1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
|
/***********************************************************************
* Copyright (c) 2021 Russell O'Connor, Jonas Nick *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or https://www.opensource.org/licenses/mit-license.php.*
***********************************************************************/
#ifndef SECP256K1_HSORT_IMPL_H
#define SECP256K1_HSORT_IMPL_H
#include "hsort.h"
/* An array is a heap when, for all non-zero indexes i, the element at index i
* compares as less than or equal to the element at index parent(i) = (i-1)/2.
*/
static SECP256K1_INLINE size_t secp256k1_heap_child1(size_t i) {
VERIFY_CHECK(i <= (SIZE_MAX - 1)/2);
return 2*i + 1;
}
static SECP256K1_INLINE size_t secp256k1_heap_child2(size_t i) {
VERIFY_CHECK(i <= SIZE_MAX/2 - 1);
return secp256k1_heap_child1(i)+1;
}
static SECP256K1_INLINE void secp256k1_heap_swap64(unsigned char *a, unsigned char *b, size_t len) {
unsigned char tmp[64];
VERIFY_CHECK(len <= 64);
memcpy(tmp, a, len);
memmove(a, b, len);
memcpy(b, tmp, len);
}
static SECP256K1_INLINE void secp256k1_heap_swap(unsigned char *arr, size_t i, size_t j, size_t stride) {
unsigned char *a = arr + i*stride;
unsigned char *b = arr + j*stride;
size_t len = stride;
while (64 < len) {
secp256k1_heap_swap64(a + (len - 64), b + (len - 64), 64);
len -= 64;
}
secp256k1_heap_swap64(a, b, len);
}
/* This function accepts an array arr containing heap_size elements, each of
* size stride. The elements in the array at indices >i satisfy the max-heap
* property, i.e., for any element at index j (where j > i), all of its children
* are smaller than the element itself. The purpose of the function is to update
* the array so that all elements at indices >=i satisfy the max-heap
* property. */
static SECP256K1_INLINE void secp256k1_heap_down(unsigned char *arr, size_t i, size_t heap_size, size_t stride,
int (*cmp)(const void *, const void *, void *), void *cmp_data) {
while (i < heap_size/2) {
VERIFY_CHECK(i <= SIZE_MAX/2 - 1);
/* Proof:
* i < heap_size/2
* i + 1 <= heap_size/2
* 2*i + 2 <= heap_size <= SIZE_MAX
* 2*i <= SIZE_MAX - 2
*/
VERIFY_CHECK(secp256k1_heap_child1(i) < heap_size);
/* Proof:
* i < heap_size/2
* i + 1 <= heap_size/2
* 2*i + 2 <= heap_size
* 2*i + 1 < heap_size
* child1(i) < heap_size
*/
/* Let [x] be notation for the contents at arr[x*stride].
*
* If [child1(i)] > [i] and [child2(i)] > [i],
* swap [i] with the larger child to ensure the new parent is larger
* than both children. When [child1(i)] == [child2(i)], swap [i] with
* [child2(i)].
* Else if [child1(i)] > [i], swap [i] with [child1(i)].
* Else if [child2(i)] > [i], swap [i] with [child2(i)].
*/
if (secp256k1_heap_child2(i) < heap_size
&& 0 <= cmp(arr + secp256k1_heap_child2(i)*stride, arr + secp256k1_heap_child1(i)*stride, cmp_data)) {
if (0 < cmp(arr + secp256k1_heap_child2(i)*stride, arr + i*stride, cmp_data)) {
secp256k1_heap_swap(arr, i, secp256k1_heap_child2(i), stride);
i = secp256k1_heap_child2(i);
} else {
/* At this point we have [child2(i)] >= [child1(i)] and we have
* [child2(i)] <= [i], and thus [child1(i)] <= [i] which means
* that the next comparison can be skipped. */
return;
}
} else if (0 < cmp(arr + secp256k1_heap_child1(i)*stride, arr + i*stride, cmp_data)) {
secp256k1_heap_swap(arr, i, secp256k1_heap_child1(i), stride);
i = secp256k1_heap_child1(i);
} else {
return;
}
}
/* heap_size/2 <= i
* heap_size/2 < i + 1
* heap_size < 2*i + 2
* heap_size <= 2*i + 1
* heap_size <= child1(i)
* Thus child1(i) and child2(i) are now out of bounds and we are at a leaf.
*/
}
/* In-place heap sort. */
static void secp256k1_hsort(void *ptr, size_t count, size_t size,
int (*cmp)(const void *, const void *, void *),
void *cmp_data) {
size_t i;
for (i = count/2; 0 < i; --i) {
secp256k1_heap_down(ptr, i-1, count, size, cmp, cmp_data);
}
for (i = count; 1 < i; --i) {
/* Extract the largest value from the heap */
secp256k1_heap_swap(ptr, 0, i-1, size);
/* Repair the heap condition */
secp256k1_heap_down(ptr, 0, i-1, size, cmp, cmp_data);
}
}
#endif
|
