/*

 * Taken from https://github.com/swenson/sort

 * Revision: 05fd77bfec049ce8b7c408c4d3dd2d51ee061a15

 * Removed all code unrelated to Timsort and made minor adjustments for

 * cross-platform compatibility.

 */

/*

 * The MIT License (MIT)

 *

 * Copyright (c) 2010-2017 Christopher Swenson.

 * Copyright (c) 2012 Vojtech Fried.

 * Copyright (c) 2012 Google Inc. All Rights Reserved.

 *

 * Permission is hereby granted, free of charge, to any person obtaining a

 * copy of this software and associated documentation files (the "Software"),

 * to deal in the Software without restriction, including without limitation

 * the rights to use, copy, modify, merge, publish, distribute, sublicense,

 * and/or sell copies of the Software, and to permit persons to whom the

 * Software is furnished to do so, subject to the following conditions:

 *

 * The above copyright notice and this permission notice shall be included in

 * all copies or substantial portions of the Software.

 *

 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING

 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER

 * DEALINGS IN THE SOFTWARE.

 */

#include <stdlib.h>

#include <stdio.h>

#include <string.h>

#ifdef HAVE_STDINT_H

#include <stdint.h>

#elif defined(_WIN32)

typedef unsigned __int64 uint64_t;

#endif

#ifndef SORT_NAME

#error "Must declare SORT_NAME"

#endif

#ifndef SORT_TYPE

#error "Must declare SORT_TYPE"

#endif

#ifndef SORT_CMP

#define SORT_CMP(x, y)  ((x) < (y) ? -1 : ((x) == (y) ? 0 : 1))

#endif

#ifndef TIM_SORT_STACK_SIZE

#define TIM_SORT_STACK_SIZE 128

#endif

#define SORT_SWAP(x,y) {SORT_TYPE __SORT_SWAP_t = (x); (x) = (y); (y) = __SORT_SWAP_t;}

/* Common, type-agnosting functions and constants that we don't want to declare twice. */

#ifndef SORT_COMMON_H

#define SORT_COMMON_H

#ifndef MAX

#define MAX(x,y) (((x) > (y) ? (x) : (y)))

#endif

#ifndef MIN

#define MIN(x,y) (((x) < (y) ? (x) : (y)))

#endif

static int compute_minrun(const uint64_t);

#ifndef CLZ

#ifdef __GNUC__

#define CLZ __builtin_clzll

#else

static int clzll(uint64_t);

/* adapted from Hacker's Delight */

static int clzll(uint64_t x) {

  int n;

  if (x == 0) {

    return 64;

  }

  n = 0;

  if (x <= 0x00000000FFFFFFFFL) {

    n = n + 32;

    x = x << 32;

  }

  if (x <= 0x0000FFFFFFFFFFFFL) {

    n = n + 16;

    x = x << 16;

  }

  if (x <= 0x00FFFFFFFFFFFFFFL) {

    n = n + 8;

    x = x << 8;

  }

  if (x <= 0x0FFFFFFFFFFFFFFFL) {

    n = n + 4;

    x = x << 4;

  }

  if (x <= 0x3FFFFFFFFFFFFFFFL) {

    n = n + 2;

    x = x << 2;

  }

  if (x <= 0x7FFFFFFFFFFFFFFFL) {

    n = n + 1;

  }

  return n;

}

#define CLZ clzll

#endif

#endif

static __inline int compute_minrun(const uint64_t size) {

  const int top_bit = 64 - CLZ(size);

  const int shift = MAX(top_bit, 6) - 6;

  const int minrun = size >> shift;

  const uint64_t mask = (1ULL << shift) - 1;

  if (mask & size) {

    return minrun + 1;

  }

  return minrun;

}

#endif /* SORT_COMMON_H */

#define SORT_CONCAT(x, y) x ## _ ## y

#define SORT_MAKE_STR1(x, y) SORT_CONCAT(x,y)

#define SORT_MAKE_STR(x) SORT_MAKE_STR1(SORT_NAME,x)

#define BINARY_INSERTION_FIND          SORT_MAKE_STR(binary_insertion_find)

#define BINARY_INSERTION_SORT_START    SORT_MAKE_STR(binary_insertion_sort_start)

