Problem 568

Reciprocal Games II First 7 significant digits of D(n)=H_n/2^n for n=123456789.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 568
# Reciprocal Games II
# First 7 significant digits of D(n)=H_n/2^n for n=123456789.

extern {
    function log(x: f64) -> f64
    function log10(x: f64) -> f64
    function exp(x: f64) -> f64
    function floor(x: f64) -> f64
}

function harmonic_asymp(n: i64) -> f64 {
    let x: f64 = n as f64
    let inv: f64 = 1.0 / x
    let inv2: f64 = inv * inv
    let gamma: f64 = 0.5772156649015329
    return log(x) + gamma + 0.5 * inv - inv2 / 12.0 + (inv2 * inv2) / 120.0
        - (inv2 * inv2 * inv2) / 252.0
}

function solve(n: i64) -> i64 {
    let H: f64 = harmonic_asymp(n)
    let L: f64 = log10(H) - (n as f64) * log10(2.0)
    let e: f64 = floor(L)
    let frac: f64 = L - e
    let ln10: f64 = log(10.0)
    let mantissa: f64 = exp(frac * ln10)
    let digits: i64 = floor(mantissa * 1000000.0 + 1e-9) as i64
    if digits >= 10000000 {
        return digits / 10
    }
    return digits
}

function main() -> i32 {
    printf("%lld\n", solve(123456789))
    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 harmonic_asymp_i64(int64_t n);
int64_t solve_i64(int64_t n);
int32_t main(void);





double harmonic_asymp_i64(int64_t n) {
    double x = ((double)(n));
    double inv = (1.0 / x);
    double inv2 = (inv * inv);
    double gamma = 0.5772156649015329;
    return (((((log(x) + gamma) + (0.5 * inv)) - (inv2 / 12.0)) + ((inv2 * inv2) / 120.0)) - (((inv2 * inv2) * inv2) / 252.0));
}

int64_t solve_i64(int64_t n) {
    double H = harmonic_asymp_i64(n);
    double L = (log10(H) - (((double)(n)) * log10(2.0)));
    double e = floor(L);
    double frac = (L - e);
    double ln10 = log(10.0);
    double mantissa = exp((frac * ln10));
    int64_t digits = ((int64_t)(floor(((mantissa * 1000000.0) + 1e-9))));
    if (digits >= 10000000) {
        return FLOW_CHECKED_DIV((digits), (10));
    }
    return digits;
}

int32_t main(void) {
    printf("%lld\n", solve_i64(123456789));
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%lld\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @log(f64) -> f64
  func.func private @log10(f64) -> f64
  func.func private @exp(f64) -> f64
  func.func private @floor(f64) -> f64
  func.func @harmonic_asymp(%arg0: i64) -> f64 {
    %0 = arith.sitofp %arg0 : i64 to f64
    %1 = arith.constant 1.0 : f32
    %3 = arith.extf %1 : f32 to f64
    %2 = arith.divf %3, %0 : f64
    %4 = arith.mulf %2, %2 : f64
    %5 = arith.constant 0.5772156649015329 : f32
    %6 = arith.extf %5 : f32 to f64
    %7 = math.log %0 : f64
    %8 = arith.addf %7, %6 : f64
    %9 = arith.constant 0.5 : f32
    %11 = arith.extf %9 : f32 to f64
    %10 = arith.mulf %11, %2 : f64
    %12 = arith.addf %8, %10 : f64
    %13 = arith.constant 12.0 : f32
    %15 = arith.extf %13 : f32 to f64
    %14 = arith.divf %4, %15 : f64
    %16 = arith.subf %12, %14 : f64
    %17 = arith.mulf %4, %4 : f64
    %18 = arith.constant 120.0 : f32
    %20 = arith.extf %18 : f32 to f64
    %19 = arith.divf %17, %20 : f64
    %21 = arith.addf %16, %19 : f64
    %22 = arith.mulf %4, %4 : f64
    %23 = arith.mulf %22, %4 : f64
    %24 = arith.constant 252.0 : f32
    %26 = arith.extf %24 : f32 to f64
    %25 = arith.divf %23, %26 : f64
    %27 = arith.subf %21, %25 : f64
    func.return %27 : f64
  }
  func.func @solve(%arg0: i64) -> i64 {
    %28 = func.call @harmonic_asymp(%arg0) : (i64) -> f64
    %29 = func.call @log10(%28) : (f64) -> f64
    %30 = arith.sitofp %arg0 : i64 to f64
    %32 = arith.constant 2.0 : f32
    %33 = arith.extf %32 : f32 to f64
    %31 = func.call @log10(%33) : (f64) -> f64
    %34 = arith.mulf %30, %31 : f64
    %35 = arith.subf %29, %34 : f64
    %36 = func.call @floor(%35) : (f64) -> f64
    %37 = arith.subf %35, %36 : f64
    %38 = arith.constant 10.0 : f32
    %39 = math.log %38 : f32
    %40 = arith.extf %39 : f32 to f64
    %41 = arith.mulf %37, %40 : f64
    %42 = math.exp %41 : f64
    %44 = arith.constant 1000000.0 : f32
    %46 = arith.extf %44 : f32 to f64
    %45 = arith.mulf %42, %46 : f64
    %47 = arith.constant 0.000000001 : f32
    %49 = arith.extf %47 : f32 to f64
    %48 = arith.addf %45, %49 : f64
    %43 = func.call @floor(%48) : (f64) -> f64
    %50 = arith.fptosi %43 : f64 to i64
    %51 = arith.constant 10000000 : i32
    %53 = arith.extsi %51 : i32 to i64
    %52 = arith.cmpi sge, %50, %53 : i64
    cf.cond_br %52, ^bb0, ^bb1
    ^bb0:
      %54 = arith.constant 10 : i32
      %56 = arith.extsi %54 : i32 to i64
      %55 = arith.divsi %50, %56 : i64
      func.return %55 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    func.return %50 : i64
  }
  func.func @main() -> i32 {
    %57 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %59 = arith.constant 123456789 : i32
    %60 = arith.extsi %59 : i32 to i64
    %58 = func.call @solve(%60) : (i64) -> i64
    %61 = llvm.call @printf(%57, %58) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %62 = arith.constant 0 : i32
    func.return %62 : i32
  }
}