# Project Euler 721
# High Powers of Irrational Numbers: G(5e6) mod 999999937.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
function sqrt(x: f64) -> f64
}
const MOD: i64 = 999999937
function clz64(n: i64) -> i32 {
if n == 0 { return 64 }
let mut count: i32 = 0
let mut x: i64 = n
if (x >> 32) == 0 { count = count + 32; x = x << 32 }
if (x >> 48) == 0 { count = count + 16; x = x << 16 }
if (x >> 56) == 0 { count = count + 8; x = x << 8 }
if (x >> 60) == 0 { count = count + 4; x = x << 4 }
if (x >> 62) == 0 { count = count + 2; x = x << 2 }
if (x >> 63) == 0 { count = count + 1 }
return count
}
function bin_exp(x: i64, a: i64, n: i64, out: ptr<i64>) -> void {
let mut A: i64 = x
let mut B: i64 = 1
let msb: i32 = 63 - clz64(n)
let mut i: i32 = msb - 1
while i >= 0 {
let na: i64 = (A * A + a % MOD * (B % MOD) % MOD * (B % MOD)) % MOD
let nb: i64 = (2 * A % MOD * B) % MOD
A = na
B = nb
if (n >> i) % 2 == 1 {
na = (x % MOD * A + a % MOD * B) % MOD
nb = (A + x % MOD * B) % MOD
A = na
B = nb
}
i = i - 1
}
out[0] = A
out[1] = B
}
function main() -> i32 {
let n: i64 = 5000000
let mut total: i64 = 0
let out: ptr<i64> = calloc(2, 8)
let mut a: i64 = 1
while a <= n {
let mut ca: i64 = sqrt(a as f64) as i64
while (ca + 1) * (ca + 1) <= a {
ca = ca + 1
}
while ca * ca > a {
ca = ca - 1
}
if ca * ca == a {
bin_exp(ca, a, a * a, out)
total = total + 2 * out[0]
} else {
bin_exp(ca + 1, a, a * a, out)
total = total + 2 * out[0] - 1
}
total = total % MOD
a = a + 1
}
free(out)
printf("%lld\n", total)
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; }
int32_t clz64_i64(int64_t n);
void bin_exp_i64_i64_i64_ptr_i64(int64_t x, int64_t a, int64_t n, int64_t* out);
int32_t main(void);
static const int64_t MOD = 999999937;
int32_t clz64_i64(int64_t n) {
if (n == 0) {
return 64;
}
int32_t count = 0;
int64_t x = n;
if (FLOW_CHECKED_SHR((x), (32)) == 0) {
count = (count + 32);
x = FLOW_CHECKED_SHL((x), (32));
}
if (FLOW_CHECKED_SHR((x), (48)) == 0) {
count = (count + 16);
x = FLOW_CHECKED_SHL((x), (16));
}
if (FLOW_CHECKED_SHR((x), (56)) == 0) {
count = (count + 8);
x = FLOW_CHECKED_SHL((x), (8));
}
if (FLOW_CHECKED_SHR((x), (60)) == 0) {
count = (count + 4);
x = FLOW_CHECKED_SHL((x), (4));
}
if (FLOW_CHECKED_SHR((x), (62)) == 0) {
count = (count + 2);
x = FLOW_CHECKED_SHL((x), (2));
}
if (FLOW_CHECKED_SHR((x), (63)) == 0) {
count = (count + 1);
}
return count;
}
void bin_exp_i64_i64_i64_ptr_i64(int64_t x, int64_t a, int64_t n, int64_t* out) {
int64_t A = x;
int64_t B = 1;
int32_t msb = (63 - clz64_i64(n));
int32_t i = (msb - 1);
while (i >= 0) {
int64_t na = FLOW_CHECKED_MOD((((A * A) + (FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD((a), (MOD)) * FLOW_CHECKED_MOD((B), (MOD)))), (MOD)) * FLOW_CHECKED_MOD((B), (MOD))))), (MOD));
int64_t nb = FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((2 * A)), (MOD)) * B)), (MOD));
A = na;
B = nb;
if (FLOW_CHECKED_MOD((FLOW_CHECKED_SHR((n), (i))), (2)) == 1) {
na = FLOW_CHECKED_MOD((((FLOW_CHECKED_MOD((x), (MOD)) * A) + (FLOW_CHECKED_MOD((a), (MOD)) * B))), (MOD));
nb = FLOW_CHECKED_MOD(((A + (FLOW_CHECKED_MOD((x), (MOD)) * B))), (MOD));
A = na;
B = nb;
}
i = (i - 1);
}
out[0] = A;
out[1] = B;
}
int32_t main(void) {
int64_t n = 5000000;
int64_t total = 0;
int64_t* out = (int64_t*)(calloc(2, 8));
int64_t a = 1;
while (a <= n) {
int64_t ca = ((int64_t)(sqrt(((double)(a)))));
while (((ca + 1) * (ca + 1)) <= a) {
ca = (ca + 1);
}
while ((ca * ca) > a) {
ca = (ca - 1);
}
if ((ca * ca) == a) {
bin_exp_i64_i64_i64_ptr_i64(ca, a, (a * a), out);
total = (total + (2 * out[0]));
} else {
bin_exp_i64_i64_i64_ptr_i64((ca + 1), a, (a * a), out);
total = ((total + (2 * out[0])) - 1);
}
total = FLOW_CHECKED_MOD((total), (MOD));
a = (a + 1);
}
free(out);
printf("%lld\n", total);
return 0;
}