Problem 040

Champernowne's constant digit product d1 × d10 × d100 × … × d1000000.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 040
# Champernowne's constant digit product d1 × d10 × d100 × … × d1000000.

function digit_at(target: i64) -> i64 {
    # find the digit at 1-based position target in Champernowne
    let mut remaining: i64 = target
    let mut digits: i64 = 1
    let mut count: i64 = 9
    let mut start: i64 = 1
    while remaining > digits * count {
        remaining = remaining - digits * count
        digits = digits + 1
        count = count * 10
        start = start * 10
    }
    let number: i64 = start + (remaining - 1) / digits
    let pos_from_left: i64 = (remaining - 1) % digits
    # extract digit
    let mut n: i64 = number
    let mut skip: i64 = digits - 1 - pos_from_left
    while skip > 0 {
        n = n / 10
        skip = skip - 1
    }
    return n % 10
}

function main() -> i32 {
    let mut prod: i64 = 1
    let mut p: i64 = 1
    while p <= 1000000 {
        prod = prod * digit_at(p)
        p = p * 10
    }
    printf("%lld\n", prod)
    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; }

int64_t digit_at_i64(int64_t target);
int32_t main(void);

int64_t digit_at_i64(int64_t target) {
    int64_t remaining = target;
    int64_t digits = 1;
    int64_t count = 9;
    int64_t start = 1;
    while (remaining > (digits * count)) {
        remaining = (remaining - (digits * count));
        digits = (digits + 1);
        count = (count * 10);
        start = (start * 10);
    }
    int64_t number = (start + FLOW_CHECKED_DIV(((remaining - 1)), (digits)));
    int64_t pos_from_left = FLOW_CHECKED_MOD(((remaining - 1)), (digits));
    int64_t n = number;
    int64_t skip = ((digits - 1) - pos_from_left);
    while (skip > 0) {
        n = FLOW_CHECKED_DIV((n), (10));
        skip = (skip - 1);
    }
    return FLOW_CHECKED_MOD((n), (10));
}

