diff options
| author | Alex Crichton <alex@alexcrichton.com> | 2014-10-14 21:57:50 -0700 |
|---|---|---|
| committer | Alex Crichton <alex@alexcrichton.com> | 2014-10-19 12:59:40 -0700 |
| commit | fb169d5543c84e11038ba2d07b538ec88fb49ca6 (patch) | |
| tree | 252d6fd6dffe26a06e39f735275979b247f40302 /src/libnum | |
| parent | c121cbab35c9ff9ba133c578976a4ec35c011bcf (diff) | |
Remove a number of deprecated crates
All of these crates have been deprecated for some time and properly live in the rust-lang organization as cargo-based crates. To update your code, depend on the rust-lang/foo repository via cargo. [breaking-change]
Diffstat (limited to 'src/libnum')
| -rw-r--r-- | src/libnum/bigint.rs | 2961 | ||||
| -rw-r--r-- | src/libnum/complex.rs | 379 | ||||
| -rw-r--r-- | src/libnum/integer.rs | 507 | ||||
| -rw-r--r-- | src/libnum/lib.rs | 73 | ||||
| -rw-r--r-- | src/libnum/rational.rs | 803 |
5 files changed, 0 insertions, 4723 deletions
diff --git a/src/libnum/bigint.rs b/src/libnum/bigint.rs deleted file mode 100644 index e52d62a040b..00000000000 --- a/src/libnum/bigint.rs +++ /dev/null @@ -1,2961 +0,0 @@ -// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`). -//! -//! A `BigUint` is represented as an array of `BigDigit`s. -//! A `BigInt` is a combination of `BigUint` and `Sign`. -//! -//! Common numerical operations are overloaded, so we can treat them -//! the same way we treat other numbers. -//! -//! ## Example -//! -//! ```rust -//! # #![allow(deprecated)] -//! use num::bigint::BigUint; -//! use std::num::{Zero, One}; -//! use std::mem::replace; -//! -//! // Calculate large fibonacci numbers. -//! fn fib(n: uint) -> BigUint { -//! let mut f0: BigUint = Zero::zero(); -//! let mut f1: BigUint = One::one(); -//! for _ in range(0, n) { -//! let f2 = f0 + f1; -//! // This is a low cost way of swapping f0 with f1 and f1 with f2. -//! f0 = replace(&mut f1, f2); -//! } -//! f0 -//! } -//! -//! // This is a very large number. -//! println!("fib(1000) = {}", fib(1000)); -//! ``` -//! -//! It's easy to generate large random numbers: -//! -//! ```rust -//! # #![allow(deprecated)] -//! use num::bigint::{ToBigInt, RandBigInt}; -//! use std::rand; -//! -//! let mut rng = rand::task_rng(); -//! let a = rng.gen_bigint(1000u); -//! -//! let low = -10000i.to_bigint().unwrap(); -//! let high = 10000i.to_bigint().unwrap(); -//! let b = rng.gen_bigint_range(&low, &high); -//! -//! // Probably an even larger number. -//! println!("{}", a * b); -//! ``` - -use Integer; -use rand::Rng; - -use std::{cmp, fmt, hash}; -use std::default::Default; -use std::from_str::FromStr; -use std::num::CheckedDiv; -use std::num::{ToPrimitive, FromPrimitive}; -use std::num::{Zero, One, ToStrRadix, FromStrRadix}; -use std::string::String; -use std::{uint, i64, u64}; - -/// A `BigDigit` is a `BigUint`'s composing element. -pub type BigDigit = u32; - -/// A `DoubleBigDigit` is the internal type used to do the computations. Its -/// size is the double of the size of `BigDigit`. -pub type DoubleBigDigit = u64; - -pub const ZERO_BIG_DIGIT: BigDigit = 0; -static ZERO_VEC: [BigDigit, ..1] = [ZERO_BIG_DIGIT]; - -#[allow(non_snake_case)] -pub mod BigDigit { - use super::BigDigit; - use super::DoubleBigDigit; - - // `DoubleBigDigit` size dependent - #[allow(non_uppercase_statics)] - pub const bits: uint = 32; - - #[allow(non_uppercase_statics)] - pub const base: DoubleBigDigit = 1 << bits; - #[allow(non_uppercase_statics)] - static lo_mask: DoubleBigDigit = (-1 as DoubleBigDigit) >> bits; - - #[inline] - fn get_hi(n: DoubleBigDigit) -> BigDigit { (n >> bits) as BigDigit } - #[inline] - fn get_lo(n: DoubleBigDigit) -> BigDigit { (n & lo_mask) as BigDigit } - - /// Split one `DoubleBigDigit` into two `BigDigit`s. - #[inline] - pub fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) { - (get_hi(n), get_lo(n)) - } - - /// Join two `BigDigit`s into one `DoubleBigDigit` - #[inline] - pub fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit { - (lo as DoubleBigDigit) | ((hi as DoubleBigDigit) << bits) - } -} - -/// A big unsigned integer type. -/// -/// A `BigUint`-typed value `BigUint { data: vec!(a, b, c) }` represents a number -/// `(a + b * BigDigit::base + c * BigDigit::base^2)`. -#[deriving(Clone)] -pub struct BigUint { - data: Vec<BigDigit> -} - -impl PartialEq for BigUint { - #[inline] - fn eq(&self, other: &BigUint) -> bool { - match self.cmp(other) { Equal => true, _ => false } - } -} -impl Eq for BigUint {} - -impl PartialOrd for BigUint { - #[inline] - fn partial_cmp(&self, other: &BigUint) -> Option<Ordering> { - Some(self.cmp(other)) - } -} - -impl Ord for BigUint { - #[inline] - fn cmp(&self, other: &BigUint) -> Ordering { - let (s_len, o_len) = (self.data.len(), other.data.len()); - if s_len < o_len { return Less; } - if s_len > o_len { return Greater; } - - for (&self_i, &other_i) in self.data.iter().rev().zip(other.data.iter().rev()) { - if self_i < other_i { return Less; } - if self_i > other_i { return Greater; } - } - return Equal; - } -} - -impl Default for BigUint { - #[inline] - fn default() -> BigUint { Zero::zero() } -} - -impl<S: hash::Writer> hash::Hash<S> for BigUint { - fn hash(&self, state: &mut S) { - // hash 0 in case it's all 0's - 0u32.hash(state); - - let mut found_first_value = false; - for elem in self.data.iter().rev() { - // don't hash any leading 0's, they shouldn't affect the hash - if found_first_value || *elem != 0 { - found_first_value = true; - elem.hash(state); - } - } - } -} - -impl fmt::Show for BigUint { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}", self.to_str_radix(10)) - } -} - -impl FromStr for BigUint { - #[inline] - fn from_str(s: &str) -> Option<BigUint> { - FromStrRadix::from_str_radix(s, 10) - } -} - -impl Num for BigUint {} - -impl BitAnd<BigUint, BigUint> for BigUint { - fn bitand(&self, other: &BigUint) -> BigUint { - BigUint::new(self.data.iter().zip(other.data.iter()).map(|(ai, bi)| *ai & *bi).collect()) - } -} - -impl BitOr<BigUint, BigUint> for BigUint { - fn bitor(&self, other: &BigUint) -> BigUint { - let zeros = ZERO_VEC.iter().cycle(); - let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) }; - let ored = a.data.iter().zip(b.data.iter().chain(zeros)).map( - |(ai, bi)| *ai | *bi - ).collect(); - return BigUint::new(ored); - } -} - -impl BitXor<BigUint, BigUint> for BigUint { - fn bitxor(&self, other: &BigUint) -> BigUint { - let zeros = ZERO_VEC.iter().cycle(); - let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) }; - let xored = a.data.iter().zip(b.data.iter().chain(zeros)).map( - |(ai, bi)| *ai ^ *bi - ).collect(); - return BigUint::new(xored); - } -} - -impl Shl<uint, BigUint> for BigUint { - #[inline] - fn shl(&self, rhs: &uint) -> BigUint { - let n_unit = *rhs / BigDigit::bits; - let n_bits = *rhs % BigDigit::bits; - return self.shl_unit(n_unit).shl_bits(n_bits); - } -} - -impl Shr<uint, BigUint> for BigUint { - #[inline] - fn shr(&self, rhs: &uint) -> BigUint { - let n_unit = *rhs / BigDigit::bits; - let n_bits = *rhs % BigDigit::bits; - return self.shr_unit(n_unit).shr_bits(n_bits); - } -} - -impl Zero for BigUint { - #[inline] - fn zero() -> BigUint { BigUint::new(Vec::new()) } - - #[inline] - fn is_zero(&self) -> bool { self.data.is_empty() } -} - -impl One for BigUint { - #[inline] - fn one() -> BigUint { BigUint::new(vec!(1)) } -} - -impl Unsigned for BigUint {} - -impl Add<BigUint, BigUint> for BigUint { - fn add(&self, other: &BigUint) -> BigUint { - let zeros = ZERO_VEC.iter().cycle(); - let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) }; - - let mut carry = 0; - let mut sum: Vec<BigDigit> = a.data.iter().zip(b.data.iter().chain(zeros)).map(|(ai, bi)| { - let (hi, lo) = BigDigit::from_doublebigdigit( - (*ai as DoubleBigDigit) + (*bi as DoubleBigDigit) + (carry as DoubleBigDigit)); - carry = hi; - lo - }).collect(); - if carry != 0 { sum.push(carry); } - return BigUint::new(sum); - } -} - -impl Sub<BigUint, BigUint> for BigUint { - fn sub(&self, other: &BigUint) -> BigUint { - let new_len = cmp::max(self.data.len(), other.data.len()); - let zeros = ZERO_VEC.iter().cycle(); - let (a, b) = (self.data.iter().chain(zeros.clone()), other.data.iter().chain(zeros)); - - let mut borrow = 0i; - let diff: Vec<BigDigit> = a.take(new_len).zip(b).map(|(ai, bi)| { - let (hi, lo) = BigDigit::from_doublebigdigit( - BigDigit::base - + (*ai as DoubleBigDigit) - - (*bi as DoubleBigDigit) - - (borrow as DoubleBigDigit) - ); - /* - hi * (base) + lo == 1*(base) + ai - bi - borrow - => ai - bi - borrow < 0 <=> hi == 0 - */ - borrow = if hi == 0 { 1 } else { 0 }; - lo - }).collect(); - - assert!(borrow == 0, - "Cannot subtract other from self because other is larger than self."); - return BigUint::new(diff); - } -} - -impl Mul<BigUint, BigUint> for BigUint { - fn mul(&self, other: &BigUint) -> BigUint { - if self.is_zero() || other.is_zero() { return Zero::zero(); } - - let (s_len, o_len) = (self.data.len(), other.data.len()); - if s_len == 1 { return mul_digit(other, self.data.as_slice()[0]); } - if o_len == 1 { return mul_digit(self, other.data.as_slice()[0]); } - - // Using Karatsuba multiplication - // (a1 * base + a0) * (b1 * base + b0) - // = a1*b1 * base^2 + - // (a1*b1 + a0*b0 - (a1-b0)*(b1-a0)) * base + - // a0*b0 - let half_len = cmp::max(s_len, o_len) / 2; - let (s_hi, s_lo) = cut_at(self, half_len); - let (o_hi, o_lo) = cut_at(other, half_len); - - let ll = s_lo * o_lo; - let hh = s_hi * o_hi; - let mm = { - let (s1, n1) = sub_sign(s_hi, s_lo); - let (s2, n2) = sub_sign(o_hi, o_lo); - match (s1, s2) { - (Equal, _) | (_, Equal) => hh + ll, - (Less, Greater) | (Greater, Less) => hh + ll + (n1 * n2), - (Less, Less) | (Greater, Greater) => hh + ll - (n1 * n2) - } - }; - - return ll + mm.shl_unit(half_len) + hh.shl_unit(half_len * 2); - - - fn mul_digit(a: &BigUint, n: BigDigit) -> BigUint { - if n == 0 { return Zero::zero(); } - if n == 1 { return (*a).clone(); } - - let mut carry = 0; - let mut prod: Vec<BigDigit> = a.data.iter().map(|ai| { - let (hi, lo) = BigDigit::from_doublebigdigit( - (*ai as DoubleBigDigit) * (n as DoubleBigDigit) + (carry as DoubleBigDigit) - ); - carry = hi; - lo - }).collect(); - if carry != 0 { prod.push(carry); } - return BigUint::new(prod); - } - - #[inline] - fn cut_at(a: &BigUint, n: uint) -> (BigUint, BigUint) { - let mid = cmp::min(a.data.len(), n); - return (BigUint::from_slice(a.data.slice(mid, a.data.len())), - BigUint::from_slice(a.data.slice(0, mid))); - } - - #[inline] - fn sub_sign(a: BigUint, b: BigUint) -> (Ordering, BigUint) { - match a.cmp(&b) { - Less => (Less, b - a), - Greater => (Greater, a - b), - _ => (Equal, Zero::zero()) - } - } - } -} - -impl Div<BigUint, BigUint> for BigUint { - #[inline] - fn div(&self, other: &BigUint) -> BigUint { - let (q, _) = self.div_rem(other); - return q; - } -} - -impl Rem<BigUint, BigUint> for BigUint { - #[inline] - fn rem(&self, other: &BigUint) -> BigUint { - let (_, r) = self.div_rem(other); - return r; - } -} - -impl Neg<BigUint> for BigUint { - #[inline] - fn neg(&self) -> BigUint { fail!() } -} - -impl CheckedAdd for BigUint { - #[inline] - fn checked_add(&self, v: &BigUint) -> Option<BigUint> { - return Some(self.add(v)); - } -} - -impl CheckedSub for BigUint { - #[inline] - fn checked_sub(&self, v: &BigUint) -> Option<BigUint> { - if *self < *v { - return None; - } - return Some(self.sub(v)); - } -} - -impl CheckedMul for BigUint { - #[inline] - fn checked_mul(&self, v: &BigUint) -> Option<BigUint> { - return Some(self.mul(v)); - } -} - -impl CheckedDiv for BigUint { - #[inline] - fn checked_div(&self, v: &BigUint) -> Option<BigUint> { - if v.is_zero() { - return None; - } - return Some(self.div(v)); - } -} - -impl Integer for BigUint { - #[inline] - fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) { - self.div_mod_floor(other) - } - - #[inline] - fn div_floor(&self, other: &BigUint) -> BigUint { - let (d, _) = self.div_mod_floor(other); - return d; - } - - #[inline] - fn mod_floor(&self, other: &BigUint) -> BigUint { - let (_, m) = self.div_mod_floor(other); - return m; - } - - fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) { - if other.is_zero() { fail!() } - if self.is_zero() { return (Zero::zero(), Zero::zero()); } - if *other == One::one() { return ((*self).clone(), Zero::zero()); } - - match self.cmp(other) { - Less => return (Zero::zero(), (*self).clone()), - Equal => return (One::one(), Zero::zero()), - Greater => {} // Do nothing - } - - let mut shift = 0; - let mut n = *other.data.last().unwrap(); - while n < (1 << BigDigit::bits - 2) { - n <<= 1; - shift += 1; - } - assert!(shift < BigDigit::bits); - let (d, m) = div_mod_floor_inner(self << shift, other << shift); - return (d, m >> shift); - - - fn div_mod_floor_inner(a: BigUint, b: BigUint) -> (BigUint, BigUint) { - let mut m = a; - let mut d: BigUint = Zero::zero(); - let mut n = 1; - while m >= b { - let (d0, d_unit, b_unit) = div_estimate(&m, &b, n); - let mut d0 = d0; - let mut prod = b * d0; - while prod > m { - // FIXME(#5992): assignment operator overloads - // d0 -= d_unit - d0 = d0 - d_unit; - // FIXME(#5992): assignment operator overloads - // prod -= b_unit; - prod = prod - b_unit - } - if d0.is_zero() { - n = 2; - continue; - } - n = 1; - // FIXME(#5992): assignment operator overloads - // d += d0; - d = d + d0; - // FIXME(#5992): assignment operator overloads - // m -= prod; - m = m - prod; - } - return (d, m); - } - - - fn div_estimate(a: &BigUint, b: &BigUint, n: uint) - -> (BigUint, BigUint, BigUint) { - if a.data.len() < n { - return (Zero::zero(), Zero::zero(), (*a).clone()); - } - - let an = a.data.tailn(a.data.len() - n); - let bn = *b.data.last().unwrap(); - let mut d = Vec::with_capacity(an.len()); - let mut carry = 0; - for elt in an.iter().rev() { - let ai = BigDigit::to_doublebigdigit(carry, *elt); - let di = ai / (bn as DoubleBigDigit); - assert!