# Project Euler 370
# Count geometric integer triangles with perimeter ≤ 2.5·10^13.
import euler.nt { gcd }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
function sqrt(x: f64) -> f64
}
# Hardware-sqrt integer square root (much faster than Newton iteration,
# which was called ~35M times in the inner loop).
function isq(n: i64) -> i64 {
if n <= 0 { return 0 }
let r: i64 = sqrt(n as f64) as i64
while r > 0 && r * r > n { r = r - 1 }
while (r + 1) * (r + 1) <= n { r = r + 1 }
return r
}
function main() -> i32 {
let N: i64 = 25000000000000
let n_max: i64 = isq(N / 3)
let spf: ptr<i32> = calloc(n_max + 1, 4)
let primes: ptr<i32> = calloc(n_max / 5 + 10, 4)
if spf == null || primes == null { return 1 }
let mut pc: i64 = 0
for i in 2..(n_max + 1) {
if spf[i] == 0 {
spf[i] = i as i32
primes[pc] = i as i32
pc = pc + 1
}
let mut j: i64 = 0
while j < pc {
let p: i64 = primes[j] as i64
let v: i64 = i * p
if v > n_max { break }
spf[v] = p as i32
if p == (spf[i] as i64) { break }
j = j + 1
}
}
if n_max >= 1 { spf[1] = 1 }
# threshold heuristic
let mut threshold: i64 = 200
let t3: i64 = isq(isq(N / 16))
# (N/16)^(1/3) approx
let mut lo: i64 = 1
let mut hi: i64 = 1000000
while lo + 1 < hi {
let mid: i64 = (lo + hi) / 2
if mid * mid * mid <= N / 16 { lo = mid } else { hi = mid }
}
if lo > threshold { threshold = lo }
let mut total: i64 = 0
let mut n: i64 = 1
while n <= n_max {
let nn: i64 = n * n
let m_ratio: i64 = (n + isq(5 * nn)) / 2
let disc: i64 = 4 * N - 3 * nn
if disc >= 0 {
let m_perim: i64 = (isq(disc) - n) / 2
let mut m_max: i64 = m_ratio
if m_perim < m_max { m_max = m_perim }
if m_max >= n {
if n <= threshold {
let mut m: i64 = n
while m <= m_max {
if gcd(m, n) == 1 {
total = total + N / (m * m + m * n + nn)
}
m = m + 1
}
} else {
# squarefree divisors of n via distinct primes
# n can have seven distinct prime factors (2·3·5·7·11·13·17),
# hence up to 128 square-free divisors.
let divs: ptr<i64> = calloc(128, 8)
let mus: ptr<i32> = calloc(128, 4)
if divs == null || mus == null { return 1 }
divs[0] = 1
mus[0] = 1
let mut dlen: i64 = 1
let mut x: i64 = n
while x > 1 {
let p: i64 = spf[x] as i64
while x % p == 0 { x = x / p }
let L: i64 = dlen
for t in 0..L {
divs[dlen] = divs[t] * p
mus[dlen] = 0 - mus[t]
dlen = dlen + 1
}
}
let mut m: i64 = n
while m <= m_max {
let S: i64 = m * m + m * n + nn
let q: i64 = N / S
let Thigh: i64 = N / q
let disc2: i64 = 4 * Thigh - 3 * nn
let mut mend: i64 = (isq(disc2) - n) / 2
if mend > m_max { mend = m_max }
# count coprime m in [m,mend]
let mut cnt: i64 = 0
let a_minus_1: i64 = m - 1
for di in 0..dlen {
let d: i64 = divs[di]
let mu: i64 = mus[di] as i64
cnt = cnt + mu * (mend / d - a_minus_1 / d)
}
total = total + q * cnt
m = mend + 1
}
free(mus)
free(divs)
}
}
}
n = n + 1
}
printf("%lld\n", total)
free(primes)
free(spf)
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 isq_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 isq_i64(int64_t n) {
if (n <= 0) {
return 0;
}
int64_t r = ((int64_t)(sqrt(((double)(n)))));
