Problem 069

Find n ≤ 1,000,000 maximizing n/φ(n). Maximized by product of smallest primes.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 069
# Find n ≤ 1,000,000 maximizing n/φ(n).
# Maximized by product of smallest primes.

function main() -> i32 {
    let primes: array<i64, 20> = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
    let mut n: i64 = 1
    let mut i: i32 = 0
    while i < 20 {
        if n * primes[i] > 1000000 {
            break
        }
        n = n * primes[i]
        i = i + 1
    }
    printf("%lld\n", n)
    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);

int32_t main(void) {
    int64_t primes[20] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 };
    int64_t n = 1;
    int32_t i = 0;
    while (i < 20) {
        if ((n * (((unsigned)(i) < 20) ? primes[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 20), flow_fault_handler("array index out of bounds"), primes[0]))) > 1000000) {
            break;
        }
        n = (n * (((unsigned)(i) < 20) ? primes[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 20), flow_fault_handler("array index out of bounds"), primes[0])));
        i = (i + 1);
    }
    printf("%lld\n", n);
    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 @main() -> i32 {
    %1 = arith.constant 2 : i32
    %2 = arith.constant 3 : i32
    %3 = arith.constant 5 : i32
    %4 = arith.constant 7 : i32
    %5 = arith.constant 11 : i32
    %6 = arith.constant 13 : i32
    %7 = arith.constant 17 : i32
    %8 = arith.constant 19 : i32
    %9 = arith.constant 23 : i32
    %10 = arith.constant 29 : i32
    %11 = arith.constant 31 : i32
    %12 = arith.constant 37 : i32
    %13 = arith.constant 41 : i32
    %14 = arith.constant 43 : i32
    %15 = arith.constant 47 : i32
    %16 = arith.constant 53 : i32
    %17 = arith.constant 59 : i32
    %18 = arith.constant 61 : i32
    %19 = arith.constant 67 : i32
    %20 = arith.constant 71 : i32
    %21 = llvm.mlir.constant(1 : i64) : i64
    %22 = llvm.alloca %21 x !llvm.array<20 x i64> : (i64) -> !llvm.ptr
    %23 = llvm.mlir.zero : !llvm.array<20 x i64>
    llvm.store %23, %22 : !llvm.array<20 x i64>, !llvm.ptr
    %24 = arith.extsi %1 : i32 to i64
    %25 = arith.extsi %2 : i32 to i64
    %26 = arith.extsi %3 : i32 to i64
    %27 = arith.extsi %4 : i32 to i64
    %28 = arith.extsi %5 : i32 to i64
    %29 = arith.extsi %6 : i32 to i64
    %30 = arith.extsi %7 : i32 to i64
    %31 = arith.extsi %8 : i32 to i64
    %32 = arith.extsi %9 : i32 to i64
    %33 = arith.extsi %10 : i32 to i64
    %34 = arith.extsi %11 : i32 to i64
    %35 = arith.extsi %12 : i32 to i64
    %36 = arith.extsi %13 : i32 to i64
    %37 = arith.extsi %14 : i32 to i64
    %38 = arith.extsi %15 : i32 to i64
    %39 = arith.extsi %16 : i32 to i64
    %40 = arith.extsi %17 : i32 to i64
    %41 = arith.extsi %18 : i32 to i64
    %42 = arith.extsi %19 : i32 to i64
    %43 = arith.extsi %20 : i32 to i64
    %44 = llvm.mlir.constant(0 : i64) : i64
    %45 = llvm.getelementptr %22[0, %44] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %24, %45 : i64, !llvm.ptr
    %46 = llvm.mlir.constant(1 : i64) : i64
    %47 = llvm.getelementptr %22[0, %46] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %25, %47 : i64, !llvm.ptr
    %48 = llvm.mlir.constant(2 : i64) : i64
    %49 = llvm.getelementptr %22[0, %48] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %26, %49 : i64, !llvm.ptr
    %50 = llvm.mlir.constant(3 : i64) : i64
    %51 = llvm.getelementptr %22[0, %50] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %27, %51 : i64, !llvm.ptr
    %52 = llvm.mlir.constant(4 : i64) : i64
    %53 = llvm.getelementptr %22[0, %52] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %28, %53 : i64, !llvm.ptr
    %54 = llvm.mlir.constant(5 : i64) : i64
    %55 = llvm.getelementptr %22[0, %54] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %29, %55 : i64, !llvm.ptr
    %56 = llvm.mlir.constant(6 : i64) : i64
    %57 = llvm.getelementptr %22[0, %56] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %30, %57 : i64, !llvm.ptr
