# Project Euler 745
# S(10^14)=sum g(n) mod 10^9+7 via squareful Dirichlet inversion.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function isqrt(n: i64) -> i64 {
if n <= 0 { return 0 }
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 main() -> i32 {
let N: i64 = 100000000000000
let mod: i64 = 1000000007
let sqrtN: i64 = isqrt(N)
let a: ptr<i64> = calloc(sqrtN + 1, 8)
if a == null { return 1 }
let mut i: i64 = sqrtN
while i >= 1 {
let mut s: i64 = N / (i * i)
let mut j: i64 = 2
while i * j <= sqrtN {
s = s - a[i * j]
j = j + 1
}
a[i] = s
i = i - 1
}
let mut total: i64 = 0
i = 1
while i <= sqrtN {
let term: i64 = ((i * i) % mod) * (a[i] % mod) % mod
total = (total + term) % mod
i = i + 1
}
printf("%lld\n", total)
free(a)
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);
int32_t main(void);
int64_t isqrt_i64(int64_t n) {
if (n <= 0) {
return 0;
}
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;
}
int32_t main(void) {
int64_t N = 100000000000000;
int64_t mod = 1000000007;
int64_t sqrtN = isqrt_i64(N);
int64_t* a = (int64_t*)(calloc((sqrtN + 1), 8));
if (a == NULL) {
return 1;
}
int64_t i = sqrtN;
while (i >= 1) {
int64_t s = FLOW_CHECKED_DIV((N), ((i * i)));
int64_t j = 2;
while ((i * j) <= sqrtN) {
s = (s - a[(i * j)]);
j = (j + 1);
}
a[i] = s;
i = (i - 1);
}
int64_t total = 0;
i = 1;
while (i <= sqrtN) {
int64_t term = FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((i * i)), (mod)) * FLOW_CHECKED_MOD((a[i]), (mod)))), (mod));
total = FLOW_CHECKED_MOD(((total + term)), (mod));
i = (i + 1);
}
printf("%lld\n", total);
free(a);
return 0;
}