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// Copyright © 2016–2018 University of Malta // This program is free software: you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public License // as published by the Free Software Foundation, either version 3 of // the License, or (at your option) any later version. // // This program is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU // General Public License for more details. // // You should have received a copy of the GNU Lesser General Public // License and a copy of the GNU General Public License along with // this program. If not, see <http://www.gnu.org/licenses/>. use {Assign, Integer}; use cast::cast; use ext::gmp as xgmp; use gmp_mpfr_sys::gmp::{self, mpq_t}; use inner::{Inner, InnerMut}; use integer::big as big_integer; use misc; use std::cmp::Ordering; use std::error::Error; use std::ffi::CString; use std::i32; use std::marker::PhantomData; use std::mem; use std::ops::Deref; use std::ptr; /** 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 ```rust use rug::Rational; let r = Rational::from((-12, 15)); let recip = Rational::from(r.recip_ref()); assert_eq!(recip, (-5, 4)); assert_eq!(recip.to_f32(), -1.25); // The numerator and denominator are stored in canonical form. let (num, den) = r.into_numer_denom(); assert_eq!(num, -4); assert_eq!(den, 5); ``` The `Rational` number type supports various functions. Most methods have three versions: 1. The first method consumes the operand. 2. The second method has a “`_mut`” suffix and mutates the operand. 3. The third method has a “`_ref`” suffix and borrows the operand. The returned item is an [incomplete-computation value][icv] that can be assigned to a `Rational` number. ```rust use rug::Rational; // 1. consume the operand let a = Rational::from((-15, 2)); let abs_a = a.abs(); assert_eq!(abs_a, (15, 2)); // 2. mutate the operand let mut b = Rational::from((-17, 2)); b.abs_mut(); assert_eq!(b, (17, 2)); // 3. borrow the operand let c = Rational::from((-19, 2)); let r = c.abs_ref(); let abs_c = Rational::from(r); assert_eq!(abs_c, (19, 2)); // c was not consumed assert_eq!(c, (-19, 2)); ``` [`Integer`]: struct.Integer.html [icv]: index.html#incomplete-computation-values */ pub struct Rational { inner: mpq_t, } fn _static_assertions() { static_assert_size!(Rational, mpq_t); } macro_rules! rat_op_int { ( $func: path; $(#[$attr: meta])* fn $method: ident($($param: ident: $T: ty),*); $(#[$attr_mut: meta])* fn $method_mut: ident; $(#[$attr_ref: meta])* fn $method_ref: ident -> $Incomplete: ident; ) => { $(#[$attr])* #[inline] pub fn $method(mut self, $($param: $T),*) -> Rational { self.$method_mut($($param),*); self } $(#[$attr_mut])* #[inline] pub fn $method_mut(&mut self, $($param: $T),*) { unsafe { let num_mut = gmp::mpq_numref(self.inner_mut()); let den_mut = gmp::mpq_denref(self.inner_mut()); $func(num_mut, self.inner(), $($param.into()),*); xgmp::mpz_set_1(den_mut); } } $(#[$attr_ref])* #[inline] pub fn $method_ref(&self, $($param: $T),*) -> $Incomplete { $Incomplete { ref_self: self, $($param,)* } } }; } macro_rules! ref_rat_op_int { ( $func: path; $(#[$attr_ref: meta])* struct $Incomplete: ident { $($param: ident: $T: ty),* } ) => { $(#[$attr_ref])* #[derive(Debug)] pub struct $Incomplete<'a> { ref_self: &'a Rational, $($param: $T,)* } impl<'a> Assign<$Incomplete<'a>> for Integer { #[inline] fn assign(&mut self, src: $Incomplete) { unsafe { $func( self.inner_mut(), src.ref_self.inner(), $(src.$param.into(),)* ); } } } from_assign! { $Incomplete<'r> => Integer } }; } macro_rules! rat_op_rat_int { ( $func: path; $(#[$attr: meta])* fn $method: ident($int: ident $(, $param: ident: $T: ty),*); $(#[$attr_mut: meta])* fn $method_mut: ident; $(#[$attr_ref: meta])* fn $method_ref: ident -> $Incomplete: ident; ) => { $(#[$attr])* #[inline] pub fn $method( mut self, mut $int: Integer, $($param: $T,)* ) -> (Self, Integer) { self.$method_mut(&mut $int); (self, $int) } $(#[$attr_mut])* #[inline] pub fn $method_mut(&mut self, $int: &mut Integer, $($param: $T),*) { unsafe { $func( self.inner_mut(), $int.inner_mut(), self.inner(), $($param.into()),* ); } } $(#[$attr_ref])* #[inline] pub fn $method_ref(&self, $($param: $T),*) -> $Incomplete { $Incomplete { ref_self: self, $($param,)* } } }; } macro_rules! ref_rat_op_rat_int { ( $func: path; $(#[$attr_ref: meta])* struct $Incomplete: ident { $($param: ident: $T: ty),* } ) => { $(#[$attr_ref])* #[derive(Debug)] pub struct $Incomplete<'a> { ref_self: &'a Rational, $($param: $T,)* } impl<'a, 'b, 'c> Assign<$Incomplete<'a>> for (&'b mut Rational, &'c mut Integer) { #[inline] fn assign(&mut self, src: $Incomplete) { unsafe { $func( self.0.inner_mut(), self.1.inner_mut(), src.ref_self.inner(), $(src.$param.into(),)* ); } } } impl<'a> From<$Incomplete<'a>> for (Rational, Integer) { #[inline] fn from(src: $Incomplete) -> Self { let mut dst = <Self as Default>::default(); <Self as Assign<$Incomplete>>::assign(&mut dst, src); dst } } }; } impl Rational { /// Constructs a new arbitrary-precision [`Rational`] number with /// value 0. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::new(); /// assert_eq!(r, 0); /// ``` /// /// [`Rational`]: struct.Rational.html #[inline] pub fn new() -> Self { unsafe { let mut ret: Rational = mem::uninitialized(); gmp::mpq_init(ret.inner_mut()); ret } } /// Creates a [`Rational`] number from an [`f32`] if it is /// [finite][`f32::is_finite`], losing no precision. /// /// If the compiler supports [`TryFrom`], this conversion can also /// be performed using `Rational::try_from(value)`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// use std::f32; /// let r = Rational::from_f32(-17125e-3).unwrap(); /// assert_eq!(r, "-17125/1000".parse::<Rational>().unwrap()); /// let inf = Rational::from_f32(f32::INFINITY); /// assert!(inf.is_none()); /// ``` /// /// [`Rational`]: struct.Rational.html /// [`TryFrom`]: https://doc.rust-lang.org/nightly/std/convert/trait.TryFrom.html /// [`f32::is_finite`]: https://doc.rust-lang.org/nightly/std/primitive.f32.html#method.is_finite /// [`f32`]: https://doc.rust-lang.org/nightly/std/primitive.f32.html #[inline] pub fn from_f32(value: f32) -> Option<Self> { Rational::from_f64(value.into()) } /// Creates a [`Rational`] number from an [`f64`] if it is /// [finite][`f64::is_finite`], losing no precision. /// /// If the compiler supports [`TryFrom`], this conversion can also /// be performed using `Rational::try_from(value)`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// use std::f64; /// let r = Rational::from_f64(-17125e-3).unwrap(); /// assert_eq!