/src/libxml2/timsort.h

Source (jump to first uncovered line)
/*
 * 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;


XML_HIDDEN
void BINARY_INSERTION_SORT(SORT_TYPE *dst, const size_t size);
XML_HIDDEN
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

Coverage Report

Created: 2025-07-11 06:13

Line	Count	Source (jump to first uncovered line)
1		/*
2		* Taken from https://github.com/swenson/sort
3		* Revision: 05fd77bfec049ce8b7c408c4d3dd2d51ee061a15
4		* Removed all code unrelated to Timsort and made minor adjustments for
5		* cross-platform compatibility.
6		*/
7
8		/*
9		* The MIT License (MIT)
10		*
11		* Copyright (c) 2010-2017 Christopher Swenson.
12		* Copyright (c) 2012 Vojtech Fried.
13		* Copyright (c) 2012 Google Inc. All Rights Reserved.
14		*
15		* Permission is hereby granted, free of charge, to any person obtaining a
16		* copy of this software and associated documentation files (the "Software"),
17		* to deal in the Software without restriction, including without limitation
18		* the rights to use, copy, modify, merge, publish, distribute, sublicense,
19		* and/or sell copies of the Software, and to permit persons to whom the
20		* Software is furnished to do so, subject to the following conditions:
21		*
22		* The above copyright notice and this permission notice shall be included in
23		* all copies or substantial portions of the Software.
24		*
25		* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
26		* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
27		* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
28		* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
29		* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
30		* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
31		* DEALINGS IN THE SOFTWARE.
32		*/
33
34		#include <stdlib.h>
35		#include <stdio.h>
36		#include <string.h>
37		#ifdef HAVE_STDINT_H
38		#include <stdint.h>
39		#elif defined(_WIN32)
40		typedef unsigned __int64 uint64_t;
41		#endif
42
43		#ifndef SORT_NAME
44		#error "Must declare SORT_NAME"
45		#endif
46
47		#ifndef SORT_TYPE
48		#error "Must declare SORT_TYPE"
49		#endif
50
51		#ifndef SORT_CMP
52		#define SORT_CMP(x, y) ((x) < (y) ? -1 : ((x) == (y) ? 0 : 1))
53		#endif
54
55		#ifndef TIM_SORT_STACK_SIZE
56		#define TIM_SORT_STACK_SIZE 128
57		#endif
58
59	820k	#define SORT_SWAP(x,y) {SORT_TYPE __SORT_SWAP_t = (x); (x) = (y); (y) = __SORT_SWAP_t;}
60
61
62		/* Common, type-agnostic functions and constants that we don't want to declare twice. */
63		#ifndef SORT_COMMON_H
64		#define SORT_COMMON_H
65
66		#ifndef MAX
67	41.0k	#define MAX(x,y) (((x) > (y) ? (x) : (y)))
68		#endif
69
70		#ifndef MIN
71	98.9k	#define MIN(x,y) (((x) < (y) ? (x) : (y)))
72		#endif
73
74		static int compute_minrun(const uint64_t);
75
76		#ifndef CLZ
77		#if defined(__GNUC__) && ((__GNUC__ == 3 && __GNUC_MINOR__ >= 4) \|\| (__GNUC__ > 3))
78	41.0k	#define CLZ __builtin_clzll
79		#else
80
81		static int clzll(uint64_t);
82
83		/* adapted from Hacker's Delight */
84		static int clzll(uint64_t x) {
85		int n;
86
87		if (x == 0) {
88		return 64;
89		}
90
91		n = 0;
92
93		if (x <= 0x00000000FFFFFFFFL) {
94		n = n + 32;
95		x = x << 32;
96		}
97
98		if (x <= 0x0000FFFFFFFFFFFFL) {
99		n = n + 16;
100		x = x << 16;
101		}
102
103		if (x <= 0x00FFFFFFFFFFFFFFL) {
104		n = n + 8;
105		x = x << 8;
106		}
