# Project Euler 417
# Sum of decimal periods of 1/n for 3<=n<=10^8.
import euler.nt { gcd }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base0 % mod
let mut e: i64 = exp0
while e > 0 {
if e % 2 == 1 {
r = ((r as i128) * (b as i128) % (mod as i128)) as i64
}
b = ((b as i128) * (b as i128) % (mod as i128)) as i64
e = e / 2
}
return r
}
function main() -> i32 {
let LIMIT: i64 = 100000000
let spf: ptr<i32> = calloc(LIMIT + 1, 4)
if spf == null { return 1 }
let mut i: i64 = 0
while i <= LIMIT { spf[i] = 0; i = i + 1 }
let primes: ptr<i32> = calloc(LIMIT / 5, 4)
let mut pc: i64 = 0
i = 2
while i <= LIMIT {
if spf[i] == 0 {
spf[i] = i as i32
primes[pc] = i as i32
pc = pc + 1
}
let mut j: i64 = 0
while j < pc {
let p: i64 = primes[j] as i64
let ip: i64 = i * p
if ip > LIMIT || p > (spf[i] as i64) { break }
spf[ip] = p as i32
j = j + 1
}
i = i + 1
}
# periods[m] for m coprime to 10
let periods: ptr<i32> = calloc(LIMIT + 1, 4)
if periods == null { return 1 }
periods[1] = 1
# Process prime powers p^k for p!=2,5
i = 0
while i < pc {
let p: i64 = primes[i] as i64
if p != 2 && p != 5 {
let mut pow: i64 = p
let mut tot: i64 = p - 1
while pow <= LIMIT {
# find order of 10 mod pow
let mut period: i64 = tot
let mut rem: i64 = period
while rem > 1 {
let q: i64 = spf[rem] as i64
if modpow(10, period / q, pow) == 1 {
period = period / q
}
rem = rem / q
}
# propagate LCM to multiples
let mut j2: i64 = 1
let end: i64 = LIMIT / pow
while j2 <= end {
if periods[j2] != 0 {
let a: i64 = periods[j2] as i64
let g: i64 = gcd(a, period)
periods[j2 * pow] = (a / g * period) as i32
}
j2 = j2 + 1
}
if pow > LIMIT / p { break }
pow = pow * p
tot = tot * p
}
}
i = i + 1
}
periods[1] = 0
let mut sum: i64 = 0
i = 3
while i <= LIMIT {
let mut n: i64 = i
while (n & 1) == 0 { n = n >> 1 }
while n % 5 == 0 { n = n / 5 }
if n > 1 {
sum = sum + (periods[n] as i64)
}
i = i + 1
}
printf("%lld\n", sum)
free(periods)
free(primes)
free(spf)
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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base0), (mod));
int64_t e = exp0;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))))));
}
b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))))));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
int32_t main(void) {
int64_t LIMIT = 100000000;
int32_t* spf = (int32_t*)(calloc((LIMIT + 1), 4));
if (spf == NULL) {
return 1;
}
int64_t i = 0;
while (i <= LIMIT) {
spf[i] = 0;
i = (i + 1);
}
int32_t* primes = (int32_t*)(calloc(FLOW_CHECKED_DIV((LIMIT), (5)), 4));
int64_t pc = 0;
i = 2;
while (i <= LIMIT) {
if (spf[i] == 0) {
spf[i] = ((int32_t)(i));
primes[pc] = ((int32_t)(i));
pc = (pc + 1);
}
int64_t j = 0;
while (j < pc) {
int64_t p = ((int64_t)(primes[j]));
int64_t ip = (i * p);
if ((ip > LIMIT || p > ((int64_t)(spf[i])))) {
break;
}
spf[ip] = ((int32_t)(p));
j = (j + 1);
}
i = (i + 1);
}
int32_t* periods = (int32_t*)(calloc((LIMIT + 1), 4));
if (periods == NULL) {
return 1;
}
periods[1] = 1;
i = 0;
while (i < pc) {
int64_t p = ((int64_t)(primes[i]));
if ((p != 2 && p != 5)) {
int64_t pow = p;
int64_t tot = (p - 1);
while (pow <= LIMIT) {
int64_t period = tot;
int64_t rem = period;
while (rem > 1) {
int64_t q = ((int64_t)(spf[rem]));
if (modpow_i64_i64_i64(10, FLOW_CHECKED_DIV((period), (q)), pow) == 1) {
period = FLOW_CHECKED_DIV((period), (q));
}
rem = FLOW_CHECKED_DIV((rem), (q));
}
int64_t j2 = 1;
int64_t end = FLOW_CHECKED_DIV((LIMIT), (pow));
while (j2 <= end) {
if (periods[j2] != 0) {
int64_t a = ((int64_t)(periods[j2]));
int64_t g = gcd_i64_i64(a, period);
periods[(j2 * pow)] = ((int32_t)((FLOW_CHECKED_DIV((a), (g)) * period)));
}
j2 = (j2 + 1);
}
if (pow > FLOW_CHECKED_DIV((LIMIT), (p))) {
break;
}
pow = (pow * p);
tot = (tot * p);
}
}
i = (i + 1);
}
periods[1] = 0;
int64_t sum = 0;
i = 3;
while (i <= LIMIT) {
int64_t n = i;
while ((n & 1) == 0) {
n = FLOW_CHECKED_SHR((n), (1));
}
while (FLOW_CHECKED_MOD((n), (5)) == 0) {
n = FLOW_CHECKED_DIV((n), (5));
}
if (n > 1) {
sum = (sum + ((int64_t)(periods[n])));
}
i = (i + 1);
}
printf("%lld\n", sum);
free(periods);
free(primes);
free(spf);
return 0;
}