(r, "-17125/1000".parse::<Rational>().unwrap()); /// let inf = Rational::from_f64(f64::INFINITY); /// assert!(inf.is_none()); /// ``` /// /// [`Rational`]: struct.Rational.html /// [`TryFrom`]: https://doc.rust-lang.org/nightly/std/convert/trait.TryFrom.html /// [`f64::is_finite`]: https://doc.rust-lang.org/nightly/std/primitive.f64.html#method.is_finite /// [`f64`]: https://doc.rust-lang.org/nightly/std/primitive.f64.html #[inline] pub fn from_f64(value: f64) -> Option<Self> { if value.is_finite() { let mut r = Rational::new(); r.assign_f64(value).unwrap(); Some(r) } else { None } } /// Parses a [`Rational`] number. /// /// # Panics /// /// Panics if `radix` is less than 2 or greater than 36. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r1 = Rational::from_str_radix("ff/a", 16).unwrap(); /// assert_eq!(r1, (255, 10)); /// let r2 = Rational::from_str_radix("+ff0/a0", 16).unwrap(); /// assert_eq!(r2, (0xff0, 0xa0)); /// assert_eq!(*r2.numer(), 51); /// assert_eq!(*r2.denom(), 2); /// ``` /// /// [`Rational`]: struct.Rational.html #[inline] pub fn from_str_radix( src: &str, radix: i32, ) -> Result<Self, ParseRationalError> { Ok(Rational::from(Rational::parse_radix( src, radix, )?)) } /// Parses a decimal string slice ([`&str`][str]) or byte slice /// ([`&[u8]`][slice]) into a [`Rational`] number. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with the /// unwrapped returned [incomplete-computation value][icv] as /// `Src`. /// /// The string must contain a numerator, and may contain a /// denominator; the numerator and denominator are separated with /// a ‘`/`’. The numerator can start with an optional minus or /// plus sign. /// /// ASCII whitespace is ignored everywhere in the string. /// Underscores are ignored anywhere except before the first digit /// of the numerator and between the ‘`/`’ and the the first digit /// of the denominator. /// /// # Examples /// /// ```rust /// use rug::Rational; /// /// let valid1 = Rational::parse("-12/23"); /// let r1 = Rational::from(valid1.unwrap()); /// assert_eq!(r1, (-12, 23)); /// let valid2 = Rational::parse("+ 12 / 23"); /// let r2 = Rational::from(valid2.unwrap()); /// assert_eq!(r2, (12, 23)); /// /// let invalid = Rational::parse("12/"); /// assert!(invalid.is_err()); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [`Rational`]: struct.Rational.html /// [icv]: index.html#incomplete-computation-values /// [slice]: https://doc.rust-lang.org/nightly/std/primitive.slice.html /// [str]: https://doc.rust-lang.org/nightly/std/primitive.str.html #[inline] pub fn parse<S: AsRef<[u8]>>( src: S, ) -> Result<ParseIncomplete, ParseRationalError> { parse(src.as_ref(), 10) } /// Parses a string slice ([`&str`][str]) or byte slice /// ([`&[u8]`][slice]) into a [`Rational`] number. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with the /// unwrapped returned [incomplete-computation value][icv] as /// `Src`. /// /// The string must contain a numerator, and may contain a /// denominator; the numerator and denominator are separated with /// a ‘`/`’. The numerator can start with an optional minus or /// plus sign. /// /// ASCII whitespace is ignored everywhere in the string. /// Underscores are ignored anywhere except before the first digit /// of the numerator and between the ‘`/`’ and the the first digit /// of the denominator. /// /// # Panics /// /// Panics if `radix` is less than 2 or greater than 36. /// /// # Examples /// /// ```rust /// use rug::Rational; /// /// let valid1 = Rational::parse_radix("12/23", 4); /// let r1 = Rational::from(valid1.unwrap()); /// assert_eq!(r1, (2 + 4 * 1, 3 + 4 * 2)); /// let valid2 = Rational::parse_radix("12 / yz", 36); /// let r2 = Rational::from(valid2.unwrap()); /// assert_eq!(r2, (2 + 36 * 1, 35 + 36 * 34)); /// /// let invalid = Rational::parse_radix("12/", 10); /// assert!(invalid.is_err()); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [`Rational`]: struct.Rational.html /// [icv]: index.html#incomplete-computation-values /// [slice]: https://doc.rust-lang.org/nightly/std/primitive.slice.html /// [str]: https://doc.rust-lang.org/nightly/std/primitive.str.html #[inline] pub fn parse_radix<S: AsRef<[u8]>>( src: S, radix: i32, ) -> Result<ParseIncomplete, ParseRationalError> { parse(src.as_ref(), radix) } /// Converts to an [`f32`], rounding towards zero. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`f32`]: https://doc.rust-lang.org/nightly/std/primitive.f32.html #[inline] pub fn to_f32(&self) -> f32 { misc::trunc_f64_to_f32(self.to_f64()) } /// Converts to an [`f64`], rounding towards zero. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`f64`]: https://doc.rust-lang.org/nightly/std/primitive.f64.html #[inline] pub fn to_f64(&self) -> f64 { unsafe { gmp::mpq_get_d(self.inner()) } } /// Returns a string representation for the specified `radix`. /// /// # Panics /// /// Panics if `radix` is less than 2 or greater than 36. /// /// # Examples /// /// ```rust /// 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"); /// ``` #[inline] pub fn to_string_radix(&self, radix: i32) -> String { let mut s = String::new(); append_to_string(&mut s, self, radix, false); s } /// Assigns from an [`f32`] if it is [finite][`f32::is_finite`], /// losing no precision. /// /// # Examples /// /// ```rust /// use rug::Rational; /// use std::f32; /// let mut r = Rational::new(); /// let ret = r.assign_f32(12.75); /// assert!(ret.is_ok()); /// assert_eq!(r, (1275, 100)); /// let ret = r.assign_f32(f32::NAN); /// assert!(ret.is_err()); /// assert_eq!(r, (1275, 100)); /// ``` /// /// [`f32::is_finite`]: https://doc.rust-lang.org/nightly/std/primitive.f32.html#method.is_finite /// [`f32`]: https://doc.rust-lang.org/nightly/std/primitive.f32.html #[inline] pub fn assign_f32(&mut self, val: f32) -> Result<(), ()> { self.assign_f64(val.into()) } /// Assigns from an [`f64`] if it is [finite][`f64::is_finite`], /// losing no precision. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let mut r = Rational::new(); /// let ret = r.assign_f64(12.75); /// assert!(ret.is_ok()); /// assert_eq!(r, (1275, 100)); /// let ret = r.assign_f64(1.0 / 0.0); /// assert!(ret.is_err()); /// assert_eq!(r, (1275, 100)); /// ``` /// /// [`f64::is_finite`]: https://doc.rust-lang.org/nightly/std/primitive.f64.html#method.is_finite /// [`f64`]: https://doc.rust-lang.org/nightly/std/primitive.f64.html #[inline] pub fn assign_f64(&mut self, val: f64) -> Result<(), ()> { if val.is_finite() { unsafe { gmp::mpq_set_d(self.inner_mut(), val); } Ok(()) } else { Err(()) } } /// Creates a new [`Rational`] number from a numerator and /// denominator without canonicalizing aftwerwards. /// /// # Safety /// /// This function is unsafe because it does not canonicalize the /// [`Rational`] number. The caller must ensure that the numerator /// and denominator are in canonical form, as the rest of the /// library assumes that they are. /// /// # Examples /// /// ```rust /// use rug::Rational; /// /// // -3 / 5 is in canonical form /// let r = unsafe { Rational::from_canonical(-3, 5) }; /// assert_eq!