# Project Euler 501
# Eight Divisors — count n<=10^12 with d(n)=8 via fixed-limit pi table.
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function iroot(n: i64, k: i32) -> i64 {
if n < 2 { return n }
let mut lo: i64 = 1
let mut hi: i64 = n
if k >= 2 {
hi = isqrt(n) + 2
if hi > n { hi = n }
}
while lo < hi {
let mid: i64 = (lo + hi + 1) / 2
let mut p: i64 = 1
let mut i: i32 = 0
let mut ov: i32 = 0
while i < k {
if p > n / mid { ov = 1; break }
p = p * mid
i = i + 1
}
if ov == 1 || p > n { hi = mid - 1 } else { lo = mid }
}
return lo
}
function main() -> i32 {
let limit: i64 = 1000000000000
let root: i64 = isqrt(limit)
let sieve: ptr<i8> = calloc(root + 1, 1)
let primes: ptr<i32> = calloc(root / 5 + 100, 4)
let small: ptr<i64> = calloc(root + 1, 8)
let large: ptr<i64> = calloc(root + 1, 8)
if sieve == null || primes == null || small == null || large == null { return 1 }
let mut i: i64 = 2
while i <= root {
sieve[i] = 1
i = i + 1
}
i = 2
while i * i <= root {
if sieve[i] == 1 {
let mut j: i64 = i * i
while j <= root {
sieve[j] = 0
j = j + i
}
}
i = i + 1
}
let mut pn: i64 = 0
i = 2
while i <= root {
if sieve[i] == 1 {
primes[pn] = i as i32
pn = pn + 1
}
i = i + 1
}
let mut x: i64 = 2
while x <= root {
small[x] = x - 1
x = x + 1
}
let mut d: i64 = 1
while d <= root {
large[d] = limit / d - 1
d = d + 1
}
let mut pi: i64 = 0
while pi < pn {
let p: i64 = primes[pi] as i64
let p2: i64 = p * p
if p2 > limit { break }
let before_p: i64 = small[p - 1]
let mut last_d: i64 = root
if limit / p2 < last_d { last_d = limit / p2 }
d = 1
while d <= last_d {
let pd: i64 = p * d
if pd <= root {
large[d] = large[d] - (large[pd] - before_p)
} else {
large[d] = large[d] - (small[limit / pd] - before_p)
}
d = d + 1
}
x = root
while x >= p2 {
small[x] = small[x] - (small[x / p] - before_p)
x = x - 1
}
pi = pi + 1
}
# pi(x) helper inline
let mut count: i64 = 0
# p*q*r
let p_stop_val: i64 = iroot(limit, 3)
let mut p_stop: i64 = 0
while p_stop < pn && (primes[p_stop] as i64) <= p_stop_val {
p_stop = p_stop + 1
}
let mut ii: i64 = 0
while ii < p_stop {
let p: i64 = primes[ii] as i64
if p * p * p >= limit { break }
let qmax: i64 = isqrt(limit / p)
let mut q_stop: i64 = 0
while q_stop < pn && (primes[q_stop] as i64) <= qmax {
q_stop = q_stop + 1
}
let mut jj: i64 = ii + 1
while jj < q_stop {
let q: i64 = primes[jj] as i64
let max_r: i64 = limit / (p * q)
if max_r <= q { break }
let mut pir: i64 = 0
if max_r <= root { pir = small[max_r] } else { pir = large[limit / max_r] }
count = count + pir - (jj + 1)
jj = jj + 1
}
ii = ii + 1
}
# p^3*q
ii = 0
while ii < p_stop {
let p: i64 = primes[ii] as i64
let p3: i64 = p * p * p
if p3 > limit { break }
let mx: i64 = limit / p3
let mut pix: i64 = 0
if mx <= root { pix = small[mx] } else { pix = large[limit / mx] }
count = count + pix
ii = ii + 1
}
let r4: i64 = iroot(limit, 4)
if r4 <= root { count = count - small[r4] } else { count = count - large[limit / r4] }
let r7: i64 = iroot(limit, 7)
if r7 <= root { count = count + small[r7] } else { count = count + large[limit / r7] }
printf("%lld\n", count)
free(sieve); free(primes); free(small); free(large)
return 0
}
Generated C
#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
while (flow_temp_head) {
flow_temp_node* n = flow_temp_head;
flow_temp_head = n->next;
free(n);
}
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
if (!node) return NULL;
node->next = flow_temp_head;
flow_temp_head = node;
if (!flow_temp_atexit_set) {
flow_temp_atexit_set = 1;
atexit(flow_temp_free_all);
}
return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
char* r = (char*)flow_temp_alloc(la + lb + 1);
if (!r) return NULL;
if (la) memcpy(r, a, la);
if (lb) memcpy(r + la, b, lb);
r[la + lb] = '\0';
return r;
}
#define __flow_in_arr(arr, val) __extension__ ({ \
int _found = 0; \
size_t _n = sizeof(arr)/sizeof((arr)[0]); \
for (size_t _i = 0; _i < _n; _i++) { \
if ((arr)[_i] == (val)) { _found = 1; break; } \
} _found; })
/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
abort();
