Trait num::integer::Integer

pub trait Integer: Sized + Num + PartialOrd<Self> + 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) -> Selfwhere 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) -> Selfwhere 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);

Implementations on Foreign Types

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 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 non-negative.

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 next_multiple_of(&self, other: &i128) -> i128

Rounds up to nearest multiple of argument.

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

Rounds down to nearest multiple of argument.

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 non-negative.

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 next_multiple_of(&self, other: &isize) -> isize

Rounds up to nearest multiple of argument.

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

Rounds down to nearest multiple of argument.

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

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

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 non-negative.

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 next_multiple_of(&self, other: &i64) -> i64

Rounds up to nearest multiple of argument.

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

Rounds down to nearest multiple of argument.

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

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

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 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 non-negative.

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 next_multiple_of(&self, other: &i8) -> i8

Rounds up to nearest multiple of argument.

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

Rounds down to nearest multiple of argument.

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

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

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 non-negative.

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 next_multiple_of(&self, other: &i32) -> i32

Rounds up to nearest multiple of argument.

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

Rounds down to nearest multiple of argument.

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

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

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 non-negative.

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 next_multiple_of(&self, other: &i16) -> i16

Rounds up to nearest multiple of argument.

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

Rounds down to nearest multiple of argument.

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

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

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 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 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)

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)

Implementors

impl Integer for BigInt

impl Integer for BigUint