Problem 779

Prime factor and exponent. sum_{K>=1} bar(f_K) = sum_{p prime} prod_{q<p}(1 - 1/q) * 1 / (p * (p - 1)^2) Sieve up to 1e6, accumulate the running product of (p-1)/p.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 779
# Prime factor and exponent.
#
# sum_{K>=1} bar(f_K) =
#   sum_{p prime} prod_{q<p}(1 - 1/q) * 1 / (p * (p - 1)^2)
#
# Sieve up to 1e6, accumulate the running product of (p-1)/p.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
    function memset(p: ptr<void>, c: i32, n: i64) -> ptr<void>
    function sqrt(x: f64) -> f64
    function floor(x: f64) -> f64
    function round(x: f64) -> f64
}

const SIEVE_LIMIT: i64 = 1000000

function main() -> i32 {
    let is_prime: ptr<i8> = calloc(SIEVE_LIMIT + 1, 1)
    if is_prime == null {
        return 1
    }
    memset(is_prime, 1, SIEVE_LIMIT + 1)
    is_prime[0] = 0
    is_prime[1] = 0

    let limit: i64 = (floor(sqrt((SIEVE_LIMIT as f64))) as i64)
    let mut i: i64 = 2
    while i <= limit {
        if is_prime[i] != 0 {
            let mut j: i64 = i * i
            while j <= SIEVE_LIMIT {
                is_prime[j] = 0
                j = j + i
            }
        }
        i = i + 1
    }

    let mut total: f64 = 0.0
    let mut curr: f64 = 1.0
    let mut p: i64 = 2
    while p <= SIEVE_LIMIT {
        if is_prime[p] != 0 {
            let dp: f64 = (p as f64)
            let term: f64 = curr * (1.0 / (dp * (dp - 1.0) * (dp - 1.0)))
            total = total + term
            curr = curr * (dp - 1.0) / dp
        }
        p = p + 1
    }

    free(is_prime)

    let result: f64 = round(total * 1e12) / 1e12
    printf("%.12f\n", result)
    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; }

int32_t main(void);

static const int64_t SIEVE_LIMIT = 1000000;







