Struct rug::rational::SmallRational
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#[repr(C)]pub struct SmallRational { /* fields omitted */ }
A small rational number that does not require any memory allocation.
This can be useful when you have a numerator and denominator that
are 32-bit or 64-bit integers and you need a reference to a
Rational
.
Although no allocation is required, setting the value of a
SmallRational
does require some computation, as the numerator
and denominator need to be canonicalized.
The SmallRational
type can be coerced to a Rational
, as it
implements Deref
with a Rational
target.
Examples
use rug::Rational; use rug::rational::SmallRational; // `a` requires a heap allocation let mut a = Rational::from((100, 13)); // `b` can reside on the stack let b = SmallRational::from((-100, 21)); a /= &*b; assert_eq!(*a.numer(), -21); assert_eq!(*a.denom(), 13);
Methods
impl SmallRational
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fn new() -> SmallRational
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Creates a SmallRational
with value 0.
Examples
use rug::rational::SmallRational; let r = SmallRational::new(); // Use r as if it were Rational. assert_eq!(*r.numer(), 0); assert_eq!(*r.denom(), 1);
unsafe fn from_canonicalized_32(neg: bool, num: u32, den: u32) -> SmallRational
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Creates a SmallRational
from a 32-bit numerator and
denominator, assuming they are in canonical form.
Safety
This function is unsafe because
it does not check that the denominator is not zero, and
it does not canonicalize the numerator and denominator.
The rest of the library assumes that SmallRational
and
Rational
structures keep their
numerators and denominators canonicalized.
Examples
use rug::rational::SmallRational; let from_unsafe = unsafe { SmallRational::from_canonicalized_32(true, 13, 10) }; // from_safe is canonicalized to the same form as from_unsafe let from_safe = SmallRational::from((130, -100)); assert_eq!(from_unsafe.numer(), from_safe.numer()); assert_eq!(from_unsafe.denom(), from_safe.denom());
unsafe fn from_canonicalized_64(neg: bool, num: u64, den: u64) -> SmallRational
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Creates a SmallRational
from a 64-bit numerator and
denominator, assuming they are in canonical form.
Safety
This function is unsafe because
it does not check that the denominator is not zero, and
it does not canonicalize the numerator and denominator.
The rest of the library assumes that SmallRational
and
Rational
structures keep their
numerators and denominators canonicalized.
Examples
use rug::rational::SmallRational; let from_unsafe = unsafe { SmallRational::from_canonicalized_64(true, 13, 10) }; // from_safe is canonicalized to the same form as from_unsafe let from_safe = SmallRational::from((130, -100)); assert_eq!(from_unsafe.numer(), from_safe.numer()); assert_eq!(from_unsafe.denom(), from_safe.denom());
unsafe fn assign_canonicalized_32(&mut self, neg: bool, num: u32, den: u32)
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Sets a SmallRational
to a 32-bit numerator and denominator,
assuming they are in canonical form.
Safety
This function is unsafe because
it does not check that the denominator is not zero, and
it does not canonicalize the numerator and denominator.
The rest of the library assumes that SmallRational
and
Rational
structures keep their
numerators and denominators canonicalized.
Examples
use rug::rational::SmallRational; let mut from_unsafe = SmallRational::new(); unsafe { from_unsafe.assign_canonicalized_32(true, 13, 10) }; // from_safe is canonicalized to the same form as from_unsafe let from_safe = SmallRational::from((130, -100)); assert_eq!(from_unsafe.numer(), from_safe.numer()); assert_eq!(from_unsafe.denom(), from_safe.denom());
unsafe fn assign_canonicalized_64(&mut self, neg: bool, num: u64, den: u64)
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Sets a SmallRational
to a 64-bit numerator and denominator,
assuming they are in canonical form.
Safety
This function is unsafe because
it does not check that the denominator is not zero, and
it does not canonicalize the numerator and denominator.
The rest of the library assumes that SmallRational
and
Rational
structures keep their
numerators and denominators canonicalized.
