# Project Euler 167
# Sum of U(2, 2n+1)_k for n=2..10, k=10^11.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function ulam_2_v_k(v: i64, k: i64) -> i64 {
if k == 1 { return 2 }
if k == 2 { return v }
let target_odd: i64 = k - 2
let m: i32 = (v + 1) as i32
let n: i32 = ((v - 1) / 2) as i32
let init_bits: ptr<i8> = calloc(m as i64, 1)
if init_bits == null { return 0 }
for t in n..(2 * n + 2) {
init_bits[t] = 1
}
let mut state: i64 = 0
for i in 0..m {
if init_bits[m - 1 - i] != 0 {
state = state | (1 << i)
}
}
let init_state: i64 = state
let mask: i64 = (1 << m) - 1
# Collect bits until period; max period for these v is modest
let max_bits: i64 = 5000000
let bits: ptr<i8> = calloc(max_bits, 1)
if bits == null { free(init_bits); return 0 }
for i in 0..m {
bits[i] = init_bits[i]
}
let mut period: i32 = 0
let mut len: i32 = m
while true {
let new_bit: i8 = ((state & 1) ^ ((state >> (m - 1)) & 1)) as i8
state = ((state << 1) & mask) | (new_bit as i64)
bits[len] = new_bit
len = len + 1
period = period + 1
if state == init_state { break }
if len as i64 >= max_bits { break }
}
# ones positions in one period of f[0..)
let ones: ptr<i32> = calloc(period as i64, 4)
if ones == null { free(bits); free(init_bits); return 0 }
let mut ones_count: i32 = 0
for i in 0..period {
if bits[i] != 0 {
ones[ones_count] = i
ones_count = ones_count + 1
}
}
let q: i64 = (target_odd - 1) / (ones_count as i64)
let r: i64 = (target_odd - 1) % (ones_count as i64)
let t_idx: i64 = q * (period as i64) + (ones[r] as i64)
let result: i64 = 2 * t_idx + 1
free(ones)
free(bits)
free(init_bits)
return result
}
function main() -> i32 {
let k: i64 = 100000000000
let mut ans: i64 = 0
for n in 2..11 {
ans = ans + ulam_2_v_k(2 * n + 1, k)
}
printf("%lld\n", ans)
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 ulam_2_v_k_i64_i64(int64_t v, int64_t k);
int32_t main(void);
int64_t ulam_2_v_k_i64_i64(int64_t v, int64_t k) {
if (k == 1) {
return 2;
}
if (k == 2) {
return v;
}
int64_t target_odd = (k - 2);
int32_t m = ((int32_t)((v + 1)));
int32_t n = ((int32_t)(FLOW_CHECKED_DIV(((v - 1)), (2))));
int8_t* init_bits = (int8_t*)(calloc(((int64_t)(m)), 1));
if (init_bits == NULL) {
return 0;
}
int32_t __flow_step_1 = 1;
for (int32_t t = n; (n <= ((2 * n) + 2)) ? t < ((2 * n) + 2) : t > ((2 * n) + 2); t += (n <= ((2 * n) + 2)) ? 1 : -1) {
init_bits[t] = 1;
}
int64_t state = 0;
int32_t __flow_step_2 = 1;
for (int32_t i = 0; (0 <= m) ? i < m : i > m; i += (0 <= m) ? 1 : -1) {
if (init_bits[((m - 1) - i)] != 0) {
state = (state | FLOW_CHECKED_SHL((1), (i)));
}
}
int64_t init_state = state;
int64_t mask = (FLOW_CHECKED_SHL((1), (m)) - 1);
int64_t max_bits = 5000000;
int8_t* bits = (int8_t*)(calloc(max_bits, 1));
if (bits == NULL) {
free(init_bits);
return 0;
}
int32_t __flow_step_3 = 1;
for (int32_t i = 0; (0 <= m) ? i < m : i > m; i += (0 <= m) ? 1 : -1) {
bits[i] = init_bits[i];
}
int32_t period = 0;
int32_t len = m;
while (1) {
int8_t new_bit = ((int8_t)(((state & 1) ^ (FLOW_CHECKED_SHR((state), ((m - 1))) & 1))));
state = ((FLOW_CHECKED_SHL((state), (1)) & mask) | ((int64_t)(new_bit)));
bits[len] = new_bit;
len = (len + 1);
period = (period + 1);
if (state == init_state) {
break;
}
if (((int64_t)(len)) >= max_bits) {
break;
}
}
int32_t* ones = (int32_t*)(calloc(((int64_t)(period)), 4));
if (ones == NULL) {
free(bits);
free(init_bits);
return 0;
}
int32_t ones_count = 0;
int32_t __flow_step_4 = 1;
for (int32_t i = 0; (0 <= period) ? i < period : i > period; i += (0 <= period) ? 1 : -1) {
if (bits[i] != 0) {
ones[ones_count] = i;
ones_count = (ones_count + 1);
}
}
int64_t q = FLOW_CHECKED_DIV(((target_odd - 1)), (((int64_t)(ones_count))));
int64_t r = FLOW_CHECKED_MOD(((target_odd - 1)), (((int64_t)(ones_count))));
int64_t t_idx = ((q * ((int64_t)(period))) + ((int64_t)(ones[r])));
int64_t result = ((2 * t_idx) + 1);
free(ones);
free(bits);
free(init_bits);
return result;
}
int32_t main(void) {
int64_t k = 100000000000;
int64_t ans = 0;
int32_t __flow_step_5 = 1;
for (int32_t n = 2; (2 <= 11) ? n < 11 : n > 11; n += (2 <= 11) ? 1 : -1) {
ans = (ans + ulam_2_v_k_i64_i64(((2 * n) + 1), k));
}
printf("%lld\n", ans);
return 0;
}