# Project Euler 956
# Root-of-unity filter over prime exponents, mod 999999001.
# Ported from native C to pure Flow. Uses i128 for modular multiplication.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
function malloc(n: i64) -> ptr<void>
}
const MOD: i64 = 999999001
const ROOT: i64 = 17
const N: i64 = 1000
function mod_pow(a: i64, e: i64, mod: i64) -> i64 {
let mut r: i64 = 1 % mod
let mut aa: i64 = a % mod
if aa < 0 {
aa = aa + mod
}
let mut ee: i64 = e
while ee > 0 {
if (ee & 1) == 1 {
r = ((r as i128) * (aa as i128) % (mod as i128)) as i64
}
aa = ((aa as i128) * (aa as i128) % (mod as i128)) as i64
ee = ee >> 1
}
return r
}
function mod_inv(a: i64, mod: i64) -> i64 {
return mod_pow(a, mod - 2, mod)
}
function main() -> i32 {
let N_lim: i64 = N
# Sieve primes up to N_lim
let is_prime: ptr<i8> = malloc((N_lim + 1) * 1) as ptr<i8>
let mut ii: i64 = 0
while ii <= N_lim {
is_prime[ii] = 1
ii = ii + 1
}
is_prime[0] = 0
is_prime[1] = 0
let primes: ptr<i64> = malloc(256 * 8) as ptr<i64>
let mut np: i64 = 0
let mut i: i64 = 2
while i <= N_lim {
if is_prime[i] == 1 {
primes[np] = i
np = np + 1
let mut j: i64 = i * i
while j <= N_lim {
is_prime[j] = 0
j = j + i
}
}
i = i + 1
}
# Compute exponents for each prime
let exps: ptr<i64> = malloc(np * 8) as ptr<i64>
let vp_in_k: ptr<i32> = malloc((N_lim + 1) * 4) as ptr<i32>
let fact_vp: ptr<i64> = malloc((N_lim + 1) * 8) as ptr<i64>
let mut pi: i64 = 0
while pi < np {
let p: i64 = primes[pi]
let mut k: i64 = 0
while k <= N_lim {
vp_in_k[k] = 0
k = k + 1
}
k = 1
while k <= N_lim {
let mut x: i64 = k
let mut c: i32 = 0
while x % p == 0 {
x = x / p
c = c + 1
}
vp_in_k[k] = c
k = k + 1
}
fact_vp[0] = 0
k = 1
while k <= N_lim {
fact_vp[k] = fact_vp[k - 1] + (vp_in_k[k] as i64)
k = k + 1
}
let mut E: i64 = 0
k = 1
while k <= N_lim {
E = E + (N_lim + 1 - k) * fact_vp[k]
k = k + 1
}
exps[pi] = E
pi = pi + 1
}
let m: i64 = N_lim
let omega: i64 = mod_pow(ROOT, (MOD - 1) / m, MOD)
let inv_m: i64 = mod_inv(m, MOD)
let mut ans: i64 = 0
let mut w: i64 = 1
let mut t: i64 = 0
while t < m {
let mut prod: i64 = 1
let mut pi2: i64 = 0
while pi2 < np {
let p: i64 = primes[pi2]
let E: i64 = exps[pi2]
let r: i64 = ((p as i128) * (w as i128) % (MOD as i128)) as i64
let mut term: i64 = 0
if r == 1 {
term = (E + 1) % MOD
} else {
let num: i64 = (mod_pow(r, E + 1, MOD) - 1 + MOD) % MOD
let den: i64 = (r - 1 + MOD) % MOD
let den_inv: i64 = mod_inv(den, MOD)
term = ((num as i128) * (den_inv as i128) % (MOD as i128)) as i64
}
prod = ((prod as i128) * (term as i128) % (MOD as i128)) as i64
pi2 = pi2 + 1
}
ans = (ans + prod) % MOD
w = ((w as i128) * (omega as i128) % (MOD as i128)) as i64
t = t + 1
}
let result: i64 = ((ans as i128) * (inv_m as i128) % (MOD as i128)) as i64
free(is_prime)
free(primes)
free(exps)
free(vp_in_k)
free(fact_vp)
printf("%lld\n", result)
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 mod_pow_i64_i64_i64(int64_t a, int64_t e, int64_t mod);
int64_t mod_inv_i64_i64(int64_t a, int64_t mod);
int32_t main(void);
static const int64_t MOD = 999999001;
static const int64_t ROOT = 17;
static const int64_t N = 1000;
int64_t mod_pow_i64_i64_i64(int64_t a, int64_t e, int64_t mod) {