int32_t main(void) {
    int64_t prod = 1;
    int64_t p = 1;
    while (p <= 1000000) {
        prod = (prod * digit_at_i64(p));
        p = (p * 10);
    }
    printf("%lld\n", prod);
    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 @digit_at(%arg0: i64) -> i64 {
    %0 = llvm.mlir.constant(1 : i64) : i64
    %1 = llvm.alloca %0 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %1 : i64, !llvm.ptr
    %2 = arith.constant 1 : i32
    %3 = arith.extsi %2 : i32 to i64
    %4 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x i64 : (i64) -> !llvm.ptr
    llvm.store %3, %5 : i64, !llvm.ptr
    %6 = arith.constant 9 : i32
    %7 = arith.extsi %6 : i32 to i64
    %8 = llvm.mlir.constant(1 : i64) : i64
    %9 = llvm.alloca %8 x i64 : (i64) -> !llvm.ptr
    llvm.store %7, %9 : i64, !llvm.ptr
    %10 = arith.constant 1 : i32
    %11 = arith.extsi %10 : i32 to i64
    %12 = llvm.mlir.constant(1 : i64) : i64
    %13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
    llvm.store %11, %13 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %14 = llvm.load %1 : !llvm.ptr -> i64
    %15 = llvm.load %5 : !llvm.ptr -> i64
    %16 = llvm.load %9 : !llvm.ptr -> i64
    %17 = arith.muli %15, %16 : i64
    %18 = arith.cmpi sgt, %14, %17 : i64
    cf.cond_br %18, ^bb1, ^bb2
    ^bb1:
      %19 = llvm.load %1 : !llvm.ptr -> i64
      %20 = llvm.load %5 : !llvm.ptr -> i64
      %21 = llvm.load %9 : !llvm.ptr -> i64
      %22 = arith.muli %20, %21 : i64
      %23 = arith.subi %19, %22 : i64
      llvm.store %23, %1 : i64, !llvm.ptr
      %24 = llvm.load %5 : !llvm.ptr -> i64
      %25 = arith.constant 1 : i32
      %27 = arith.extsi %25 : i32 to i64
      %26 = arith.addi %24, %27 : i64
      llvm.store %26, %5 : i64, !llvm.ptr
      %28 = llvm.load %9 : !llvm.ptr -> i64
      %29 = arith.constant 10 : i32
      %31 = arith.extsi %29 : i32 to i64
      %30 = arith.muli %28, %31 : i64
      llvm.store %30, %9 : i64, !llvm.ptr
      %32 = llvm.load %13 : !llvm.ptr -> i64
      %33 = arith.constant 10 : i32
      %35 = arith.extsi %33 : i32 to i64
      %34 = arith.muli %32, %35 : i64
      llvm.store %34, %13 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %36 = llvm.load %13 : !llvm.ptr -> i64
    %37 = llvm.load %1 : !llvm.ptr -> i64
    %38 = arith.constant 1 : i32
    %40 = arith.extsi %38 : i32 to i64
    %39 = arith.subi %37, %40 : i64
    %41 = llvm.load %5 : !llvm.ptr -> i64
    %42 = arith.divsi %39, %41 : i64
    %43 = arith.addi %36, %42 : i64
    %44 = llvm.load %1 : !llvm.ptr -> i64
    %45 = arith.constant 1 : i32
    %47 = arith.extsi %45 : i32 to i64
    %46 = arith.subi %44, %47 : i64
    %48 = llvm.load %5 : !llvm.ptr -> i64
    %49 = arith.remsi %46, %48 : i64
    %50 = llvm.mlir.constant(1 : i64) : i64
    %51 = llvm.alloca %50 x i64 : (i64) -> !llvm.ptr
    llvm.store %43, %51 : i64, !llvm.ptr
    %52 = llvm.load %5 : !llvm.ptr -> i64
    %53 = arith.constant 1 : i32
    %55 = arith.extsi %53 : i32 to i64
    %54 = arith.subi %52, %55 : i64
    %56 = arith.subi %54, %49 : i64
    %57 = llvm.mlir.constant(1 : i64) : i64
    %58 = llvm.alloca %57 x i64 : (i64) -> !llvm.ptr
    llvm.store %56, %58 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %59 = llvm.load %58 : !llvm.ptr -> i64
    %60 = arith.constant 0 : i32
    %62 = arith.extsi %60 : i32 to i64
    %61 = arith.cmpi sgt, %59, %62 : i64
    cf.cond_br %61, ^bb4, ^bb5
    ^bb4:
      %63 = llvm.load %51 : !llvm.ptr -> i64
      %64 = arith.constant 10 : i32
      %66 = arith.extsi %64 : i32 to i64
      %65 = arith.divsi %63, %66 : i64
      llvm.store %65, %51 : i64, !llvm.ptr
      %67 = llvm.load %58 : !llvm.ptr -> i64
      %68 = arith.constant 1 : i32
      %70 = arith.extsi %68 : i32 to i64
      %69 = arith.subi %67, %70 : i64
      llvm.store %69, %58 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %71 = llvm.load %51 : !llvm.ptr -> i64
    %72 = arith.constant 10 : i32
    %74 = arith.extsi %72 : i32 to i64
    %73 = arith.remsi %71, %74 : i64
    func.return %73 : i64
  }
  func.func @main() -> i32 {
    %75 = arith.constant 1 : i32
    %76 = arith.extsi %75 : i32 to i64
    %77 = llvm.mlir.constant(1 : i64) : i64
    %78 = llvm.alloca %77 x i64 : (i64) -> !llvm.ptr
    llvm.store %76, %78 : i64, !llvm.ptr
    %79 = arith.constant 1 : i32
    %80 = arith.extsi %79 : i32 to i64
    %81 = llvm.mlir.constant(1 : i64) : i64
    %82 = llvm.alloca %81 x i64 : (i64) -> !llvm.ptr
    llvm.store %80, %82 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %83 = llvm.load %82 : !llvm.ptr -> i64
    %84 = arith.constant 1000000 : i32
    %86 = arith.extsi %84 : i32 to i64
    %85 = arith.cmpi sle, %83, %86 : i64
    cf.cond_br %85, ^bb7, ^bb8
    ^bb7:
      %87 = llvm.load %78 : !llvm.ptr -> i64
      %89 = llvm.load %82 : !llvm.ptr -> i64
      %88 = func.call @digit_at(%89) : (i64) -> i64
      %90 = arith.muli %87, %88 : i64
      llvm.store %90, %78 : i64, !llvm.ptr
      %91 = llvm.load %82 : !llvm.ptr -> i64
      %92 = arith.constant 10 : i32
      %94 = arith.extsi %92 : i32 to i64
      %93 = arith.muli %91, %94 : i64
      llvm.store %93, %82 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %95 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %96 = llvm.load %78 : !llvm.ptr -> i64
    %97 = llvm.call @printf(%95, %96) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %98 = arith.constant 0 : i32
    func.return %98 : i32
  }
}