(di < BigDigit::base); - carry = (ai % (bn as DoubleBigDigit)) as BigDigit; - d.push(di as BigDigit) - } - d.reverse(); - - let shift = (a.data.len() - an.len()) - (b.data.len() - 1); - if shift == 0 { - return (BigUint::new(d), One::one(), (*b).clone()); - } - let one: BigUint = One::one(); - return (BigUint::new(d).shl_unit(shift), - one.shl_unit(shift), - b.shl_unit(shift)); - } - } - - /// Calculates the Greatest Common Divisor (GCD) of the number and `other`. - /// - /// The result is always positive. - #[inline] - fn gcd(&self, other: &BigUint) -> BigUint { - // Use Euclid's algorithm - let mut m = (*self).clone(); - let mut n = (*other).clone(); - while !m.is_zero() { - let temp = m; - m = n % temp; - n = temp; - } - return n; - } - - /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. - #[inline] - fn lcm(&self, other: &BigUint) -> BigUint { ((*self * *other) / self.gcd(other)) } - - /// Deprecated, use `is_multiple_of` instead. - #[deprecated = "function renamed to `is_multiple_of`"] - #[inline] - fn divides(&self, other: &BigUint) -> bool { return self.is_multiple_of(other); } - - /// Returns `true` if the number is a multiple of `other`. - #[inline] - fn is_multiple_of(&self, other: &BigUint) -> bool { (*self % *other).is_zero() } - - /// Returns `true` if the number is divisible by `2`. - #[inline] - fn is_even(&self) -> bool { - // Considering only the last digit. - match self.data.as_slice().head() { - Some(x) => x.is_even(), - None => true - } - } - - /// Returns `true` if the number is not divisible by `2`. - #[inline] - fn is_odd(&self) -> bool { !self.is_even() } -} - -impl ToPrimitive for BigUint { - #[inline] - fn to_i64(&self) -> Option<i64> { - self.to_u64().and_then(|n| { - // If top bit of u64 is set, it's too large to convert to i64. - if n >> 63 == 0 { - Some(n as i64) - } else { - None - } - }) - } - - // `DoubleBigDigit` size dependent - #[inline] - fn to_u64(&self) -> Option<u64> { - match self.data.len() { - 0 => Some(0), - 1 => Some(self.data.as_slice()[0] as u64), - 2 => Some(BigDigit::to_doublebigdigit(self.data.as_slice()[1], self.data.as_slice()[0]) - as u64), - _ => None - } - } -} - -impl FromPrimitive for BigUint { - #[inline] - fn from_i64(n: i64) -> Option<BigUint> { - if n > 0 { - FromPrimitive::from_u64(n as u64) - } else if n == 0 { - Some(Zero::zero()) - } else { - None - } - } - - // `DoubleBigDigit` size dependent - #[inline] - fn from_u64(n: u64) -> Option<BigUint> { - let n = match BigDigit::from_doublebigdigit(n) { - (0, 0) => Zero::zero(), - (0, n0) => BigUint::new(vec!(n0)), - (n1, n0) => BigUint::new(vec!(n0, n1)) - }; - Some(n) - } -} - -/// A generic trait for converting a value to a `BigUint`. -pub trait ToBigUint { - /// Converts the value of `self` to a `BigUint`. - fn to_biguint(&self) -> Option<BigUint>; -} - -impl ToBigUint for BigInt { - #[inline] - fn to_biguint(&self) -> Option<BigUint> { - if self.sign == Plus { - Some(self.data.clone()) - } else if self.sign == NoSign { - Some(Zero::zero()) - } else { - None - } - } -} - -impl ToBigUint for BigUint { - #[inline] - fn to_biguint(&self) -> Option<BigUint> { - Some(self.clone()) - } -} - -macro_rules! impl_to_biguint( - ($T:ty, $from_ty:path) => { - impl ToBigUint for $T { - #[inline] - fn to_biguint(&self) -> Option<BigUint> { - $from_ty(*self) - } - } - } -) - -impl_to_biguint!(int, FromPrimitive::from_int) -impl_to_biguint!(i8, FromPrimitive::from_i8) -impl_to_biguint!(i16, FromPrimitive::from_i16) -impl_to_biguint!(i32, FromPrimitive::from_i32) -impl_to_biguint!(i64, FromPrimitive::from_i64) -impl_to_biguint!(uint, FromPrimitive::from_uint) -impl_to_biguint!(u8, FromPrimitive::from_u8) -impl_to_biguint!(u16, FromPrimitive::from_u16) -impl_to_biguint!(u32, FromPrimitive::from_u32) -impl_to_biguint!(u64, FromPrimitive::from_u64) - -impl ToStrRadix for BigUint { - fn to_str_radix(&self, radix: uint) -> String { - assert!(1 < radix && radix <= 16, "The radix must be within (1, 16]"); - let (base, max_len) = get_radix_base(radix); - if base == BigDigit::base { - return fill_concat(self.data.as_slice(), radix, max_len) - } - return fill_concat(convert_base(self, base).as_slice(), radix, max_len); - - fn convert_base(n: &BigUint, base: DoubleBigDigit) -> Vec<BigDigit> { - let divider = base.to_biguint().unwrap(); - let mut result = Vec::new(); - let mut m = n.clone(); - while m >= divider { - let (d, m0) = m.div_mod_floor(÷r); - result.push(m0.to_uint().unwrap() as BigDigit); - m = d; - } - if !m.is_zero() { - result.push(m.to_uint().unwrap() as BigDigit); - } - return result; - } - - fn fill_concat(v: &[BigDigit], radix: uint, l: uint) -> String { - if v.is_empty() { - return "0".to_string() - } - let mut s = String::with_capacity(v.len() * l); - for n in v.iter().rev() { - let ss = (*n as uint).to_str_radix(radix); - s.push_str("0".repeat(l - ss.len()).as_slice()); - s.push_str(ss.as_slice()); - } - s.as_slice().trim_left_chars('0').to_string() - } - } -} - -impl FromStrRadix for BigUint { - /// Creates and initializes a `BigUint`. - #[inline] - fn from_str_radix(s: &str, radix: uint) -> Option<BigUint> { - BigUint::parse_bytes(s.as_bytes(), radix) - } -} - -impl BigUint { - /// Creates and initializes a `BigUint`. - /// - /// The digits are be in base 2^32. - #[inline] - pub fn new(mut digits: Vec<BigDigit>) -> BigUint { - // omit trailing zeros - let new_len = digits.iter().rposition(|n| *n != 0).map_or(0, |p| p + 1); - digits.truncate(new_len); - BigUint { data: digits } - } - - /// Creates and initializes a `BigUint`. - /// - /// The digits are be in base 2^32. - #[inline] - pub fn from_slice(slice: &[BigDigit]) -> BigUint { - BigUint::new(Vec::from_slice(slice)) - } - - /// Creates and initializes a `BigUint`. - pub fn parse_bytes(buf: &[u8], radix: uint) -> Option<BigUint> { - let (base, unit_len) = get_radix_base(radix); - let base_num = match base.to_biguint() { - Some(base_num) => base_num, - None => { return None; } - }; - - let mut end = buf.len(); - let mut n: BigUint = Zero::zero(); - let mut power: BigUint = One::one(); - loop { - let start = cmp::max(end, unit_len) - unit_len; - match uint::parse_bytes(buf[start..end], radix) { - Some(d) => { - let d: Option<BigUint> = FromPrimitive::from_uint(d); - match d { - Some(d) => { - // FIXME(#5992): assignment operator overloads - // n += d * power; - n = n + d * power; - } - None => { return None; } - } - } - None => { return None; } - } - if end <= unit_len { - return Some(n); - } - end -= unit_len; - // FIXME(#5992): assignment operator overloads - // power *= base_num; - power = power * base_num; - } - } - - #[inline] - fn shl_unit(&self, n_unit: uint) -> BigUint { - if n_unit == 0 || self.is_zero() { return (*self).clone(); } - - BigUint::new(Vec::from_elem(n_unit, ZERO_BIG_DIGIT).append(self.data.as_slice())) - } - - #[inline] - fn shl_bits(&self, n_bits: uint) -> BigUint { - if n_bits == 0 || self.is_zero() { return (*self).clone(); } - - let mut carry = 0; - let mut shifted: Vec<BigDigit> = self.data.iter().map(|elem| { - let (hi, lo) = BigDigit::from_doublebigdigit( - (*elem as DoubleBigDigit) << n_bits | (carry as DoubleBigDigit) - ); - carry = hi; - lo - }).collect(); - if carry != 0 { shifted.push(carry); } - return BigUint::new(shifted); - } - - #[inline] - fn shr_unit(&self, n_unit: uint) -> BigUint { - if n_unit == 0 { return (*self).clone(); } - if self.data.len() < n_unit { return Zero::zero(); } - return BigUint::from_slice( - self.data.slice(n_unit, self.data.len()) - ); - } - - #[inline] - fn shr_bits(&self, n_bits: uint) -> BigUint { - if n_bits == 0 || self.data.is_empty() { return (*self).clone(); } - - let mut borrow = 0; - let mut shifted_rev = Vec::with_capacity(self.data.len()); - for elem in self.data.iter().rev() { - shifted_rev.push((*elem >> n_bits) | borrow); - borrow = *elem << (BigDigit::bits - n_bits); - } - let shifted = { shifted_rev.reverse(); shifted_rev }; - return BigUint::new(shifted); - } - - /// Determines the fewest bits necessary to express the `BigUint`. - pub fn bits(&self) -> uint { - if self.is_zero() { return 0; } - let zeros = self.data.last().unwrap().leading_zeros(); - return self.data.len()*BigDigit::bits - zeros; - } -} - -// `DoubleBigDigit` size dependent -#[inline] -fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) { - match radix { - 2 => (4294967296, 32), - 3 => (3486784401, 20), - 4 => (4294967296, 16), - 5 => (1220703125, 13), - 6 => (2176782336, 12), - 7 => (1977326743, 11), - 8 => (1073741824, 10), - 9 => (3486784401, 10), - 10 => (1000000000, 9), - 11 => (2357947691, 9), - 12 => (429981696, 8), - 13 => (815730721, 8), - 14 => (1475789056, 8), - 15 => (2562890625, 8), - 16 => (4294967296, 8), - _ => fail!("The radix must be within (1, 16]") - } -} - -/// A Sign is a `BigInt`'s composing element. -#[deriving(PartialEq, PartialOrd, Eq, Ord, Clone, Show)] -pub enum Sign { Minus, NoSign, Plus } - -impl Neg<Sign> for Sign { - /// Negate Sign value. - #[inline] - fn neg(&self) -> Sign { - match *self { - Minus => Plus, - NoSign => NoSign, - Plus => Minus - } - } -} - -/// A big signed integer type. -#[deriving(Clone)] -pub struct BigInt { - sign: Sign, - data: BigUint -} - -impl PartialEq for BigInt { - #[inline] - fn eq(&self, other: &BigInt) -> bool { - self.cmp(other) == Equal - } -} - -impl Eq for BigInt {} - -impl PartialOrd for BigInt { - #[inline] - fn partial_cmp(&self, other: &BigInt) -> Option<Ordering> { - Some(self.cmp(other)) - } -} - -impl Ord for BigInt { - #[inline] - fn cmp(&self, other: &BigInt) -> Ordering { - let scmp = self.sign.cmp(&other.sign); - if scmp != Equal { return scmp; } - - match self.sign { - NoSign => Equal, - Plus => self.data.cmp(&other.data), - Minus => other.data.cmp(&self.data), - } - } -} - -impl Default for BigInt { - #[inline] - fn default() -> BigInt { Zero::zero() } -} - -impl fmt::Show for BigInt { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}", self.to_str_radix(10)) - } -} - -impl<S: hash::Writer> hash::Hash<S> for BigInt { - fn hash(&self, state: &mut S) { - (self.sign == Plus).hash(state); - self.data.hash(state); - } -} - -impl FromStr for BigInt { - #[inline] - fn from_str(s: &str) -> Option<BigInt> { - FromStrRadix::from_str_radix(s, 10) - } -} - -impl Num for BigInt {} - -impl Shl<uint, BigInt> for BigInt { - #[inline] - fn shl(&self, rhs: &uint) -> BigInt { - BigInt::from_biguint(self.sign, self.data << *rhs) - } -} - -impl Shr<uint, BigInt> for BigInt { - #[inline] - fn shr(&self, rhs: &uint) -> BigInt { - BigInt::from_biguint(self.sign, self.data >> *rhs) - } -} - -impl Zero for BigInt { - #[inline] - fn zero() -> BigInt { - BigInt::from_biguint(NoSign, Zero::zero()) - } - - #[inline] - fn is_zero(&self) -> bool { self.sign == NoSign } -} - -impl One for BigInt { - #[inline] - fn one() -> BigInt { - BigInt::from_biguint(Plus, One::one()) - } -} - -impl Signed for BigInt { - #[inline] - fn abs(&self) -> BigInt { - match self.sign { - Plus | NoSign => self.clone(), - Minus => BigInt::from_biguint(Plus, self.data.clone()) - } - } - - #[inline] - fn abs_sub(&self, other: &BigInt) -> BigInt { - if *self <= *other { Zero::zero() } else { *self - *other } - } - - #[inline] - fn signum(&self) -> BigInt { - match self.sign { - Plus => BigInt::from_biguint(Plus, One::one()), - Minus => BigInt::from_biguint(Minus, One::one()), - NoSign => Zero::zero(), - } - } - - #[inline] - fn is_positive(&self) -> bool { self.sign == Plus } - - #[inline] - fn is_negative(&self) -> bool { self.sign == Minus } -} - -impl Add<BigInt, BigInt> for BigInt { - #[inline] - fn add(&self, other: &BigInt) -> BigInt { - match (self.sign, other.sign) { - (NoSign, _) => other.clone(), - (_, NoSign) => self.clone(), - (Plus, Plus) => BigInt::from_biguint(Plus, self.data + other.data), - (Plus, Minus) => self - (-*other), - (Minus, Plus) => other - (-*self), - (Minus, Minus) => -((-self) + (-*other)) - } - } -} - -impl Sub<BigInt, BigInt> for BigInt { - #[inline] - fn sub(&self, other: &BigInt) -> BigInt { - match (self.sign, other.sign) { - (NoSign, _) => -other, - (_, NoSign) => self.clone(), - (Plus, Plus) => match self.data.cmp(&other.data) { - Less => BigInt::from_biguint(Minus, other.data - self.data), - Greater => BigInt::from_biguint(Plus, self.data - other.data), - Equal => Zero::zero() - }, - (Plus, Minus) => self + (-*other), - (Minus, Plus) => -((-self) + *other), - (Minus, Minus) => (-other) - (-*self) - } - } -} - -impl Mul<BigInt, BigInt> for BigInt { - #[inline] - fn mul(&self, other: &BigInt) -> BigInt { - match (self.sign, other.sign) { - (NoSign, _) | (_, NoSign) => Zero::zero(), - (Plus, Plus) | (Minus, Minus) => { - BigInt::from_biguint(Plus, self.data * other.data) - }, - (Plus, Minus) | (Minus, Plus) => { - BigInt::from_biguint(Minus, self.data * other.data) - } - } - } -} - -impl Div<BigInt, BigInt> for BigInt { - #[inline] - fn div(&self, other: &BigInt) -> BigInt { - let (q, _) = self.div_rem(other); - q - } -} - -impl Rem<BigInt, BigInt> for BigInt { - #[inline] - fn rem(&self, other: &BigInt) -> BigInt { - let (_, r) = self.div_rem(other); - r - } -} - -impl Neg<BigInt> for BigInt { - #[inline] - fn neg(&self) -> BigInt { - BigInt::from_biguint(self.sign.neg(), self.data.clone()) - } -} - -impl CheckedAdd for BigInt { - #[inline] - fn checked_add(&self, v: &BigInt) -> Option<BigInt> { - return Some(self.add(v)); - } -} - -impl CheckedSub for BigInt { - #[inline] - fn checked_sub(&self, v: &BigInt) -> Option<BigInt> { - return Some(self.sub(v)); - } -} - -impl CheckedMul for BigInt { - #[inline] - fn checked_mul(&self, v: &BigInt) -> Option<BigInt> { - return Some(self.mul(v)); - } -} - -impl CheckedDiv for BigInt { - #[inline] - fn checked_div(&self, v: &BigInt) -> Option<BigInt> { - if v.is_zero() { - return None; - } - return Some(self.div(v)); - } -} - - -impl Integer for BigInt { - #[inline] - fn div_rem(&self, other: &BigInt) -> (BigInt, BigInt) { - // r.sign == self.sign - let (d_ui, r_ui) = self.data.div_mod_floor(&other.data); - let d = BigInt::from_biguint(Plus, d_ui); - let r = BigInt::from_biguint(Plus, r_ui); - match (self.sign, other.sign) { - (_, NoSign) => fail!(), - (Plus, Plus) | (NoSign, Plus) => ( d, r), - (Plus, Minus) | (NoSign, Minus) => (-d, r), - (Minus, Plus) => (-d, -r), - (Minus, Minus) => ( d, -r) - } - } - - #[inline] - fn div_floor(&self, other: &BigInt) -> BigInt { - let (d, _) = self.div_mod_floor(other); - d - } - - #[inline] - fn mod_floor(&self, other: &BigInt) -> BigInt { - let (_, m) = self.div_mod_floor(other); - m - } - - fn div_mod_floor(&self, other: &BigInt) -> (BigInt, BigInt) { - // m.sign == other.sign - let (d_ui, m_ui) = self.data.div_rem(&other.data); - let d = BigInt::from_biguint(Plus, d_ui); - let m = BigInt::from_biguint(Plus, m_ui); - match (self.sign, other.sign) { - (_, NoSign) => fail!