Examples
use rug::rational::SmallRational; let mut from_unsafe = SmallRational::new(); unsafe { from_unsafe.assign_canonicalized_64(true, 13, 10) }; // from_safe is canonicalized to the same form as from_unsafe let from_safe = SmallRational::from((130, -100)); assert_eq!(from_unsafe.numer(), from_safe.numer()); assert_eq!(from_unsafe.denom(), from_safe.denom());
Methods from Deref<Target = Rational>
fn to_integer(&self) -> Integer
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Converts to an Integer
, rounding
towards zero.
Examples
use rug::Rational; let pos = Rational::from((139, 10)); let posi = pos.to_integer(); assert_eq!(posi, 13); let neg = Rational::from((-139, 10)); let negi = neg.to_integer(); assert_eq!(negi, -13);
fn copy_to_integer(&self, i: &mut Integer)
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Converts to an Integer
inside i
,
rounding towards zero.
Examples
use rug::{Integer, Rational}; let mut i = Integer::new(); assert_eq!(i, 0); let pos = Rational::from((139, 10)); pos.copy_to_integer(&mut i); assert_eq!(i, 13); let neg = Rational::from((-139, 10)); neg.copy_to_integer(&mut i); assert_eq!(i, -13);
fn to_f32(&self) -> f32
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Converts to an f32
, rounding towards zero.
Examples
use rug::Rational; use rug::rational::SmallRational; use std::f32; let min = Rational::from_f32(f32::MIN).unwrap(); let minus_small = min - &*SmallRational::from((7, 2)); // minus_small is truncated to f32::MIN assert_eq!(minus_small.to_f32(), f32::MIN); let times_three_two = minus_small * &*SmallRational::from((3, 2)); // times_three_two is too small assert_eq!(times_three_two.to_f32(), f32::NEG_INFINITY);
fn to_f64(&self) -> f64
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Converts to an f64
, rounding towards zero.
Examples
use rug::Rational; use rug::rational::SmallRational; use std::f64; // An `f64` has 53 bits of precision. let exact = 0x1f_1234_5678_9aff_u64; let den = 0x1000_u64; let r = Rational::from((exact, den)); assert_eq!(r.to_f64(), exact as f64 / den as f64); // large has 56 ones let large = 0xff_1234_5678_9aff_u64; // trunc has 53 ones followed by 3 zeros let trunc = 0xff_1234_5678_9af8_u64; let j = Rational::from((large, den)); assert_eq!(j.to_f64(), trunc as f64 / den as f64); let max = Rational::from_f64(f64::MAX).unwrap(); let plus_small = max + &*SmallRational::from((7, 2)); // plus_small is truncated to f64::MAX assert_eq!(plus_small.to_f64(), f64::MAX); let times_three_two = plus_small * &*SmallRational::from((3, 2)); // times_three_two is too large assert_eq!(times_three_two.to_f64(), f64::INFINITY);
fn to_string_radix(&self, radix: i32) -> String
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Returns a string representation for the specified radix
.
Examples
use rug::Rational; let r1 = Rational::from(0); assert_eq!(r1.to_string_radix(10), "0"); let r2 = Rational::from((15, 5)); assert_eq!(r2.to_string_radix(10), "3"); let r3 = Rational::from((10, -6)); assert_eq!(r3.to_string_radix(10), "-5/3"); assert_eq!(r3.to_string_radix(5), "-10/3");
Panics
Panics if radix
is less than 2 or greater than 36.
fn numer(&self) -> &Integer
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Borrows the numerator as an Integer
.
Examples
use rug::Rational; let r = Rational::from((12, -20)); // r will be canonicalized to -3 / 5 assert_eq!(*r.numer(), -3)
fn denom(&self) -> &Integer
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Borrows the denominator as an
Integer
.
Examples
use rug::Rational; let r = Rational::from((12, -20)); // r will be canonicalized to -3 / 5 assert_eq!(*r.denom(), 5);
fn as_numer_denom(&self) -> (&Integer, &Integer)
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Borrows the numerator and denominator as
Integer
values.
Examples
use rug::Rational; let r = Rational::from((12, -20)); // r will be canonicalized to -3 / 5 let (num, den) = r.as_numer_denom(); assert_eq!(*num, -3); assert_eq!(*den, 5);
fn into_numer_denom(self) -> (Integer, Integer)
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Converts into numerator and denominator integers.
