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/*********************************************************************** | ||
* 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.* | ||
***********************************************************************/ | ||
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#ifndef SECP256K1_HSORT_H | ||
#define SECP256K1_HSORT_H | ||
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#include <stddef.h> | ||
#include <string.h> | ||
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/* In-place, iterative heapsort with an interface matching glibc's qsort_r. This | ||
* is preferred over standard library implementations because they generally | ||
* make no guarantee about being fast for malicious inputs. | ||
* Remeber that heapsort is unstable. | ||
* | ||
* See the qsort_r manpage for a description of the interface. | ||
*/ | ||
static void secp256k1_hsort(void *ptr, size_t count, size_t size, | ||
int (*cmp)(const void *, const void *, void *), | ||
void *cmp_data); | ||
#endif |
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/*********************************************************************** | ||
* 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.* | ||
***********************************************************************/ | ||
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#ifndef SECP256K1_HSORT_IMPL_H | ||
#define SECP256K1_HSORT_IMPL_H | ||
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#include "hsort.h" | ||
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/* 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. | ||
*/ | ||
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static SECP256K1_INLINE size_t secp256k1_heap_child1(size_t i) { | ||
VERIFY_CHECK(i <= (SIZE_MAX - 1)/2); | ||
return 2*i + 1; | ||
} | ||
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static SECP256K1_INLINE size_t secp256k1_heap_child2(size_t i) { | ||
VERIFY_CHECK(i <= SIZE_MAX/2 - 1); | ||
return secp256k1_heap_child1(i)+1; | ||
} | ||
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static SECP256K1_INLINE void secp256k1_heap_swap64(unsigned char *a, size_t i, size_t j, size_t stride) { | ||
unsigned char tmp[64]; | ||
VERIFY_CHECK(stride <= 64); | ||
memcpy(tmp, a + i*stride, stride); | ||
memmove(a + i*stride, a + j*stride, stride); | ||
memcpy(a + j*stride, tmp, stride); | ||
} | ||
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static SECP256K1_INLINE void secp256k1_heap_swap(unsigned char *a, size_t i, size_t j, size_t stride) { | ||
while (64 < stride) { | ||
secp256k1_heap_swap64(a + (stride - 64), i, j, 64); | ||
stride -= 64; | ||
} | ||
secp256k1_heap_swap64(a, i, j, stride); | ||
} | ||
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static SECP256K1_INLINE void secp256k1_heap_down(unsigned char *a, 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 | ||
*/ | ||
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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 | ||
*/ | ||
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/* Let [x] be notation for the contents at a[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(a + secp256k1_heap_child2(i)*stride, a + secp256k1_heap_child1(i)*stride, cmp_data)) { | ||
if (0 < cmp(a + secp256k1_heap_child2(i)*stride, a + i*stride, cmp_data)) { | ||
secp256k1_heap_swap(a, 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(a + secp256k1_heap_child1(i)*stride, a + i*stride, cmp_data)) { | ||
secp256k1_heap_swap(a, 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. | ||
*/ | ||
} | ||
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/* 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; | ||
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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); | ||
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/* Repair the heap condition */ | ||
secp256k1_heap_down(ptr, 0, i-1, size, cmp, cmp_data); | ||
} | ||
} | ||
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#endif |
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