(), - (Plus, Plus) | (NoSign, Plus) => (d, m), - (Plus, Minus) | (NoSign, Minus) => if m.is_zero() { - (-d, Zero::zero()) - } else { - (-d - One::one(), m + *other) - }, - (Minus, Plus) => if m.is_zero() { - (-d, Zero::zero()) - } else { - (-d - One::one(), other - m) - }, - (Minus, Minus) => (d, -m) - } - } - - /// Calculates the Greatest Common Divisor (GCD) of the number and `other`. - /// - /// The result is always positive. - #[inline] - fn gcd(&self, other: &BigInt) -> BigInt { - BigInt::from_biguint(Plus, self.data.gcd(&other.data)) - } - - /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. - #[inline] - fn lcm(&self, other: &BigInt) -> BigInt { - BigInt::from_biguint(Plus, self.data.lcm(&other.data)) - } - - /// Deprecated, use `is_multiple_of` instead. - #[deprecated = "function renamed to `is_multiple_of`"] - #[inline] - fn divides(&self, other: &BigInt) -> bool { return self.is_multiple_of(other); } - - /// Returns `true` if the number is a multiple of `other`. - #[inline] - fn is_multiple_of(&self, other: &BigInt) -> bool { self.data.is_multiple_of(&other.data) } - - /// Returns `true` if the number is divisible by `2`. - #[inline] - fn is_even(&self) -> bool { self.data.is_even() } - - /// Returns `true` if the number is not divisible by `2`. - #[inline] - fn is_odd(&self) -> bool { self.data.is_odd() } -} - -impl ToPrimitive for BigInt { - #[inline] - fn to_i64(&self) -> Option<i64> { - match self.sign { - Plus => self.data.to_i64(), - NoSign => Some(0), - Minus => { - self.data.to_u64().and_then(|n| { - let m: u64 = 1 << 63; - if n < m { - Some(-(n as i64)) - } else if n == m { - Some(i64::MIN) - } else { - None - } - }) - } - } - } - - #[inline] - fn to_u64(&self) -> Option<u64> { - match self.sign { - Plus => self.data.to_u64(), - NoSign => Some(0), - Minus => None - } - } -} - -impl FromPrimitive for BigInt { - #[inline] - fn from_i64(n: i64) -> Option<BigInt> { - if n > 0 { - FromPrimitive::from_u64(n as u64).and_then(|n| { - Some(BigInt::from_biguint(Plus, n)) - }) - } else if n < 0 { - FromPrimitive::from_u64(u64::MAX - (n as u64) + 1).and_then( - |n| { - Some(BigInt::from_biguint(Minus, n)) - }) - } else { - Some(Zero::zero()) - } - } - - #[inline] - fn from_u64(n: u64) -> Option<BigInt> { - if n == 0 { - Some(Zero::zero()) - } else { - FromPrimitive::from_u64(n).and_then(|n| { - Some(BigInt::from_biguint(Plus, n)) - }) - } - } -} - -/// A generic trait for converting a value to a `BigInt`. -pub trait ToBigInt { - /// Converts the value of `self` to a `BigInt`. - fn to_bigint(&self) -> Option<BigInt>; -} - -impl ToBigInt for BigInt { - #[inline] - fn to_bigint(&self) -> Option<BigInt> { - Some(self.clone()) - } -} - -impl ToBigInt for BigUint { - #[inline] - fn to_bigint(&self) -> Option<BigInt> { - if self.is_zero() { - Some(Zero::zero()) - } else { - Some(BigInt { sign: Plus, data: self.clone() }) - } - } -} - -macro_rules! impl_to_bigint( - ($T:ty, $from_ty:path) => { - impl ToBigInt for $T { - #[inline] - fn to_bigint(&self) -> Option<BigInt> { - $from_ty(*self) - } - } - } -) - -impl_to_bigint!(int, FromPrimitive::from_int) -impl_to_bigint!(i8, FromPrimitive::from_i8) -impl_to_bigint!(i16, FromPrimitive::from_i16) -impl_to_bigint!(i32, FromPrimitive::from_i32) -impl_to_bigint!(i64, FromPrimitive::from_i64) -impl_to_bigint!(uint, FromPrimitive::from_uint) -impl_to_bigint!(u8, FromPrimitive::from_u8) -impl_to_bigint!(u16, FromPrimitive::from_u16) -impl_to_bigint!(u32, FromPrimitive::from_u32) -impl_to_bigint!(u64, FromPrimitive::from_u64) - -impl ToStrRadix for BigInt { - #[inline] - fn to_str_radix(&self, radix: uint) -> String { - match self.sign { - Plus => self.data.to_str_radix(radix), - NoSign => "0".to_string(), - Minus => format!("-{}", self.data.to_str_radix(radix)), - } - } -} - -impl FromStrRadix for BigInt { - /// Creates and initializes a BigInt. - #[inline] - fn from_str_radix(s: &str, radix: uint) -> Option<BigInt> { - BigInt::parse_bytes(s.as_bytes(), radix) - } -} - -pub trait RandBigInt { - /// Generate a random `BigUint` of the given bit size. - fn gen_biguint(&mut self, bit_size: uint) -> BigUint; - - /// Generate a random BigInt of the given bit size. - fn gen_bigint(&mut self, bit_size: uint) -> BigInt; - - /// Generate a random `BigUint` less than the given bound. Fails - /// when the bound is zero. - fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint; - - /// Generate a random `BigUint` within the given range. The lower - /// bound is inclusive; the upper bound is exclusive. Fails when - /// the upper bound is not greater than the lower bound. - fn gen_biguint_range(&mut self, lbound: &BigUint, ubound: &BigUint) -> BigUint; - - /// Generate a random `BigInt` within the given range. The lower - /// bound is inclusive; the upper bound is exclusive. Fails when - /// the upper bound is not greater than the lower bound. - fn gen_bigint_range(&mut self, lbound: &BigInt, ubound: &BigInt) -> BigInt; -} - -impl<R: Rng> RandBigInt for R { - fn gen_biguint(&mut self, bit_size: uint) -> BigUint { - let (digits, rem) = bit_size.div_rem(&BigDigit::bits); - let mut data = Vec::with_capacity(digits+1); - for _ in range(0, digits) { - data.push(self.gen()); - } - if rem > 0 { - let final_digit: BigDigit = self.gen(); - data.push(final_digit >> (BigDigit::bits - rem)); - } - BigUint::new(data) - } - - fn gen_bigint(&mut self, bit_size: uint) -> BigInt { - // Generate a random BigUint... - let biguint = self.gen_biguint(bit_size); - // ...and then randomly assign it a Sign... - let sign = if biguint.is_zero() { - // ...except that if the BigUint is zero, we need to try - // again with probability 0.5. This is because otherwise, - // the probability of generating a zero BigInt would be - // double that of any other number. - if self.gen() { - return self.gen_bigint(bit_size); - } else { - NoSign - } - } else if self.gen() { - Plus - } else { - Minus - }; - BigInt::from_biguint(sign, biguint) - } - - fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint { - assert!(!bound.is_zero()); - let bits = bound.bits(); - loop { - let n = self.gen_biguint(bits); - if n < *bound { return n; } - } - } - - fn gen_biguint_range(&mut self, - lbound: &BigUint, - ubound: &BigUint) - -> BigUint { - assert!(*lbound < *ubound); - return *lbound + self.gen_biguint_below(&(*ubound - *lbound)); - } - - fn gen_bigint_range(&mut self, - lbound: &BigInt, - ubound: &BigInt) - -> BigInt { - assert!(*lbound < *ubound); - let delta = (*ubound - *lbound).to_biguint().unwrap(); - return *lbound + self.gen_biguint_below(&delta).to_bigint().unwrap(); - } -} - -impl BigInt { - /// Creates and initializes a BigInt. - /// - /// The digits are be in base 2^32. - #[inline] - pub fn new(sign: Sign, digits: Vec<BigDigit>) -> BigInt { - BigInt::from_biguint(sign, BigUint::new(digits)) - } - - /// Creates and initializes a `BigInt`. - /// - /// The digits are be in base 2^32. - #[inline] - pub fn from_biguint(sign: Sign, data: BigUint) -> BigInt { - if sign == NoSign || data.is_zero() { - return BigInt { sign: NoSign, data: Zero::zero() }; - } - BigInt { sign: sign, data: data } - } - - /// Creates and initializes a `BigInt`. - #[inline] - pub fn from_slice(sign: Sign, slice: &[BigDigit]) -> BigInt { - BigInt::from_biguint(sign, BigUint::from_slice(slice)) - } - - /// Creates and initializes a `BigInt`. - pub fn parse_bytes(buf: &[u8], radix: uint) -> Option<BigInt> { - if buf.is_empty() { return None; } - let mut sign = Plus; - let mut start = 0; - if buf[0] == b'-' { - sign = Minus; - start = 1; - } - return BigUint::parse_bytes(buf[start..], radix) - .map(|bu| BigInt::from_biguint(sign, bu)); - } - - /// Converts this `BigInt` into a `BigUint`, if it's not negative. - #[inline] - pub fn to_biguint(&self) -> Option<BigUint> { - match self.sign { - Plus => Some(self.data.clone()), - NoSign => Some(Zero::zero()), - Minus => None - } - } -} - -#[cfg(test)] -mod biguint_tests { - use Integer; - use super::{BigDigit, BigUint, ToBigUint}; - use super::{Plus, BigInt, RandBigInt, ToBigInt}; - - use std::cmp::{Less, Equal, Greater}; - use std::from_str::FromStr; - use std::i64; - use std::num::{Zero, One, FromStrRadix, ToStrRadix}; - use std::num::{ToPrimitive, FromPrimitive}; - use std::num::CheckedDiv; - use std::rand::task_rng; - use std::u64; - use std::hash::hash; - - #[test] - fn test_from_slice() { - fn check(slice: &[BigDigit], data: &[BigDigit]) { - assert!(data == BigUint::from_slice(slice).data.as_slice()); - } - check([1], [1]); - check([0, 0, 0], []); - check([1, 2, 0, 0], [1, 2]); - check([0, 0, 1, 2], [0, 0, 1, 2]); - check([0, 0, 1, 2, 0, 0], [0, 0, 1, 2]); - check([-1], [-1]); - } - - #[test] - fn test_cmp() { - let data: [&[_], ..7] = [ &[], &[1], &[2], &[-1], &[0, 1], &[2, 1], &[1, 1, 1] ]; - let data: Vec<BigUint> = data.iter().map(|v| BigUint::from_slice(*v)).collect(); - for (i, ni) in data.iter().enumerate() { - for (j0, nj) in data.slice(i, data.len()).iter().enumerate() { - let j = j0 + i; - if i == j { - assert_eq!(ni.cmp(nj), Equal); - assert_eq!(nj.cmp(ni), Equal); - assert_eq!(ni, nj); - assert!(!(ni != nj)); - assert!(ni <= nj); - assert!(ni >= nj); - assert!(!(ni < nj)); - assert!(!(ni > nj)); - } else { - assert_eq!(ni.cmp(nj), Less); - assert_eq!(nj.cmp(ni), Greater); - - assert!(!(ni == nj)); - assert!(ni != nj); - - assert!(ni <= nj); - assert!(!(ni >= nj)); - assert!(ni < nj); - assert!(!(ni > nj)); - - assert!(!(nj <= ni)); - assert!(nj >= ni); - assert!(!(nj < ni)); - assert!(nj > ni); - } - } - } - } - - #[test] - fn test_hash() { - let a = BigUint::new(vec!()); - let b = BigUint::new(vec!(0)); - let c = BigUint::new(vec!(1)); - let d = BigUint::new(vec!(1,0,0,0,0,0)); - let e = BigUint::new(vec!(0,0,0,0,0,1)); - assert!(hash(&a) == hash(&b)); - assert!(hash(&b) != hash(&c)); - assert!(hash(&c) == hash(&d)); - assert!(hash(&d) != hash(&e)); - } - - #[test] - fn test_bitand() { - fn check(left: &[BigDigit], - right: &[BigDigit], - expected: &[BigDigit]) { - assert_eq!(BigUint::from_slice(left) & BigUint::from_slice(right), - BigUint::from_slice(expected)); - } - check([], [], []); - check([268, 482, 17], - [964, 54], - [260, 34]); - } - - #[test] - fn test_bitor() { - fn check(left: &[BigDigit], - right: &[BigDigit], - expected: &[BigDigit]) { - assert_eq!(BigUint::from_slice(left) | BigUint::from_slice(right), - BigUint::from_slice(expected)); - } - check([], [], []); - check([268, 482, 17], - [964, 54], - [972, 502, 17]); - } - - #[test] - fn test_bitxor() { - fn check(left: &[BigDigit], - right: &[BigDigit], - expected: &[BigDigit]) { - assert_eq!(BigUint::from_slice(left) ^ BigUint::from_slice(right), - BigUint::from_slice(expected)); - } - check([], [], []); - check([268, 482, 17], - [964, 54], - [712, 468, 17]); - } - - #[test] - fn test_shl() { - fn check(s: &str, shift: uint, ans: &str) { - let opt_biguint: Option<BigUint> = FromStrRadix::from_str_radix(s, 16); - let bu = (opt_biguint.unwrap() << shift).to_str_radix(16); - assert_eq!(bu.as_slice(), ans); - } - - check("0", 3, "0"); - check("1", 3, "8"); - - check("1\ - 0000\ - 0000\ - 0000\ - 0001\ - 0000\ - 0000\ - 0000\ - 0001", - 3, - "8\ - 0000\ - 0000\ - 0000\ - 0008\ - 0000\ - 0000\ - 0000\ - 0008"); - check("1\ - 0000\ - 0001\ - 0000\ - 0001", - 2, - "4\ - 0000\ - 0004\ - 0000\ - 0004"); - check("1\ - 0001\ - 0001", - 1, - "2\ - 0002\ - 0002"); - - check("\ - 4000\ - 0000\ - 0000\ - 0000", - 3, - "2\ - 0000\ - 0000\ - 0000\ - 0000"); - check("4000\ - 0000", - 2, - "1\ - 0000\ - 0000"); - check("4000", - 2, - "1\ - 0000"); - - check("4000\ - 0000\ - 0000\ - 0000", - 67, - "2\ - 0000\ - 0000\ - 0000\ - 0000\ - 0000\ - 0000\ - 0000\ - 0000"); - check("4000\ - 0000", - 35, - "2\ - 0000\ - 0000\ - 0000\ - 0000"); - check("4000", - 19, - "2\ - 0000\ - 0000"); - - check("fedc\ - ba98\ - 7654\ - 3210\ - fedc\ - ba98\ - 7654\ - 3210", - 4, - "f\ - edcb\ - a987\ - 6543\ - 210f\ - edcb\ - a987\ - 6543\ - 2100"); - check("88887777666655554444333322221111", 16, - "888877776666555544443333222211110000"); - } - - #[test] - fn test_shr() { - fn check(s: &str, shift: uint, ans: &str) { - let opt_biguint: Option<BigUint> = - FromStrRadix::from_str_radix(s, 16); - let bu = (opt_biguint.unwrap() >> shift).to_str_radix(16); - assert_eq!(bu.as_slice(), ans); - } - - check("0", 3, "0"); - check("f", 3, "1"); - - check("1\ - 0000\ - 0000\ - 0000\ - 0001\ - 0000\ - 0000\ - 0000\ - 0001", - 3, - "2000\ - 0000\ - 0000\ - 0000\ - 2000\ - 0000\ - 0000\ - 0000"); - check("1\ - 0000\ - 0001\ - 0000\ - 0001", - 2, - "4000\ - 0000\ - 4000\ - 0000"); - check("1\ - 0001\ - 0001", - 1, - "8000\ - 8000"); - - check("2\ - 0000\ - 0000\ - 0000\ - 0001\ - 0000\ - 0000\ - 0000\ - 0001", - 67, - "4000\ - 0000\ - 0000\ - 0000"); - check("2\ - 0000\ - 0001\ - 0000\ - 0001", - 35, - "4000\ - 0000"); - check("2\ - 0001\ - 0001", - 19, - "4000"); - - check("1\ - 0000\ - 0000\ - 0000\ - 0000", - 1, - "8000\ - 0000\ - 0000\ - 0000"); - check("1\ - 0000\ - 0000", - 1, - "8000\ - 0000"); - check("1\ - 0000", - 1, - "8000"); - check("f\ - edcb\ - a987\ - 6543\ - 210f\ - edcb\ - a987\ - 6543\ - 2100", - 4, - "fedc\ - ba98\ - 7654\ - 3210\ - fedc\ - ba98\ - 7654\ - 3210"); - - check("888877776666555544443333222211110000", 16, - "88887777666655554444333322221111"); - } - - // `DoubleBigDigit` size dependent - #[test] - fn test_convert_i64() { - fn check(b1: BigUint, i: i64) { - let b2: BigUint = FromPrimitive::from_i64(i).unwrap(); - assert!(b1 == b2); - assert!(b1.to_i64().unwrap() == i); - } - - check(Zero::zero(), 0); - check(One::one(), 1); - check(i64::MAX.to_biguint().unwrap(), i64::MAX); - - check(BigUint::new(vec!( )), 0); - check(BigUint::new(vec!( 1 )), (1 << (0*BigDigit::bits))); - check(BigUint::new(vec!(-1 )), (1 << (1*BigDigit::bits)) - 1); - check(BigUint::new(vec!( 0, 1 )), (1 << (1*BigDigit::bits))); - check(BigUint::new(vec!(-1, -1 >> 1)), i64::MAX); - - assert_eq!(i64::MIN.to_biguint(), None); - assert_eq!(BigUint::new(vec!(-1, -1 )).to_i64(), None); - assert_eq!(BigUint::new(vec!( 0, 0, 1)).to_i64(), None); - assert_eq!(BigUint::new(vec!(-1, -1, -1)).to_i64(), None); - } - - // `DoubleBigDigit` size dependent - #[test] - fn test_convert_u64() { - fn check(b1: BigUint, u: u64) { - let b2: BigUint = FromPrimitive::from_u64(u).unwrap(); - assert!(b1 == b2); - assert!(b1.to_u64().unwrap() == u); - } - - check(Zero::zero(), 0); - check(One::one(), 1); - check(u64::MIN.to_biguint().unwrap(), u64::MIN); - check(u64::MAX.to_biguint().unwrap(), u64::MAX); - - check(BigUint::new(vec!( )), 0); - check(BigUint::new(vec!( 1 )), (1 << (0*BigDigit::bits))); - check(BigUint::new(vec!(-1 )), (1 << (1*BigDigit::bits)) - 1); - check(BigUint::new(vec!( 0, 1)), (1 << (1*BigDigit::bits))); - check(BigUint::new(vec!(-1, -1)), u64::MAX); - - assert_eq!(BigUint::new(vec!( 0, 0, 1)).to_u64(), None); - assert_eq!(BigUint::new(vec!(-1, -1, -1)).to_u64(), None); - } - - #[test] - fn test_convert_to_bigint() { - fn check(n: BigUint, ans: BigInt) { - assert_eq!