# Project Euler 984
# Closed-form even polynomial for f(10^18) mod 10^9+7.
const MOD: i64 = 1000000007
function modpow(base0: i64, exp0: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base0 % MOD
let mut e: i64 = exp0
while e > 0 {
if (e & 1) != 0 {
r = ((r as i128) * (b as i128) % (MOD as i128)) as i64
}
b = ((b as i128) * (b as i128) % (MOD as i128)) as i64
e = e >> 1
}
return r
}
function f_even_mod(n: i64) -> i64 {
let mut powers: [i64; 9]
powers[0] = 1
let x: i64 = n % MOD
let mut i: i64 = 1
while i <= 8 {
powers[i] = ((powers[i - 1] as i128) * (x as i128) % (MOD as i128)) as i64
i = i + 1
}
let mut total: i64 = (MOD - 419) % MOD
# (num, den, power)
let nums: [i64; 8] = [31, 31, 67, 41, 313, -5699, 16049, 29413]
let dens: [i64; 8] = [40320, 3360, 1440, 320, 1440, 240, 420, 140]
let pows: [i64; 8] = [8, 7, 6, 5, 4, 3, 2, 1]
i = 0
while i < 8 {
let inv: i64 = modpow(dens[i], MOD - 2)
let mut term: i64 = nums[i] % MOD
if term < 0 { term = term + MOD }
term = ((term as i128) * (powers[pows[i]] as i128) % (MOD as i128)) as i64
term = ((term as i128) * (inv as i128) % (MOD as i128)) as i64
total = (total + term) % MOD
i = i + 1
}
return total
}
function main() -> i32 {
printf("%lld\n", f_even_mod(1000000000000000000))
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 modpow_i64_i64(int64_t base0, int64_t exp0);
int64_t f_even_mod_i64(int64_t n);
int32_t main(void);
static const int64_t MOD = 1000000007;
int64_t modpow_i64_i64(int64_t base0, int64_t exp0) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base0), (MOD));
int64_t e = exp0;
while (e > 0) {
if ((e & 1) != 0) {
r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(MOD))))));
}
b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(MOD))))));
e = FLOW_CHECKED_SHR((e), (1));
}
return r;
}
int64_t f_even_mod_i64(int64_t n) {
int64_t powers[9];
powers[0] = 1;
int64_t x = FLOW_CHECKED_MOD((n), (MOD));
int64_t i = 1;
while (i <= 8) {
powers[i] = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)((((unsigned)((i - 1)) < 9) ? powers[(i - 1)] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)((i - 1)), 9), flow_fault_handler("array index out of bounds"), powers[0])))) * ((__int128)(x)))), (((__int128)(MOD))))));
i = (i + 1);
}
int64_t total = FLOW_CHECKED_MOD(((MOD - 419)), (MOD));
int64_t nums[8] = { 31, 31, 67, 41, 313, (-5699), 16049, 29413 };
int64_t dens[8] = { 40320, 3360, 1440, 320, 1440, 240, 420, 140 };
int64_t pows[8] = { 8, 7, 6, 5, 4, 3, 2, 1 };
i = 0;
while (i < 8) {
int64_t inv = modpow_i64_i64((((unsigned)(i) < 8) ? dens[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 8), flow_fault_handler("array index out of bounds"), dens[0])), (MOD - 2));
int64_t term = FLOW_CHECKED_MOD(((((unsigned)(i) < 8) ? nums[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 8), flow_fault_handler("array index out of bounds"), nums[0]))), (MOD));
if (term < 0) {
term = (term + MOD);
}
term = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(term)) * ((__int128)((((unsigned)((((unsigned)(i) < 8) ? pows[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 8), flow_fault_handler("array index out of bounds"), pows[0]))) < 9) ? powers[(((unsigned)(i) < 8) ? pows[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 8), flow_fault_handler("array index out of bounds"), pows[0]))] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)((((unsigned)(i) < 8) ? pows[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 8), flow_fault_handler("array index out of bounds"), pows[0]))), 9), flow_fault_handler("array index out of bounds"), powers[0])))))), (((__int128)(MOD))))));
term = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(term)) * ((__int128)(inv)))), (((__int128)(MOD))))));
total = FLOW_CHECKED_MOD(((total + term)), (MOD));
i = (i + 1);
}
return total;
}
int32_t main(void) {
printf("%lld\n", f_even_mod_i64(1000000000000000000));
return 0;
}