Problem 063

How many n-digit positive integers exist that are also an nth power? 10^(n-1) <= a^n < 10^n => a < 10, and a >= 10^((n-1)/n) For a from 1..9, count n where floor(n*log10(a))+1 == n

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 063
# How many n-digit positive integers exist that are also an nth power?

# 10^(n-1) <= a^n < 10^n  =>  a < 10, and a >= 10^((n-1)/n)
# For a from 1..9, count n where floor(n*log10(a))+1 == n

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

function mul_small(digits: ptr<i32>, len: i32, m: i64) -> i32 {
    let mut carry: i64 = 0
    let mut i: i32 = 0
    while i < len {
        let v: i64 = (digits[i] as i64) * m + carry
        digits[i] = (v % 10) as i32
        carry = v / 10
        i = i + 1
    }
    while carry > 0 {
        digits[len] = (carry % 10) as i32
        carry = carry / 10
        len = len + 1
    }
    return len
}

function main() -> i32 {
    let width: i32 = 50
    let digits: ptr<i32> = calloc(width as i64, 4)
    if digits == null { return 1 }

    let mut count: i64 = 0
    let mut a: i64 = 1
    while a <= 9 {
        let mut i: i32 = 0
        while i < width {
            digits[i] = 0
            i = i + 1
        }
        digits[0] = 1
        let mut len: i32 = 1
        let mut n: i32 = 1
        while n <= 40 {
            len = mul_small(digits, len, a)
            if len == n {
                count = count + 1
            }
            if len > n {
                break
            }
            n = n + 1
        }
        a = a + 1
    }
    printf("%lld\n", count)
    free(digits)
    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 mul_small_ptr_i32_i32_i64(int32_t* digits, int32_t len, int64_t m);
int32_t main(void);



int32_t mul_small_ptr_i32_i32_i64(int32_t* digits, int32_t len, int64_t m) {
    int64_t carry = 0;
    int32_t i = 0;
    while (i < len) {
        int64_t v = ((((int64_t)(digits[i])) * m) + carry);
        digits[i] = ((int32_t)(FLOW_CHECKED_MOD((v), (10))));
        carry = FLOW_CHECKED_DIV((v), (10));
        i = (i + 1);
    }
    while (carry > 0) {
        digits[len] = ((int32_t)(FLOW_CHECKED_MOD((carry), (10))));
        carry = FLOW_CHECKED_DIV((carry), (10));
        len = (len + 1);
    }
    return len;
}

