# Project Euler 496
# Incenter/circumcenter — F(10^9) via A=2B triangle parametrization.
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function squarefree_divs(p: i64, spf: ptr<i32>, ds: ptr<i64>, cs: ptr<i64>) -> i64 {
let mut primes: array<i64, 16> = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
let mut pc: i64 = 0
let mut x: i64 = p
while x > 1 {
let pr: i64 = spf[x] as i64
primes[pc] = pr
pc = pc + 1
while x % pr == 0 {
x = x / pr
}
}
ds[0] = 1
cs[0] = 1
let mut dcount: i64 = 1
let mut i: i64 = 0
while i < pc {
let pr: i64 = primes[i]
let m: i64 = dcount
let mut j: i64 = 0
while j < m {
ds[dcount] = ds[j] * pr
cs[dcount] = 0 - cs[j] * pr
dcount = dcount + 1
j = j + 1
}
i = i + 1
}
return dcount
}
function coprime_prefix_sum(ds: ptr<i64>, cs: ptr<i64>, dcount: i64, x: i64) -> i64 {
if x <= 0 { return 0 }
let mut total: i64 = 0
let mut i: i64 = 0
while i < dcount {
let d: i64 = ds[i]
let coef: i64 = cs[i]
let nn: i64 = x / d
total = total + coef * (nn * (nn + 1) / 2)
i = i + 1
}
return total
}
function F(L: i64) -> i64 {
let p_max: i64 = isqrt(L) + 1
let spf: ptr<i32> = calloc(p_max + 1, 4)
let ds: ptr<i64> = calloc(64, 8)
let cs: ptr<i64> = calloc(64, 8)
if spf == null || ds == null || cs == null { return 0 }
let mut i: i64 = 0
while i <= p_max {
spf[i] = i as i32
i = i + 1
}
let lim: i64 = isqrt(p_max)
i = 2
while i <= lim {
if (spf[i] as i64) == i {
let mut j: i64 = i * i
while j <= p_max {
if (spf[j] as i64) == j {
spf[j] = i as i32
}
j = j + i
}
}
i = i + 1
}
let mut ans: i64 = 0
let mut p: i64 = 1
while p <= p_max {
let q_low: i64 = p + 1
let mut q_high: i64 = 2 * p - 1
let limq: i64 = L / p
if limq < q_high { q_high = limq }
if q_low <= q_high {
let M: i64 = L / p
let dcount: i64 = squarefree_divs(p, spf, ds, cs)
let mut q: i64 = q_low
while q <= q_high {
let v: i64 = M / q
let mut q_end: i64 = M / v
if q_end > q_high { q_end = q_high }
let sum_q: i64 = coprime_prefix_sum(ds, cs, dcount, q_end) - coprime_prefix_sum(ds, cs, dcount, q - 1)
if sum_q != 0 {
let tri: i64 = v * (v + 1) / 2
ans = ans + p * tri * sum_q
}
q = q_end + 1
}
}
p = p + 1
}
free(spf)
free(ds)
free(cs)
return ans
}
function main() -> i32 {
if F(15) != 45 {
printf("%lld\n", F(15))
return 1
}
printf("%lld\n", F(1000000000))
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 squarefree_divs_i64_ptr_i32_ptr_i64_ptr_i64(int64_t p, int32_t* spf, int64_t* ds, int64_t* cs);
int64_t coprime_prefix_sum_ptr_i64_ptr_i64_i64_i64(int64_t* ds, int64_t* cs, int64_t dcount, int64_t x);
int64_t F_i64(int64_t L);
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 squarefree_divs_i64_ptr_i32_ptr_i64_ptr_i64(int64_t p, int32_t* spf, int64_t* ds, int64_t* cs) {
int64_t primes[16] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
int64_t pc = 0;
int64_t x = p;
while (x > 1) {
int64_t pr = ((int64_t)(spf[x]));
primes[pc] = pr;
pc = (pc + 1);
while (FLOW_CHECKED_MOD((x), (pr)) == 0) {
x = FLOW_CHECKED_DIV((x), (pr));
}
}
ds[0] = 1;
cs[0] = 1;
int64_t dcount = 1;
int64_t i = 0;
while (i < pc) {
int64_t pr = (((unsigned)(i) < 16) ? primes[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 16), flow_fault_handler("array index out of bounds"), primes[0]));
int64_t m = dcount;
int64_t j = 0;
while (j < m) {
ds[dcount] = (ds[j] * pr);
cs[dcount] = (0 - (cs[j] * pr));
dcount = (dcount + 1);
j = (j + 1);
}
i = (i + 1);
}
return dcount;
}
int64_t coprime_prefix_sum_ptr_i64_ptr_i64_i64_i64(int64_t* ds, int64_t* cs, int64_t dcount, int64_t x) {
if (x <= 0) {
return 0;
}
int64_t total = 0;
int64_t i = 0;
while (i < dcount) {
int64_t d = ds[i];
int64_t coef = cs[i];
int64_t nn = FLOW_CHECKED_DIV((x), (d));
total = (total + (coef * FLOW_CHECKED_DIV(((nn * (nn + 1))), (2))));
i = (i + 1);
}
return total;
}
int64_t F_i64(int64_t L) {
int64_t p_max = (isqrt_i64(L) + 1);
int32_t* spf = (int32_t*)(calloc((p_max + 1), 4));
int64_t* ds = (int64_t*)(calloc(64, 8));
int64_t* cs = (int64_t*)(calloc(64, 8));
if (((spf == NULL || ds == NULL) || cs == NULL)) {
return 0;
}
int64_t i = 0;
while (i <= p_max) {
spf[i] = ((int32_t)(i));
i = (i + 1);
}
int64_t lim = isqrt_i64(p_max);
i = 2;
while (i <= lim) {
if (((int64_t)(spf[i])) == i) {
int64_t j = (i * i);
while (j <= p_max) {
if (((int64_t)(spf[j])) == j) {
spf[j] = ((int32_t)(i));
}
j = (j + i);
}
}
i = (i + 1);
}
int64_t ans = 0;
int64_t p = 1;
while (p <= p_max) {
int64_t q_low = (p + 1);
int64_t q_high = ((2 * p) - 1);
int64_t limq = FLOW_CHECKED_DIV((L), (p));
if (limq < q_high) {
q_high = limq;
}
if (q_low <= q_high) {
int64_t M = FLOW_CHECKED_DIV((L), (p));
int64_t dcount = squarefree_divs_i64_ptr_i32_ptr_i64_ptr_i64(p, spf, ds, cs);
int64_t q = q_low;
while (q <= q_high) {
int64_t v = FLOW_CHECKED_DIV((M), (q));
int64_t q_end = FLOW_CHECKED_DIV((M), (v));
if (q_end > q_high) {
q_end = q_high;
}
int64_t sum_q = (coprime_prefix_sum_ptr_i64_ptr_i64_i64_i64(ds, cs, dcount, q_end) - coprime_prefix_sum_ptr_i64_ptr_i64_i64_i64(ds, cs, dcount, (q - 1)));
if (sum_q != 0) {
int64_t tri = FLOW_CHECKED_DIV(((v * (v + 1))), (2));
ans = (ans + ((p * tri) * sum_q));
}
q = (q_end + 1);
}
}
p = (p + 1);
}
free(spf);
free(ds);
free(cs);
return ans;
}
int32_t main(void) {
if (F_i64(15) != 45) {
printf("%lld\n", F_i64(15));
return 1;
}
printf("%lld\n", F_i64(1000000000));
return 0;
}