(n.to_bigint().unwrap(), ans); - assert_eq!(n.to_bigint().unwrap().to_biguint().unwrap(), n); - } - check(Zero::zero(), Zero::zero()); - check(BigUint::new(vec!(1,2,3)), - BigInt::from_biguint(Plus, BigUint::new(vec!(1,2,3)))); - } - - static SUM_TRIPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] = &[ - (&[], &[], &[]), - (&[], &[ 1], &[ 1]), - (&[ 1], &[ 1], &[ 2]), - (&[ 1], &[ 1, 1], &[ 2, 1]), - (&[ 1], &[-1], &[ 0, 1]), - (&[ 1], &[-1, -1], &[ 0, 0, 1]), - (&[-1, -1], &[-1, -1], &[-2, -1, 1]), - (&[ 1, 1, 1], &[-1, -1], &[ 0, 1, 2]), - (&[ 2, 2, 1], &[-1, -2], &[ 1, 1, 2]) - ]; - - #[test] - fn test_add() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - assert!(a + b == c); - assert!(b + a == c); - } - } - - #[test] - fn test_sub() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - assert!(c - a == b); - assert!(c - b == a); - } - } - - #[test] - #[should_fail] - fn test_sub_fail_on_underflow() { - let (a, b) : (BigUint, BigUint) = (Zero::zero(), One::one()); - a - b; - } - - static MUL_TRIPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] = &[ - (&[], &[], &[]), - (&[], &[ 1], &[]), - (&[ 2], &[], &[]), - (&[ 1], &[ 1], &[1]), - (&[ 2], &[ 3], &[ 6]), - (&[ 1], &[ 1, 1, 1], &[1, 1, 1]), - (&[ 1, 2, 3], &[ 3], &[ 3, 6, 9]), - (&[ 1, 1, 1], &[-1], &[-1, -1, -1]), - (&[ 1, 2, 3], &[-1], &[-1, -2, -2, 2]), - (&[ 1, 2, 3, 4], &[-1], &[-1, -2, -2, -2, 3]), - (&[-1], &[-1], &[ 1, -2]), - (&[-1, -1], &[-1], &[ 1, -1, -2]), - (&[-1, -1, -1], &[-1], &[ 1, -1, -1, -2]), - (&[-1, -1, -1, -1], &[-1], &[ 1, -1, -1, -1, -2]), - (&[-1/2 + 1], &[ 2], &[ 0, 1]), - (&[0, -1/2 + 1], &[ 2], &[ 0, 0, 1]), - (&[ 1, 2], &[ 1, 2, 3], &[1, 4, 7, 6]), - (&[-1, -1], &[-1, -1, -1], &[1, 0, -1, -2, -1]), - (&[-1, -1, -1], &[-1, -1, -1, -1], &[1, 0, 0, -1, -2, -1, -1]), - (&[ 0, 0, 1], &[ 1, 2, 3], &[0, 0, 1, 2, 3]), - (&[ 0, 0, 1], &[ 0, 0, 0, 1], &[0, 0, 0, 0, 0, 1]) - ]; - - static DIV_REM_QUADRUPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] - = &[ - (&[ 1], &[ 2], &[], &[1]), - (&[ 1, 1], &[ 2], &[-1/2+1], &[1]), - (&[ 1, 1, 1], &[ 2], &[-1/2+1, -1/2+1], &[1]), - (&[ 0, 1], &[-1], &[1], &[1]), - (&[-1, -1], &[-2], &[2, 1], &[3]) - ]; - - #[test] - fn test_mul() { - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - assert!(a * b == c); - assert!(b * a == c); - } - - for elm in DIV_REM_QUADRUPLES.iter() { - let (a_vec, b_vec, c_vec, d_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - let d = BigUint::from_slice(d_vec); - - assert!(a == b * c + d); - assert!(a == c * b + d); - } - } - - #[test] - fn test_div_rem() { - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - if !a.is_zero() { - assert_eq!(c.div_rem(&a), (b.clone(), Zero::zero())); - } - if !b.is_zero() { - assert_eq!(c.div_rem(&b), (a.clone(), Zero::zero())); - } - } - - for elm in DIV_REM_QUADRUPLES.iter() { - let (a_vec, b_vec, c_vec, d_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - let d = BigUint::from_slice(d_vec); - - if !b.is_zero() { assert!(a.div_rem(&b) == (c, d)); } - } - } - - #[test] - fn test_checked_add() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - assert!(a.checked_add(&b).unwrap() == c); - assert!(b.checked_add(&a).unwrap() == c); - } - } - - #[test] - fn test_checked_sub() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - assert!(c.checked_sub(&a).unwrap() == b); - assert!(c.checked_sub(&b).unwrap() == a); - - if a > c { - assert!(a.checked_sub(&c).is_none()); - } - if b > c { - assert!(b.checked_sub(&c).is_none()); - } - } - } - - #[test] - fn test_checked_mul() { - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - assert!(a.checked_mul(&b).unwrap() == c); - assert!(b.checked_mul(&a).unwrap() == c); - } - - for elm in DIV_REM_QUADRUPLES.iter() { - let (a_vec, b_vec, c_vec, d_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - let d = BigUint::from_slice(d_vec); - - assert!(a == b.checked_mul(&c).unwrap() + d); - assert!(a == c.checked_mul(&b).unwrap() + d); - } - } - - #[test] - fn test_checked_div() { - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigUint::from_slice(a_vec); - let b = BigUint::from_slice(b_vec); - let c = BigUint::from_slice(c_vec); - - if !a.is_zero() { - assert!(c.checked_div(&a).unwrap() == b); - } - if !b.is_zero() { - assert!(c.checked_div(&b).unwrap() == a); - } - - assert!(c.checked_div(&Zero::zero()).is_none()); - } - } - - #[test] - fn test_gcd() { - fn check(a: uint, b: uint, c: uint) { - let big_a: BigUint = FromPrimitive::from_uint(a).unwrap(); - let big_b: BigUint = FromPrimitive::from_uint(b).unwrap(); - let big_c: BigUint = FromPrimitive::from_uint(c).unwrap(); - - assert_eq!(big_a.gcd(&big_b), big_c); - } - - check(10, 2, 2); - check(10, 3, 1); - check(0, 3, 3); - check(3, 3, 3); - check(56, 42, 14); - } - - #[test] - fn test_lcm() { - fn check(a: uint, b: uint, c: uint) { - let big_a: BigUint = FromPrimitive::from_uint(a).unwrap(); - let big_b: BigUint = FromPrimitive::from_uint(b).unwrap(); - let big_c: BigUint = FromPrimitive::from_uint(c).unwrap(); - - assert_eq!(big_a.lcm(&big_b), big_c); - } - - check(1, 0, 0); - check(0, 1, 0); - check(1, 1, 1); - check(8, 9, 72); - check(11, 5, 55); - check(99, 17, 1683); - } - - #[test] - fn test_is_even() { - let one: BigUint = FromStr::from_str("1").unwrap(); - let two: BigUint = FromStr::from_str("2").unwrap(); - let thousand: BigUint = FromStr::from_str("1000").unwrap(); - let big: BigUint = FromStr::from_str("1000000000000000000000").unwrap(); - let bigger: BigUint = FromStr::from_str("1000000000000000000001").unwrap(); - assert!(one.is_odd()); - assert!(two.is_even()); - assert!(thousand.is_even()); - assert!(big.is_even()); - assert!(bigger.is_odd()); - assert!((one << 64).is_even()); - assert!(((one << 64) + one).is_odd()); - } - - fn to_str_pairs() -> Vec<(BigUint, Vec<(uint, String)>)> { - let bits = BigDigit::bits; - vec!(( Zero::zero(), vec!( - (2, "0".to_string()), (3, "0".to_string()) - )), ( BigUint::from_slice([ 0xff ]), vec!( - (2, "11111111".to_string()), - (3, "100110".to_string()), - (4, "3333".to_string()), - (5, "2010".to_string()), - (6, "1103".to_string()), - (7, "513".to_string()), - (8, "377".to_string()), - (9, "313".to_string()), - (10, "255".to_string()), - (11, "212".to_string()), - (12, "193".to_string()), - (13, "168".to_string()), - (14, "143".to_string()), - (15, "120".to_string()), - (16, "ff".to_string()) - )), ( BigUint::from_slice([ 0xfff ]), vec!( - (2, "111111111111".to_string()), - (4, "333333".to_string()), - (16, "fff".to_string()) - )), ( BigUint::from_slice([ 1, 2 ]), vec!( - (2, - format!("10{}1", "0".repeat(bits - 1))), - (4, - format!("2{}1", "0".repeat(bits / 2 - 1))), - (10, match bits { - 32 => "8589934593".to_string(), - 16 => "131073".to_string(), - _ => fail!() - }), - (16, - format!("2{}1", "0".repeat(bits / 4 - 1))) - )), ( BigUint::from_slice([ 1, 2, 3 ]), vec!( - (2, - format!("11{}10{}1", - "0".repeat(bits - 2), - "0".repeat(bits - 1))), - (4, - format!("3{}2{}1", - "0".repeat(bits / 2 - 1), - "0".repeat(bits / 2 - 1))), - (10, match bits { - 32 => "55340232229718589441".to_string(), - 16 => "12885032961".to_string(), - _ => fail!() - }), - (16, - format!("3{}2{}1", - "0".repeat(bits / 4 - 1), - "0".repeat(bits / 4 - 1))) - )) ) - } - - #[test] - fn test_to_str_radix() { - let r = to_str_pairs(); - for num_pair in r.iter() { - let &(ref n, ref rs) = num_pair; - for str_pair in rs.iter() { - let &(ref radix, ref str) = str_pair; - assert_eq!(n.to_str_radix(*radix).as_slice(), - str.as_slice()); - } - } - } - - #[test] - fn test_from_str_radix() { - let r = to_str_pairs(); - for num_pair in r.iter() { - let &(ref n, ref rs) = num_pair; - for str_pair in rs.iter() { - let &(ref radix, ref str) = str_pair; - assert_eq!(n, - &FromStrRadix::from_str_radix(str.as_slice(), - *radix).unwrap()); - } - } - - let zed: Option<BigUint> = FromStrRadix::from_str_radix("Z", 10); - assert_eq!(zed, None); - let blank: Option<BigUint> = FromStrRadix::from_str_radix("_", 2); - assert_eq!(blank, None); - let minus_one: Option<BigUint> = FromStrRadix::from_str_radix("-1", - 10); - assert_eq!(minus_one, None); - } - - #[test] - fn test_factor() { - fn factor(n: uint) -> BigUint { - let mut f: BigUint = One::one(); - for i in range(2, n + 1) { - // FIXME(#5992): assignment operator overloads - // f *= FromPrimitive::from_uint(i); - f = f * FromPrimitive::from_uint(i).unwrap(); - } - return f; - } - - fn check(n: uint, s: &str) { - let n = factor(n); - let ans = match FromStrRadix::from_str_radix(s, 10) { - Some(x) => x, None => fail!() - }; - assert_eq!(n, ans); - } - - check(3, "6"); - check(10, "3628800"); - check(20, "2432902008176640000"); - check(30, "265252859812191058636308480000000"); - } - - #[test] - fn test_bits() { - assert_eq!(BigUint::new(vec!(0,0,0,0)).bits(), 0); - let n: BigUint = FromPrimitive::from_uint(0).unwrap(); - assert_eq!(n.bits(), 0); - let n: BigUint = FromPrimitive::from_uint(1).unwrap(); - assert_eq!(n.bits(), 1); - let n: BigUint = FromPrimitive::from_uint(3).unwrap(); - assert_eq!(n.bits(), 2); - let n: BigUint = FromStrRadix::from_str_radix("4000000000", 16).unwrap(); - assert_eq!(n.bits(), 39); - let one: BigUint = One::one(); - assert_eq!((one << 426).bits(), 427); - } - - #[test] - fn test_rand() { - let mut rng = task_rng(); - let _n: BigUint = rng.gen_biguint(137); - assert!(rng.gen_biguint(0).is_zero()); - } - - #[test] - fn test_rand_range() { - let mut rng = task_rng(); - - for _ in range(0u, 10) { - assert_eq!(rng.gen_bigint_range(&FromPrimitive::from_uint(236).unwrap(), - &FromPrimitive::from_uint(237).unwrap()), - FromPrimitive::from_uint(236).unwrap()); - } - - let l = FromPrimitive::from_uint(403469000 + 2352).unwrap(); - let u = FromPrimitive::from_uint(403469000 + 3513).unwrap(); - for _ in range(0u, 1000) { - let n: BigUint = rng.gen_biguint_below(&u); - assert!(n < u); - - let n: BigUint = rng.gen_biguint_range(&l, &u); - assert!(n >= l); - assert!(n < u); - } - } - - #[test] - #[should_fail] - fn test_zero_rand_range() { - task_rng().gen_biguint_range(&FromPrimitive::from_uint(54).unwrap(), - &FromPrimitive::from_uint(54).unwrap()); - } - - #[test] - #[should_fail] - fn test_negative_rand_range() { - let mut rng = task_rng(); - let l = FromPrimitive::from_uint(2352).unwrap(); - let u = FromPrimitive::from_uint(3513).unwrap(); - // Switching u and l should fail: - let _n: BigUint = rng.gen_biguint_range(&u, &l); - } -} - -#[cfg(test)] -mod bigint_tests { - use Integer; - use super::{BigDigit, BigUint, ToBigUint}; - use super::{Sign, Minus, NoSign, Plus, BigInt, RandBigInt, ToBigInt}; - - use std::cmp::{Less, Equal, Greater}; - use std::i64; - use std::num::CheckedDiv; - use std::num::{Zero, One, FromStrRadix, ToStrRadix}; - use std::num::{ToPrimitive, FromPrimitive}; - use std::rand::task_rng; - use std::u64; - use std::hash::hash; - - #[test] - fn test_from_biguint() { - fn check(inp_s: Sign, inp_n: uint, ans_s: Sign, ans_n: uint) { - let inp = BigInt::from_biguint(inp_s, FromPrimitive::from_uint(inp_n).unwrap()); - let ans = BigInt { sign: ans_s, data: FromPrimitive::from_uint(ans_n).unwrap()}; - assert_eq!(inp, ans); - } - check(Plus, 1, Plus, 1); - check(Plus, 0, NoSign, 0); - check(Minus, 1, Minus, 1); - check(NoSign, 1, NoSign, 0); - } - - #[test] - fn test_cmp() { - let vs: [&[BigDigit], ..4] = [ &[2 as BigDigit], &[1, 1], &[2, 1], &[1, 1, 1] ]; - let mut nums = Vec::new(); - for s in vs.iter().rev() { - nums.push(BigInt::from_slice(Minus, *s)); - } - nums.push(Zero::zero()); - nums.extend(vs.iter().map(|s| BigInt::from_slice(Plus, *s))); - - for (i, ni) in nums.iter().enumerate() { - for (j0, nj) in nums.slice(i, nums.len()).iter().enumerate() { - let j = i + j0; - if i == j { - assert_eq!(ni.cmp(nj), Equal); - assert_eq!(nj.cmp(ni), Equal); - assert_eq!(ni, nj); - assert!(!(ni != nj)); - assert!(ni <= nj); - assert!(ni >= nj); - assert!(!(ni < nj)); - assert!(!(ni > nj)); - } else { - assert_eq!(ni.cmp(nj), Less); - assert_eq!(nj.cmp(ni), Greater); - - assert!(!(ni == nj)); - assert!(ni != nj); - - assert!(ni <= nj); - assert!(!(ni >= nj)); - assert!(ni < nj); - assert!(!(ni > nj)); - - assert!(!(nj <= ni)); - assert!(nj >= ni); - assert!(!(nj < ni)); - assert!(nj > ni); - } - } - } - } - - #[test] - fn test_hash() { - let a = BigInt::new(NoSign, vec!()); - let b = BigInt::new(NoSign, vec!(0)); - let c = BigInt::new(Plus, vec!(1)); - let d = BigInt::new(Plus, vec!(1,0,0,0,0,0)); - let e = BigInt::new(Plus, vec!(0,0,0,0,0,1)); - let f = BigInt::new(Minus, vec!(1)); - assert!(hash(&a) == hash(&b)); - assert!(hash(&b) != hash(&c)); - assert!(hash(&c) == hash(&d)); - assert!(hash(&d) != hash(&e)); - assert!(hash(&c) != hash(&f)); - } - - #[test] - fn test_convert_i64() { - fn check(b1: BigInt, i: i64) { - let b2: BigInt = FromPrimitive::from_i64(i).unwrap(); - assert!(b1 == b2); - assert!(b1.to_i64().unwrap() == i); - } - - check(Zero::zero(), 0); - check(One::one(), 1); - check(i64::MIN.to_bigint().unwrap(), i64::MIN); - check(i64::MAX.to_bigint().unwrap(), i64::MAX); - - assert_eq!( - (i64::MAX as u64 + 1).to_bigint().unwrap().to_i64(), - None); - - assert_eq!( - BigInt::from_biguint(Plus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_i64(), - None); - - assert_eq!( - BigInt::from_biguint(Minus, BigUint::new(vec!(1,0,0,1<<(BigDigit::bits-1)))).to_i64(), - None); - - assert_eq!( - BigInt::from_biguint(Minus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_i64(), - None); - } - - #[test] - fn test_convert_u64() { - fn check(b1: BigInt, u: u64) { - let b2: BigInt = FromPrimitive::from_u64(u).unwrap(); - assert!(b1 == b2); - assert!(b1.to_u64().unwrap() == u); - } - - check(Zero::zero(), 0); - check(One::one(), 1); - check(u64::MIN.to_bigint().unwrap(), u64::MIN); - check(u64::MAX.to_bigint().unwrap(), u64::MAX); - - assert_eq!( - BigInt::from_biguint(Plus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_u64(), - None); - - let max_value: BigUint = FromPrimitive::from_u64(u64::MAX).unwrap(); - assert_eq!(BigInt::from_biguint(Minus, max_value).to_u64(), None); - assert_eq!(BigInt::from_biguint(Minus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_u64(), None); - } - - #[test] - fn test_convert_to_biguint() { - fn check(n: BigInt, ans_1: BigUint) { - assert_eq!(n.to_biguint().unwrap(), ans_1); - assert_eq!(n.to_biguint().unwrap().to_bigint().unwrap(), n); - } - let zero: BigInt = Zero::zero(); - let unsigned_zero: BigUint = Zero::zero(); - let positive = BigInt::from_biguint( - Plus, BigUint::new(vec!