Problem 820

nth Digit Reciprocals — S(n)=sum_k floor(10*(10^(n-1) mod k)/k).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 820
# nth Digit Reciprocals — S(n)=sum_k floor(10*(10^(n-1) mod k)/k).

function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
    if mod == 1 { return 0 }
    let mut r: i64 = 1
    let mut b: i64 = base0 % mod
    let mut e: i64 = exp0
    while e > 0 {
        if (e & 1) != 0 {
            r = ((r as i128) * (b as i128) % (mod as i128)) as i64
        }
        b = ((b as i128) * (b as i128) % (mod as i128)) as i64
        e = e >> 1
    }
    return r
}

function d(n: i64, k: i64) -> i64 {
    return (10 * modpow(10, n - 1, k)) / k
}

function S(n: i64) -> i64 {
    let mut total: i64 = 0
    let mut k: i64 = 1
    while k <= n {
        total = total + d(n, k)
        k = k + 1
    }
    return total
}

function main() -> i32 {
    printf("%lld\n", S(10000000))
    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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int64_t d_i64_i64(int64_t n, int64_t k);
int64_t S_i64(int64_t n);
int32_t main(void);

int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
    if (mod == 1) {
        return 0;
    }
    int64_t r = 1;
    int64_t b = FLOW_CHECKED_MOD((base0), (mod));
    int64_t e = exp0;
    while (e > 0) {
        if ((e & 1) != 0) {
            r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))))));
        }
        b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))))));
        e = FLOW_CHECKED_SHR((e), (1));
    }
    return r;
}

int64_t d_i64_i64(int64_t n, int64_t k) {
    return FLOW_CHECKED_DIV(((10 * modpow_i64_i64_i64(10, (n - 1), k))), (k));
}

int64_t S_i64(int64_t n) {
    int64_t total = 0;
    int64_t k = 1;
    while (k <= n) {
        total = (total + d_i64_i64(n, k));
        k = (k + 1);
    }
    return total;
}