(r, (-3, 5)); /// ``` /// /// [`Rational`]: struct.Rational.html pub unsafe fn from_canonical<Num, Den>(num: Num, den: Den) -> Self where Integer: From<Num> + From<Den>, { let mut dst: Rational = mem::uninitialized(); { let (dnum, dden) = dst.as_mut_numer_denom_no_canonicalization(); ptr::write(dnum, Integer::from(num)); ptr::write(dden, Integer::from(den)); } dst } /// Assigns to the numerator and denominator without /// canonicalizing aftwerwards. /// /// # Safety /// /// This function is unsafe because it does not canonicalize the /// [`Rational`] number after the assignment. The caller must /// ensure that the numerator and denominator are in canonical /// form, as the rest of the library assumes that they are. /// /// # Examples /// /// ```rust /// use rug::Rational; /// /// let mut r = Rational::new(); /// // -3 / 5 is in canonical form /// unsafe { /// r.assign_canonical(-3, 5); /// } /// assert_eq!(r, (-3, 5)); /// ``` /// /// [`Rational`]: struct.Rational.html pub unsafe fn assign_canonical<Num, Den>(&mut self, num: Num, den: Den) where Integer: Assign<Num> + Assign<Den>, { let (dst_num, dst_den) = self.as_mut_numer_denom_no_canonicalization(); dst_num.assign(num); dst_den.assign(den); } /// Creates a [`Rational`] number from an initialized /// [GMP rational number][`mpq_t`]. /// /// # Safety /// /// * The value must be initialized. /// * The [`gmp_mpfr_sys::gmp::mpq_t`][`mpq_t`] type can be /// considered as a kind of pointer, so there can be multiple /// copies of it. Since this function takes over ownership, no /// other copies of the passed value should exist. /// * The numerator and denominator must be in canonical form, as /// the rest of the library assumes that they are. Most GMP /// functions leave the rational number in canonical form, but /// assignment functions do not. Check the /// [GMP documentation][gmp mpq] for details. /// /// # Examples /// /// ```rust /// extern crate gmp_mpfr_sys; /// extern crate rug; /// use gmp_mpfr_sys::gmp; /// use rug::Rational; /// use std::mem; /// fn main() { /// let r = unsafe { /// let mut q = mem::uninitialized(); /// gmp::mpq_init(&mut q); /// gmp::mpq_set_si(&mut q, -145, 10); /// gmp::mpq_canonicalize(&mut q); /// // q is initialized and unique /// Rational::from_raw(q) /// }; /// assert_eq!(r, (-145, 10)); /// // since r is a Rational now, deallocation is automatic /// } /// ``` /// /// [`Rational`]: struct.Rational.html /// [`mpq_t`]: https://docs.rs/gmp-mpfr-sys/~1.1/gmp_mpfr_sys/gmp/struct.mpq_t.html /// [gmp mpq]: https://tspiteri.gitlab.io/gmp-mpfr-sys/gmp/Rational-Number-Functions.html#index-Rational-number-functions #[inline] pub unsafe fn from_raw(raw: mpq_t) -> Self { Rational { inner: raw } } /// Converts a [`Rational`] number into a /// [GMP rational number][`mpq_t`]. /// /// The returned object should be freed to avoid memory leaks. /// /// # Examples /// /// ```rust /// extern crate gmp_mpfr_sys; /// extern crate rug; /// use gmp_mpfr_sys::gmp; /// use rug::Rational; /// fn main() { /// let r = Rational::from((-145, 10)); /// let mut q = r.into_raw(); /// unsafe { /// let d = gmp::mpq_get_d(&q); /// assert_eq!(d, -14.5); /// // free object to prevent memory leak /// gmp::mpq_clear(&mut q); /// } /// } /// ``` /// /// [`Rational`]: struct.Rational.html /// [`mpq_t`]: https://docs.rs/gmp-mpfr-sys/~1.1/gmp_mpfr_sys/gmp/struct.mpq_t.html #[inline] pub fn into_raw(self) -> mpq_t { let ret = self.inner; mem::forget(self); ret } /// Returns a pointer to the inner [GMP rational number][`mpq_t`]. /// /// The returned pointer will be valid for as long as `self` is /// valid. /// /// # Examples /// /// ```rust /// extern crate gmp_mpfr_sys; /// extern crate rug; /// use gmp_mpfr_sys::gmp; /// use rug::Rational; /// fn main() { /// let r = Rational::from((-145, 10)); /// let q_ptr = r.as_raw(); /// unsafe { /// let d = gmp::mpq_get_d(q_ptr); /// assert_eq!(d, -14.5); /// } /// // r is still valid /// assert_eq!(r, (-145, 10)); /// } /// ``` /// /// [`mpq_t`]: https://docs.rs/gmp-mpfr-sys/~1.1/gmp_mpfr_sys/gmp/struct.mpq_t.html #[inline] pub fn as_raw(&self) -> *const mpq_t { self.inner() } /// Returns an unsafe mutable pointer to the inner /// [GMP rational number][`mpq_t`]. /// /// The returned pointer will be valid for as long as `self` is /// valid. /// /// # Examples /// /// ```rust /// extern crate gmp_mpfr_sys; /// extern crate rug; /// use gmp_mpfr_sys::gmp; /// use rug::Rational; /// fn main() { /// let mut r = Rational::from((-145, 10)); /// let q_ptr = r.as_raw_mut(); /// unsafe { /// gmp::mpq_inv(q_ptr, q_ptr); /// } /// assert_eq!(r, (-10, 145)); /// } /// ``` /// /// [`mpq_t`]: https://docs.rs/gmp-mpfr-sys/~1.1/gmp_mpfr_sys/gmp/struct.mpq_t.html #[inline] pub fn as_raw_mut(&mut self) -> *mut mpq_t { unsafe { self.inner_mut() } } /// Borrows the numerator as an [`Integer`]. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((12, -20)); /// // r will be canonicalized to -3 / 5 /// assert_eq!(*r.numer(), -3) /// ``` /// /// [`Integer`]: struct.Integer.html #[inline] pub fn numer(&self) -> &Integer { unsafe { &*cast_ptr!(gmp::mpq_numref_const(self.inner()), Integer) } } /// Borrows the denominator as an [`Integer`]. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((12, -20)); /// // r will be canonicalized to -3 / 5 /// assert_eq!(*r.denom(), 5); /// ``` /// /// [`Integer`]: struct.Integer.html #[inline] pub fn denom(&self) -> &Integer { unsafe { &*cast_ptr!(gmp::mpq_denref_const(self.inner()), Integer) } } /// Calls a function with mutable references to the numerator and /// denominator, then canonicalizes the number. /// /// The denominator must not be zero when the function returns. /// /// # Panics /// /// Panics if the denominator is zero when the function returns. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let mut r = Rational::from((3, 5)); /// r.mutate_numer_denom(|num, den| { /// // change r from 3/5 to 4/8, which is equal to 1/2 /// *num += 1; /// *den += 3; /// }); /// assert_eq!(*r.numer(), 1); /// assert_eq!