Problem 145

How many reversible numbers below one billion?

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 145
# How many reversible numbers below one billion?

function powi(base: i64, exp: i64) -> i64 {
    let mut r: i64 = 1
    let mut e: i64 = exp
    while e > 0 {
        r = r * base
        e = e - 1
    }
    return r
}

function count_by_length(length: i64) -> i64 {
    if length % 2 == 0 {
        return 20 * powi(30, length / 2 - 1)
    }
    if length % 4 == 3 {
        return 100 * powi(500, (length - 3) / 4)
    }
    return 0
}

function main() -> i32 {
    let mut total: i64 = 0
    let mut length: i64 = 1
    while length <= 9 {
        total = total + count_by_length(length)
        length = length + 1
    }
    printf("%lld\n", total)
    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 powi_i64_i64(int64_t base, int64_t exp);
int64_t count_by_length_i64(int64_t length);
int32_t main(void);

int64_t powi_i64_i64(int64_t base, int64_t exp) {
    int64_t r = 1;
    int64_t e = exp;
    while (e > 0) {
        r = (r * base);
        e = (e - 1);
    }
    return r;
}

int64_t count_by_length_i64(int64_t length) {
    if (FLOW_CHECKED_MOD((length), (2)) == 0) {
        return (20 * powi_i64_i64(30, (FLOW_CHECKED_DIV((length), (2)) - 1)));
    }
    if (FLOW_CHECKED_MOD((length), (4)) == 3) {
        return (100 * powi_i64_i64(500, FLOW_CHECKED_DIV(((length - 3)), (4))));
    }
    return 0;
}

int32_t main(void) {
    int64_t total = 0;
    int64_t length = 1;
    while (length <= 9) {
        total = (total + count_by_length_i64(length));
        length = (length + 1);
    }
    printf("%lld\n", total);
    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 @powi(%arg0: i64, %arg1: i64) -> i64 {
    %0 = arith.constant 1 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : i64, !llvm.ptr
    %4 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %5 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %6 = llvm.load %5 : !llvm.ptr -> i64
    %7 = arith.constant 0 : i32
    %9 = arith.extsi %7 : i32 to i64
    %8 = arith.cmpi sgt, %6, %9 : i64
    cf.cond_br %8, ^bb1, ^bb2
    ^bb1:
      %10 = llvm.load %3 : !llvm.ptr -> i64
      %11 = arith.muli %10, %arg0 : i64
      llvm.store %11, %3 : i64, !llvm.ptr
      %12 = llvm.load %5 : !llvm.ptr -> i64
      %13 = arith.constant 1 : i32
      %15 = arith.extsi %13 : i32 to i64
      %14 = arith.subi %12, %15 : i64
      llvm.store %14, %5 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %16 = llvm.load %3 : !llvm.ptr -> i64
    func.return %16 : i64
  }
  func.func @count_by_length(%arg0: i64) -> i64 {
    %17 = arith.constant 2 : i32
    %19 = arith.extsi %17 : i32 to i64
    %18 = arith.remsi %arg0, %19 : i64
    %20 = arith.constant 0 : i32
    %22 = arith.extsi %20 : i32 to i64
    %21 = arith.cmpi eq, %18, %22 : i64
    cf.cond_br %21, ^bb3, ^bb4
    ^bb3:
      %23 = arith.constant 20 : i32
      %25 = arith.constant 30 : i32
      %26 = arith.constant 2 : i32
      %28 = arith.extsi %26 : i32 to i64
      %27 = arith.divsi %arg0, %28 : i64
      %29 = arith.constant 1 : i32
      %31 = arith.extsi %29 : i32 to i64
      %30 = arith.subi %27, %31 : i64
      %32 = arith.extsi %25 : i32 to i64
      %24 = func.call @powi(%32, %30) : (i64, i64) -> i64
      %34 = arith.extsi %23 : i32 to i64
      %33 = arith.muli %34, %24 : i64
      func.return %33 : i64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %35 = arith.constant 4 : i32
    %37 = arith.extsi %35 : i32 to i64
    %36 = arith.remsi %arg0, %37 : i64
    %38 = arith.constant 3 : i32
    %40 = arith.extsi %38 : i32 to i64
    %39 = arith.cmpi eq, %36, %40 : i64
    cf.cond_br %39, ^bb6, ^bb7
    ^bb6:
      %41 = arith.constant 100 : i32
      %43 = arith.constant 500 : i32
      %44 = arith.constant 3 : i32
      %46 = arith.extsi %44 : i32 to i64
      %45 = arith.subi %arg0, %46 : i64
      %47 = arith.constant 4 : i32
      %49 = arith.extsi %47 : i32 to i64
      %48 = arith.divsi %45, %49 : i64
      %50 = arith.extsi %43 : i32 to i64
      %42 = func.call @powi(%50, %48) : (i64, i64) -> i64
      %52 = arith.extsi %41 : i32 to i64
      %51 = arith.muli %52, %42 : i64
      func.return %51 : i64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %53 = arith.constant 0 : i32
    %54 = arith.extsi %53 : i32 to i64
    func.return %54 : i64
  }
  func.func @main() -> i32 {
    %55 = arith.constant 0 : i32
    %56 = arith.extsi %55 : i32 to i64
    %57 = llvm.mlir.constant(1 : i64) : i64
    %58 = llvm.alloca %57 x i64 : (i64) -> !llvm.ptr
    llvm.store %56, %58 : i64, !llvm.ptr
    %59 = arith.constant 1 : i32
    %60 = arith.extsi %59 : i32 to i64
    %61 = llvm.mlir.constant(1 : i64) : i64
    %62 = llvm.alloca %61 x i64 : (i64) -> !llvm.ptr
    llvm.store %60, %62 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %63 = llvm.load %62 : !llvm.ptr -> i64
    %64 = arith.constant 9 : i32
    %66 = arith.extsi %64 : i32 to i64
    %65 = arith.cmpi sle, %63, %66 : i64
    cf.cond_br %65, ^bb10, ^bb11
    ^bb10:
      %67 = llvm.load %58 : !llvm.ptr -> i64
      %69 = llvm.load %62 : !llvm.ptr -> i64
      %68 = func.call @count_by_length(%69) : (i64) -> i64
      %70 = arith.addi %67, %68 : i64
      llvm.store %70, %58 : i64, !llvm.ptr
      %71 = llvm.load %62 : !llvm.ptr -> i64
      %72 = arith.constant 1 : i32
      %74 = arith.extsi %72 : i32 to i64
      %73 = arith.addi %71, %74 : i64
      llvm.store %73, %62 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %75 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %76 = llvm.load %58 : !llvm.ptr -> i64
    %77 = llvm.call @printf(%75, %76) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %78 = arith.constant 0 : i32
    func.return %78 : i32
  }
}