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+/*
+ * 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-agnostic 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
+#if defined(__GNUC__) && ((__GNUC__ == 3 && __GNUC_MINOR__ >= 4) || (__GNUC__ > 3))
+#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) {
+ k--;
+ 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
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