107
108		if (x <= 0x0FFFFFFFFFFFFFFFL) {
109		n = n + 4;
110		x = x << 4;
111		}
112
113		if (x <= 0x3FFFFFFFFFFFFFFFL) {
114		n = n + 2;
115		x = x << 2;
116		}
117
118		if (x <= 0x7FFFFFFFFFFFFFFFL) {
119		n = n + 1;
120		}
121
122		return n;
123		}
124
125		#define CLZ clzll
126		#endif
127		#endif
128
129	41.0k	static __inline int compute_minrun(const uint64_t size) {
130	41.0k	const int top_bit = 64 - CLZ(size);
131	41.0k	const int shift = MAX(top_bit, 6) - 6;
132	41.0k	const int minrun = size >> shift;
133	41.0k	const uint64_t mask = (1ULL << shift) - 1;
134
135	41.0k	if (mask & size) {
136	28.4k	return minrun + 1;
137	28.4k	}
138
139	12.6k	return minrun;
140	41.0k	}
141
142		#endif /* SORT_COMMON_H */
143
144	5.46M	#define SORT_CONCAT(x, y) x ## _ ## y
145	5.46M	#define SORT_MAKE_STR1(x, y) SORT_CONCAT(x,y)
146	5.46M	#define SORT_MAKE_STR(x) SORT_MAKE_STR1(SORT_NAME,x)
147
148	2.32M	#define BINARY_INSERTION_FIND SORT_MAKE_STR(binary_insertion_find)
149	1.36M	#define BINARY_INSERTION_SORT_START SORT_MAKE_STR(binary_insertion_sort_start)
150	1.31M	#define BINARY_INSERTION_SORT SORT_MAKE_STR(binary_insertion_sort)
151	8.16k	#define REVERSE_ELEMENTS SORT_MAKE_STR(reverse_elements)
152	140k	#define COUNT_RUN SORT_MAKE_STR(count_run)
153	83.5k	#define CHECK_INVARIANT SORT_MAKE_STR(check_invariant)
154		#define TIM_SORT SORT_MAKE_STR(tim_sort)
155	98.9k	#define TIM_SORT_RESIZE SORT_MAKE_STR(tim_sort_resize)
156	98.9k	#define TIM_SORT_MERGE SORT_MAKE_STR(tim_sort_merge)
157	30.0k	#define TIM_SORT_COLLAPSE SORT_MAKE_STR(tim_sort_collapse)
158
159		#ifndef MAX
160		#define MAX(x,y) (((x) > (y) ? (x) : (y)))
161		#endif
162		#ifndef MIN
163		#define MIN(x,y) (((x) < (y) ? (x) : (y)))
164		#endif
165
166		typedef struct {
167		size_t start;
168		size_t length;
169		} TIM_SORT_RUN_T;
170
171
172		XML_HIDDEN
173		void BINARY_INSERTION_SORT(SORT_TYPE *dst, const size_t size);
174		XML_HIDDEN
175		void TIM_SORT(SORT_TYPE *dst, const size_t size);
176
177
178		/* Function used to do a binary search for binary insertion sort */
179		static __inline size_t BINARY_INSERTION_FIND(SORT_TYPE *dst, const SORT_TYPE x,
180	2.32M	const size_t size) {
181	2.32M	size_t l, c, r;
182	2.32M	SORT_TYPE cx;
183	2.32M	l = 0;
184	2.32M	r = size - 1;
185	2.32M	c = r >> 1;
186
187		/* check for out of bounds at the beginning. */
188	2.32M	if (SORT_CMP(x, dst[0]) < 0) {
189	338k	return 0;
190	1.98M	} else if (SORT_CMP(x, dst[r]) > 0) {
191	0	return r;
192	0	}
193
194	1.98M	cx = dst[c];
195
196	5.77M	while (1) {
197	5.77M	const int val = SORT_CMP(x, cx);
198
199	5.77M	if (val < 0) {
200	660k	if (c - l <= 1) {
201	278k	return c;
202	278k	}
203
204	382k	r = c;
205	5.11M	} else { /* allow = for stability. The binary search favors the right. */
206	5.11M	if (r - c <= 1) {
207	1.71M	return c + 1;
208	1.71M	}
209
210	3.40M	l = c;
211	3.40M	}
212
213	3.78M	c = l + ((r - l) >> 1);
214	3.78M	cx = dst[c];
215	3.78M	}
216	1.98M	}
217
218		/* Binary insertion sort, but knowing that the first "start" entries are sorted. Used in timsort. */
219	1.36M	static void BINARY_INSERTION_SORT_START(SORT_TYPE *dst, const size_t start, const size_t size) {
220	1.36M	size_t i;
221
222	21.7M	for (i = start; i < size; i++) {
223	20.4M	size_t j;
224	20.4M	SORT_TYPE x;
225	20.4M	size_t location;
226
227		/* If this entry is already correct, just move along */