(*r.denom(), 2); /// ``` /// /// This method does not check that the numerator and denominator /// are in canonical form before calling `func`. This means that /// this method can be used to canonicalize the number after some /// unsafe methods that do not leave the number in cononical form. /// /// ```rust /// use rug::Rational; /// let mut r = Rational::from((3, 5)); /// unsafe { /// // leave r in non-canonical form /// *r.as_mut_numer_denom_no_canonicalization().0 += 1; /// *r.as_mut_numer_denom_no_canonicalization().1 -= 13; /// } /// // At this point, r is still not canonical: 4 / -8 /// assert_eq!(*r.numer(), 4); /// assert_eq!(*r.denom(), -8); /// r.mutate_numer_denom(|_, _| {}); /// // Now r is in canonical form: -1 / 2 /// assert_eq!(*r.numer(), -1); /// assert_eq!(*r.denom(), 2); /// ``` pub fn mutate_numer_denom<F>(&mut self, func: F) where F: FnOnce(&mut Integer, &mut Integer), { unsafe { let numer_ptr = cast_ptr_mut!(gmp::mpq_numref(self.inner_mut()), Integer); let denom_ptr = cast_ptr_mut!(gmp::mpq_denref(self.inner_mut()), Integer); func(&mut *numer_ptr, &mut *denom_ptr); assert_ne!( self.denom().cmp0(), Ordering::Equal, "division by zero" ); gmp::mpq_canonicalize(self.inner_mut()); } } /// Borrows the numerator and denominator mutably without /// canonicalizing aftwerwards. /// /// # Safety /// /// This function is unsafe because it does not canonicalize the /// [`Rational`] number when the borrow ends. The caller must /// ensure that the numerator and denominator are left in /// canonical form, as the rest of the library assumes that they /// are. /// /// # Examples /// /// ```rust /// use rug::Rational; /// /// let mut r = Rational::from((3, 5)); /// { /// let (num, den) = unsafe { /// r.as_mut_numer_denom_no_canonicalization() /// }; /// // Add one to r by adding den to num. Since num and den /// // are relatively prime, r remains in canonical form. /// *num += &*den; /// } /// assert_eq!(r, (8, 5)); /// ``` /// /// This method can also be used to group some operations before /// canonicalization. This is usually not beneficial, as early /// canonicalization usually means subsequent arithmetic /// operations have less work to do. /// /// ```rust /// use rug::Rational; /// let mut r = Rational::from((3, 5)); /// unsafe { /// // first operation: add 1 to numerator /// *r.as_mut_numer_denom_no_canonicalization().0 += 1; /// // second operation: subtract 13 from denominator /// *r.as_mut_numer_denom_no_canonicalization().1 -= 13; /// } /// // At this point, r is still not canonical: 4 / -8 /// assert_eq!(*r.numer(), 4); /// assert_eq!(*r.denom(), -8); /// r.mutate_numer_denom(|_, _| {}); /// // Now r is in canonical form: -1 / 2 /// assert_eq!(*r.numer(), -1); /// assert_eq!(*r.denom(), 2); /// ``` /// /// [`Rational`]: struct.Rational.html #[inline] pub unsafe fn as_mut_numer_denom_no_canonicalization( &mut self, ) -> (&mut Integer, &mut Integer) { ( &mut *cast_ptr_mut!(gmp::mpq_numref(self.inner_mut()), Integer), &mut *cast_ptr_mut!(gmp::mpq_denref(self.inner_mut()), Integer), ) } /// Converts into numerator and denominator [`Integer`] values. /// /// This function reuses the allocated memory and does not /// allocate any new memory. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Integer`]: struct.Integer.html #[inline] pub fn into_numer_denom(self) -> (Integer, Integer) { let raw = self.into_raw(); unsafe { let num = ptr::read(gmp::mpq_numref_const(&raw)); let den = ptr::read(gmp::mpq_denref_const(&raw)); (Integer::from_raw(num), Integer::from_raw(den)) } } /// Borrows a negated copy of the [`Rational`] number. /// /// The returned object implements /// [`Deref<Target = Rational>`][`Deref`]. /// /// This method performs a shallow copy and negates it, and /// negation does not change the allocated data. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Deref`]: https://doc.rust-lang.org/nightly/std/ops/trait.Deref.html /// [`Rational`]: struct.Rational.html #[inline] pub fn as_neg(&self) -> BorrowRational { let mut ret = BorrowRational { inner: self.inner, phantom: PhantomData, }; let size = self.numer() .inner() .size .checked_neg() .expect("overflow"); unsafe { (*gmp::mpq_numref(&mut ret.inner)).size = size; } ret } /// Borrows an absolute copy of the [`Rational`] number. /// /// The returned object implements /// [`Deref<Target = Rational>`][`Deref`]. /// /// This method performs a shallow copy and possibly negates it, /// and negation does not change the allocated data. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Deref`]: https://doc.rust-lang.org/nightly/std/ops/trait.Deref.html /// [`Rational`]: struct.Rational.html #[inline] pub fn as_abs(&self) -> BorrowRational { let mut ret = BorrowRational { inner: self.inner, phantom: PhantomData, }; let size = self.numer() .inner() .size .checked_abs() .expect("overflow"); unsafe { (*gmp::mpq_numref(&mut ret.inner)).size = size; } ret } /// Borrows a reciprocal copy of the [`Rational`] number. /// /// The returned object implements /// [`Deref<Target = Rational>`][`Deref`]. /// /// This method performs some shallow copying, swapping numerator /// and denominator and making sure the sign is in the numerator. /// /// # Panics /// /// Panics if the value is zero. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Deref`]: https://doc.rust-lang.org/nightly/std/ops/trait.Deref.html /// [`Rational`]: struct.Rational.html pub fn as_recip(&self) -> BorrowRational { assert_ne!(self.cmp0(), Ordering::Equal, "division by zero"); let mut inner: mpq_t = unsafe { mem::uninitialized() }; unsafe { let mut dst_num = ptr::read(self.denom().inner()); let mut dst_den = ptr::read(self.numer().inner()); if dst_den.size < 0 { dst_den.size = dst_den.size.wrapping_neg(); dst_num.size = dst_num.size.checked_neg().expect("overflow"); } ptr::write(gmp::mpq_numref(&mut inner), dst_num); ptr::write(gmp::mpq_denref(&mut inner), dst_den); } BorrowRational { inner, phantom: PhantomData, } } /// Returns the same result as [`self.cmp(&0.into())`][`cmp`], but /// is faster. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`cmp`]: https://doc.rust-lang.org/nightly/std/cmp/trait.Ord.html#tymethod.cmp #[inline] pub fn cmp0(&self) -> Ordering { self.numer().cmp0() } /// Compares the absolute values. /// /// # Examples /// /// ```rust /// use rug::Rational; /// use std::cmp::Ordering; /// let a = Rational::from((-23, 10)); /// let b = Rational::from((-47, 5)); /// assert_eq!(a.cmp(&b), Ordering::Greater); /// assert_eq!(a.cmp_abs(&b), Ordering::Less); /// ``` #[inline] pub fn cmp_abs(&self, other: &Self) -> Ordering { self.as_abs().cmp(&*other.as_abs()) } math_op1! { gmp::mpq_abs; /// Computes the absolute value. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((-100, 17)); /// let abs = r.abs(); /// assert_eq!