# Project Euler 515
# Dissonant Numbers — D(10^9,10^5,10^5) via inv(k-1) mod p.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function isqrt(n: i64) -> i64 {
if n < 2 { return n }
let mut x: i64 = n
let mut y: i64 = (x + 1) / 2
while y < x {
x = y
y = (x + n / x) / 2
}
return x
}
function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base0 % mod
let mut e: i64 = exp0
while e > 0 {
if (e & 1) == 1 {
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 / 2
}
return r
}
function main() -> i32 {
let a: i64 = 1000000000
let b: i64 = 100000
let k: i64 = 100000
let high: i64 = a + b
let lim: i64 = isqrt(high - 1)
let sieve: ptr<i8> = calloc(lim + 1, 1)
let small: ptr<i32> = calloc(lim + 1, 4)
let seg: ptr<i8> = calloc(b, 1)
if sieve == null || small == null || seg == null { return 1 }
let mut i: i64 = 2
while i <= lim {
sieve[i] = 1
i = i + 1
}
i = 2
while i * i <= lim {
if sieve[i] == 1 {
let mut j: i64 = i * i
while j <= lim {
sieve[j] = 0
j = j + i
}
}
i = i + 1
}
let mut sn: i64 = 0
i = 2
while i <= lim {
if sieve[i] == 1 {
small[sn] = i as i32
sn = sn + 1
}
i = i + 1
}
i = 0
while i < b {
seg[i] = 1
i = i + 1
}
let mut si: i64 = 0
while si < sn {
let p: i64 = small[si] as i64
let mut m: i64 = ((a + p - 1) / p) * p
if m < p * p { m = p * p }
while m < high {
seg[m - a] = 0
m = m + p
}
si = si + 1
}
let x: i64 = k - 1
let mut total: i64 = 0
i = 0
while i < b {
if seg[i] == 1 {
let p: i64 = a + i
if p >= 2 {
total = total + modpow(x, p - 2, p)
}
}
i = i + 1
}
printf("%lld\n", total)
free(sieve); free(small); free(seg)
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 isqrt_i64(int64_t n);
int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int32_t main(void);
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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base0), (mod));
int64_t e = exp0;
while (e > 0) {
if ((e & 1) == 1) {
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_DIV((e), (2));
}
return r;
}
int32_t main(void) {
int64_t a = 1000000000;
int64_t b = 100000;
int64_t k = 100000;
int64_t high = (a + b);
int64_t lim = isqrt_i64((high - 1));
int8_t* sieve = (int8_t*)(calloc((lim + 1), 1));
int32_t* small = (int32_t*)(calloc((lim + 1), 4));
int8_t* seg = (int8_t*)(calloc(b, 1));
if (((sieve == NULL || small == NULL) || seg == NULL)) {
return 1;
}
int64_t i = 2;
while (i <= lim) {
sieve[i] = 1;
i = (i + 1);
}
i = 2;
while ((i * i) <= lim) {
if (sieve[i] == 1) {
int64_t j = (i * i);
while (j <= lim) {
sieve[j] = 0;
j = (j + i);
}
}
i = (i + 1);
}
int64_t sn = 0;
i = 2;
while (i <= lim) {
if (sieve[i] == 1) {
small[sn] = ((int32_t)(i));
sn = (sn + 1);
}
i = (i + 1);
}
i = 0;
while (i < b) {
seg[i] = 1;
i = (i + 1);
}
int64_t si = 0;
while (si < sn) {
int64_t p = ((int64_t)(small[si]));
int64_t m = (FLOW_CHECKED_DIV((((a + p) - 1)), (p)) * p);
if (m < (p * p)) {
m = (p * p);
}
while (m < high) {
seg[(m - a)] = 0;
m = (m + p);
}
si = (si + 1);
}
int64_t x = (k - 1);
int64_t total = 0;
i = 0;
while (i < b) {
if (seg[i] == 1) {
int64_t p = (a + i);
if (p >= 2) {
total = (total + modpow_i64_i64_i64(x, (p - 2), p));
}
}
i = (i + 1);
}
printf("%lld\n", total);
free(sieve);
free(small);
free(seg);
return 0;
}