Problem 193

Count squarefree numbers below 2^50 via Mobius inversion. Uses a struct to pair mu and prime flags, and for-ranges for the sieve.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 193
# Count squarefree numbers below 2^50 via Mobius inversion.
#
# Uses a struct to pair mu and prime flags, and for-ranges for the sieve.

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

struct SieveEntry {
    mu: i8,
    prime: i8
}

function main() -> i32 {
    let N: i64 = 1
    N = N << 50
    # lim = floor(sqrt(N)) = 2^25
    let lim: i64 = 1
    lim = lim << 25
    let entries: ptr<SieveEntry> = calloc(lim + 1, 2) as ptr<SieveEntry>
    if entries == null { return 1 }

    let mut i: i64 = 0
    while i <= lim {
        entries[i] = SieveEntry { mu: 1, prime: 1 }
        i = i + 1
    }
    entries[0].prime = 0
    entries[1].prime = 0

    i = 2
    while i <= lim {
        if entries[i].prime == 1 {
            let mut j: i64 = i * i
            while j <= lim {
                entries[j].prime = 0
                j = j + i
            }
            j = i
            while j <= lim {
                entries[j].mu = (0 - entries[j].mu) as i8
                j = j + i
            }
            let sq: i64 = i * i
            j = sq
            while j <= lim {
                entries[j].mu = 0
                j = j + sq
            }
        }
        i = i + 1
    }

    let mut S: i64 = 0
    let mut d: i64 = 1
    while d <= lim {
        let m: i64 = entries[d].mu as i64
        if m != 0 {
            S = S + m * (N / (d * d))
        }
        d = d + 1
    }
    printf("%lld\n", S)
    free(entries)
    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; }

typedef struct SieveEntry SieveEntry;

struct SieveEntry {
    int8_t mu;
    int8_t prime;
};

int32_t main(void);



