# Project Euler 517
# A Real Recursion — sum G(p) for primes in (10^7, 10^7+10^4) mod 1e9+7.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1000000007
const LOW: i64 = 10000000
const HIGH: i64 = 10010000
function isqrt(n: i64) -> i64 {
if n < 2 { return n }
let mut x: i64 = n
let mut y: i64 = (x + 1) / 2
while y < x {
x = y
y = (x + n / x) / 2
}
return x
}
function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base0 % mod
let mut e: i64 = exp0
while e > 0 {
if (e & 1) != 0 {
r = ((r as i128) * (b as i128) % (mod as i128)) as i64
}
b = ((b as i128) * (b as i128) % (mod as i128)) as i64
e = e >> 1
}
return r
}
function comb(n: i64, k: i64, fact: ptr<i64>, invfact: ptr<i64>) -> i64 {
if k < 0 || k > n { return 0 }
let a: i128 = (fact[n] as i128) * (invfact[k] as i128) % (MOD as i128)
return (a * (invfact[n - k] as i128) % (MOD as i128)) as i64
}
function G(n: i64, fact: ptr<i64>, invfact: ptr<i64>, u: ptr<i64>) -> i64 {
let a_floor: i64 = isqrt(n)
let mut m: i64 = 1
while m <= a_floor + 1 {
u[m] = n - isqrt(m * m * n) - 1
m = m + 1
}
let mut ans: i64 = 0
m = 1
while m <= a_floor {
let c: i64 = u[m]
let i: i64 = m - 1
ans = (ans + comb(c + i, i, fact, invfact)) % MOD
m = m + 1
}
let mut c0: i64 = 0
while c0 <= a_floor - 1 {
let upper: i64 = u[c0 + 1]
if upper >= 0 {
let mut lower: i64 = u[c0 + 2] + 1
if lower < 0 { lower = 0 }
if lower <= upper {
ans = (ans + comb(c0 + upper + 1, c0 + 1, fact, invfact)) % MOD
if lower > 0 {
ans = (ans - comb(c0 + lower, c0 + 1, fact, invfact) + MOD) % MOD
}
}
}
c0 = c0 + 1
}
return ans % MOD
}
function is_prime(x: i64) -> i32 {
if x < 2 { return 0 }
let mut i: i64 = 2
while i * i <= x {
if x % i == 0 { return 0 }
i = i + 1
}
return 1
}
function main() -> i32 {
let maxn: i64 = HIGH
let fact: ptr<i64> = calloc(maxn + 1, 8)
let invfact: ptr<i64> = calloc(maxn + 1, 8)
let u: ptr<i64> = calloc(maxn + 4, 8)
if fact == null || invfact == null || u == null { return 1 }
fact[0] = 1
let mut i: i64 = 1
while i <= maxn {
fact[i] = (fact[i - 1] * i) % MOD
i = i + 1
}
invfact[maxn] = modpow(fact[maxn], MOD - 2, MOD)
i = maxn
while i > 0 {
invfact[i - 1] = (invfact[i] * i) % MOD
i = i - 1
}
let mut total: i64 = 0
let mut pr: i64 = LOW + 1
while pr < HIGH {
if is_prime(pr) == 1 {
total = (total + G(pr, fact, invfact, u)) % MOD
}
pr = pr + 1
}
printf("%lld\n", total)
free(fact)
free(invfact)
free(u)
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 isqrt_i64(int64_t n);
int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int64_t comb_i64_i64_ptr_i64_ptr_i64(int64_t n, int64_t k, int64_t* fact, int64_t* invfact);
int64_t G_i64_ptr_i64_ptr_i64_ptr_i64(int64_t n, int64_t* fact, int64_t* invfact, int64_t* u);
int32_t is_prime_i64(int64_t x);
int32_t main(void);