(1,2,3))); - let negative = -positive; - - check(zero, unsigned_zero); - check(positive, BigUint::new(vec!(1,2,3))); - - assert_eq!(negative.to_biguint(), None); - } - - static SUM_TRIPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] = &[ - (&[], &[], &[]), - (&[], &[ 1], &[ 1]), - (&[ 1], &[ 1], &[ 2]), - (&[ 1], &[ 1, 1], &[ 2, 1]), - (&[ 1], &[-1], &[ 0, 1]), - (&[ 1], &[-1, -1], &[ 0, 0, 1]), - (&[-1, -1], &[-1, -1], &[-2, -1, 1]), - (&[ 1, 1, 1], &[-1, -1], &[ 0, 1, 2]), - (&[ 2, 2, 1], &[-1, -2], &[ 1, 1, 2]) - ]; - - #[test] - fn test_add() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - assert!(a + b == c); - assert!(b + a == c); - assert!(c + (-a) == b); - assert!(c + (-b) == a); - assert!(a + (-c) == (-b)); - assert!(b + (-c) == (-a)); - assert!((-a) + (-b) == (-c)) - assert!(a + (-a) == Zero::zero()); - } - } - - #[test] - fn test_sub() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - assert!(c - a == b); - assert!(c - b == a); - assert!((-b) - a == (-c)) - assert!((-a) - b == (-c)) - assert!(b - (-a) == c); - assert!(a - (-b) == c); - assert!((-c) - (-a) == (-b)); - assert!(a - a == Zero::zero()); - } - } - - static MUL_TRIPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] = &[ - (&[], &[], &[]), - (&[], &[ 1], &[]), - (&[ 2], &[], &[]), - (&[ 1], &[ 1], &[1]), - (&[ 2], &[ 3], &[ 6]), - (&[ 1], &[ 1, 1, 1], &[1, 1, 1]), - (&[ 1, 2, 3], &[ 3], &[ 3, 6, 9]), - (&[ 1, 1, 1], &[-1], &[-1, -1, -1]), - (&[ 1, 2, 3], &[-1], &[-1, -2, -2, 2]), - (&[ 1, 2, 3, 4], &[-1], &[-1, -2, -2, -2, 3]), - (&[-1], &[-1], &[ 1, -2]), - (&[-1, -1], &[-1], &[ 1, -1, -2]), - (&[-1, -1, -1], &[-1], &[ 1, -1, -1, -2]), - (&[-1, -1, -1, -1], &[-1], &[ 1, -1, -1, -1, -2]), - (&[-1/2 + 1], &[ 2], &[ 0, 1]), - (&[0, -1/2 + 1], &[ 2], &[ 0, 0, 1]), - (&[ 1, 2], &[ 1, 2, 3], &[1, 4, 7, 6]), - (&[-1, -1], &[-1, -1, -1], &[1, 0, -1, -2, -1]), - (&[-1, -1, -1], &[-1, -1, -1, -1], &[1, 0, 0, -1, -2, -1, -1]), - (&[ 0, 0, 1], &[ 1, 2, 3], &[0, 0, 1, 2, 3]), - (&[ 0, 0, 1], &[ 0, 0, 0, 1], &[0, 0, 0, 0, 0, 1]) - ]; - - static DIV_REM_QUADRUPLES: &'static [(&'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit], - &'static [BigDigit])] - = &[ - (&[ 1], &[ 2], &[], &[1]), - (&[ 1, 1], &[ 2], &[-1/2+1], &[1]), - (&[ 1, 1, 1], &[ 2], &[-1/2+1, -1/2+1], &[1]), - (&[ 0, 1], &[-1], &[1], &[1]), - (&[-1, -1], &[-2], &[2, 1], &[3]) - ]; - - #[test] - fn test_mul() { - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - assert!(a * b == c); - assert!(b * a == c); - - assert!((-a) * b == -c); - assert!((-b) * a == -c); - } - - for elm in DIV_REM_QUADRUPLES.iter() { - let (a_vec, b_vec, c_vec, d_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - let d = BigInt::from_slice(Plus, d_vec); - - assert!(a == b * c + d); - assert!(a == c * b + d); - } - } - - #[test] - fn test_div_mod_floor() { - fn check_sub(a: &BigInt, b: &BigInt, ans_d: &BigInt, ans_m: &BigInt) { - let (d, m) = a.div_mod_floor(b); - if !m.is_zero() { - assert_eq!(m.sign, b.sign); - } - assert!(m.abs() <= b.abs()); - assert!(*a == b * d + m); - assert!(d == *ans_d); - assert!(m == *ans_m); - } - - fn check(a: &BigInt, b: &BigInt, d: &BigInt, m: &BigInt) { - if m.is_zero() { - check_sub(a, b, d, m); - check_sub(a, &b.neg(), &d.neg(), m); - check_sub(&a.neg(), b, &d.neg(), m); - check_sub(&a.neg(), &b.neg(), d, m); - } else { - check_sub(a, b, d, m); - check_sub(a, &b.neg(), &(d.neg() - One::one()), &(m - *b)); - check_sub(&a.neg(), b, &(d.neg() - One::one()), &(b - *m)); - check_sub(&a.neg(), &b.neg(), d, &m.neg()); - } - } - - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - if !a.is_zero() { check(&c, &a, &b, &Zero::zero()); } - if !b.is_zero() { check(&c, &b, &a, &Zero::zero()); } - } - - for elm in DIV_REM_QUADRUPLES.iter() { - let (a_vec, b_vec, c_vec, d_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - let d = BigInt::from_slice(Plus, d_vec); - - if !b.is_zero() { - check(&a, &b, &c, &d); - } - } - } - - - #[test] - fn test_div_rem() { - fn check_sub(a: &BigInt, b: &BigInt, ans_q: &BigInt, ans_r: &BigInt) { - let (q, r) = a.div_rem(b); - if !r.is_zero() { - assert_eq!(r.sign, a.sign); - } - assert!(r.abs() <= b.abs()); - assert!(*a == b * q + r); - assert!(q == *ans_q); - assert!(r == *ans_r); - } - - fn check(a: &BigInt, b: &BigInt, q: &BigInt, r: &BigInt) { - check_sub(a, b, q, r); - check_sub(a, &b.neg(), &q.neg(), r); - check_sub(&a.neg(), b, &q.neg(), &r.neg()); - check_sub(&a.neg(), &b.neg(), q, &r.neg()); - } - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - if !a.is_zero() { check(&c, &a, &b, &Zero::zero()); } - if !b.is_zero() { check(&c, &b, &a, &Zero::zero()); } - } - - for elm in DIV_REM_QUADRUPLES.iter() { - let (a_vec, b_vec, c_vec, d_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - let d = BigInt::from_slice(Plus, d_vec); - - if !b.is_zero() { - check(&a, &b, &c, &d); - } - } - } - - #[test] - fn test_checked_add() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - assert!(a.checked_add(&b).unwrap() == c); - assert!(b.checked_add(&a).unwrap() == c); - assert!(c.checked_add(&(-a)).unwrap() == b); - assert!(c.checked_add(&(-b)).unwrap() == a); - assert!(a.checked_add(&(-c)).unwrap() == (-b)); - assert!(b.checked_add(&(-c)).unwrap() == (-a)); - assert!((-a).checked_add(&(-b)).unwrap() == (-c)) - assert!(a.checked_add(&(-a)).unwrap() == Zero::zero()); - } - } - - #[test] - fn test_checked_sub() { - for elm in SUM_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - assert!(c.checked_sub(&a).unwrap() == b); - assert!(c.checked_sub(&b).unwrap() == a); - assert!((-b).checked_sub(&a).unwrap() == (-c)) - assert!((-a).checked_sub(&b).unwrap() == (-c)) - assert!(b.checked_sub(&(-a)).unwrap() == c); - assert!(a.checked_sub(&(-b)).unwrap() == c); - assert!((-c).checked_sub(&(-a)).unwrap() == (-b)); - assert!(a.checked_sub(&a).unwrap() == Zero::zero()); - } - } - - #[test] - fn test_checked_mul() { - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - assert!(a.checked_mul(&b).unwrap() == c); - assert!(b.checked_mul(&a).unwrap() == c); - - assert!((-a).checked_mul(&b).unwrap() == -c); - assert!((-b).checked_mul(&a).unwrap() == -c); - } - - for elm in DIV_REM_QUADRUPLES.iter() { - let (a_vec, b_vec, c_vec, d_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - let d = BigInt::from_slice(Plus, d_vec); - - assert!(a == b.checked_mul(&c).unwrap() + d); - assert!(a == c.checked_mul(&b).unwrap() + d); - } - } - #[test] - fn test_checked_div() { - for elm in MUL_TRIPLES.iter() { - let (a_vec, b_vec, c_vec) = *elm; - let a = BigInt::from_slice(Plus, a_vec); - let b = BigInt::from_slice(Plus, b_vec); - let c = BigInt::from_slice(Plus, c_vec); - - if !a.is_zero() { - assert!(c.checked_div(&a).unwrap() == b); - assert!((-c).checked_div(&(-a)).unwrap() == b); - assert!((-c).checked_div(&a).unwrap() == -b); - } - if !b.is_zero() { - assert!(c.checked_div(&b).unwrap() == a); - assert!((-c).checked_div(&(-b)).unwrap() == a); - assert!((-c).checked_div(&b).unwrap() == -a); - } - - assert!(c.checked_div(&Zero::zero()).is_none()); - assert!((-c).checked_div(&Zero::zero()).is_none()); - } - } - - #[test] - fn test_gcd() { - fn check(a: int, b: int, c: int) { - let big_a: BigInt = FromPrimitive::from_int(a).unwrap(); - let big_b: BigInt = FromPrimitive::from_int(b).unwrap(); - let big_c: BigInt = FromPrimitive::from_int(c).unwrap(); - - assert_eq!(big_a.gcd(&big_b), big_c); - } - - check(10, 2, 2); - check(10, 3, 1); - check(0, 3, 3); - check(3, 3, 3); - check(56, 42, 14); - check(3, -3, 3); - check(-6, 3, 3); - check(-4, -2, 2); - } - - #[test] - fn test_lcm() { - fn check(a: int, b: int, c: int) { - let big_a: BigInt = FromPrimitive::from_int(a).unwrap(); - let big_b: BigInt = FromPrimitive::from_int(b).unwrap(); - let big_c: BigInt = FromPrimitive::from_int(c).unwrap(); - - assert_eq!(big_a.lcm(&big_b), big_c); - } - - check(1, 0, 0); - check(0, 1, 0); - check(1, 1, 1); - check(-1, 1, 1); - check(1, -1, 1); - check(-1, -1, 1); - check(8, 9, 72); - check(11, 5, 55); - } - - #[test] - fn test_abs_sub() { - let zero: BigInt = Zero::zero(); - let one: BigInt = One::one(); - assert_eq!((-one).abs_sub(&one), zero); - let one: BigInt = One::one(); - let zero: BigInt = Zero::zero(); - assert_eq!(one.abs_sub(&one), zero); - let one: BigInt = One::one(); - let zero: BigInt = Zero::zero(); - assert_eq!(one.abs_sub(&zero), one); - let one: BigInt = One::one(); - let two: BigInt = FromPrimitive::from_int(2).unwrap(); - assert_eq!(one.abs_sub(&-one), two); - } - - #[test] - fn test_to_str_radix() { - fn check(n: int, ans: &str) { - let n: BigInt = FromPrimitive::from_int(n).unwrap(); - assert!(ans == n.to_str_radix(10).as_slice()); - } - check(10, "10"); - check(1, "1"); - check(0, "0"); - check(-1, "-1"); - check(-10, "-10"); - } - - - #[test] - fn test_from_str_radix() { - fn check(s: &str, ans: Option<int>) { - let ans = ans.map(|n| { - let x: BigInt = FromPrimitive::from_int(n).unwrap(); - x - }); - assert_eq!(FromStrRadix::from_str_radix(s, 10), ans); - } - check("10", Some(10)); - check("1", Some(1)); - check("0", Some(0)); - check("-1", Some(-1)); - check("-10", Some(-10)); - check("Z", None); - check("_", None); - - // issue 10522, this hit an edge case that caused it to - // attempt to allocate a vector of size (-1u) == huge. - let x: BigInt = - from_str(format!("1{}", "0".repeat(36)).as_slice()).unwrap(); - let _y = x.to_string(); - } - - #[test] - fn test_neg() { - assert!(-BigInt::new(Plus, vec!(1, 1, 1)) == - BigInt::new(Minus, vec!(1, 1, 1))); - assert!(-BigInt::new(Minus, vec!(1, 1, 1)) == - BigInt::new(Plus, vec!(1, 1, 1))); - let zero: BigInt = Zero::zero(); - assert_eq!(-zero, zero); - } - - #[test] - fn test_rand() { - let mut rng = task_rng(); - let _n: BigInt = rng.gen_bigint(137); - assert!(rng.gen_bigint(0).is_zero()); - } - - #[test] - fn test_rand_range() { - let mut rng = task_rng(); - - for _ in range(0u, 10) { - assert_eq!(rng.gen_bigint_range(&FromPrimitive::from_uint(236).unwrap(), - &FromPrimitive::from_uint(237).unwrap()), - FromPrimitive::from_uint(236).unwrap()); - } - - fn check(l: BigInt, u: BigInt) { - let mut rng = task_rng(); - for _ in range(0u, 1000) { - let n: BigInt = rng.gen_bigint_range(&l, &u); - assert!(n >= l); - assert!(n < u); - } - } - let l: BigInt = FromPrimitive::from_uint(403469000 + 2352).unwrap(); - let u: BigInt = FromPrimitive::from_uint(403469000 + 3513).unwrap(); - check( l.clone(), u.clone()); - check(-l.clone(), u.clone()); - check(-u.clone(), -l.clone()); - } - - #[test] - #[should_fail] - fn test_zero_rand_range() { - task_rng().gen_bigint_range(&FromPrimitive::from_int(54).unwrap(), - &FromPrimitive::from_int(54).unwrap()); - } - - #[test] - #[should_fail] - fn test_negative_rand_range() { - let mut rng = task_rng(); - let l = FromPrimitive::from_uint(2352).unwrap(); - let u = FromPrimitive::from_uint(3513).unwrap(); - // Switching u and l should fail: - let _n: BigInt = rng.gen_bigint_range(&u, &l); - } -} - -#[cfg(test)] -mod bench { - extern crate test; - use self::test::Bencher; - use super::BigUint; - use std::iter; - use std::mem::replace; - use std::num::{FromPrimitive, Zero, One}; - - fn factorial(n: uint) -> BigUint { - let mut f: BigUint = One::one(); - for i in iter::range_inclusive(1, n) { - f = f * FromPrimitive::from_uint(i).unwrap(); - } - f - } - - fn fib(n: uint) -> BigUint { - let mut f0: BigUint = Zero::zero(); - let mut f1: BigUint = One::one(); - for _ in range(0, n) { - let f2 = f0 + f1; - f0 = replace(&mut f1, f2); - } - f0 - } - - #[bench] - fn factorial_100(b: &mut Bencher) { - b.iter(|| { - factorial(100); - }); - } - - #[bench] - fn fib_100(b: &mut Bencher) { - b.iter(|| { - fib(100); - }); - } - - #[bench] - fn to_string(b: &mut Bencher) { - let fac = factorial(100); - let fib = fib(100); - b.iter(|| { - fac.to_string(); - }); - b.iter(|| { - fib.to_string(); - }); - } - - #[bench] - fn shr(b: &mut Bencher) { - let n = { let one : BigUint = One::one(); one << 1000 }; - b.iter(|| { - let mut m = n.clone(); - for _ in range(0u, 10) { - m = m >> 1; - } - }) - } -} diff --git a/src/libnum/complex.rs b/src/libnum/complex.rs deleted file mode 100644 index 6690b1d5ddc..00000000000 --- a/src/libnum/complex.rs +++ /dev/null @@ -1,379 +0,0 @@ -// Copyright 2013 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - - -//! Complex numbers. - -use std::fmt; -use std::num::{Zero, One, ToStrRadix}; - -// FIXME #1284: handle complex NaN & infinity etc. This -// probably doesn't map to C's _Complex correctly. - -/// A complex number in Cartesian form. -#[deriving(PartialEq, Clone, Hash)] -pub struct Complex<T> { - /// Real portion of the complex number - pub re: T, - /// Imaginary portion of the complex number - pub im: T -} - -pub type Complex32 = Complex<f32>; -pub type Complex64 = Complex<f64>; - -impl<T: Clone + Num> Complex<T> { - /// Create a new Complex - #[inline] - pub fn new(re: T, im: T) -> Complex<T> { - Complex { re: re, im: im } - } - - /// Returns the square of the norm (since `T` doesn't necessarily - /// have a sqrt function), i.e. `re^2 + im^2`. - #[inline] - pub fn norm_sqr(&self) -> T { - self.re * self.re + self.im * self.im - } - - - /// Returns the complex conjugate. i.e. `re - i im` - #[inline] - pub fn conj(&self) -> Complex<T> { - Complex::new(self.re.clone(), -self.im) - } - - - /// Multiplies `self` by the scalar `t`. - #[inline] - pub fn scale(&self, t: T) -> Complex<T> { - Complex::new(self.re * t, self.im * t) - } - - /// Divides `self` by the scalar `t`. - #[inline] - pub fn unscale(&self, t: T) -> Complex<T> { - Complex::new(self.re / t, self.im / t) - } - - /// Returns `1/self` - #[inline] - pub fn inv(&self) -> Complex<T> { - let norm_sqr = self.norm_sqr(); - Complex::new(self.re / norm_sqr, - -self.im / norm_sqr) - } -} - -impl<T: Clone + FloatMath> Complex<T> { - /// Calculate |self| - #[inline] - pub fn norm(&self) -> T { - self.re.hypot(self.im) - } -} - -impl<T: Clone + FloatMath> Complex<T> { - /// Calculate the principal Arg of self. - #[inline] - pub fn arg(&self) -> T { - self.im.atan2(self.re) - } - /// Convert to polar form (r, theta), such that `self = r * exp(i - /// * theta)` - #[inline] - pub fn to_polar(&self) -> (T, T) { - (self.norm(), self.arg()) - } - /// Convert a polar representation into a complex number. - #[inline] - pub fn from_polar(r: &T, theta: &T) -> Complex<T> { - Complex::new(*r * theta.cos(), *r * theta.sin()) - } -} - -/* arithmetic */ -// (a + i b) + (c + i d) == (a + c) + i (b + d) -impl<T: Clone + Num> Add<Complex<T>, Complex<T>> for Complex<T> { - #[inline] - fn add(&self, other: &Complex<T>) -> Complex<T> { - Complex::new(self.re + other.re, self.im + other.im) - } -} -// (a + i b) - (c + i d) == (a - c) + i (b - d) -impl<T: Clone + Num> Sub<Complex<T>, Complex<T>> for Complex<T> { - #[inline] - fn sub(&self, other: &Complex<T>) -> Complex<T> { - Complex::new(self.re - other.re, self.im - other.im) - } -} -// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c) -impl<T: Clone + Num> Mul<Complex<T>, Complex<T>> for Complex<T> { - #[inline] - fn mul(&self, other: &Complex<T>) -> Complex<T> { - Complex::new(self.re*other.re - self.im*other.im, - self.re*other.im + self.im*other.re) - } -} - -// (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d) -// == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)] -impl<T: Clone + Num> Div<Complex<T>, Complex<T>> for Complex<T> { - #[inline] - fn div(&self, other: &Complex<T>) -> Complex<T> { - let norm_sqr = other.norm_sqr(); - Complex::new((self.re*other.re + self.im*other.im) / norm_sqr, - (self.im*other.re - self.re*other.im) / norm_sqr) - } -} - -impl<T: Clone + Num> Neg<Complex<T>> for Complex<T> { - #[inline] - fn neg(&self) -> Complex<T> { - Complex::new(-self.re, -self.im) - } -} - -/* constants */ -impl<T: Clone + Num> Zero for Complex<T> { - #[inline] - fn zero() -> Complex<T> { - Complex::new(Zero::zero(), Zero::zero()) - } - - #[inline] - fn is_zero(&self) -> bool { - self.re.is_zero() && self.im.is_zero() - } -} - -impl<T: Clone + Num> One for Complex<T> { - #[inline] - fn one() -> Complex<T> { - Complex::new(One::one(), Zero::zero()) - } -} - -/* string conversions */ -impl<T: fmt::Show + Num + PartialOrd> fmt::Show for Complex<T> { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - if self.im < Zero::zero() { - write!