while ((r > 0 && (r * r) > n)) {
r = (r - 1);
}
while (((r + 1) * (r + 1)) <= n) {
r = (r + 1);
}
return r;
}
int32_t main(void) {
int64_t N = 25000000000000;
int64_t n_max = isq_i64(FLOW_CHECKED_DIV((N), (3)));
int32_t* spf = (int32_t*)(calloc((n_max + 1), 4));
int32_t* primes = (int32_t*)(calloc((FLOW_CHECKED_DIV((n_max), (5)) + 10), 4));
if ((spf == NULL || primes == NULL)) {
return 1;
}
int64_t pc = 0;
int32_t __flow_step_1 = 1;
for (int32_t i = 2; (2 <= (n_max + 1)) ? i < (n_max + 1) : i > (n_max + 1); i += (2 <= (n_max + 1)) ? 1 : -1) {
if (spf[i] == 0) {
spf[i] = ((int32_t)(i));
primes[pc] = ((int32_t)(i));
pc = (pc + 1);
}
int64_t j = 0;
while (j < pc) {
int64_t p = ((int64_t)(primes[j]));
int64_t v = (i * p);
if (v > n_max) {
break;
}
spf[v] = ((int32_t)(p));
if (p == ((int64_t)(spf[i]))) {
break;
}
j = (j + 1);
}
}
if (n_max >= 1) {
spf[1] = 1;
}
int64_t threshold = 200;
int64_t t3 = isq_i64(isq_i64(FLOW_CHECKED_DIV((N), (16))));
int64_t lo = 1;
int64_t hi = 1000000;
while ((lo + 1) < hi) {
int64_t mid = FLOW_CHECKED_DIV(((lo + hi)), (2));
if (((mid * mid) * mid) <= FLOW_CHECKED_DIV((N), (16))) {
lo = mid;
} else {
hi = mid;
}
}
if (lo > threshold) {
threshold = lo;
}
int64_t total = 0;
int64_t n = 1;
while (n <= n_max) {
int64_t nn = (n * n);
int64_t m_ratio = FLOW_CHECKED_DIV(((n + isq_i64((5 * nn)))), (2));
int64_t disc = ((4 * N) - (3 * nn));
if (disc >= 0) {
int64_t m_perim = FLOW_CHECKED_DIV(((isq_i64(disc) - n)), (2));
int64_t m_max = m_ratio;
if (m_perim < m_max) {
m_max = m_perim;
}
if (m_max >= n) {
if (n <= threshold) {
int64_t m = n;
while (m <= m_max) {
if (gcd_i64_i64(m, n) == 1) {
total = (total + FLOW_CHECKED_DIV((N), ((((m * m) + (m * n)) + nn))));
}
m = (m + 1);
}
} else {
int64_t* divs = (int64_t*)(calloc(128, 8));
int32_t* mus = (int32_t*)(calloc(128, 4));
if ((divs == NULL || mus == NULL)) {
return 1;
}
divs[0] = 1;
mus[0] = 1;
int64_t dlen = 1;
int64_t x = n;
while (x > 1) {
int64_t p = ((int64_t)(spf[x]));
while (FLOW_CHECKED_MOD((x), (p)) == 0) {
x = FLOW_CHECKED_DIV((x), (p));
}
int64_t L = dlen;
int32_t __flow_step_2 = 1;
for (int32_t t = 0; (0 <= L) ? t < L : t > L; t += (0 <= L) ? 1 : -1) {
divs[dlen] = (divs[t] * p);
mus[dlen] = (0 - mus[t]);
dlen = (dlen + 1);
}
}
int64_t m = n;
while (m <= m_max) {
int64_t S = (((m * m) + (m * n)) + nn);
int64_t q = FLOW_CHECKED_DIV((N), (S));
int64_t Thigh = FLOW_CHECKED_DIV((N), (q));
int64_t disc2 = ((4 * Thigh) - (3 * nn));
int64_t mend = FLOW_CHECKED_DIV(((isq_i64(disc2) - n)), (2));
if (mend > m_max) {
mend = m_max;
}
int64_t cnt = 0;
int64_t a_minus_1 = (m - 1);
int32_t __flow_step_3 = 1;
for (int32_t di = 0; (0 <= dlen) ? di < dlen : di > dlen; di += (0 <= dlen) ? 1 : -1) {
int64_t d = divs[di];
int64_t mu = ((int64_t)(mus[di]));
cnt = (cnt + (mu * (FLOW_CHECKED_DIV((mend), (d)) - FLOW_CHECKED_DIV((a_minus_1), (d)))));
}
total = (total + (q * cnt));
m = (mend + 1);
}
free(mus);
free(divs);
}
}
}
n = (n + 1);
}
printf("%lld\n", total);
free(primes);
free(spf);
return 0;
}