static const int64_t MOD = 1000000007;
static const int64_t LOW = 10000000;
static const int64_t HIGH = 10010000;
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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base0), (mod));
int64_t e = exp0;
while (e > 0) {
if ((e & 1) != 0) {
r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))))));
}
b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))))));
e = FLOW_CHECKED_SHR((e), (1));
}
return r;
}
int64_t comb_i64_i64_ptr_i64_ptr_i64(int64_t n, int64_t k, int64_t* fact, int64_t* invfact) {
if ((k < 0 || k > n)) {
return 0;
}
__int128 a = FLOW_CHECKED_MOD(((((__int128)(fact[n])) * ((__int128)(invfact[k])))), (((__int128)(MOD))));
return ((int64_t)(FLOW_CHECKED_MOD(((a * ((__int128)(invfact[(n - k)])))), (((__int128)(MOD))))));
}
int64_t G_i64_ptr_i64_ptr_i64_ptr_i64(int64_t n, int64_t* fact, int64_t* invfact, int64_t* u) {
int64_t a_floor = isqrt_i64(n);
int64_t m = 1;
while (m <= (a_floor + 1)) {
u[m] = ((n - isqrt_i64(((m * m) * n))) - 1);
m = (m + 1);
}
int64_t ans = 0;
m = 1;
while (m <= a_floor) {
int64_t c = u[m];
int64_t i = (m - 1);
ans = FLOW_CHECKED_MOD(((ans + comb_i64_i64_ptr_i64_ptr_i64((c + i), i, fact, invfact))), (MOD));
m = (m + 1);
}
int64_t c0 = 0;
while (c0 <= (a_floor - 1)) {
int64_t upper = u[(c0 + 1)];
if (upper >= 0) {
int64_t lower = (u[(c0 + 2)] + 1);
if (lower < 0) {
lower = 0;
}
if (lower <= upper) {
ans = FLOW_CHECKED_MOD(((ans + comb_i64_i64_ptr_i64_ptr_i64(((c0 + upper) + 1), (c0 + 1), fact, invfact))), (MOD));
if (lower > 0) {
ans = FLOW_CHECKED_MOD((((ans - comb_i64_i64_ptr_i64_ptr_i64((c0 + lower), (c0 + 1), fact, invfact)) + MOD)), (MOD));
}
}
}
c0 = (c0 + 1);
}
return FLOW_CHECKED_MOD((ans), (MOD));
}
int32_t is_prime_i64(int64_t x) {
if (x < 2) {
return 0;
}
int64_t i = 2;
while ((i * i) <= x) {
if (FLOW_CHECKED_MOD((x), (i)) == 0) {
return 0;
}
i = (i + 1);
}
return 1;
}
int32_t main(void) {
int64_t maxn = HIGH;
int64_t* fact = (int64_t*)(calloc((maxn + 1), 8));
int64_t* invfact = (int64_t*)(calloc((maxn + 1), 8));
int64_t* u = (int64_t*)(calloc((maxn + 4), 8));
if (((fact == NULL || invfact == NULL) || u == NULL)) {
return 1;
}
fact[0] = 1;
int64_t i = 1;
while (i <= maxn) {
fact[i] = FLOW_CHECKED_MOD(((fact[(i - 1)] * i)), (MOD));
i = (i + 1);
}
invfact[maxn] = modpow_i64_i64_i64(fact[maxn], (MOD - 2), MOD);
i = maxn;
while (i > 0) {
invfact[(i - 1)] = FLOW_CHECKED_MOD(((invfact[i] * i)), (MOD));
i = (i - 1);
}
int64_t total = 0;
int64_t pr = (LOW + 1);
while (pr < HIGH) {
if (is_prime_i64(pr) == 1) {
total = FLOW_CHECKED_MOD(((total + G_i64_ptr_i64_ptr_i64_ptr_i64(pr, fact, invfact, u))), (MOD));
}
pr = (pr + 1);
}
printf("%lld\n", total);
free(fact);
free(invfact);
free(u);
return 0;
}