# Project Euler 549
# Divisibility of Factorials — S(10^8) via prime-power sieve.
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function fact_val(n0: i64, p: i64) -> i64 {
let mut n: i64 = n0
let mut total: i64 = 0
while n > 0 {
n = n / p
total = total + n
}
return total
}
function threshold(p: i64, exponent: i64) -> i64 {
let mut lo: i64 = 1
let mut hi: i64 = p * exponent
while lo < hi {
let mid: i64 = (lo + hi) / 2
if fact_val(mid, p) >= exponent {
hi = mid
} else {
lo = mid + 1
}
}
return lo
}
function main() -> i32 {
let limit: i64 = 100000000
let values: ptr<i32> = calloc(limit + 1, 4)
let sieve: ptr<i8> = calloc(limit + 1, 1)
if values == null || sieve == null { return 1 }
let mut i: i64 = 2
while i <= limit {
sieve[i] = 1
i = i + 1
}
i = 2
while i * i <= limit {
if sieve[i] == 1 {
let mut j: i64 = i * i
while j <= limit {
sieve[j] = 0
j = j + i
}
}
i = i + 1
}
# Initial: s(p*k) at least p for prime p
let mut p: i64 = 2
while p <= limit {
if sieve[p] == 1 {
let mut m: i64 = p
while m <= limit {
values[m] = p as i32
m = m + p
}
}
p = p + 1
}
let root: i64 = isqrt(limit)
p = 2
while p <= root {
if sieve[p] == 1 {
let mut power: i64 = p * p
let mut exponent: i64 = 2
while power <= limit {
let thr: i64 = threshold(p, exponent)
let mut m: i64 = power
while m <= limit {
if (values[m] as i64) < thr {
values[m] = thr as i32
}
m = m + power
}
# careful overflow for large p^e
if power > limit / p { break }
power = power * p
exponent = exponent + 1
}
}
p = p + 1
}
let mut total: i64 = 0
i = 2
while i <= limit {
total = total + (values[i] as i64)
i = i + 1
}
printf("%lld\n", total)
free(values)
free(sieve)
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 fact_val_i64_i64(int64_t n0, int64_t p);
int64_t threshold_i64_i64(int64_t p, int64_t exponent);
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 fact_val_i64_i64(int64_t n0, int64_t p) {
int64_t n = n0;
int64_t total = 0;
while (n > 0) {
n = FLOW_CHECKED_DIV((n), (p));
total = (total + n);
}
return total;
}
int64_t threshold_i64_i64(int64_t p, int64_t exponent) {
int64_t lo = 1;
int64_t hi = (p * exponent);
while (lo < hi) {
int64_t mid = FLOW_CHECKED_DIV(((lo + hi)), (2));
if (fact_val_i64_i64(mid, p) >= exponent) {
hi = mid;
} else {
lo = (mid + 1);
}
}
return lo;
}
int32_t main(void) {
int64_t limit = 100000000;
int32_t* values = (int32_t*)(calloc((limit + 1), 4));
int8_t* sieve = (int8_t*)(calloc((limit + 1), 1));
if ((values == NULL || sieve == NULL)) {
return 1;
}
int64_t i = 2;
while (i <= limit) {
sieve[i] = 1;
i = (i + 1);
}
i = 2;
while ((i * i) <= limit) {
if (sieve[i] == 1) {
int64_t j = (i * i);
while (j <= limit) {
sieve[j] = 0;
j = (j + i);
}
}
i = (i + 1);
}
int64_t p = 2;
while (p <= limit) {
if (sieve[p] == 1) {
int64_t m = p;
while (m <= limit) {
values[m] = ((int32_t)(p));
m = (m + p);
}
}
p = (p + 1);
}
int64_t root = isqrt_i64(limit);
p = 2;
while (p <= root) {
if (sieve[p] == 1) {
int64_t power = (p * p);
int64_t exponent = 2;
while (power <= limit) {
int64_t thr = threshold_i64_i64(p, exponent);
int64_t m = power;
while (m <= limit) {
if (((int64_t)(values[m])) < thr) {
values[m] = ((int32_t)(thr));
}
m = (m + power);
}
if (power > FLOW_CHECKED_DIV((limit), (p))) {
break;
}
power = (power * p);
exponent = (exponent + 1);
}
}
p = (p + 1);
}
int64_t total = 0;
i = 2;
while (i <= limit) {
total = (total + ((int64_t)(values[i])));
i = (i + 1);
}
printf("%lld\n", total);
free(values);
free(sieve);
return 0;
}