/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: 2025-08-26 07:08

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	1.24M	#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	14.8k	#define MAX(x,y) (((x) > (y) ? (x) : (y)))
68		#endif
69
70		#ifndef MIN
71	91.1k	#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	14.8k	#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	14.8k	static __inline int compute_minrun(const uint64_t size) {
130	14.8k	const int top_bit = 64 - CLZ(size);
131	14.8k	const int shift = MAX(top_bit, 6) - 6;
132	14.8k	const int minrun = size >> shift;
133	14.8k	const uint64_t mask = (1ULL << shift) - 1;
134
135	14.8k	if (mask & size) {
136	7.22k	return minrun + 1;
137	7.22k	}
138
139	7.67k	return minrun;
140	14.8k	}
141
142		#endif /* SORT_COMMON_H */
143
144	761k	#define SORT_CONCAT(x, y) x ## _ ## y
145	761k	#define SORT_MAKE_STR1(x, y) SORT_CONCAT(x,y)
146	761k	#define SORT_MAKE_STR(x) SORT_MAKE_STR1(SORT_NAME,x)
147
148	113k	#define BINARY_INSERTION_FIND SORT_MAKE_STR(binary_insertion_find)
149	130k	#define BINARY_INSERTION_SORT_START SORT_MAKE_STR(binary_insertion_sort_start)
150	72.6k	#define BINARY_INSERTION_SORT SORT_MAKE_STR(binary_insertion_sort)
151	941	#define REVERSE_ELEMENTS SORT_MAKE_STR(reverse_elements)
152	106k	#define COUNT_RUN SORT_MAKE_STR(count_run)
153	115k	#define CHECK_INVARIANT SORT_MAKE_STR(check_invariant)
154		#define TIM_SORT SORT_MAKE_STR(tim_sort)
155	91.1k	#define TIM_SORT_RESIZE SORT_MAKE_STR(tim_sort_resize)
156	91.1k	#define TIM_SORT_MERGE SORT_MAKE_STR(tim_sort_merge)
157	40.4k	#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	113k	const size_t size) {
181	113k	size_t l, c, r;
182	113k	SORT_TYPE cx;
183	113k	l = 0;
184	113k	r = size - 1;
185	113k	c = r >> 1;
186
187		/* check for out of bounds at the beginning. */
188	113k	if (SORT_CMP(x, dst[0]) < 0) {
189	31.3k	return 0;
190	82.1k	} else if (SORT_CMP(x, dst[r]) > 0) {
191	0	return r;
192	0	}
193
194	82.1k	cx = dst[c];
195
196	376k	while (1) {
197	376k	const int val = SORT_CMP(x, cx);
198
199	376k	if (val < 0) {
200	195k	if (c - l <= 1) {
201	60.1k	return c;
202	60.1k	}
203
204	135k	r = c;
205	180k	} else { /* allow = for stability. The binary search favors the right. */
206	180k	if (r - c <= 1) {
207	22.0k	return c + 1;
208	22.0k	}
209
210	158k	l = c;
211	158k	}
212
213	294k	c = l + ((r - l) >> 1);
214	294k	cx = dst[c];
215	294k	}
216	82.1k	}
217
218		/* Binary insertion sort, but knowing that the first "start" entries are sorted. Used in timsort. */
219	130k	static void BINARY_INSERTION_SORT_START(SORT_TYPE *dst, const size_t start, const size_t size) {
220	130k	size_t i;
221
222	1.89M	for (i = start; i < size; i++) {
223	1.76M	size_t j;
224	1.76M	SORT_TYPE x;
225	1.76M	size_t location;
226
227		/* If this entry is already correct, just move along */
228	1.76M	if (SORT_CMP(dst[i - 1], dst[i]) <= 0) {
229	1.65M	continue;
230	1.65M	}
231
