Problem 015

Lattice paths through a 20×20 grid (only right/down). Central binomial C(40, 20) via multiplicative formula.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 015
# Lattice paths through a 20×20 grid (only right/down).
# Central binomial C(40, 20) via multiplicative formula.

function binomial(n: i64, k0: i64) -> i64 {
    let mut k: i64 = k0
    if k > n - k {
        k = n - k
    }
    let mut result: i64 = 1
    for i in 1..(k + 1) {
        result = result * (n - k + i) / i
    }
    return result
}

function main() -> i32 {
    printf("%lld\n", binomial(40, 20))
    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 binomial_i64_i64(int64_t n, int64_t k0);
int32_t main(void);

int64_t binomial_i64_i64(int64_t n, int64_t k0) {
    int64_t k = k0;
    if (k > (n - k)) {
        k = (n - k);
    }
    int64_t result = 1;
    int32_t __flow_step_1 = 1;
    for (int32_t i = 1; (1 <= (k + 1)) ? i < (k + 1) : i > (k + 1); i += (1 <= (k + 1)) ? 1 : -1) {
        result = FLOW_CHECKED_DIV(((result * ((n - k) + i))), (i));
    }
    return result;
}

int32_t main(void) {
    printf("%lld\n", binomial_i64_i64(40, 20));
    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 @binomial(%arg0: i64, %arg1: i64) -> i64 {
    %0 = llvm.mlir.constant(1 : i64) : i64
    %1 = llvm.alloca %0 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %1 : i64, !llvm.ptr
    %2 = llvm.load %1 : !llvm.ptr -> i64
    %3 = llvm.load %1 : !llvm.ptr -> i64
    %4 = arith.subi %arg0, %3 : i64
    %5 = arith.cmpi sgt, %2, %4 : i64
    cf.cond_br %5, ^bb0, ^bb1
    ^bb0:
      %6 = llvm.load %1 : !llvm.ptr -> i64
      %7 = arith.subi %arg0, %6 : i64
      llvm.store %7, %1 : i64, !llvm.ptr
      cf.br ^bb2
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %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 1 : i32
    %13 = llvm.load %1 : !llvm.ptr -> i64
    %14 = arith.constant 1 : i32
    %16 = arith.extsi %14 : i32 to i64
    %15 = arith.addi %13, %16 : i64
    %17 = arith.index_cast %12 : i32 to index
    %18 = arith.index_cast %15 : i32 to index
    %20 = arith.constant 1 : index
    %21 = arith.constant -1 : index
    %22 = arith.cmpi sle, %17, %18 : index
    %19 = arith.select %22, %20, %21 : index
    cf.br ^bb3(%17 : index)
    ^bb3(%23: index):
    %24 = arith.cmpi slt, %23, %18 : index
    %25 = arith.cmpi sgt, %23, %18 : index
    %26 = arith.select %22, %24, %25 : i1
    cf.cond_br %26, ^bb4(%23 : index), ^bb5(%23 : index)
    ^bb4(%27: index):
      %28 = llvm.load %11 : !llvm.ptr -> i64
      %29 = llvm.load %1 : !llvm.ptr -> i64
      %30 = arith.subi %arg0, %29 : i64
      %32 = arith.trunci %30 : i64 to i32
      %33 = arith.index_cast %27 : index to i32
      %31 = arith.addi %32, %33 : i32
      %35 = arith.extsi %31 : i32 to i64
      %34 = arith.muli %28, %35 : i64
      %37 = arith.trunci %34 : i64 to i32
      %38 = arith.index_cast %27 : index to i32
      %36 = arith.divsi %37, %38 : i32
      %39 = arith.extsi %36 : i32 to i64
      llvm.store %39, %11 : i64, !llvm.ptr
      %40 = arith.addi %27, %19 : index
      cf.br ^bb3(%40 : index)
    ^bb5(%41: index):
    %42 = llvm.load %11 : !llvm.ptr -> i64
    func.return %42 : i64
  }
  func.func @main() -> i32 {
    %43 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %45 = arith.constant 40 : i32
    %46 = arith.constant 20 : i32
    %47 = arith.extsi %45 : i32 to i64
    %48 = arith.extsi %46 : i32 to i64
    %44 = func.call @binomial(%47, %48) : (i64, i64) -> i64
    %49 = llvm.call @printf(%43, %44) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %50 = arith.constant 0 : i32
    func.return %50 : i32
  }
}