# Project Euler 263
# Sum of first four engineers' paradises (verify practical conditions).
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
function fopen(path: string, mode: string) -> ptr<void>
function fclose(f: ptr<void>) -> i32
function fgetc(f: ptr<void>) -> i32
}
function is_practical(n0: i64, primes: ptr<i64>, pc: i64) -> bool {
let mut n: i64 = n0
if n == 1 { return true }
if n < 1 || (n % 2) == 1 { return false }
let fac_p: ptr<i64> = calloc(64, 8)
let fac_e: ptr<i64> = calloc(64, 8)
let mut fc: i64 = 0
let mut x: i64 = n
let mut i: i64 = 0
while i < pc {
let p: i64 = primes[i]
if p * p > x { break }
if x % p == 0 {
let mut e: i64 = 0
while x % p == 0 {
x = x / p
e = e + 1
}
fac_p[fc] = p
fac_e[fc] = e
fc = fc + 1
}
i = i + 1
}
if x > 1 {
fac_p[fc] = x
fac_e[fc] = 1
fc = fc + 1
}
if fc == 0 || fac_p[0] != 2 {
free(fac_p); free(fac_e)
return false
}
let mut sigma_prefix: i64 = (1 << (fac_e[0] + 1)) - 1
i = 1
while i < fc {
let p: i64 = fac_p[i]
let a: i64 = fac_e[i]
if p > sigma_prefix + 1 {
free(fac_p); free(fac_e)
return false
}
let mut pw: i64 = 1
let mut t: i64 = 0
while t <= a {
pw = pw * p
t = t + 1
}
sigma_prefix = sigma_prefix * ((pw - 1) / (p - 1))
i = i + 1
}
free(fac_p); free(fac_e)
return true
}
function read_i64(f: ptr<void>, out: ptr<i64>) -> bool {
let mut c: i32 = fgetc(f)
while c == 32 || c == 10 || c == 13 || c == 9 {
c = fgetc(f)
}
if c < 0 { return false }
let mut v: i64 = 0
while c >= 48 && c <= 57 {
v = v * 10 + (c - 48)
c = fgetc(f)
}
out[0] = v
return true
}
function main() -> i32 {
let small_lim: i64 = 50000
let is_comp: ptr<i8> = calloc(small_lim + 1, 1)
let primes: ptr<i64> = calloc(10000, 8)
let mut pc: i64 = 0
let mut i: i64 = 2
while i <= small_lim {
if is_comp[i] == 0 {
primes[pc] = i
pc = pc + 1
let mut j: i64 = i * i
while j <= small_lim {
is_comp[j] = 1
j = j + i
}
}
i = i + 1
}
let f: ptr<void> = fopen("data/p263_candidates.txt", "r")
let tmp: ptr<i64> = calloc(1, 8)
let mut sum: i64 = 0
let mut count: i64 = 0
while read_i64(f, tmp) {
let n: i64 = tmp[0]
if n % 4 == 0 && is_practical(n - 8, primes, pc) && is_practical(n - 4, primes, pc) && is_practical(n, primes, pc) && is_practical(n + 4, primes, pc) && is_practical(n + 8, primes, pc) {
sum = sum + n
count = count + 1
}
}
fclose(f)
printf("%lld\n", sum)
free(is_comp); free(primes); free(tmp)
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);
bool is_practical_i64_ptr_i64_i64(int64_t n0, int64_t* primes, int64_t pc);
bool read_i64_ptr_void_ptr_i64(void* f, int64_t* out);
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;
}
bool is_practical_i64_ptr_i64_i64(int64_t n0, int64_t* primes, int64_t pc) {
int64_t n = n0;
if (n == 1) {
return 1;
}
if ((n < 1 || FLOW_CHECKED_MOD((n), (2)) == 1)) {
return 0;
}
int64_t* fac_p = (int64_t*)(calloc(64, 8));
int64_t* fac_e = (int64_t*)(calloc(64, 8));
int64_t fc = 0;
int64_t x = n;
int64_t i = 0;
while (i < pc) {
int64_t p = primes[i];
if ((p * p) > x) {
break;
}
if (FLOW_CHECKED_MOD((x), (p)) == 0) {
int64_t e = 0;
while (FLOW_CHECKED_MOD((x), (p)) == 0) {
x = FLOW_CHECKED_DIV((x), (p));
e = (e + 1);
}
fac_p[fc] = p;
fac_e[fc] = e;
fc = (fc + 1);
}
i = (i + 1);
}
if (x > 1) {
fac_p[fc] = x;
fac_e[fc] = 1;
fc = (fc + 1);
}
if ((fc == 0 || fac_p[0] != 2)) {
free(fac_p);
free(fac_e);
return 0;
}
int64_t sigma_prefix = (FLOW_CHECKED_SHL((1), ((fac_e[0] + 1))) - 1);
i = 1;
while (i < fc) {
int64_t p = fac_p[i];
int64_t a = fac_e[i];
if (p > (sigma_prefix + 1)) {
free(fac_p);
free(fac_e);
return 0;
}
int64_t pw = 1;
int64_t t = 0;
while (t <= a) {
pw = (pw * p);
t = (t + 1);
}
sigma_prefix = (sigma_prefix * FLOW_CHECKED_DIV(((pw - 1)), ((p - 1))));
i = (i + 1);
}
free(fac_p);
free(fac_e);
return 1;
}
bool read_i64_ptr_void_ptr_i64(void* f, int64_t* out) {
int32_t c = fgetc(f);
while ((((c == 32 || c == 10) || c == 13) || c == 9)) {
c = fgetc(f);
}
if (c < 0) {
return 0;
}
int64_t v = 0;
while ((c >= 48 && c <= 57)) {
v = ((v * 10) + (c - 48));
c = fgetc(f);
}
out[0] = v;
return 1;
}
int32_t main(void) {
int64_t small_lim = 50000;
int8_t* is_comp = (int8_t*)(calloc((small_lim + 1), 1));
int64_t* primes = (int64_t*)(calloc(10000, 8));
int64_t pc = 0;
int64_t i = 2;
while (i <= small_lim) {
if (is_comp[i] == 0) {
primes[pc] = i;
pc = (pc + 1);
int64_t j = (i * i);
while (j <= small_lim) {
is_comp[j] = 1;
j = (j + i);
}
}
i = (i + 1);
}
void* f = (void*)(fopen("data/p263_candidates.txt", "r"));
int64_t* tmp = (int64_t*)(calloc(1, 8));
int64_t sum = 0;
int64_t count = 0;
while (read_i64_ptr_void_ptr_i64(f, tmp)) {
int64_t n = tmp[0];
if ((((((FLOW_CHECKED_MOD((n), (4)) == 0 && is_practical_i64_ptr_i64_i64((n - 8), primes, pc)) && is_practical_i64_ptr_i64_i64((n - 4), primes, pc)) && is_practical_i64_ptr_i64_i64(n, primes, pc)) && is_practical_i64_ptr_i64_i64((n + 4), primes, pc)) && is_practical_i64_ptr_i64_i64((n + 8), primes, pc))) {
sum = (sum + n);
count = (count + 1);
}
}
fclose(f);
printf("%lld\n", sum);
free(is_comp);
free(primes);
free(tmp);
return 0;
}