Problem 225

124th odd number that does not divide any term of the tribonacci sequence.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 225
# 124th odd number that does not divide any term of the tribonacci sequence.

function divides_trib(mod: i64) -> bool {
    let mut a: i64 = 1
    let mut b: i64 = 1
    let mut c: i64 = 1
    # period at most mod^3; detect return to (1,1,1) or zero
    let mut steps: i64 = 0
    let limit: i64 = mod * mod * mod + 5
    while steps < limit {
        let nxt: i64 = (a + b + c) % mod
        if nxt == 0 { return true }
        a = b
        b = c
        c = nxt
        if a == 1 && b == 1 && c == 1 { return false }
        steps = steps + 1
    }
    return false
}

function main() -> i32 {
    let mut count: i32 = 0
    let mut n: i64 = 1
    while true {
        n = n + 2
        if !divides_trib(n) {
            count = count + 1
            if count == 124 {
                printf("%lld\n", n)
                return 0
            }
        }
    }
    return 1
}

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; }

bool divides_trib_i64(int64_t mod);
int32_t main(void);

bool divides_trib_i64(int64_t mod) {
    int64_t a = 1;
    int64_t b = 1;
    int64_t c = 1;
    int64_t steps = 0;
    int64_t limit = (((mod * mod) * mod) + 5);
    while (steps < limit) {
        int64_t nxt = FLOW_CHECKED_MOD((((a + b) + c)), (mod));
        if (nxt == 0) {
            return 1;
        }
        a = b;
        b = c;
        c = nxt;
        if (((a == 1 && b == 1) && c == 1)) {
            return 0;
        }
        steps = (steps + 1);
    }
    return 0;
}

int32_t main(void) {
    int32_t count = 0;
    int64_t n = 1;
    while (1) {
        n = (n + 2);
        if ((!(divides_trib_i64(n)))) {
            count = (count + 1);
            if (count == 124) {
                printf("%lld\n", n);
                return 0;
            }
        }
    }
    return 1;
}