228	20.4M	if (SORT_CMP(dst[i - 1], dst[i]) <= 0) {
229	18.1M	continue;
230	18.1M	}
231
232		/* Else we need to find the right place, shift everything over, and squeeze in */
233	2.32M	x = dst[i];
234	2.32M	location = BINARY_INSERTION_FIND(dst, x, i);
235
236	7.77M	for (j = i - 1; j >= location; j--) {
237	5.78M	dst[j + 1] = dst[j];
238
239	5.78M	if (j == 0) { /* check edge case because j is unsigned */
240	338k	break;
241	338k	}
242	5.78M	}
243
244	2.32M	dst[location] = x;
245	2.32M	}
246	1.36M	}
247
248		/* Binary insertion sort */
249	1.31M	void BINARY_INSERTION_SORT(SORT_TYPE *dst, const size_t size) {
250		/* don't bother sorting an array of size <= 1 */
251	1.31M	if (size <= 1) {
252	0	return;
253	0	}
254
255	1.31M	BINARY_INSERTION_SORT_START(dst, 1, size);
256	1.31M	}
257
258		/* timsort implementation, based on timsort.txt */
259
260	8.16k	static __inline void REVERSE_ELEMENTS(SORT_TYPE *dst, size_t start, size_t end) {
261	828k	while (1) {
262	828k	if (start >= end) {
263	8.16k	return;
264	8.16k	}
265
266	820k	SORT_SWAP(dst[start], dst[end]);
267	820k	start++;
268	820k	end--;
269	820k	}
270	8.16k	}
271
272	140k	static size_t COUNT_RUN(SORT_TYPE *dst, const size_t start, const size_t size) {
273	140k	size_t curr;
274
275	140k	if (size - start == 1) {
276	33.7k	return 1;
277	33.7k	}
278
279	106k	if (start >= size - 2) {
280	399	if (SORT_CMP(dst[size - 2], dst[size - 1]) > 0) {
281	89	SORT_SWAP(dst[size - 2], dst[size - 1]);
282	89	}
283
284	399	return 2;
285	399	}
286
287	105k	curr = start + 2;
288
289	105k	if (SORT_CMP(dst[start], dst[start + 1]) <= 0) {
290		/* increasing run */
291	31.2M	while (1) {
292	31.2M	if (curr == size - 1) {
293	37.7k	break;
294	37.7k	}
295
296	31.2M	if (SORT_CMP(dst[curr - 1], dst[curr]) > 0) {
297	59.9k	break;
298	59.9k	}
299
300	31.1M	curr++;
301	31.1M	}
302
303	97.7k	return curr - start;
304	97.7k	} else {
305		/* decreasing run */
306	1.63M	while (1) {
307	1.63M	if (curr == size - 1) {
308	1.04k	break;
309	1.04k	}
310
311	1.63M	if (SORT_CMP(dst[curr - 1], dst[curr]) <= 0) {
312	7.11k	break;
313	7.11k	}
314
315	1.62M	curr++;
316	1.62M	}
317
318		/* reverse in-place */
319	8.16k	REVERSE_ELEMENTS(dst, start, curr - 1);
320	8.16k	return curr - start;
321	8.16k	}
322	105k	}
323
324	83.5k	static int CHECK_INVARIANT(TIM_SORT_RUN_T *stack, const int stack_curr) {
325	83.5k	size_t A, B, C;
326
327	83.5k	if (stack_curr < 2) {
328	2.49k	return 1;
329	2.49k	}
330
331	81.0k	if (stack_curr == 2) {
332	4.01k	const size_t A1 = stack[stack_curr - 2].length;
333	4.01k	const size_t B1 = stack[stack_curr - 1].length;
334
335	4.01k	if (A1 <= B1) {
336	307	return 0;
337	307	}
338
339	3.70k	return 1;
340	4.01k	}
341
342	77.0k	A = stack[stack_curr - 3].length;
343	77.0k	B = stack[stack_curr - 2].length;
344	77.0k	C = stack[stack_curr - 1].length;
345
346	77.0k	if ((A <= B + C) \|\| (B <= C)) {
347	29.7k	return 0;
348	29.7k	}
349
350	47.2k	return 1;
351	77.0k	}
352
353		typedef struct {
354		size_t alloc;
355		SORT_TYPE *storage;
356		} TEMP_STORAGE_T;
357
358	98.9k	static void TIM_SORT_RESIZE(TEMP_STORAGE_T *store, const size_t new_size) {
359	98.9k	if (store->alloc < new_size) {
360	45.9k	SORT_TYPE tempstore = (SORT_TYPE )realloc(store->storage, new_size * sizeof(SORT_TYPE));
361
362	45.9k	if (tempstore == NULL) {
363	0	fprintf(stderr, "Error allocating temporary storage for tim sort: need %lu bytes",