232		/* Else we need to find the right place, shift everything over, and squeeze in */
233	113k	x = dst[i];
234	113k	location = BINARY_INSERTION_FIND(dst, x, i);
235
236	1.92M	for (j = i - 1; j >= location; j--) {
237	1.84M	dst[j + 1] = dst[j];
238
239	1.84M	if (j == 0) { /* check edge case because j is unsigned */
240	31.3k	break;
241	31.3k	}
242	1.84M	}
243
244	113k	dst[location] = x;
245	113k	}
246	130k	}
247
248		/* Binary insertion sort */
249	72.6k	void BINARY_INSERTION_SORT(SORT_TYPE *dst, const size_t size) {
250		/* don't bother sorting an array of size <= 1 */
251	72.6k	if (size <= 1) {
252	0	return;
253	0	}
254
255	72.6k	BINARY_INSERTION_SORT_START(dst, 1, size);
256	72.6k	}
257
258		/* timsort implementation, based on timsort.txt */
259
260	941	static __inline void REVERSE_ELEMENTS(SORT_TYPE *dst, size_t start, size_t end) {
261	1.24M	while (1) {
262	1.24M	if (start >= end) {
263	941	return;
264	941	}
265
266	1.24M	SORT_SWAP(dst[start], dst[end]);
267	1.24M	start++;
268	1.24M	end--;
269	1.24M	}
270	941	}
271
272	106k	static size_t COUNT_RUN(SORT_TYPE *dst, const size_t start, const size_t size) {
273	106k	size_t curr;
274
275	106k	if (size - start == 1) {
276	14.6k	return 1;
277	14.6k	}
278
279	91.4k	if (start >= size - 2) {
280	4	if (SORT_CMP(dst[size - 2], dst[size - 1]) > 0) {
281	1	SORT_SWAP(dst[size - 2], dst[size - 1]);
282	1	}
283
284	4	return 2;
285	4	}
286
287	91.3k	curr = start + 2;
288
289	91.3k	if (SORT_CMP(dst[start], dst[start + 1]) <= 0) {
290		/* increasing run */
291	14.6M	while (1) {
292	14.6M	if (curr == size - 1) {
293	14.6k	break;
294	14.6k	}
295
296	14.6M	if (SORT_CMP(dst[curr - 1], dst[curr]) > 0) {
297	75.7k	break;
298	75.7k	}
299
300	14.5M	curr++;
301	14.5M	}
302
303	90.4k	return curr - start;
304	90.4k	} else {
305		/* decreasing run */
306	2.48M	while (1) {
307	2.48M	if (curr == size - 1) {
308	45	break;
309	45	}
310
311	2.48M	if (SORT_CMP(dst[curr - 1], dst[curr]) <= 0) {
312	896	break;
313	896	}
314
315	2.48M	curr++;
316	2.48M	}
317
318		/* reverse in-place */
319	941	REVERSE_ELEMENTS(dst, start, curr - 1);
320	941	return curr - start;
321	941	}
322	91.3k	}
323
324	115k	static int CHECK_INVARIANT(TIM_SORT_RUN_T *stack, const int stack_curr) {
325	115k	size_t A, B, C;
326
327	115k	if (stack_curr < 2) {
328	1.25k	return 1;
329	1.25k	}
330
331	114k	if (stack_curr == 2) {
332	3.46k	const size_t A1 = stack[stack_curr - 2].length;
333	3.46k	const size_t B1 = stack[stack_curr - 1].length;
334
335	3.46k	if (A1 <= B1) {
336	1	return 0;
337	1	}
338
339	3.46k	return 1;
340	3.46k	}
341
342	110k	A = stack[stack_curr - 3].length;
343	110k	B = stack[stack_curr - 2].length;
344	110k	C = stack[stack_curr - 1].length;
345
346	110k	if ((A <= B + C) \|\| (B <= C)) {
347	40.4k	return 0;
348	40.4k	}
349
350	70.2k	return 1;
351	110k	}
352
353		typedef struct {
354		size_t alloc;
355		SORT_TYPE *storage;
356		} TEMP_STORAGE_T;
357
358	91.1k	static void TIM_SORT_RESIZE(TEMP_STORAGE_T *store, const size_t new_size) {
