# Project Euler 273
# Sum of a for squarefree n<=150 = product of distinct 4k+1 primes.
import euler.nt { is_prime }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function abs64(a: i64) -> i64 {
if a < 0 { return -a }
return a
}
function find_ab(prime: i64, a_out: ptr<i64>, b_out: ptr<i64>) -> void {
let mut b: i64 = 1
while b * b < prime {
let mut a: i64 = 1
while a < b {
if a * a + b * b == prime {
a_out[0] = a
b_out[0] = b
return
}
a = a + 1
}
b = b + 1
}
}
function search(sols_a: ptr<i64>, sols_b: ptr<i64>, sc: i64, primes_a: ptr<i64>, primes_b: ptr<i64>, pc: i64, index: i64) -> i64 {
if index == pc {
let mut sum: i64 = 0
let mut i: i64 = 0
while i < sc {
# skip seed (0,1)
if !(sols_a[i] == 0 && sols_b[i] == 1) {
sum = sum + sols_a[i]
}
i = i + 1
}
return sum
}
let ca: i64 = primes_a[index]
let cb: i64 = primes_b[index]
let next_a: ptr<i64> = calloc(sc * 2 + 2, 8)
let next_b: ptr<i64> = calloc(sc * 2 + 2, 8)
let mut nc: i64 = 0
let mut i: i64 = 0
while i < sc {
let sa: i64 = sols_a[i]
let sb: i64 = sols_b[i]
let mut x: i64 = sa * ca + sb * cb
let mut y: i64 = abs64(sa * cb - sb * ca)
if x > y {
let t: i64 = x
x = y
y = t
}
next_a[nc] = x
next_b[nc] = y
nc = nc + 1
if !(sa == 0 && sb == 1) {
x = abs64(sa * ca - sb * cb)
y = sa * cb + sb * ca
if x > y {
let t2: i64 = x
x = y
y = t2
}
next_a[nc] = x
next_b[nc] = y
nc = nc + 1
}
i = i + 1
}
let without: i64 = search(sols_a, sols_b, sc, primes_a, primes_b, pc, index + 1)
let withv: i64 = search(next_a, next_b, nc, primes_a, primes_b, pc, index + 1)
free(next_a)
free(next_b)
return withv + without
}
function main() -> i32 {
let limit: i64 = 150
let primes_a: ptr<i64> = calloc(40, 8)
let primes_b: ptr<i64> = calloc(40, 8)
let mut pc: i64 = 0
let mut i: i64 = 5
while i <= limit {
if i % 4 == 1 && is_prime(i) {
let a: ptr<i64> = calloc(1, 8)
let b: ptr<i64> = calloc(1, 8)
find_ab(i, a, b)
primes_a[pc] = a[0]
primes_b[pc] = b[0]
pc = pc + 1
free(a); free(b)
}
i = i + 4
}
let sols_a: ptr<i64> = calloc(1, 8)
let sols_b: ptr<i64> = calloc(1, 8)
sols_a[0] = 0
sols_b[0] = 1
printf("%lld\n", search(sols_a, sols_b, 1, primes_a, primes_b, pc, 0))
free(sols_a); free(sols_b); free(primes_a); free(primes_b)
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);
int64_t abs64_i64(int64_t a);
void find_ab_i64_ptr_i64_ptr_i64(int64_t prime, int64_t* a_out, int64_t* b_out);
int64_t search_ptr_i64_ptr_i64_i64_ptr_i64_ptr_i64_i64_i64(int64_t* sols_a, int64_t* sols_b, int64_t sc, int64_t* primes_a, int64_t* primes_b, int64_t pc, int64_t index);
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;
}
int64_t abs64_i64(int64_t a) {
if (a < 0) {
return (-a);
}
return a;
}
void find_ab_i64_ptr_i64_ptr_i64(int64_t prime, int64_t* a_out, int64_t* b_out) {
int64_t b = 1;
while ((b * b) < prime) {
int64_t a = 1;
while (a < b) {
if (((a * a) + (b * b)) == prime) {
a_out[0] = a;
b_out[0] = b;
return;
}
a = (a + 1);
}
b = (b + 1);
}
}
int64_t search_ptr_i64_ptr_i64_i64_ptr_i64_ptr_i64_i64_i64(int64_t* sols_a, int64_t* sols_b, int64_t sc, int64_t* primes_a, int64_t* primes_b, int64_t pc, int64_t index) {
if (index == pc) {
int64_t sum = 0;
int64_t i = 0;
while (i < sc) {
if ((!((sols_a[i] == 0 && sols_b[i] == 1)))) {
sum = (sum + sols_a[i]);
}
i = (i + 1);
}
return sum;
}
int64_t ca = primes_a[index];
int64_t cb = primes_b[index];
int64_t* next_a = (int64_t*)(calloc(((sc * 2) + 2), 8));
int64_t* next_b = (int64_t*)(calloc(((sc * 2) + 2), 8));
int64_t nc = 0;
int64_t i = 0;
while (i < sc) {
int64_t sa = sols_a[i];
int64_t sb = sols_b[i];
int64_t x = ((sa * ca) + (sb * cb));
int64_t y = abs64_i64(((sa * cb) - (sb * ca)));
if (x > y) {
int64_t t = x;
x = y;
y = t;
}
next_a[nc] = x;
next_b[nc] = y;
nc = (nc + 1);
if ((!((sa == 0 && sb == 1)))) {
x = abs64_i64(((sa * ca) - (sb * cb)));
y = ((sa * cb) + (sb * ca));
if (x > y) {
int64_t t2 = x;
x = y;
y = t2;
}
next_a[nc] = x;
next_b[nc] = y;
nc = (nc + 1);
}
i = (i + 1);
}
int64_t without = search_ptr_i64_ptr_i64_i64_ptr_i64_ptr_i64_i64_i64(sols_a, sols_b, sc, primes_a, primes_b, pc, (index + 1));
int64_t withv = search_ptr_i64_ptr_i64_i64_ptr_i64_ptr_i64_i64_i64(next_a, next_b, nc, primes_a, primes_b, pc, (index + 1));
free(next_a);
free(next_b);
return (withv + without);
}
int32_t main(void) {
int64_t limit = 150;
int64_t* primes_a = (int64_t*)(calloc(40, 8));
int64_t* primes_b = (int64_t*)(calloc(40, 8));
int64_t pc = 0;
int64_t i = 5;
while (i <= limit) {
if ((FLOW_CHECKED_MOD((i), (4)) == 1 && is_prime_i64(i))) {
int64_t* a = (int64_t*)(calloc(1, 8));
int64_t* b = (int64_t*)(calloc(1, 8));
find_ab_i64_ptr_i64_ptr_i64(i, a, b);
primes_a[pc] = a[0];
primes_b[pc] = b[0];
pc = (pc + 1);
free(a);
free(b);
}
i = (i + 4);
}
int64_t* sols_a = (int64_t*)(calloc(1, 8));
int64_t* sols_b = (int64_t*)(calloc(1, 8));
sols_a[0] = 0;
sols_b[0] = 1;
printf("%lld\n", search_ptr_i64_ptr_i64_i64_ptr_i64_ptr_i64_i64_i64(sols_a, sols_b, 1, primes_a, primes_b, pc, 0));
free(sols_a);
free(sols_b);
free(primes_a);
free(primes_b);
return 0;
}