# Project Euler 959
# Asymmetric Random Walk: f(89, 97).
# f(a,b) = 1/G where G = sum_{k>=0} C((a+b)k, ak) / 2^{(a+b)k},
# computed in log space via lgamma.
extern {
function lgamma(x: f64) -> f64
function log(x: f64) -> f64
function exp(x: f64) -> f64
}
function gcd_l(x: i64, y: i64) -> i64 {
let mut a: i64 = x
let mut b: i64 = y
while b != 0 {
let t: i64 = a % b
a = b
b = t
}
if a < 0 {
return -a
}
return a
}
function f_ab(a0: i64, b0: i64) -> f64 {
let g: i64 = gcd_l(a0, b0)
let mut a: i64 = a0 / g
let mut b: i64 = b0 / g
if a == b {
return 0.0
}
if a > b {
let t: i64 = a
a = b
b = t
}
let m: i64 = a + b
let log2: f64 = log(2.0)
let mut S: f64 = 0.0
let mut k: i64 = 0
while true {
let mk: i64 = m * k
let ak: i64 = a * k
let bk: i64 = b * k
let log_t: f64 = lgamma((mk + 1) as f64)
- lgamma((ak + 1) as f64)
- lgamma((bk + 1) as f64)
- (mk as f64) * log2
if log_t < -700.0 {
break
}
let t: f64 = exp(log_t)
S = S + t
if t < 1e-17 * S {
break
}
k = k + 1
if k > 200000 {
break
}
}
return 1.0 / S
}
function main() -> i32 {
printf("%.9f\n", f_ab(89, 97))
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; }
double lgamma(double x);
int64_t gcd_l_i64_i64(int64_t x, int64_t y);
double f_ab_i64_i64(int64_t a0, int64_t b0);
int32_t main(void);
int64_t gcd_l_i64_i64(int64_t x, int64_t y) {
int64_t a = x;
int64_t b = y;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
if (a < 0) {
return (-a);
}
return a;
}
double f_ab_i64_i64(int64_t a0, int64_t b0) {
int64_t g = gcd_l_i64_i64(a0, b0);
int64_t a = FLOW_CHECKED_DIV((a0), (g));
int64_t b = FLOW_CHECKED_DIV((b0), (g));
if (a == b) {
return 0.0;
}
if (a > b) {
int64_t t = a;
a = b;
b = t;
}
int64_t m = (a + b);
double log2 = log(2.0);
double S = 0.0;
int64_t k = 0;
while (1) {
int64_t mk = (m * k);
int64_t ak = (a * k);
int64_t bk = (b * k);
double log_t = (((lgamma(((double)((mk + 1)))) - lgamma(((double)((ak + 1))))) - lgamma(((double)((bk + 1))))) - (((double)(mk)) * log2));
if (log_t < (-700.0)) {
break;
}
double t = exp(log_t);
S = (S + t);
if (t < (1e-17 * S)) {
break;
}
k = (k + 1);
if (k > 200000) {
break;
}
}
return (1.0 / S);
}
int32_t main(void) {
printf("%.9f\n", f_ab_i64_i64(89, 97));
return 0;
}