Problem 694

Cube-full divisors: S(10^18) via DFS over p^3 | n cube-fulls. Ported from native C to pure Flow.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 694
# Cube-full divisors: S(10^18) via DFS over p^3 | n cube-fulls.
# Ported from native C to pure Flow.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
    function cbrt(x: f64) -> f64
}

let mut N: i64 = 0
let mut primes: ptr<i64> = null
let mut pc: i64 = 0

function generate(curr0: i64, idx: i64) -> i64 {
    let mut total: i64 = 0
    let p: i64 = primes[idx]
    if curr0 > N / (p * p * p) {
        return 0
    }
    let mut curr: i64 = curr0 * (p * p * p)
    while curr <= N {
        total = total + N / curr
        for j in (idx + 1)..pc {
            let t: i64 = generate(curr, j)
            if t == 0 {
                break
            }
            total = total + t
        }
        if curr > N / p {
            break
        }
        curr = curr * p
    }
    return total
}

function main() -> i32 {
    N = 1000000000000000000
    let lim: i64 = (cbrt(N as f64) + 2.0) as i64
    let sieve: ptr<i8> = calloc(lim + 1, 1) as ptr<i8>
    primes = calloc(lim, 8) as ptr<i64>
    pc = 0
    let mut i: i64 = 2
    while i <= lim {
        if sieve[i] == 0 {
            primes[pc] = i
            pc = pc + 1
            let mut j: i64 = i * i
            while j <= lim {
                sieve[j] = 1
                j = j + i
            }
        }
        i = i + 1
    }
    let mut ans: i64 = N
    for i in 0..pc {
        ans = ans + generate(1, i)
    }
    free(sieve as ptr<void>)
    free(primes as ptr<void>)
    printf("%lld\n", ans)
    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; }

double cbrt(double x);
int64_t generate_i64_i64(int64_t curr0, int64_t idx);
int32_t main(void);

/* Module statics */
static int64_t N = 0;
static int64_t* primes = NULL;
static int64_t pc = 0;




int64_t generate_i64_i64(int64_t curr0, int64_t idx) {
    int64_t total = 0;
    int64_t p = primes[idx];
    if (curr0 > FLOW_CHECKED_DIV((N), (((p * p) * p)))) {
        return 0;
    }
    int64_t curr = (curr0 * ((p * p) * p));
    while (curr <= N) {
        total = (total + FLOW_CHECKED_DIV((N), (curr)));
        int32_t __flow_step_1 = 1;
        for (int32_t j = (idx + 1); ((idx + 1) <= pc) ? j < pc : j > pc; j += ((idx + 1) <= pc) ? 1 : -1) {
            int64_t t = generate_i64_i64(curr, j);
            if (t == 0) {
                break;
            }
            total = (total + t);
        }
        if (curr > FLOW_CHECKED_DIV((N), (p))) {
            break;
        }
        curr = (curr * p);
    }
    return total;
}

