# Project Euler 308
# FRACTRAN PRIMEGAME steps until 2^(p_10001).
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function sum_floor_range(n: i64, lo: i64, hi: i64) -> i64 {
let mut s: i64 = 0
let mut d: i64 = lo
while d <= hi {
let q: i64 = n / d
let mut dmax: i64 = n / q
if dmax > hi { dmax = hi }
s = s + q * (dmax - d + 1)
d = dmax + 1
}
return s
}
function main() -> i32 {
# 10001st prime via sieve
let limit: i64 = 120000
let is_prime: ptr<i8> = calloc(limit + 1, 1)
let mut i: i64 = 0
while i <= limit {
is_prime[i] = 1
i = i + 1
}
is_prime[0] = 0
is_prime[1] = 0
i = 2
while i * i <= limit {
if is_prime[i] == 1 {
let mut j: i64 = i * i
while j <= limit {
is_prime[j] = 0
j = j + i
}
}
i = i + 1
}
let mut count: i64 = 0
let mut p: i64 = 0
i = 2
while i <= limit {
if is_prime[i] == 1 {
count = count + 1
if count == 10001 {
p = i
break
}
}
i = i + 1
}
let spf: ptr<i32> = calloc(p + 1, 4)
i = 0
while i <= p {
spf[i] = i as i32
i = i + 1
}
i = 2
while i * i <= p {
if spf[i] == i as i32 {
let mut j: i64 = i * i
while j <= p {
if spf[j] == j as i32 {
spf[j] = i as i32
}
j = j + i
}
}
i = i + 1
}
let mut steps: i64 = 0
let mut prev_b: i64 = 0
let mut N: i64 = 2
while N <= p {
let mut bN: i64 = 1
if N >= 2 {
let s: i64 = spf[N] as i64
if s != N {
bN = N / s
} else {
bN = 1
}
}
let extra: i64 = 0
if N != 2 {
extra = prev_b - 1
}
let sfloor: i64 = sum_floor_range(N, bN, N - 1)
let cost: i64 = (N - 1) + (6 * N + 2) * (N - bN) + 2 * sfloor + extra
steps = steps + cost
prev_b = bN
N = N + 1
}
printf("%lld\n", steps)
free(is_prime)
free(spf)
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 sum_floor_range_i64_i64_i64(int64_t n, int64_t lo, int64_t hi);
int32_t main(void);
int64_t sum_floor_range_i64_i64_i64(int64_t n, int64_t lo, int64_t hi) {
int64_t s = 0;
int64_t d = lo;
while (d <= hi) {
int64_t q = FLOW_CHECKED_DIV((n), (d));
int64_t dmax = FLOW_CHECKED_DIV((n), (q));
if (dmax > hi) {
dmax = hi;
}
s = (s + (q * ((dmax - d) + 1)));
d = (dmax + 1);
}
return s;
}
int32_t main(void) {
int64_t limit = 120000;
int8_t* is_prime = (int8_t*)(calloc((limit + 1), 1));
int64_t i = 0;
while (i <= limit) {
is_prime[i] = 1;
i = (i + 1);
}
is_prime[0] = 0;
is_prime[1] = 0;
i = 2;
while ((i * i) <= limit) {
if (is_prime[i] == 1) {
int64_t j = (i * i);
while (j <= limit) {
is_prime[j] = 0;
j = (j + i);
}
}
i = (i + 1);
}
int64_t count = 0;
int64_t p = 0;
i = 2;
while (i <= limit) {
if (is_prime[i] == 1) {
count = (count + 1);
if (count == 10001) {
p = i;
break;
}
}
i = (i + 1);
}
int32_t* spf = (int32_t*)(calloc((p + 1), 4));
i = 0;
while (i <= p) {
spf[i] = ((int32_t)(i));
i = (i + 1);
}
i = 2;
while ((i * i) <= p) {
if (spf[i] == ((int32_t)(i))) {
int64_t j = (i * i);
while (j <= p) {
if (spf[j] == ((int32_t)(j))) {
spf[j] = ((int32_t)(i));
}
j = (j + i);
}
}
i = (i + 1);
}
int64_t steps = 0;
int64_t prev_b = 0;
int64_t N = 2;
while (N <= p) {
int64_t bN = 1;
if (N >= 2) {
int64_t s = ((int64_t)(spf[N]));
if (s != N) {
bN = FLOW_CHECKED_DIV((N), (s));
} else {
bN = 1;
}
}
int64_t extra = 0;
if (N != 2) {
extra = (prev_b - 1);
}
int64_t sfloor = sum_floor_range_i64_i64_i64(N, bN, (N - 1));
int64_t cost = ((((N - 1) + (((6 * N) + 2) * (N - bN))) + (2 * sfloor)) + extra);
steps = (steps + cost);
prev_b = bN;
N = (N + 1);
}
printf("%lld\n", steps);
free(is_prime);
free(spf);
return 0;
}