# Project Euler 366
# Stone Game III / Fibonacci Nim: sum M(n) for n≤10^18 mod 10^8.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function mulmod(a: i64, b: i64, mod: i64) -> i64 {
let mut x: i64 = a % mod
if x < 0 { x = x + mod }
let mut y: i64 = b % mod
if y < 0 { y = y + mod }
let mut res: i64 = 0
while y > 0 {
if y % 2 == 1 {
res = res + x
if res >= mod { res = res - mod }
}
x = x + x
if x >= mod { x = x - mod }
y = y / 2
}
return res
}
function half_product(a: i64, b: i64, mod: i64) -> i64 {
# (a * b / 2) % mod, assuming a*b is even. mod = 10^8 even, no inv(2).
if a % 2 == 0 {
return mulmod(a / 2, b, mod)
}
return mulmod(a, b / 2, mod)
}
function main() -> i32 {
let MOD: i64 = 100000000
let TARGET: i64 = 1000000000000000000
let fib: ptr<i64> = calloc(200, 8)
if fib == null { return 1 }
fib[1] = 1
fib[2] = 2
let mut flen: i64 = 3
while true {
let nxt: i64 = fib[flen - 1] + fib[flen - 2]
fib[flen] = nxt
flen = flen + 1
if nxt > TARGET { break }
}
let mut total: i64 = 0
let mut i: i64 = 1
while i < flen - 1 {
let Fi: i64 = fib[i]
if Fi > TARGET { break }
let mut max_k: i64 = fib[i + 1] - 1
if max_k > TARGET { max_k = TARGET }
let mut max_m0: i64 = max_k - Fi
if max_m0 > 0 && i - 1 >= 1 {
if max_m0 > fib[i - 1] - 1 { max_m0 = fib[i - 1] - 1 }
if max_m0 > 0 {
let mut S: i64 = 0
let mut LB: i64 = 1
let mut j: i64 = 0
while true {
let idx: i64 = i - 2 * j
if idx < 1 { break }
let mut U: i64 = S + (fib[idx] - 1) / 2
if U > max_m0 { U = max_m0 }
if LB <= U {
let cnt: i64 = U - LB + 1
let sum_m: i64 = half_product(LB + U, cnt, MOD)
let sub: i64 = mulmod(cnt, S, MOD)
total = total + sum_m - sub
total = total % MOD
if total < 0 { total = total + MOD }
}
if idx - 2 < 1 { break }
let need: i64 = S + (fib[idx] + 1) / 2
if need > LB { LB = need }
S = S + fib[idx - 2]
j = j + 1
if LB > max_m0 { break }
}
}
}
i = i + 1
}
printf("%lld\n", total % MOD)
free(fib)
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 mulmod_i64_i64_i64(int64_t a, int64_t b, int64_t mod);
int64_t half_product_i64_i64_i64(int64_t a, int64_t b, int64_t mod);
int32_t main(void);
int64_t mulmod_i64_i64_i64(int64_t a, int64_t b, int64_t mod) {
int64_t x = FLOW_CHECKED_MOD((a), (mod));
if (x < 0) {
x = (x + mod);
}
int64_t y = FLOW_CHECKED_MOD((b), (mod));
if (y < 0) {
y = (y + mod);
}
int64_t res = 0;
while (y > 0) {
if (FLOW_CHECKED_MOD((y), (2)) == 1) {
res = (res + x);
if (res >= mod) {
res = (res - mod);
}
}
x = (x + x);
if (x >= mod) {
x = (x - mod);
}
y = FLOW_CHECKED_DIV((y), (2));
}
return res;
}
int64_t half_product_i64_i64_i64(int64_t a, int64_t b, int64_t mod) {
if (FLOW_CHECKED_MOD((a), (2)) == 0) {
return mulmod_i64_i64_i64(FLOW_CHECKED_DIV((a), (2)), b, mod);
}
return mulmod_i64_i64_i64(a, FLOW_CHECKED_DIV((b), (2)), mod);
}
int32_t main(void) {
int64_t MOD = 100000000;
int64_t TARGET = 1000000000000000000;
int64_t* fib = (int64_t*)(calloc(200, 8));
if (fib == NULL) {
return 1;
}
fib[1] = 1;
fib[2] = 2;
int64_t flen = 3;
while (1) {
int64_t nxt = (fib[(flen - 1)] + fib[(flen - 2)]);
fib[flen] = nxt;
flen = (flen + 1);
if (nxt > TARGET) {
break;
}
}
int64_t total = 0;
int64_t i = 1;
while (i < (flen - 1)) {
int64_t Fi = fib[i];
if (Fi > TARGET) {
break;
}
int64_t max_k = (fib[(i + 1)] - 1);
if (max_k > TARGET) {
max_k = TARGET;
}
int64_t max_m0 = (max_k - Fi);
if ((max_m0 > 0 && (i - 1) >= 1)) {
if (max_m0 > (fib[(i - 1)] - 1)) {
max_m0 = (fib[(i - 1)] - 1);
}
if (max_m0 > 0) {
int64_t S = 0;
int64_t LB = 1;
int64_t j = 0;
while (1) {
int64_t idx = (i - (2 * j));
if (idx < 1) {
break;
}
int64_t U = (S + FLOW_CHECKED_DIV(((fib[idx] - 1)), (2)));
if (U > max_m0) {
U = max_m0;
}
if (LB <= U) {
int64_t cnt = ((U - LB) + 1);
int64_t sum_m = half_product_i64_i64_i64((LB + U), cnt, MOD);
int64_t sub = mulmod_i64_i64_i64(cnt, S, MOD);
total = ((total + sum_m) - sub);
total = FLOW_CHECKED_MOD((total), (MOD));
if (total < 0) {
total = (total + MOD);
}
}
if ((idx - 2) < 1) {
break;
}
int64_t need = (S + FLOW_CHECKED_DIV(((fib[idx] + 1)), (2)));
if (need > LB) {
LB = need;
}
S = (S + fib[(idx - 2)]);
j = (j + 1);
if (LB > max_m0) {
break;
}
}
}
}
i = (i + 1);
}
printf("%lld\n", FLOW_CHECKED_MOD((total), (MOD)));
free(fib);
return 0;
}