src/libextra/sort.rs

// Copyright 2012 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.

//! Sorting methods


use std::cmp::{Eq, Ord};
use std::util::swap;
use std::vec;

type Le<'self, T> = &'self fn(v1: &T, v2: &T) -> bool;

/**
 * Merge sort. Returns a new vector containing the sorted list.
 *
 * Has worst case O(n log n) performance, best case O(n), but
 * is not space efficient. This is a stable sort.
 */
pub fn merge_sort<T:Clone>(v: &[T], le: Le<T>) -> ~[T] {
    type Slice = (uint, uint);

    return merge_sort_(v, (0u, v.len()), le);

    fn merge_sort_<T:Clone>(v: &[T], slice: Slice, le: Le<T>) -> ~[T] {
        let begin = slice.first();
        let end = slice.second();

        let v_len = end - begin;
        if v_len == 0 { return ~[]; }
        if v_len == 1 { return ~[v[begin].clone()]; }

        let mid = v_len / 2 + begin;
        let a = (begin, mid);
        let b = (mid, end);
        return merge(|x,y| le(x,y), merge_sort_(v, a, |x,y| le(x,y)),
                                    merge_sort_(v, b, |x,y| le(x,y)));
    }

    fn merge<T:Clone>(le: Le<T>, a: &[T], b: &[T]) -> ~[T] {
        let mut rs = vec::with_capacity(a.len() + b.len());
        let a_len = a.len();
        let mut a_ix = 0;
        let b_len = b.len();
        let mut b_ix = 0;
        while a_ix < a_len && b_ix < b_len {
            if le(&a[a_ix], &b[b_ix]) {
                rs.push(a[a_ix].clone());
                a_ix += 1;
            } else {
                rs.push(b[b_ix].clone());
                b_ix += 1;
            }
        }
        rs.push_all(a.slice(a_ix, a_len));
        rs.push_all(b.slice(b_ix, b_len));
        rs
    }
}

fn part<T>(arr: &mut [T], left: uint,
           right: uint, pivot: uint, compare_func: Le<T>) -> uint {
    arr.swap(pivot, right);
    let mut storage_index: uint = left;
    let mut i: uint = left;
    while i < right {
        if compare_func(&arr[i], &arr[right]) {
            arr.swap(i, storage_index);
            storage_index += 1;
        }
        i += 1;
    }
    arr.swap(storage_index, right);
    return storage_index;
}

fn qsort<T>(arr: &mut [T], left: uint,
            right: uint, compare_func: Le<T>) {
    if right > left {
        let pivot = (left + right) / 2u;
        let new_pivot = part::<T>(arr, left, right, pivot, |x,y| compare_func(x,y));
        if new_pivot != 0u {
            // Need to do this check before recursing due to overflow
            qsort::<T>(arr, left, new_pivot - 1u, |x,y| compare_func(x,y));
        }
        qsort::<T>(arr, new_pivot + 1u, right, compare_func);
    }
}

/**
 * Quicksort. Sorts a mut vector in place.
 *
 * Has worst case O(n^2) performance, average case O(n log n).
 * This is an unstable sort.
 */
pub fn quick_sort<T>(arr: &mut [T], compare_func: Le<T>) {
    let len = arr.len();
    if len == 0u { return; }
    qsort::<T>(arr, 0u, len - 1u, compare_func);
}

fn qsort3<T:Clone + Ord + Eq>(arr: &mut [T], left: int, right: int) {
    if right <= left { return; }
    let v: T = arr[right].clone();
    let mut i: int = left - 1;
    let mut j: int = right;
    let mut p: int = i;
    let mut q: int = j;
    loop {
        i += 1;
        while arr[i] < v { i += 1; }
        j -= 1;
        while v < arr[j] {
            if j == left { break; }
            j -= 1;
        }
        if i >= j { break; }
        arr.swap(i as uint, j as uint);
        if arr[i] == v {
            p += 1;
            arr.swap(p as uint, i as uint);
        }
        if v == arr[j] {
            q -= 1;
            arr.swap(j as uint, q as uint);
        }
    }
    arr.swap(i as uint, right as uint);
    j = i - 1;
    i += 1;
    let mut k: int = left;
    while k < p {
        arr.swap(k as uint, j as uint);
        k += 1;
        j -= 1;
        if k == arr.len() as int { break; }
    }
    k = right - 1;
    while k > q {
        arr.swap(i as uint, k as uint);
        k -= 1;
        i += 1;
        if k == 0 { break; }
    }
    qsort3::<T>(arr, left, j);
    qsort3::<T>(arr, i, right);
}

