# Project Euler 281
# Sum f(m,n) for f(m,n) <= 10^15.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function phi(n0: i64) -> i64 {
if n0 == 1 { return 1 }
let mut n: i64 = n0
let mut result: i64 = 1
let mut d: i64 = 2
while n > 1 {
let mut count: i64 = 0
while n % d == 0 {
count = count + 1
n = n / d
}
if count > 0 {
let mut p: i64 = 1
let mut i: i64 = 0
while i < count - 1 {
p = p * d
i = i + 1
}
result = result * p * (d - 1)
}
d = d + 1
if d * d > n {
if n > 1 {
result = result * (n - 1)
}
break
}
}
return result
}
function factorial(n: i64) -> i64 {
let mut r: i64 = 1
let mut i: i64 = 2
while i <= n {
r = r * i
i = i + 1
}
return r
}
function f_mn(m: i64, n: i64) -> i64 {
let mut total: i64 = 0
let mut d: i64 = 1
while d <= n {
if n % d == 0 {
# phi(n/d) * (m*d)! / (d!)^m
let ph: i64 = phi(n / d)
let mut num: i64 = factorial(m * d)
let den_one: i64 = factorial(d)
let mut den: i64 = 1
let mut i: i64 = 0
while i < m {
den = den * den_one
i = i + 1
}
total = total + ph * (num / den)
}
d = d + 1
}
return total / (m * n)
}
function main() -> i32 {
let limit: i64 = 1000000000000000
let mut total: i64 = 0
let mut m: i64 = 2
while m < 100 {
let mut n: i64 = 1
while n < 100 {
# avoid factorial overflow: m*d with d|n, m*n small enough
if m * n > 20 {
# factorials get huge; use careful multiplicative formula
break
}
let t: i64 = f_mn(m, n)
if t <= limit {
total = total + t
} else {
break
}
n = n + 1
}
m = m + 1
}
# Recompute properly with big-safe multiplicative binomial-style
# Restart with safer f
total = 0
m = 2
while m < 40 {
let mut n: i64 = 1
while n < 40 {
let mut s: i64 = 0
let mut d: i64 = 1
let mut overflow: bool = false
while d <= n {
if n % d == 0 {
let ph: i64 = phi(n / d)
# compute (m*d)! / (d!)^m multiplicatively
let mut val: i64 = 1
let md: i64 = m * d
# val = C(md, d) * C(md-d, d) * ... * C(d, d) = (md)!/(d!)^m
let mut take: i64 = 0
while take < m {
let start: i64 = take * d + 1
let end: i64 = (take + 1) * d
# multiply by C(end, d) wait: sequential
# Better: multiply (take*d+1)..(take*d+d) / 1..d
let mut num_i: i64 = 1
while num_i <= d {
# multiply (take*d + num_i) / num_i
# check overflow
let mul: i64 = take * d + num_i
if val > 2000000000000000000 / mul {
overflow = true
break
}
val = val * mul / num_i
num_i = num_i + 1
}
if overflow { break }
take = take + 1
}
if overflow { break }
if ph > 0 && val > 2000000000000000000 / ph {
overflow = true
break
}
s = s + ph * val
}
d = d + 1
}
if overflow { break }
let t: i64 = s / (m * n)
if t <= 0 { break }
if t <= limit {
total = total + t
} else {
break
}
n = n + 1
}
m = m + 1
}
printf("%lld\n", total)
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 phi_i64(int64_t n0);
int64_t factorial_i64(int64_t n);
int64_t f_mn_i64_i64(int64_t m, int64_t n);
int32_t main(void);
int64_t phi_i64(int64_t n0) {
if (n0 == 1) {
return 1;
}
int64_t n = n0;
int64_t result = 1;
int64_t d = 2;
while (n > 1) {
int64_t count = 0;
while (FLOW_CHECKED_MOD((n), (d)) == 0) {
count = (count + 1);
n = FLOW_CHECKED_DIV((n), (d));
}
if (count > 0) {
int64_t p = 1;
int64_t i = 0;
while (i < (count - 1)) {
p = (p * d);
i = (i + 1);
}
result = ((result * p) * (d - 1));
}
d = (d + 1);
if ((d * d) > n) {
if (n > 1) {
result = (result * (n - 1));
}
break;
}
}
return result;
}
int64_t factorial_i64(int64_t n) {
int64_t r = 1;
int64_t i = 2;
while (i <= n) {
r = (r * i);
i = (i + 1);
}
return r;
}
int64_t f_mn_i64_i64(int64_t m, int64_t n) {
int64_t total = 0;
int64_t d = 1;
while (d <= n) {
if (FLOW_CHECKED_MOD((n), (d)) == 0) {
int64_t ph = phi_i64(FLOW_CHECKED_DIV((n), (d)));
int64_t num = factorial_i64((m * d));
int64_t den_one = factorial_i64(d);
int64_t den = 1;
int64_t i = 0;
while (i < m) {
den = (den * den_one);
i = (i + 1);
}
total = (total + (ph * FLOW_CHECKED_DIV((num), (den))));
}
d = (d + 1);
}
return FLOW_CHECKED_DIV((total), ((m * n)));
}
int32_t main(void) {
int64_t limit = 1000000000000000;
int64_t total = 0;
int64_t m = 2;
while (m < 100) {
int64_t n = 1;
while (n < 100) {
if ((m * n) > 20) {
break;
}
int64_t t = f_mn_i64_i64(m, n);
if (t <= limit) {
total = (total + t);
} else {
break;
}
n = (n + 1);
}
m = (m + 1);
}
total = 0;
m = 2;
while (m < 40) {
int64_t n = 1;
while (n < 40) {
int64_t s = 0;
int64_t d = 1;
bool overflow = 0;
while (d <= n) {
if (FLOW_CHECKED_MOD((n), (d)) == 0) {
int64_t ph = phi_i64(FLOW_CHECKED_DIV((n), (d)));
int64_t val = 1;
int64_t md = (m * d);
int64_t take = 0;
while (take < m) {
int64_t start = ((take * d) + 1);
int64_t end = ((take + 1) * d);
int64_t num_i = 1;
while (num_i <= d) {
int64_t mul = ((take * d) + num_i);
if (val > FLOW_CHECKED_DIV((2000000000000000000), (mul))) {
overflow = 1;
break;
}
val = FLOW_CHECKED_DIV(((val * mul)), (num_i));
num_i = (num_i + 1);
}
if (overflow) {
break;
}
take = (take + 1);
}
if (overflow) {
break;
}
if ((ph > 0 && val > FLOW_CHECKED_DIV((2000000000000000000), (ph)))) {
overflow = 1;
break;
}
s = (s + (ph * val));
}
d = (d + 1);
}
if (overflow) {
break;
}
int64_t t = FLOW_CHECKED_DIV((s), ((m * n)));
if (t <= 0) {
break;
}
if (t <= limit) {
total = (total + t);
} else {
break;
}
n = (n + 1);
}
m = (m + 1);
}
printf("%lld\n", total);
return 0;
}