int64_t r = FLOW_CHECKED_MOD((1), (mod));
int64_t aa = FLOW_CHECKED_MOD((a), (mod));
if (aa < 0) {
aa = (aa + mod);
}
int64_t ee = e;
while (ee > 0) {
if ((ee & 1) == 1) {
r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(aa)))), (((__int128)(mod))))));
}
aa = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(aa)) * ((__int128)(aa)))), (((__int128)(mod))))));
ee = FLOW_CHECKED_SHR((ee), (1));
}
return r;
}
int64_t mod_inv_i64_i64(int64_t a, int64_t mod) {
return mod_pow_i64_i64_i64(a, (mod - 2), mod);
}
int32_t main(void) {
int64_t N_lim = N;
int8_t* is_prime = (int8_t*)(((int8_t*)(malloc(((N_lim + 1) * 1)))));
int64_t ii = 0;
while (ii <= N_lim) {
is_prime[ii] = 1;
ii = (ii + 1);
}
is_prime[0] = 0;
is_prime[1] = 0;
int64_t* primes = (int64_t*)(((int64_t*)(malloc((256 * 8)))));
int64_t np = 0;
int64_t i = 2;
while (i <= N_lim) {
if (is_prime[i] == 1) {
primes[np] = i;
np = (np + 1);
int64_t j = (i * i);
while (j <= N_lim) {
is_prime[j] = 0;
j = (j + i);
}
}
i = (i + 1);
}
int64_t* exps = (int64_t*)(((int64_t*)(malloc((np * 8)))));
int32_t* vp_in_k = (int32_t*)(((int32_t*)(malloc(((N_lim + 1) * 4)))));
int64_t* fact_vp = (int64_t*)(((int64_t*)(malloc(((N_lim + 1) * 8)))));
int64_t pi = 0;
while (pi < np) {
int64_t p = primes[pi];
int64_t k = 0;
while (k <= N_lim) {
vp_in_k[k] = 0;
k = (k + 1);
}
k = 1;
while (k <= N_lim) {
int64_t x = k;
int32_t c = 0;
while (FLOW_CHECKED_MOD((x), (p)) == 0) {
x = FLOW_CHECKED_DIV((x), (p));
c = (c + 1);
}
vp_in_k[k] = c;
k = (k + 1);
}
fact_vp[0] = 0;
k = 1;
while (k <= N_lim) {
fact_vp[k] = (fact_vp[(k - 1)] + ((int64_t)(vp_in_k[k])));
k = (k + 1);
}
int64_t E = 0;
k = 1;
while (k <= N_lim) {
E = (E + (((N_lim + 1) - k) * fact_vp[k]));
k = (k + 1);
}
exps[pi] = E;
pi = (pi + 1);
}
int64_t m = N_lim;
int64_t omega = mod_pow_i64_i64_i64(ROOT, FLOW_CHECKED_DIV(((MOD - 1)), (m)), MOD);
int64_t inv_m = mod_inv_i64_i64(m, MOD);
int64_t ans = 0;
int64_t w = 1;
int64_t t = 0;
while (t < m) {
int64_t prod = 1;
int64_t pi2 = 0;
while (pi2 < np) {
int64_t p = primes[pi2];
int64_t E = exps[pi2];
int64_t r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(p)) * ((__int128)(w)))), (((__int128)(MOD))))));
int64_t term = 0;
if (r == 1) {
term = FLOW_CHECKED_MOD(((E + 1)), (MOD));
} else {
int64_t num = FLOW_CHECKED_MOD((((mod_pow_i64_i64_i64(r, (E + 1), MOD) - 1) + MOD)), (MOD));
int64_t den = FLOW_CHECKED_MOD((((r - 1) + MOD)), (MOD));
int64_t den_inv = mod_inv_i64_i64(den, MOD);
term = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(num)) * ((__int128)(den_inv)))), (((__int128)(MOD))))));
}
prod = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(prod)) * ((__int128)(term)))), (((__int128)(MOD))))));
pi2 = (pi2 + 1);
}
ans = FLOW_CHECKED_MOD(((ans + prod)), (MOD));
w = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(w)) * ((__int128)(omega)))), (((__int128)(MOD))))));
t = (t + 1);
}
int64_t result = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(ans)) * ((__int128)(inv_m)))), (((__int128)(MOD))))));
free(is_prime);
free(primes);
free(exps);
free(vp_in_k);
free(fact_vp);
printf("%lld\n", result);
return 0;
}