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--
-- GSL shell interactive interface to GSL library
-- Based on the Lua programming language
--
-- Copyright (C) 2009-2013 Francesco Abbate.
-- See Copyright Notice in gsl-shell-jit.c
--
-- This file provided an implementation of the quicksort algorithm.
-- Based on the libstdc++ std::sort implementation included with GCC.
--
local bit = require 'bit'
local band, rshift = bit.band, bit.rshift
local insertion_thresold = 16
local function less_than(a, b)
return a < b
end
local function lg2(a)
local c = 0
while a > 0 do
a = rshift(a, 1)
c = c + 1
end
return c - 1
end
local function div2(a)
return rshift(a, 1)
end
local function heapsort(array, i0, i1, f)
f = f or less_than
local function push_heap(first, hole, top, value)
local parent = div2(hole - 1)
while hole > top and f(array[first + parent], value) do
array[first + hole] = array[first + parent]
hole = parent
parent = div2(hole - 1)
end
array[first + hole] = value
end
local function adjust_heap(first, hole, len, value)
local top = hole
local second = hole
while second < div2(len - 1) do
second = 2 * (second + 1)
if f(array[first + second], array[first + (second - 1)]) then
second = second - 1
end
array[first + hole] = array[first + second]
hole = second
end
if band(len, 1) == 0 and second == div2(len - 2) then
second = 2 * (second + 1)
array[first + hole] = array[first + (second - 1)]
hole = second - 1
end
push_heap(first, hole, top, value)
end
local function pop_heap(first, last, result)
local value = array[result]
array[result] = array[first]
adjust_heap(first, 0, last - first, value)
end
local function make_heap(first, last)
if last - first < 2 then return end
local len = last - first
local parent = div2(len - 2)
while true do
local value = array[first + parent]
adjust_heap(first, parent, len, value)
if parent == 0 then
return
end
parent = parent - 1
end
end
local function heap_select(first, middle, last)
make_heap(first, middle)
for i = middle, last - 1 do
if f(array[i], array[first]) then
pop_heap(first, middle, i)
end
end
end
local function sort_heap(first, last)
while last - first > 1 do
last = last - 1
pop_heap(first, last, last)
end
end
heap_select(i0, i1 + 1, i1 + 1)
sort_heap(i0, i1 + 1)
end
local function insertion_sort(array, compare, istart, iend)
for i = istart + 1, iend do
local current_value = array[i]
local hole_index = i
while hole_index > istart and compare(current_value, array[hole_index - 1]) do
array[hole_index] = array[hole_index - 1]
hole_index = hole_index - 1
end
array[hole_index] = current_value
end
end
local function quicksort(array, i0, i1, f)
f = f or less_than
local function move_median_first(a, b, c)
if f(array[a], array[b]) then
if f(array[b], array[c]) then
array[a], array[b] = array[b], array[a]
else
array[a], array[c] = array[c], array[a]
end
elseif f(array[a], array[c]) then
return
elseif f(array[b], array[c]) then
array[a], array[c] = array[c], array[a]
else
array[a], array[b] = array[b], array[a]
end
end
local function partition(first, last, pivot_value)
while true do
while f(array[first], pivot_value) do
first = first + 1
end
while f(pivot_value, array[last]) do
last = last - 1
end
if first >= last then
return first
end
array[first], array[last] = array[last], array[first]
first = first + 1
last = last - 1
end
end
local function partition_pivot(first, last)
local mid = div2(first + last)
move_median_first(first, mid, last)
return partition(first + 1, last, array[first])
end
local function quicksort_loop(first, last, depth)
while last - first > insertion_thresold do
if depth == 0 then
heapsort(array, first, last, f)
return
end
depth = depth - 1
local cut = partition_pivot(first, last)
quicksort_loop(cut, last, depth)
-- array[first], array[first + 1] = array[first + 1], array[first]
last = cut - 1
end
end
local complete = quicksort_loop(i0, i1, 2 * lg2(i1 - i0 + 1))
insertion_sort(array, f, i0, i1)
end
local function array_search(array, i0, i1, val)
for k = i0, i1 do
if array[k] == val then return k end
end
end
-- sort arrays "array" and "slave" in place for indices from i0 to i1
-- based on values of "array" using the comparison function "f"
local function quicksort_mirror(array, slave, i0, i1, f)
local function swap(index, a, b)
array[a], array[b] = array[b], array[a]
slave[a], slave[b] = slave[b], slave[a]
index[a], index[b] = index[b], index[a]
end
local n = i1 - i0 + 1
local id, iv = {}, {}
for k = 1, n do id[k], iv[k] = k, k end
quicksort(id, i0, i1, function(a, b) return f(array[a], array[b]) end)
for k = 1, n do
local val = id[k]
if val > k then
swap(iv, k, val)
elseif val < k then
val = array_search(iv, k, n, val)
swap(iv, k, val)
end
end
end
return {quicksort = quicksort, quicksort_mirror = quicksort_mirror,
heapsort = heapsort}
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