Struct gmp_mpfr::Rational

pub struct Rational { /* fields omitted */ }

An arbitrary-precision rational number.

A rational number is made up of a numerator Integer and denominator Integer. After rational number functions, the number is always in canonical form, that is, the denominator is always greater than zero, and there are no common factors. Zero is stored as 0/1.

Examples

use gmp_mpfr::{Integer, Rational};

let r = Rational::from((-12, 15));
let (num, den) = r.into_numer_denom();
assert!(num == -4);
assert!(den == 5);
let one = Rational::from((num, Integer::from(-4)));
assert!(one == 1);

Methods

impl Rational

fn new() -> Rational

Constructs a new arbitrary-precision rational number with value 0.

fn to_f64(&self) -> f64

Converts self to an f64, rounding towards zero.

fn to_f32(&self) -> f32

Converts self to an f32, rounding towards zero.

fn numer(&self) -> &Integer

Borrows the numerator.

fn denom(&self) -> &Integer

Borrows the denominator.

fn as_numer_denom(&self) -> (&Integer, &Integer)

Borrows the numerator and denominator.

fn as_mut_numer_denom(&mut self) -> MutNumerDenom

Borrows the numerator and denominator mutably. The number is canonicalized when the borrow ends. The denominator must not be zero when the borrow ends.

Examples

use gmp_mpfr::Rational;

let mut r = Rational::from((3, 5));
{
    let mut num_den = r.as_mut_numer_denom();
    // change r from 3/5 to 4/8, which is equal to 1/2
    *num_den.0 += 1;
    *num_den.1 += 3;
    // borrow ends here
}
let num_den = r.as_numer_denom();
assert!(*num_den.0 == 1 && *num_den.1 == 2);

Panics

Panics if the denominator is zero when the borrow ends.

fn into_numer_denom(self) -> (Integer, Integer)

Converts self into numerator and denominator integers, consuming self.

fn abs(&mut self) -> &mut Rational

Computes the absolute value of self

fn recip(&mut self) -> &mut Rational

Computes the reciprocal of self.

fn sign(&self) -> Ordering

Returns Less if self is less than zero, Greater if self is greater than zero, or Equal if self is equal to zero.

fn to_string_radix(&self, radix: i32) -> String

Returns a string representation of self for the specified radix. If radix is > 36, 'a' to 'z' represent digits 10 to 36, and 'A' to 'Z' represent digits 37 to 62. The exponent is encoded in decimal.

Panics

Panics if radix is less than 2 or greater than 62.

Trait Implementations

impl<'a> From<&'a Float> for Rational

fn from(val: &Float) -> Rational

Constructs a Rational from a Float, preserving all the precision of the value. The value must not be a NaN or infinite.

Examples

use gmp_mpfr::{Float, FromPrec, Rational};

let large_f = Float::from_prec(6.5, 16);
let large_r = Rational::from(&large_f); // borrow
let small_f = Float::from_prec(-0.125, 16);
let small_r = Rational::from(small_f); // move

assert!(*large_r.numer() == 13);
assert!(*large_r.denom() == 2);
assert!(*small_r.numer() == -1);
assert!(*small_r.denom() == 8);

Panics

Panics if val is a NaN or infinite.

impl From<Float> for Rational

fn from(val: Float) -> Rational

Constructs a Rational from a Float, preserving all the precision of the value. The value must not be a NaN or infinite. See the borrowing implementor.

Panics

Panics if val is a NaN or infinite.

impl<'a> Assign<&'a Float> for Rational

fn assign(&mut self, val: &'a Float)

Assigns from a Float, preserving all the precision of the value. The value must not be a NaN or infinite.

