# Project Euler 101
# Sum of FITs for the degree-10 generating function u_n = 1 - n + n^2 - ... + n^10.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function u(n: i64) -> i64 {
# sum_{k=0}^{10} (-n)^k
let mut term: i64 = 1
let mut s: i64 = 0
let mut k: i64 = 0
while k <= 10 {
s = s + term
term = term * (-n)
k = k + 1
}
return s
}
# Lagrange interpolation of first k terms, evaluated at x = k+1.
function fit(k: i32, ys: ptr<i64>) -> i64 {
let x: i64 = (k + 1) as i64
let mut res: i64 = 0
let mut i: i32 = 0
while i < k {
let mut num: i64 = 1
let mut den: i64 = 1
let mut j: i32 = 0
while j < k {
if i != j {
num = num * (x - ((j + 1) as i64))
den = den * (((i + 1) as i64) - ((j + 1) as i64))
}
j = j + 1
}
res = res + ys[i] * num / den
i = i + 1
}
return res
}
function main() -> i32 {
let ys: ptr<i64> = calloc(11, 8)
if ys == null { return 1 }
let mut n: i64 = 1
while n <= 10 {
ys[n - 1] = u(n)
n = n + 1
}
let mut total: i64 = 0
let mut k: i32 = 1
while k <= 10 {
total = total + fit(k, ys)
k = k + 1
}
printf("%lld\n", total)
free(ys)
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 u_i64(int64_t n);
int64_t fit_i32_ptr_i64(int32_t k, int64_t* ys);
int32_t main(void);
int64_t u_i64(int64_t n) {
int64_t term = 1;
int64_t s = 0;
int64_t k = 0;
while (k <= 10) {
s = (s + term);
term = (term * (-n));
k = (k + 1);
}
return s;
}
int64_t fit_i32_ptr_i64(int32_t k, int64_t* ys) {
int64_t x = ((int64_t)((k + 1)));
int64_t res = 0;
int32_t i = 0;
while (i < k) {
int64_t num = 1;
int64_t den = 1;
int32_t j = 0;
while (j < k) {
if (i != j) {
num = (num * (x - ((int64_t)((j + 1)))));
den = (den * (((int64_t)((i + 1))) - ((int64_t)((j + 1)))));
}
j = (j + 1);
}
res = (res + FLOW_CHECKED_DIV(((ys[i] * num)), (den)));
i = (i + 1);
}
return res;
}
int32_t main(void) {
int64_t* ys = (int64_t*)(calloc(11, 8));
if (ys == NULL) {
return 1;
}
int64_t n = 1;
while (n <= 10) {
ys[(n - 1)] = u_i64(n);
n = (n + 1);
}
int64_t total = 0;
int32_t k = 1;
while (k <= 10) {
total = (total + fit_i32_ptr_i64(k, ys));
k = (k + 1);
}
printf("%lld\n", total);
free(ys);
return 0;
}