/**
 * Fancy quicksort. Sorts a mut vector in place.
 *
 * Based on algorithm presented by ~[Sedgewick and Bentley]
 * (http://www.cs.princeton.edu/~rs/talks/QuicksortIsOptimal.pdf).
 * According to these slides this is the algorithm of choice for
 * 'randomly ordered keys, abstract compare' & 'small number of key values'.
 *
 * This is an unstable sort.
 */
pub fn quick_sort3<T:Clone + Ord + Eq>(arr: &mut [T]) {
    if arr.len() <= 1 { return; }
    let len = arr.len(); // FIXME(#5074) nested calls
    qsort3(arr, 0, (len - 1) as int);
}

#[allow(missing_doc)]
pub trait Sort {
    fn qsort(self);
}

impl<'self, T:Clone + Ord + Eq> Sort for &'self mut [T] {
    fn qsort(self) { quick_sort3(self); }
}

static MIN_MERGE: uint = 64;
static MIN_GALLOP: uint = 7;
static INITIAL_TMP_STORAGE: uint = 128;

#[allow(missing_doc)]
pub fn tim_sort<T:Clone + Ord>(array: &mut [T]) {
    let size = array.len();
    if size < 2 {
        return;
    }

    if size < MIN_MERGE {
        let init_run_len = count_run_ascending(array);
        binarysort(array, init_run_len);
        return;
    }

    let mut ms = MergeState();
    let min_run = min_run_length(size);

    let mut idx = 0;
    let mut remaining = size;
    loop {
        let run_len: uint = {
            // This scope contains the slice `arr` here:
            let arr = array.mut_slice(idx, size);
            let mut run_len: uint = count_run_ascending(arr);

            if run_len < min_run {
                let force = if remaining <= min_run {remaining} else {min_run};
                let slice = arr.mut_slice(0, force);
                binarysort(slice, run_len);
                run_len = force;
            }

            run_len
        };

        ms.push_run(idx, run_len);
        ms.merge_collapse(array);

        idx += run_len;
        remaining -= run_len;
        if remaining == 0 { break; }
    }

    ms.merge_force_collapse(array);
}

fn binarysort<T:Clone + Ord>(array: &mut [T], start: uint) {
    let size = array.len();
    let mut start = start;
    assert!(start <= size);

    if start == 0 { start += 1; }

    while start < size {
        let pivot = array[start].clone();
        let mut left = 0;
        let mut right = start;
        assert!(left <= right);

        while left < right {
            let mid = (left + right) >> 1;
            if pivot < array[mid] {
                right = mid;
            } else {
                left = mid+1;
            }
        }
        assert_eq!(left, right);
        let n = start-left;

        shift_vec(array, left+1, left, n);
        array[left] = pivot;
        start += 1;
    }
}

// Reverse the order of elements in a slice, in place
fn reverse_slice<T>(v: &mut [T], start: uint, end:uint) {
    let mut i = start;
    while i < end / 2 {
        v.swap(i, end - i - 1);
        i += 1;
    }
}

fn min_run_length(n: uint) -> uint {
    let mut n = n;
    let mut r = 0;   // becomes 1 if any 1 bits are shifted off

    while n >= MIN_MERGE {
        r |= n & 1;
        n >>= 1;
    }
    return n + r;
}

fn count_run_ascending<T:Clone + Ord>(array: &mut [T]) -> uint {
    let size = array.len();
    assert!(size > 0);
    if size == 1 { return 1; }

    let mut run = 2;
    if array[1] < array[0] {
        while run < size && array[run] < array[run-1] {
            run += 1;
        }
        reverse_slice(array, 0, run);
    } else {
        while run < size && array[run] >= array[run-1] {
            run += 1;
        }
    }

    return run;
}

fn gallop_left<T:Clone + Ord>(key: &T,
                             array: &[T],
                             hint: uint)
                          -> uint {
    let size = array.len();
    assert!(size != 0 && hint < size);

    let mut last_ofs = 0;
    let mut ofs = 1;