(abs, (100, 17)); /// ``` fn abs(); /// Computes the absolute value. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let mut r = Rational::from((-100, 17)); /// r.abs_mut(); /// assert_eq!(r, (100, 17)); /// ``` fn abs_mut; /// Computes the absolute value. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((-100, 17)); /// let r_ref = r.abs_ref(); /// let abs = Rational::from(r_ref); /// assert_eq!(abs, (100, 17)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn abs_ref -> AbsIncomplete; } rat_op_int! { xgmp::mpq_signum; /// Computes the signum. /// /// * 0 if the value is zero /// * 1 if the value is positive /// * −1 if the value is negative /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((-100, 17)); /// let signum = r.signum(); /// assert_eq!(signum, -1); /// ``` fn signum(); /// Computes the signum. /// /// * 0 if the value is zero /// * 1 if the value is positive /// * −1 if the value is negative /// /// # Examples /// /// ```rust /// use rug::Rational; /// let mut r = Rational::from((-100, 17)); /// r.signum_mut(); /// assert_eq!(r, -1); /// ``` fn signum_mut; /// Computes the signum. /// /// * 0 if the value is zero /// * 1 if the value is positive /// * −1 if the value is negative /// /// [`Assign<Src> for Integer`][`Assign`], /// [`Assign<Src> for Rational`][`Assign`], /// [`From<Src> for Integer`][`From`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::{Integer, Rational}; /// let r = Rational::from((-100, 17)); /// let r_ref = r.signum_ref(); /// let signum = Integer::from(r_ref); /// assert_eq!(signum, -1); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn signum_ref -> SignumIncomplete; } /// Clamps the value within the specified bounds. /// /// # Panics /// /// Panics if the maximum value is less than the minimum value. /// /// # Examples /// /// ```rust /// 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)); /// ``` #[inline] pub fn clamp<'a, 'b, Min, Max>(mut self, min: &'a Min, max: &'b Max) -> Self where Self: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'b Max>, { self.clamp_mut(min, max); self } /// Clamps the value within the specified bounds. /// /// # Panics /// /// Panics if the maximum value is less than the minimum value. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let min = (-3, 2); /// let max = (3, 2); /// let mut too_small = Rational::from((-5, 2)); /// too_small.clamp_mut(&min, &max); /// assert_eq!(too_small, (-3, 2)); /// let mut in_range = Rational::from((1, 2)); /// in_range.clamp_mut(&min, &max); /// assert_eq!(in_range, (1, 2)); /// ``` pub fn clamp_mut<'a, 'b, Min, Max>(&mut self, min: &'a Min, max: &'b Max) where Self: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'b Max>, { if (&*self).lt(min) { self.assign(min); assert!(!(&*self).gt(max), "minimum larger than maximum"); } else if (&*self).gt(max) { self.assign(max); assert!(!(&*self).lt(min), "minimum larger than maximum"); } } /// Clamps the value within the specified bounds. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with the /// returned [incomplete-computation value][icv] as `Src`. /// /// # Panics /// /// Panics if the maximum value is less than the minimum value. /// /// # Examples /// /// ```rust /// 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)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values #[inline] pub fn clamp_ref<'a, Min, Max>( &'a self, min: &'a Min, max: &'a Max, ) -> ClampIncomplete<'a, Min, Max> where Self: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'a Max>, { ClampIncomplete { ref_self: self, min, max, } } math_op1! { xgmp::mpq_inv_check; /// Computes the reciprocal. /// /// # Panics /// /// Panics if the value is zero. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((-100, 17)); /// let recip = r.recip(); /// assert_eq!(recip, (-17, 100)); /// ``` fn recip(); /// Computes the reciprocal. /// /// This method never reallocates or copies the heap data. It /// simply swaps the allocated data of the numerator and /// denominator and makes sure the denominator is stored as /// positive. /// /// # Panics /// /// Panics if the value is zero. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let mut r = Rational::from((-100, 17)); /// r.recip_mut(); /// assert_eq!(r, (-17, 100)); /// ``` fn recip_mut; /// Computes the reciprocal. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((-100, 17)); /// let r_ref = r.recip_ref(); /// let recip = Rational::from(r_ref); /// assert_eq!(recip, (-17, 100)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn recip_ref -> RecipIncomplete; } rat_op_int! { xgmp::mpq_trunc; /// Rounds the number towards zero. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -3.7 /// let r1 = Rational::from((-37, 10)); /// let trunc1 = r1.trunc(); /// assert_eq!(trunc1, -3); /// // 3.3 /// let r2 = Rational::from((33, 10)); /// let trunc2 = r2.trunc(); /// assert_eq!(trunc2, 3); /// ``` fn trunc(); /// Rounds the number towards zero. /// /// # Examples /// /// ```rust /// use rug::{Assign, Rational}; /// // -3.7 /// let mut r = Rational::from((-37, 10)); /// r.trunc_mut(); /// assert_eq!(r, -3); /// // 3.3 /// r.assign((33, 10)); /// r.trunc_mut(); /// assert_eq!(r, 3); /// ``` fn trunc_mut; /// Rounds the number towards zero. /// /// [`Assign<Src> for Integer`][`Assign`], /// [`Assign<Src> for Rational`][`Assign`], /// [`From<Src> for Integer`][`From`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn trunc_ref -> TruncIncomplete; } math_op1! { xgmp::mpq_trunc_fract; /// Computes the fractional part of the number. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -100/17 = -5 - 15/17 /// let r = Rational::from((-100, 17)); /// let rem = r.rem_trunc(); /// assert_eq!(rem, (-15, 17)); /// ``` fn rem_trunc(); /// Computes the fractional part of the number. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -100/17 = -5 - 15/17 /// let mut r = Rational::from((-100, 17)); /// r.rem_trunc_mut(); /// assert_eq!(r, (-15, 17)); /// ``` fn rem_trunc_mut; /// Computes the fractional part of the number. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -100/17 = -5 - 15/17 /// let r = Rational::from((-100, 17)); /// let r_ref = r.rem_trunc_ref(); /// let rem = Rational::from(r_ref); /// assert_eq!(rem, (-15, 17)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn rem_trunc_ref -> RemTruncIncomplete; } rat_op_rat_int! { xgmp::mpq_trunc_fract_whole; /// Computes the fractional and truncated parts of the number. /// /// The initial value of `trunc` is ignored. /// /// # Examples /// /// ```rust /// 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(trunc); /// Computes the fractional and truncated parts of the number. /// /// The initial value of `trunc` is ignored. /// /// # Examples /// /// ```rust /// use rug::{Integer, Rational}; /// // -100/17 = -5 - 15/17 /// let mut r = Rational::from((-100, 17)); /// let mut whole = Integer::new(); /// r.fract_trunc_mut(&mut whole); /// assert_eq!