int32_t main(void) {
    N = 1000000000000000000;
    int64_t lim = ((int64_t)((cbrt(((double)(N))) + 2.0)));
    int8_t* sieve = (int8_t*)(((int8_t*)(calloc((lim + 1), 1))));
    primes = ((int64_t*)(calloc(lim, 8)));
    pc = 0;
    int64_t i = 2;
    while (i <= lim) {
        if (sieve[i] == 0) {
            primes[pc] = i;
            pc = (pc + 1);
            int64_t j = (i * i);
            while (j <= lim) {
                sieve[j] = 1;
                j = (j + i);
            }
        }
        i = (i + 1);
    }
    int64_t ans = N;
    int32_t __flow_step_2 = 1;
    for (int32_t i = 0; (0 <= pc) ? i < pc : i > pc; i += (0 <= pc) ? 1 : -1) {
        ans = (ans + generate_i64_i64(1, i));
    }
    free(((void*)(sieve)));
    free(((void*)(primes)));
    printf("%lld\n", ans);
    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 private @cbrt(f64) -> f64
  // Module static: N
  llvm.mlir.global internal @N(0 : i64) : i64
  // Module static: primes
  llvm.mlir.global internal @primes() {addr_space = 0 : i32} : !llvm.ptr {
    %0 = llvm.mlir.zero : !llvm.ptr
    llvm.return %0 : !llvm.ptr
  }
  // Module static: pc
  llvm.mlir.global internal @pc(0 : i64) : i64
  func.func @generate(%arg0: i64, %arg1: i64) -> i64 {
    %1 = arith.constant 0 : i32
    %2 = arith.extsi %1 : i32 to i64
    %3 = llvm.mlir.constant(1 : i64) : i64
    %4 = llvm.alloca %3 x i64 : (i64) -> !llvm.ptr
    llvm.store %2, %4 : i64, !llvm.ptr
    %6 = llvm.mlir.addressof @primes : !llvm.ptr
    %7 = llvm.load %6 : !llvm.ptr -> !llvm.ptr
    %8 = llvm.getelementptr %7[%arg1] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %5 = llvm.load %8 : !llvm.ptr -> i64
    %9 = llvm.mlir.addressof @N : !llvm.ptr
    %10 = llvm.load %9 : !llvm.ptr -> i64
    %11 = arith.muli %5, %5 : i64
    %12 = arith.muli %11, %5 : i64
    %13 = arith.divsi %10, %12 : i64
    %14 = arith.cmpi sgt, %arg0, %13 : i64
    cf.cond_br %14, ^bb0, ^bb1
    ^bb0:
      %15 = arith.constant 0 : i32
      %16 = arith.extsi %15 : i32 to i64
      func.return %16 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %17 = arith.muli %5, %5 : i64
    %18 = arith.muli %17, %5 : i64
    %19 = arith.muli %arg0, %18 : i64
    %20 = llvm.mlir.constant(1 : i64) : i64
    %21 = llvm.alloca %20 x i64 : (i64) -> !llvm.ptr
    llvm.store %19, %21 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %22 = llvm.load %21 : !llvm.ptr -> i64
    %23 = llvm.mlir.addressof @N : !llvm.ptr
    %24 = llvm.load %23 : !llvm.ptr -> i64
    %25 = arith.cmpi sle, %22, %24 : i64
    cf.cond_br %25, ^bb4, ^bb5
    ^bb4:
      %26 = llvm.load %4 : !llvm.ptr -> i64
      %27 = llvm.mlir.addressof @N : !llvm.ptr
      %28 = llvm.load %27 : !llvm.ptr -> i64
      %29 = llvm.load %21 : !llvm.ptr -> i64
      %30 = arith.divsi %28, %29 : i64
      %31 = arith.addi %26, %30 : i64
      llvm.store %31, %4 : i64, !llvm.ptr
      %32 = arith.constant 1 : i32
      %34 = arith.extsi %32 : i32 to i64
      %33 = arith.addi %arg1, %34 : i64
      %35 = llvm.mlir.addressof @pc : !llvm.ptr
      %36 = llvm.load %35 : !llvm.ptr -> i64
      %37 = arith.index_cast %33 : i32 to index
      %38 = arith.index_cast %36 : i32 to index
      %40 = arith.constant 1 : index
      %41 = arith.constant -1 : index
      %42 = arith.cmpi sle, %37, %38 : index
      %39 = arith.select %42, %40, %41 : index
      cf.br ^bb6(%37 : index)
      ^bb6(%43: index):
      %44 = arith.cmpi slt, %43, %38 : index
      %45 = arith.cmpi sgt, %43, %38 : index
