# Project Euler 257
# Count triangles with angular-bisector area ratio integer, perimeter <= 1e8.
import euler.nt { gcd, isqrt }
function main() -> i32 {
let N: i64 = 100000000
let mut total: i64 = N / 3
# k=2
let x_max2: i64 = isqrt(N * 2 / 6) + 50
let mut x: i64 = 3
while x <= x_max2 {
let y_max: i64 = isqrt(2 * x * x)
let mut y: i64 = x + 1
while y <= y_max {
if gcd(x, y) == 1 {
let mut a: i64 = 0
let mut b: i64 = 0
let mut c: i64 = 0
if y % 2 == 1 {
let g0: i64 = y
a = g0 * x
b = g0 * (x + y)
c = x * (2 * x + y)
} else {
let g0: i64 = y / 2
a = g0 * x
b = g0 * (x + y)
c = (x * (2 * x + y)) / 2
}
let p: i64 = a + b + c
if p <= N {
total = total + N / p
}
}
y = y + 1
}
x = x + 1
}
# k=3
let x_max3: i64 = isqrt(N) + 50
x = 2
while x <= x_max3 {
let y_max: i64 = isqrt(3 * x * x)
let x_odd: i64 = x % 2
let mut y: i64 = x + 1
while y <= y_max {
if gcd(x, y) == 1 {
let mut denom2: i64 = 0
if x_odd == 0 {
if y % 3 == 0 { denom2 = y / 3 } else { denom2 = y }
} else {
if y % 2 == 0 {
if y % 3 == 0 { denom2 = (2 * y) / 3 } else { denom2 = 2 * y }
} else {
if y % 3 == 0 { denom2 = y / 3 } else { denom2 = y }
}
}
let mut g0: i64 = 0
if (x + y) % 2 == 0 {
g0 = denom2
} else {
if denom2 % 2 == 0 { g0 = denom2 } else { g0 = 2 * denom2 }
}
let a: i64 = g0 * x
let b: i64 = g0 * (x + y) / 2
let c: i64 = g0 * x * (3 * x + y) / (2 * y)
let p: i64 = a + b + c
if p <= N && p > 0 {
total = total + N / p
}
}
y = y + 1
}
x = x + 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);
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;
}
int32_t main(void) {
int64_t N = 100000000;
int64_t total = FLOW_CHECKED_DIV((N), (3));
int64_t x_max2 = (isqrt_i64(FLOW_CHECKED_DIV(((N * 2)), (6))) + 50);
int64_t x = 3;
while (x <= x_max2) {
int64_t y_max = isqrt_i64(((2 * x) * x));
int64_t y = (x + 1);
while (y <= y_max) {
if (gcd_i64_i64(x, y) == 1) {
int64_t a = 0;
int64_t b = 0;
int64_t c = 0;
if (FLOW_CHECKED_MOD((y), (2)) == 1) {
int64_t g0 = y;
a = (g0 * x);
b = (g0 * (x + y));
c = (x * ((2 * x) + y));
} else {
int64_t g0 = FLOW_CHECKED_DIV((y), (2));
a = (g0 * x);
b = (g0 * (x + y));
c = FLOW_CHECKED_DIV(((x * ((2 * x) + y))), (2));
}
int64_t p = ((a + b) + c);
if (p <= N) {
total = (total + FLOW_CHECKED_DIV((N), (p)));
}
}
y = (y + 1);
}
x = (x + 1);
}
int64_t x_max3 = (isqrt_i64(N) + 50);
x = 2;
while (x <= x_max3) {
int64_t y_max = isqrt_i64(((3 * x) * x));
int64_t x_odd = FLOW_CHECKED_MOD((x), (2));
int64_t y = (x + 1);
while (y <= y_max) {
if (gcd_i64_i64(x, y) == 1) {
int64_t denom2 = 0;
if (x_odd == 0) {
if (FLOW_CHECKED_MOD((y), (3)) == 0) {
denom2 = FLOW_CHECKED_DIV((y), (3));
} else {
denom2 = y;
}
} else {
if (FLOW_CHECKED_MOD((y), (2)) == 0) {
if (FLOW_CHECKED_MOD((y), (3)) == 0) {
denom2 = FLOW_CHECKED_DIV(((2 * y)), (3));
} else {
denom2 = (2 * y);
}
} else {
if (FLOW_CHECKED_MOD((y), (3)) == 0) {
denom2 = FLOW_CHECKED_DIV((y), (3));
} else {
denom2 = y;
}
}
}
int64_t g0 = 0;
if (FLOW_CHECKED_MOD(((x + y)), (2)) == 0) {
g0 = denom2;
} else {
if (FLOW_CHECKED_MOD((denom2), (2)) == 0) {
g0 = denom2;
} else {
g0 = (2 * denom2);
}
}
int64_t a = (g0 * x);
int64_t b = FLOW_CHECKED_DIV(((g0 * (x + y))), (2));
int64_t c = FLOW_CHECKED_DIV((((g0 * x) * ((3 * x) + y))), ((2 * y)));
int64_t p = ((a + b) + c);
if ((p <= N && p > 0)) {
total = (total + FLOW_CHECKED_DIV((N), (p)));
}
}
y = (y + 1);
}
x = (x + 1);
}
printf("%lld\n", total);
return 0;
}