# Project Euler 942
# Mersenne's Square Root — Gauss sum mod 10^9+7 for R(q), q=1122659.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1000000007
function gauss_sum_mod(q: i64) -> i64 {
let qr: ptr<i8> = calloc(q, 1)
let half: i64 = (q - 1) / 2
let mut sq: i64 = 1
let mut delta: i64 = 3
let mut i: i64 = 0
while i < half {
qr[sq] = 1
sq = sq + delta
if sq >= q { sq = sq - q }
delta = delta + 2
i = i + 1
}
let mut s: i64 = 0
let mut pow2: i64 = 2
let mut a: i64 = 1
while a < q {
if qr[a] != 0 {
s = s + pow2
if s >= MOD { s = s - MOD }
} else {
s = s - pow2
if s < 0 { s = s + MOD }
}
pow2 = pow2 * 2
if pow2 >= MOD { pow2 = pow2 - MOD }
a = a + 1
}
free(qr)
return s
}
function modpow2(q: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = 2
let mut e: i64 = q
while e > 0 {
if (e & 1) == 1 { r = (r * b) % MOD }
b = (b * b) % MOD
e = e / 2
}
return r
}
function r_mod(q: i64) -> i64 {
let g: i64 = gauss_sum_mod(q)
let p_mod: i64 = (modpow2(q) - 1 + MOD) % MOD
let r: i64 = q & 7
if r == 1 || r == 3 {
return (p_mod - g + MOD) % MOD
}
return g
}
function main() -> i32 {
# q from problem statement (Mersenne prime exponent)
printf("%lld\n", r_mod(74207281))
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 gauss_sum_mod_i64(int64_t q);
int64_t modpow2_i64(int64_t q);
int64_t r_mod_i64(int64_t q);
int32_t main(void);
static const int64_t MOD = 1000000007;
int64_t gauss_sum_mod_i64(int64_t q) {
int8_t* qr = (int8_t*)(calloc(q, 1));
int64_t half = FLOW_CHECKED_DIV(((q - 1)), (2));
int64_t sq = 1;
int64_t delta = 3;
int64_t i = 0;
while (i < half) {
qr[sq] = 1;
sq = (sq + delta);
if (sq >= q) {
sq = (sq - q);
}
delta = (delta + 2);
i = (i + 1);
}
int64_t s = 0;
int64_t pow2 = 2;
int64_t a = 1;
while (a < q) {
if (qr[a] != 0) {
s = (s + pow2);
if (s >= MOD) {
s = (s - MOD);
}
} else {
s = (s - pow2);
if (s < 0) {
s = (s + MOD);
}
}
pow2 = (pow2 * 2);
if (pow2 >= MOD) {
pow2 = (pow2 - MOD);
}
a = (a + 1);
}
free(qr);
return s;
}
int64_t modpow2_i64(int64_t q) {
int64_t r = 1;
int64_t b = 2;
int64_t e = q;
while (e > 0) {
if ((e & 1) == 1) {
r = FLOW_CHECKED_MOD(((r * b)), (MOD));
}
b = FLOW_CHECKED_MOD(((b * b)), (MOD));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
int64_t r_mod_i64(int64_t q) {
int64_t g = gauss_sum_mod_i64(q);
int64_t p_mod = FLOW_CHECKED_MOD((((modpow2_i64(q) - 1) + MOD)), (MOD));
int64_t r = (q & 7);
if ((r == 1 || r == 3)) {
return FLOW_CHECKED_MOD((((p_mod - g) + MOD)), (MOD));
}
return g;
}
int32_t main(void) {
printf("%lld\n", r_mod_i64(74207281));
return 0;
}