# Project Euler 878
# XOR-Equation B — count orbits with invariant <= 1e6 and b <= 1e17.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function clmul(x0: i64, y0: i64) -> i64 {
let mut x: i64 = x0
let mut y: i64 = y0
if x == 0 || y == 0 { return 0 }
let mut bx: i64 = 0
let mut by: i64 = 0
let mut t: i64 = x
while t > 0 {
bx = bx + (t & 1)
t = t >> 1
}
t = y
while t > 0 {
by = by + (t & 1)
t = t >> 1
}
if bx < by {
let tmp: i64 = x
x = y
y = tmp
}
let mut result: i64 = 0
while y != 0 {
let bit: i64 = y & -y
let mut sh: i64 = 0
let mut b: i64 = bit
while b > 1 {
b = b >> 1
sh = sh + 1
}
result = result ^ (x << sh)
y = y ^ bit
}
return result
}
function count_forward(a0: i64, b0: i64, limit: i64) -> i64 {
let mut a: i64 = a0
let mut b: i64 = b0
let mut total: i64 = 0
while b <= limit {
total = total + 1
let na: i64 = b
let nb: i64 = a ^ (b << 1)
a = na
b = nb
}
return total
}
function G(limit: i64, max_value: i64) -> i64 {
if max_value == 0 { return 1 }
let mut bl: i64 = 0
let mut mv: i64 = max_value
while mv > 0 {
bl = bl + 1
mv = mv >> 1
}
let seed_limit: i64 = 1 << ((bl + 2) / 2)
let squares: ptr<i64> = calloc(seed_limit, 8)
let mut x: i64 = 0
while x < seed_limit {
squares[x] = clmul(x, x)
x = x + 1
}
let mut total: i64 = 1
let mut a: i64 = 0
while a < seed_limit {
let square_a: i64 = squares[a]
let mut b: i64 = a
if b < 1 { b = 1 }
while b < seed_limit {
let invariant: i64 = square_a ^ squares[b] ^ (clmul(a, b) << 1)
if invariant <= max_value {
if (b ^ (a << 1)) > a {
total = total + count_forward(a, b, limit)
}
}
b = b + 1
}
a = a + 1
}
free(squares)
return total
}
function main() -> i32 {
printf("%lld\n", G(100000000000000000, 1000000))
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 clmul_i64_i64(int64_t x0, int64_t y0);
int64_t count_forward_i64_i64_i64(int64_t a0, int64_t b0, int64_t limit);
int64_t G_i64_i64(int64_t limit, int64_t max_value);
int32_t main(void);
int64_t clmul_i64_i64(int64_t x0, int64_t y0) {
int64_t x = x0;
int64_t y = y0;
if ((x == 0 || y == 0)) {
return 0;
}
int64_t bx = 0;
int64_t by = 0;
int64_t t = x;
while (t > 0) {
bx = (bx + (t & 1));
t = FLOW_CHECKED_SHR((t), (1));
}
t = y;
while (t > 0) {
by = (by + (t & 1));
t = FLOW_CHECKED_SHR((t), (1));
}
if (bx < by) {
int64_t tmp = x;
x = y;
y = tmp;
}
int64_t result = 0;
while (y != 0) {
int64_t bit = (y & (-y));
int64_t sh = 0;
int64_t b = bit;
while (b > 1) {
b = FLOW_CHECKED_SHR((b), (1));
sh = (sh + 1);
}
result = (result ^ FLOW_CHECKED_SHL((x), (sh)));
y = (y ^ bit);
}
return result;
}
int64_t count_forward_i64_i64_i64(int64_t a0, int64_t b0, int64_t limit) {
int64_t a = a0;
int64_t b = b0;
int64_t total = 0;
while (b <= limit) {
total = (total + 1);
int64_t na = b;
int64_t nb = (a ^ FLOW_CHECKED_SHL((b), (1)));
a = na;
b = nb;
}
return total;
}
int64_t G_i64_i64(int64_t limit, int64_t max_value) {
if (max_value == 0) {
return 1;
}
int64_t bl = 0;
int64_t mv = max_value;
while (mv > 0) {
bl = (bl + 1);
mv = FLOW_CHECKED_SHR((mv), (1));
}
int64_t seed_limit = FLOW_CHECKED_SHL((1), (FLOW_CHECKED_DIV(((bl + 2)), (2))));
int64_t* squares = (int64_t*)(calloc(seed_limit, 8));
int64_t x = 0;
while (x < seed_limit) {
squares[x] = clmul_i64_i64(x, x);
x = (x + 1);
}
int64_t total = 1;
int64_t a = 0;
while (a < seed_limit) {
int64_t square_a = squares[a];
int64_t b = a;
if (b < 1) {
b = 1;
}
while (b < seed_limit) {
int64_t invariant = ((square_a ^ squares[b]) ^ FLOW_CHECKED_SHL((clmul_i64_i64(a, b)), (1)));
if (invariant <= max_value) {
if ((b ^ FLOW_CHECKED_SHL((a), (1))) > a) {
total = (total + count_forward_i64_i64_i64(a, b, limit));
}
}
b = (b + 1);
}
a = (a + 1);
}
free(squares);
return total;
}
int32_t main(void) {
printf("%lld\n", G_i64_i64(100000000000000000, 1000000));
return 0;
}