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 @divides_trib(%arg0: i64) -> i1 {
    %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 = arith.constant 1 : i32
    %5 = arith.extsi %4 : i32 to i64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x i64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : i64, !llvm.ptr
    %8 = arith.constant 1 : i32
    %9 = arith.extsi %8 : i32 to i64
    %10 = llvm.mlir.constant(1 : i64) : i64
    %11 = llvm.alloca %10 x i64 : (i64) -> !llvm.ptr
    llvm.store %9, %11 : i64, !llvm.ptr
    %12 = arith.constant 0 : i32
    %13 = arith.extsi %12 : i32 to i64
    %14 = llvm.mlir.constant(1 : i64) : i64
    %15 = llvm.alloca %14 x i64 : (i64) -> !llvm.ptr
    llvm.store %13, %15 : i64, !llvm.ptr
    %16 = arith.muli %arg0, %arg0 : i64
    %17 = arith.muli %16, %arg0 : i64
    %18 = arith.constant 5 : i32
    %20 = arith.extsi %18 : i32 to i64
    %19 = arith.addi %17, %20 : i64
    cf.br ^bb0
    ^bb0:
    %21 = llvm.load %15 : !llvm.ptr -> i64
    %22 = arith.cmpi slt, %21, %19 : i64
    cf.cond_br %22, ^bb1, ^bb2
    ^bb1:
      %23 = llvm.load %3 : !llvm.ptr -> i64
      %24 = llvm.load %7 : !llvm.ptr -> i64
      %25 = arith.addi %23, %24 : i64
      %26 = llvm.load %11 : !llvm.ptr -> i64
      %27 = arith.addi %25, %26 : i64
      %28 = arith.remsi %27, %arg0 : i64
      %29 = arith.constant 0 : i32
      %31 = arith.extsi %29 : i32 to i64
      %30 = arith.cmpi eq, %28, %31 : i64
      cf.cond_br %30, ^bb3, ^bb4
      ^bb3:
        %32 = arith.constant 1 : i1
        func.return %32 : i1
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %33 = llvm.load %7 : !llvm.ptr -> i64
      llvm.store %33, %3 : i64, !llvm.ptr
      %34 = llvm.load %11 : !llvm.ptr -> i64
      llvm.store %34, %7 : i64, !llvm.ptr
      llvm.store %28, %11 : i64, !llvm.ptr
      %35 = llvm.load %3 : !llvm.ptr -> i64
      %36 = arith.constant 1 : i32
      %38 = arith.extsi %36 : i32 to i64
      %37 = arith.cmpi eq, %35, %38 : i64
      %39 = scf.if %37 -> (i1) {
        %40 = llvm.load %7 : !llvm.ptr -> i64
        %41 = arith.constant 1 : i32
        %43 = arith.extsi %41 : i32 to i64
        %42 = arith.cmpi eq, %40, %43 : i64
        scf.yield %42 : i1
      } else {
        %44 = arith.constant false
        scf.yield %44 : i1
      }
      %45 = scf.if %39 -> (i1) {
        %46 = llvm.load %11 : !llvm.ptr -> i64
        %47 = arith.constant 1 : i32
        %49 = arith.extsi %47 : i32 to i64
        %48 = arith.cmpi eq, %46, %49 : i64
        scf.yield %48 : i1
      } else {
        %50 = arith.constant false
        scf.yield %50 : i1
      }
      cf.cond_br %45, ^bb6, ^bb7
      ^bb6:
        %51 = arith.constant 0 : i1
        func.return %51 : i1
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %52 = llvm.load %15 : !llvm.ptr -> i64
      %53 = arith.constant 1 : i32
      %55 = arith.extsi %53 : i32 to i64
      %54 = arith.addi %52, %55 : i64
      llvm.store %54, %15 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %56 = arith.constant 0 : i1
    func.return %56 : i1
  }
  func.func @main() -> i32 {
    %57 = arith.constant 0 : i32
    %58 = llvm.mlir.constant(1 : i64) : i64
    %59 = llvm.alloca %58 x i32 : (i64) -> !llvm.ptr
    llvm.store %57, %59 : i32, !llvm.ptr
    %60 = arith.constant 1 : i32
    %61 = arith.extsi %60 : i32 to i64
    %62 = llvm.mlir.constant(1 : i64) : i64
    %63 = llvm.alloca %62 x i64 : (i64) -> !llvm.ptr
    llvm.store %61, %63 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %64 = arith.constant 1 : i1
    cf.cond_br %64, ^bb10, ^bb11
    ^bb10:
      %65 = llvm.load %63 : !llvm.ptr -> i64
      %66 = arith.constant 2 : i32
      %68 = arith.extsi %66 : i32 to i64
      %67 = arith.addi %65, %68 : i64
      llvm.store %67, %63 : i64, !llvm.ptr
      %70 = llvm.load %63 : !llvm.ptr -> i64
      %69 = func.call @divides_trib(%70) : (i64) -> i1
      %72 = arith.constant 1 : i1
      %71 = arith.xori %69, %72 : i1
      cf.cond_br %71, ^bb12, ^bb13
      ^bb12:
        %74 = llvm.load %59 : !llvm.ptr -> i32
        %75 = arith.constant 1 : i32
        %76 = arith.addi %74, %75 : i32
        llvm.store %76, %59 : i32, !llvm.ptr
        %77 = llvm.load %59 : !llvm.ptr -> i32
        %78 = arith.constant 124 : i32
        %79 = arith.cmpi eq, %77, %78 : i32
        cf.cond_br %79, ^bb15, ^bb16
        ^bb15:
          %80 = llvm.mlir.addressof @str_0 : !llvm.ptr
          %81 = llvm.load %63 : !llvm.ptr -> i64
          %82 = llvm.call @printf(%80, %81) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
          %83 = arith.constant 0 : i32
          func.return %83 : i32
        ^bb16:
          cf.br ^bb17
        ^bb17:
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      cf.br ^bb9
    ^bb11:
    %84 = arith.constant 1 : i32
    func.return %84 : i32
  }
}