Problem 028

Sum of both diagonals in a 1001×1001 spiral.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 028
# Sum of both diagonals in a 1001×1001 spiral.

function solve(size: i64) -> i64 {
    # Corners of layer with side 2k+1: n², n²-n+1, n²-2n+2, n²-3n+3 where n=2k+1
    let mut total: i64 = 1
    for n in 3..(size + 1) step 2 {
        total = total + 4 * n * n - 6 * (n - 1)
    }
    return total
}

function main() -> i32 {
    printf("%lld\n", solve(1001))
    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 solve_i64(int64_t size);
int32_t main(void);

int64_t solve_i64(int64_t size) {
    int64_t total = 1;
    int32_t __flow_step_1 = 2;
    #pragma clang loop vectorize(enable) interleave(enable)
    #pragma GCC ivdep
    for (int32_t n = 3; (__flow_step_1 > 0) ? n < (size + 1) : n > (size + 1); n += __flow_step_1) {
        total = ((total + ((4 * n) * n)) - (6 * (n - 1)));
    }
    return total;
}

int32_t main(void) {
    printf("%lld\n", solve_i64(1001));
    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 @solve(%arg0: 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 = arith.constant 3 : i32
    %5 = arith.constant 1 : i32
    %7 = arith.extsi %5 : i32 to i64
    %6 = arith.addi %arg0, %7 : i64
    %8 = arith.index_cast %4 : i32 to index
    %9 = arith.index_cast %6 : i32 to index
    %10 = arith.constant 2 : index
    scf.for %11 = %8 to %9 step %10 {
      %12 = llvm.load %3 : !llvm.ptr -> i64
      %13 = arith.constant 4 : i32
      %15 = arith.index_cast %11 : index to i32
      %14 = arith.muli %13, %15 : i32
      %17 = arith.index_cast %11 : index to i32
      %16 = arith.muli %14, %17 : i32
      %19 = arith.extsi %16 : i32 to i64
      %18 = arith.addi %12, %19 : i64
      %20 = arith.constant 6 : i32
      %21 = arith.constant 1 : i32
      %23 = arith.index_cast %11 : index to i32
      %22 = arith.subi %23, %21 : i32
      %24 = arith.muli %20, %22 : i32
      %26 = arith.extsi %24 : i32 to i64
      %25 = arith.subi %18, %26 : i64
      llvm.store %25, %3 : i64, !llvm.ptr
    }
    %27 = llvm.load %3 : !llvm.ptr -> i64
    func.return %27 : i64
  }
  func.func @main() -> i32 {
    %28 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %30 = arith.constant 1001 : i32
    %31 = arith.extsi %30 : i32 to i64
    %29 = func.call @solve(%31) : (i64) -> i64
    %32 = llvm.call @printf(%28, %29) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %33 = arith.constant 0 : i32
    func.return %33 : i32
  }
}