(f, "{}-{}i", self.re, -self.im) - } else { - write!(f, "{}+{}i", self.re, self.im) - } - } -} - -impl<T: ToStrRadix + Num + PartialOrd> ToStrRadix for Complex<T> { - fn to_str_radix(&self, radix: uint) -> String { - if self.im < Zero::zero() { - format!("{}-{}i", - self.re.to_str_radix(radix), - (-self.im).to_str_radix(radix)) - } else { - format!("{}+{}i", - self.re.to_str_radix(radix), - self.im.to_str_radix(radix)) - } - } -} - -#[cfg(test)] -mod test { - #![allow(non_uppercase_statics)] - - use super::{Complex64, Complex}; - use std::num::{Zero, One, Float}; - use std::hash::hash; - - pub const _0_0i : Complex64 = Complex { re: 0.0, im: 0.0 }; - pub const _1_0i : Complex64 = Complex { re: 1.0, im: 0.0 }; - pub const _1_1i : Complex64 = Complex { re: 1.0, im: 1.0 }; - pub const _0_1i : Complex64 = Complex { re: 0.0, im: 1.0 }; - pub const _neg1_1i : Complex64 = Complex { re: -1.0, im: 1.0 }; - pub const _05_05i : Complex64 = Complex { re: 0.5, im: 0.5 }; - pub const all_consts : [Complex64, .. 5] = [_0_0i, _1_0i, _1_1i, _neg1_1i, _05_05i]; - - #[test] - fn test_consts() { - // check our constants are what Complex::new creates - fn test(c : Complex64, r : f64, i: f64) { - assert_eq!(c, Complex::new(r,i)); - } - test(_0_0i, 0.0, 0.0); - test(_1_0i, 1.0, 0.0); - test(_1_1i, 1.0, 1.0); - test(_neg1_1i, -1.0, 1.0); - test(_05_05i, 0.5, 0.5); - - assert_eq!(_0_0i, Zero::zero()); - assert_eq!(_1_0i, One::one()); - } - - #[test] - #[cfg_attr(target_arch = "x86", ignore)] - // FIXME #7158: (maybe?) currently failing on x86. - fn test_norm() { - fn test(c: Complex64, ns: f64) { - assert_eq!(c.norm_sqr(), ns); - assert_eq!(c.norm(), ns.sqrt()) - } - test(_0_0i, 0.0); - test(_1_0i, 1.0); - test(_1_1i, 2.0); - test(_neg1_1i, 2.0); - test(_05_05i, 0.5); - } - - #[test] - fn test_scale_unscale() { - assert_eq!(_05_05i.scale(2.0), _1_1i); - assert_eq!(_1_1i.unscale(2.0), _05_05i); - for &c in all_consts.iter() { - assert_eq!(c.scale(2.0).unscale(2.0), c); - } - } - - #[test] - fn test_conj() { - for &c in all_consts.iter() { - assert_eq!(c.conj(), Complex::new(c.re, -c.im)); - assert_eq!(c.conj().conj(), c); - } - } - - #[test] - fn test_inv() { - assert_eq!(_1_1i.inv(), _05_05i.conj()); - assert_eq!(_1_0i.inv(), _1_0i.inv()); - } - - #[test] - #[should_fail] - fn test_divide_by_zero_natural() { - let n = Complex::new(2i, 3i); - let d = Complex::new(0, 0); - let _x = n / d; - } - - #[test] - #[should_fail] - #[ignore] - fn test_inv_zero() { - // FIXME #5736: should this really fail, or just NaN? - _0_0i.inv(); - } - - #[test] - fn test_arg() { - fn test(c: Complex64, arg: f64) { - assert!((c.arg() - arg).abs() < 1.0e-6) - } - test(_1_0i, 0.0); - test(_1_1i, 0.25 * Float::pi()); - test(_neg1_1i, 0.75 * Float::pi()); - test(_05_05i, 0.25 * Float::pi()); - } - - #[test] - fn test_polar_conv() { - fn test(c: Complex64) { - let (r, theta) = c.to_polar(); - assert!((c - Complex::from_polar(&r, &theta)).norm() < 1e-6); - } - for &c in all_consts.iter() { test(c); } - } - - mod arith { - use super::{_0_0i, _1_0i, _1_1i, _0_1i, _neg1_1i, _05_05i, all_consts}; - use std::num::Zero; - - #[test] - fn test_add() { - assert_eq!(_05_05i + _05_05i, _1_1i); - assert_eq!(_0_1i + _1_0i, _1_1i); - assert_eq!(_1_0i + _neg1_1i, _0_1i); - - for &c in all_consts.iter() { - assert_eq!(_0_0i + c, c); - assert_eq!(c + _0_0i, c); - } - } - - #[test] - fn test_sub() { - assert_eq!(_05_05i - _05_05i, _0_0i); - assert_eq!(_0_1i - _1_0i, _neg1_1i); - assert_eq!(_0_1i - _neg1_1i, _1_0i); - - for &c in all_consts.iter() { - assert_eq!(c - _0_0i, c); - assert_eq!(c - c, _0_0i); - } - } - - #[test] - fn test_mul() { - assert_eq!(_05_05i * _05_05i, _0_1i.unscale(2.0)); - assert_eq!(_1_1i * _0_1i, _neg1_1i); - - // i^2 & i^4 - assert_eq!(_0_1i * _0_1i, -_1_0i); - assert_eq!(_0_1i * _0_1i * _0_1i * _0_1i, _1_0i); - - for &c in all_consts.iter() { - assert_eq!(c * _1_0i, c); - assert_eq!(_1_0i * c, c); - } - } - #[test] - fn test_div() { - assert_eq!(_neg1_1i / _0_1i, _1_1i); - for &c in all_consts.iter() { - if c != Zero::zero() { - assert_eq!(c / c, _1_0i); - } - } - } - #[test] - fn test_neg() { - assert_eq!(-_1_0i + _0_1i, _neg1_1i); - assert_eq!((-_0_1i) * _0_1i, _1_0i); - for &c in all_consts.iter() { - assert_eq!(-(-c), c); - } - } - } - - #[test] - fn test_to_string() { - fn test(c : Complex64, s: String) { - assert_eq!(c.to_string(), s); - } - test(_0_0i, "0+0i".to_string()); - test(_1_0i, "1+0i".to_string()); - test(_0_1i, "0+1i".to_string()); - test(_1_1i, "1+1i".to_string()); - test(_neg1_1i, "-1+1i".to_string()); - test(-_neg1_1i, "1-1i".to_string()); - test(_05_05i, "0.5+0.5i".to_string()); - } - - #[test] - fn test_hash() { - let a = Complex::new(0i32, 0i32); - let b = Complex::new(1i32, 0i32); - let c = Complex::new(0i32, 1i32); - assert!(hash(&a) != hash(&b)); - assert!(hash(&b) != hash(&c)); - assert!(hash(&c) != hash(&a)); - } -} diff --git a/src/libnum/integer.rs b/src/libnum/integer.rs deleted file mode 100644 index c5d076a70b5..00000000000 --- a/src/libnum/integer.rs +++ /dev/null @@ -1,507 +0,0 @@ -// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! Integer trait and functions. - -pub trait Integer: Num + PartialOrd - + Div<Self, Self> - + Rem<Self, Self> { - /// Floored integer division. - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert!(( 8i).div_floor(& 3) == 2); - /// assert!(( 8i).div_floor(&-3) == -3); - /// assert!((-8i).div_floor(& 3) == -3); - /// assert!((-8i).div_floor(&-3) == 2); - /// - /// assert!(( 1i).div_floor(& 2) == 0); - /// assert!(( 1i).div_floor(&-2) == -1); - /// assert!((-1i).div_floor(& 2) == -1); - /// assert!((-1i).div_floor(&-2) == 0); - /// ``` - fn div_floor(&self, other: &Self) -> Self; - - /// Floored integer modulo, satisfying: - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// # let n = 1i; let d = 1i; - /// assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n) - /// ``` - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert!(( 8i).mod_floor(& 3) == 2); - /// assert!(( 8i).mod_floor(&-3) == -1); - /// assert!((-8i).mod_floor(& 3) == 1); - /// assert!((-8i).mod_floor(&-3) == -2); - /// - /// assert!(( 1i).mod_floor(& 2) == 1); - /// assert!(( 1i).mod_floor(&-2) == -1); - /// assert!((-1i).mod_floor(& 2) == 1); - /// assert!((-1i).mod_floor(&-2) == -1); - /// ``` - fn mod_floor(&self, other: &Self) -> Self; - - /// Greatest Common Divisor (GCD). - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert_eq!(6i.gcd(&8), 2); - /// assert_eq!(7i.gcd(&3), 1); - /// ``` - fn gcd(&self, other: &Self) -> Self; - - /// Lowest Common Multiple (LCM). - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert_eq!(7i.lcm(&3), 21); - /// assert_eq!(2i.lcm(&4), 4); - /// ``` - fn lcm(&self, other: &Self) -> Self; - - /// Deprecated, use `is_multiple_of` instead. - #[deprecated = "function renamed to `is_multiple_of`"] - fn divides(&self, other: &Self) -> bool; - - /// Returns `true` if `other` is a multiple of `self`. - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert_eq!(9i.is_multiple_of(&3), true); - /// assert_eq!(3i.is_multiple_of(&9), false); - /// ``` - fn is_multiple_of(&self, other: &Self) -> bool; - - /// Returns `true` if the number is even. - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert_eq!(3i.is_even(), false); - /// assert_eq!(4i.is_even(), true); - /// ``` - fn is_even(&self) -> bool; - - /// Returns `true` if the number is odd. - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert_eq!(3i.is_odd(), true); - /// assert_eq!(4i.is_odd(), false); - /// ``` - fn is_odd(&self) -> bool; - - /// Simultaneous truncated integer division and modulus. - /// Returns `(quotient, remainder)`. - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert_eq!(( 8i).div_rem( &3), ( 2, 2)); - /// assert_eq!(( 8i).div_rem(&-3), (-2, 2)); - /// assert_eq!((-8i).div_rem( &3), (-2, -2)); - /// assert_eq!((-8i).div_rem(&-3), ( 2, -2)); - /// - /// assert_eq!(( 1i).div_rem( &2), ( 0, 1)); - /// assert_eq!(( 1i).div_rem(&-2), ( 0, 1)); - /// assert_eq!((-1i).div_rem( &2), ( 0, -1)); - /// assert_eq!((-1i).div_rem(&-2), ( 0, -1)); - /// ``` - #[inline] - fn div_rem(&self, other: &Self) -> (Self, Self) { - (*self / *other, *self % *other) - } - - /// Simultaneous floored integer division and modulus. - /// Returns `(quotient, remainder)`. - /// - /// # Examples - /// - /// ``` - /// # #![allow(deprecated)] - /// # use num::Integer; - /// assert_eq!(( 8i).div_mod_floor( &3), ( 2, 2)); - /// assert_eq!(( 8i).div_mod_floor(&-3), (-3, -1)); - /// assert_eq!((-8i).div_mod_floor( &3), (-3, 1)); - /// assert_eq!((-8i).div_mod_floor(&-3), ( 2, -2)); - /// - /// assert_eq!(( 1i).div_mod_floor( &2), ( 0, 1)); - /// assert_eq!(( 1i).div_mod_floor(&-2), (-1, -1)); - /// assert_eq!((-1i).div_mod_floor( &2), (-1, 1)); - /// assert_eq!((-1i).div_mod_floor(&-2), ( 0, -1)); - /// ``` - fn div_mod_floor(&self, other: &Self) -> (Self, Self) { - (self.div_floor(other), self.mod_floor(other)) - } -} - -/// Simultaneous integer division and modulus -#[inline] pub fn div_rem<T: Integer>(x: T, y: T) -> (T, T) { x.div_rem(&y) } -/// Floored integer division -#[inline] pub fn div_floor<T: Integer>(x: T, y: T) -> T { x.div_floor(&y) } -/// Floored integer modulus -#[inline] pub fn mod_floor<T: Integer>(x: T, y: T) -> T { x.mod_floor(&y) } -/// Simultaneous floored integer division and modulus -#[inline] pub fn div_mod_floor<T: Integer>(x: T, y: T) -> (T, T) { x.div_mod_floor(&y) } - -/// Calculates the Greatest Common Divisor (GCD) of the number and `other`. The -/// result is always positive. -#[inline(always)] pub fn gcd<T: Integer>(x: T, y: T) -> T { x.gcd(&y) } -/// Calculates the Lowest Common Multiple (LCM) of the number and `other`. -#[inline(always)] pub fn lcm<T: Integer>(x: T, y: T) -> T { x.lcm(&y) } - -macro_rules! impl_integer_for_int { - ($T:ty, $test_mod:ident) => ( - impl Integer for $T { - /// Floored integer division - #[inline] - fn div_floor(&self, other: &$T) -> $T { - // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_, - // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf) - match self.div_rem(other) { - (d, r) if (r > 0 && *other < 0) - || (r < 0 && *other > 0) => d - 1, - (d, _) => d, - } - } - - /// Floored integer modulo - #[inline] - fn mod_floor(&self, other: &$T) -> $T { - // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_, - // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf) - match *self % *other { - r if (r > 0 && *other < 0) - || (r < 0 && *other > 0) => r + *other, - r => r, - } - } - - /// Calculates `div_floor` and `mod_floor` simultaneously - #[inline] - fn div_mod_floor(&self, other: &$T) -> ($T,$T) { - // Algorithm from [Daan Leijen. _Division and Modulus for Computer Scientists_, - // December 2001](http://research.microsoft.com/pubs/151917/divmodnote-letter.pdf) - match self.div_rem(other) { - (d, r) if (r > 0 && *other < 0) - || (r < 0 && *other > 0) => (d - 1, r + *other), - (d, r) => (d, r), - } - } - - /// Calculates the Greatest Common Divisor (GCD) of the number and - /// `other`. The result is always positive. - #[inline] - fn gcd(&self, other: &$T) -> $T { - // Use Euclid's algorithm - let mut m = *self; - let mut n = *other; - while m != 0 { - let temp = m; - m = n % temp; - n = temp; - } - n.abs() - } - - /// Calculates the Lowest Common Multiple (LCM) of the number and - /// `other`. - #[inline] - fn lcm(&self, other: &$T) -> $T { - // should not have to recalculate abs - ((*self * *other) / self.gcd(other)).abs() - } - - /// Deprecated, use `is_multiple_of` instead. - #[deprecated = "function renamed to `is_multiple_of`"] - #[inline] - fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); } - - /// Returns `true` if the number is a multiple of `other`. - #[inline] - fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 } - - /// Returns `true` if the number is divisible by `2` - #[inline] - fn is_even(&self) -> bool { self & 1 == 0 } - - /// Returns `true` if the number is not divisible by `2` - #[inline] - fn is_odd(&self) -> bool { !self.is_even() } - } - - #[cfg(test)] - mod $test_mod { - use Integer; - - /// Checks that the division rule holds for: - /// - /// - `n`: numerator (dividend) - /// - `d`: denominator (divisor) - /// - `qr`: quotient and remainder - #[cfg(test)] - fn test_division_rule((n,d): ($T,$T), (q,r): ($T,$T)) { - assert_eq!(d * q + r, n); - } - - #[test] - fn test_div_rem() { - fn test_nd_dr(nd: ($T,$T), qr: ($T,$T)) { - let (n,d) = nd; - let separate_div_rem = (n / d, n % d); - let combined_div_rem = n.div_rem(&d); - - assert_eq!(separate_div_rem, qr); - assert_eq!