# Project Euler 404
# C(10^17): count of (a,b,c) from ellipse intersections.
import euler.nt { isqrt }
function gcd_abs(a0: i64, b0: i64) -> i64 {
let mut a: i64 = a0
let mut b: i64 = b0
if a < 0 { a = 0 - a }
if b < 0 { b = 0 - b }
while b != 0 {
let t: i64 = a % b
a = b
b = t
}
return a
}
function mod_euclid(a: i64, m: i64) -> i64 {
let mut r: i64 = a % m
if r < 0 { r = r + m }
return r
}
function is_odd(n: i64) -> bool {
return mod_euclid(n, 2) == 1
}
function main() -> i32 {
let LIMIT: i64 = 100000000000000000
let m_max: i64 = ((2 * LIMIT) |> isqrt |> isqrt) + 1
let mut total: i64 = 0
let mut m: i64 = 1
while m <= m_max {
let m2: i64 = m * m
let mut n_start: i64 = 0 - (m / 3)
if m % 3 == 0 {
n_start = n_start + 1
}
let mut n: i64 = n_start
while n < 0 {
if !(is_odd(m) && is_odd(n)) {
if mod_euclid(m - 2 * n, 5) != 0 {
if gcd_abs(m, 0 - n) == 1 {
let n2: i64 = n * n
let mn: i64 = m * n
let p: i64 = m2 - n2 - 4 * mn
let r: i64 = m2 - n2 + mn
let a0: i128 = (p as i128) * (r as i128)
if a0 > (0 as i128) && a0 <= (LIMIT as i128) {
total = total + ((LIMIT as i128) / a0) as i64
}
}
}
}
n = n + 1
}
n = m / 2 + 1
while n < m {
if !(is_odd(m) && is_odd(n)) {
if mod_euclid(m - 2 * n, 5) != 0 {
if gcd_abs(m, n) == 1 {
let n2: i64 = n * n
let mn: i64 = m * n
let p: i64 = n2 + 4 * mn - m2
let r: i64 = m2 - n2 + mn
let a0: i128 = (p as i128) * (r as i128)
if a0 > (0 as i128) && a0 <= (LIMIT as i128) {
total = total + ((LIMIT as i128) / a0) as i64
}
}
}
}
n = n + 1
}
m = m + 1
}
printf("%lld\n", total)
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 gcd_abs_i64_i64(int64_t a0, int64_t b0);
int64_t mod_euclid_i64_i64(int64_t a, int64_t m);
bool is_odd_i64(int64_t n);
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 gcd_abs_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
if (a < 0) {
a = (0 - a);
}
if (b < 0) {
b = (0 - b);
}
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t mod_euclid_i64_i64(int64_t a, int64_t m) {
int64_t r = FLOW_CHECKED_MOD((a), (m));
if (r < 0) {
r = (r + m);
}
return r;
}
bool is_odd_i64(int64_t n) {
return mod_euclid_i64_i64(n, 2) == 1;
}
int32_t main(void) {
int64_t LIMIT = 100000000000000000;
int64_t m_max = (isqrt_i64(isqrt_i64((2 * LIMIT))) + 1);
int64_t total = 0;
int64_t m = 1;
while (m <= m_max) {
int64_t m2 = (m * m);
int64_t n_start = (0 - FLOW_CHECKED_DIV((m), (3)));
if (FLOW_CHECKED_MOD((m), (3)) == 0) {
n_start = (n_start + 1);
}
int64_t n = n_start;
while (n < 0) {
if ((!((is_odd_i64(m) && is_odd_i64(n))))) {
if (mod_euclid_i64_i64((m - (2 * n)), 5) != 0) {
if (gcd_abs_i64_i64(m, (0 - n)) == 1) {
int64_t n2 = (n * n);
int64_t mn = (m * n);
int64_t p = ((m2 - n2) - (4 * mn));
int64_t r = ((m2 - n2) + mn);
__int128 a0 = (((__int128)(p)) * ((__int128)(r)));
if ((a0 > ((__int128)(0)) && a0 <= ((__int128)(LIMIT)))) {
total = (total + ((int64_t)(FLOW_CHECKED_DIV((((__int128)(LIMIT))), (a0)))));
}
}
}
}
n = (n + 1);
}
n = (FLOW_CHECKED_DIV((m), (2)) + 1);
while (n < m) {
if ((!((is_odd_i64(m) && is_odd_i64(n))))) {
if (mod_euclid_i64_i64((m - (2 * n)), 5) != 0) {
if (gcd_abs_i64_i64(m, n) == 1) {
int64_t n2 = (n * n);
int64_t mn = (m * n);
int64_t p = ((n2 + (4 * mn)) - m2);
int64_t r = ((m2 - n2) + mn);
__int128 a0 = (((__int128)(p)) * ((__int128)(r)));
if ((a0 > ((__int128)(0)) && a0 <= ((__int128)(LIMIT)))) {
total = (total + ((int64_t)(FLOW_CHECKED_DIV((((__int128)(LIMIT))), (a0)))));
}
}
}
}
n = (n + 1);
}
m = (m + 1);
}
printf("%lld\n", total);
return 0;
}