timsort.h - platform/external/libxml2 - Gitiles

 /*
  * 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) {
   /* don't bother sorting an array of size 1 */
   if (size <= 1) {
     return;
   }

   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;

   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
	/*
	* 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) {
	/* don't bother sorting an array of size 1 */
	if (size <= 1) {
	return;
	}

	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;

	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