int32_t main(void) {
    int64_t N = 1;
    N = FLOW_CHECKED_SHL((N), (50));
    int64_t lim = 1;
    lim = FLOW_CHECKED_SHL((lim), (25));
    SieveEntry* entries = (SieveEntry*)(((SieveEntry*)(calloc((lim + 1), 2))));
    if (entries == NULL) {
        return 1;
    }
    int64_t i = 0;
    while (i <= lim) {
        entries[i] = (SieveEntry){ .mu = 1, .prime = 1 };
        i = (i + 1);
    }
    entries[0].prime = 0;
    entries[1].prime = 0;
    i = 2;
    while (i <= lim) {
        if (entries[i].prime == 1) {
            int64_t j = (i * i);
            while (j <= lim) {
                entries[j].prime = 0;
                j = (j + i);
            }
            j = i;
            while (j <= lim) {
                entries[j].mu = ((int8_t)((0 - entries[j].mu)));
                j = (j + i);
            }
            int64_t sq = (i * i);
            j = sq;
            while (j <= lim) {
                entries[j].mu = 0;
                j = (j + sq);
            }
        }
        i = (i + 1);
    }
    int64_t S = 0;
    int64_t d = 1;
    while (d <= lim) {
        int64_t m = ((int64_t)(entries[d].mu));
        if (m != 0) {
            S = (S + (m * FLOW_CHECKED_DIV((N), ((d * d)))));
        }
        d = (d + 1);
    }
    printf("%lld\n", S);
    free(entries);
    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) -> ()
  // Struct: SieveEntry
  // Fields:
  //   mu: i8
  //   prime: i8
  func.func @main() -> i32 {
    %0 = arith.constant 1 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 50 : i32
    %4 = arith.extsi %2 : i32 to i64
    %3 = arith.shli %1, %4 : i64
    %5 = arith.constant 1 : i32
    %6 = arith.extsi %5 : i32 to i64
    %7 = arith.constant 25 : i32
    %9 = arith.extsi %7 : i32 to i64
    %8 = arith.shli %6, %9 : i64
    %11 = arith.constant 1 : i32
    %13 = arith.extsi %11 : i32 to i64
    %12 = arith.addi %8, %13 : i64
    %14 = arith.constant 2 : i32
    %15 = arith.extsi %14 : i32 to i64
    %10 = func.call @calloc(%12, %15) : (i64, i64) -> !llvm.ptr
    %16 = llvm.mlir.zero : !llvm.ptr
    %17 = llvm.icmp "eq" %10, %16 : !llvm.ptr
    cf.cond_br %17, ^bb0, ^bb1
    ^bb0:
      %18 = arith.constant 1 : i32
      func.return %18 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %19 = arith.constant 0 : i32
    %20 = arith.extsi %19 : i32 to i64
    %21 = llvm.mlir.constant(1 : i64) : i64
    %22 = llvm.alloca %21 x i64 : (i64) -> !llvm.ptr
    llvm.store %20, %22 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %23 = llvm.load %22 : !llvm.ptr -> i64
    %24 = arith.cmpi sle, %23, %8 : i64
    cf.cond_br %24, ^bb4, ^bb5
    ^bb4:
      %25 = llvm.mlir.undef : !llvm.struct<(i8, i8)>
      %26 = arith.constant 1 : i32
      %27 = arith.trunci %26 : i32 to i8
      %28 = llvm.insertvalue %27, %25[0] : !llvm.struct<(i8, i8)>
      %29 = arith.constant 1 : i32
      %30 = arith.trunci %29 : i32 to i8
      %31 = llvm.insertvalue %30, %28[1] : !llvm.struct<(i8, i8)>
      %32 = llvm.load %22 : !llvm.ptr -> i64
      %33 = llvm.getelementptr %10[%32] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
      llvm.store %31, %33 : !llvm.struct<(i8, i8)>, !llvm.ptr
      %34 = llvm.load %22 : !llvm.ptr -> i64
      %35 = arith.constant 1 : i32
      %37 = arith.extsi %35 : i32 to i64
      %36 = arith.addi %34, %37 : i64
      llvm.store %36, %22 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %38 = arith.constant 0 : i32
    %39 = arith.constant 0 : i32
    %40 = arith.extsi %39 : i32 to i64
    %41 = llvm.getelementptr %10[%40] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
    %42 = arith.trunci %38 : i32 to i8
    %43 = llvm.getelementptr %41[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
    llvm.store %42, %43 : i8, !llvm.ptr
    %44 = arith.constant 0 : i32
    %45 = arith.constant 1 : i32
    %46 = arith.extsi %45 : i32 to i64
    %47 = llvm.getelementptr %10[%46] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
    %48 = arith.trunci %44 : i32 to i8
    %49 = llvm.getelementptr %47[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
    llvm.store %48, %49 : i8, !llvm.ptr
    %50 = arith.constant 2 : i32
    %51 = arith.extsi %50 : i32 to i64
    llvm.store %51, %22 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %52 = llvm.load %22 : !llvm.ptr -> i64
    %53 = arith.cmpi sle, %52, %8 : i64
    cf.cond_br %53, ^bb7, ^bb8
    ^bb7:
      %55 = llvm.load %22 : !llvm.ptr -> i64
      %56 = llvm.getelementptr %10[%55] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
      %54 = llvm.load %56 : !llvm.ptr -> !llvm.struct<(i8, i8)>
      %57 = llvm.load %22 : !llvm.ptr -> i64
      %58 = llvm.getelementptr %10[%57] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
      %59 = llvm.getelementptr %58[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
      %60 = llvm.load %59 : !llvm.ptr -> i8
      %61 = arith.constant 1 : i32
      %63 = arith.extsi %60 : i8 to i32
      %62 = arith.cmpi eq, %63, %61 : i32
      cf.cond_br %62, ^bb9, ^bb10
      ^bb9:
        %64 = llvm.load %22 : !llvm.ptr -> i64
        %65 = llvm.load %22 : !llvm.ptr -> i64
        %66 = arith.muli %64, %65 : i64
        %67 = llvm.mlir.constant(1 : i64) : i64
        %68 = llvm.alloca %67 x i64 : (i64) -> !llvm.ptr
        llvm.store %66, %68 : i64, !llvm.ptr
        cf.br ^bb12
        ^bb12:
        %69 = llvm.load %68 : !llvm.ptr -> i64
        %70 = arith.cmpi sle, %69, %8 : i64
        cf.cond_br %70, ^bb13, ^bb14
        ^bb13:
          %71 = arith.constant 0 : i32
