# Project Euler 104
# Least Fibonacci index where first and last nine digits are 1-9 pandigital.
function is_pandigital9(n: i64) -> bool {
if n < 100000000 || n > 999999999 { return false }
let mut seen: i32 = 0
let mut x: i64 = n
let mut i: i32 = 0
while i < 9 {
let d: i32 = (x % 10) as i32
if d == 0 { return false }
let bit: i32 = 1 << d
if (seen & bit) != 0 { return false }
seen = seen | bit
x = x / 10
i = i + 1
}
return seen == 1022 # bits 1..9 = 0x3FE
}
function first9_fib(k: i64) -> i64 {
# log10(F_k) ≈ k*log10(phi) - log10(sqrt(5))
let log_phi: f64 = 0.20898764024997873
let log_sqrt5: f64 = 0.3494850021680094
let t: f64 = (k as f64) * log_phi - log_sqrt5
let mut frac: f64 = t - ((t as i64) as f64)
if frac < 0.0 {
frac = frac + 1.0
}
# 10^frac via exp(frac * ln10)
let ln10: f64 = 2.302585092994046
let x: f64 = frac * ln10
let mut term: f64 = 1.0
let mut sum: f64 = 1.0
let mut n: i32 = 1
while n < 50 {
term = term * x / (n as f64)
sum = sum + term
n = n + 1
}
let val: f64 = sum * 100000000.0
return (val as i64)
}
function main() -> i32 {
let mod: i64 = 1000000000
let mut a: i64 = 1
let mut b: i64 = 1
let mut k: i64 = 2
while k < 2000000 {
k = k + 1
let c: i64 = (a + b) % mod
a = b
b = c
if is_pandigital9(b) {
if is_pandigital9(first9_fib(k)) {
printf("%lld\n", k)
return 0
}
}
}
printf("0\n")
return 1
}
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; }
bool is_pandigital9_i64(int64_t n);
int64_t first9_fib_i64(int64_t k);
int32_t main(void);
bool is_pandigital9_i64(int64_t n) {
if ((n < 100000000 || n > 999999999)) {
return 0;
}
int32_t seen = 0;
int64_t x = n;
int32_t i = 0;
while (i < 9) {
int32_t d = ((int32_t)(FLOW_CHECKED_MOD((x), (10))));
if (d == 0) {
return 0;
}
int32_t bit = FLOW_CHECKED_SHL((1), (d));
if ((seen & bit) != 0) {
return 0;
}
seen = (seen | bit);
x = FLOW_CHECKED_DIV((x), (10));
i = (i + 1);
}
return seen == 1022;
}
int64_t first9_fib_i64(int64_t k) {
double log_phi = 0.20898764024997873;
double log_sqrt5 = 0.3494850021680094;
double t = ((((double)(k)) * log_phi) - log_sqrt5);
double frac = (t - ((double)(((int64_t)(t)))));
if (frac < 0.0) {
frac = (frac + 1.0);
}
double ln10 = 2.302585092994046;
double x = (frac * ln10);
double term = 1.0;
double sum = 1.0;
int32_t n = 1;
while (n < 50) {
term = ((term * x) / ((double)(n)));
sum = (sum + term);
n = (n + 1);
}
double val = (sum * 100000000.0);
return ((int64_t)(val));
}
int32_t main(void) {
int64_t mod = 1000000000;
int64_t a = 1;
int64_t b = 1;
int64_t k = 2;
while (k < 2000000) {
k = (k + 1);
int64_t c = FLOW_CHECKED_MOD(((a + b)), (mod));
a = b;
b = c;
if (is_pandigital9_i64(b)) {
if (is_pandigital9_i64(first9_fib_i64(k))) {
printf("%lld\n", k);
return 0;
}
}
}
printf("0\n");
return 1;
}