Problem 088

Sum of all minimal product-sum numbers for 2≤k≤12000.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 088
# Sum of all minimal product-sum numbers for 2≤k≤12000.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
}

function search(prod: i32, sum: i32, cnt: i32, start: i32, limit: i32, kmax: i32, min_n: ptr<i32>) -> void {
    if cnt > 0 {
        let k: i32 = prod - sum + cnt
        if k >= 2 && k <= kmax {
            if prod < min_n[k] {
                min_n[k] = prod
            }
        }
    }
    let mut f: i32 = start
    while prod * f <= limit {
        search(prod * f, sum + f, cnt + 1, f, limit, kmax, min_n)
        f = f + 1
    }
}

function main() -> i32 {
    let kmax: i32 = 12000
    let limit: i32 = 2 * kmax
    let min_n: ptr<i32> = calloc((kmax + 1) as i64, 4)
    if min_n == null { return 1 }
    let mut k: i32 = 0
    while k <= kmax {
        min_n[k] = limit + 1
        k = k + 1
    }
    search(1, 0, 0, 2, limit, kmax, min_n)

    let used: ptr<i8> = calloc((limit + 1) as i64, 1)
    if used == null { return 1 }
    let mut total: i64 = 0
    k = 2
    while k <= kmax {
        let n: i32 = min_n[k]
        if used[n] == 0 {
            used[n] = 1
            total = total + (n as i64)
        }
        k = k + 1
    }
    printf("%lld\n", total)
    free(min_n)
    free(used)
    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; }

void search_i32_i32_i32_i32_i32_i32_ptr_i32(int32_t prod, int32_t sum, int32_t cnt, int32_t start, int32_t limit, int32_t kmax, int32_t* min_n);
int32_t main(void);



void search_i32_i32_i32_i32_i32_i32_ptr_i32(int32_t prod, int32_t sum, int32_t cnt, int32_t start, int32_t limit, int32_t kmax, int32_t* min_n) {
    if (cnt > 0) {
        int32_t k = ((prod - sum) + cnt);
        if ((k >= 2 && k <= kmax)) {
            if (prod < min_n[k]) {
                min_n[k] = prod;
            }
        }
    }
    int32_t f = start;
    while ((prod * f) <= limit) {
        search_i32_i32_i32_i32_i32_i32_ptr_i32((prod * f), (sum + f), (cnt + 1), f, limit, kmax, min_n);
        f = (f + 1);
    }
}