#define BINARY_INSERTION_SORT          SORT_MAKE_STR(binary_insertion_sort)

#define REVERSE_ELEMENTS               SORT_MAKE_STR(reverse_elements)

#define COUNT_RUN                      SORT_MAKE_STR(count_run)

#define CHECK_INVARIANT                SORT_MAKE_STR(check_invariant)

#define TIM_SORT                       SORT_MAKE_STR(tim_sort)

#define TIM_SORT_RESIZE                SORT_MAKE_STR(tim_sort_resize)

#define TIM_SORT_MERGE                 SORT_MAKE_STR(tim_sort_merge)

#define TIM_SORT_COLLAPSE              SORT_MAKE_STR(tim_sort_collapse)

#ifndef MAX

#define MAX(x,y) (((x) > (y) ? (x) : (y)))

#endif

#ifndef MIN

#define MIN(x,y) (((x) < (y) ? (x) : (y)))

#endif

typedef struct {

  size_t start;

  size_t length;

} TIM_SORT_RUN_T;

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

void TIM_SORT(SORT_TYPE *dst, const size_t size);

/* Function used to do a binary search for binary insertion sort */

static __inline size_t BINARY_INSERTION_FIND(SORT_TYPE *dst, const SORT_TYPE x,

    const size_t size) {

  size_t l, c, r;

  SORT_TYPE cx;

  l = 0;

  r = size - 1;

  c = r >> 1;

  /* check for out of bounds at the beginning. */

  if (SORT_CMP(x, dst[0]) < 0) {

    return 0;

  } else if (SORT_CMP(x, dst[r]) > 0) {

    return r;

  }

  cx = dst[c];

  while (1) {

    const int val = SORT_CMP(x, cx);

    if (val < 0) {

      if (c - l <= 1) {

        return c;

      }

      r = c;

    } else { /* allow = for stability. The binary search favors the right. */

      if (r - c <= 1) {

        return c + 1;

      }

      l = c;

    }

    c = l + ((r - l) >> 1);

    cx = dst[c];

  }

}

/* Binary insertion sort, but knowing that the first "start" entries are sorted.  Used in timsort. */

static void BINARY_INSERTION_SORT_START(SORT_TYPE *dst, const size_t start, const size_t size) {

  size_t i;

  for (i = start; i < size; i++) {

    size_t j;

    SORT_TYPE x;

    size_t location;

    /* If this entry is already correct, just move along */

    if (SORT_CMP(dst[i - 1], dst[i]) <= 0) {

      continue;

    }

    /* Else we need to find the right place, shift everything over, and squeeze in */

    x = dst[i];

    location = BINARY_INSERTION_FIND(dst, x, i);

    for (j = i - 1; j >= location; j--) {

      dst[j + 1] = dst[j];

      if (j == 0) { /* check edge case because j is unsigned */

        break;

      }

    }

    dst[location] = x;

  }

}

/* Binary insertion sort */

void BINARY_INSERTION_SORT(SORT_TYPE *dst, const size_t size) {

  /* don't bother sorting an array of size <= 1 */

  if (size <= 1) {

    return;

  }

  BINARY_INSERTION_SORT_START(dst, 1, size);

}

/* timsort implementation, based on timsort.txt */

static __inline void REVERSE_ELEMENTS(SORT_TYPE *dst, size_t start, size_t end) {

  while (1) {

    if (start >= end) {

      return;

    }

    SORT_SWAP(dst[start], dst[end]);

    start++;

    end--;

  }

}

static size_t COUNT_RUN(SORT_TYPE *dst, const size_t start, const size_t size) {

  size_t curr;

  if (size - start == 1) {

    return 1;

  }

  if (start >= size - 2) {

    if (SORT_CMP(dst[size - 2], dst[size - 1]) > 0) {

      SORT_SWAP(dst[size - 2], dst[size - 1]);

    }

    return 2;

  }

  curr = start + 2;

  if (SORT_CMP(dst[start], dst[start + 1]) <= 0) {

    /* increasing run */

    while (1) {

      if (curr == size - 1) {

        break;

      }

      if (SORT_CMP(dst[curr - 1], dst[curr]) > 0) {

        break;

      }

      curr++;

    }

    return curr - start;

