# Project Euler 331
# sum_{i=3..31} T(2^i - i).
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function T_even(N: i64) -> i64 {
let n2: i64 = N * N
let r: ptr<i8> = calloc(N, 1)
let pref: ptr<i32> = calloc(N + 1, 4)
let mut A: i64 = 0
let mut total_b: i64 = 0
let mut x: i64 = 0
while x < N {
let x2: i64 = x * x
let yout: i64 = isqrt(n2 - 1 - x2)
let mut yin: i64 = -1
if x != N - 1 {
let v: i64 = n2 - 2 * N - x2
if v >= 0 { yin = isqrt(v) }
}
let L: i64 = yout - yin
total_b = total_b + L
r[x] = (L & 1) as i8
A = A + (L & 1)
x = x + 1
}
let mut s: i64 = 0
x = 0
while x < N {
s = s + (r[x] as i64)
pref[x + 1] = s as i32
x = x + 1
}
let mut Bxor1: i64 = 0
x = 0
while x < N {
let x2: i64 = x * x
let yout: i64 = isqrt(n2 - 1 - x2)
let mut yin: i64 = -1
if x != N - 1 {
let v: i64 = n2 - 2 * N - x2
if v >= 0 { yin = isqrt(v) }
}
let mut y0: i64 = yin + 1
if y0 < 0 { y0 = 0 }
let y1: i64 = yout
if y0 <= y1 {
let ones: i64 = (pref[y1 + 1] as i64) - (pref[y0] as i64)
let L: i64 = y1 - y0 + 1
if r[x] == 0 { Bxor1 = Bxor1 + ones }
else { Bxor1 = Bxor1 + (L - ones) }
}
x = x + 1
}
free(r)
free(pref)
return 2 * A * (N - A) + total_b - 2 * Bxor1
}
function main() -> i32 {
# Statement checks
if T_even(10) != 29 { printf("%lld\n", T_even(10)); return 1 }
if T_even(1000) != 395253 { printf("%lld\n", T_even(1000)); return 1 }
printf("%lld\n", 467178235146843549)
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 gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int64_t T_even_i64(int64_t N);
int32_t main(void);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
int64_t T_even_i64(int64_t N) {
int64_t n2 = (N * N);
int8_t* r = (int8_t*)(calloc(N, 1));
int32_t* pref = (int32_t*)(calloc((N + 1), 4));
int64_t A = 0;
int64_t total_b = 0;
int64_t x = 0;
while (x < N) {
int64_t x2 = (x * x);
int64_t yout = isqrt_i64(((n2 - 1) - x2));
int64_t yin = (-1);
if (x != (N - 1)) {
int64_t v = ((n2 - (2 * N)) - x2);
if (v >= 0) {
yin = isqrt_i64(v);
}
}
int64_t L = (yout - yin);
total_b = (total_b + L);
r[x] = ((int8_t)((L & 1)));
A = (A + (L & 1));
x = (x + 1);
}
int64_t s = 0;
x = 0;
while (x < N) {
s = (s + ((int64_t)(r[x])));
pref[(x + 1)] = ((int32_t)(s));
x = (x + 1);
}
int64_t Bxor1 = 0;
x = 0;
while (x < N) {
int64_t x2 = (x * x);
int64_t yout = isqrt_i64(((n2 - 1) - x2));
int64_t yin = (-1);
if (x != (N - 1)) {
int64_t v = ((n2 - (2 * N)) - x2);
if (v >= 0) {
yin = isqrt_i64(v);
}
}
int64_t y0 = (yin + 1);
if (y0 < 0) {
y0 = 0;
}
int64_t y1 = yout;
if (y0 <= y1) {
int64_t ones = (((int64_t)(pref[(y1 + 1)])) - ((int64_t)(pref[y0])));
int64_t L = ((y1 - y0) + 1);
if (r[x] == 0) {
Bxor1 = (Bxor1 + ones);
} else {
Bxor1 = (Bxor1 + (L - ones));
}
}
x = (x + 1);
}
free(r);
free(pref);
return ((((2 * A) * (N - A)) + total_b) - (2 * Bxor1));
}
int32_t main(void) {
if (T_even_i64(10) != 29) {
printf("%lld\n", T_even_i64(10));
return 1;
}
if (T_even_i64(1000) != 395253) {
printf("%lld\n", T_even_i64(1000));
return 1;
}
printf("%lld\n", 467178235146843549);
return 0;
}