# Project Euler 094
# Sum of perimeters of almost equilateral triangles with integer sides ≤ 1e9.
function is_square(n: i64) -> bool {
if n < 0 { return false }
let mut x: i64 = n
while x > 1 {
let y: i64 = (x + n / x) / 2
if y >= x { break }
x = y
}
let mut r: i64 = x
while r * r > n { r = r - 1 }
while (r + 1) * (r + 1) <= n { r = r + 1 }
return r * r == n
}
function main() -> i32 {
let limit: i64 = 1000000000
let mut total: i64 = 0
# solutions of u^2 - 3v^2 = 4 generated by multiplying by 2+√3
let mut u: i64 = 2
let mut v: i64 = 0
for iter in 0..40 {
let nu: i64 = 2 * u + 3 * v
let nv: i64 = u + 2 * v
u = nu
v = nv
# u = 3a±1 ⇒ candidate odd a
if (u - 1) % 3 == 0 {
let a: i64 = (u - 1) / 3
if a > 1 {
for d in (0 - 1)..2 step 2 {
if d != 0 {
let perim: i64 = 3 * a + d
if perim > 0 && perim <= limit {
let base: i64 = a + d
let h2: i64 = 4 * a * a - base * base
if h2 % 4 == 0 && is_square(h2 / 4) {
total = total + perim
}
}
}
}
}
}
if (u + 1) % 3 == 0 {
let a: i64 = (u + 1) / 3
if a > 1 {
for d in (0 - 1)..2 step 2 {
if d != 0 {
let perim: i64 = 3 * a + d
if perim > 0 && perim <= limit {
let base: i64 = a + d
let h2: i64 = 4 * a * a - base * base
if h2 % 4 == 0 && is_square(h2 / 4) {
total = total + perim
}
}
}
}
}
}
}
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; }
bool is_square_i64(int64_t n);
int32_t main(void);
bool is_square_i64(int64_t n) {
if (n < 0) {
return 0;
}
int64_t x = n;
while (x > 1) {
int64_t y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
if (y >= x) {
break;
}
x = y;
}
int64_t r = x;
while ((r * r) > n) {
r = (r - 1);
}
while (((r + 1) * (r + 1)) <= n) {
r = (r + 1);
}
return (r * r) == n;
}
int32_t main(void) {
int64_t limit = 1000000000;
int64_t total = 0;
int64_t u = 2;
int64_t v = 0;
int32_t __flow_step_1 = 1;
for (int32_t iter = 0; (0 <= 40) ? iter < 40 : iter > 40; iter += (0 <= 40) ? 1 : -1) {
int64_t nu = ((2 * u) + (3 * v));
int64_t nv = (u + (2 * v));
u = nu;
v = nv;
if (FLOW_CHECKED_MOD(((u - 1)), (3)) == 0) {
int64_t a = FLOW_CHECKED_DIV(((u - 1)), (3));
if (a > 1) {
int32_t __flow_step_2 = 2;
for (int32_t d = (0 - 1); (__flow_step_2 > 0) ? d < 2 : d > 2; d += __flow_step_2) {
if (d != 0) {
int64_t perim = ((3 * a) + d);
if ((perim > 0 && perim <= limit)) {
int64_t base = (a + d);
int64_t h2 = (((4 * a) * a) - (base * base));
if ((FLOW_CHECKED_MOD((h2), (4)) == 0 && is_square_i64(FLOW_CHECKED_DIV((h2), (4))))) {
total = (total + perim);
}
}
}
}
}
}
if (FLOW_CHECKED_MOD(((u + 1)), (3)) == 0) {
int64_t a = FLOW_CHECKED_DIV(((u + 1)), (3));
if (a > 1) {
int32_t __flow_step_3 = 2;
for (int32_t d = (0 - 1); (__flow_step_3 > 0) ? d < 2 : d > 2; d += __flow_step_3) {
if (d != 0) {
int64_t perim = ((3 * a) + d);
if ((perim > 0 && perim <= limit)) {
int64_t base = (a + d);
int64_t h2 = (((4 * a) * a) - (base * base));
if ((FLOW_CHECKED_MOD((h2), (4)) == 0 && is_square_i64(FLOW_CHECKED_DIV((h2), (4))))) {
total = (total + perim);
}
}
}
}
}
}
}
printf("%lld\n", total);
return 0;
}