/*
* Taken from https://github.com/swenson/sort
* Revision: 05fd77bfec049ce8b7c408c4d3dd2d51ee061a15
* Removed all code unrelated to Timsort and made minor adjustments for
* cross-platform compatibility.
*/
/*
* The MIT License (MIT)
*
* Copyright (c) 2010-2017 Christopher Swenson.
* Copyright (c) 2012 Vojtech Fried.
* Copyright (c) 2012 Google Inc. All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*/
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#ifdef HAVE_STDINT_H
#include <stdint.h>
#elif defined(_WIN32)
typedef unsigned __int64 uint64_t;
#endif
#ifndef SORT_NAME
#error "Must declare SORT_NAME"
#endif
#ifndef SORT_TYPE
#error "Must declare SORT_TYPE"
#endif
#ifndef SORT_CMP
#define SORT_CMP(x, y) ((x) < (y) ? -1 : ((x) == (y) ? 0 : 1))
#endif
#ifndef TIM_SORT_STACK_SIZE
#define TIM_SORT_STACK_SIZE 128
#endif
#define SORT_SWAP(x,y) {SORT_TYPE __SORT_SWAP_t = (x); (x) = (y); (y) = __SORT_SWAP_t;}
/* Common, type-agnosting functions and constants that we don't want to declare twice. */
#ifndef SORT_COMMON_H
#define SORT_COMMON_H
#ifndef MAX
#define MAX(x,y) (((x) > (y) ? (x) : (y)))
#endif
#ifndef MIN
#define MIN(x,y) (((x) < (y) ? (x) : (y)))
#endif
static int compute_minrun(const uint64_t);
#ifndef CLZ
#ifdef __GNUC__
#define CLZ __builtin_clzll
#else
static int clzll(uint64_t);
/* adapted from Hacker's Delight */
static int clzll(uint64_t x) {
int n;
if (x == 0) {
return 64;
}
n = 0;
if (x <= 0x00000000FFFFFFFFL) {
n = n + 32;
x = x << 32;
}
if (x <= 0x0000FFFFFFFFFFFFL) {
n = n + 16;
x = x << 16;
}
if (x <= 0x00FFFFFFFFFFFFFFL) {
n = n + 8;
x = x << 8;
}
if (x <= 0x0FFFFFFFFFFFFFFFL) {
n = n + 4;
x = x << 4;
}
if (x <= 0x3FFFFFFFFFFFFFFFL) {
n = n + 2;
x = x << 2;
}
if (x <= 0x7FFFFFFFFFFFFFFFL) {
n = n + 1;
}
return n;
}
#define CLZ clzll
#endif
#endif
static __inline int compute_minrun(const uint64_t size) {
const int top_bit = 64 - CLZ(size);
const int shift = MAX(top_bit, 6) - 6;
const int minrun = size >> shift;
const uint64_t mask = (1ULL << shift) - 1;
if (mask & size) {
return minrun + 1;
}
return minrun;
}
#endif /* SORT_COMMON_H */
#define SORT_CONCAT(x, y) x ## _ ## y
#define SORT_MAKE_STR1(x, y) SORT_CONCAT(x,y)
#define SORT_MAKE_STR(x) SORT_MAKE_STR1(SORT_NAME,x)
#define BINARY_INSERTION_FIND SORT_MAKE_STR(binary_insertion_find)
#define BINARY_INSERTION_SORT_START SORT_MAKE_STR(binary_insertion_sort_start)
#define BINARY_INSERTION_SORT SORT_MAKE_STR(binary_insertion_sort)
#define REVERSE_ELEMENTS SORT_MAKE_STR(reverse_elements)
#define COUNT_RUN SORT_MAKE_STR(count_run)
#define CHECK_INVARIANT SORT_MAKE_STR(check_invariant)
#define TIM_SORT SORT_MAKE_STR(tim_sort)
#define TIM_SORT_RESIZE SORT_MAKE_STR(tim_sort_resize)
#define TIM_SORT_MERGE SORT_MAKE_STR(tim_sort_merge)
#define TIM_SORT_COLLAPSE SORT_MAKE_STR(tim_sort_collapse)
#ifndef MAX
#define MAX(x,y) (((x) > (y) ? (x) : (y)))
#endif
#ifndef MIN
#define MIN(x,y) (((x) < (y) ? (x) : (y)))
#endif
typedef struct {
size_t start;
size_t length;
} TIM_SORT_RUN_T;
void BINARY_INSERTION_SORT(SORT_TYPE *dst, const size_t size);
void TIM_SORT(SORT_TYPE *dst, const size_t size);
/* Function used to do a binary search for binary insertion sort */
static __inline size_t BINARY_INSERTION_FIND(SORT_TYPE *dst, const SORT_TYPE x,
const size_t size) {
size_t l, c, r;
SORT_TYPE cx;
l = 0;
r = size - 1;
c = r >> 1;
/* check for out of bounds at the beginning. */
if (SORT_CMP(x, dst[0]) < 0) {
return 0;
} else if (SORT_CMP(x, dst[r]) > 0) {
return r;
}
cx = dst[c];
while (1) {
const int val = SORT_CMP(x, cx);
if (val < 0) {
if (c - l <= 1) {
return c;
}
r = c;
} else { /* allow = for stability. The binary search favors the right. */
if (r - c <= 1) {
return c + 1;
}
l = c;
}
c = l + ((r - l) >> 1);
