference as a triple of Self values.

The more significant value always comes first. Subtraction 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 sub_dddmmmsss from longlong.h, FLINT 2.7.1, where (dh, dm, dl) is returned.

impl XXXSubYYYToZZZ for u32

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

Subtracts two numbers, each composed of three Self values, returning the difference as a triple of Self values.

The more significant value always comes first. Subtraction 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 sub_dddmmmsss from longlong.h, FLINT 2.7.1, where (dh, dm, dl) is returned.

impl XXXSubYYYToZZZ for u64

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

Subtracts two numbers, each composed of three Self values, returning the difference as a triple of Self values.

The more significant value always comes first. Subtraction 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 sub_dddmmmsss from longlong.h, FLINT 2.7.1, where (dh, dm, dl) is returned.

impl XXXSubYYYToZZZ for u128

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

Subtracts two numbers, each composed of three Self values, returning the difference as a triple of Self values.

The more significant value always comes first. Subtraction 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 sub_dddmmmsss from longlong.h, FLINT 2.7.1, where (dh, dm, dl) is returned.

impl XXXSubYYYToZZZ for usize

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

Subtracts two numbers, each composed of three usize values, returning the difference as a triple of usize values.

The more significant value always comes first. Subtraction 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 sub_dddmmmsss from longlong.h, FLINT 2.7.1, where (dh, dm, dl) is returned.

Implementors