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 divides(&self, other: &Self) -> bool;
    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 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 { ... }
}

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

Deprecated, use is_multiple_of instead.

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 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);

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: &i8) -> i8

Floored integer division

fn mod_floor(&self, other: &i8) -> i8

Floored integer modulo

fn div_mod_floor(&self, other: &i8) -> (i8, i8)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &i8) -> i8

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

fn lcm(&self, other: &i8) -> i8

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

fn gcd_lcm(&self, other: &i8) -> (i8, i8)

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

fn divides(&self, other: &i8) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &i8) -> 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: &i8) -> (i8, i8)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &i8) -> i8

fn extended_gcd_lcm(&self, other: &i8) -> (ExtendedGcd<i8>, i8)

impl Integer for i16

fn div_floor(&self, other: &i16) -> i16

Floored integer division

fn mod_floor(&self, other: &i16) -> i16

Floored integer modulo

fn div_mod_floor(&self, other: &i16) -> (i16, i16)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &i16) -> i16

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

fn lcm(&self, other: &i16) -> i16

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

fn gcd_lcm(&self, other: &i16) -> (i16, i16)

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

fn divides(&self, other: &i16) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &i16) -> 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: &i16) -> (i16, i16)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &i16) -> i16

fn extended_gcd_lcm(&self, other: &i16) -> (ExtendedGcd<i16>, i16)

impl Integer for i32

fn div_floor(&self, other: &i32) -> i32

Floored integer division

fn mod_floor(&self, other: &i32) -> i32

Floored integer modulo

fn div_mod_floor(&self, other: &i32) -> (i32, i32)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &i32) -> i32

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

fn lcm(&self, other: &i32) -> i32

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

fn gcd_lcm(&self, other: &i32) -> (i32, i32)

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

fn divides(&self, other: &i32) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &i32) -> 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: &i32) -> (i32, i32)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &i32) -> i32

fn extended_gcd_lcm(&self, other: &i32) -> (ExtendedGcd<i32>, i32)

impl Integer for i64

fn div_floor(&self, other: &i64) -> i64

Floored integer division

fn mod_floor(&self, other: &i64) -> i64

Floored integer modulo

fn div_mod_floor(&self, other: &i64) -> (i64, i64)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &i64) -> i64

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

fn lcm(&self, other: &i64) -> i64

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

fn gcd_lcm(&self, other: &i64) -> (i64, i64)

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

fn divides(&self, other: &i64) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &i64) -> 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: &i64) -> (i64, i64)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &i64) -> i64

fn extended_gcd_lcm(&self, other: &i64) -> (ExtendedGcd<i64>, i64)

impl Integer for i128

fn div_floor(&self, other: &i128) -> i128

Floored integer division

fn mod_floor(&self, other: &i128) -> i128

Floored integer modulo

fn div_mod_floor(&self, other: &i128) -> (i128, i128)

Calculates div_floor and mod_floor simultaneously

fn gcd(&self, other: &i128) -> i128

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

fn lcm(&self, other: &i128) -> i128

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

fn gcd_lcm(&self, other: &i128) -> (i128, i128)

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

fn divides(&self, other: &i128) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &i128) -> 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: &i128) -> (i128, i128)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &i128) -> i128

fn extended_gcd_lcm(&self, other: &i128) -> (ExtendedGcd<i128>, i128)

impl Integer for isize

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

Floored integer division

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

Floored integer modulo

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

Calculates div_floor and mod_floor simultaneously

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

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

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

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

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

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

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

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &isize) -> 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: &isize) -> (isize, isize)

Simultaneous truncated integer division and modulus.

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

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

impl Integer for u8

fn div_floor(&self, other: &u8) -> u8

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

fn mod_floor(&self, other: &u8) -> u8

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

fn gcd(&self, other: &u8) -> u8

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

fn lcm(&self, other: &u8) -> u8

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

fn gcd_lcm(&self, other: &u8) -> (u8, u8)

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

fn divides(&self, other: &u8) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &u8) -> 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: &u8) -> (u8, u8)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &u8) -> u8

fn extended_gcd_lcm(&self, other: &u8) -> (ExtendedGcd<u8>, u8)

impl Integer for u16

fn div_floor(&self, other: &u16) -> u16

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

fn mod_floor(&self, other: &u16) -> u16

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

fn gcd(&self, other: &u16) -> u16

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

fn lcm(&self, other: &u16) -> u16

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

fn gcd_lcm(&self, other: &u16) -> (u16, u16)

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

fn divides(&self, other: &u16) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &u16) -> 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: &u16) -> (u16, u16)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &u16) -> u16

fn extended_gcd_lcm(&self, other: &u16) -> (ExtendedGcd<u16>, u16)

impl Integer for u32

fn div_floor(&self, other: &u32) -> u32

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

fn mod_floor(&self, other: &u32) -> u32

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

fn gcd(&self, other: &u32) -> u32

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

fn lcm(&self, other: &u32) -> u32

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

fn gcd_lcm(&self, other: &u32) -> (u32, u32)

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

fn divides(&self, other: &u32) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &u32) -> 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: &u32) -> (u32, u32)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &u32) -> u32

fn extended_gcd_lcm(&self, other: &u32) -> (ExtendedGcd<u32>, u32)

impl Integer for u64

fn div_floor(&self, other: &u64) -> u64

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

fn mod_floor(&self, other: &u64) -> u64

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

fn gcd(&self, other: &u64) -> u64

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

fn lcm(&self, other: &u64) -> u64

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

fn gcd_lcm(&self, other: &u64) -> (u64, u64)

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

fn divides(&self, other: &u64) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &u64) -> 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: &u64) -> (u64, u64)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &u64) -> u64

fn extended_gcd_lcm(&self, other: &u64) -> (ExtendedGcd<u64>, u64)

impl Integer for u128

fn div_floor(&self, other: &u128) -> u128

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

fn mod_floor(&self, other: &u128) -> u128

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

fn gcd(&self, other: &u128) -> u128

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

fn lcm(&self, other: &u128) -> u128

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

fn gcd_lcm(&self, other: &u128) -> (u128, u128)

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

fn divides(&self, other: &u128) -> bool

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &u128) -> 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: &u128) -> (u128, u128)

Simultaneous truncated integer division and modulus.

fn div_ceil(&self, other: &u128) -> u128

fn extended_gcd_lcm(&self, other: &u128) -> (ExtendedGcd<u128>, u128)

impl Integer for usize

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

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

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

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

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

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

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

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

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

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

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

Deprecated, use is_multiple_of instead.

fn is_multiple_of(&self, other: &usize) -> 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: &usize) -> (usize, usize)

Simultaneous truncated integer division and modulus.

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

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

Implementors

impl Integer for BigInt

impl Integer for BigUint