int32_t main(void) {
    int8_t* is_prime = (int8_t*)(calloc((SIEVE_LIMIT + 1), 1));
    if (is_prime == NULL) {
        return 1;
    }
    memset(is_prime, 1, (SIEVE_LIMIT + 1));
    is_prime[0] = 0;
    is_prime[1] = 0;
    int64_t limit = ((int64_t)(floor(sqrt(((double)(SIEVE_LIMIT))))));
    int64_t i = 2;
    while (i <= limit) {
        if (is_prime[i] != 0) {
            int64_t j = (i * i);
            while (j <= SIEVE_LIMIT) {
                is_prime[j] = 0;
                j = (j + i);
            }
        }
        i = (i + 1);
    }
    double total = 0.0;
    double curr = 1.0;
    int64_t p = 2;
    while (p <= SIEVE_LIMIT) {
        if (is_prime[p] != 0) {
            double dp = ((double)(p));
            double term = (curr * (1.0 / ((dp * (dp - 1.0)) * (dp - 1.0))));
            total = (total + term);
            curr = ((curr * (dp - 1.0)) / dp);
        }
        p = (p + 1);
    }
    free(is_prime);
    double result = (round((total * 1e12)) / 1e12);
    printf("%.12f\n", result);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.12f\n\00") {addr_space = 0 : i32} : !llvm.array<7 x i8>
  func.func private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func private @memset(!llvm.ptr, i32, i64) -> !llvm.ptr
  func.func private @sqrt(f64) -> f64
  func.func private @floor(f64) -> f64
  func.func private @round(f64) -> f64
  // Constant: SIEVE_LIMIT
  llvm.mlir.global internal constant @SIEVE_LIMIT(1000000 : i64) : i64
  func.func @main() -> i32 {
    %1 = llvm.mlir.addressof @SIEVE_LIMIT : !llvm.ptr
    %2 = llvm.load %1 : !llvm.ptr -> i64
    %3 = arith.constant 1 : i32
    %5 = arith.extsi %3 : i32 to i64
    %4 = arith.addi %2, %5 : i64
    %6 = arith.constant 1 : i32
    %7 = arith.extsi %6 : i32 to i64
    %0 = func.call @calloc(%4, %7) : (i64, i64) -> !llvm.ptr
    %8 = llvm.mlir.zero : !llvm.ptr
    %9 = llvm.icmp "eq" %0, %8 : !llvm.ptr
    cf.cond_br %9, ^bb0, ^bb1
    ^bb0:
      %10 = arith.constant 1 : i32
      func.return %10 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %12 = arith.constant 1 : i32
    %13 = llvm.mlir.addressof @SIEVE_LIMIT : !llvm.ptr
    %14 = llvm.load %13 : !llvm.ptr -> i64
    %15 = arith.constant 1 : i32
    %17 = arith.extsi %15 : i32 to i64
    %16 = arith.addi %14, %17 : i64
    %11 = func.call @memset(%0, %12, %16) : (!llvm.ptr, i32, i64) -> !llvm.ptr
    %18 = arith.constant 0 : i32
    %19 = arith.constant 0 : i32
    %20 = arith.trunci %18 : i32 to i8
    %21 = arith.extsi %19 : i32 to i64
    %22 = llvm.getelementptr %0[%21] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %20, %22 : i8, !llvm.ptr
    %23 = arith.constant 0 : i32
    %24 = arith.constant 1 : i32
    %25 = arith.trunci %23 : i32 to i8
    %26 = arith.extsi %24 : i32 to i64
    %27 = llvm.getelementptr %0[%26] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %25, %27 : i8, !llvm.ptr
    %29 = llvm.mlir.addressof @SIEVE_LIMIT : !llvm.ptr
    %30 = llvm.load %29 : !llvm.ptr -> i64
    %31 = arith.sitofp %30 : i64 to f64
    %32 = math.sqrt %31 : f64
    %28 = func.call @floor(%32) : (f64) -> f64
    %33 = arith.fptosi %28 : f64 to i64
    %34 = arith.constant 2 : 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
    cf.br ^bb3
    ^bb3:
    %38 = llvm.load %37 : !llvm.ptr -> i64
    %39 = arith.cmpi sle, %38, %33 : i64
    cf.cond_br %39, ^bb4, ^bb5
    ^bb4:
      %41 = llvm.load %37 : !llvm.ptr -> i64
      %42 = llvm.getelementptr %0[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %40 = llvm.load %42 : !llvm.ptr -> i8
      %43 = arith.constant 0 : i32
      %45 = arith.extsi %40 : i8 to i32
      %44 = arith.cmpi ne, %45, %43 : i32
      cf.cond_br %44, ^bb6, ^bb7
      ^bb6:
        %46 = llvm.load %37 : !llvm.ptr -> i64
        %47 = llvm.load %37 : !llvm.ptr -> i64
        %48 = arith.muli %46, %47 : i64
        %49 = llvm.mlir.constant(1 : i64) : i64
        %50 = llvm.alloca %49 x i64 : (i64) -> !llvm.ptr
        llvm.store %48, %50 : i64, !llvm.ptr
        cf.br ^bb9
        ^bb9:
        %51 = llvm.load %50 : !llvm.ptr -> i64
        %52 = llvm.mlir.addressof @SIEVE_LIMIT : !llvm.ptr