    if *key > array[hint] {
        // Gallop right until array[hint+last_ofs] < key <= array[hint+ofs]
        let max_ofs = size - hint;
        while ofs < max_ofs && *key > array[hint+ofs] {
            last_ofs = ofs;
            ofs = (ofs << 1) + 1;
            if ofs < last_ofs { ofs = max_ofs; } // uint overflow guard
        }
        if ofs > max_ofs { ofs = max_ofs; }

        last_ofs += hint;
        ofs += hint;
    } else {
        let max_ofs = hint + 1;
        while ofs < max_ofs && *key <= array[hint-ofs] {
            last_ofs = ofs;
            ofs = (ofs << 1) + 1;
            if ofs < last_ofs { ofs = max_ofs; } // uint overflow guard
        }

        if ofs > max_ofs { ofs = max_ofs; }

        let tmp = last_ofs;
        last_ofs = hint - ofs;
        ofs = hint - tmp;
    }
    assert!((last_ofs < ofs || last_ofs+1 < ofs+1) && ofs <= size);

    last_ofs += 1;
    while last_ofs < ofs {
        let m = last_ofs + ((ofs - last_ofs) >> 1);
        if *key > array[m] {
            last_ofs = m+1;
        } else {
            ofs = m;
        }
    }
    assert_eq!(last_ofs, ofs);
    return ofs;
}

fn gallop_right<T:Clone + Ord>(key: &T,
                              array: &[T],
                              hint: uint)
                           -> uint {
    let size = array.len();
    assert!(size != 0 && hint < size);

    let mut last_ofs = 0;
    let mut ofs = 1;

    if *key >= array[hint] {
        // Gallop right until array[hint+last_ofs] <= key < array[hint+ofs]
        let max_ofs = size - hint;
        while ofs < max_ofs && *key >= array[hint+ofs] {
            last_ofs = ofs;
            ofs = (ofs << 1) + 1;
            if ofs < last_ofs { ofs = max_ofs; }
        }
        if ofs > max_ofs { ofs = max_ofs; }

        last_ofs += hint;
        ofs += hint;
    } else {
        // Gallop left until array[hint-ofs] <= key < array[hint-last_ofs]
        let max_ofs = hint + 1;
        while ofs < max_ofs && *key < array[hint-ofs] {
            last_ofs = ofs;
            ofs = (ofs << 1) + 1;
            if ofs < last_ofs { ofs = max_ofs; }
        }
        if ofs > max_ofs { ofs = max_ofs; }

        let tmp = last_ofs;
        last_ofs = hint - ofs;
        ofs = hint - tmp;
    }

    assert!((last_ofs < ofs || last_ofs+1 < ofs+1) && ofs <= size);

    last_ofs += 1;
    while last_ofs < ofs {
        let m = last_ofs + ((ofs - last_ofs) >> 1);

        if *key >= array[m] {
            last_ofs = m + 1;
        } else {
            ofs = m;
        }
    }
    assert_eq!(last_ofs, ofs);
    return ofs;
}

struct RunState {
    base: uint,
    len: uint,
}

struct MergeState<T> {
    min_gallop: uint,
    runs: ~[RunState],
}

// Fixme (#3853) Move into MergeState
fn MergeState<T>() -> MergeState<T> {
    MergeState {
        min_gallop: MIN_GALLOP,
        runs: ~[],
    }
}

impl<T:Clone + Ord> MergeState<T> {
    fn push_run(&mut self, run_base: uint, run_len: uint) {
        let tmp = RunState{base: run_base, len: run_len};
        self.runs.push(tmp);
    }

    fn merge_at(&mut self, n: uint, array: &mut [T]) {
        let size = self.runs.len();
        assert!(size >= 2);
        assert!(n == size-2 || n == size-3);

        let mut b1 = self.runs[n].base;
        let mut l1 = self.runs[n].len;
        let b2 = self.runs[n+1].base;
        let l2 = self.runs[n+1].len;

        assert!(l1 > 0 && l2 > 0);
        assert_eq!(b1 + l1, b2);

        self.runs[n].len = l1 + l2;
        if n == size-3 {
            self.runs[n+1].base = self.runs[n+2].base;
            self.runs[n+1].len = self.runs[n+2].len;
        }

        let k = { // constrain lifetime of slice below
            let slice = array.slice(b1, b1+l1);
            gallop_right(&array[b2], slice, 0)
        };
        b1 += k;
        l1 -= k;
        if l1 != 0 {
            let l2 = { // constrain lifetime of slice below
                let slice = array.slice(b2, b2+l2);
                gallop_left(&array[b1+l1-1],slice,l2-1)
            };
            if l2 > 0 {
                if l1 <= l2 {
                    self.merge_lo(array, b1, l1, b2, l2);
                } else {
                    self.merge_hi(array, b1, l1, b2, l2);
                }
            }
        }
        self.runs.pop();
    }