      %46 = arith.select %42, %44, %45 : i1
      cf.cond_br %46, ^bb7(%43 : index), ^bb8(%43 : index)
      ^bb7(%47: index):
        %49 = llvm.load %21 : !llvm.ptr -> i64
        %50 = arith.index_cast %47 : index to i64
        %48 = func.call @generate(%49, %50) : (i64, i64) -> i64
        %51 = arith.constant 0 : i32
        %53 = arith.extsi %51 : i32 to i64
        %52 = arith.cmpi eq, %48, %53 : i64
        cf.cond_br %52, ^bb9, ^bb10
        ^bb9:
          cf.br ^bb8(%47 : index)
        ^bb10:
          cf.br ^bb11
        ^bb11:
        %54 = llvm.load %4 : !llvm.ptr -> i64
        %55 = arith.addi %54, %48 : i64
        llvm.store %55, %4 : i64, !llvm.ptr
        %56 = arith.addi %47, %39 : index
        cf.br ^bb6(%56 : index)
      ^bb8(%57: index):
      %58 = llvm.load %21 : !llvm.ptr -> i64
      %59 = llvm.mlir.addressof @N : !llvm.ptr
      %60 = llvm.load %59 : !llvm.ptr -> i64
      %61 = arith.divsi %60, %5 : i64
      %62 = arith.cmpi sgt, %58, %61 : i64
      cf.cond_br %62, ^bb12, ^bb13
      ^bb12:
        cf.br ^bb5
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %63 = llvm.load %21 : !llvm.ptr -> i64
      %64 = arith.muli %63, %5 : i64
      llvm.store %64, %21 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %65 = llvm.load %4 : !llvm.ptr -> i64
    func.return %65 : i64
  }
  func.func @main() -> i32 {
    %66 = arith.constant 999999995705032704 : i32
    %67 = arith.extsi %66 : i32 to i64
    %68 = llvm.mlir.addressof @N : !llvm.ptr
    llvm.store %67, %68 : i64, !llvm.ptr
    %70 = llvm.mlir.addressof @N : !llvm.ptr
    %71 = llvm.load %70 : !llvm.ptr -> i64
    %72 = arith.sitofp %71 : i64 to f64
    %69 = func.call @cbrt(%72) : (f64) -> f64
    %73 = arith.constant 2.0 : f32
    %75 = arith.extf %73 : f32 to f64
    %74 = arith.addf %69, %75 : f64
    %76 = arith.fptosi %74 : f64 to i64
    %78 = arith.constant 1 : i32
    %80 = arith.extsi %78 : i32 to i64
    %79 = arith.addi %76, %80 : i64
    %81 = arith.constant 1 : i32
    %82 = arith.extsi %81 : i32 to i64
    %77 = func.call @calloc(%79, %82) : (i64, i64) -> !llvm.ptr
    %84 = arith.constant 8 : i32
    %85 = arith.extsi %84 : i32 to i64
    %83 = func.call @calloc(%76, %85) : (i64, i64) -> !llvm.ptr
    %86 = llvm.mlir.addressof @primes : !llvm.ptr
    llvm.store %83, %86 : !llvm.ptr, !llvm.ptr
    %87 = arith.constant 0 : i32
    %88 = arith.extsi %87 : i32 to i64
    %89 = llvm.mlir.addressof @pc : !llvm.ptr
    llvm.store %88, %89 : i64, !llvm.ptr
    %90 = arith.constant 2 : i32
    %91 = arith.extsi %90 : i32 to i64
    %92 = llvm.mlir.constant(1 : i64) : i64
    %93 = llvm.alloca %92 x i64 : (i64) -> !llvm.ptr
    llvm.store %91, %93 : i64, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %94 = llvm.load %93 : !llvm.ptr -> i64
    %95 = arith.cmpi sle, %94, %76 : i64
    cf.cond_br %95, ^bb16, ^bb17
    ^bb16:
      %97 = llvm.load %93 : !llvm.ptr -> i64
      %98 = llvm.getelementptr %77[%97] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %96 = llvm.load %98 : !llvm.ptr -> i8
      %99 = arith.constant 0 : i32
      %101 = arith.extsi %96 : i8 to i32
      %100 = arith.cmpi eq, %101, %99 : i32
      cf.cond_br %100, ^bb18, ^bb19
      ^bb18:
        %102 = llvm.load %93 : !llvm.ptr -> i64
        %103 = llvm.mlir.addressof @primes : !llvm.ptr
        %104 = llvm.load %103 : !llvm.ptr -> !llvm.ptr
        %105 = llvm.mlir.addressof @pc : !llvm.ptr
        %106 = llvm.load %105 : !llvm.ptr -> i64
