Problem 323

Expected steps until 32-bit OR reaches all-ones; 10 decimal places.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 323
# Expected steps until 32-bit OR reaches all-ones; 10 decimal places.

extern {
    function pow(x: f64, y: f64) -> f64
}

function main() -> i32 {
    let max_bits: f64 = 32.0
    let epsilon: f64 = 0.00000000001
    let mut result: f64 = 0.0
    let mut round: f64 = 0.0
    while true {
        let has_zero: f64 = pow(0.5, round)
        let is_done: f64 = pow(1.0 - has_zero, max_bits)
        let delta: f64 = 1.0 - is_done
        if delta < epsilon { break }
        result = result + delta
        round = round + 1.0
    }
    printf("%.10f\n", result)
    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 main(void);


int32_t main(void) {
    double max_bits = 32.0;
    double epsilon = 0.00000000001;
    double result = 0.0;
    double round = 0.0;
    while (1) {
        double has_zero = pow(0.5, round);
        double is_done = pow((1.0 - has_zero), max_bits);
        double delta = (1.0 - is_done);
        if (delta < epsilon) {
            break;
        }
        result = (result + delta);
        round = (round + 1.0);
    }
    printf("%.10f\n", result);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.10f\n\00") {addr_space = 0 : i32} : !llvm.array<7 x i8>
  func.func private @pow(f64, f64) -> f64
  func.func @main() -> i32 {
    %0 = arith.constant 32.0 : f32
    %1 = arith.extf %0 : f32 to f64
    %2 = arith.constant 0.00000000001 : f32
    %3 = arith.extf %2 : f32 to f64
    %4 = arith.constant 0.0 : f32
    %5 = arith.extf %4 : f32 to f64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x f64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : f64, !llvm.ptr
    %8 = arith.constant 0.0 : f32
    %9 = arith.extf %8 : f32 to f64
    %10 = llvm.mlir.constant(1 : i64) : i64
    %11 = llvm.alloca %10 x f64 : (i64) -> !llvm.ptr
    llvm.store %9, %11 : f64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %12 = arith.constant 1 : i1
    cf.cond_br %12, ^bb1, ^bb2
    ^bb1:
      %14 = arith.constant 0.5 : f32
      %15 = llvm.load %11 : !llvm.ptr -> f64
      %16 = arith.extf %14 : f32 to f64
      %13 = func.call @pow(%16, %15) : (f64, f64) -> f64
      %18 = arith.constant 1.0 : f32
      %20 = arith.extf %18 : f32 to f64
      %19 = arith.subf %20, %13 : f64
      %17 = func.call @pow(%19, %1) : (f64, f64) -> f64
      %21 = arith.constant 1.0 : f32
      %23 = arith.extf %21 : f32 to f64
      %22 = arith.subf %23, %17 : f64
      %24 = arith.cmpf olt, %22, %3 : f64
      cf.cond_br %24, ^bb3, ^bb4
      ^bb3:
        cf.br ^bb2
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %25 = llvm.load %7 : !llvm.ptr -> f64
      %26 = arith.addf %25, %22 : f64
      llvm.store %26, %7 : f64, !llvm.ptr
      %27 = llvm.load %11 : !llvm.ptr -> f64
      %28 = arith.constant 1.0 : f32
      %30 = arith.extf %28 : f32 to f64
      %29 = arith.addf %27, %30 : f64
      llvm.store %29, %11 : f64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %31 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %32 = llvm.load %7 : !llvm.ptr -> f64
    %33 = llvm.call @printf(%31, %32) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %34 = arith.constant 0 : i32
    func.return %34 : i32
  }
}