    fn merge_lo(&mut self, array: &mut [T], base1: uint, len1: uint,
                base2: uint, len2: uint) {
        assert!(len1 != 0 && len2 != 0 && base1+len1 == base2);

        let mut tmp = array.slice(base1, base1 + len1).to_owned();

        let mut c1 = 0;
        let mut c2 = base2;
        let mut dest = base1;
        let mut len1 = len1;
        let mut len2 = len2;

        array.swap(dest, c2);
        dest += 1; c2 += 1; len2 -= 1;

        if len2 == 0 {
            copy_vec(array, dest, tmp.slice(0, len1));
            return;
        }
        if len1 == 1 {
            shift_vec(array, dest, c2, len2);
            swap(&mut tmp[c1], &mut array[dest+len2]);
            return;
        }

        let mut min_gallop = self.min_gallop;
        loop {
            let mut count1 = 0;
            let mut count2 = 0;
            let mut break_outer = false;

            loop {
                assert!(len1 > 1 && len2 != 0);
                if array[c2] < tmp[c1] {
                    array.swap(dest, c2);
                    dest += 1; c2 += 1; len2 -= 1;
                    count2 += 1; count1 = 0;
                    if len2 == 0 {
                        break_outer = true;
                    }
                } else {
                    swap(&mut array[dest], &mut tmp[c1]);
                    dest += 1; c1 += 1; len1 -= 1;
                    count1 += 1; count2 = 0;
                    if len1 == 1 {
                        break_outer = true;
                    }
                }
                if break_outer || ((count1 | count2) >= min_gallop) {
                    break;
                }
            }
            if break_outer { break; }

            // Start to gallop
            loop {
                assert!(len1 > 1 && len2 != 0);

                count1 = {
                    let tmp_view = tmp.slice(c1, c1+len1);
                    gallop_right(&array[c2], tmp_view, 0)
                };
                if count1 != 0 {
                    copy_vec(array, dest, tmp.slice(c1, c1+count1));
                    dest += count1; c1 += count1; len1 -= count1;
                    if len1 <= 1 { break_outer = true; break; }
                }
                array.swap(dest, c2);
                dest += 1; c2 += 1; len2 -= 1;
                if len2 == 0 { break_outer = true; break; }

                count2 = {
                    let tmp_view = array.slice(c2, c2+len2);
                    gallop_left(&tmp[c1], tmp_view, 0)
                };
                if count2 != 0 {
                    shift_vec(array, dest, c2, count2);
                    dest += count2; c2 += count2; len2 -= count2;
                    if len2 == 0 { break_outer = true; break; }
                }
                swap(&mut array[dest], &mut tmp[c1]);
                dest += 1; c1 += 1; len1 -= 1;
                if len1 == 1 { break_outer = true; break; }
                min_gallop -= 1;
                if !(count1 >= MIN_GALLOP || count2 >= MIN_GALLOP) {
                    break;
                }
            }
            if break_outer { break; }
            if min_gallop < 0 { min_gallop = 0; }
            min_gallop += 2; // Penalize for leaving gallop
        }
        self.min_gallop = if min_gallop < 1 { 1 } else { min_gallop };

        if len1 == 1 {
            assert!(len2 > 0);
            shift_vec(array, dest, c2, len2);
            swap(&mut array[dest+len2], &mut tmp[c1]);
        } else if len1 == 0 {
            fail!("Comparison violates its contract!");
        } else {
            assert_eq!(len2, 0);
            assert!(len1 > 1);
            copy_vec(array, dest, tmp.slice(c1, c1+len1));
        }
    }

    fn merge_hi(&mut self, array: &mut [T], base1: uint, len1: uint,
                base2: uint, len2: uint) {
        assert!(len1 != 1 && len2 != 0 && base1 + len1 == base2);

        let mut tmp = array.slice(base2, base2 + len2).to_owned();

        let mut c1 = base1 + len1 - 1;
        let mut c2 = len2 - 1;
        let mut dest = base2 + len2 - 1;
        let mut len1 = len1;
        let mut len2 = len2;