This function reuses the allocated memory and does not allocate any new memory.
Examples
use rug::Rational; let r = Rational::from((12, -20)); // r will be canonicalized to -3 / 5 let (num, den) = r.into_numer_denom(); assert_eq!(num, -3); assert_eq!(den, 5);
fn as_neg(&self) -> BorrowRational
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Borrows a negated copy of the Rational
number.
The returned object implements Deref
with a Rational
target. This method performs a shallow copy and negates it,
and negation does not change the allocated data.
Examples
use rug::Rational; let r = Rational::from((7, 11)); let neg_r = r.as_neg(); assert_eq!(*neg_r, (-7, 11)); // methods taking &self can be used on the returned object let reneg_r = neg_r.as_neg(); assert_eq!(*reneg_r, (7, 11)); assert_eq!(*reneg_r, r);
fn as_abs(&self) -> BorrowRational
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Borrows an absolute copy of the Rational
number.
The returned object implements Deref
with a Rational
target. This method performs a shallow copy and possibly
negates it, and negation does not change the allocated data.
Examples
use rug::Rational; let r = Rational::from((-7, 11)); let abs_r = r.as_abs(); assert_eq!(*abs_r, (7, 11)); // methods taking &self can be used on the returned object let reabs_r = abs_r.as_abs(); assert_eq!(*reabs_r, (7, 11)); assert_eq!(*reabs_r, *abs_r);
fn as_recip(&self) -> BorrowRational
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Borrows a reciprocal copy of the Rational
number.
The returned object implements Deref
with a Rational
target. This method performs some shallow copying, swapping
numerator and denominator and making sure the sign is in the
numerator.
Examples
use rug::Rational; let r = Rational::from((-7, 11)); let recip_r = r.as_recip(); assert_eq!(*recip_r, (-11, 7)); // methods taking &self can be used on the returned object let rerecip_r = recip_r.as_recip(); assert_eq!(*rerecip_r, (-7, 11)); assert_eq!(*rerecip_r, r);
Panics
Panics if the value is zero.
fn cmp0(&self) -> Ordering
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Returns the same result as self.cmp(&0)
, but is faster.
Examples
use rug::Rational; use std::cmp::Ordering; assert_eq!(Rational::from((-5, 7)).cmp0(), Ordering::Less); assert_eq!(Rational::from(0).cmp0(), Ordering::Equal); assert_eq!(Rational::from((5, 7)).cmp0(), Ordering::Greater);
fn abs(self) -> Rational
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Computes the absolute value.
Examples
use rug::Rational; let r = Rational::from((-100, 17)); let abs = r.abs(); assert_eq!(abs, (100, 17));
fn abs_ref(&self) -> AbsRef
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Computes the absolute value.
Examples
use rug::Rational; let r = Rational::from((-100, 17)); let rr = r.abs_ref(); let abs = Rational::from(rr); assert_eq!(abs, (100, 17));
fn clamp<'a, 'b, Min, Max>(self, min: &'a Min, max: &'b Max) -> Rational where
Rational: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'b Max>,
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Rational: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'b Max>,
Clamps the value within the specified bounds.
Examples
use rug::Rational; let min = (-3, 2); let max = (3, 2); let too_small = Rational::from((-5, 2)); let clamped1 = too_small.clamp(&min, &max); assert_eq!(clamped1, (-3, 2)); let in_range = Rational::from((1, 2)); let clamped2 = in_range.clamp(&min, &max); assert_eq!(clamped2, (1, 2));
Panics
Panics if the maximum value is less than the minimum value.
fn clamp_ref<'a, Min, Max>(
&'a self,
min: &'a Min,
max: &'a Max
) -> ClampRef<'a, Min, Max> where
Rational: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'a Max>,
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&'a self,
min: &'a Min,
max: &'a Max
) -> ClampRef<'a, Min, Max> where
Rational: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'a Max>,
Clamps the value within the specified bounds.