359	91.1k	if (store->alloc < new_size) {
360	17.6k	SORT_TYPE tempstore = (SORT_TYPE )realloc(store->storage, new_size * sizeof(SORT_TYPE));
361
362	17.6k	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	17.6k	store->storage = tempstore;
369	17.6k	store->alloc = new_size;
370	17.6k	}
371	91.1k	}
372
373		static void TIM_SORT_MERGE(SORT_TYPE dst, const TIM_SORT_RUN_T stack, const int stack_curr,
374	91.1k	TEMP_STORAGE_T *store) {
375	91.1k	const size_t A = stack[stack_curr - 2].length;
376	91.1k	const size_t B = stack[stack_curr - 1].length;
377	91.1k	const size_t curr = stack[stack_curr - 2].start;
378	91.1k	SORT_TYPE *storage;
379	91.1k	size_t i, j, k;
380	91.1k	TIM_SORT_RESIZE(store, MIN(A, B));
381	91.1k	storage = store->storage;
382
383		/* left merge */
384	91.1k	if (A < B) {
385	21.8k	memcpy(storage, &dst[curr], A * sizeof(SORT_TYPE));
386	21.8k	i = 0;
387	21.8k	j = curr + A;
388
389	8.40M	for (k = curr; k < curr + A + B; k++) {
390	8.40M	if ((i < A) && (j < curr + A + B)) {
391	8.34M	if (SORT_CMP(storage[i], dst[j]) <= 0) {
392	8.09M	dst[k] = storage[i++];
393	8.09M	} else {
394	249k	dst[k] = dst[j++];
395	249k	}
396	8.34M	} else if (i < A) {
397	38.2k	dst[k] = storage[i++];
398	38.2k	} else {
399	21.8k	break;
400	21.8k	}
401	8.40M	}
402	69.2k	} else {
403		/* right merge */
404	69.2k	memcpy(storage, &dst[curr + A], B * sizeof(SORT_TYPE));
405	69.2k	i = B;
406	69.2k	j = curr + A;
407	69.2k	k = curr + A + B;
408
409	16.3M	while (k > curr) {
410	16.3M	k--;
411	16.3M	if ((i > 0) && (j > curr)) {
412	16.2M	if (SORT_CMP(dst[j - 1], storage[i - 1]) > 0) {
413	3.25M	dst[k] = dst[--j];
414	13.0M	} else {
415	13.0M	dst[k] = storage[--i];
416	13.0M	}
417	16.2M	} else if (i > 0) {
418	48	dst[k] = storage[--i];
419	69.1k	} else {
420	69.1k	break;
421	69.1k	}
422	16.3M	}
423	69.2k	}
424	91.1k	}
425
426		static int TIM_SORT_COLLAPSE(SORT_TYPE dst, TIM_SORT_RUN_T stack, int stack_curr,
427	40.4k	TEMP_STORAGE_T *store, const size_t size) {
428	114k	while (1) {
429	114k	size_t A, B, C, D;
430	114k	int ABC, BCD, CD;
431
432		/* if the stack only has one thing on it, we are done with the collapse */
433	114k	if (stack_curr <= 1) {
434	0	break;
435	0	}
436
437		/* if this is the last merge, just do it */
438	114k	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	114k	else if ((stack_curr == 2) && (stack[0].length <= stack[1].length)) {
446	1.25k	TIM_SORT_MERGE(dst, stack, stack_curr, store);
447	1.25k	stack[0].length += stack[1].length;
448	1.25k	stack_curr--;
449	1.25k	break;
450	113k	} else if (stack_curr == 2) {
451	3.02k	break;
452	3.02k	}
453
454	110k	B = stack[stack_curr - 3].length;
455	110k	C = stack[stack_curr - 2].length;
456	110k	D = stack[stack_curr - 1].length;
457
458	110k	if (stack_curr >= 4) {
459	101k	A = stack[stack_curr - 4].length;
460	101k	ABC = (A <= B + C);
461	101k	} else {
462	8.86k	ABC = 0;
463	8.86k	}
464
465	110k	BCD = (B <= C + D) \|\| ABC;
