# Natural merge sort in C

I have this C implementation of the natural merge sort:

#include "stable_sort.h"
#include <stdbool.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>

typedef struct run_length_queue {
int*   storage;
size_t capacity;
size_t head;
size_t tail;
size_t size;
size_t mask;
} run_length_queue;

static size_t fix_capacity(size_t capacity)
{
size_t ret = 1;

while (ret < capacity)
{
ret <<= 1;
}

return ret;
}

static size_t max(size_t a, size_t b)
{
return a > b ? a : b;
}

static const size_t MINIMUM_RUN_LENGTH_QUEUE_CAPACITY = 256;
static const size_t BITS_PER_BYTE = 8;

static run_length_queue* run_length_queue_alloc(size_t capacity)
{
run_length_queue* queue;

capacity = max(capacity, MINIMUM_RUN_LENGTH_QUEUE_CAPACITY);
capacity = fix_capacity(capacity);

queue = malloc(sizeof(*queue));

if (!queue)
{
return NULL;
}

queue->storage = malloc(sizeof(int) * capacity);

if (!queue->storage)
{
free(queue);
return NULL;
}

queue->capacity = capacity;
queue->mask = capacity - 1;
queue->head = 0;
queue->tail = 0;
queue->size = 0;

return queue;
}

static void run_length_queue_enqueue(run_length_queue* queue, size_t run_size)
{
queue->storage[queue->tail] = run_size;
queue->tail = (queue->tail + 1) & queue->mask;
queue->size++;
}

static void run_length_queue_add_to_last(run_length_queue* queue,
size_t run_size)
{
queue->storage[(queue->tail - 1) & queue->mask] += run_size;
}

static size_t run_length_queue_dequeue(run_length_queue* queue)
{
size_t run_length = queue->storage[queue->head];
queue->head = (queue->head + 1) & queue->mask;
queue->size--;
return run_length;
}

static size_t run_length_queue_size(run_length_queue* queue)
{
return queue->size;
}

static void run_length_queue_free(run_length_queue* queue)
{
if (queue && queue->storage)
{
free(queue->storage);
}
}

static void reverse_run(char* base, size_t num, size_t size, void* swap_buffer)
{
size_t left = 0;
size_t right = num - 1;

while (left < right)
{
memcpy(swap_buffer, base + size * left, size);
memcpy(base + size * left, base + size * right, size);
memcpy(base + size * right, swap_buffer, size);

++left;
--right;
}
}

static run_length_queue*
build_run_length_queue(void* base,
size_t num,
size_t size,
int (*cmp)(const void*, const void*))
{
run_length_queue* queue;
size_t head;
size_t left;
size_t right;
size_t last;
size_t run_length;
bool previous_was_descending;
void* swap_buffer = malloc(size);
queue = run_length_queue_alloc((num >> 1) + 1);

if (!queue)
{
return NULL;
}

left = 0;
right = 1;
last = num - 1;
previous_was_descending = false;

while (left < last)
{
head = left;

/* Decide the direction of the next run. */
if (cmp(((char*) base) + size * left++,
((char*) base) + size * right++) <= 0)
{
/* The run is ascending. */
while (left < last
&& cmp(((char*) base) + size * left,
((char*) base) + size * right) <= 0)
{
++left;
++right;
}

run_length = left - head + 1;

if (previous_was_descending)
{
if (cmp(((char*) base) + (head - 1) * size,
((char*) base) + head * size) <= 0)
{
run_length_queue_add_to_last(queue, run_length);
}
else
{
run_length_queue_enqueue(queue, run_length);
}
}
else
{
run_length_queue_enqueue(queue, run_length);
}

previous_was_descending = false;
}
else
{
/* Scan a strictly descending run. */
while (left < last
&& cmp(((char*) base) + size * left,
((char*) base) + size * right) > 0)
{
++left;
++right;
}

run_length = left - head + 1;
reverse_run(((char*) base) + head * size,
run_length,
size,
swap_buffer);

if (previous_was_descending)
{
if (cmp(((char*) base) + size * (head - 1),
((char*) base) + size * head) <= 0)
{
run_length_queue_add_to_last(queue, run_length);
}
else
{
run_length_queue_enqueue(queue, run_length);
}
}
else
{
run_length_queue_enqueue(queue, run_length);
}