Examples

use gmp_mpfr::{Assign, Float, FromPrec, Rational};

let large_f = Float::from_prec(6.5, 16);
let mut large_r = Rational::new();
large_r.assign(&large_f); // borrow
let small_f = Float::from_prec(-0.125, 16);
let mut small_r = Rational::new();
small_r.assign(small_f); // move

assert!(*large_r.numer() == 13);
assert!(*large_r.denom() == 2);
assert!(*small_r.numer() == -1);
assert!(*small_r.denom() == 8);

Panics

Panics if val is a NaN or infinite.

impl<'a> Assign<Float> for Rational

fn assign(&mut self, val: Float)

Assigns from a Float, preserving all the precision of the value. The value must not be a NaN or infinite. See the borrowing implementor.

Panics

Panics if val is a NaN or infinite.

impl Add<Float> for Rational

type Output = Float

The resulting type after applying the + operator

fn add(self, op: Float) -> Float

The method for the + operator

impl<'a> Add<&'a Float> for Rational

type Output = Float

The resulting type after applying the + operator

fn add(self, op: &'a Float) -> Float

The method for the + operator

impl AddRound<Float> for Rational

type Output = Float

The resulting type after the addition.

fn add_round(self, op: Float, round: Round) -> (Float, Ordering)

Performs the addition.

impl<'a> AddRound<&'a Float> for Rational

type Output = Float

The resulting type after the addition.

fn add_round(self, op: &'a Float, round: Round) -> (Float, Ordering)

Performs the addition.

impl Mul<Float> for Rational

type Output = Float

The resulting type after applying the * operator

fn mul(self, op: Float) -> Float

The method for the * operator

impl<'a> Mul<&'a Float> for Rational

type Output = Float

The resulting type after applying the * operator

fn mul(self, op: &'a Float) -> Float

The method for the * operator

impl MulRound<Float> for Rational

type Output = Float

The resulting type after the multiplication.

fn mul_round(self, op: Float, round: Round) -> (Float, Ordering)

Performs the multiplication.

impl<'a> MulRound<&'a Float> for Rational

type Output = Float

The resulting type after the multiplication.

fn mul_round(self, op: &'a Float, round: Round) -> (Float, Ordering)

Performs the multiplication.

impl PartialEq<Float> for Rational

fn eq(&self, other: &Float) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<Float> for Rational

fn partial_cmp(&self, other: &Float) -> Option<Ordering>

Returns the ordering of self and other, or None if other is a NaN.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl Drop for Rational

fn drop(&mut self)

A method called when the value goes out of scope.

impl Default for Rational

fn default() -> Rational

Returns the "default value" for a type.

impl Clone for Rational

fn clone(&self) -> Rational

Returns a copy of the value.

fn clone_from(&mut self, source: &Rational)

Performs copy-assignment from source.

impl<'a> From<&'a Rational> for Rational

fn from(t: &'a Rational) -> Rational

Constructs a Rational from another Rational.

impl From<Integer> for Rational

fn from(val: Integer) -> Rational

Constructs a Rational from an Integer. This constructor allocates one Integer for the denominator and reuses val for the numerator.

impl<'a> From<&'a Integer> for Rational

fn from(t: &'a Integer) -> Rational

Constructs a Rational from an Integer.

impl From<(Integer, Integer)> for Rational

fn from((num, den): (Integer, Integer)) -> Rational

Constructs a Rational from a numerator Integer and denominator Integer. This constructor does not allocate, as it reuses the Integer components.

Panics

Panics if the denominator is zero.

impl<'a> From<(&'a Integer, &'a Integer)> for Rational

fn from(t: (&'a Integer, &'a Integer)) -> Rational

Constructs a Rational from a numerator Integer and denominator Integer.

impl From<u32> for Rational

fn from(t: u32) -> Rational

Constructs a Rational from a u32.

impl From<i32> for Rational

fn from(t: i32) -> Rational

Constructs a Rational from an i32.

impl From<f64> for Rational

fn from(t: f64) -> Rational

Constructs a Rational from an f64, losing no precision.

Panics

Panics if t is a NaN or infinite.

impl From<f32> for Rational

fn from(t: f32) -> Rational

Constructs a Rational from an f32, losing no precision.

