Problem 855

Delphi Paper: S(5,8) = (5!)^8 * (8!)^5 / (40!)^2, a tiny value ~6.88e-57. Computed in log-space via lgamma to avoid overflow, then exponentiated.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 855
# Delphi Paper: S(5,8) = (5!)^8 * (8!)^5 / (40!)^2, a tiny value ~6.88e-57.
# Computed in log-space via lgamma to avoid overflow, then exponentiated.

extern {
    function lgamma(x: f64) -> f64
    function exp(x: f64) -> f64
}

function main() -> i32 {
    let a: f64 = 5.0
    let b: f64 = 8.0
    let log_s: f64 = b * lgamma(a + 1.0) + a * lgamma(b + 1.0) - 2.0 * lgamma(a * b + 1.0)
    printf("%.10e\n", exp(log_s))
    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);
int32_t main(void);



int32_t main(void) {
    double a = 5.0;
    double b = 8.0;
    double log_s = (((b * lgamma((a + 1.0))) + (a * lgamma((b + 1.0)))) - (2.0 * lgamma(((a * b) + 1.0))));
    printf("%.10e\n", exp(log_s));
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.10e\n\00") {addr_space = 0 : i32} : !llvm.array<7 x i8>
  func.func private @lgamma(f64) -> f64
  func.func private @exp(f64) -> f64
  func.func @main() -> i32 {
    %0 = arith.constant 5.0 : f32
    %1 = arith.extf %0 : f32 to f64
    %2 = arith.constant 8.0 : f32
    %3 = arith.extf %2 : f32 to f64
    %5 = arith.constant 1.0 : f32
    %7 = arith.extf %5 : f32 to f64
    %6 = arith.addf %1, %7 : f64
    %4 = func.call @lgamma(%6) : (f64) -> f64
    %8 = arith.mulf %3, %4 : f64
    %10 = arith.constant 1.0 : f32
    %12 = arith.extf %10 : f32 to f64
    %11 = arith.addf %3, %12 : f64
    %9 = func.call @lgamma(%11) : (f64) -> f64
    %13 = arith.mulf %1, %9 : f64
    %14 = arith.addf %8, %13 : f64
    %15 = arith.constant 2.0 : f32
    %17 = arith.mulf %1, %3 : f64
    %18 = arith.constant 1.0 : f32
    %20 = arith.extf %18 : f32 to f64
    %19 = arith.addf %17, %20 : f64
    %16 = func.call @lgamma(%19) : (f64) -> f64
    %22 = arith.extf %15 : f32 to f64
    %21 = arith.mulf %22, %16 : f64
    %23 = arith.subf %14, %21 : f64
    %24 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %25 = math.exp %23 : f64
    %26 = llvm.call @printf(%24, %25) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %27 = arith.constant 0 : i32
    func.return %27 : i32
  }
}