# Project Euler 153
# Sum of Gaussian integer divisors with positive real part, n=1..10^8.
import euler.nt { gcd, isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function grouped_sum(n: i64) -> i64 {
if n <= 0 { return 0 }
let mut total: i64 = 0
let mut k: i64 = 1
while k <= n {
let q: i64 = n / k
let k2: i64 = n / q
total = total + q * (k + k2) * (k2 - k + 1) / 2
k = k2 + 1
}
return total
}
# Binary search F for key q among sorted keys
function lookup_F(q: i64, keys: ptr<i64>, vals: ptr<i64>, nkeys: i32) -> i64 {
let mut lo: i32 = 0
let mut hi: i32 = nkeys - 1
while lo <= hi {
let mid: i32 = (lo + hi) / 2
if keys[mid] == q { return vals[mid] }
if keys[mid] < q {
lo = mid + 1
} else {
hi = mid - 1
}
}
return grouped_sum(q)
}
function main() -> i32 {
let N: i64 = 100000000
# Precompute F(q) for all q = N/k
let maxkeys: i32 = 40000
let keys: ptr<i64> = calloc(maxkeys as i64, 8)
let vals: ptr<i64> = calloc(maxkeys as i64, 8)
if keys == null || vals == null { return 1 }
let mut nkeys: i32 = 0
let mut k: i64 = 1
while k <= N {
let q: i64 = N / k
keys[nkeys] = q
vals[nkeys] = grouped_sum(q)
nkeys = nkeys + 1
k = N / q + 1
}
# sort by keys ascending (they come descending)
let mut i: i32 = 0
while i < nkeys / 2 {
let j: i32 = nkeys - 1 - i
let tk: i64 = keys[i]
keys[i] = keys[j]
keys[j] = tk
let tv: i64 = vals[i]
vals[i] = vals[j]
vals[j] = tv
i = i + 1
}
let mut ans: i64 = lookup_F(N, keys, vals, nkeys)
ans = ans + 2 * lookup_F(N / 2, keys, vals, nkeys)
let max_a: i64 = isqrt(N / 2)
let mut a: i64 = 1
while a <= max_a {
let a2: i64 = a * a
let mut b: i64 = a + 1
let bmax: i64 = isqrt(N - a2)
while b <= bmax {
if gcd(a, b) == 1 {
let v: i64 = a2 + b * b
ans = ans + 2 * (a + b) * lookup_F(N / v, keys, vals, nkeys)
}
b = b + 1
}
a = a + 1
}
printf("%lld\n", ans)
free(keys)
free(vals)
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 grouped_sum_i64(int64_t n);
int64_t lookup_F_i64_ptr_i64_ptr_i64_i32(int64_t q, int64_t* keys, int64_t* vals, int32_t nkeys);
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 grouped_sum_i64(int64_t n) {
if (n <= 0) {
return 0;
}
int64_t total = 0;
int64_t k = 1;
while (k <= n) {
int64_t q = FLOW_CHECKED_DIV((n), (k));
int64_t k2 = FLOW_CHECKED_DIV((n), (q));
total = (total + FLOW_CHECKED_DIV((((q * (k + k2)) * ((k2 - k) + 1))), (2)));
k = (k2 + 1);
}
return total;
}
int64_t lookup_F_i64_ptr_i64_ptr_i64_i32(int64_t q, int64_t* keys, int64_t* vals, int32_t nkeys) {
int32_t lo = 0;
int32_t hi = (nkeys - 1);
while (lo <= hi) {
int32_t mid = FLOW_CHECKED_DIV(((lo + hi)), (2));
if (keys[mid] == q) {
return vals[mid];
}
if (keys[mid] < q) {
lo = (mid + 1);
} else {
hi = (mid - 1);
}
}
return grouped_sum_i64(q);
}
int32_t main(void) {
int64_t N = 100000000;
int32_t maxkeys = 40000;
int64_t* keys = (int64_t*)(calloc(((int64_t)(maxkeys)), 8));
int64_t* vals = (int64_t*)(calloc(((int64_t)(maxkeys)), 8));
if ((keys == NULL || vals == NULL)) {
return 1;
}
int32_t nkeys = 0;
int64_t k = 1;
while (k <= N) {
int64_t q = FLOW_CHECKED_DIV((N), (k));
keys[nkeys] = q;
vals[nkeys] = grouped_sum_i64(q);
nkeys = (nkeys + 1);
k = (FLOW_CHECKED_DIV((N), (q)) + 1);
}
int32_t i = 0;
while (i < FLOW_CHECKED_DIV((nkeys), (2))) {
int32_t j = ((nkeys - 1) - i);
int64_t tk = keys[i];
keys[i] = keys[j];
keys[j] = tk;
int64_t tv = vals[i];
vals[i] = vals[j];
vals[j] = tv;
i = (i + 1);
}
int64_t ans = lookup_F_i64_ptr_i64_ptr_i64_i32(N, keys, vals, nkeys);
ans = (ans + (2 * lookup_F_i64_ptr_i64_ptr_i64_i32(FLOW_CHECKED_DIV((N), (2)), keys, vals, nkeys)));
int64_t max_a = isqrt_i64(FLOW_CHECKED_DIV((N), (2)));
int64_t a = 1;
while (a <= max_a) {
int64_t a2 = (a * a);
int64_t b = (a + 1);
int64_t bmax = isqrt_i64((N - a2));
while (b <= bmax) {
if (gcd_i64_i64(a, b) == 1) {
int64_t v = (a2 + (b * b));
ans = (ans + ((2 * (a + b)) * lookup_F_i64_ptr_i64_ptr_i64_i32(FLOW_CHECKED_DIV((N), (v)), keys, vals, nkeys)));
}
b = (b + 1);
}
a = (a + 1);
}
printf("%lld\n", ans);
free(keys);
free(vals);
return 0;
}