# Project Euler 127
# Sum of c for abc-hits with c < 120000.
import euler.nt { gcd }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function main() -> i32 {
let limit: i64 = 120000
let rad: ptr<i64> = calloc(limit, 8)
if rad == null { return 1 }
let mut i: i64 = 0
while i < limit {
rad[i] = 1
i = i + 1
}
i = 2
while i < limit {
if rad[i] == 1 {
let mut j: i64 = i
while j < limit {
rad[j] = rad[j] * i
j = j + i
}
}
i = i + 1
}
# pairs (rad, n) sorted by rad via counting into buckets is heavy;
# collect indices 1..limit-1 and sort by rad (insertion on small groups / shell)
let idx: ptr<i64> = calloc(limit, 8)
if idx == null { free(rad); return 1 }
let mut m: i64 = 0
i = 1
while i < limit {
idx[m] = i
m = m + 1
i = i + 1
}
# shell sort by rad[idx[k]]
let mut gap: i64 = m / 2
while gap > 0 {
let mut k: i64 = gap
while k < m {
let v: i64 = idx[k]
let mut j: i64 = k
while j >= gap && rad[idx[j - gap]] > rad[v] {
idx[j] = idx[j - gap]
j = j - gap
}
idx[j] = v
k = k + 1
}
gap = gap / 2
}
let mut total: i64 = 0
let mut c: i64 = 3
while c < limit {
let radc: i64 = rad[c]
let cutoff: i64 = c / radc
let mut t: i64 = 0
while t < m {
let a: i64 = idx[t]
let rada: i64 = rad[a]
if rada >= cutoff { break }
if 2 * a < c {
let b: i64 = c - a
if rada * rad[b] * radc < c && gcd(rada, rad[b]) == 1 {
total = total + c
}
}
t = t + 1
}
c = c + 1
}
printf("%lld\n", total)
free(idx)
free(rad)
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 gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int32_t main(void);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
int32_t main(void) {
int64_t limit = 120000;
int64_t* rad = (int64_t*)(calloc(limit, 8));
if (rad == NULL) {
return 1;
}
int64_t i = 0;
while (i < limit) {
rad[i] = 1;
i = (i + 1);
}
i = 2;
while (i < limit) {
if (rad[i] == 1) {
int64_t j = i;
while (j < limit) {
rad[j] = (rad[j] * i);
j = (j + i);
}
}
i = (i + 1);
}
int64_t* idx = (int64_t*)(calloc(limit, 8));
if (idx == NULL) {
free(rad);
return 1;
}
int64_t m = 0;
i = 1;
while (i < limit) {
idx[m] = i;
m = (m + 1);
i = (i + 1);
}
int64_t gap = FLOW_CHECKED_DIV((m), (2));
while (gap > 0) {
int64_t k = gap;
while (k < m) {
int64_t v = idx[k];
int64_t j = k;
while ((j >= gap && rad[idx[(j - gap)]] > rad[v])) {
idx[j] = idx[(j - gap)];
j = (j - gap);
}
idx[j] = v;
k = (k + 1);
}
gap = FLOW_CHECKED_DIV((gap), (2));
}
int64_t total = 0;
int64_t c = 3;
while (c < limit) {
int64_t radc = rad[c];
int64_t cutoff = FLOW_CHECKED_DIV((c), (radc));
int64_t t = 0;
while (t < m) {
int64_t a = idx[t];
int64_t rada = rad[a];
if (rada >= cutoff) {
break;
}
if ((2 * a) < c) {
int64_t b = (c - a);
if ((((rada * rad[b]) * radc) < c && gcd_i64_i64(rada, rad[b]) == 1)) {
total = (total + c);
}
}
t = (t + 1);
}
c = (c + 1);
}
printf("%lld\n", total);
free(idx);
free(rad);
return 0;
}