cx = dst[c];
}
}
/* Binary insertion sort, but knowing that the first "start" entries are sorted. Used in timsort. */
static void BINARY_INSERTION_SORT_START(SORT_TYPE *dst, const size_t start, const size_t size) {
size_t i;
for (i = start; i < size; i++) {
size_t j;
SORT_TYPE x;
size_t location;
/* If this entry is already correct, just move along */
if (SORT_CMP(dst[i - 1], dst[i]) <= 0) {
continue;
}
/* Else we need to find the right place, shift everything over, and squeeze in */
x = dst[i];
location = BINARY_INSERTION_FIND(dst, x, i);
for (j = i - 1; j >= location; j--) {
dst[j + 1] = dst[j];
if (j == 0) { /* check edge case because j is unsigned */
break;
}
}
dst[location] = x;
}
}
/* Binary insertion sort */
void BINARY_INSERTION_SORT(SORT_TYPE *dst, const size_t size) {
/* don't bother sorting an array of size <= 1 */
if (size <= 1) {
return;
}
BINARY_INSERTION_SORT_START(dst, 1, size);
}
/* timsort implementation, based on timsort.txt */
static __inline void REVERSE_ELEMENTS(SORT_TYPE *dst, size_t start, size_t end) {
while (1) {
if (start >= end) {
return;
}
SORT_SWAP(dst[start], dst[end]);
start++;
end--;
}
}
static size_t COUNT_RUN(SORT_TYPE *dst, const size_t start, const size_t size) {
size_t curr;
if (size - start == 1) {
return 1;
}
if (start >= size - 2) {
if (SORT_CMP(dst[size - 2], dst[size - 1]) > 0) {
SORT_SWAP(dst[size - 2], dst[size - 1]);
}
return 2;
}
curr = start + 2;
if (SORT_CMP(dst[start], dst[start + 1]) <= 0) {
/* increasing run */
while (1) {
if (curr == size - 1) {
break;
}
if (SORT_CMP(dst[curr - 1], dst[curr]) > 0) {
break;
}
curr++;
}
return curr - start;
} else {
/* decreasing run */
while (1) {
if (curr == size - 1) {
break;
}
if (SORT_CMP(dst[curr - 1], dst[curr]) <= 0) {
break;
}
curr++;
}
/* reverse in-place */
REVERSE_ELEMENTS(dst, start, curr - 1);
return curr - start;
}
}
static int CHECK_INVARIANT(TIM_SORT_RUN_T *stack, const int stack_curr) {
size_t A, B, C;
if (stack_curr < 2) {
return 1;
}
if (stack_curr == 2) {
const size_t A1 = stack[stack_curr - 2].length;
const size_t B1 = stack[stack_curr - 1].length;
if (A1 <= B1) {
return 0;
}
return 1;
}
A = stack[stack_curr - 3].length;
B = stack[stack_curr - 2].length;
C = stack[stack_curr - 1].length;
if ((A <= B + C) || (B <= C)) {
return 0;
}
return 1;
}
typedef struct {
size_t alloc;
SORT_TYPE *storage;
} TEMP_STORAGE_T;
static void TIM_SORT_RESIZE(TEMP_STORAGE_T *store, const size_t new_size) {
if (store->alloc < new_size) {
SORT_TYPE *tempstore = (SORT_TYPE *)realloc(store->storage, new_size * sizeof(SORT_TYPE));
if (tempstore == NULL) {
fprintf(stderr, "Error allocating temporary storage for tim sort: need %lu bytes",
(unsigned long)(sizeof(SORT_TYPE) * new_size));
exit(1);
}
store->storage = tempstore;
store->alloc = new_size;
}
}
static void TIM_SORT_MERGE(SORT_TYPE *dst, const TIM_SORT_RUN_T *stack, const int stack_curr,
TEMP_STORAGE_T *store) {
const size_t A = stack[stack_curr - 2].length;
const size_t B = stack[stack_curr - 1].length;
const size_t curr = stack[stack_curr - 2].start;
SORT_TYPE *storage;
size_t i, j, k;
TIM_SORT_RESIZE(store, MIN(A, B));
storage = store->storage;
/* left merge */
if (A < B) {
memcpy(storage, &dst[curr], A * sizeof(SORT_TYPE));
i = 0;
j = curr + A;
for (k = curr; k < curr + A + B; k++) {
if ((i < A) && (j < curr + A + B)) {
if (SORT_CMP(storage[i], dst[j]) <= 0) {
dst[k] = storage[i++];
} else {
dst[k] = dst[j++];
}
} else if (i < A) {
dst[k] = storage[i++];
} else {
break;
}
}
} else {
/* right merge */
memcpy(storage, &dst[curr + A], B * sizeof(SORT_TYPE));
i = B;
j = curr + A;
k = curr + A + B;
while (k-- > curr) {
if ((i > 0) && (j > curr)) {
if (SORT_CMP(dst[j - 1], storage[i - 1]) > 0) {
dst[k] = dst[--j];