previous_was_descending = true;
}

++left;
++right;
}

if (left == last)
{
if (cmp(((char*) base) + size * (last - 1),
((char*) base) + size * last) <= 0)
{
run_length_queue_add_to_last(queue, 1);
}
else
{
run_length_queue_enqueue(queue, 1);
}
}

free(swap_buffer);
return queue;
}

void merge(void* source,
void* target,
size_t size,
size_t offset,
size_t left_run_length,
size_t right_run_length,
int (*cmp)(const void*, const void*))
{
size_t left  = offset;
size_t right = left + left_run_length;
const size_t left_bound = right;
const size_t right_bound = right + right_run_length;
size_t target_index = offset;

while (left < left_bound && right < right_bound)
{
if (cmp(((char*) source) + size * right,
((char*) source) + size * left) < 0)
{
memcpy(((char*) target) + size * target_index,
((char*) source) + size * right,
size);
++right;
}
else
{
memcpy(((char*) target) + size * target_index,
((char*) source) + size * left,
size);
++left;
}

++target_index;
}

memcpy(((char*) target) + size * target_index,
((char*) source) + size * left,
(left_bound - left) * size);

memcpy(((char*) target) + size * target_index,
((char*) source) + size * right,
(right_bound - right) * size);
}

static size_t get_number_of_leading_zeros(size_t number)
{
size_t mask = 1;
size_t number_of_leading_zeros = 0;

mask <<= (sizeof number) * BITS_PER_BYTE - 1;

while (mask && ((mask & number) == 0))
{
++number_of_leading_zeros;
mask >>= 1;
}

return number_of_leading_zeros;
}

static size_t get_number_of_merge_passes(size_t runs)
{
return sizeof(size_t) * BITS_PER_BYTE -
get_number_of_leading_zeros(runs - 1);
}

void stable_sort(void* base, size_t num, size_t size, int (*comparator)(const void*, const void*))
{
size_t i;

run_length_queue* queue;

void* buffer;
void* source;
void* target;
void* tmp;

size_t offset;
size_t merge_passes;
size_t runs_remaining;
size_t tail_run_length;
size_t left_run_length;
size_t right_run_length;

if (!base || !comparator || num < 2 || size == 0)
{
return;
}

buffer = malloc(num * size);

if (!buffer)
{
qsort(base, num, size, comparator);
return;
}

queue = build_run_length_queue(base, num, size, comparator);

if (!queue)
{
/* Cannot allocate the run length queue. Resort to qsort and possibly
fail in the same manner as qsort. */
qsort(base, num, size, comparator);
return;
}

merge_passes = get_number_of_merge_passes(run_length_queue_size(queue));

if ((merge_passes & 1) == 1)
{
source = buffer;
target = base;
memcpy(buffer, base, num * size);
}
else
{
source = base;
target = buffer;
}

offset = 0;
runs_remaining = run_length_queue_size(queue);

while (run_length_queue_size(queue) > 1)
{
left_run_length  = run_length_queue_dequeue(queue);
right_run_length = run_length_queue_dequeue(queue);

merge(source,
target,
size,
offset,
left_run_length,
right_run_length,
comparator);

run_length_queue_enqueue(queue, left_run_length + right_run_length);
runs_remaining -= 2;
offset += left_run_length + right_run_length;

switch (runs_remaining)
{
case 1:
tail_run_length = run_length_queue_dequeue(queue);
memcpy(((char*) target) + offset * size,
((char*) source) + offset * size,
size * tail_run_length);
run_length_queue_enqueue(queue, tail_run_length);
/* FALL THROUGH! */

case 0:
runs_remaining = run_length_queue_size(queue);
offset = 0;

tmp = source;
source = target;
target = tmp;
break;
}
}

run_length_queue_free(queue);
free(buffer);
}


(You can find the demo driver here.)

My primary concern is performance: qsort beats my implementation easily by the factor of 2. Is there any chance of squeezing a little bit more performance? Please, tell me about other aspects of the code snippet as well.