#if defined(__GNUC__) || defined(__clang__)
__builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")
#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#include <math.h>
void* _ui_state = NULL;
static inline float i32_to_f32(int32_t v) { return (float)v; }
/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }
int64_t gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int64_t iroot_i64_i32(int64_t n, int32_t k);
int32_t main(void);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
int64_t iroot_i64_i32(int64_t n, int32_t k) {
if (n < 2) {
return n;
}
int64_t lo = 1;
int64_t hi = n;
if (k >= 2) {
hi = (isqrt_i64(n) + 2);
if (hi > n) {
hi = n;
}
}
while (lo < hi) {
int64_t mid = FLOW_CHECKED_DIV((((lo + hi) + 1)), (2));
int64_t p = 1;
int32_t i = 0;
int32_t ov = 0;
while (i < k) {
if (p > FLOW_CHECKED_DIV((n), (mid))) {
ov = 1;
break;
}
p = (p * mid);
i = (i + 1);
}
if ((ov == 1 || p > n)) {
hi = (mid - 1);
} else {
lo = mid;
}
}
return lo;
}
int32_t main(void) {
int64_t limit = 1000000000000;
int64_t root = isqrt_i64(limit);
int8_t* sieve = (int8_t*)(calloc((root + 1), 1));
int32_t* primes = (int32_t*)(calloc((FLOW_CHECKED_DIV((root), (5)) + 100), 4));
int64_t* small = (int64_t*)(calloc((root + 1), 8));
int64_t* large = (int64_t*)(calloc((root + 1), 8));
if ((((sieve == NULL || primes == NULL) || small == NULL) || large == NULL)) {
return 1;
}
int64_t i = 2;
while (i <= root) {
sieve[i] = 1;
i = (i + 1);
}
i = 2;
while ((i * i) <= root) {
if (sieve[i] == 1) {
int64_t j = (i * i);
while (j <= root) {
sieve[j] = 0;
j = (j + i);
}
}
i = (i + 1);
}
int64_t pn = 0;
i = 2;
while (i <= root) {
if (sieve[i] == 1) {
primes[pn] = ((int32_t)(i));
pn = (pn + 1);
}
i = (i + 1);
}
int64_t x = 2;
while (x <= root) {
small[x] = (x - 1);
x = (x + 1);
}
int64_t d = 1;
while (d <= root) {
large[d] = (FLOW_CHECKED_DIV((limit), (d)) - 1);
d = (d + 1);
}
int64_t pi = 0;
while (pi < pn) {
int64_t p = ((int64_t)(primes[pi]));
int64_t p2 = (p * p);
if (p2 > limit) {
break;
}
int64_t before_p = small[(p - 1)];
int64_t last_d = root;
if (FLOW_CHECKED_DIV((limit), (p2)) < last_d) {
last_d = FLOW_CHECKED_DIV((limit), (p2));
}
d = 1;
while (d <= last_d) {
int64_t pd = (p * d);
if (pd <= root) {
large[d] = (large[d] - (large[pd] - before_p));
} else {
large[d] = (large[d] - (small[FLOW_CHECKED_DIV((limit), (pd))] - before_p));
}
d = (d + 1);
}
x = root;
while (x >= p2) {
small[x] = (small[x] - (small[FLOW_CHECKED_DIV((x), (p))] - before_p));
x = (x - 1);
}
pi = (pi + 1);
}
int64_t count = 0;
int64_t p_stop_val = iroot_i64_i32(limit, 3);
int64_t p_stop = 0;
while ((p_stop < pn && ((int64_t)(primes[p_stop])) <= p_stop_val)) {
p_stop = (p_stop + 1);
}
int64_t ii = 0;
while (ii < p_stop) {
int64_t p = ((int64_t)(primes[ii]));
if (((p * p) * p) >= limit) {
break;
}
int64_t qmax = isqrt_i64(FLOW_CHECKED_DIV((limit), (p)));
int64_t q_stop = 0;
while ((q_stop < pn && ((int64_t)(primes[q_stop])) <= qmax)) {
q_stop = (q_stop + 1);
}
int64_t jj = (ii + 1);
while (jj < q_stop) {
int64_t q = ((int64_t)(primes[jj]));
int64_t max_r = FLOW_CHECKED_DIV((limit), ((p * q)));
if (max_r <= q) {
break;
}
int64_t pir = 0;
if (max_r <= root) {
pir = small[max_r];
} else {
pir = large[FLOW_CHECKED_DIV((limit), (max_r))];
}
count = ((count + pir) - (jj + 1));
jj = (jj + 1);
}
ii = (ii + 1);
}
ii = 0;
while (ii < p_stop) {
int64_t p = ((int64_t)(primes[ii]));
int64_t p3 = ((p * p) * p);
if (p3 > limit) {
break;
}
int64_t mx = FLOW_CHECKED_DIV((limit), (p3));
int64_t pix = 0;
if (mx <= root) {
pix = small[mx];
} else {
pix = large[FLOW_CHECKED_DIV((limit), (mx))];
}
count = (count + pix);
ii = (ii + 1);
}
int64_t r4 = iroot_i64_i32(limit, 4);
if (r4 <= root) {
count = (count - small[r4]);
} else {
count = (count - large[FLOW_CHECKED_DIV((limit), (r4))]);
}
int64_t r7 = iroot_i64_i32(limit, 7);
if (r7 <= root) {
count = (count + small[r7]);
} else {
count = (count + large[FLOW_CHECKED_DIV((limit), (r7))]);
}
printf("%lld\n", count);
free(sieve);
free(primes);
free(small);
free(large);
return 0;
}