(r, (-15, 17)); /// assert_eq!(whole, -5); /// ``` fn fract_trunc_mut; /// Computes the fractional and truncated parts of the number. /// /// [`Assign<Src> for (Rational, Integer)`][`Assign`], /// [`Assign<Src> for (&mut Rational, &mut Integer)`][`Assign`] /// and [`From<Src> for (Rational, Integer)`][`From`] are /// implemented with the returned /// [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn fract_trunc_ref -> FractTruncIncomplete; } rat_op_int! { xgmp::mpq_ceil; /// Rounds the number upwards (towards plus infinity). /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -3.7 /// let r1 = Rational::from((-37, 10)); /// let ceil1 = r1.ceil(); /// assert_eq!(ceil1, -3); /// // 3.3 /// let r2 = Rational::from((33, 10)); /// let ceil2 = r2.ceil(); /// assert_eq!(ceil2, 4); /// ``` fn ceil(); /// Rounds the number upwards (towards plus infinity). /// /// # Examples /// /// ```rust /// use rug::{Assign, Rational}; /// // -3.7 /// let mut r = Rational::from((-37, 10)); /// r.ceil_mut(); /// assert_eq!(r, -3); /// // 3.3 /// r.assign((33, 10)); /// r.ceil_mut(); /// assert_eq!(r, 4); /// ``` fn ceil_mut; /// Rounds the number upwards (towards plus infinity). /// /// [`Assign<Src> for Integer`][`Assign`], /// [`Assign<Src> for Rational`][`Assign`], /// [`From<Src> for Integer`][`From`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn ceil_ref -> CeilIncomplete; } math_op1! { xgmp::mpq_ceil_fract; /// Computes the non-positive remainder after rounding up. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // 100/17 = 6 - 2/17 /// let r = Rational::from((100, 17)); /// let rem = r.rem_ceil(); /// assert_eq!(rem, (-2, 17)); /// ``` fn rem_ceil(); /// Computes the non-positive remainder after rounding up. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // 100/17 = 6 - 2/17 /// let mut r = Rational::from((100, 17)); /// r.rem_ceil_mut(); /// assert_eq!(r, (-2, 17)); /// ``` fn rem_ceil_mut; /// Computes the non-positive remainder after rounding up. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // 100/17 = 6 - 2/17 /// let r = Rational::from((100, 17)); /// let r_ref = r.rem_ceil_ref(); /// let rem = Rational::from(r_ref); /// assert_eq!(rem, (-2, 17)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn rem_ceil_ref -> RemCeilIncomplete; } rat_op_rat_int! { xgmp::mpq_ceil_fract_whole; /// Computes the fractional and ceil parts of the number. /// /// The fractional part cannot greater than zero. The initial /// value of `ceil` is ignored. /// /// # Examples /// /// ```rust /// 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(ceil); /// Computes the fractional and ceil parts of the number. /// /// The fractional part cannot be greater than zero. The initial /// value of `ceil` is ignored. /// /// # Examples /// /// ```rust /// use rug::{Integer, Rational}; /// // 100/17 = 6 - 2/17 /// let mut r = Rational::from((100, 17)); /// let mut ceil = Integer::new(); /// r.fract_ceil_mut(&mut ceil); /// assert_eq!(r, (-2, 17)); /// assert_eq!(ceil, 6); /// ``` fn fract_ceil_mut; /// Computes the fractional and ceil parts of the number. /// /// The fractional part cannot be greater than zero. /// /// [`Assign<Src> for (Rational, Integer)`][`Assign`], /// [`Assign<Src> for (&mut Rational, &mut Integer)`][`Assign`] /// and [`From<Src> for (Rational, Integer)`][`From`] are /// implemented with the returned /// [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn fract_ceil_ref -> FractCeilIncomplete; } rat_op_int! { xgmp::mpq_floor; /// Rounds the number downwards (towards minus infinity). /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -3.7 /// let r1 = Rational::from((-37, 10)); /// let floor1 = r1.floor(); /// assert_eq!(floor1, -4); /// // 3.3 /// let r2 = Rational::from((33, 10)); /// let floor2 = r2.floor(); /// assert_eq!(floor2, 3); /// ``` fn floor(); /// Rounds the number downwards (towards minus infinity). /// /// ```rust /// use rug::{Assign, Rational}; /// // -3.7 /// let mut r = Rational::from((-37, 10)); /// r.floor_mut(); /// assert_eq!(r, -4); /// // 3.3 /// r.assign((33, 10)); /// r.floor_mut(); /// assert_eq!(r, 3); /// ``` fn floor_mut; /// Rounds the number downwards (towards minus infinity). /// /// [`Assign<Src> for Integer`][`Assign`], /// [`Assign<Src> for Rational`][`Assign`], /// [`From<Src> for Integer`][`From`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn floor_ref -> FloorIncomplete; } math_op1! { xgmp::mpq_floor_fract; /// Computes the non-negative remainder after rounding down. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -100/17 = -6 + 2/17 /// let r = Rational::from((-100, 17)); /// let rem = r.rem_floor(); /// assert_eq!(rem, (2, 17)); /// ``` fn rem_floor(); /// Computes the non-negative remainder after rounding down. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -100/17 = -6 + 2/17 /// let mut r = Rational::from((-100, 17)); /// r.rem_floor_mut(); /// assert_eq!(r, (2, 17)); /// ``` fn rem_floor_mut; /// Computes the non-negative remainder after rounding down. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -100/17 = -6 + 2/17 /// let r = Rational::from((-100, 17)); /// let r_ref = r.rem_floor_ref(); /// let rem = Rational::from(r_ref); /// assert_eq!(rem, (2, 17)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn rem_floor_ref -> RemFloorIncomplete; } rat_op_rat_int! { xgmp::mpq_floor_fract_whole; /// Computes the fractional and floor parts of the number. /// /// The fractional part cannot be negative. The initial value of /// `floor` is ignored. /// /// # Examples /// /// ```rust /// 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(floor); /// Computes the fractional and floor parts of the number. /// /// The fractional part cannot be negative. The initial value of /// `floor` is ignored. /// /// # Examples /// /// ```rust /// use rug::{Integer, Rational}; /// // -100/17 = -6 + 2/17 /// let mut r = Rational::from((-100, 17)); /// let mut floor = Integer::new(); /// r.fract_floor_mut(&mut floor); /// assert_eq!(r, (2, 17)); /// assert_eq!