Problem 190

Sum floor(P_m) for m=2..15 maximizing prod x_k^k with sum x_i = m. Optimum: x_k = 2k/(m+1).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 190
# Sum floor(P_m) for m=2..15 maximizing prod x_k^k with sum x_i = m.
# Optimum: x_k = 2k/(m+1).

extern {
    function log(x: f64) -> f64
    function exp(x: f64) -> f64
    function floor(x: f64) -> f64
}

function floor_Pm(m: i64) -> i64 {
    let mut s: f64 = 0.0
    let mut k: i64 = 1
    while k <= m {
        let xk: f64 = (2.0 * (k as f64)) / ((m + 1) as f64)
        s = s + (k as f64) * log(xk)
        k = k + 1
    }
    return floor(exp(s)) as i64
}

function main() -> i32 {
    let mut total: i64 = 0
    let mut m: i64 = 2
    while m <= 15 {
        total = total + floor_Pm(m)
        m = m + 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 floor_Pm_i64(int64_t m);
int32_t main(void);




int64_t floor_Pm_i64(int64_t m) {
    double s = 0.0;
    int64_t k = 1;
    while (k <= m) {
        double xk = ((2.0 * ((double)(k))) / ((double)((m + 1))));
        s = (s + (((double)(k)) * log(xk)));
        k = (k + 1);
    }
    return ((int64_t)(floor(exp(s))));
}

int32_t main(void) {
    int64_t total = 0;
    int64_t m = 2;
    while (m <= 15) {
        total = (total + floor_Pm_i64(m));
        m = (m + 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 private @log(f64) -> f64
  func.func private @exp(f64) -> f64
  func.func private @floor(f64) -> f64
  func.func @floor_Pm(%arg0: i64) -> i64 {
    %0 = arith.constant 0.0 : f32
    %1 = arith.extf %0 : f32 to f64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x f64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : f64, !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
    cf.br ^bb0
    ^bb0:
    %8 = llvm.load %7 : !llvm.ptr -> i64
    %9 = arith.cmpi sle, %8, %arg0 : i64
    cf.cond_br %9, ^bb1, ^bb2
    ^bb1:
      %10 = arith.constant 2.0 : f32
      %11 = llvm.load %7 : !llvm.ptr -> i64
      %12 = arith.sitofp %11 : i64 to f64
      %14 = arith.extf %10 : f32 to f64
      %13 = arith.mulf %14, %12 : f64
      %15 = arith.constant 1 : i32
      %17 = arith.extsi %15 : i32 to i64
      %16 = arith.addi %arg0, %17 : i64
      %18 = arith.sitofp %16 : i64 to f64
      %19 = arith.divf %13, %18 : f64
      %20 = llvm.load %3 : !llvm.ptr -> f64
      %21 = llvm.load %7 : !llvm.ptr -> i64
      %22 = arith.sitofp %21 : i64 to f64
      %23 = math.log %19 : f64
      %24 = arith.mulf %22, %23 : f64
      %25 = arith.addf %20, %24 : f64
      llvm.store %25, %3 : f64, !llvm.ptr
      %26 = llvm.load %7 : !llvm.ptr -> i64
      %27 = arith.constant 1 : i32
      %29 = arith.extsi %27 : i32 to i64
      %28 = arith.addi %26, %29 : i64
      llvm.store %28, %7 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %31 = llvm.load %3 : !llvm.ptr -> f64
    %32 = math.exp %31 : f64
    %30 = func.call @floor(%32) : (f64) -> f64
    %33 = arith.fptosi %30 : f64 to i64
    func.return %33 : i64
  }
  func.func @main() -> i32 {
    %34 = arith.constant 0 : i32
    %35 = arith.extsi %34 : i32 to i64
    %36 = llvm.mlir.constant(1 : i64) : i64
    %37 = llvm.alloca %36 x i64 : (i64) -> !llvm.ptr
    llvm.store %35, %37 : i64, !llvm.ptr
    %38 = arith.constant 2 : i32
    %39 = arith.extsi %38 : i32 to i64
    %40 = llvm.mlir.constant(1 : i64) : i64
    %41 = llvm.alloca %40 x i64 : (i64) -> !llvm.ptr
    llvm.store %39, %41 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %42 = llvm.load %41 : !llvm.ptr -> i64
    %43 = arith.constant 15 : i32
    %45 = arith.extsi %43 : i32 to i64
    %44 = arith.cmpi sle, %42, %45 : i64
    cf.cond_br %44, ^bb4, ^bb5
    ^bb4:
      %46 = llvm.load %37 : !llvm.ptr -> i64
      %48 = llvm.load %41 : !llvm.ptr -> i64
      %47 = func.call @floor_Pm(%48) : (i64) -> i64
      %49 = arith.addi %46, %47 : i64
      llvm.store %49, %37 : i64, !llvm.ptr
      %50 = llvm.load %41 : !llvm.ptr -> i64
      %51 = arith.constant 1 : i32
      %53 = arith.extsi %51 : i32 to i64
      %52 = arith.addi %50, %53 : i64
      llvm.store %52, %41 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %54 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %55 = llvm.load %37 : !llvm.ptr -> i64
    %56 = llvm.call @printf(%54, %55) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %57 = arith.constant 0 : i32
    func.return %57 : i32
  }
}