# Project Euler 279
# Count triangles with angles 60/90/120 and perimeter <= 10^8.
import euler.nt { gcd, isqrt }
function search90(limit: i64) -> i64 {
let mut result: i64 = 0
let last: i64 = isqrt(limit / 2)
let mut m: i64 = 2
while m < last {
let mut n: i64 = (m % 2) + 1
while n < m {
if gcd(m, n) == 1 {
let a: i64 = m * m - n * n
let b: i64 = 2 * m * n
let c: i64 = m * m + n * n
let total: i64 = a + b + c
if total > limit { break }
result = result + limit / total
}
n = n + 2
}
m = m + 1
}
return result
}
function search60(limit: i64) -> i64 {
let last: i64 = isqrt(limit * 3 / 2)
let mut result: i64 = 0
let mut m: i64 = 2
while m < last {
let mut n: i64 = 1
while 2 * n <= m {
if gcd(m, n) == 1 {
let a: i64 = m * m - m * n + n * n
let b: i64 = 2 * m * n - n * n
let c: i64 = m * m - n * n
let mut total: i64 = a + b + c
if a % 3 == 0 && b % 3 == 0 && c % 3 == 0 {
total = total / 3
}
if total > 3 * limit { break }
if total <= limit {
result = result + limit / total
}
}
n = n + 1
}
m = m + 1
}
return result
}
function search120(limit: i64) -> i64 {
let mut result: i64 = 0
let last: i64 = isqrt(limit * 3 / 2)
let mut m: i64 = 2
while m < last {
let mut n: i64 = 1
while 2 * n <= m {
if gcd(m, n) == 1 {
let a: i64 = m * m + m * n + n * n
let b: i64 = 2 * m * n + n * n
let c: i64 = m * m - n * n
if b > c { break }
let mut total: i64 = a + b + c
if a % 3 == 0 && b % 3 == 0 && c % 3 == 0 {
total = total / 3
}
if total > 3 * limit { break }
result = result + limit / total
}
n = n + 1
}
m = m + 1
}
return result
}
function main() -> i32 {
let limit: i64 = 100000000
printf("%lld\n", search60(limit) + search90(limit) + search120(limit))
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 search90_i64(int64_t limit);
int64_t search60_i64(int64_t limit);
int64_t search120_i64(int64_t limit);
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 search90_i64(int64_t limit) {
int64_t result = 0;
int64_t last = isqrt_i64(FLOW_CHECKED_DIV((limit), (2)));
int64_t m = 2;
while (m < last) {
int64_t n = (FLOW_CHECKED_MOD((m), (2)) + 1);
while (n < m) {
if (gcd_i64_i64(m, n) == 1) {
int64_t a = ((m * m) - (n * n));
int64_t b = ((2 * m) * n);
int64_t c = ((m * m) + (n * n));
int64_t total = ((a + b) + c);
if (total > limit) {
break;
}
result = (result + FLOW_CHECKED_DIV((limit), (total)));
}
n = (n + 2);
}
m = (m + 1);
}
return result;
}
int64_t search60_i64(int64_t limit) {
int64_t last = isqrt_i64(FLOW_CHECKED_DIV(((limit * 3)), (2)));
int64_t result = 0;
int64_t m = 2;
while (m < last) {
int64_t n = 1;
while ((2 * n) <= m) {
if (gcd_i64_i64(m, n) == 1) {
int64_t a = (((m * m) - (m * n)) + (n * n));
int64_t b = (((2 * m) * n) - (n * n));
int64_t c = ((m * m) - (n * n));
int64_t total = ((a + b) + c);
if (((FLOW_CHECKED_MOD((a), (3)) == 0 && FLOW_CHECKED_MOD((b), (3)) == 0) && FLOW_CHECKED_MOD((c), (3)) == 0)) {
total = FLOW_CHECKED_DIV((total), (3));
}
if (total > (3 * limit)) {
break;
}
if (total <= limit) {
result = (result + FLOW_CHECKED_DIV((limit), (total)));
}
}
n = (n + 1);
}
m = (m + 1);
}
return result;
}
int64_t search120_i64(int64_t limit) {
int64_t result = 0;
int64_t last = isqrt_i64(FLOW_CHECKED_DIV(((limit * 3)), (2)));
int64_t m = 2;
while (m < last) {
int64_t n = 1;
while ((2 * n) <= m) {
if (gcd_i64_i64(m, n) == 1) {
int64_t a = (((m * m) + (m * n)) + (n * n));
int64_t b = (((2 * m) * n) + (n * n));
int64_t c = ((m * m) - (n * n));
if (b > c) {
break;
}
int64_t total = ((a + b) + c);
if (((FLOW_CHECKED_MOD((a), (3)) == 0 && FLOW_CHECKED_MOD((b), (3)) == 0) && FLOW_CHECKED_MOD((c), (3)) == 0)) {
total = FLOW_CHECKED_DIV((total), (3));
}
if (total > (3 * limit)) {
break;
}
result = (result + FLOW_CHECKED_DIV((limit), (total)));
}
n = (n + 1);
}
m = (m + 1);
}
return result;
}
int32_t main(void) {
int64_t limit = 100000000;
printf("%lld\n", ((search60_i64(limit) + search90_i64(limit)) + search120_i64(limit)));
return 0;
}