(floor, -6); /// ``` fn fract_floor_mut; /// Computes the fractional and floor parts of the number. /// /// The fractional part cannot be negative. /// /// [`Assign<Src> for (Rational, Integer)`][`Assign`], /// [`Assign<Src> for (&mut Rational, &mut Integer)`][`Assign`] /// and [`From<Src> for (Rational, Integer)`][`From`] are /// implemented with the returned /// [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn fract_floor_ref -> FractFloorIncomplete; } rat_op_int! { xgmp::mpq_round; /// Rounds the number to the nearest integer. /// /// When the number lies exactly between two integers, it is /// rounded away from zero. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -3.5 /// let r1 = Rational::from((-35, 10)); /// let round1 = r1.round(); /// assert_eq!(round1, -4); /// // 3.7 /// let r2 = Rational::from((37, 10)); /// let round2 = r2.round(); /// assert_eq!(round2, 4); /// ``` fn round(); /// Rounds the number to the nearest integer. /// /// When the number lies exactly between two integers, it is /// rounded away from zero. /// /// # Examples /// /// ```rust /// use rug::{Assign, Rational}; /// // -3.5 /// let mut r = Rational::from((-35, 10)); /// r.round_mut(); /// assert_eq!(r, -4); /// // 3.7 /// r.assign((37, 10)); /// r.round_mut(); /// assert_eq!(r, 4); /// ``` fn round_mut; /// Rounds the number to the nearest integer. /// /// When the number lies exactly between two integers, it is /// rounded away from zero. /// /// [`Assign<Src> for Integer`][`Assign`], /// [`Assign<Src> for Rational`][`Assign`], /// [`From<Src> for Integer`][`From`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// 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); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn round_ref -> RoundIncomplete; } math_op1! { xgmp::mpq_round_fract; /// Computes the remainder after rounding to the nearest /// integer. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -3.5 = -4 + 0.5 = -4 + 1/2 /// let r1 = Rational::from((-35, 10)); /// let rem1 = r1.rem_round(); /// assert_eq!(rem1, (1, 2)); /// // 3.7 = 4 - 0.3 = 4 - 3/10 /// let r2 = Rational::from((37, 10)); /// let rem2 = r2.rem_round(); /// assert_eq!(rem2, (-3, 10)); /// ``` fn rem_round(); /// Computes the remainder after rounding to the nearest /// integer. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -3.5 = -4 + 0.5 = -4 + 1/2 /// let mut r1 = Rational::from((-35, 10)); /// r1.rem_round_mut(); /// assert_eq!(r1, (1, 2)); /// // 3.7 = 4 - 0.3 = 4 - 3/10 /// let mut r2 = Rational::from((37, 10)); /// r2.rem_round_mut(); /// assert_eq!(r2, (-3, 10)); /// ``` fn rem_round_mut; /// Computes the remainder after rounding to the nearest /// integer. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// // -3.5 = -4 + 0.5 = -4 + 1/2 /// let r1 = Rational::from((-35, 10)); /// let r_ref1 = r1.rem_round_ref(); /// let rem1 = Rational::from(r_ref1); /// assert_eq!(rem1, (1, 2)); /// // 3.7 = 4 - 0.3 = 4 - 3/10 /// let r2 = Rational::from((37, 10)); /// let r_ref2 = r2.rem_round_ref(); /// let rem2 = Rational::from(r_ref2); /// assert_eq!(rem2, (-3, 10)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn rem_round_ref -> RemRoundIncomplete; } rat_op_rat_int! { xgmp::mpq_round_fract_whole; /// Computes the fractional and rounded parts of the number. /// /// The fractional part is positive when the number is rounded /// down and negative when the number is rounded up. When the /// number lies exactly between two integers, it is rounded away /// from zero. /// /// # Examples /// /// ```rust /// use rug::{Integer, Rational}; /// // -3.5 = -4 + 0.5 = -4 + 1/2 /// let r1 = Rational::from((-35, 10)); /// let (fract1, round1) = r1.fract_round(Integer::new()); /// assert_eq!(fract1, (1, 2)); /// assert_eq!(round1, -4); /// // 3.7 = 4 - 0.3 = 4 - 3/10 /// let r2 = Rational::from((37, 10)); /// let (fract2, round2) = r2.fract_round(Integer::new()); /// assert_eq!(fract2, (-3, 10)); /// assert_eq!(round2, 4); /// ``` fn fract_round(round); /// Computes the fractional and round parts of the number. /// /// The fractional part is positive when the number is rounded /// down and negative when the number is rounded up. When the /// number lies exactly between two integers, it is rounded away /// from zero. /// /// # Examples /// /// ```rust /// use rug::{Integer, Rational}; /// // -3.5 = -4 + 0.5 = -4 + 1/2 /// let mut r1 = Rational::from((-35, 10)); /// let mut round1 = Integer::new(); /// r1.fract_round_mut(&mut round1); /// assert_eq!(r1, (1, 2)); /// assert_eq!(round1, -4); /// // 3.7 = 4 - 0.3 = 4 - 3/10 /// let mut r2 = Rational::from((37, 10)); /// let mut round2 = Integer::new(); /// r2.fract_round_mut(&mut round2); /// assert_eq!(r2, (-3, 10)); /// assert_eq!(round2, 4); /// ``` fn fract_round_mut; /// Computes the fractional and round parts of the number. /// /// The fractional part is positive when the number is rounded /// down and negative when the number is rounded up. When the /// number lies exactly between two integers, it is rounded away /// from zero. /// /// [`Assign<Src> for (Rational, Integer)`][`Assign`], /// [`Assign<Src> for (&mut Rational, &mut Integer)`][`Assign`] /// and [`From<Src> for (Rational, Integer)`][`From`] are /// implemented with the returned /// [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer, Rational}; /// // -3.5 = -4 + 0.5 = -4 + 1/2 /// let r1 = Rational::from((-35, 10)); /// let r_ref1 = r1.fract_round_ref(); /// let (mut fract1, mut round1) = (Rational::new(), Integer::new()); /// (&mut fract1, &mut round1).assign(r_ref1); /// assert_eq!(fract1, (1, 2)); /// assert_eq!(round1, -4); /// // 3.7 = 4 - 0.3 = 4 - 3/10 /// let r2 = Rational::from((37, 10)); /// let r_ref2 = r2.fract_round_ref(); /// let (mut fract2, mut round2) = (Rational::new(), Integer::new()); /// (&mut fract2, &mut round2).assign(r_ref2); /// assert_eq!(fract2, (-3, 10)); /// assert_eq!(round2, 4); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn fract_round_ref -> FractRoundIncomplete; } math_op1! { xgmp::mpq_square; /// Computes the square. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((-13, 2)); /// let square = r.square(); /// assert_eq!(square, (169, 4)); /// ``` fn square(); /// Computes the square. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let mut r = Rational::from((-13, 2)); /// r.square_mut(); /// assert_eq!(r, (169, 4)); /// ``` fn square_mut; /// Computes the square. /// /// [`Assign<Src> for Rational`][`Assign`] and /// [`From<Src> for Rational`][`From`] are implemented with /// the returned [incomplete-computation value][icv] as `Src`. /// /// # Examples /// /// ```rust /// use rug::Rational; /// let r = Rational::from((-13, 2)); /// assert_eq!