466	110k	CD = (C <= D);
467
468		/* Both invariants are good */
469	110k	if (!BCD && !CD) {
470	36.1k	break;
471	36.1k	}
472
473		/* left merge */
474	73.9k	if (BCD && !CD) {
475	14.7k	TIM_SORT_MERGE(dst, stack, stack_curr - 1, store);
476	14.7k	stack[stack_curr - 3].length += stack[stack_curr - 2].length;
477	14.7k	stack[stack_curr - 2] = stack[stack_curr - 1];
478	14.7k	stack_curr--;
479	59.1k	} else {
480		/* right merge */
481	59.1k	TIM_SORT_MERGE(dst, stack, stack_curr, store);
482	59.1k	stack[stack_curr - 2].length += stack[stack_curr - 1].length;
483	59.1k	stack_curr--;
484	59.1k	}
485	73.9k	}
486
487	40.4k	return stack_curr;
488	40.4k	}
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	106k	size_t *curr) {
497	106k	size_t len = COUNT_RUN(dst, *curr, size);
498	106k	size_t run = minrun;
499
500	106k	if (run > size - *curr) {
501	14.8k	run = size - *curr;
502	14.8k	}
503
504	106k	if (run > len) {
505	57.8k	BINARY_INSERTION_SORT_START(&dst[*curr], len, run);
506	57.8k	len = run;
507	57.8k	}
508
509	106k	run_stack[stack_curr].start = curr;
510	106k	run_stack[*stack_curr].length = len;
511	106k	(*stack_curr)++;
512	106k	*curr += len;
513
514	106k	if (*curr == size) {
515		/* finish up */
516	30.8k	while (*stack_curr > 1) {
517	15.9k	TIM_SORT_MERGE(dst, run_stack, *stack_curr, store);
518	15.9k	run_stack[stack_curr - 2].length += run_stack[stack_curr - 1].length;
519	15.9k	(*stack_curr)--;
520	15.9k	}
521
522	14.8k	if (store->storage != NULL) {
523	14.8k	free(store->storage);
524	14.8k	store->storage = NULL;
525	14.8k	}
526
527	14.8k	return 0;
528	14.8k	}
529
530	91.1k	return 1;
531	106k	}
532
533	90.4k	void TIM_SORT(SORT_TYPE *dst, const size_t size) {
534	90.4k	size_t minrun;
535	90.4k	TEMP_STORAGE_T _store, *store;
536	90.4k	TIM_SORT_RUN_T run_stack[TIM_SORT_STACK_SIZE];
537	90.4k	size_t stack_curr = 0;
538	90.4k	size_t curr = 0;
539
540		/* don't bother sorting an array of size 1 */
541	90.4k	if (size <= 1) {
542	2.91k	return;
543	2.91k	}
544
545	87.5k	if (size < 64) {
546	72.6k	BINARY_INSERTION_SORT(dst, size);
547	72.6k	return;
548	72.6k	}
549
550		/* compute the minimum run length */
551	14.8k	minrun = compute_minrun(size);
552		/* temporary storage for merges */
553	14.8k	store = &_store;
554	14.8k	store->alloc = 0;
555	14.8k	store->storage = NULL;
556
557	14.8k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
558	0	return;
559	0	}
560
561	14.8k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
562	13.6k	return;
563	13.6k	}
564
565	1.22k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
566	18	return;
567	18	}
568
569	115k	while (1) {
570	115k	if (!CHECK_INVARIANT(run_stack, stack_curr)) {
571	40.4k	stack_curr = TIM_SORT_COLLAPSE(dst, run_stack, stack_curr, store, size);
572	40.4k	continue;
573	40.4k	}
574
575	75.0k	if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {
576	1.20k	return;
577	1.20k	}
578	75.0k	}
579	1.20k	}
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