        array.swap(dest, c1);
        dest -= 1; c1 -= 1; len1 -= 1;

        if len1 == 0 {
            copy_vec(array, dest-(len2-1), tmp.slice(0, len2));
            return;
        }
        if len2 == 1 {
            dest -= len1;
            c1 -= len1;
            shift_vec(array, dest+1, c1+1, len1);
            swap(&mut array[dest], &mut tmp[c2]);
            return;
        }

        let mut min_gallop = self.min_gallop;
        loop {
            let mut count1 = 0;
            let mut count2 = 0;
            let mut break_outer = false;

            loop {
                assert!(len1 != 0 && len2 > 1);
                if tmp[c2] < array[c1] {
                    array.swap(dest, c1);
                    dest -= 1; c1 -= 1; len1 -= 1;
                    count1 += 1; count2 = 0;
                    if len1 == 0 {
                        break_outer = true;
                    }
                } else {
                    swap(&mut array[dest], &mut tmp[c2]);
                    dest -= 1; c2 -= 1; len2 -= 1;
                    count2 += 1; count1 = 0;
                    if len2 == 1 {
                        break_outer = true;
                    }
                }
                if break_outer || ((count1 | count2) >= min_gallop) {
                    break;
                }
            }
            if break_outer { break; }

            // Start to gallop
            loop {
                assert!(len2 > 1 && len1 != 0);

                { // constrain scope of tmp_view:
                    let tmp_view = array.mut_slice(base1, base1+len1);
                    count1 = len1 - gallop_right(
                        &tmp[c2], tmp_view, len1-1);
                }

                if count1 != 0 {
                    dest -= count1; c1 -= count1; len1 -= count1;
                    shift_vec(array, dest+1, c1+1, count1);
                    if len1 == 0 { break_outer = true; break; }
                }

                swap(&mut array[dest], &mut tmp[c2]);
                dest -= 1; c2 -= 1; len2 -= 1;
                if len2 == 1 { break_outer = true; break; }

                let count2;
                { // constrain scope of tmp_view
                    let tmp_view = tmp.mut_slice(0, len2);
                    count2 = len2 - gallop_left(&array[c1],
                                                tmp_view,
                                                len2-1);
                }

                if count2 != 0 {
                    dest -= count2; c2 -= count2; len2 -= count2;
                    copy_vec(array, dest+1, tmp.slice(c2+1, c2+1+count2));
                    if len2 <= 1 { break_outer = true; break; }
                }
                array.swap(dest, c1);
                dest -= 1; c1 -= 1; len1 -= 1;
                if len1 == 0 { break_outer = true; break; }
                min_gallop -= 1;
                if !(count1 >= MIN_GALLOP || count2 >= MIN_GALLOP) {
                    break;
                }
            }

            if break_outer { break; }
            if min_gallop < 0 { min_gallop = 0; }
            min_gallop += 2; // Penalize for leaving gallop
        }
        self.min_gallop = if min_gallop < 1 { 1 } else { min_gallop };

        if len2 == 1 {
            assert!(len1 > 0);
            dest -= len1;
            c1 -= len1;
            shift_vec(array, dest+1, c1+1, len1);
            swap(&mut array[dest], &mut tmp[c2]);
        } else if len2 == 0 {
            fail!("Comparison violates its contract!");
        } else {
            assert_eq!(len1, 0);
            assert!(len2 != 0);
            copy_vec(array, dest-(len2-1), tmp.slice(0, len2));
        }
    }

    fn merge_collapse(&mut self, array: &mut [T]) {
        while self.runs.len() > 1 {
            let mut n = self.runs.len()-2;
            if n > 0 &&
                self.runs[n-1].len <= self.runs[n].len + self.runs[n+1].len
            {
                if self.runs[n-1].len < self.runs[n+1].len { n -= 1; }
            } else if self.runs[n].len <= self.runs[n+1].len {
                /* keep going */
            } else {
                break;
            }
            self.merge_at(n, array);
        }
    }

    fn merge_force_collapse(&mut self, array: &mut [T]) {
        while self.runs.len() > 1 {
            let mut n = self.runs.len()-2;
            if n > 0 {
                if self.runs[n-1].len < self.runs[n+1].len {
                    n -= 1;
                }
            }
            self.merge_at(n, array);
        }
    }
}