Panics

Panics if t is a NaN or infinite.

impl From<(u32, u32)> for Rational

fn from(t: (u32, u32)) -> Rational

Constructs a Rational from a numerator u32 and denominator u32.

impl From<(i32, u32)> for Rational

fn from(t: (i32, u32)) -> Rational

Constructs a Rational from a numerator i32 and denominator u32.

impl From<(i32, i32)> for Rational

fn from(t: (i32, i32)) -> Rational

Constructs a Rational from a numerator i32 and denominator i32.

impl<'a> Assign<&'a Rational> for Rational

fn assign(&mut self, other: &'a Rational)

Assigns from another Rational.

impl Assign<Rational> for Rational

fn assign(&mut self, other: Rational)

Assigns from another Rational.

impl<'a> Assign<&'a Integer> for Rational

fn assign(&mut self, val: &'a Integer)

Assigns from an Integer.

impl Assign<Integer> for Rational

fn assign(&mut self, other: Integer)

Assigns from an Integer.

impl Assign<(Integer, Integer)> for Rational

fn assign(&mut self, (num, den): (Integer, Integer))

Assigns from a numerator Integer and a denominator Integer.

Panics

Panics if the denominator is zero.

impl<'a> Assign<(&'a Integer, &'a Integer)> for Rational

fn assign(&mut self, (num, den): (&Integer, &Integer))

Assigns from a numerator Integer and a denominator Integer.

Panics

Panics if the denominator is zero.

impl Assign<u32> for Rational

fn assign(&mut self, val: u32)

Assigns from a u32.

impl Assign<i32> for Rational

fn assign(&mut self, val: i32)

Assigns from an i32.

impl Assign<f64> for Rational

fn assign(&mut self, f: f64)

Assigns from an f64, losing no precision.

Panics

Panics if f is a NaN or infinite.

impl Assign<f32> for Rational

fn assign(&mut self, f: f32)

Assigns from an f32, losing no precision.

Panics

Panics if f is a NaN or infinite.

impl Assign<(u32, u32)> for Rational

fn assign(&mut self, (num, den): (u32, u32))

Assigns from a numerator u32 and a denominator u32.

Panics

Panics if the denominator is zero.

impl Assign<(i32, u32)> for Rational

fn assign(&mut self, (num, den): (i32, u32))

Assigns from a numerator i32 and a denominator u32.

Panics

Panics if the denominator is zero.

impl Assign<(i32, i32)> for Rational

fn assign(&mut self, (num, den): (i32, i32))

Assigns from a numerator i32 and a denominator i32.

Panics

Panics if the denominator is zero.

impl<'a> Add<&'a Rational> for Rational

type Output = Rational

The resulting type after applying the + operator

fn add(self, op: &'a Rational) -> Rational

The method for the + operator

impl Add<Rational> for Rational

type Output = Rational

The resulting type after applying the + operator

fn add(self, op: Rational) -> Rational

The method for the + operator

impl<'a> AddAssign<&'a Rational> for Rational

fn add_assign(&mut self, op: &'a Rational)

The method for the += operator

impl AddAssign<Rational> for Rational

fn add_assign(&mut self, op: Rational)

The method for the += operator

impl<'a> Sub<&'a Rational> for Rational

type Output = Rational

The resulting type after applying the - operator

fn sub(self, op: &'a Rational) -> Rational

The method for the - operator

impl Sub<Rational> for Rational

type Output = Rational

The resulting type after applying the - operator

fn sub(self, op: Rational) -> Rational

The method for the - operator

impl<'a> SubAssign<&'a Rational> for Rational

fn sub_assign(&mut self, op: &'a Rational)

The method for the -= operator

impl SubAssign<Rational> for Rational

fn sub_assign(&mut self, op: Rational)