  } else {

    /* decreasing run */

    while (1) {

      if (curr == size - 1) {

        break;

      }

      if (SORT_CMP(dst[curr - 1], dst[curr]) <= 0) {

        break;

      }

      curr++;

    }

    /* reverse in-place */

    REVERSE_ELEMENTS(dst, start, curr - 1);

    return curr - start;

  }

}

static int CHECK_INVARIANT(TIM_SORT_RUN_T *stack, const int stack_curr) {

  size_t A, B, C;

  if (stack_curr < 2) {

    return 1;

  }

  if (stack_curr == 2) {

    const size_t A1 = stack[stack_curr - 2].length;

    const size_t B1 = stack[stack_curr - 1].length;

    if (A1 <= B1) {

      return 0;

    }

    return 1;

  }

  A = stack[stack_curr - 3].length;

  B = stack[stack_curr - 2].length;

  C = stack[stack_curr - 1].length;

  if ((A <= B + C) || (B <= C)) {

    return 0;

  }

  return 1;

}

typedef struct {

  size_t alloc;

  SORT_TYPE *storage;

} TEMP_STORAGE_T;

static void TIM_SORT_RESIZE(TEMP_STORAGE_T *store, const size_t new_size) {

  if (store->alloc < new_size) {

    SORT_TYPE *tempstore = (SORT_TYPE *)realloc(store->storage, new_size * sizeof(SORT_TYPE));

    if (tempstore == NULL) {

      fprintf(stderr, "Error allocating temporary storage for tim sort: need %lu bytes",

              (unsigned long)(sizeof(SORT_TYPE) * new_size));

      exit(1);

    }

    store->storage = tempstore;

    store->alloc = new_size;

  }

}

static void TIM_SORT_MERGE(SORT_TYPE *dst, const TIM_SORT_RUN_T *stack, const int stack_curr,

                           TEMP_STORAGE_T *store) {

  const size_t A = stack[stack_curr - 2].length;

  const size_t B = stack[stack_curr - 1].length;

  const size_t curr = stack[stack_curr - 2].start;

  SORT_TYPE *storage;

  size_t i, j, k;

  TIM_SORT_RESIZE(store, MIN(A, B));

  storage = store->storage;

  /* left merge */

  if (A < B) {

    memcpy(storage, &dst[curr], A * sizeof(SORT_TYPE));

    i = 0;

    j = curr + A;

    for (k = curr; k < curr + A + B; k++) {

      if ((i < A) && (j < curr + A + B)) {

        if (SORT_CMP(storage[i], dst[j]) <= 0) {

          dst[k] = storage[i++];

        } else {

          dst[k] = dst[j++];

        }

      } else if (i < A) {

        dst[k] = storage[i++];

      } else {

        break;

      }

    }

  } else {

    /* right merge */

    memcpy(storage, &dst[curr + A], B * sizeof(SORT_TYPE));

    i = B;

    j = curr + A;

    k = curr + A + B;

    while (k-- > curr) {

      if ((i > 0) && (j > curr)) {

        if (SORT_CMP(dst[j - 1], storage[i - 1]) > 0) {

          dst[k] = dst[--j];

        } else {

          dst[k] = storage[--i];

        }

      } else if (i > 0) {

        dst[k] = storage[--i];

      } else {

        break;

      }

    }

  }

}

static int TIM_SORT_COLLAPSE(SORT_TYPE *dst, TIM_SORT_RUN_T *stack, int stack_curr,

                             TEMP_STORAGE_T *store, const size_t size) {

  while (1) {

    size_t A, B, C, D;

    int ABC, BCD, CD;

    /* if the stack only has one thing on it, we are done with the collapse */

    if (stack_curr <= 1) {

      break;

    }

    /* if this is the last merge, just do it */

    if ((stack_curr == 2) && (stack[0].length + stack[1].length == size)) {

      TIM_SORT_MERGE(dst, stack, stack_curr, store);

      stack[0].length += stack[1].length;

      stack_curr--;

      break;

    }

    /* check if the invariant is off for a stack of 2 elements */

    else if ((stack_curr == 2) && (stack[0].length <= stack[1].length)) {

      TIM_SORT_MERGE(dst, stack, stack_curr, store);

      stack[0].length += stack[1].length;

      stack_curr--;

      break;

