# Project Euler 271
# Sum of x where x^3 ≡ 1 (mod 13082761331670030), excluding 1.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function mulmod(a0: i64, b0: i64, mod: i64) -> i64 {
let mut a: i64 = a0 % mod
let mut b: i64 = b0 % mod
if a < 0 { a = a + mod }
if b < 0 { b = b + mod }
let mut result: i64 = 0
while b > 0 {
if b % 2 == 1 {
result = result + a
if result >= mod { result = result - mod }
}
a = a + a
if a >= mod { a = a - mod }
b = b / 2
}
return result
}
function mod_inverse(a0: i64, m: i64) -> i64 {
let mut a: i64 = a0 % m
let mut b: i64 = m
let mut x0: i64 = 1
let mut x1: i64 = 0
while b != 0 {
let q: i64 = a / b
let t: i64 = a % b
a = b
b = t
let tx: i64 = x0 - q * x1
x0 = x1
x1 = tx
}
if x0 < 0 { x0 = x0 + m }
return x0
}
function crt(a1: i64, a2: i64, n1: i64, n2: i64) -> i64 {
let mod: i64 = n1 * n2
let p: i64 = mod_inverse(n1 % n2, n2)
let q: i64 = mod_inverse(n2 % n1, n1)
let t1: i64 = mulmod(mulmod(a1, q, mod), n2, mod)
let t2: i64 = mulmod(mulmod(a2, p, mod), n1, mod)
let s: i64 = t1 + t2
if s >= mod { s = s - mod }
return s
}
function main() -> i32 {
let factors: ptr<i64> = calloc(14, 8)
factors[0]=2; factors[1]=3; factors[2]=5; factors[3]=7; factors[4]=11
factors[5]=13; factors[6]=17; factors[7]=19; factors[8]=23; factors[9]=29
factors[10]=31; factors[11]=37; factors[12]=41; factors[13]=43
let MAXS: i64 = 2000
let sol: ptr<i64> = calloc(MAXS, 8)
let nsol: ptr<i64> = calloc(MAXS, 8)
if sol == null || nsol == null { return 1 }
let mut sc: i64 = 1
sol[0] = 1
let mut cur_n: i64 = 2
let mut fi: i64 = 1
while fi < 14 {
let p: i64 = factors[fi]
let roots: ptr<i64> = calloc(p, 8)
let mut rc: i64 = 0
let mut x: i64 = 0
while x < p {
if mulmod(mulmod(x, x, p), x, p) == 1 {
roots[rc] = x
rc = rc + 1
}
x = x + 1
}
let mut nc: i64 = 0
let mut i: i64 = 0
while i < sc {
let mut j: i64 = 0
while j < rc {
nsol[nc] = crt(sol[i], roots[j], cur_n, p)
nc = nc + 1
j = j + 1
}
i = i + 1
}
i = 0
while i < nc {
sol[i] = nsol[i]
i = i + 1
}
sc = nc
cur_n = cur_n * p
free(roots)
fi = fi + 1
}
let mut total: i64 = 0
let mut i: i64 = 0
while i < sc {
total = total + sol[i]
i = i + 1
}
total = total - 1
printf("%lld\n", total)
free(sol); free(nsol); free(factors)
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 mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_inverse_i64_i64(int64_t a0, int64_t m);
int64_t crt_i64_i64_i64_i64(int64_t a1, int64_t a2, int64_t n1, int64_t n2);
int32_t main(void);
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));
if (a < 0) {
a = (a + mod);
}
if (b < 0) {
b = (b + mod);
}
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = (result + a);
if (result >= mod) {
result = (result - mod);
}
}
a = (a + a);
if (a >= mod) {
a = (a - mod);
}
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_inverse_i64_i64(int64_t a0, int64_t m) {
int64_t a = FLOW_CHECKED_MOD((a0), (m));
int64_t b = m;
int64_t x0 = 1;
int64_t x1 = 0;
while (b != 0) {
int64_t q = FLOW_CHECKED_DIV((a), (b));
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
int64_t tx = (x0 - (q * x1));
x0 = x1;
x1 = tx;
}
if (x0 < 0) {
x0 = (x0 + m);
}
return x0;
}
int64_t crt_i64_i64_i64_i64(int64_t a1, int64_t a2, int64_t n1, int64_t n2) {
int64_t mod = (n1 * n2);
int64_t p = mod_inverse_i64_i64(FLOW_CHECKED_MOD((n1), (n2)), n2);
int64_t q = mod_inverse_i64_i64(FLOW_CHECKED_MOD((n2), (n1)), n1);
int64_t t1 = mulmod_i64_i64_i64(mulmod_i64_i64_i64(a1, q, mod), n2, mod);
int64_t t2 = mulmod_i64_i64_i64(mulmod_i64_i64_i64(a2, p, mod), n1, mod);
int64_t s = (t1 + t2);
if (s >= mod) {
s = (s - mod);
}
return s;
}
int32_t main(void) {
int64_t* factors = (int64_t*)(calloc(14, 8));
factors[0] = 2;
factors[1] = 3;
factors[2] = 5;
factors[3] = 7;
factors[4] = 11;
factors[5] = 13;
factors[6] = 17;
factors[7] = 19;
factors[8] = 23;
factors[9] = 29;
factors[10] = 31;
factors[11] = 37;
factors[12] = 41;
factors[13] = 43;
int64_t MAXS = 2000;
int64_t* sol = (int64_t*)(calloc(MAXS, 8));
int64_t* nsol = (int64_t*)(calloc(MAXS, 8));
if ((sol == NULL || nsol == NULL)) {
return 1;
}
int64_t sc = 1;
sol[0] = 1;
int64_t cur_n = 2;
int64_t fi = 1;
while (fi < 14) {
int64_t p = factors[fi];
int64_t* roots = (int64_t*)(calloc(p, 8));
int64_t rc = 0;
int64_t x = 0;
while (x < p) {
if (mulmod_i64_i64_i64(mulmod_i64_i64_i64(x, x, p), x, p) == 1) {
roots[rc] = x;
rc = (rc + 1);
}
x = (x + 1);
}
int64_t nc = 0;
int64_t i = 0;
while (i < sc) {
int64_t j = 0;
while (j < rc) {
nsol[nc] = crt_i64_i64_i64_i64(sol[i], roots[j], cur_n, p);
nc = (nc + 1);
j = (j + 1);
}
i = (i + 1);
}
i = 0;
while (i < nc) {
sol[i] = nsol[i];
i = (i + 1);
}
sc = nc;
cur_n = (cur_n * p);
free(roots);
fi = (fi + 1);
}
int64_t total = 0;
int64_t i = 0;
while (i < sc) {
total = (total + sol[i]);
i = (i + 1);
}
total = (total - 1);
printf("%lld\n", total);
free(sol);
free(nsol);
free(factors);
return 0;
}