#[inline]
fn copy_vec<T:Clone>(dest: &mut [T],
                    s1: uint,
                    from: &[T]) {
    assert!(s1+from.len() <= dest.len());

    for (i, v) in from.iter().enumerate() {
        dest[s1+i] = (*v).clone();
    }
}

#[inline]
fn shift_vec<T:Clone>(dest: &mut [T], s1: uint, s2: uint, len: uint) {
    assert!(s1+len <= dest.len());

    let tmp = dest.slice(s2, s2+len).to_owned();
    copy_vec(dest, s1, tmp);
}

#[cfg(test)]
mod test_qsort3 {
    use sort::*;


    fn check_sort(v1: &mut [int], v2: &mut [int]) {
        let len = v1.len();
        quick_sort3::<int>(v1);
        let mut i = 0;
        while i < len {
            assert_eq!(v2[i], v1[i]);
            i += 1;
        }
    }

    #[test]
    fn test() {
        {
            let mut v1 = ~[3, 7, 4, 5, 2, 9, 5, 8];
            let mut v2 = ~[2, 3, 4, 5, 5, 7, 8, 9];
            check_sort(v1, v2);
        }
        {
            let mut v1 = ~[1, 1, 1];
            let mut v2 = ~[1, 1, 1];
            check_sort(v1, v2);
        }
        {
            let mut v1: ~[int] = ~[];
            let mut v2: ~[int] = ~[];
            check_sort(v1, v2);
        }
        { let mut v1 = ~[9]; let mut v2 = ~[9]; check_sort(v1, v2); }
        {
            let mut v1 = ~[9, 3, 3, 3, 9];
            let mut v2 = ~[3, 3, 3, 9, 9];
            check_sort(v1, v2);
        }
    }
}

#[cfg(test)]
mod test_qsort {
    use sort::*;

    fn check_sort(v1: &mut [int], v2: &mut [int]) {
        let len = v1.len();
        fn leual(a: &int, b: &int) -> bool { *a <= *b }
        quick_sort::<int>(v1, leual);
        let mut i = 0u;
        while i < len {
            // debug!(v2[i]);
            assert_eq!(v2[i], v1[i]);
            i += 1;
        }
    }

    #[test]
    fn test() {
        {
            let mut v1 = ~[3, 7, 4, 5, 2, 9, 5, 8];
            let mut v2 = ~[2, 3, 4, 5, 5, 7, 8, 9];
            check_sort(v1, v2);
        }
        {
            let mut v1 = ~[1, 1, 1];
            let mut v2 = ~[1, 1, 1];
            check_sort(v1, v2);
        }
        {
            let mut v1: ~[int] = ~[];
            let mut v2: ~[int] = ~[];
            check_sort(v1, v2);
        }
        { let mut v1 = ~[9]; let mut v2 = ~[9]; check_sort(v1, v2); }
        {
            let mut v1 = ~[9, 3, 3, 3, 9];
            let mut v2 = ~[3, 3, 3, 9, 9];
            check_sort(v1, v2);
        }
    }

    // Regression test for #750
    #[test]
    fn test_simple() {
        let mut names = ~[2, 1, 3];

        let expected = ~[1, 2, 3];

        do quick_sort(names) |x, y| { *x < *y };

        let immut_names = names;

        for (&a, &b) in expected.iter().zip(immut_names.iter()) {
            debug!("%d %d", a, b);
            assert_eq!(a, b);
        }
    }
}

#[cfg(test)]
mod tests {

    use sort::*;

    fn check_sort(v1: &[int], v2: &[int]) {
        let len = v1.len();
        pub fn le(a: &int, b: &int) -> bool { *a <= *b }
        let f = le;
        let v3 = merge_sort::<int>(v1, f);
        let mut i = 0u;
        while i < len {
            debug!(v3[i]);
            assert_eq!(v3[i], v2[i]);
            i += 1;
        }
    }

    #[test]
    fn test() {
        {
            let v1 = ~[3, 7, 4, 5, 2, 9, 5, 8];
            let v2 = ~[2, 3, 4, 5, 5, 7, 8, 9];
            check_sort(v1, v2);
        }
        { let v1 = ~[1, 1, 1]; let v2 = ~[1, 1, 1]; check_sort(v1, v2); }
        { let v1:~[int] = ~[]; let v2:~[int] = ~[]; check_sort(v1, v2); }
        { let v1 = ~[9]; let v2 = ~[9]; check_sort(v1, v2); }
        {
            let v1 = ~[9, 3, 3, 3, 9];
            let v2 = ~[3, 3, 3, 9, 9];
            check_sort(v1, v2);
        }
    }