} else {
dst[k] = storage[--i];
}
} else if (i > 0) {
dst[k] = storage[--i];
} else {
break;
}
}
}
}
static int TIM_SORT_COLLAPSE(SORT_TYPE *dst, TIM_SORT_RUN_T *stack, int stack_curr,
TEMP_STORAGE_T *store, const size_t size) {
while (1) {
size_t A, B, C, D;
int ABC, BCD, CD;
/* if the stack only has one thing on it, we are done with the collapse */
if (stack_curr <= 1) {
break;
}
/* if this is the last merge, just do it */
if ((stack_curr == 2) && (stack[0].length + stack[1].length == size)) {
TIM_SORT_MERGE(dst, stack, stack_curr, store);
stack[0].length += stack[1].length;
stack_curr--;
break;
}
/* check if the invariant is off for a stack of 2 elements */
else if ((stack_curr == 2) && (stack[0].length <= stack[1].length)) {
TIM_SORT_MERGE(dst, stack, stack_curr, store);
stack[0].length += stack[1].length;
stack_curr--;
break;
} else if (stack_curr == 2) {
break;
}
B = stack[stack_curr - 3].length;
C = stack[stack_curr - 2].length;
D = stack[stack_curr - 1].length;
if (stack_curr >= 4) {
A = stack[stack_curr - 4].length;
ABC = (A <= B + C);
} else {
ABC = 0;
}
BCD = (B <= C + D) || ABC;
CD = (C <= D);
/* Both invariants are good */
if (!BCD && !CD) {
break;
}
/* left merge */
if (BCD && !CD) {
TIM_SORT_MERGE(dst, stack, stack_curr - 1, store);
stack[stack_curr - 3].length += stack[stack_curr - 2].length;
stack[stack_curr - 2] = stack[stack_curr - 1];
stack_curr--;
} else {
/* right merge */
TIM_SORT_MERGE(dst, stack, stack_curr, store);
stack[stack_curr - 2].length += stack[stack_curr - 1].length;
stack_curr--;
}
}
return stack_curr;
}
static __inline int PUSH_NEXT(SORT_TYPE *dst,
const size_t size,
TEMP_STORAGE_T *store,
const size_t minrun,
TIM_SORT_RUN_T *run_stack,
size_t *stack_curr,
size_t *curr) {
size_t len = COUNT_RUN(dst, *curr, size);
size_t run = minrun;
if (run > size - *curr) {
run = size - *curr;
}
if (run > len) {
BINARY_INSERTION_SORT_START(&dst[*curr], len, run);
len = run;
}
run_stack[*stack_curr].start = *curr;
run_stack[*stack_curr].length = len;
(*stack_curr)++;
*curr += len;
if (*curr == size) {
/* finish up */
while (*stack_curr > 1) {
TIM_SORT_MERGE(dst, run_stack, *stack_curr, store);
run_stack[*stack_curr - 2].length += run_stack[*stack_curr - 1].length;
(*stack_curr)--;
}
if (store->storage != NULL) {
free(store->storage);
store->storage = NULL;
}
return 0;
}
return 1;
}
void TIM_SORT(SORT_TYPE *dst, const size_t size) {
size_t minrun;
TEMP_STORAGE_T _store, *store;
TIM_SORT_RUN_T run_stack[TIM_SORT_STACK_SIZE];
size_t stack_curr = 0;
size_t curr = 0;
/* don't bother sorting an array of size 1 */
if (size <= 1) {
return;
}
if (size < 64) {
BINARY_INSERTION_SORT(dst, size);
return;
}
/* compute the minimum run length */
minrun = compute_minrun(size);
/* temporary storage for merges */
store = &_store;
store->alloc = 0;
store->storage = NULL;
if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
return;
}
if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
return;
}
if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
return;
}
while (1) {
if (!CHECK_INVARIANT(run_stack, stack_curr)) {
stack_curr = TIM_SORT_COLLAPSE(dst, run_stack, stack_curr, store, size);
continue;
}
if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
return;
}
}
}
#undef SORT_CONCAT
#undef SORT_MAKE_STR1
#undef SORT_MAKE_STR
#undef SORT_NAME
#undef SORT_TYPE
#undef SORT_CMP
#undef TEMP_STORAGE_T
#undef TIM_SORT_RUN_T
#undef PUSH_NEXT
#undef SORT_SWAP
#undef SORT_CONCAT
#undef SORT_MAKE_STR1
#undef SORT_MAKE_STR
#undef BINARY_INSERTION_FIND
#undef BINARY_INSERTION_SORT_START
#undef BINARY_INSERTION_SORT
#undef REVERSE_ELEMENTS
#undef COUNT_RUN
#undef TIM_SORT
#undef TIM_SORT_RESIZE
#undef TIM_SORT_COLLAPSE
#undef TIM_SORT_RUN_T
#undef TEMP_STORAGE_T