# Project Euler 570
# Snowflakes
# G(n)=6*gcd(2*4^(n-2)-3^(n-2), 7n+3); sum G(3)..G(10^7).
import euler.nt { gcd }
function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
let mut result: i64 = 1
let mut base: i64 = base0 % mod
let mut exp: i64 = exp0
if base < 0 { base = base + mod }
while exp > 0 {
if (exp & 1) != 0 {
result = ((result as i128) * (base as i128) % (mod as i128)) as i64
}
base = ((base as i128) * (base as i128) % (mod as i128)) as i64
exp = exp >> 1
}
return result
}
function sum_G(N: i64) -> i64 {
let mut total_d: i64 = 0
let mut n: i64 = 4
while n <= N {
let m: i64 = 7 * n + 3
let inv3: i64 = (2 * m + 1) / 3
let b: i64 = (4 * inv3) % m
let t: i64 = modpow(b, n - 2, m)
let x: i64 = (2 * t - 1) % m
if x < 0 { total_d = total_d + gcd(x + m, m) } else { total_d = total_d + gcd(x, m) }
n = n + 3
}
n = 5
while n <= N {
let m: i64 = 7 * n + 3
let inv3: i64 = (m + 1) / 3
let b: i64 = (4 * inv3) % m
let t: i64 = modpow(b, n - 2, m)
let x: i64 = (2 * t - 1) % m
if x < 0 { total_d = total_d + gcd(x + m, m) } else { total_d = total_d + gcd(x, m) }
n = n + 3
}
n = 3
while n <= N {
let m: i64 = 7 * n + 3
let mut x: i64 = (2 * modpow(4, n - 2, m) - modpow(3, n - 2, m)) % m
if x < 0 { x = x + m }
total_d = total_d + gcd(x, m)
n = n + 3
}
return 6 * total_d
}
function main() -> i32 {
printf("%lld\n", sum_G(10000000))
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);
int64_t sum_G_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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
int64_t result = 1;
int64_t base = FLOW_CHECKED_MOD((base0), (mod));
int64_t exp = exp0;
if (base < 0) {
base = (base + mod);
}
while (exp > 0) {
if ((exp & 1) != 0) {
result = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(result)) * ((__int128)(base)))), (((__int128)(mod))))));
}
base = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(base)) * ((__int128)(base)))), (((__int128)(mod))))));
exp = FLOW_CHECKED_SHR((exp), (1));
}
return result;
}
int64_t sum_G_i64(int64_t N) {
int64_t total_d = 0;
int64_t n = 4;
while (n <= N) {
int64_t m = ((7 * n) + 3);
int64_t inv3 = FLOW_CHECKED_DIV((((2 * m) + 1)), (3));
int64_t b = FLOW_CHECKED_MOD(((4 * inv3)), (m));
int64_t t = modpow_i64_i64_i64(b, (n - 2), m);
int64_t x = FLOW_CHECKED_MOD((((2 * t) - 1)), (m));
if (x < 0) {
total_d = (total_d + gcd_i64_i64((x + m), m));
} else {
total_d = (total_d + gcd_i64_i64(x, m));
}
n = (n + 3);
}
n = 5;
while (n <= N) {
int64_t m = ((7 * n) + 3);
int64_t inv3 = FLOW_CHECKED_DIV(((m + 1)), (3));
int64_t b = FLOW_CHECKED_MOD(((4 * inv3)), (m));
int64_t t = modpow_i64_i64_i64(b, (n - 2), m);
int64_t x = FLOW_CHECKED_MOD((((2 * t) - 1)), (m));
if (x < 0) {
total_d = (total_d + gcd_i64_i64((x + m), m));
} else {
total_d = (total_d + gcd_i64_i64(x, m));
}
n = (n + 3);
}
n = 3;
while (n <= N) {
int64_t m = ((7 * n) + 3);
int64_t x = FLOW_CHECKED_MOD((((2 * modpow_i64_i64_i64(4, (n - 2), m)) - modpow_i64_i64_i64(3, (n - 2), m))), (m));
if (x < 0) {
x = (x + m);
}
total_d = (total_d + gcd_i64_i64(x, m));
n = (n + 3);
}
return (6 * total_d);
}
int32_t main(void) {
printf("%lld\n", sum_G_i64(10000000));
return 0;
}