int32_t main(void) {
    printf("%lld\n", S_i64(10000000));
    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 @modpow(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
    %0 = arith.constant 1 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.cmpi eq, %arg2, %2 : i64
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      %3 = arith.constant 0 : i32
      %4 = arith.extsi %3 : i32 to i64
      func.return %4 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %5 = arith.constant 1 : i32
    %6 = arith.extsi %5 : i32 to i64
    %7 = llvm.mlir.constant(1 : i64) : i64
    %8 = llvm.alloca %7 x i64 : (i64) -> !llvm.ptr
    llvm.store %6, %8 : i64, !llvm.ptr
    %9 = arith.remsi %arg0, %arg2 : i64
    %10 = llvm.mlir.constant(1 : i64) : i64
    %11 = llvm.alloca %10 x i64 : (i64) -> !llvm.ptr
    llvm.store %9, %11 : i64, !llvm.ptr
    %12 = llvm.mlir.constant(1 : i64) : i64
    %13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %13 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %14 = llvm.load %13 : !llvm.ptr -> i64
    %15 = arith.constant 0 : i32
    %17 = arith.extsi %15 : i32 to i64
    %16 = arith.cmpi sgt, %14, %17 : i64
    cf.cond_br %16, ^bb4, ^bb5
    ^bb4:
      %18 = llvm.load %13 : !llvm.ptr -> i64
      %19 = arith.constant 1 : i32
      %21 = arith.extsi %19 : i32 to i64
      %20 = arith.andi %18, %21 : i64
      %22 = arith.constant 0 : i32
      %24 = arith.extsi %22 : i32 to i64
      %23 = arith.cmpi ne, %20, %24 : i64
      cf.cond_br %23, ^bb6, ^bb7
      ^bb6:
        %25 = llvm.load %8 : !llvm.ptr -> i64
        %26 = arith.extsi %25 : i64 to i128
        %27 = llvm.load %11 : !llvm.ptr -> i64
        %28 = arith.extsi %27 : i64 to i128
        %30 = arith.trunci %26 : i128 to i64
        %31 = arith.trunci %28 : i128 to i64
        %29 = arith.muli %30, %31 : i64
        %32 = arith.extsi %arg2 : i64 to i128
        %34 = arith.trunci %32 : i128 to i64
        %33 = arith.remsi %29, %34 : i64
        llvm.store %33, %8 : i64, !llvm.ptr
        cf.br ^bb8
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %35 = llvm.load %11 : !llvm.ptr -> i64
      %36 = arith.extsi %35 : i64 to i128
      %37 = llvm.load %11 : !llvm.ptr -> i64
      %38 = arith.extsi %37 : i64 to i128
      %40 = arith.trunci %36 : i128 to i64
      %41 = arith.trunci %38 : i128 to i64
      %39 = arith.muli %40, %41 : i64
      %42 = arith.extsi %arg2 : i64 to i128
      %44 = arith.trunci %42 : i128 to i64
      %43 = arith.remsi %39, %44 : i64
      llvm.store %43, %11 : i64, !llvm.ptr
      %45 = llvm.load %13 : !llvm.ptr -> i64
      %46 = arith.constant 1 : i32
      %48 = arith.extsi %46 : i32 to i64
      %47 = arith.shrsi %45, %48 : i64
      llvm.store %47, %13 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %49 = llvm.load %8 : !llvm.ptr -> i64
    func.return %49 : i64
  }
  func.func @d(%arg0: i64, %arg1: i64) -> i64 {
    %50 = arith.constant 10 : i32
    %52 = arith.constant 10 : i32
    %53 = arith.constant 1 : i32
    %55 = arith.extsi %53 : i32 to i64
    %54 = arith.subi %arg0, %55 : i64
    %56 = arith.extsi %52 : i32 to i64
    %51 = func.call @modpow(%56, %54, %arg1) : (i64, i64, i64) -> i64
    %58 = arith.extsi %50 : i32 to i64
    %57 = arith.muli %58, %51 : i64
    %59 = arith.divsi %57, %arg1 : i64
    func.return %59 : i64
  }
  func.func @S(%arg0: i64) -> i64 {
    %60 = arith.constant 0 : i32
    %61 = arith.extsi %60 : i32 to i64
    %62 = llvm.mlir.constant(1 : i64) : i64
    %63 = llvm.alloca %62 x i64 : (i64) -> !llvm.ptr
    llvm.store %61, %63 : i64, !llvm.ptr
    %64 = arith.constant 1 : i32
    %65 = arith.extsi %64 : i32 to i64
    %66 = llvm.mlir.constant(1 : i64) : i64
    %67 = llvm.alloca %66 x i64 : (i64) -> !llvm.ptr
    llvm.store %65, %67 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %68 = llvm.load %67 : !llvm.ptr -> i64
    %69 = arith.cmpi sle, %68, %arg0 : i64
    cf.cond_br %69, ^bb10, ^bb11
    ^bb10:
      %70 = llvm.load %63 : !llvm.ptr -> i64
      %72 = llvm.load %67 : !llvm.ptr -> i64
      %71 = func.call @d(%arg0, %72) : (i64, i64) -> i64
      %73 = arith.addi %70, %71 : i64
      llvm.store %73, %63 : i64, !llvm.ptr
      %74 = llvm.load %67 : !llvm.ptr -> i64
      %75 = arith.constant 1 : i32
      %77 = arith.extsi %75 : i32 to i64
      %76 = arith.addi %74, %77 : i64
      llvm.store %76, %67 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %78 = llvm.load %63 : !llvm.ptr -> i64
    func.return %78 : i64
  }
  func.func @main() -> i32 {
    %79 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %81 = arith.constant 10000000 : i32
    %82 = arith.extsi %81 : i32 to i64
    %80 = func.call @S(%82) : (i64) -> i64
    %83 = llvm.call @printf(%79, %80) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %84 = arith.constant 0 : i32
    func.return %84 : i32
  }
}