364	0	(unsigned long)(sizeof(SORT_TYPE) * new_size));
365	0	exit(1);
366	0	}
367
368	45.9k	store->storage = tempstore;
369	45.9k	store->alloc = new_size;
370	45.9k	}
371	98.9k	}
372
373		static void TIM_SORT_MERGE(SORT_TYPE dst, const TIM_SORT_RUN_T stack, const int stack_curr,
374	98.9k	TEMP_STORAGE_T *store) {
375	98.9k	const size_t A = stack[stack_curr - 2].length;
376	98.9k	const size_t B = stack[stack_curr - 1].length;
377	98.9k	const size_t curr = stack[stack_curr - 2].start;
378	98.9k	SORT_TYPE *storage;
379	98.9k	size_t i, j, k;
380	98.9k	TIM_SORT_RESIZE(store, MIN(A, B));
381	98.9k	storage = store->storage;
382
383		/* left merge */
384	98.9k	if (A < B) {
385	18.0k	memcpy(storage, &dst[curr], A * sizeof(SORT_TYPE));
386	18.0k	i = 0;
387	18.0k	j = curr + A;
388
389	5.49M	for (k = curr; k < curr + A + B; k++) {
390	5.49M	if ((i < A) && (j < curr + A + B)) {
391	5.47M	if (SORT_CMP(storage[i], dst[j]) <= 0) {
392	5.13M	dst[k] = storage[i++];
393	5.13M	} else {
394	339k	dst[k] = dst[j++];
395	339k	}
396	5.47M	} else if (i < A) {
397	6.71k	dst[k] = storage[i++];
398	17.0k	} else {
399	17.0k	break;
400	17.0k	}
401	5.49M	}
402	80.8k	} else {
403		/* right merge */
404	80.8k	memcpy(storage, &dst[curr + A], B * sizeof(SORT_TYPE));
405	80.8k	i = B;
406	80.8k	j = curr + A;
407	80.8k	k = curr + A + B;
408
409	10.0M	while (k > curr) {
410	10.0M	k--;
411	10.0M	if ((i > 0) && (j > curr)) {
412	9.99M	if (SORT_CMP(dst[j - 1], storage[i - 1]) > 0) {
413	2.02M	dst[k] = dst[--j];
414	7.97M	} else {
415	7.97M	dst[k] = storage[--i];
416	7.97M	}
417	9.99M	} else if (i > 0) {
418	1.26k	dst[k] = storage[--i];
419	80.1k	} else {
420	80.1k	break;
421	80.1k	}
422	10.0M	}
423	80.8k	}
424	98.9k	}
425
426		static int TIM_SORT_COLLAPSE(SORT_TYPE dst, TIM_SORT_RUN_T stack, int stack_curr,
427	30.0k	TEMP_STORAGE_T *store, const size_t size) {
428	82.2k	while (1) {
429	82.2k	size_t A, B, C, D;
430	82.2k	int ABC, BCD, CD;
431
432		/* if the stack only has one thing on it, we are done with the collapse */
433	82.2k	if (stack_curr <= 1) {
434	0	break;
435	0	}
436
437		/* if this is the last merge, just do it */
438	82.2k	if ((stack_curr == 2) && (stack[0].length + stack[1].length == size)) {
439	0	TIM_SORT_MERGE(dst, stack, stack_curr, store);
440	0	stack[0].length += stack[1].length;
441	0	stack_curr--;
442	0	break;
443	0	}
444		/* check if the invariant is off for a stack of 2 elements */
445	82.2k	else if ((stack_curr == 2) && (stack[0].length <= stack[1].length)) {
446	2.49k	TIM_SORT_MERGE(dst, stack, stack_curr, store);
447	2.49k	stack[0].length += stack[1].length;
448	2.49k	stack_curr--;
449	2.49k	break;
450	79.7k	} else if (stack_curr == 2) {
451	3.18k	break;
452	3.18k	}
453
454	76.5k	B = stack[stack_curr - 3].length;
455	76.5k	C = stack[stack_curr - 2].length;
456	76.5k	D = stack[stack_curr - 1].length;
457
458	76.5k	if (stack_curr >= 4) {
459	68.1k	A = stack[stack_curr - 4].length;
460	68.1k	ABC = (A <= B + C);
461	68.1k	} else {
462	8.42k	ABC = 0;
463	8.42k	}
464
465	76.5k	BCD = (B <= C + D) \|\| ABC;
466	76.5k	CD = (C <= D);
467
468		/* Both invariants are good */
469	76.5k	if (!BCD && !CD) {
470	24.4k	break;
471	24.4k	}
472
473		/* left merge */
474	52.1k	if (BCD && !CD) {
475	11.1k	TIM_SORT_MERGE(dst, stack, stack_curr - 1, store);
476	11.1k	stack[stack_curr - 3].length += stack[stack_curr - 2].length;
