# Project Euler 813
# XOR-Powers — degrees of (1+x+x^3)^exp over GF(2); sum 2^d mod 1e9+7.
# exp = 8^12 * 12^8 = 2^52 * 6561; work in i128 for degree values.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1000000007
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 toggle(degs: ptr<i128>, n: ptr<i64>, val: i128) -> void {
let mut lo: i64 = 0
let mut hi: i64 = n[0]
while lo < hi {
let mid: i64 = (lo + hi) / 2
if degs[mid] < val {
lo = mid + 1
} else {
hi = mid
}
}
if lo < n[0] && degs[lo] == val {
let mut i: i64 = lo
while i + 1 < n[0] {
degs[i] = degs[i + 1]
i = i + 1
}
n[0] = n[0] - 1
} else {
let mut i: i64 = n[0]
while i > lo {
degs[i] = degs[i - 1]
i = i - 1
}
degs[lo] = val
n[0] = n[0] + 1
}
}
function solve() -> i64 {
# Bit values of exp = 6561 << 52
let bits: ptr<i128> = calloc(16, 16)
let mut bcount: i64 = 0
let mut coeff: i64 = 6561
let mut k: i64 = 0
while coeff > 0 {
if (coeff & 1) != 0 {
# 2^(52+k) as i128
let mut p: i128 = 1
let mut e: i64 = 0
while e < 52 + k {
p = p << 1
e = e + 1
}
bits[bcount] = p
bcount = bcount + 1
}
coeff = coeff >> 1
k = k + 1
}
let mut cap: i64 = 1
let mut i: i64 = 0
while i < bcount {
cap = cap * 3
i = i + 1
}
let degs: ptr<i128> = calloc(cap + 8, 16)
let mut n: i64 = 1
degs[0] = 0
i = 0
while i < bcount {
let bv: i128 = bits[i]
let newd: ptr<i128> = calloc(cap + 8, 16)
let mut nn: i64 = 0
let mut j: i64 = 0
while j < n {
let d0: i128 = degs[j]
toggle(newd, &nn, d0)
toggle(newd, &nn, d0 + bv)
toggle(newd, &nn, d0 + 3 * bv)
j = j + 1
}
j = 0
while j < nn {
degs[j] = newd[j]
j = j + 1
}
n = nn
free(newd)
i = i + 1
}
let mut ans: i64 = 0
i = 0
while i < n {
# 2^d mod MOD; reduce d mod (MOD-1)
let dmod: i64 = (degs[i] % ((MOD - 1) as i128)) as i64
if dmod < 0 {
# shouldn't happen for nonnegative degrees
}
ans = (ans + modpow(2, dmod, MOD)) % MOD
i = i + 1
}
free(bits)
free(degs)
return ans
}
function main() -> i32 {
printf("%lld\n", solve())
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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
void toggle_ptr_i128_ptr_i64_i128(__int128* degs, int64_t* n, __int128 val);
int64_t solve(void);
int32_t main(void);
static const int64_t MOD = 1000000007;
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;
}
void toggle_ptr_i128_ptr_i64_i128(__int128* degs, int64_t* n, __int128 val) {
int64_t lo = 0;
int64_t hi = n[0];
while (lo < hi) {
int64_t mid = FLOW_CHECKED_DIV(((lo + hi)), (2));
if (degs[mid] < val) {
lo = (mid + 1);
} else {
hi = mid;
}
}
if ((lo < n[0] && degs[lo] == val)) {
int64_t i = lo;
while ((i + 1) < n[0]) {
degs[i] = degs[(i + 1)];
i = (i + 1);
}
n[0] = (n[0] - 1);
} else {
int64_t i = n[0];
while (i > lo) {
degs[i] = degs[(i - 1)];
i = (i - 1);
}
degs[lo] = val;
n[0] = (n[0] + 1);
}
}
int64_t solve(void) {
__int128* bits = (__int128*)(calloc(16, 16));
int64_t bcount = 0;
int64_t coeff = 6561;
int64_t k = 0;
while (coeff > 0) {
if ((coeff & 1) != 0) {
__int128 p = 1;
int64_t e = 0;
while (e < (52 + k)) {
p = FLOW_CHECKED_SHL((p), (1));
e = (e + 1);
}
bits[bcount] = p;
bcount = (bcount + 1);
}
coeff = FLOW_CHECKED_SHR((coeff), (1));
k = (k + 1);
}
int64_t cap = 1;
int64_t i = 0;
while (i < bcount) {
cap = (cap * 3);
i = (i + 1);
}
__int128* degs = (__int128*)(calloc((cap + 8), 16));
int64_t n = 1;
degs[0] = 0;
i = 0;
while (i < bcount) {
__int128 bv = bits[i];
__int128* newd = (__int128*)(calloc((cap + 8), 16));
int64_t nn = 0;
int64_t j = 0;
while (j < n) {
__int128 d0 = degs[j];
toggle_ptr_i128_ptr_i64_i128(newd, (&(nn)), d0);
toggle_ptr_i128_ptr_i64_i128(newd, (&(nn)), (d0 + bv));
toggle_ptr_i128_ptr_i64_i128(newd, (&(nn)), (d0 + (3 * bv)));
j = (j + 1);
}
j = 0;
while (j < nn) {
degs[j] = newd[j];
j = (j + 1);
}
n = nn;
free(newd);
i = (i + 1);
}
int64_t ans = 0;
i = 0;
while (i < n) {
int64_t dmod = ((int64_t)(FLOW_CHECKED_MOD((degs[i]), (((__int128)((MOD - 1)))))));
if (dmod < 0) {
}
ans = FLOW_CHECKED_MOD(((ans + modpow_i64_i64_i64(2, dmod, MOD))), (MOD));
i = (i + 1);
}
free(bits);
free(degs);
return ans;
}
int32_t main(void) {
printf("%lld\n", solve());
return 0;
}