        %107 = llvm.getelementptr %104[%106] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        llvm.store %102, %107 : i64, !llvm.ptr
        %108 = llvm.mlir.addressof @pc : !llvm.ptr
        %109 = llvm.load %108 : !llvm.ptr -> i64
        %110 = arith.constant 1 : i32
        %112 = arith.extsi %110 : i32 to i64
        %111 = arith.addi %109, %112 : i64
        %113 = llvm.mlir.addressof @pc : !llvm.ptr
        llvm.store %111, %113 : i64, !llvm.ptr
        %114 = llvm.load %93 : !llvm.ptr -> i64
        %115 = llvm.load %93 : !llvm.ptr -> i64
        %116 = arith.muli %114, %115 : i64
        %117 = llvm.mlir.constant(1 : i64) : i64
        %118 = llvm.alloca %117 x i64 : (i64) -> !llvm.ptr
        llvm.store %116, %118 : i64, !llvm.ptr
        cf.br ^bb21
        ^bb21:
        %119 = llvm.load %118 : !llvm.ptr -> i64
        %120 = arith.cmpi sle, %119, %76 : i64
        cf.cond_br %120, ^bb22, ^bb23
        ^bb22:
          %121 = arith.constant 1 : i32
          %122 = llvm.load %118 : !llvm.ptr -> i64
          %123 = arith.trunci %121 : i32 to i8
          %124 = llvm.getelementptr %77[%122] : (!llvm.ptr, i64) -> !llvm.ptr, i8
          llvm.store %123, %124 : i8, !llvm.ptr
          %125 = llvm.load %118 : !llvm.ptr -> i64
          %126 = llvm.load %93 : !llvm.ptr -> i64
          %127 = arith.addi %125, %126 : i64
          llvm.store %127, %118 : i64, !llvm.ptr
          cf.br ^bb21
        ^bb23:
        cf.br ^bb20
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %128 = llvm.load %93 : !llvm.ptr -> i64
      %129 = arith.constant 1 : i32
      %131 = arith.extsi %129 : i32 to i64
      %130 = arith.addi %128, %131 : i64
      llvm.store %130, %93 : i64, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %132 = llvm.mlir.addressof @N : !llvm.ptr
    %133 = llvm.load %132 : !llvm.ptr -> i64
    %134 = llvm.mlir.constant(1 : i64) : i64
    %135 = llvm.alloca %134 x i64 : (i64) -> !llvm.ptr
    llvm.store %133, %135 : i64, !llvm.ptr
    %136 = arith.constant 0 : i32
    %137 = llvm.mlir.addressof @pc : !llvm.ptr
    %138 = llvm.load %137 : !llvm.ptr -> i64
    %139 = arith.index_cast %136 : i32 to index
    %140 = arith.index_cast %138 : i32 to index
    %142 = arith.constant 1 : index
    %143 = arith.constant -1 : index
    %144 = arith.cmpi sle, %139, %140 : index
    %141 = arith.select %144, %142, %143 : index
    cf.br ^bb24(%139 : index)
    ^bb24(%145: index):
    %146 = arith.cmpi slt, %145, %140 : index
    %147 = arith.cmpi sgt, %145, %140 : index
    %148 = arith.select %144, %146, %147 : i1
    cf.cond_br %148, ^bb25(%145 : index), ^bb26(%145 : index)
    ^bb25(%149: index):
      %150 = llvm.load %135 : !llvm.ptr -> i64
      %152 = arith.constant 1 : i32
      %153 = arith.extsi %152 : i32 to i64
      %154 = arith.index_cast %149 : index to i64
      %151 = func.call @generate(%153, %154) : (i64, i64) -> i64
      %155 = arith.addi %150, %151 : i64
      llvm.store %155, %135 : i64, !llvm.ptr
      %156 = arith.addi %149, %141 : index
      cf.br ^bb24(%156 : index)
    ^bb26(%157: index):
    func.call @free(%77) : (!llvm.ptr) -> ()
    %160 = llvm.mlir.addressof @primes : !llvm.ptr
    %161 = llvm.load %160 : !llvm.ptr -> !llvm.ptr
    func.call @free(%161) : (!llvm.ptr) -> ()
    %162 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %163 = llvm.load %135 : !llvm.ptr -> i64
    %164 = llvm.call @printf(%162, %163) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %165 = arith.constant 0 : i32
    func.return %165 : i32
  }
}