    %58 = llvm.mlir.constant(7 : i64) : i64
    %59 = llvm.getelementptr %22[0, %58] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %31, %59 : i64, !llvm.ptr
    %60 = llvm.mlir.constant(8 : i64) : i64
    %61 = llvm.getelementptr %22[0, %60] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %32, %61 : i64, !llvm.ptr
    %62 = llvm.mlir.constant(9 : i64) : i64
    %63 = llvm.getelementptr %22[0, %62] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %33, %63 : i64, !llvm.ptr
    %64 = llvm.mlir.constant(10 : i64) : i64
    %65 = llvm.getelementptr %22[0, %64] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %34, %65 : i64, !llvm.ptr
    %66 = llvm.mlir.constant(11 : i64) : i64
    %67 = llvm.getelementptr %22[0, %66] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %35, %67 : i64, !llvm.ptr
    %68 = llvm.mlir.constant(12 : i64) : i64
    %69 = llvm.getelementptr %22[0, %68] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %36, %69 : i64, !llvm.ptr
    %70 = llvm.mlir.constant(13 : i64) : i64
    %71 = llvm.getelementptr %22[0, %70] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %37, %71 : i64, !llvm.ptr
    %72 = llvm.mlir.constant(14 : i64) : i64
    %73 = llvm.getelementptr %22[0, %72] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %38, %73 : i64, !llvm.ptr
    %74 = llvm.mlir.constant(15 : i64) : i64
    %75 = llvm.getelementptr %22[0, %74] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %39, %75 : i64, !llvm.ptr
    %76 = llvm.mlir.constant(16 : i64) : i64
    %77 = llvm.getelementptr %22[0, %76] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %40, %77 : i64, !llvm.ptr
    %78 = llvm.mlir.constant(17 : i64) : i64
    %79 = llvm.getelementptr %22[0, %78] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %41, %79 : i64, !llvm.ptr
    %80 = llvm.mlir.constant(18 : i64) : i64
    %81 = llvm.getelementptr %22[0, %80] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %42, %81 : i64, !llvm.ptr
    %82 = llvm.mlir.constant(19 : i64) : i64
    %83 = llvm.getelementptr %22[0, %82] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
    llvm.store %43, %83 : i64, !llvm.ptr
    %84 = arith.constant 1 : i32
    %85 = arith.extsi %84 : i32 to i64
    %86 = llvm.mlir.constant(1 : i64) : i64
    %87 = llvm.alloca %86 x i64 : (i64) -> !llvm.ptr
    llvm.store %85, %87 : i64, !llvm.ptr
    %88 = arith.constant 0 : i32
    %89 = llvm.mlir.constant(1 : i64) : i64
    %90 = llvm.alloca %89 x i32 : (i64) -> !llvm.ptr
    llvm.store %88, %90 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %91 = llvm.load %90 : !llvm.ptr -> i32
    %92 = arith.constant 20 : i32
    %93 = arith.cmpi slt, %91, %92 : i32
    cf.cond_br %93, ^bb1, ^bb2
    ^bb1:
      %94 = llvm.load %87 : !llvm.ptr -> i64
      %96 = llvm.load %90 : !llvm.ptr -> i32
      %97 = arith.extsi %96 : i32 to i64
      %98 = llvm.getelementptr %22[0, %97] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
      %95 = llvm.load %98 : !llvm.ptr -> i64
      %99 = arith.muli %94, %95 : i64
      %100 = arith.constant 1000000 : i32
      %102 = arith.extsi %100 : i32 to i64
      %101 = arith.cmpi sgt, %99, %102 : i64
      cf.cond_br %101, ^bb3, ^bb4
      ^bb3:
        cf.br ^bb2
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %103 = llvm.load %87 : !llvm.ptr -> i64
      %105 = llvm.load %90 : !llvm.ptr -> i32
      %106 = arith.extsi %105 : i32 to i64
      %107 = llvm.getelementptr %22[0, %106] : (!llvm.ptr, i64) -> !llvm.ptr, !llvm.array<20 x i64>
      %104 = llvm.load %107 : !llvm.ptr -> i64
      %108 = arith.muli %103, %104 : i64
      llvm.store %108, %87 : i64, !llvm.ptr
      %109 = llvm.load %90 : !llvm.ptr -> i32
      %110 = arith.constant 1 : i32
      %111 = arith.addi %109, %110 : i32
      llvm.store %111, %90 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %112 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %113 = llvm.load %87 : !llvm.ptr -> i64
    %114 = llvm.call @printf(%112, %113) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %115 = arith.constant 0 : i32
    func.return %115 : i32
  }
}