Integer in num_integer

Integer in num_integer - Rust

pub trait Integer: Sized + Num + PartialOrd + Ord + Eq {
Show 16 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);

    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,
    { ... }
}

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);

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);

Greatest Common Divisor (GCD).

Examples

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

Lowest Common Multiple (LCM).

Examples

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

Deprecated, use is_multiple_of instead.

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);

Returns true if the number is even.

Examples

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

Returns true if the number is odd.

Examples

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

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));

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);

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));

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));

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

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));

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);

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);

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impl Integer for i8

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Floored integer division

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Floored integer modulo

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Calculates div_floor and mod_floor simultaneously

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

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

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

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Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2

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Returns true if the number is not divisible by 2

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Simultaneous truncated integer division and modulus.

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Rounds up to nearest multiple of argument.

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Rounds down to nearest multiple of argument.

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impl Integer for i16

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Floored integer division

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Floored integer modulo

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Calculates div_floor and mod_floor simultaneously

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

source

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

source

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

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Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2

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Returns true if the number is not divisible by 2

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Simultaneous truncated integer division and modulus.

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Rounds up to nearest multiple of argument.

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Rounds down to nearest multiple of argument.

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impl Integer for i32

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Floored integer division

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Floored integer modulo

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Calculates div_floor and mod_floor simultaneously

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2

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Returns true if the number is not divisible by 2

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Simultaneous truncated integer division and modulus.

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Rounds up to nearest multiple of argument.

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Rounds down to nearest multiple of argument.

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impl Integer for i64

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Floored integer division

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Floored integer modulo

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Calculates div_floor and mod_floor simultaneously

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2

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Returns true if the number is not divisible by 2

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Simultaneous truncated integer division and modulus.

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Rounds up to nearest multiple of argument.

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Rounds down to nearest multiple of argument.

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impl Integer for isize

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Floored integer division

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Floored integer modulo

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Calculates div_floor and mod_floor simultaneously

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

source

Returns true if the number is divisible by 2

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Returns true if the number is not divisible by 2

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Simultaneous truncated integer division and modulus.

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Rounds up to nearest multiple of argument.

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Rounds down to nearest multiple of argument.

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impl Integer for i128

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Floored integer division

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Floored integer modulo

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Calculates div_floor and mod_floor simultaneously

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2

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Returns true if the number is not divisible by 2

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Simultaneous truncated integer division and modulus.

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Rounds up to nearest multiple of argument.

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Rounds down to nearest multiple of argument.

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impl Integer for u8

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

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

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2.

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Returns true if the number is not divisible by 2.

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Simultaneous truncated integer division and modulus.

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impl Integer for u16

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

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

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2.

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Returns true if the number is not divisible by 2.

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Simultaneous truncated integer division and modulus.

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impl Integer for u32

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

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

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

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Returns true if the number is a multiple of other.

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Returns true if the number is divisible by 2.

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Returns true if the number is not divisible by 2.

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Simultaneous truncated integer division and modulus.

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impl Integer for u64

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

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

source

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

source

Returns true if the number is a multiple of other.

source

Returns true if the number is divisible by 2.

source

Returns true if the number is not divisible by 2.

source

Simultaneous truncated integer division and modulus.

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impl Integer for usize

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

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

source

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

source

Returns true if the number is a multiple of other.

source

Returns true if the number is divisible by 2.

source

Returns true if the number is not divisible by 2.

source

Simultaneous truncated integer division and modulus.

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impl Integer for u128

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

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

source

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

source

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

source

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

source

Deprecated, use is_multiple_of instead.

source

Returns true if the number is a multiple of other.

source

Returns true if the number is divisible by 2.

source

Returns true if the number is not divisible by 2.

source

Simultaneous truncated integer division and modulus.

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