Problem 129

Least n > 10^6 with A(n) > 10^6 (repunit divisibility).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 129
# Least n > 10^6 with A(n) > 10^6 (repunit divisibility).

function A(n: i64) -> i64 {
    if n % 2 == 0 || n % 5 == 0 { return 0 }
    let mut k: i64 = 1
    let mut r: i64 = 1
    while r != 0 {
        r = (r * 10 + 1) % n
        k = k + 1
    }
    return k
}

function main() -> i32 {
    let limit: i64 = 1000000
    let mut n: i64 = limit
    while A(n) <= limit {
        n = n + 1
    }
    printf("%lld\n", n)
    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; }

int64_t A_i64(int64_t n);
int32_t main(void);

int64_t A_i64(int64_t n) {
    if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (5)) == 0)) {
        return 0;
    }
    int64_t k = 1;
    int64_t r = 1;
    while (r != 0) {
        r = FLOW_CHECKED_MOD((((r * 10) + 1)), (n));
        k = (k + 1);
    }
    return k;
}

int32_t main(void) {
    int64_t limit = 1000000;
    int64_t n = limit;
    while (A_i64(n) <= limit) {
        n = (n + 1);
    }
    printf("%lld\n", n);
    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 @A(%arg0: i64) -> i64 {
    %0 = arith.constant 2 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.remsi %arg0, %2 : i64
    %3 = arith.constant 0 : i32
    %5 = arith.extsi %3 : i32 to i64
    %4 = arith.cmpi eq, %1, %5 : i64
    %6 = scf.if %4 -> (i1) {
      %7 = arith.constant true
      scf.yield %7 : i1
    } else {
      %8 = arith.constant 5 : i32
      %10 = arith.extsi %8 : i32 to i64
      %9 = arith.remsi %arg0, %10 : i64
      %11 = arith.constant 0 : i32
      %13 = arith.extsi %11 : i32 to i64
      %12 = arith.cmpi eq, %9, %13 : i64
      scf.yield %12 : i1
    }
    cf.cond_br %6, ^bb0, ^bb1
    ^bb0:
      %14 = arith.constant 0 : i32
      %15 = arith.extsi %14 : i32 to i64
      func.return %15 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %16 = arith.constant 1 : i32
    %17 = arith.extsi %16 : i32 to i64
    %18 = llvm.mlir.constant(1 : i64) : i64
    %19 = llvm.alloca %18 x i64 : (i64) -> !llvm.ptr
    llvm.store %17, %19 : i64, !llvm.ptr
    %20 = arith.constant 1 : i32
    %21 = arith.extsi %20 : i32 to i64
    %22 = llvm.mlir.constant(1 : i64) : i64
    %23 = llvm.alloca %22 x i64 : (i64) -> !llvm.ptr
    llvm.store %21, %23 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %24 = llvm.load %23 : !llvm.ptr -> i64
    %25 = arith.constant 0 : i32
    %27 = arith.extsi %25 : i32 to i64
    %26 = arith.cmpi ne, %24, %27 : i64
    cf.cond_br %26, ^bb4, ^bb5
    ^bb4:
      %28 = llvm.load %23 : !llvm.ptr -> i64
      %29 = arith.constant 10 : i32
      %31 = arith.extsi %29 : i32 to i64
      %30 = arith.muli %28, %31 : i64
      %32 = arith.constant 1 : i32
      %34 = arith.extsi %32 : i32 to i64
      %33 = arith.addi %30, %34 : i64
      %35 = arith.remsi %33, %arg0 : i64
      llvm.store %35, %23 : i64, !llvm.ptr
      %36 = llvm.load %19 : !llvm.ptr -> i64
      %37 = arith.constant 1 : i32
      %39 = arith.extsi %37 : i32 to i64
      %38 = arith.addi %36, %39 : i64
      llvm.store %38, %19 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %40 = llvm.load %19 : !llvm.ptr -> i64
    func.return %40 : i64
  }
  func.func @main() -> i32 {
    %41 = arith.constant 1000000 : i32
    %42 = arith.extsi %41 : i32 to i64
    %43 = llvm.mlir.constant(1 : i64) : i64
    %44 = llvm.alloca %43 x i64 : (i64) -> !llvm.ptr
    llvm.store %42, %44 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %46 = llvm.load %44 : !llvm.ptr -> i64
    %45 = func.call @A(%46) : (i64) -> i64
    %47 = arith.cmpi sle, %45, %42 : i64
    cf.cond_br %47, ^bb7, ^bb8
    ^bb7:
      %48 = llvm.load %44 : !llvm.ptr -> i64
      %49 = arith.constant 1 : i32
      %51 = arith.extsi %49 : i32 to i64
      %50 = arith.addi %48, %51 : i64
      llvm.store %50, %44 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %52 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %53 = llvm.load %44 : !llvm.ptr -> i64
    %54 = llvm.call @printf(%52, %53) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %55 = arith.constant 0 : i32
    func.return %55 : i32
  }
}