    } else if (stack_curr == 2) {

      break;

    }

    B = stack[stack_curr - 3].length;

    C = stack[stack_curr - 2].length;

    D = stack[stack_curr - 1].length;

    if (stack_curr >= 4) {

      A = stack[stack_curr - 4].length;

      ABC = (A <= B + C);

    } else {

      ABC = 0;

    }

    BCD = (B <= C + D) || ABC;

    CD = (C <= D);

    /* Both invariants are good */

    if (!BCD && !CD) {

      break;

    }

    /* left merge */

    if (BCD && !CD) {

      TIM_SORT_MERGE(dst, stack, stack_curr - 1, store);

      stack[stack_curr - 3].length += stack[stack_curr - 2].length;

      stack[stack_curr - 2] = stack[stack_curr - 1];

      stack_curr--;

    } else {

      /* right merge */

      TIM_SORT_MERGE(dst, stack, stack_curr, store);

      stack[stack_curr - 2].length += stack[stack_curr - 1].length;

      stack_curr--;

    }

  }

  return stack_curr;

}

static __inline int PUSH_NEXT(SORT_TYPE *dst,

                              const size_t size,

                              TEMP_STORAGE_T *store,

                              const size_t minrun,

                              TIM_SORT_RUN_T *run_stack,

                              size_t *stack_curr,

                              size_t *curr) {

  size_t len = COUNT_RUN(dst, *curr, size);

  size_t run = minrun;

  if (run > size - *curr) {

    run = size - *curr;

  }

  if (run > len) {

    BINARY_INSERTION_SORT_START(&dst[*curr], len, run);

    len = run;

  }

  run_stack[*stack_curr].start = *curr;

  run_stack[*stack_curr].length = len;

  (*stack_curr)++;

  *curr += len;

  if (*curr == size) {

    /* finish up */

    while (*stack_curr > 1) {

      TIM_SORT_MERGE(dst, run_stack, *stack_curr, store);

      run_stack[*stack_curr - 2].length += run_stack[*stack_curr - 1].length;

      (*stack_curr)--;

    }

    if (store->storage != NULL) {

      free(store->storage);

      store->storage = NULL;

    }

    return 0;

  }

  return 1;

}

void TIM_SORT(SORT_TYPE *dst, const size_t size) {

  size_t minrun;

  TEMP_STORAGE_T _store, *store;

  TIM_SORT_RUN_T run_stack[TIM_SORT_STACK_SIZE];

  size_t stack_curr = 0;

  size_t curr = 0;

  /* don't bother sorting an array of size 1 */

  if (size <= 1) {

    return;

  }

  if (size < 64) {

    BINARY_INSERTION_SORT(dst, size);

    return;

  }

  /* compute the minimum run length */

  minrun = compute_minrun(size);

  /* temporary storage for merges */

  store = &_store;

  store->alloc = 0;

  store->storage = NULL;

  if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {

    return;

  }

  if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {

    return;

  }

  if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {

    return;

  }

  while (1) {

    if (!CHECK_INVARIANT(run_stack, stack_curr)) {

      stack_curr = TIM_SORT_COLLAPSE(dst, run_stack, stack_curr, store, size);

      continue;

    }

    if (!PUSH_NEXT(dst, size, store, minrun, run_stack, &stack_curr, &curr)) {

      return;

    }

  }

}

#undef SORT_CONCAT

#undef SORT_MAKE_STR1

#undef SORT_MAKE_STR

#undef SORT_NAME

#undef SORT_TYPE

#undef SORT_CMP

#undef TEMP_STORAGE_T

#undef TIM_SORT_RUN_T

#undef PUSH_NEXT

#undef SORT_SWAP

#undef SORT_CONCAT

#undef SORT_MAKE_STR1

#undef SORT_MAKE_STR

#undef BINARY_INSERTION_FIND

#undef BINARY_INSERTION_SORT_START

#undef BINARY_INSERTION_SORT

#undef REVERSE_ELEMENTS

#undef COUNT_RUN

#undef TIM_SORT

#undef TIM_SORT_RESIZE

#undef TIM_SORT_COLLAPSE

#undef TIM_SORT_RUN_T

#undef TEMP_STORAGE_T