477	11.1k	stack[stack_curr - 2] = stack[stack_curr - 1];
478	11.1k	stack_curr--;
479	41.0k	} else {
480		/* right merge */
481	41.0k	TIM_SORT_MERGE(dst, stack, stack_curr, store);
482	41.0k	stack[stack_curr - 2].length += stack[stack_curr - 1].length;
483	41.0k	stack_curr--;
484	41.0k	}
485	52.1k	}
486
487	30.0k	return stack_curr;
488	30.0k	}
489
490		static __inline int PUSH_NEXT(SORT_TYPE *dst,
491		const size_t size,
492		TEMP_STORAGE_T *store,
493		const size_t minrun,
494		TIM_SORT_RUN_T *run_stack,
495		size_t *stack_curr,
496	140k	size_t *curr) {
497	140k	size_t len = COUNT_RUN(dst, *curr, size);
498	140k	size_t run = minrun;
499
500	140k	if (run > size - *curr) {
501	38.5k	run = size - *curr;
502	38.5k	}
503
504	140k	if (run > len) {
505	56.2k	BINARY_INSERTION_SORT_START(&dst[*curr], len, run);
506	56.2k	len = run;
507	56.2k	}
508
509	140k	run_stack[stack_curr].start = curr;
510	140k	run_stack[*stack_curr].length = len;
511	140k	(*stack_curr)++;
512	140k	*curr += len;
513
514	140k	if (*curr == size) {
515		/* finish up */
516	85.3k	while (*stack_curr > 1) {
517	44.2k	TIM_SORT_MERGE(dst, run_stack, *stack_curr, store);
518	44.2k	run_stack[stack_curr - 2].length += run_stack[stack_curr - 1].length;
519	44.2k	(*stack_curr)--;
520	44.2k	}
521
522	41.0k	if (store->storage != NULL) {
523	41.0k	free(store->storage);
524	41.0k	store->storage = NULL;
525	41.0k	}
526
527	41.0k	return 0;
528	41.0k	}
529
530	98.9k	return 1;
531	140k	}
532
533	1.38M	void TIM_SORT(SORT_TYPE *dst, const size_t size) {
534	1.38M	size_t minrun;
535	1.38M	TEMP_STORAGE_T _store, *store;
536	1.38M	TIM_SORT_RUN_T run_stack[TIM_SORT_STACK_SIZE];
537	1.38M	size_t stack_curr = 0;
538	1.38M	size_t curr = 0;
539
540		/* don't bother sorting an array of size 1 */
541	1.38M	if (size <= 1) {
542	29.4k	return;
543	29.4k	}
544
545	1.35M	if (size < 64) {
546	1.31M	BINARY_INSERTION_SORT(dst, size);
547	1.31M	return;
548	1.31M	}
549
550		/* compute the minimum run length */
551	41.0k	minrun = compute_minrun(size);
552		/* temporary storage for merges */
553	41.0k	store = &_store;
554	41.0k	store->alloc = 0;
555	41.0k	store->storage = NULL;
556
557	41.0k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
558	0	return;
559	0	}
560
561	41.0k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
562	36.6k	return;
563	36.6k	}
564
565	4.39k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
566	1.13k	return;
567	1.13k	}
568
569	83.5k	while (1) {
570	83.5k	if (!CHECK_INVARIANT(run_stack, stack_curr)) {
571	30.0k	stack_curr = TIM_SORT_COLLAPSE(dst, run_stack, stack_curr, store, size);
572	30.0k	continue;
573	30.0k	}
574
575	53.4k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
576	3.25k	return;
577	3.25k	}
578	53.4k	}
579	3.25k	}
580
581		#undef SORT_CONCAT
582		#undef SORT_MAKE_STR1
583		#undef SORT_MAKE_STR
584		#undef SORT_NAME
585		#undef SORT_TYPE
586		#undef SORT_CMP
587		#undef TEMP_STORAGE_T
588		#undef TIM_SORT_RUN_T
589		#undef PUSH_NEXT
590		#undef SORT_SWAP
591		#undef SORT_CONCAT
592		#undef SORT_MAKE_STR1
593		#undef SORT_MAKE_STR
594		#undef BINARY_INSERTION_FIND
595		#undef BINARY_INSERTION_SORT_START
596		#undef BINARY_INSERTION_SORT
597		#undef REVERSE_ELEMENTS
598		#undef COUNT_RUN
599		#undef TIM_SORT
600		#undef TIM_SORT_RESIZE
601		#undef TIM_SORT_COLLAPSE
602		#undef TIM_SORT_RUN_T
603		#undef TEMP_STORAGE_T