    #[test]
    fn test_merge_sort_mutable() {
        pub fn le(a: &int, b: &int) -> bool { *a <= *b }
        let v1 = ~[3, 2, 1];
        let v2 = merge_sort(v1, le);
        assert_eq!(v2, ~[1, 2, 3]);
    }

    #[test]
    fn test_merge_sort_stability() {
        // tjc: funny that we have to use parens
        fn ile(x: &(&'static str), y: &(&'static str)) -> bool
        {
            // FIXME: #4318 Instead of to_ascii and to_str_ascii, could use
            // to_ascii_move and to_str_move to not do a unnecessary clone.
            // (Actually, could just remove the to_str_* call, but needs an deriving(Ord) on
            // Ascii)
            let x = x.to_ascii().to_lower().to_str_ascii();
            let y = y.to_ascii().to_lower().to_str_ascii();
            x <= y
        }

        let names1 = ~["joe bob", "Joe Bob", "Jack Brown", "JOE Bob",
                       "Sally Mae", "JOE BOB", "Alex Andy"];
        let names2 = ~["Alex Andy", "Jack Brown", "joe bob", "Joe Bob",
                       "JOE Bob", "JOE BOB", "Sally Mae"];
        let names3 = merge_sort(names1, ile);
        assert_eq!(names3, names2);
    }
}

#[cfg(test)]
mod test_tim_sort {

    use sort::tim_sort;
    use std::rand::Rng;
    use std::rand;
    use std::vec;

    #[deriving(Clone)]
    struct CVal {
        val: float,
    }

    impl Ord for CVal {
        fn lt(&self, other: &CVal) -> bool {
            let mut rng = rand::rng();
            if rng.gen::<float>() > 0.995 {
                fail!("It's happening!!!");
            }
            (*self).val < other.val
        }
        fn le(&self, other: &CVal) -> bool { (*self).val <= other.val }
        fn gt(&self, other: &CVal) -> bool { (*self).val > other.val }
        fn ge(&self, other: &CVal) -> bool { (*self).val >= other.val }
    }

    fn check_sort(v1: &mut [int], v2: &mut [int]) {
        let len = v1.len();
        tim_sort::<int>(v1);
        let mut i = 0u;
        while i < len {
            // debug!(v2[i]);
            assert_eq!(v2[i], v1[i]);
            i += 1u;
        }
    }

    #[test]
    fn test() {
        {
            let mut v1 = ~[3, 7, 4, 5, 2, 9, 5, 8];
            let mut v2 = ~[2, 3, 4, 5, 5, 7, 8, 9];
            check_sort(v1, v2);
        }
        {
            let mut v1 = ~[1, 1, 1];
            let mut v2 = ~[1, 1, 1];
            check_sort(v1, v2);
        }
        {
            let mut v1: ~[int] = ~[];
            let mut v2: ~[int] = ~[];
            check_sort(v1, v2);
        }
        { let mut v1 = ~[9]; let mut v2 = ~[9]; check_sort(v1, v2); }
        {
            let mut v1 = ~[9, 3, 3, 3, 9];
            let mut v2 = ~[3, 3, 3, 9, 9];
            check_sort(v1, v2);
        }
    }

    #[test]
    #[should_fail]
    #[cfg(unix)]
    fn crash_test() {
        let mut rng = rand::rng();
        let mut arr = do vec::from_fn(1000) |_i| {
            CVal { val: rng.gen() }
        };

        tim_sort(arr);
        fail!("Guarantee the fail");
    }

    #[deriving(Clone)]
    struct DVal {
        val: uint,
    }

    impl Ord for DVal {
        fn lt(&self, _x: &DVal) -> bool { true }
        fn le(&self, _x: &DVal) -> bool { true }
        fn gt(&self, _x: &DVal) -> bool { true }
        fn ge(&self, _x: &DVal) -> bool { true }
    }

    #[test]
    fn test_bad_Ord_impl() {
        let mut rng = rand::rng();
        let mut arr = do vec::from_fn(500) |_i| {
            DVal { val: rng.gen() }
        };

        tim_sort(arr);
    }
}

#[cfg(test)]
mod big_tests {

    use sort::*;

    use std::rand::Rng;
    use std::rand;
    use std::vec;