(combined_div_rem, qr); - - test_division_rule(nd, separate_div_rem); - test_division_rule(nd, combined_div_rem); - } - - test_nd_dr(( 8, 3), ( 2, 2)); - test_nd_dr(( 8, -3), (-2, 2)); - test_nd_dr((-8, 3), (-2, -2)); - test_nd_dr((-8, -3), ( 2, -2)); - - test_nd_dr(( 1, 2), ( 0, 1)); - test_nd_dr(( 1, -2), ( 0, 1)); - test_nd_dr((-1, 2), ( 0, -1)); - test_nd_dr((-1, -2), ( 0, -1)); - } - - #[test] - fn test_div_mod_floor() { - fn test_nd_dm(nd: ($T,$T), dm: ($T,$T)) { - let (n,d) = nd; - let separate_div_mod_floor = (n.div_floor(&d), n.mod_floor(&d)); - let combined_div_mod_floor = n.div_mod_floor(&d); - - assert_eq!(separate_div_mod_floor, dm); - assert_eq!(combined_div_mod_floor, dm); - - test_division_rule(nd, separate_div_mod_floor); - test_division_rule(nd, combined_div_mod_floor); - } - - test_nd_dm(( 8, 3), ( 2, 2)); - test_nd_dm(( 8, -3), (-3, -1)); - test_nd_dm((-8, 3), (-3, 1)); - test_nd_dm((-8, -3), ( 2, -2)); - - test_nd_dm(( 1, 2), ( 0, 1)); - test_nd_dm(( 1, -2), (-1, -1)); - test_nd_dm((-1, 2), (-1, 1)); - test_nd_dm((-1, -2), ( 0, -1)); - } - - #[test] - fn test_gcd() { - assert_eq!((10 as $T).gcd(&2), 2 as $T); - assert_eq!((10 as $T).gcd(&3), 1 as $T); - assert_eq!((0 as $T).gcd(&3), 3 as $T); - assert_eq!((3 as $T).gcd(&3), 3 as $T); - assert_eq!((56 as $T).gcd(&42), 14 as $T); - assert_eq!((3 as $T).gcd(&-3), 3 as $T); - assert_eq!((-6 as $T).gcd(&3), 3 as $T); - assert_eq!((-4 as $T).gcd(&-2), 2 as $T); - } - - #[test] - fn test_lcm() { - assert_eq!((1 as $T).lcm(&0), 0 as $T); - assert_eq!((0 as $T).lcm(&1), 0 as $T); - assert_eq!((1 as $T).lcm(&1), 1 as $T); - assert_eq!((-1 as $T).lcm(&1), 1 as $T); - assert_eq!((1 as $T).lcm(&-1), 1 as $T); - assert_eq!((-1 as $T).lcm(&-1), 1 as $T); - assert_eq!((8 as $T).lcm(&9), 72 as $T); - assert_eq!((11 as $T).lcm(&5), 55 as $T); - } - - #[test] - fn test_even() { - assert_eq!((-4 as $T).is_even(), true); - assert_eq!((-3 as $T).is_even(), false); - assert_eq!((-2 as $T).is_even(), true); - assert_eq!((-1 as $T).is_even(), false); - assert_eq!((0 as $T).is_even(), true); - assert_eq!((1 as $T).is_even(), false); - assert_eq!((2 as $T).is_even(), true); - assert_eq!((3 as $T).is_even(), false); - assert_eq!((4 as $T).is_even(), true); - } - - #[test] - fn test_odd() { - assert_eq!((-4 as $T).is_odd(), false); - assert_eq!((-3 as $T).is_odd(), true); - assert_eq!((-2 as $T).is_odd(), false); - assert_eq!((-1 as $T).is_odd(), true); - assert_eq!((0 as $T).is_odd(), false); - assert_eq!((1 as $T).is_odd(), true); - assert_eq!((2 as $T).is_odd(), false); - assert_eq!((3 as $T).is_odd(), true); - assert_eq!((4 as $T).is_odd(), false); - } - } - ) -} - -impl_integer_for_int!(i8, test_integer_i8) -impl_integer_for_int!(i16, test_integer_i16) -impl_integer_for_int!(i32, test_integer_i32) -impl_integer_for_int!(i64, test_integer_i64) -impl_integer_for_int!(int, test_integer_int) - -macro_rules! impl_integer_for_uint { - ($T:ty, $test_mod:ident) => ( - impl Integer for $T { - /// Unsigned integer division. Returns the same result as `div` (`/`). - #[inline] - fn div_floor(&self, other: &$T) -> $T { *self / *other } - - /// Unsigned integer modulo operation. Returns the same result as `rem` (`%`). - #[inline] - fn mod_floor(&self, other: &$T) -> $T { *self % *other } - - /// Calculates the Greatest Common Divisor (GCD) of the number and `other` - #[inline] - fn gcd(&self, other: &$T) -> $T { - // Use Euclid's algorithm - let mut m = *self; - let mut n = *other; - while m != 0 { - let temp = m; - m = n % temp; - n = temp; - } - n - } - - /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. - #[inline] - fn lcm(&self, other: &$T) -> $T { - (*self * *other) / self.gcd(other) - } - - /// Deprecated, use `is_multiple_of` instead. - #[deprecated = "function renamed to `is_multiple_of`"] - #[inline] - fn divides(&self, other: &$T) -> bool { return self.is_multiple_of(other); } - - /// Returns `true` if the number is a multiple of `other`. - #[inline] - fn is_multiple_of(&self, other: &$T) -> bool { *self % *other == 0 } - - /// Returns `true` if the number is divisible by `2`. - #[inline] - fn is_even(&self) -> bool { self & 1 == 0 } - - /// Returns `true` if the number is not divisible by `2`. - #[inline] - fn is_odd(&self) -> bool { !self.is_even() } - } - - #[cfg(test)] - mod $test_mod { - use Integer; - - #[test] - fn test_div_mod_floor() { - assert_eq!((10 as $T).div_floor(&(3 as $T)), 3 as $T); - assert_eq!((10 as $T).mod_floor(&(3 as $T)), 1 as $T); - assert_eq!((10 as $T).div_mod_floor(&(3 as $T)), (3 as $T, 1 as $T)); - assert_eq!((5 as $T).div_floor(&(5 as $T)), 1 as $T); - assert_eq!((5 as $T).mod_floor(&(5 as $T)), 0 as $T); - assert_eq!((5 as $T).div_mod_floor(&(5 as $T)), (1 as $T, 0 as $T)); - assert_eq!((3 as $T).div_floor(&(7 as $T)), 0 as $T); - assert_eq!((3 as $T).mod_floor(&(7 as $T)), 3 as $T); - assert_eq!((3 as $T).div_mod_floor(&(7 as $T)), (0 as $T, 3 as $T)); - } - - #[test] - fn test_gcd() { - assert_eq!((10 as $T).gcd(&2), 2 as $T); - assert_eq!((10 as $T).gcd(&3), 1 as $T); - assert_eq!((0 as $T).gcd(&3), 3 as $T); - assert_eq!((3 as $T).gcd(&3), 3 as $T); - assert_eq!((56 as $T).gcd(&42), 14 as $T); - } - - #[test] - #[allow(type_overflow)] - fn test_lcm() { - assert_eq!((1 as $T).lcm(&0), 0 as $T); - assert_eq!((0 as $T).lcm(&1), 0 as $T); - assert_eq!((1 as $T).lcm(&1), 1 as $T); - assert_eq!((8 as $T).lcm(&9), 72 as $T); - assert_eq!((11 as $T).lcm(&5), 55 as $T); - assert_eq!((99 as $T).lcm(&17), 1683 as $T); - } - - #[test] - fn test_is_multiple_of() { - assert!((6 as $T).is_multiple_of(&(6 as $T))); - assert!((6 as $T).is_multiple_of(&(3 as $T))); - assert!((6 as $T).is_multiple_of(&(1 as $T))); - } - - #[test] - fn test_even() { - assert_eq!((0 as $T).is_even(), true); - assert_eq!((1 as $T).is_even(), false); - assert_eq!((2 as $T).is_even(), true); - assert_eq!((3 as $T).is_even(), false); - assert_eq!((4 as $T).is_even(), true); - } - - #[test] - fn test_odd() { - assert_eq!((0 as $T).is_odd(), false); - assert_eq!((1 as $T).is_odd(), true); - assert_eq!((2 as $T).is_odd(), false); - assert_eq!((3 as $T).is_odd(), true); - assert_eq!((4 as $T).is_odd(), false); - } - } - ) -} - -impl_integer_for_uint!(u8, test_integer_u8) -impl_integer_for_uint!(u16, test_integer_u16) -impl_integer_for_uint!(u32, test_integer_u32) -impl_integer_for_uint!(u64, test_integer_u64) -impl_integer_for_uint!(uint, test_integer_uint) diff --git a/src/libnum/lib.rs b/src/libnum/lib.rs deleted file mode 100644 index 063bb17e09a..00000000000 --- a/src/libnum/lib.rs +++ /dev/null @@ -1,73 +0,0 @@ -// Copyright 2014 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! Simple numerics. -//! -//! This crate contains arbitrary-sized integer, rational, and complex types. -//! -//! ## Example -//! -//! This example uses the BigRational type and [Newton's method][newt] to -//! approximate a square root to arbitrary precision: -//! -//! ``` -//! # #![allow(deprecated)] -//! extern crate num; -//! -//! use num::bigint::BigInt; -//! use num::rational::{Ratio, BigRational}; -//! -//! fn approx_sqrt(number: u64, iterations: uint) -> BigRational { -//! let start: Ratio<BigInt> = Ratio::from_integer(FromPrimitive::from_u64(number).unwrap()); -//! let mut approx = start.clone(); -//! -//! for _ in range(0, iterations) { -//! approx = (approx + (start / approx)) / -//! Ratio::from_integer(FromPrimitive::from_u64(2).unwrap()); -//! } -//! -//! approx -//! } -//! -//! fn main() { -//! println!("{}", approx_sqrt(10, 4)); // prints 4057691201/1283082416 -//! } -//! ``` -//! -//! [newt]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method - -#![allow(unknown_features)] -#![feature(macro_rules, slicing_syntax)] -#![feature(default_type_params)] - -#![crate_name = "num"] -#![deprecated = "This is now a cargo package located at: \ - https://github.com/rust-lang/num"] -#![allow(deprecated)] -#![crate_type = "rlib"] -#![crate_type = "dylib"] -#![license = "MIT/ASL2"] -#![doc(html_logo_url = "http://www.rust-lang.org/logos/rust-logo-128x128-blk-v2.png", - html_favicon_url = "http://www.rust-lang.org/favicon.ico", - html_root_url = "http://doc.rust-lang.org/nightly/", - html_playground_url = "http://play.rust-lang.org/")] -#![allow(deprecated)] // from_str_radix - -extern crate rand; - -pub use bigint::{BigInt, BigUint}; -pub use rational::{Rational, BigRational}; -pub use complex::Complex; -pub use integer::Integer; - -pub mod bigint; -pub mod complex; -pub mod integer; -pub mod rational; diff --git a/src/libnum/rational.rs b/src/libnum/rational.rs deleted file mode 100644 index ceaf685c19a..00000000000 --- a/src/libnum/rational.rs +++ /dev/null @@ -1,803 +0,0 @@ -// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! Rational numbers - -use Integer; - -use std::cmp; -use std::fmt; -use std::from_str::FromStr; -use std::num; -use std::num::{Zero, One, ToStrRadix, FromStrRadix}; - -use bigint::{BigInt, BigUint, Sign, Plus, Minus}; - -/// Represents the ratio between 2 numbers. -#[deriving(Clone, Hash)] -#[allow(missing_doc)] -pub struct Ratio<T> { - numer: T, - denom: T -} - -/// Alias for a `Ratio` of machine-sized integers. -pub type Rational = Ratio<int>; -pub type Rational32 = Ratio<i32>; -pub type Rational64 = Ratio<i64>; - -/// Alias for arbitrary precision rationals. -pub type BigRational = Ratio<BigInt>; - -impl<T: Clone + Integer + PartialOrd> - Ratio<T> { - /// Creates a ratio representing the integer `t`. - #[inline] - pub fn from_integer(t: T) -> Ratio<T> { - Ratio::new_raw(t, One::one()) - } - - /// Creates a ratio without checking for `denom == 0` or reducing. - #[inline] - pub fn new_raw(numer: T, denom: T) -> Ratio<T> { - Ratio { numer: numer, denom: denom } - } - - /// Create a new Ratio. Fails if `denom == 0`. - #[inline] - pub fn new(numer: T, denom: T) -> Ratio<T> { - if denom == Zero::zero() { - fail!("denominator == 0"); - } - let mut ret = Ratio::new_raw(numer, denom); - ret.reduce(); - ret - } - - /// Converts to an integer. - #[inline] - pub fn to_integer(&self) -> T { - self.trunc().numer - } - - /// Gets an immutable reference to the numerator. - #[inline] - pub fn numer<'a>(&'a self) -> &'a T { - &self.numer - } - - /// Gets an immutable reference to the denominator. - #[inline] - pub fn denom<'a>(&'a self) -> &'a T { - &self.denom - } - - /// Returns true if the rational number is an integer (denominator is 1). - #[inline] - pub fn is_integer(&self) -> bool { - self.denom == One::one() - } - - /// Put self into lowest terms, with denom > 0. - fn reduce(&mut self) { - let g : T = self.numer.gcd(&self.denom); - - // FIXME(#5992): assignment operator overloads - // self.numer /= g; - self.numer = self.numer / g; - // FIXME(#5992): assignment operator overloads - // self.denom /= g; - self.denom = self.denom / g; - - // keep denom positive! - if self.denom < Zero::zero() { - self.numer = -self.numer; - self.denom = -self.denom; - } - } - - /// Returns a `reduce`d copy of self. - pub fn reduced(&self) -> Ratio<T> { - let mut ret = self.clone(); - ret.reduce(); - ret - } - - /// Returns the reciprocal. - #[inline] - pub fn recip(&self) -> Ratio<T> { - Ratio::new_raw(self.denom.clone(), self.numer.clone()) - } - - /// Rounds towards minus infinity. - #[inline] - pub fn floor(&self) -> Ratio<T> { - if *self < Zero::zero() { - Ratio::from_integer((self.numer - self.denom + One::one()) / self.denom) - } else { - Ratio::from_integer(self.numer / self.denom) - } - } - - /// Rounds towards plus infinity. - #[inline] - pub fn ceil(&self) -> Ratio<T> { - if *self < Zero::zero() { - Ratio::from_integer(self.numer / self.denom) - } else { - Ratio::from_integer((self.numer + self.denom - One::one()) / self.denom) - } - } - - /// Rounds to the nearest integer. Rounds half-way cases away from zero. - #[inline] - pub fn round(&self) -> Ratio<T> { - let one: T = One::one(); - let two: T = one + one; - - // Find unsigned fractional part of rational number - let fractional = self.fract().abs(); - - // The algorithm compares the unsigned fractional part with 1/2, that - // is, a/b >= 1/2, or a >= b/2. For odd denominators, we use - // a >= (b/2)+1. This avoids overflow issues. - let half_or_larger = if fractional.denom().is_even() { - *fractional.numer() >= *fractional.denom() / two - } else { - *fractional.numer() >= (*fractional.denom() / two) + one - }; - - if half_or_larger { - if *self >= Zero::zero() { - self.trunc() + One::one() - } else { - self.trunc() - One::one() - } - } else { - self.trunc() - } - } - - /// Rounds towards zero. - #[inline] - pub fn trunc(&self) -> Ratio<T> { - Ratio::from_integer(self.numer / self.denom) - } - - /// Returns the fractional part of a number. - #[inline] - pub fn fract(&self) -> Ratio<T> { - Ratio::new_raw(self.numer % self.denom, self.denom.clone()) - } -} - -impl Ratio<BigInt> { - /// Converts a float into a rational number. - pub fn from_float<T: Float>(f: T) -> Option<BigRational> { - if !f.is_finite() { - return None; - } - let (mantissa, exponent, sign) = f.integer_decode(); - let bigint_sign: Sign = if sign == 1 { Plus } else { Minus }; - if exponent < 0 { - let one: BigInt = One::one(); - let denom: BigInt = one << ((-exponent) as uint); - let numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap(); - Some(Ratio::new(BigInt::from_biguint(bigint_sign, numer), denom)) - } else { - let mut numer: BigUint = FromPrimitive::from_u64(mantissa).unwrap(); - numer = numer << (exponent as uint); - Some(Ratio::from_integer(BigInt::from_biguint(bigint_sign, numer))) - } - } -} - -/* Comparisons */ - -// comparing a/b and c/d is the same as comparing a*d and b*c, so we -// abstract that pattern. The following macro takes a trait and either -// a comma-separated list of "method name -> return value" or just -// "method name" (return value is bool in that case) -macro_rules! cmp_impl { - (impl $imp:ident, $($method:ident),+) => { - cmp_impl!(impl $imp, $($method -> bool),+) - }; - // return something other than a Ratio<T> - (impl $imp:ident, $($method:ident -> $res:ty),*) => { - impl<T: Mul<T,T> + $imp> $imp for Ratio<T> { - $( - #[inline] - fn $method(&self, other: &Ratio<T>) -> $res { - (self.numer * other.denom). $method (&(self.denom*other.numer)) - } - )* - } - }; -} -cmp_impl!(impl PartialEq, eq, ne) -cmp_impl!(impl PartialOrd, lt -> bool, gt -> bool, le -> bool, ge -> bool, - partial_cmp -> Option<cmp::Ordering>) -cmp_impl!(impl Eq, ) -cmp_impl!