/* Split LINEAR into a linear sequence with low values and an erratic
sequence with high values, put the linear one (of longest possible
length) into LINEAR and the erratic one into ERRATIC. This is O(N). */
static inline void
fde_split (fde_vector *linear, fde_vector *erratic)
{
size_t count = linear->count;
size_t linear_max = (size_t) -1;
size_t previous_max[count];
size_t i, j;
for (i = 0; i < count; i++)
{
for (j = linear_max;
j != (size_t) -1
&& fde_compare (linear->array[i], linear->array[j]) < 0;
j = previous_max[j])
{
erratic->array[erratic->count++] = linear->array[j];
linear->array[j] = (fde *) NULL;
}
previous_max[i] = j;
linear_max = i;
}
for (i = 0, j = 0; i < count; i++)
if (linear->array[i] != (fde *) NULL)
linear->array[j++] = linear->array[i];
linear->count = j;
}
/* Split LINEAR into a linear sequence with low values and an erratic
sequence with high values, put the linear one (of longest possible
length) into LINEAR and the erratic one into ERRATIC. This is O(N).
Because the longest linear sequence we are trying to locate within the
incoming LINEAR array can be interspersed with (high valued) erratic
entries. We construct a chain indicating the sequenced entries.
To avoid having to allocate this chain, we overlay it onto the space of
the ERRATIC array during construction. A final pass iterates over the
chain to determine what should be placed in the ERRATIC array, and
what is the linear sequence. This overlay is safe from aliasing. */
static inline void
fde_split (fde_vector *linear, fde_vector *erratic)
{
static fde *marker;
size_t count = linear->count;
fde **chain_end = ▮
size_t i, j, k;
/* This should optimize out, but it is wise to make sure this assumption
is correct. Should these have different sizes, we cannot cast between
them and the overlaying onto ERRATIC will not work. */
if (sizeof (fde *) != sizeof (fde **))
abort ();
for (i = 0; i < count; i++)
{
fde **probe;
for (probe = chain_end;
probe != &marker && fde_compare (linear->array[i], *probe) < 0;
probe = chain_end)
{
chain_end = (fde **)erratic->array[probe - linear->array];
erratic->array[probe - linear->array] = NULL;
}
erratic->array[i] = (fde *)chain_end;
chain_end = &linear->array[i];
}
/* Each entry in LINEAR which is part of the linear sequence we have
discovered will correspond to a non-NULL entry in the chain we built in
the ERRATIC array. */
for (i = j = k = 0; i < count; i++)
if (erratic->array[i])
linear->array[j++] = linear->array[i];
else
erratic->array[k++] = linear->array[i];
linear->count = j;
erratic->count = k;
}
/* Merge V1 and V2, both sorted, and put the result into V1. */
static void
fde_merge (fde_vector *v1, const fde_vector *v2)
{
size_t i1, i2;
fde * fde2;
i2 = v2->count;
if (i2 > 0)
{
i1 = v1->count;
do {
i2--;
fde2 = v2->array[i2];
while (i1 > 0 && fde_compare (v1->array[i1-1], fde2) > 0)
{
v1->array[i1+i2] = v1->array[i1-1];
i1--;
}
v1->array[i1+i2] = fde2;
} while (i2 > 0);
v1->count += v2->count;
}
}
/* This is O(n log(n)). BSD/OS defines heapsort in stdlib.h, so we must
use a name that does not conflict. */
static inline void
frame_heapsort (fde_vector *erratic)
{
/* For a description of this algorithm, see:
Samuel P. Harbison, Guy L. Steele Jr.: C, a reference manual, 2nd ed.,
p. 60-61. */
fde ** a = erratic->array;
/* A portion of the array is called a "heap" if for all i>=0:
If i and 2i+1 are valid indices, then a[i] >= a[2i+1].
If i and 2i+2 are valid indices, then a[i] >= a[2i+2]. */
#define SWAP(x,y) do { fde * tmp = x; x = y; y = tmp; } while (0)
size_t n = erratic->count;
size_t m = n;
size_t i;
while (m > 0)
{
/* Invariant: a[m..n-1] is a heap. */
m--;
for (i = m; 2*i+1 < n; )
{
if (2*i+2 < n
&& fde_compare (a[2*i+2], a[2*i+1]) > 0
&& fde_compare (a[2*i+2], a[i]) > 0)
{
SWAP (a[i], a[2*i+2]);
i = 2*i+2;
}
else if (fde_compare (a[2*i+1], a[i]) > 0)
{
SWAP (a[i], a[2*i+1]);
i = 2*i+1;
}
else
break;
}
}
while (n > 1)
{
/* Invariant: a[0..n-1] is a heap. */
n--;
SWAP (a[0], a[n]);
for (i = 0; 2*i+1 < n; )
{
if (2*i+2 < n
&& fde_compare (a[2*i+2], a[2*i+1]) > 0
&& fde_compare (a[2*i+2], a[i]) > 0)
{
SWAP (a[i], a[2*i+2]);
i = 2*i+2;
}
else if (fde_compare (a[2*i+1], a[i]) > 0)
{
SWAP (a[i], a[2*i+1]);
i = 2*i+1;
}
else
break;
}
}
#undef SWAP
}