        %53 = llvm.load %52 : !llvm.ptr -> i64
        %54 = arith.cmpi sle, %51, %53 : i64
        cf.cond_br %54, ^bb10, ^bb11
        ^bb10:
          %55 = arith.constant 0 : i32
          %56 = llvm.load %50 : !llvm.ptr -> i64
          %57 = arith.trunci %55 : i32 to i8
          %58 = llvm.getelementptr %0[%56] : (!llvm.ptr, i64) -> !llvm.ptr, i8
          llvm.store %57, %58 : i8, !llvm.ptr
          %59 = llvm.load %50 : !llvm.ptr -> i64
          %60 = llvm.load %37 : !llvm.ptr -> i64
          %61 = arith.addi %59, %60 : i64
          llvm.store %61, %50 : i64, !llvm.ptr
          cf.br ^bb9
        ^bb11:
        cf.br ^bb8
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %62 = llvm.load %37 : !llvm.ptr -> i64
      %63 = arith.constant 1 : i32
      %65 = arith.extsi %63 : i32 to i64
      %64 = arith.addi %62, %65 : i64
      llvm.store %64, %37 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %66 = arith.constant 0.0 : f32
    %67 = arith.extf %66 : f32 to f64
    %68 = llvm.mlir.constant(1 : i64) : i64
    %69 = llvm.alloca %68 x f64 : (i64) -> !llvm.ptr
    llvm.store %67, %69 : f64, !llvm.ptr
    %70 = arith.constant 1.0 : f32
    %71 = arith.extf %70 : f32 to f64
    %72 = llvm.mlir.constant(1 : i64) : i64
    %73 = llvm.alloca %72 x f64 : (i64) -> !llvm.ptr
    llvm.store %71, %73 : f64, !llvm.ptr
    %74 = arith.constant 2 : i32
    %75 = arith.extsi %74 : i32 to i64
    %76 = llvm.mlir.constant(1 : i64) : i64
    %77 = llvm.alloca %76 x i64 : (i64) -> !llvm.ptr
    llvm.store %75, %77 : i64, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %78 = llvm.load %77 : !llvm.ptr -> i64
    %79 = llvm.mlir.addressof @SIEVE_LIMIT : !llvm.ptr
    %80 = llvm.load %79 : !llvm.ptr -> i64
    %81 = arith.cmpi sle, %78, %80 : i64
    cf.cond_br %81, ^bb13, ^bb14
    ^bb13:
      %83 = llvm.load %77 : !llvm.ptr -> i64
      %84 = llvm.getelementptr %0[%83] : (!llvm.ptr, i64) -> !llvm.ptr, i8
      %82 = llvm.load %84 : !llvm.ptr -> i8
      %85 = arith.constant 0 : i32
      %87 = arith.extsi %82 : i8 to i32
      %86 = arith.cmpi ne, %87, %85 : i32
      cf.cond_br %86, ^bb15, ^bb16
      ^bb15:
        %88 = llvm.load %77 : !llvm.ptr -> i64
        %89 = arith.sitofp %88 : i64 to f64
        %90 = llvm.load %73 : !llvm.ptr -> f64
        %91 = arith.constant 1.0 : f32
        %92 = arith.constant 1.0 : f32
        %94 = arith.extf %92 : f32 to f64
        %93 = arith.subf %89, %94 : f64
        %95 = arith.mulf %89, %93 : f64
        %96 = arith.constant 1.0 : f32
        %98 = arith.extf %96 : f32 to f64
        %97 = arith.subf %89, %98 : f64
        %99 = arith.mulf %95, %97 : f64
        %101 = arith.extf %91 : f32 to f64
        %100 = arith.divf %101, %99 : f64
        %102 = arith.mulf %90, %100 : f64
        %103 = llvm.load %69 : !llvm.ptr -> f64
        %104 = arith.addf %103, %102 : f64
        llvm.store %104, %69 : f64, !llvm.ptr
        %105 = llvm.load %73 : !llvm.ptr -> f64
        %106 = arith.constant 1.0 : f32
        %108 = arith.extf %106 : f32 to f64
        %107 = arith.subf %89, %108 : f64
        %109 = arith.mulf %105, %107 : f64
        %110 = arith.divf %109, %89 : f64
        llvm.store %110, %73 : f64, !llvm.ptr
        cf.br ^bb17
      ^bb16:
        cf.br ^bb17
      ^bb17:
      %111 = llvm.load %77 : !llvm.ptr -> i64
      %112 = arith.constant 1 : i32
      %114 = arith.extsi %112 : i32 to i64
      %113 = arith.addi %111, %114 : i64
      llvm.store %113, %77 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    func.call @free(%0) : (!llvm.ptr) -> ()
    %117 = llvm.load %69 : !llvm.ptr -> f64
    %118 = arith.constant 1000000000000 : f32
    %120 = arith.extf %118 : f32 to f64
    %119 = arith.mulf %117, %120 : f64
    %116 = func.call @round(%119) : (f64) -> f64
    %121 = arith.constant 1000000000000 : f32
    %123 = arith.extf %121 : f32 to f64
    %122 = arith.divf %116, %123 : f64
    %124 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %125 = llvm.call @printf(%124, %122) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %126 = arith.constant 0 : i32
    func.return %126 : i32
  }
}