Examples
use rug::Rational; let min = (-3, 2); let max = (3, 2); let too_small = Rational::from((-5, 2)); let r1 = too_small.clamp_ref(&min, &max); let clamped1 = Rational::from(r1); assert_eq!(clamped1, (-3, 2)); let in_range = Rational::from((1, 2)); let r2 = in_range.clamp_ref(&min, &max); let clamped2 = Rational::from(r2); assert_eq!(clamped2, (1, 2));
Panics
Panics if the maximum value is less than the minimum value.
fn recip(self) -> Rational
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Computes the reciprocal.
Examples
use rug::Rational; let r = Rational::from((-100, 17)); let recip = r.recip(); assert_eq!(recip, (-17, 100));
Panics
Panics if the value is zero.
fn recip_ref(&self) -> RecipRef
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Computes the reciprocal.
Examples
use rug::Rational; let r = Rational::from((-100, 17)); let rr = r.recip_ref(); let recip = Rational::from(rr); assert_eq!(recip, (-17, 100));
fn ceil(self) -> Integer
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Rounds the number upwards (towards plus infinity) and returns
it as an Integer
.
Examples
use rug::Rational; // -3.7 let r1 = Rational::from((-37, 10)); let i1 = r1.ceil(); assert_eq!(i1, -3); // 3.3 let r2 = Rational::from((33, 10)); let i2 = r2.ceil(); assert_eq!(i2, 4);
fn ceil_ref(&self) -> CeilRef
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Rounds the number upwards (towards plus infinity).
Examples
use rug::{Assign, Integer, Rational}; let mut ceil = Integer::new(); // -3.7 let r1 = Rational::from((-37, 10)); ceil.assign(r1.ceil_ref()); assert_eq!(ceil, -3); // 3.3 let r2 = Rational::from((33, 10)); ceil.assign(r2.ceil_ref()); assert_eq!(ceil, 4);
fn floor(self) -> Integer
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Rounds the number downwards (towards minus infinity) and
returns it as an Integer
.
Examples
use rug::Rational; // -3.7 let r1 = Rational::from((-37, 10)); let i1 = r1.floor(); assert_eq!(i1, -4); // 3.3 let r2 = Rational::from((33, 10)); let i2 = r2.floor(); assert_eq!(i2, 3);
fn floor_ref(&self) -> FloorRef
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Rounds the number downwards (towards minus infinity).
Examples
use rug::{Assign, Integer, Rational}; let mut floor = Integer::new(); // -3.7 let r1 = Rational::from((-37, 10)); floor.assign(r1.floor_ref()); assert_eq!(floor, -4); // 3.3 let r2 = Rational::from((33, 10)); floor.assign(r2.floor_ref()); assert_eq!(floor, 3);
fn round(self) -> Integer
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Rounds the number to the nearest integer and returns it as an
Integer
.
When the number lies exactly between two integers, it is rounded away from zero.
Examples
use rug::Rational; // -3.5 let r1 = Rational::from((-35, 10)); let i1 = r1.round(); assert_eq!(i1, -4); // 3.7 let r2 = Rational::from((37, 10)); let i2 = r2.round(); assert_eq!(i2, 4);
fn round_ref(&self) -> RoundRef
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Rounds the number to the nearest integer.
When the number lies exactly between two integers, it is rounded away from zero.
Examples
use rug::{Assign, Integer, Rational}; let mut round = Integer::new(); // -3.5 let r1 = Rational::from((-35, 10)); round.assign(r1.round_ref()); assert_eq!(round, -4); // 3.7 let r2 = Rational::from((37, 10)); round.assign(r2.round_ref()); assert_eq!(round, 4);
fn trunc(self) -> Integer
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Rounds the number towards zero and returns it as an
Integer
.
Examples
use rug::Rational; // -3.7 let r1 = Rational::from((-37, 10)); let i1 = r1.trunc(); assert_eq!(i1, -3); // 3.3 let r2 = Rational::from((33, 10)); let i2 = r2.trunc(); assert_eq!(i2, 3);
fn trunc_ref(&self) -> TruncRef
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Rounds the number towards zero.
