Problem 001

Sum of all multiples of 3 or 5 below 1000. Inclusion-exclusion with closed-form arithmetic series. Each sum is step + 2*step + ... + k*step = step * k*(k+1)/2.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 001
# Sum of all multiples of 3 or 5 below 1000.
#
# Inclusion-exclusion with closed-form arithmetic series.
# Each sum is step + 2*step + ... + k*step = step * k*(k+1)/2.

function sum_ap(n: i64, step: i64) -> i64 {
    let k: i64 = (n - 1) / step
    return step * k * (k + 1) / 2
}

function main() -> i32 {
    println(sum_ap(1000, 3) + sum_ap(1000, 5) - sum_ap(1000, 15))
    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 sum_ap_i64_i64(int64_t n, int64_t step);
int32_t main(void);

int64_t sum_ap_i64_i64(int64_t n, int64_t step) {
    int64_t k = FLOW_CHECKED_DIV(((n - 1)), (step));
    return FLOW_CHECKED_DIV((((step * k) * (k + 1))), (2));
}

int32_t main(void) {
    FLOW_LOG("%lld\n", ((sum_ap_i64_i64(1000, 3) + sum_ap_i64_i64(1000, 5)) - sum_ap_i64_i64(1000, 15)));
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%d\n\00") {addr_space = 0 : i32} : !llvm.array<4 x i8>
  func.func @sum_ap(%arg0: i64, %arg1: i64) -> i64 {
    %0 = arith.constant 1 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.subi %arg0, %2 : i64
    %3 = arith.divsi %1, %arg1 : i64
    %4 = arith.muli %arg1, %3 : i64
    %5 = arith.constant 1 : i32
    %7 = arith.extsi %5 : i32 to i64
    %6 = arith.addi %3, %7 : i64
    %8 = arith.muli %4, %6 : i64
    %9 = arith.constant 2 : i32
    %11 = arith.extsi %9 : i32 to i64
    %10 = arith.divsi %8, %11 : i64
    func.return %10 : i64
  }
  func.func @main() -> i32 {
    %13 = arith.constant 1000 : i32
    %14 = arith.constant 3 : i32
    %15 = arith.extsi %13 : i32 to i64
    %16 = arith.extsi %14 : i32 to i64
    %12 = func.call @sum_ap(%15, %16) : (i64, i64) -> i64
    %18 = arith.constant 1000 : i32
    %19 = arith.constant 5 : i32
    %20 = arith.extsi %18 : i32 to i64
    %21 = arith.extsi %19 : i32 to i64
    %17 = func.call @sum_ap(%20, %21) : (i64, i64) -> i64
    %22 = arith.addi %12, %17 : i64
    %24 = arith.constant 1000 : i32
    %25 = arith.constant 15 : i32
    %26 = arith.extsi %24 : i32 to i64
    %27 = arith.extsi %25 : i32 to i64
    %23 = func.call @sum_ap(%26, %27) : (i64, i64) -> i64
    %28 = arith.subi %22, %23 : i64
    %29 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %30 = llvm.call @printf(%29, %28) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %31 = arith.constant 0 : i32
    %32 = arith.constant 0 : i32
    func.return %32 : i32
  }
}