    #[test]
    fn test_unique() {
        let low = 5;
        let high = 10;
        tabulate_unique(low, high);
    }

    #[test]
    fn test_managed() {
        let low = 5;
        let high = 10;
        tabulate_managed(low, high);
    }

    fn multiplyVec<T:Clone>(arr: &[T], num: uint) -> ~[T] {
        let size = arr.len();
        let res = do vec::from_fn(num) |i| {
            arr[i % size].clone()
        };
        res
    }

    fn makeRange(n: uint) -> ~[uint] {
        let one = do vec::from_fn(n) |i| { i };
        let mut two = one.clone();
        two.reverse();
        vec::append(two, one)
    }

    fn tabulate_unique(lo: uint, hi: uint) {
        fn isSorted<T:Ord>(arr: &[T]) {
            for i in range(0u, arr.len() - 1) {
                if arr[i] > arr[i+1] {
                    fail!("Array not sorted");
                }
            }
        }

        let mut rng = rand::rng();

        for i in range(lo, hi) {
            let n = 1 << i;
            let mut arr: ~[float] = do vec::from_fn(n) |_i| {
                rng.gen()
            };

            tim_sort(arr); // *sort
            isSorted(arr);

            arr.reverse();
            tim_sort(arr); // \sort
            isSorted(arr);

            tim_sort(arr); // /sort
            isSorted(arr);

            do 3.times {
                let i1 = rng.gen_integer_range(0u, n);
                let i2 = rng.gen_integer_range(0u, n);
                arr.swap(i1, i2);
            }
            tim_sort(arr); // 3sort
            isSorted(arr);

            if n >= 10 {
                let size = arr.len();
                let mut idx = 1;
                while idx <= 10 {
                    arr[size-idx] = rng.gen();
                    idx += 1;
                }
            }
            tim_sort(arr); // +sort
            isSorted(arr);

            do (n/100).times {
                let idx = rng.gen_integer_range(0u, n);
                arr[idx] = rng.gen();
            }
            tim_sort(arr);
            isSorted(arr);

            let mut arr = if n > 4 {
                let part = arr.slice(0, 4);
                multiplyVec(part, n)
            } else { arr };
            tim_sort(arr); // ~sort
            isSorted(arr);

            let mut arr = vec::from_elem(n, -0.5);
            tim_sort(arr); // =sort
            isSorted(arr);

            let half = n / 2;
            let mut arr = makeRange(half).map(|i| *i as float);
            tim_sort(arr); // !sort
            isSorted(arr);
        }
    }

    fn tabulate_managed(lo: uint, hi: uint) {
        fn isSorted<T:Ord>(arr: &[@T]) {
            for i in range(0u, arr.len() - 1) {
                if arr[i] > arr[i+1] {
                    fail!("Array not sorted");
                }
            }
        }

        let mut rng = rand::rng();

        for i in range(lo, hi) {
            let n = 1 << i;
            let arr: ~[@float] = do vec::from_fn(n) |_i| {
                @rng.gen()
            };
            let mut arr = arr;

            tim_sort(arr); // *sort
            isSorted(arr);

            arr.reverse();
            tim_sort(arr); // \sort
            isSorted(arr);

            tim_sort(arr); // /sort
            isSorted(arr);

            do 3.times {
                let i1 = rng.gen_integer_range(0u, n);
                let i2 = rng.gen_integer_range(0u, n);
                arr.swap(i1, i2);
            }
            tim_sort(arr); // 3sort
            isSorted(arr);

            if n >= 10 {
                let size = arr.len();
                let mut idx = 1;
                while idx <= 10 {
                    arr[size-idx] = @rng.gen();
                    idx += 1;
                }
            }
            tim_sort(arr); // +sort
            isSorted(arr);

            do (n/100).times {
                let idx = rng.gen_integer_range(0u, n);
                arr[idx] = @rng.gen();
            }
            tim_sort(arr);
            isSorted(arr);

            let mut arr = if n > 4 {
                let part = arr.slice(0, 4);
                multiplyVec(part, n)
            } else { arr };
            tim_sort(arr); // ~sort
            isSorted(arr);

            let mut arr = vec::from_elem(n, @(-0.5));
            tim_sort(arr); // =sort
            isSorted(arr);

            let half = n / 2;
            let mut arr = makeRange(half).map(|i| @(*i as float));
            tim_sort(arr); // !sort
            isSorted(arr);
        }
    }
}