• A small leak: when there is no queue after build_run_length_queue you should free the buffer you malloced. In fact you also leak queue itself (run_length_queue_free doesn't free it). – ratchet freak Feb 9 '16 at 11:37

## 3 Answers

When in doubt, profile!

I built your code with -lprofiler, and pprof told me that

 213  23.5%  23.5%      213  23.5% _build_run_length_queue
184  20.3%  43.9%      326  36.0% _merge
109  12.0%  55.9%      846  93.5% _main


Building the queue is a culprit.

I also run some experiments on your code. It turned out that joining runs doesn't affect the performance whatsoever. The big-O constant was 0.0137 with joining and 0.0143 without.

That makes me guess that reversing descending runs is just a waste of time. I would seriously consider implementing 3 merge routines - merge two ascending runs, merge two descending runs, and merge ascending and descending runs (they would be almost identical, the only difference is in a run traversal direction).

As a minor optimization I also recommend to object-deorient the queue. Notice that you remove two slots, and put back one. This means that the beginning of the queue always have room. Something along the lines of

    while (queue_size(queue) > 1) {
int get = 0;
int put = 0;
while (remaining_runs > 1) {
left_run_length  = queue->storage[get++];
right_run_length  = queue->storage[get++];
....
queue->storage[put++] = left_run_length + right_run_length;
}


to spare few function calls and maskings.

You can allocate queue on the stack and have run_length_queue_alloc simply initialize it (and rename to run_length_queue_init).

There is a define for how many bits there are in per sizeof unit: CHAR_BIT in limits.h.

get_number_of_leading_zeros typically has a compiler intrinsic (called bitscan reverse in windows or __builtin_clz in GCC) which translates to a single instruction on most CPUs.

### fix_capacity()

I have some comments about this function:

static size_t fix_capacity(size_t capacity)
{
size_t ret = 1;

while (ret < capacity)
{
ret <<= 1;
}

return ret;
}

1. If you pass in a large enough capacity value, this function will loop forever. For example, if size_t is 32 bits, passing in any value 0x80000001 or larger will cause ret to reach 0x80000000, and then loop again to reach 0, and the loop forever at value 0.
2. You might be able to perform this operation without a loop, depending on if you have a CLZ operation available. For example, if size_t is 32 bits and you are using gnu:

static size_t fix_capacity(size_t capacity)
{
return 2UL << (32 - __builtin_clz(capacity - 1));
}


Note that this function returns 0 if the capacity is greater than 0x80000000, and requires a minimum capacity of 2 (which is guaranteed because you previously set the minimum to MINIMUM_RUN_LENGTH_QUEUE_CAPACITY).

### Duplicated code

This code appears in both the if and else halves of your code in build_run_length_queue():

        if (previous_was_descending)
{
if (cmp(((char*) base) + size * (head - 1),
((char*) base) + size * head) <= 0)
{
run_length_queue_add_to_last(queue, run_length);
}
else
{
run_length_queue_enqueue(queue, run_length);
}
}
else
{
run_length_queue_enqueue(queue, run_length);
}


You could pull that code out of both places and put it after the if statement. The end result would look like this:

    if (cmp(((char*) base) + size * left++,
((char*) base) + size * right++) <= 0)
{
/* The run is ascending. */
while (left < last
&& cmp(((char*) base) + size * left,
((char*) base) + size * right) <= 0)
{
++left;
++right;
}

run_length = left - head + 1;

current_run_was_descending = false;
}
else
{
/* Scan a strictly descending run. */
while (left < last
&& cmp(((char*) base) + size * left,
((char*) base) + size * right) > 0)
{
++left;
++right;
}

run_length = left - head + 1;
reverse_run(((char*) base) + head * size,
run_length,
size,
swap_buffer);

current_run_was_descending = true;
}

if (previous_was_descending)
{
if (cmp(((char*) base) + size * (head - 1),
((char*) base) + size * head) <= 0)
{
run_length_queue_add_to_last(queue, run_length);
}
else
{
run_length_queue_enqueue(queue, run_length);
}
}
else
{
run_length_queue_enqueue(queue, run_length);
}
previous_was_descending = current_run_was_descending;
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