Trait Integer

pub trait Integer:
    Sized
    + Num
    + PartialOrd
    + Ord
    + Eq {
    // Required methods
    fn div_floor(&self, other: &Self) -> Self;
    fn mod_floor(&self, other: &Self) -> Self;
    fn gcd(&self, other: &Self) -> Self;
    fn lcm(&self, other: &Self) -> Self;
    fn is_multiple_of(&self, other: &Self) -> bool;
    fn is_even(&self) -> bool;
    fn is_odd(&self) -> bool;
    fn div_rem(&self, other: &Self) -> (Self, Self);

    // Provided methods
    fn div_ceil(&self, other: &Self) -> Self { ... }
    fn gcd_lcm(&self, other: &Self) -> (Self, Self) { ... }
    fn extended_gcd(&self, other: &Self) -> ExtendedGcd<Self>
       where Self: Clone { ... }
    fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)
       where Self: Clone + Signed { ... }
    fn divides(&self, other: &Self) -> bool { ... }
    fn div_mod_floor(&self, other: &Self) -> (Self, Self) { ... }
    fn next_multiple_of(&self, other: &Self) -> Self
       where Self: Clone { ... }
    fn prev_multiple_of(&self, other: &Self) -> Self
       where Self: Clone { ... }
    fn dec(&mut self)
       where Self: Clone { ... }
    fn inc(&mut self)
       where Self: Clone { ... }
}

Required Methods

fn div_floor(&self, other: &Self) -> Self

Floored integer division.

Examples

assert!(( 8).div_floor(& 3) ==  2);
assert!(( 8).div_floor(&-3) == -3);
assert!((-8).div_floor(& 3) == -3);
assert!((-8).div_floor(&-3) ==  2);

assert!(( 1).div_floor(& 2) ==  0);
assert!(( 1).div_floor(&-2) == -1);
assert!((-1).div_floor(& 2) == -1);
assert!((-1).div_floor(&-2) ==  0);

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo, satisfying:

assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)

Examples

assert!(( 8).mod_floor(& 3) ==  2);
assert!(( 8).mod_floor(&-3) == -1);
assert!((-8).mod_floor(& 3) ==  1);
assert!((-8).mod_floor(&-3) == -2);

assert!(( 1).mod_floor(& 2) ==  1);
assert!(( 1).mod_floor(&-2) == -1);
assert!((-1).mod_floor(& 2) ==  1);
assert!((-1).mod_floor(&-2) == -1);

fn gcd(&self, other: &Self) -> Self

Greatest Common Divisor (GCD).

Examples

assert_eq!(6.gcd(&8), 2);
assert_eq!(7.gcd(&3), 1);

fn lcm(&self, other: &Self) -> Self

Lowest Common Multiple (LCM).

Examples

assert_eq!(7.lcm(&3), 21);
assert_eq!(2.lcm(&4), 4);
assert_eq!(0.lcm(&0), 0);

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if self is a multiple of other.

Examples

assert_eq!(9.is_multiple_of(&3), true);
assert_eq!(3.is_multiple_of(&9), false);

fn is_even(&self) -> bool

Returns true if the number is even.

Examples

assert_eq!(3.is_even(), false);
assert_eq!(4.is_even(), true);

fn is_odd(&self) -> bool

Returns true if the number is odd.

Examples

assert_eq!(3.is_odd(), true);
assert_eq!(4.is_odd(), false);

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus. Returns (quotient, remainder).

Examples

assert_eq!(( 8).div_rem( &3), ( 2,  2));
assert_eq!(( 8).div_rem(&-3), (-2,  2));
assert_eq!((-8).div_rem( &3), (-2, -2));
assert_eq!((-8).div_rem(&-3), ( 2, -2));

assert_eq!(( 1).div_rem( &2), ( 0,  1));
assert_eq!(( 1).div_rem(&-2), ( 0,  1));
assert_eq!((-1).div_rem( &2), ( 0, -1));
assert_eq!((-1).div_rem(&-2), ( 0, -1));

Provided Methods

fn div_ceil(&self, other: &Self) -> Self

Ceiled integer division.

Examples

assert_eq!(( 8).div_ceil( &3),  3);
assert_eq!(( 8).div_ceil(&-3), -2);
assert_eq!((-8).div_ceil( &3), -2);
assert_eq!((-8).div_ceil(&-3),  3);

assert_eq!(( 1).div_ceil( &2), 1);
assert_eq!(( 1).div_ceil(&-2), 0);
assert_eq!((-1).div_ceil( &2), 0);
assert_eq!((-1).div_ceil(&-2), 1);

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) together.

Potentially more efficient than calling gcd and lcm individually for identical inputs.

Examples

assert_eq!(10.gcd_lcm(&4), (2, 20));
assert_eq!(8.gcd_lcm(&9), (1, 72));

fn extended_gcd(&self, other: &Self) -> ExtendedGcd<Self>

where Self: Clone,

Greatest common divisor and Bézout coefficients.

Examples

fn check<A: Copy + Integer + NumAssign>(a: A, b: A) -> bool {
    let ExtendedGcd { gcd, x, y, .. } = a.extended_gcd(&b);
    gcd == x * a + y * b
}
assert!(check(10isize, 4isize));
assert!(check(8isize,  9isize));

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

where Self: Clone + Signed,

Greatest common divisor, least common multiple, and Bézout coefficients.

fn divides(&self, other: &Self) -> bool

👎Deprecated: Please use is_multiple_of instead

Deprecated, use is_multiple_of instead.