(Rational::from(r.square_ref()), (169, 4)); /// ``` /// /// [`Assign`]: trait.Assign.html /// [`From`]: https://doc.rust-lang.org/nightly/std/convert/trait.From.html /// [icv]: index.html#incomplete-computation-values fn square_ref -> SquareIncomplete; } } ref_math_op1! { Rational; gmp::mpq_abs; struct AbsIncomplete {} } ref_rat_op_int! { xgmp::mpq_signum; struct SignumIncomplete {} } #[derive(Debug)] pub struct ClampIncomplete<'a, Min, Max> where Rational: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'a Max>, Min: 'a, Max: 'a, { ref_self: &'a Rational, min: &'a Min, max: &'a Max, } impl<'a, Min, Max> Assign<ClampIncomplete<'a, Min, Max>> for Rational where Self: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'a Max>, Min: 'a, Max: 'a, { #[inline] fn assign(&mut self, src: ClampIncomplete<'a, Min, Max>) { if src.ref_self.lt(src.min) { self.assign(src.min); assert!( !(&*self).gt(src.max), "minimum larger than maximum" ); } else if src.ref_self.gt(src.max) { self.assign(src.max); assert!( !(&*self).lt(src.min), "minimum larger than maximum" ); } else { self.assign(src.ref_self); } } } impl<'a, Min, Max> From<ClampIncomplete<'a, Min, Max>> for Rational where Self: PartialOrd<Min> + PartialOrd<Max> + Assign<&'a Min> + Assign<&'a Max>, Min: 'a, Max: 'a, { #[inline] fn from(src: ClampIncomplete<'a, Min, Max>) -> Self { let mut dst = Rational::new(); dst.assign(src); dst } } ref_math_op1! { Rational; xgmp::mpq_inv_check; struct RecipIncomplete {} } ref_rat_op_int! { xgmp::mpq_trunc; struct TruncIncomplete {} } ref_math_op1! { Rational; xgmp::mpq_trunc_fract; struct RemTruncIncomplete {} } ref_rat_op_rat_int! { xgmp::mpq_trunc_fract_whole; struct FractTruncIncomplete {} } ref_rat_op_int! { xgmp::mpq_ceil; struct CeilIncomplete {} } ref_math_op1! { Rational; xgmp::mpq_ceil_fract; struct RemCeilIncomplete {} } ref_rat_op_rat_int! { xgmp::mpq_ceil_fract_whole; struct FractCeilIncomplete {} } ref_rat_op_int! { xgmp::mpq_floor; struct FloorIncomplete {} } ref_math_op1! { Rational; xgmp::mpq_floor_fract; struct RemFloorIncomplete {} } ref_rat_op_rat_int! { xgmp::mpq_floor_fract_whole; struct FractFloorIncomplete {} } ref_rat_op_int! { xgmp::mpq_round; struct RoundIncomplete {} } ref_math_op1! { Rational; xgmp::mpq_round_fract; struct RemRoundIncomplete {} } ref_rat_op_rat_int! { xgmp::mpq_round_fract_whole; struct FractRoundIncomplete {} } ref_math_op1! { Rational; xgmp::mpq_square; struct SquareIncomplete {} } #[derive(Debug)] pub struct BorrowRational<'a> { inner: mpq_t, phantom: PhantomData<&'a Rational>, } impl<'a> Deref for BorrowRational<'a> { type Target = Rational; #[inline] fn deref(&self) -> &Rational { let ptr = cast_ptr!(&self.inner, Rational); unsafe { &*ptr } } } pub(crate) fn append_to_string( s: &mut String, r: &Rational, radix: i32, to_upper: bool, ) { let (num, den) = (r.numer(), r.denom()); let is_whole = *den == 1; let cap_for_den_nul = if is_whole { 1 } else { big_integer::req_chars(den, radix, 2) }; let cap = big_integer::req_chars(num, radix, cap_for_den_nul); s.reserve(cap); big_integer::append_to_string(s, num, radix, to_upper); if !is_whole { s.push('/'); big_integer::append_to_string(s, den, radix, to_upper); } } #[derive(Debug)] pub struct ParseIncomplete { c_string: CString, radix: i32, } impl Assign<ParseIncomplete> for Rational { #[inline] fn assign(&mut self, src: ParseIncomplete) { unsafe { let err = gmp::mpq_set_str( self.inner_mut(), src.c_string.as_ptr(), cast(src.radix), ); assert_eq!(err, 0); gmp::mpq_canonicalize(self.inner_mut()); } } } impl From<ParseIncomplete> for Rational { #[inline] fn from(src: ParseIncomplete) -> Self { let mut dst = Rational::new(); dst.assign(src); dst } } fn parse( bytes: &[u8], radix: i32, ) -> Result<ParseIncomplete, ParseRationalError> { use self::ParseErrorKind as Kind; use self::ParseRationalError as Error; assert!(radix >= 2 && radix <= 36, "radix out of range"); let bradix: u8 = cast(radix); let small_bound = b'a' - 10 + bradix; let capital_bound = b'A' - 10 + bradix; let digit_bound = b'0' + bradix; let mut v = Vec::with_capacity(bytes.len() + 1); let mut has_sign = false; let mut has_digits = false; let mut denom = false; let mut division_by_zero = false; for &b in bytes { if b == b'/' { if denom { return Err(Error { kind: Kind::TooManySlashes, }); } if !has_digits { return Err(Error { kind: Kind::NumerNoDigits, }); } v.push(b'/'); has_digits = false; denom = true; division_by_zero = true; continue; } let valid_digit = match b { b'+' if !denom && !has_sign && !has_digits => { has_sign = true; continue; } b'-' if !denom && !has_sign && !has_digits => { v.push(b'-'); has_sign = true; continue; } b'_' if has_digits => continue, b' ' | b'\t' | b'\n' | 0x0b | 0x0c | 0x0d => continue, _ if b >= b'a' => b < small_bound, _ if b >= b'A' => b < capital_bound, b'0'...b'9' => b < digit_bound, _ => false, }; if !valid_digit { return Err(Error { kind: Kind::InvalidDigit, }); } v.push(b); has_digits = true; division_by_zero = division_by_zero && b == b'0'; } if !has_digits { return Err(Error { kind: if denom { Kind::DenomNoDigits } else { Kind::NoDigits }, }); } if division_by_zero { return Err(Error { kind: Kind::DenomZero, }); } // we've only added b'-' and digits, so we know there are no nuls let c_string = unsafe { CString::from_vec_unchecked(v) }; Ok(ParseIncomplete { c_string, radix, }) } #[derive(Debug)] /** An error which can be returned when parsing a [`Rational`] number. See the [`Rational::parse_radix`] method for details on what strings are accepted. # Examples ```rust use rug::Rational; use rug::rational::ParseRationalError; // This string is not a rational number. let s = "something completely different (_!_!_)"; let error: ParseRationalError = match Rational::parse_radix(s, 4) { Ok(_) => unreachable!(), Err(error) => error, }; println!("Parse error: {:?}", error); ``` [`Rational::parse_radix`]: ../struct.Rational.html#method.parse_radix [`Rational`]: ../struct.Rational.html */ pub struct ParseRationalError { kind: ParseErrorKind, } #[derive(Debug)] enum ParseErrorKind { InvalidDigit, NoDigits, NumerNoDigits, DenomNoDigits, TooManySlashes, DenomZero, } impl Error for ParseRationalError { fn description(&self) -> &str { use self::ParseErrorKind::*; match self.kind { InvalidDigit => "invalid digit found in string", NoDigits => "string has no digits", NumerNoDigits => "string has no digits for numerator", DenomNoDigits => "string has no digits for denominator", TooManySlashes => "more than one / found in string", DenomZero => "string has zero denominator", } } } impl Inner for Rational { type Output = mpq_t; #[inline] fn inner(&self) -> &mpq_t { &self.inner } } impl InnerMut for Rational { #[inline] unsafe fn inner_mut(&mut self) -> &mut mpq_t { &mut self.inner } }