int32_t main(void) {
    int32_t kmax = 12000;
    int32_t limit = (2 * kmax);
    int32_t* min_n = (int32_t*)(calloc(((int64_t)((kmax + 1))), 4));
    if (min_n == NULL) {
        return 1;
    }
    int32_t k = 0;
    while (k <= kmax) {
        min_n[k] = (limit + 1);
        k = (k + 1);
    }
    search_i32_i32_i32_i32_i32_i32_ptr_i32(1, 0, 0, 2, limit, kmax, min_n);
    int8_t* used = (int8_t*)(calloc(((int64_t)((limit + 1))), 1));
    if (used == NULL) {
        return 1;
    }
    int64_t total = 0;
    k = 2;
    while (k <= kmax) {
        int32_t n = min_n[k];
        if (used[n] == 0) {
            used[n] = 1;
            total = (total + ((int64_t)(n)));
        }
        k = (k + 1);
    }
    printf("%lld\n", total);
    free(min_n);
    free(used);
    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 @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func @search(%arg0: i32, %arg1: i32, %arg2: i32, %arg3: i32, %arg4: i32, %arg5: i32, %arg6: !llvm.ptr) -> () {
    %0 = arith.constant 0 : i32
    %1 = arith.cmpi sgt, %arg2, %0 : i32
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      %2 = arith.subi %arg0, %arg1 : i32
      %3 = arith.addi %2, %arg2 : i32
      %4 = arith.constant 2 : i32
      %5 = arith.cmpi sge, %3, %4 : i32
      %6 = scf.if %5 -> (i1) {
        %7 = arith.cmpi sle, %3, %arg5 : i32
        scf.yield %7 : i1
      } else {
        %8 = arith.constant false
        scf.yield %8 : i1
      }
      cf.cond_br %6, ^bb3, ^bb4
      ^bb3:
        %10 = arith.extsi %3 : i32 to i64
        %11 = llvm.getelementptr %arg6[%10] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %9 = llvm.load %11 : !llvm.ptr -> i32
        %12 = arith.cmpi slt, %arg0, %9 : i32
        cf.cond_br %12, ^bb6, ^bb7
        ^bb6:
          %13 = arith.extsi %3 : i32 to i64
          %14 = llvm.getelementptr %arg6[%13] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          llvm.store %arg0, %14 : i32, !llvm.ptr
          cf.br ^bb8
        ^bb7:
          cf.br ^bb8
        ^bb8:
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      cf.br ^bb2
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %15 = llvm.mlir.constant(1 : i64) : i64
    %16 = llvm.alloca %15 x i32 : (i64) -> !llvm.ptr
    llvm.store %arg3, %16 : i32, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %17 = llvm.load %16 : !llvm.ptr -> i32
    %18 = arith.muli %arg0, %17 : i32
    %19 = arith.cmpi sle, %18, %arg4 : i32
    cf.cond_br %19, ^bb10, ^bb11
    ^bb10:
      %21 = llvm.load %16 : !llvm.ptr -> i32
      %22 = arith.muli %arg0, %21 : i32
      %23 = llvm.load %16 : !llvm.ptr -> i32
      %24 = arith.addi %arg1, %23 : i32
      %25 = arith.constant 1 : i32
      %26 = arith.addi %arg2, %25 : i32
      %27 = llvm.load %16 : !llvm.ptr -> i32
      func.call @search(%22, %24, %26, %27, %arg4, %arg5, %arg6) : (i32, i32, i32, i32, i32, i32, !llvm.ptr) -> ()
      %28 = llvm.load %16 : !llvm.ptr -> i32
      %29 = arith.constant 1 : i32
      %30 = arith.addi %28, %29 : i32
      llvm.store %30, %16 : i32, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    func.return
  }
  func.func @main() -> i32 {
    %31 = arith.constant 12000 : i32
    %32 = arith.constant 2 : i32
    %33 = arith.muli %32, %31 : i32
    %35 = arith.constant 1 : i32
    %36 = arith.addi %31, %35 : i32
    %37 = arith.extsi %36 : i32 to i64
    %38 = arith.constant 4 : i32
    %39 = arith.extsi %38 : i32 to i64
    %34 = func.call @calloc(%37, %39) : (i64, i64) -> !llvm.ptr
    %40 = llvm.mlir.zero : !llvm.ptr
    %41 = llvm.icmp "eq" %34, %40 : !llvm.ptr
    cf.cond_br %41, ^bb12, ^bb13
    ^bb12:
      %42 = arith.constant 1 : i32
      func.return %42 : i32
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %43 = arith.constant 0 : i32
    %44 = llvm.mlir.constant(1 : i64) : i64
    %45 = llvm.alloca %44 x i32 : (i64) -> !llvm.ptr
    llvm.store %43, %45 : i32, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %46 = llvm.load %45 : !llvm.ptr -> i32
    %47 = arith.cmpi sle, %46, %31 : i32
    cf.cond_br %47, ^bb16, ^bb17
    ^bb16:
      %48 = arith.constant 1 : i32
      %49 = arith.addi %33, %48 : i32
      %50 = llvm.load %45 : !llvm.ptr -> i32
      %51 = arith.extsi %50 : i32 to i64
      %52 = llvm.getelementptr %34[%51] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %49, %52 : i32, !llvm.ptr
      %53 = llvm.load %45 : !llvm.ptr -> i32
      %54 = arith.constant 1 : i32
      %55 = arith.addi %53, %54 : i32
      llvm.store %55, %45 : i32, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %57 = arith.constant 1 : i32
    %58 = arith.constant 0 : i32
    %59 = arith.constant 0 : i32
    %60 = arith.constant 2 : i32
    func.call @search(%57, %58, %59, %60, %33, %31, %34) : (i32, i32, i32, i32, i32, i32, !llvm.ptr) -> ()
    %62 = arith.constant 1 : i32
    %63 = arith.addi %33, %62 : i32
    %64 = arith.extsi %63 : i32 to i64
    %65 = arith.constant 1 : i32
    %66 = arith.extsi %65 : i32 to i64
    %61 = func.call @calloc(%64, %66) : (i64, i64) -> !llvm.ptr
    %67 = llvm.mlir.zero : !llvm.ptr
    %68 = llvm.icmp "eq" %61, %67 : !llvm.ptr
    cf.cond_br %68, ^bb18, ^bb19
    ^bb18:
      %69 = arith.constant 1 : i32
      func.return %69 : i32
    ^bb19:
      cf.br ^bb20
    ^bb20:
    %70 = arith.constant 0 : i32
    %71 = arith.extsi %70 : i32 to i64
    %72 = llvm.mlir.constant(1 : i64) : i64
    %73 = llvm.alloca %72 x i64 : (i64) -> !llvm.ptr
    llvm.store %71, %73 : i64, !llvm.ptr
    %74 = arith.constant 2 : i32
    llvm.store %74, %45 : i32, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %75 = llvm.load %45 : !llvm.ptr -> i32
    %76 = arith.cmpi sle, %75, %31 : i32
    cf.cond_br %76, ^bb22, ^bb23
    ^bb22:
      %78 = llvm.load %45 : !llvm.ptr -> i32
      %79 = arith.extsi %78 : i32 to i64
      %80 = llvm.getelementptr %34[%79] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %77 = llvm.load %80 : !llvm.ptr -> i32
      %82 = arith.extsi %77 : i32 to i64
      %83 = llvm.getelementptr %61[%82] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %81 = llvm.load %83 : !llvm.ptr -> i8
      %84 = arith.constant 0 : i32
      %86 = arith.extsi %81 : i8 to i32
      %85 = arith.cmpi eq, %86, %84 : i32
      cf.cond_br %85, ^bb24, ^bb25
      ^bb24:
        %87 = arith.constant 1 : i32
        %88 = arith.trunci %87 : i32 to i8
        %89 = arith.extsi %77 : i32 to i64
        %90 = llvm.getelementptr %61[%89] : (!llvm.ptr, i64) -> !llvm.ptr, i8
        llvm.store %88, %90 : i8, !llvm.ptr
        %91 = llvm.load %73 : !llvm.ptr -> i64
        %92 = arith.extsi %77 : i32 to i64
        %93 = arith.addi %91, %92 : i64
        llvm.store %93, %73 : i64, !llvm.ptr
        cf.br ^bb26
      ^bb25:
        cf.br ^bb26
      ^bb26:
      %94 = llvm.load %45 : !llvm.ptr -> i32
      %95 = arith.constant 1 : i32
      %96 = arith.addi %94, %95 : i32
      llvm.store %96, %45 : i32, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %97 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %98 = llvm.load %73 : !llvm.ptr -> i64
    %99 = llvm.call @printf(%97, %98) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%34) : (!llvm.ptr) -> ()
    func.call @free(%61) : (!llvm.ptr) -> ()
    %102 = arith.constant 0 : i32
    func.return %102 : i32
  }
}