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Simultaneous floored integer division and modulus. Returns (quotient, remainder).

Examples

assert_eq!(( 8).div_mod_floor( &3), ( 2,  2));
assert_eq!(( 8).div_mod_floor(&-3), (-3, -1));
assert_eq!((-8).div_mod_floor( &3), (-3,  1));
assert_eq!((-8).div_mod_floor(&-3), ( 2, -2));

assert_eq!(( 1).div_mod_floor( &2), ( 0,  1));
assert_eq!(( 1).div_mod_floor(&-2), (-1, -1));
assert_eq!((-1).div_mod_floor( &2), (-1,  1));
assert_eq!((-1).div_mod_floor(&-2), ( 0, -1));

fn next_multiple_of(&self, other: &Self) -> Self

where Self: Clone,

Rounds up to nearest multiple of argument.

Notes

For signed types, a.next_multiple_of(b) = a.prev_multiple_of(b.neg()).

Examples

assert_eq!(( 16).next_multiple_of(& 8),  16);
assert_eq!(( 23).next_multiple_of(& 8),  24);
assert_eq!(( 16).next_multiple_of(&-8),  16);
assert_eq!(( 23).next_multiple_of(&-8),  16);
assert_eq!((-16).next_multiple_of(& 8), -16);
assert_eq!((-23).next_multiple_of(& 8), -16);
assert_eq!((-16).next_multiple_of(&-8), -16);
assert_eq!((-23).next_multiple_of(&-8), -24);

fn prev_multiple_of(&self, other: &Self) -> Self

where Self: Clone,

Rounds down to nearest multiple of argument.

Notes

For signed types, a.prev_multiple_of(b) = a.next_multiple_of(b.neg()).

Examples

assert_eq!(( 16).prev_multiple_of(& 8),  16);
assert_eq!(( 23).prev_multiple_of(& 8),  16);
assert_eq!(( 16).prev_multiple_of(&-8),  16);
assert_eq!(( 23).prev_multiple_of(&-8),  24);
assert_eq!((-16).prev_multiple_of(& 8), -16);
assert_eq!((-23).prev_multiple_of(& 8), -24);
assert_eq!((-16).prev_multiple_of(&-8), -16);
assert_eq!((-23).prev_multiple_of(&-8), -16);

fn dec(&mut self)

where Self: Clone,

Decrements self by one.

Examples

let mut x: i32 = 43;
x.dec();
assert_eq!(x, 42);

fn inc(&mut self)

where Self: Clone,

Increments self by one.

Examples

let mut x: i32 = 41;
x.inc();
assert_eq!(x, 42);

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 Integer for i8

fn div_floor(&self, other: &Self) -> Self

Floored integer division

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other. The result is always non-negative.

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn next_multiple_of(&self, other: &Self) -> Self

Rounds up to nearest multiple of argument.

fn prev_multiple_of(&self, other: &Self) -> Self

Rounds down to nearest multiple of argument.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for i16

fn div_floor(&self, other: &Self) -> Self

Floored integer division

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other. The result is always non-negative.

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn next_multiple_of(&self, other: &Self) -> Self

Rounds up to nearest multiple of argument.

fn prev_multiple_of(&self, other: &Self) -> Self

Rounds down to nearest multiple of argument.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for i32

fn div_floor(&self, other: &Self) -> Self

Floored integer division

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other. The result is always non-negative.

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn next_multiple_of(&self, other: &Self) -> Self

Rounds up to nearest multiple of argument.

fn prev_multiple_of(&self, other: &Self) -> Self

Rounds down to nearest multiple of argument.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for i64

fn div_floor(&self, other: &Self) -> Self

Floored integer division

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other. The result is always non-negative.

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn next_multiple_of(&self, other: &Self) -> Self

Rounds up to nearest multiple of argument.

fn prev_multiple_of(&self, other: &Self) -> Self

Rounds down to nearest multiple of argument.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for i128

fn div_floor(&self, other: &Self) -> Self

Floored integer division

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other. The result is always non-negative.

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn next_multiple_of(&self, other: &Self) -> Self

Rounds up to nearest multiple of argument.

fn prev_multiple_of(&self, other: &Self) -> Self

Rounds down to nearest multiple of argument.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for isize

fn div_floor(&self, other: &Self) -> Self

Floored integer division

fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other. The result is always non-negative.

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn next_multiple_of(&self, other: &Self) -> Self

Rounds up to nearest multiple of argument.

fn prev_multiple_of(&self, other: &Self) -> Self

Rounds down to nearest multiple of argument.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for u8

fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as div (/).

fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as rem (%).

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2.

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2.

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for u16

fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as div (/).

fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as rem (%).

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2.

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2.

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for u32

fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as div (/).

fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as rem (%).

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2.

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2.

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for u64

fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as div (/).

fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as rem (%).

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2.

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2.

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for u128

fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as div (/).

fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as rem (%).

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2.

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2.

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

impl Integer for usize

fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as div (/).

fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as rem (%).

fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and other

fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and other.

fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and other.

fn is_multiple_of(&self, other: &Self) -> bool

Returns true if the number is a multiple of other.

fn is_even(&self) -> bool

Returns true if the number is divisible by 2.

fn is_odd(&self) -> bool

Returns true if the number is not divisible by 2.

fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &Self) -> Self

fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)

Implementors