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#define SWAP(x, y) do { x ^= y; y ^= x; x ^= y; } while (0)
#define MIN(x, y) ((x) < (y) ? (x) : (y))
#define MAX(x, y) ((x) > (y) ? (x) : (y))
#define DIV_ROUND_UP(n, d) (((n) + (d) - 1) / (d))
STATIC int64_t factorial(int64_t);
STATIC bool isperm(size_t n, const uint8_t [n]);
STATIC int64_t permtoindex(size_t n, const uint8_t [n]);
STATIC void indextoperm(int64_t, size_t n, uint8_t [n]);
STATIC int permsign(size_t n, const uint8_t [n]);
STATIC int64_t digitstosumzero(size_t n, const uint8_t [n], uint8_t);
STATIC void sumzerotodigits(int64_t, size_t n, uint8_t, uint8_t [n]);
STATIC double intpow(double, uint64_t);
STATIC int64_t
factorial(int64_t n)
{
int64_t i, ret;
if (n > FACTORIAL_MAX) {
LOG("Error: won't compute factorial for n=%" PRId64 " because"
" it is larger than %" PRId64 "\n", n, FACTORIAL_MAX);
return -1;
}
if (n < 0)
return 0;
for (i = 1, ret = 1; i <= n; i++)
ret *= i;
return ret;
}
STATIC bool
isperm(size_t n, const uint8_t a[n])
{
size_t i;
bool aux[FACTORIAL_MAX+1];
if (n > (size_t)FACTORIAL_MAX) {
LOG("Error: won't compute 'isperm()' for n=%zu because"
" it is larger than %" PRId64 "\n", n, FACTORIAL_MAX);
return false;
}
memset(aux, false, n);
for (i = 0; i < n; i++) {
if (a[i] >= n)
return false;
else
aux[a[i]] = true;
}
for (i = 0; i < n; i++)
if (!aux[i])
return false;
return true;
}
STATIC int64_t
permtoindex(size_t n, const uint8_t a[n])
{
size_t i, j;
int64_t c, ret;
if (n > (size_t)FACTORIAL_MAX) {
LOG("Error: won't compute 'permtoindex()' for n=%zu because "
"it is larger than %" PRId64 "\n", n, FACTORIAL_MAX);
return -1;
}
if (!isperm(n, a))
return -1;
for (i = 0, ret = 0; i < n; i++) {
for (j = i+1, c = 0; j < n; j++)
c += (a[i] > a[j]) ? 1 : 0;
ret += factorial(n-i-1) * c;
}
return ret;
}
STATIC void
indextoperm(int64_t p, size_t n, uint8_t r[n])
{
int64_t c;
size_t i, j;
uint8_t a[FACTORIAL_MAX+1];
if (n > FACTORIAL_MAX) {
LOG("Error: won't compute 'indextoperm()' for n=%zu because "
"it is larger than %" PRId64 "\n", n, FACTORIAL_MAX);
goto indextoperm_error;
}
memset(a, 0, n);
if (p < 0 || p >= factorial(n))
goto indextoperm_error;
for (i = 0; i < n; i++) {
for (j = 0, c = 0; c <= p / factorial(n-i-1); j++)
c += a[j] ? 0 : 1;
r[i] = j-1;
a[j-1] = 1;
p %= factorial(n-i-1);
}
if (!isperm(n, r))
goto indextoperm_error;
return;
indextoperm_error:
memset(r, UINT8_ERROR, n);
}
STATIC int
permsign(size_t n, const uint8_t a[n])
{
size_t i, j, ret;
for (i = 0, ret = 0; i < n; i++)
for (j = i+1; j < n; j++)
ret += a[i] > a[j] ? 1 : 0;
return ret % 2;
}
STATIC int64_t
digitstosumzero(size_t n, const uint8_t a[n], uint8_t b)
{
int64_t ret, p;
size_t i, sum;
if (!((n == 8 && b == 3 ) || (n == 12 && b == 2))) {
LOG("Error: won't compute 'sumzero' for n=%zu and b=%" PRIu8
" (use n=8 b=3 or n=12 b=2)\n", n, b);
return -1;
}
for (i = 1, ret = 0, p = 1, sum = 0; i < n; i++, p *= (int64_t)b) {
if (a[i] >= b) {
LOG("Error: digit %" PRIu8 " larger than maximum"
" (b=%" PRIu8 "\n", a[i], b);
return -1;
}
sum += a[i];
ret += p * (int64_t)a[i];
}
if ((sum + a[0]) % b != 0) {
LOG("Error: digits do not have sum zero modulo b\n");
return -1;
}
return ret;
}
STATIC void
sumzerotodigits(int64_t d, size_t n, uint8_t b, uint8_t a[n])
{
uint8_t sum;
size_t i;
if (!((n == 8 && b == 3 ) || (n == 12 && b == 2))) {
LOG("Error: won't compute 'digits' for n=%zu and b=%" PRIu8
" (use n=8 b=3 or n=12 b=2)\n", n, b);
goto sumzerotodigits_error;
}
for (i = 1, sum = 0; i < n; i++, d /= (int64_t)b) {
a[i] = (uint8_t)(d % (int64_t)b);
sum += a[i];
}
a[0] = (b - (sum % b)) % b;
return;
sumzerotodigits_error:
memset(a, UINT8_ERROR, n);
}
STATIC double
intpow(double b, uint64_t e)
{
double r;
if (e == 0)
return 1;
r = intpow(b, e/2);
return e % 2 == 0 ? r * r : b * r * r;
}
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