# Project Euler 258
# g_{10^18} mod 20092010 for lagged Fibonacci.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function mul_poly(a: ptr<i64>, b: ptr<i64>, out: ptr<i64>) -> void {
let MOD: i64 = 20092010
let D: i64 = 2000
let mut c: ptr<i64> = calloc(2 * D - 1, 8)
let mut i: i64 = 0
while i < D {
if a[i] != 0 {
let mut j: i64 = 0
while j < D {
if b[j] != 0 {
c[i + j] = c[i + j] + a[i] * b[j]
}
j = j + 1
}
}
i = i + 1
}
# fold x^D = x + 1
i = 0
while i < D {
out[i] = c[i] % MOD
i = i + 1
}
i = 0
while i < D - 1 {
let hi: i64 = c[D + i] % MOD
out[i] = (out[i] + hi) % MOD
out[i + 1] = (out[i + 1] + hi) % MOD
i = i + 1
}
# one more fold pass in case of carry into degree D
# after first fold, degrees stay < D; but sums may need another fold if we added to create overflow in sense of poly - actually max degree stays D-1
free(c)
}
function main() -> i32 {
let MOD: i64 = 20092010
let D: i64 = 2000
let n: i64 = 1000000000000000000
let a: ptr<i64> = calloc(D, 8)
let r: ptr<i64> = calloc(D, 8)
let tmp: ptr<i64> = calloc(D, 8)
if a == null || r == null || tmp == null { return 1 }
# a = x = [0,1,0,...]
a[1] = 1
# r = 1
r[0] = 1
let mut e: i64 = n
while e > 0 {
if e % 2 == 1 {
mul_poly(r, a, tmp)
let mut i: i64 = 0
while i < D {
r[i] = tmp[i]
i = i + 1
}
}
mul_poly(a, a, tmp)
let mut i: i64 = 0
while i < D {
a[i] = tmp[i]
i = i + 1
}
e = e / 2
}
# g_n = sum of coefficients (initial all 1s)
let mut sum: i64 = 0
let mut i: i64 = 0
while i < D {
sum = (sum + r[i]) % MOD
i = i + 1
}
printf("%lld\n", sum)
free(a); free(r); free(tmp)
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; }
void mul_poly_ptr_i64_ptr_i64_ptr_i64(int64_t* a, int64_t* b, int64_t* out);
int32_t main(void);
void mul_poly_ptr_i64_ptr_i64_ptr_i64(int64_t* a, int64_t* b, int64_t* out) {
int64_t MOD = 20092010;
int64_t D = 2000;
int64_t* c = (int64_t*)(calloc(((2 * D) - 1), 8));
int64_t i = 0;
while (i < D) {
if (a[i] != 0) {
int64_t j = 0;
while (j < D) {
if (b[j] != 0) {
c[(i + j)] = (c[(i + j)] + (a[i] * b[j]));
}
j = (j + 1);
}
}
i = (i + 1);
}
i = 0;
while (i < D) {
out[i] = FLOW_CHECKED_MOD((c[i]), (MOD));
i = (i + 1);
}
i = 0;
while (i < (D - 1)) {
int64_t hi = FLOW_CHECKED_MOD((c[(D + i)]), (MOD));
out[i] = FLOW_CHECKED_MOD(((out[i] + hi)), (MOD));
out[(i + 1)] = FLOW_CHECKED_MOD(((out[(i + 1)] + hi)), (MOD));
i = (i + 1);
}
free(c);
}
int32_t main(void) {
int64_t MOD = 20092010;
int64_t D = 2000;
int64_t n = 1000000000000000000;
int64_t* a = (int64_t*)(calloc(D, 8));
int64_t* r = (int64_t*)(calloc(D, 8));
int64_t* tmp = (int64_t*)(calloc(D, 8));
if (((a == NULL || r == NULL) || tmp == NULL)) {
return 1;
}
a[1] = 1;
r[0] = 1;
int64_t e = n;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
mul_poly_ptr_i64_ptr_i64_ptr_i64(r, a, tmp);
int64_t i = 0;
while (i < D) {
r[i] = tmp[i];
i = (i + 1);
}
}
mul_poly_ptr_i64_ptr_i64_ptr_i64(a, a, tmp);
int64_t i = 0;
while (i < D) {
a[i] = tmp[i];
i = (i + 1);
}
e = FLOW_CHECKED_DIV((e), (2));
}
int64_t sum = 0;
int64_t i = 0;
while (i < D) {
sum = FLOW_CHECKED_MOD(((sum + r[i])), (MOD));
i = (i + 1);
}
printf("%lld\n", sum);
free(a);
free(r);
free(tmp);
return 0;
}