          %72 = llvm.load %68 : !llvm.ptr -> i64
          %73 = llvm.getelementptr %10[%72] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          %74 = arith.trunci %71 : i32 to i8
          %75 = llvm.getelementptr %73[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          llvm.store %74, %75 : i8, !llvm.ptr
          %76 = llvm.load %68 : !llvm.ptr -> i64
          %77 = llvm.load %22 : !llvm.ptr -> i64
          %78 = arith.addi %76, %77 : i64
          llvm.store %78, %68 : i64, !llvm.ptr
          cf.br ^bb12
        ^bb14:
        %79 = llvm.load %22 : !llvm.ptr -> i64
        llvm.store %79, %68 : i64, !llvm.ptr
        cf.br ^bb15
        ^bb15:
        %80 = llvm.load %68 : !llvm.ptr -> i64
        %81 = arith.cmpi sle, %80, %8 : i64
        cf.cond_br %81, ^bb16, ^bb17
        ^bb16:
          %82 = arith.constant 0 : i32
          %84 = llvm.load %68 : !llvm.ptr -> i64
          %85 = llvm.getelementptr %10[%84] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          %83 = llvm.load %85 : !llvm.ptr -> !llvm.struct<(i8, i8)>
          %86 = llvm.load %68 : !llvm.ptr -> i64
          %87 = llvm.getelementptr %10[%86] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          %88 = llvm.getelementptr %87[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          %89 = llvm.load %88 : !llvm.ptr -> i8
          %91 = arith.extsi %89 : i8 to i32
          %90 = arith.subi %82, %91 : i32
          %92 = arith.trunci %90 : i32 to i8
          %93 = llvm.load %68 : !llvm.ptr -> i64
          %94 = llvm.getelementptr %10[%93] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          %95 = llvm.getelementptr %94[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          llvm.store %92, %95 : i8, !llvm.ptr
          %96 = llvm.load %68 : !llvm.ptr -> i64
          %97 = llvm.load %22 : !llvm.ptr -> i64
          %98 = arith.addi %96, %97 : i64
          llvm.store %98, %68 : i64, !llvm.ptr
          cf.br ^bb15
        ^bb17:
        %99 = llvm.load %22 : !llvm.ptr -> i64
        %100 = llvm.load %22 : !llvm.ptr -> i64
        %101 = arith.muli %99, %100 : i64
        llvm.store %101, %68 : i64, !llvm.ptr
        cf.br ^bb18
        ^bb18:
        %102 = llvm.load %68 : !llvm.ptr -> i64
        %103 = arith.cmpi sle, %102, %8 : i64
        cf.cond_br %103, ^bb19, ^bb20
        ^bb19:
          %104 = arith.constant 0 : i32
          %105 = llvm.load %68 : !llvm.ptr -> i64
          %106 = llvm.getelementptr %10[%105] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          %107 = arith.trunci %104 : i32 to i8
          %108 = llvm.getelementptr %106[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
          llvm.store %107, %108 : i8, !llvm.ptr
          %109 = llvm.load %68 : !llvm.ptr -> i64
          %110 = arith.addi %109, %101 : i64
          llvm.store %110, %68 : i64, !llvm.ptr
          cf.br ^bb18
        ^bb20:
        cf.br ^bb11
      ^bb10:
        cf.br ^bb11
      ^bb11:
      %111 = llvm.load %22 : !llvm.ptr -> i64
      %112 = arith.constant 1 : i32
      %114 = arith.extsi %112 : i32 to i64
      %113 = arith.addi %111, %114 : i64
      llvm.store %113, %22 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %115 = arith.constant 0 : i32
    %116 = arith.extsi %115 : i32 to i64
    %117 = llvm.mlir.constant(1 : i64) : i64
    %118 = llvm.alloca %117 x i64 : (i64) -> !llvm.ptr
    llvm.store %116, %118 : i64, !llvm.ptr
    %119 = arith.constant 1 : i32
    %120 = arith.extsi %119 : i32 to i64
    %121 = llvm.mlir.constant(1 : i64) : i64
    %122 = llvm.alloca %121 x i64 : (i64) -> !llvm.ptr
    llvm.store %120, %122 : i64, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %123 = llvm.load %122 : !llvm.ptr -> i64
    %124 = arith.cmpi sle, %123, %8 : i64
    cf.cond_br %124, ^bb22, ^bb23
    ^bb22:
      %126 = llvm.load %122 : !llvm.ptr -> i64
      %127 = llvm.getelementptr %10[%126] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
      %125 = llvm.load %127 : !llvm.ptr -> !llvm.struct<(i8, i8)>
      %128 = llvm.load %122 : !llvm.ptr -> i64
      %129 = llvm.getelementptr %10[%128] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.struct<(i8, i8)>
      %130 = llvm.getelementptr %129[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(i8, i8)>
      %131 = llvm.load %130 : !llvm.ptr -> i8
      %132 = arith.extsi %131 : i8 to i64
      %133 = arith.constant 0 : i32
      %135 = arith.extsi %133 : i32 to i64
      %134 = arith.cmpi ne, %132, %135 : i64
      cf.cond_br %134, ^bb24, ^bb25
      ^bb24:
        %136 = llvm.load %118 : !llvm.ptr -> i64
        %137 = llvm.load %122 : !llvm.ptr -> i64
        %138 = llvm.load %122 : !llvm.ptr -> i64
        %139 = arith.muli %137, %138 : i64
        %140 = arith.divsi %3, %139 : i64
        %141 = arith.muli %132, %140 : i64
        %142 = arith.addi %136, %141 : i64
        llvm.store %142, %118 : i64, !llvm.ptr
        cf.br ^bb26
      ^bb25:
        cf.br ^bb26
      ^bb26:
      %143 = llvm.load %122 : !llvm.ptr -> i64
      %144 = arith.constant 1 : i32
      %146 = arith.extsi %144 : i32 to i64
      %145 = arith.addi %143, %146 : i64
      llvm.store %145, %122 : i64, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %147 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %148 = llvm.load %118 : !llvm.ptr -> i64
    %149 = llvm.call @printf(%147, %148) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%10) : (!llvm.ptr) -> ()
    %151 = arith.constant 0 : i32
    func.return %151 : i32
  }
}