The method for the -= operator

impl<'a> Mul<&'a Rational> for Rational

type Output = Rational

The resulting type after applying the * operator

fn mul(self, op: &'a Rational) -> Rational

The method for the * operator

impl Mul<Rational> for Rational

type Output = Rational

The resulting type after applying the * operator

fn mul(self, op: Rational) -> Rational

The method for the * operator

impl<'a> MulAssign<&'a Rational> for Rational

fn mul_assign(&mut self, op: &'a Rational)

The method for the *= operator

impl MulAssign<Rational> for Rational

fn mul_assign(&mut self, op: Rational)

The method for the *= operator

impl<'a> Div<&'a Rational> for Rational

type Output = Rational

The resulting type after applying the / operator

fn div(self, op: &'a Rational) -> Rational

The method for the / operator

impl Div<Rational> for Rational

type Output = Rational

The resulting type after applying the / operator

fn div(self, op: Rational) -> Rational

The method for the / operator

impl<'a> DivAssign<&'a Rational> for Rational

fn div_assign(&mut self, op: &'a Rational)

The method for the /= operator

impl DivAssign<Rational> for Rational

fn div_assign(&mut self, op: Rational)

The method for the /= operator

impl SubFromAssign for Rational

fn sub_from_assign(&mut self, lhs: Rational)

Peforms the subtraction.

impl<'a> SubFromAssign<&'a Rational> for Rational

fn sub_from_assign(&mut self, lhs: &Rational)

Peforms the subtraction.

impl DivFromAssign for Rational

fn div_from_assign(&mut self, lhs: Rational)

Peforms the division.

impl<'a> DivFromAssign<&'a Rational> for Rational

fn div_from_assign(&mut self, lhs: &Rational)

Peforms the division.

impl Shl<u32> for Rational

type Output = Rational

The resulting type after applying the << operator

fn shl(self, op: u32) -> Rational

Multiplies self by 2 to the power of op.

impl ShlAssign<u32> for Rational

fn shl_assign(&mut self, op: u32)

Multiplies self by 2 to the power of op.

impl Shr<u32> for Rational

type Output = Rational

The resulting type after applying the >> operator

fn shr(self, op: u32) -> Rational

Divides self by 2 to the power of op.

impl ShrAssign<u32> for Rational

fn shr_assign(&mut self, op: u32)

Divides self by 2 to the power of op.

impl Pow<i32> for Rational

type Output = Rational

The resulting type after the power operation.

fn pow(self, op: i32) -> Rational

Performs the power operation.

impl PowAssign<i32> for Rational

fn pow_assign(&mut self, op: i32)

Peforms the power operation.

impl Neg for Rational

type Output = Rational

The resulting type after applying the - operator

fn neg(self) -> Rational

The method for the unary - operator

impl NegAssign for Rational

fn neg_assign(&mut self)

Peforms the negation.

impl Eq for Rational

impl Ord for Rational

fn cmp(&self, other: &Rational) -> Ordering

This method returns an Ordering between self and other.

impl PartialEq for Rational

fn eq(&self, other: &Rational) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd for Rational

fn partial_cmp(&self, other: &Rational) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialEq<Integer> for Rational

fn eq(&self, other: &Integer) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<Integer> for Rational

fn partial_cmp(&self, other: &Integer) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialEq<u32> for Rational

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<u32> for Rational

fn partial_cmp(&self, other: &u32) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialEq<i32> for Rational

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<i32> for Rational

fn partial_cmp(&self, other: &i32) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialEq<(u32, u32)> for Rational

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<(u32, u32)> for Rational

fn partial_cmp(&self, other: &(u32, u32)) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialEq<(i32, u32)> for Rational

fn eq(&self, other: &(i32, u32)) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<(i32, u32)> for Rational

fn partial_cmp(&self, other: &(i32, u32)) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialEq<(i32, i32)> for Rational

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<(i32, i32)> for Rational

fn partial_cmp(&self, other: &(i32, i32)) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl Display for Rational

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl Debug for Rational

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl Binary for Rational

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl Octal for Rational

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl LowerHex for Rational

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl UpperHex for Rational

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.