(impl Ord, cmp -> cmp::Ordering) - -/* Arithmetic */ -// a/b * c/d = (a*c)/(b*d) -impl<T: Clone + Integer + PartialOrd> - Mul<Ratio<T>,Ratio<T>> for Ratio<T> { - #[inline] - fn mul(&self, rhs: &Ratio<T>) -> Ratio<T> { - Ratio::new(self.numer * rhs.numer, self.denom * rhs.denom) - } -} - -// (a/b) / (c/d) = (a*d)/(b*c) -impl<T: Clone + Integer + PartialOrd> - Div<Ratio<T>,Ratio<T>> for Ratio<T> { - #[inline] - fn div(&self, rhs: &Ratio<T>) -> Ratio<T> { - Ratio::new(self.numer * rhs.denom, self.denom * rhs.numer) - } -} - -// Abstracts the a/b `op` c/d = (a*d `op` b*d) / (b*d) pattern -macro_rules! arith_impl { - (impl $imp:ident, $method:ident) => { - impl<T: Clone + Integer + PartialOrd> - $imp<Ratio<T>,Ratio<T>> for Ratio<T> { - #[inline] - fn $method(&self, rhs: &Ratio<T>) -> Ratio<T> { - Ratio::new((self.numer * rhs.denom).$method(&(self.denom * rhs.numer)), - self.denom * rhs.denom) - } - } - } -} - -// a/b + c/d = (a*d + b*c)/(b*d) -arith_impl!(impl Add, add) - -// a/b - c/d = (a*d - b*c)/(b*d) -arith_impl!(impl Sub, sub) - -// a/b % c/d = (a*d % b*c)/(b*d) -arith_impl!(impl Rem, rem) - -impl<T: Clone + Integer + PartialOrd> - Neg<Ratio<T>> for Ratio<T> { - #[inline] - fn neg(&self) -> Ratio<T> { - Ratio::new_raw(-self.numer, self.denom.clone()) - } -} - -/* Constants */ -impl<T: Clone + Integer + PartialOrd> - Zero for Ratio<T> { - #[inline] - fn zero() -> Ratio<T> { - Ratio::new_raw(Zero::zero(), One::one()) - } - - #[inline] - fn is_zero(&self) -> bool { - *self == Zero::zero() - } -} - -impl<T: Clone + Integer + PartialOrd> - One for Ratio<T> { - #[inline] - fn one() -> Ratio<T> { - Ratio::new_raw(One::one(), One::one()) - } -} - -impl<T: Clone + Integer + PartialOrd> - Num for Ratio<T> {} - -impl<T: Clone + Integer + PartialOrd> - num::Signed for Ratio<T> { - #[inline] - fn abs(&self) -> Ratio<T> { - if self.is_negative() { -self.clone() } else { self.clone() } - } - - #[inline] - fn abs_sub(&self, other: &Ratio<T>) -> Ratio<T> { - if *self <= *other { Zero::zero() } else { *self - *other } - } - - #[inline] - fn signum(&self) -> Ratio<T> { - if *self > Zero::zero() { - num::one() - } else if self.is_zero() { - num::zero() - } else { - - num::one::<Ratio<T>>() - } - } - - #[inline] - fn is_positive(&self) -> bool { *self > Zero::zero() } - - #[inline] - fn is_negative(&self) -> bool { *self < Zero::zero() } -} - -/* String conversions */ -impl<T: fmt::Show + Eq + One> fmt::Show for Ratio<T> { - /// Renders as `numer/denom`. If denom=1, renders as numer. - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - if self.denom == One::one() { - write!(f, "{}", self.numer) - } else { - write!(f, "{}/{}", self.numer, self.denom) - } - } -} - -impl<T: ToStrRadix> ToStrRadix for Ratio<T> { - /// Renders as `numer/denom` where the numbers are in base `radix`. - fn to_str_radix(&self, radix: uint) -> String { - format!("{}/{}", - self.numer.to_str_radix(radix), - self.denom.to_str_radix(radix)) - } -} - -impl<T: FromStr + Clone + Integer + PartialOrd> - FromStr for Ratio<T> { - /// Parses `numer/denom` or just `numer`. - fn from_str(s: &str) -> Option<Ratio<T>> { - let mut split = s.splitn(1, '/'); - - let num = split.next().and_then(|n| FromStr::from_str(n)); - let den = split.next().or(Some("1")).and_then(|d| FromStr::from_str(d)); - - match (num, den) { - (Some(n), Some(d)) => Some(Ratio::new(n, d)), - _ => None - } - } -} - -impl<T: FromStrRadix + Clone + Integer + PartialOrd> - FromStrRadix for Ratio<T> { - /// Parses `numer/denom` where the numbers are in base `radix`. - fn from_str_radix(s: &str, radix: uint) -> Option<Ratio<T>> { - let split: Vec<&str> = s.splitn(1, '/').collect(); - if split.len() < 2 { - None - } else { - let a_option: Option<T> = FromStrRadix::from_str_radix( - *split.get(0), - radix); - a_option.and_then(|a| { - let b_option: Option<T> = - FromStrRadix::from_str_radix(*split.get(1), radix); - b_option.and_then(|b| { - Some(Ratio::new(a.clone(), b.clone())) - }) - }) - } - } -} - -#[cfg(test)] -mod test { - - use super::{Ratio, Rational, BigRational}; - use std::num::{Zero, One, FromStrRadix, FromPrimitive, ToStrRadix}; - use std::from_str::FromStr; - use std::hash::hash; - use std::num; - use std::i32; - - pub static _0 : Rational = Ratio { numer: 0, denom: 1}; - pub static _1 : Rational = Ratio { numer: 1, denom: 1}; - pub static _2: Rational = Ratio { numer: 2, denom: 1}; - pub static _1_2: Rational = Ratio { numer: 1, denom: 2}; - pub static _3_2: Rational = Ratio { numer: 3, denom: 2}; - #[allow(non_uppercase_statics)] - pub static _neg1_2: Rational = Ratio { numer: -1, denom: 2}; - pub static _1_3: Rational = Ratio { numer: 1, denom: 3}; - #[allow(non_uppercase_statics)] - pub static _neg1_3: Rational = Ratio { numer: -1, denom: 3}; - pub static _2_3: Rational = Ratio { numer: 2, denom: 3}; - #[allow(non_uppercase_statics)] - pub static _neg2_3: Rational = Ratio { numer: -2, denom: 3}; - - pub fn to_big(n: Rational) -> BigRational { - Ratio::new( - FromPrimitive::from_int(n.numer).unwrap(), - FromPrimitive::from_int(n.denom).unwrap() - ) - } - - #[test] - fn test_test_constants() { - // check our constants are what Ratio::new etc. would make. - assert_eq!(_0, Zero::zero()); - assert_eq!(_1, One::one()); - assert_eq!(_2, Ratio::from_integer(2i)); - assert_eq!(_1_2, Ratio::new(1i,2i)); - assert_eq!(_3_2, Ratio::new(3i,2i)); - assert_eq!(_neg1_2, Ratio::new(-1i,2i)); - } - - #[test] - fn test_new_reduce() { - let one22 = Ratio::new(2i,2); - - assert_eq!(one22, One::one()); - } - #[test] - #[should_fail] - fn test_new_zero() { - let _a = Ratio::new(1i,0); - } - - - #[test] - fn test_cmp() { - assert!(_0 == _0 && _1 == _1); - assert!(_0 != _1 && _1 != _0); - assert!(_0 < _1 && !(_1 < _0)); - assert!(_1 > _0 && !(_0 > _1)); - - assert!(_0 <= _0 && _1 <= _1); - assert!(_0 <= _1 && !(_1 <= _0)); - - assert!(_0 >= _0 && _1 >= _1); - assert!(_1 >= _0 && !(_0 >= _1)); - } - - - #[test] - fn test_to_integer() { - assert_eq!(_0.to_integer(), 0); - assert_eq!(_1.to_integer(), 1); - assert_eq!(_2.to_integer(), 2); - assert_eq!(_1_2.to_integer(), 0); - assert_eq!(_3_2.to_integer(), 1); - assert_eq!(_neg1_2.to_integer(), 0); - } - - - #[test] - fn test_numer() { - assert_eq!(_0.numer(), &0); - assert_eq!(_1.numer(), &1); - assert_eq!(_2.numer(), &2); - assert_eq!(_1_2.numer(), &1); - assert_eq!(_3_2.numer(), &3); - assert_eq!(_neg1_2.numer(), &(-1)); - } - #[test] - fn test_denom() { - assert_eq!(_0.denom(), &1); - assert_eq!(_1.denom(), &1); - assert_eq!(_2.denom(), &1); - assert_eq!(_1_2.denom(), &2); - assert_eq!(_3_2.denom(), &2); - assert_eq!(_neg1_2.denom(), &2); - } - - - #[test] - fn test_is_integer() { - assert!(_0.is_integer()); - assert!(_1.is_integer()); - assert!(_2.is_integer()); - assert!(!_1_2.is_integer()); - assert!(!_3_2.is_integer()); - assert!(!_neg1_2.is_integer()); - } - - #[test] - fn test_show() { - assert_eq!(format!("{}", _2), "2".to_string()); - assert_eq!(format!("{}", _1_2), "1/2".to_string()); - assert_eq!(format!("{}", _0), "0".to_string()); - assert_eq!(format!("{}", Ratio::from_integer(-2i)), "-2".to_string()); - } - - mod arith { - use super::{_0, _1, _2, _1_2, _3_2, _neg1_2, to_big}; - use super::super::{Ratio, Rational}; - - #[test] - fn test_add() { - fn test(a: Rational, b: Rational, c: Rational) { - assert_eq!(a + b, c); - assert_eq!(to_big(a) + to_big(b), to_big(c)); - } - - test(_1, _1_2, _3_2); - test(_1, _1, _2); - test(_1_2, _3_2, _2); - test(_1_2, _neg1_2, _0); - } - - #[test] - fn test_sub() { - fn test(a: Rational, b: Rational, c: Rational) { - assert_eq!(a - b, c); - assert_eq!(to_big(a) - to_big(b), to_big(c)) - } - - test(_1, _1_2, _1_2); - test(_3_2, _1_2, _1); - test(_1, _neg1_2, _3_2); - } - - #[test] - fn test_mul() { - fn test(a: Rational, b: Rational, c: Rational) { - assert_eq!(a * b, c); - assert_eq!(to_big(a) * to_big(b), to_big(c)) - } - - test(_1, _1_2, _1_2); - test(_1_2, _3_2, Ratio::new(3i,4i)); - test(_1_2, _neg1_2, Ratio::new(-1i, 4i)); - } - - #[test] - fn test_div() { - fn test(a: Rational, b: Rational, c: Rational) { - assert_eq!(a / b, c); - assert_eq!(to_big(a) / to_big(b), to_big(c)) - } - - test(_1, _1_2, _2); - test(_3_2, _1_2, _1 + _2); - test(_1, _neg1_2, _neg1_2 + _neg1_2 + _neg1_2 + _neg1_2); - } - - #[test] - fn test_rem() { - fn test(a: Rational, b: Rational, c: Rational) { - assert_eq!(a % b, c); - assert_eq!(to_big(a) % to_big(b), to_big(c)) - } - - test(_3_2, _1, _1_2); - test(_2, _neg1_2, _0); - test(_1_2, _2, _1_2); - } - - #[test] - fn test_neg() { - fn test(a: Rational, b: Rational) { - assert_eq!(-a, b); - assert_eq!(-to_big(a), to_big(b)) - } - - test(_0, _0); - test(_1_2, _neg1_2); - test(-_1, _1); - } - #[test] - fn test_zero() { - assert_eq!(_0 + _0, _0); - assert_eq!(_0 * _0, _0); - assert_eq!(_0 * _1, _0); - assert_eq!(_0 / _neg1_2, _0); - assert_eq!(_0 - _0, _0); - } - #[test] - #[should_fail] - fn test_div_0() { - let _a = _1 / _0; - } - } - - #[test] - fn test_round() { - assert_eq!(_1_3.ceil(), _1); - assert_eq!(_1_3.floor(), _0); - assert_eq!(_1_3.round(), _0); - assert_eq!(_1_3.trunc(), _0); - - assert_eq!(_neg1_3.ceil(), _0); - assert_eq!(_neg1_3.floor(), -_1); - assert_eq!(_neg1_3.round(), _0); - assert_eq!(_neg1_3.trunc(), _0); - - assert_eq!(_2_3.ceil(), _1); - assert_eq!(_2_3.floor(), _0); - assert_eq!(_2_3.round(), _1); - assert_eq!(_2_3.trunc(), _0); - - assert_eq!(_neg2_3.ceil(), _0); - assert_eq!(_neg2_3.floor(), -_1); - assert_eq!(_neg2_3.round(), -_1); - assert_eq!(_neg2_3.trunc(), _0); - - assert_eq!(_1_2.ceil(), _1); - assert_eq!(_1_2.floor(), _0); - assert_eq!(_1_2.round(), _1); - assert_eq!(_1_2.trunc(), _0); - - assert_eq!(_neg1_2.ceil(), _0); - assert_eq!(_neg1_2.floor(), -_1); - assert_eq!(_neg1_2.round(), -_1); - assert_eq!(_neg1_2.trunc(), _0); - - assert_eq!(_1.ceil(), _1); - assert_eq!(_1.floor(), _1); - assert_eq!(_1.round(), _1); - assert_eq!(_1.trunc(), _1); - - // Overflow checks - - let _neg1 = Ratio::from_integer(-1); - let _large_rat1 = Ratio::new(i32::MAX, i32::MAX-1); - let _large_rat2 = Ratio::new(i32::MAX-1, i32::MAX); - let _large_rat3 = Ratio::new(i32::MIN+2, i32::MIN+1); - let _large_rat4 = Ratio::new(i32::MIN+1, i32::MIN+2); - let _large_rat5 = Ratio::new(i32::MIN+2, i32::MAX); - let _large_rat6 = Ratio::new(i32::MAX, i32::MIN+2); - let _large_rat7 = Ratio::new(1, i32::MIN+1); - let _large_rat8 = Ratio::new(1, i32::MAX); - - assert_eq!(_large_rat1.round(), One::one()); - assert_eq!(_large_rat2.round(), One::one()); - assert_eq!(_large_rat3.round(), One::one()); - assert_eq!(_large_rat4.round(), One::one()); - assert_eq!(_large_rat5.round(), _neg1); - assert_eq!(_large_rat6.round(), _neg1); - assert_eq!(_large_rat7.round(), Zero::zero()); - assert_eq!(_large_rat8.round(), Zero::zero()); - } - - #[test] - fn test_fract() { - assert_eq!(_1.fract(), _0); - assert_eq!(_neg1_2.fract(), _neg1_2); - assert_eq!(_1_2.fract(), _1_2); - assert_eq!(_3_2.fract(), _1_2); - } - - #[test] - fn test_recip() { - assert_eq!(_1 * _1.recip(), _1); - assert_eq!(_2 * _2.recip(), _1); - assert_eq!(_1_2 * _1_2.recip(), _1); - assert_eq!(_3_2 * _3_2.recip(), _1); - assert_eq!(_neg1_2 * _neg1_2.recip(), _1); - } - - #[test] - fn test_to_from_str() { - fn test(r: Rational, s: String) { - assert_eq!(FromStr::from_str(s.as_slice()), Some(r)); - assert_eq!(r.to_string(), s); - } - test(_1, "1".to_string()); - test(_0, "0".to_string()); - test(_1_2, "1/2".to_string()); - test(_3_2, "3/2".to_string()); - test(_2, "2".to_string()); - test(_neg1_2, "-1/2".to_string()); - } - #[test] - fn test_from_str_fail() { - fn test(s: &str) { - let rational: Option<Rational> = FromStr::from_str(s); - assert_eq!(rational, None); - } - - let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1"]; - for &s in xs.iter() { - test(s); - } - } - - #[test] - fn test_to_from_str_radix() { - fn test(r: Rational, s: String, n: uint) { - assert_eq!(FromStrRadix::from_str_radix(s.as_slice(), n), - Some(r)); - assert_eq!(r.to_str_radix(n).to_string(), s); - } - fn test3(r: Rational, s: String) { test(r, s, 3) } - fn test16(r: Rational, s: String) { test(r, s, 16) } - - test3(_1, "1/1".to_string()); - test3(_0, "0/1".to_string()); - test3(_1_2, "1/2".to_string()); - test3(_3_2, "10/2".to_string()); - test3(_2, "2/1".to_string()); - test3(_neg1_2, "-1/2".to_string()); - test3(_neg1_2 / _2, "-1/11".to_string()); - - test16(_1, "1/1".to_string()); - test16(_0, "0/1".to_string()); - test16(_1_2, "1/2".to_string()); - test16(_3_2, "3/2".to_string()); - test16(_2, "2/1".to_string()); - test16(_neg1_2, "-1/2".to_string()); - test16(_neg1_2 / _2, "-1/4".to_string()); - test16(Ratio::new(13i,15i), "d/f".to_string()); - test16(_1_2*_1_2*_1_2*_1_2, "1/10".to_string()); - } - - #[test] - fn test_from_str_radix_fail() { - fn test(s: &str) { - let radix: Option<Rational> = FromStrRadix::from_str_radix(s, 3); - assert_eq!(radix, None); - } - - let xs = ["0 /1", "abc", "", "1/", "--1/2","3/2/1", "3/2"]; - for &s in xs.iter() { - test(s); - } - } - - #[test] - fn test_from_float() { - fn test<T: Float>(given: T, (numer, denom): (&str, &str)) { - let ratio: BigRational = Ratio::from_float(given).unwrap(); - assert_eq!(ratio, Ratio::new( - FromStr::from_str(numer).unwrap(), - FromStr::from_str(denom).unwrap())); - } - - // f32 - test(3.14159265359f32, ("13176795", "4194304")); - test(2f32.powf(100.), ("1267650600228229401496703205376", "1")); - test(-2f32.powf(100.), ("-1267650600228229401496703205376", "1")); - test(1.0 / 2f32.powf(100.), ("1", "1267650600228229401496703205376")); - test(684729.48391f32, ("1369459", "2")); - test(-8573.5918555f32, ("-4389679", "512")); - - // f64 - test(3.14159265359f64, ("3537118876014453", "1125899906842624")); - test(2f64.powf(100.), ("1267650600228229401496703205376", "1")); - test(-2f64.powf(100.), ("-1267650600228229401496703205376", "1")); - test(684729.48391f64, ("367611342500051", "536870912")); - test(-8573.5918555f64, ("-4713381968463931", "549755813888")); - test(1.0 / 2f64.powf(100.), ("1", "1267650600228229401496703205376")); - } - - #[test] - fn test_from_float_fail() { - use std::{f32, f64}; - - assert_eq!(Ratio::from_float(f32::NAN), None); - assert_eq!(Ratio::from_float(f32::INFINITY), None); - assert_eq!(Ratio::from_float(f32::NEG_INFINITY), None); - assert_eq!(Ratio::from_float(f64::NAN), None); - assert_eq!(Ratio::from_float(f64::INFINITY), None); - assert_eq!(Ratio::from_float(f64::NEG_INFINITY), None); - } - - #[test] - fn test_signed() { - assert_eq!(_neg1_2.abs(), _1_2); - assert_eq!(_3_2.abs_sub(&_1_2), _1); - assert_eq!(_1_2.abs_sub(&_3_2), Zero::zero()); - assert_eq!(_1_2.signum(), One::one()); - assert_eq!(_neg1_2.signum(), - num::one::<Ratio<int>>()); - assert!(_neg1_2.is_negative()); - assert!(! _neg1_2.is_positive()); - assert!(! _1_2.is_negative()); - } - - #[test] - fn test_hash() { - assert!(hash(&_0) != hash(&_1)); - assert!(hash(&_0) != hash(&_3_2)); - } -} |