Examples
use rug::{Assign, Integer, Rational}; let mut trunc = Integer::new(); // -3.7 let r1 = Rational::from((-37, 10)); trunc.assign(r1.trunc_ref()); assert_eq!(trunc, -3); // 3.3 let r2 = Rational::from((33, 10)); trunc.assign(r2.trunc_ref()); assert_eq!(trunc, 3);
fn fract(self) -> Rational
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Computes the fractional part of the number.
Examples
use rug::Rational; // -100/17 = -5 15/17 let r = Rational::from((-100, 17)); let fract = r.fract(); assert_eq!(fract, (-15, 17));
fn fract_ref(&self) -> FractRef
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Computes the fractional part of the number.
Examples
use rug::Rational; let r = Rational::from((-100, 17)); let rr = r.fract_ref(); let fract = Rational::from(rr); assert_eq!(fract, (-15, 17));
fn fract_trunc(self, trunc: Integer) -> (Rational, Integer)
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Computes the fractional and truncated parts of the number.
The initial value of trunc
is ignored.
Examples
use rug::{Integer, Rational}; // -100/17 = -5 15/17 let r = Rational::from((-100, 17)); let (fract, trunc) = r.fract_trunc(Integer::new()); assert_eq!(fract, (-15, 17)); assert_eq!(trunc, -5);
fn fract_trunc_ref(&self) -> FractTruncRef
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Computes the fractional and truncated parts of the number.
Examples
use rug::{Assign, Integer, Rational}; // -100/17 = -5 15/17 let r = Rational::from((-100, 17)); let r_ref = r.fract_trunc_ref(); let (mut fract, mut trunc) = (Rational::new(), Integer::new()); (&mut fract, &mut trunc).assign(r_ref); assert_eq!(fract, (-15, 17)); assert_eq!(trunc, -5);
fn fract_floor(self, floor: Integer) -> (Rational, Integer)
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Computes the fractional and floor parts of the number.
The fractional part cannot be negative. The initial value of
floor
is ignored.
Examples
use rug::{Integer, Rational}; // -100/17 = -6 + 2/17 let r = Rational::from((-100, 17)); let (fract, floor) = r.fract_floor(Integer::new()); assert_eq!(fract, (2, 17)); assert_eq!(floor, -6);
fn fract_floor_ref(&self) -> FractFloorRef
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Computes the fractional and floor parts of the number.
The fractional part cannot be negative.
Examples
use rug::{Assign, Integer, Rational}; // -100/17 = -6 + 2/17 let r = Rational::from((-100, 17)); let r_ref = r.fract_floor_ref(); let (mut fract, mut floor) = (Rational::new(), Integer::new()); (&mut fract, &mut floor).assign(r_ref); assert_eq!(fract, (2, 17)); assert_eq!(floor, -6);
fn fract_ceil(self, ceil: Integer) -> (Rational, Integer)
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Computes the fractional and ceil parts of the number.
The fractional part cannot greater than zero. The initial
value of ceil
is ignored.
Examples
use rug::{Integer, Rational}; // 100/17 = 6 - 2/17 let r = Rational::from((100, 17)); let (fract, ceil) = r.fract_ceil(Integer::new()); assert_eq!(fract, (-2, 17)); assert_eq!(ceil, 6);
fn fract_ceil_ref(&self) -> FractCeilRef
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Computes the fractional and ceil parts of the number.
The fractional part cannot be greater than zero.
Examples
use rug::{Assign, Integer, Rational}; // 100/17 = 6 - 2/17 let r = Rational::from((100, 17)); let r_ref = r.fract_ceil_ref(); let (mut fract, mut ceil) = (Rational::new(), Integer::new()); (&mut fract, &mut ceil).assign(r_ref); assert_eq!(fract, (-2, 17)); assert_eq!(ceil, 6);
Trait Implementations
impl Default for SmallRational
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fn default() -> SmallRational
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Returns the "default value" for a type. Read more
impl Deref for SmallRational
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type Target = Rational
The resulting type after dereferencing.
fn deref(&self) -> &Rational
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Dereferences the value.
impl<T> From<T> for SmallRational where
SmallRational: Assign<T>,
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SmallRational: Assign<T>,
fn from(val: T) -> SmallRational
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Performs the conversion.