int32_t main(void) {
    int32_t width = 50;
    int32_t* digits = (int32_t*)(calloc(((int64_t)(width)), 4));
    if (digits == NULL) {
        return 1;
    }
    int64_t count = 0;
    int64_t a = 1;
    while (a <= 9) {
        int32_t i = 0;
        while (i < width) {
            digits[i] = 0;
            i = (i + 1);
        }
        digits[0] = 1;
        int32_t len = 1;
        int32_t n = 1;
        while (n <= 40) {
            len = mul_small_ptr_i32_i32_i64(digits, len, a);
            if (len == n) {
                count = (count + 1);
            }
            if (len > n) {
                break;
            }
            n = (n + 1);
        }
        a = (a + 1);
    }
    printf("%lld\n", count);
    free(digits);
    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) -> ()
  func.func @mul_small(%arg0: !llvm.ptr, %arg1: i32, %arg2: i64) -> i32 {
    %0 = arith.constant 0 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : i64, !llvm.ptr
    %4 = arith.constant 0 : i32
    %5 = llvm.mlir.constant(1 : i64) : i64
    %6 = llvm.alloca %5 x i32 : (i64) -> !llvm.ptr
    llvm.store %4, %6 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %7 = llvm.load %6 : !llvm.ptr -> i32
    %8 = arith.cmpi slt, %7, %arg1 : i32
    cf.cond_br %8, ^bb1, ^bb2
    ^bb1:
      %10 = llvm.load %6 : !llvm.ptr -> i32
      %11 = arith.extsi %10 : i32 to i64
      %12 = llvm.getelementptr %arg0[%11] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %9 = llvm.load %12 : !llvm.ptr -> i32
      %13 = arith.extsi %9 : i32 to i64
      %14 = arith.muli %13, %arg2 : i64
      %15 = llvm.load %3 : !llvm.ptr -> i64
      %16 = arith.addi %14, %15 : i64
      %17 = arith.constant 10 : i32
      %19 = arith.extsi %17 : i32 to i64
      %18 = arith.remsi %16, %19 : i64
      %20 = arith.trunci %18 : i64 to i32
      %21 = llvm.load %6 : !llvm.ptr -> i32
      %22 = arith.extsi %21 : i32 to i64
      %23 = llvm.getelementptr %arg0[%22] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %20, %23 : i32, !llvm.ptr
      %24 = arith.constant 10 : i32
      %26 = arith.extsi %24 : i32 to i64
      %25 = arith.divsi %16, %26 : i64
      llvm.store %25, %3 : i64, !llvm.ptr
      %27 = llvm.load %6 : !llvm.ptr -> i32
      %28 = arith.constant 1 : i32
      %29 = arith.addi %27, %28 : i32
      llvm.store %29, %6 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    cf.br ^bb3(%arg1 : i32)
    ^bb3(%30: i32):
    %31 = llvm.load %3 : !llvm.ptr -> i64
    %32 = arith.constant 0 : i32
    %34 = arith.extsi %32 : i32 to i64
    %33 = arith.cmpi sgt, %31, %34 : i64
    cf.cond_br %33, ^bb4(%30 : i32), ^bb5(%30 : i32)
    ^bb4(%35: i32):
      %36 = llvm.load %3 : !llvm.ptr -> i64
      %37 = arith.constant 10 : i32
      %39 = arith.extsi %37 : i32 to i64
      %38 = arith.remsi %36, %39 : i64
      %40 = arith.trunci %38 : i64 to i32
      %41 = arith.extsi %35 : i32 to i64
      %42 = llvm.getelementptr %arg0[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %40, %42 : i32, !llvm.ptr
      %43 = llvm.load %3 : !llvm.ptr -> i64
      %44 = arith.constant 10 : i32
      %46 = arith.extsi %44 : i32 to i64
      %45 = arith.divsi %43, %46 : i64
      llvm.store %45, %3 : i64, !llvm.ptr
      %47 = arith.constant 1 : i32
      %48 = arith.addi %35, %47 : i32
      cf.br ^bb3(%48 : i32)
    ^bb5(%49: i32):
    func.return %49 : i32
  }
  func.func @main() -> i32 {
    %50 = arith.constant 50 : i32
    %52 = arith.extsi %50 : i32 to i64
    %53 = arith.constant 4 : i32
    %54 = arith.extsi %53 : i32 to i64
    %51 = func.call @calloc(%52, %54) : (i64, i64) -> !llvm.ptr
    %55 = llvm.mlir.zero : !llvm.ptr
    %56 = llvm.icmp "eq" %51, %55 : !llvm.ptr
    cf.cond_br %56, ^bb6, ^bb7
    ^bb6:
      %57 = arith.constant 1 : i32
      func.return %57 : i32
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %58 = arith.constant 0 : i32
    %59 = arith.extsi %58 : i32 to i64
    %60 = llvm.mlir.constant(1 : i64) : i64
    %61 = llvm.alloca %60 x i64 : (i64) -> !llvm.ptr
    llvm.store %59, %61 : i64, !llvm.ptr
    %62 = arith.constant 1 : i32
    %63 = arith.extsi %62 : i32 to i64
    %64 = llvm.mlir.constant(1 : i64) : i64
    %65 = llvm.alloca %64 x i64 : (i64) -> !llvm.ptr
    llvm.store %63, %65 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %66 = llvm.load %65 : !llvm.ptr -> i64
    %67 = arith.constant 9 : i32
    %69 = arith.extsi %67 : i32 to i64
    %68 = arith.cmpi sle, %66, %69 : i64
    cf.cond_br %68, ^bb10, ^bb11
    ^bb10:
      %70 = arith.constant 0 : i32
      %71 = llvm.mlir.constant(1 : i64) : i64
      %72 = llvm.alloca %71 x i32 : (i64) -> !llvm.ptr
      llvm.store %70, %72 : i32, !llvm.ptr
      cf.br ^bb12
      ^bb12:
      %73 = llvm.load %72 : !llvm.ptr -> i32
      %74 = arith.cmpi slt, %73, %50 : i32
      cf.cond_br %74, ^bb13, ^bb14
      ^bb13:
        %75 = arith.constant 0 : i32
        %76 = llvm.load %72 : !llvm.ptr -> i32
        %77 = arith.extsi %76 : i32 to i64
        %78 = llvm.getelementptr %51[%77] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        llvm.store %75, %78 : i32, !llvm.ptr
        %79 = llvm.load %72 : !llvm.ptr -> i32
        %80 = arith.constant 1 : i32
        %81 = arith.addi %79, %80 : i32
        llvm.store %81, %72 : i32, !llvm.ptr
        cf.br ^bb12
      ^bb14:
      %82 = arith.constant 1 : i32
      %83 = arith.constant 0 : i32
      %84 = arith.extsi %83 : i32 to i64
      %85 = llvm.getelementptr %51[%84] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %82, %85 : i32, !llvm.ptr
      %86 = arith.constant 1 : i32
      %87 = llvm.mlir.constant(1 : i64) : i64
      %88 = llvm.alloca %87 x i32 : (i64) -> !llvm.ptr
      llvm.store %86, %88 : i32, !llvm.ptr
      %89 = arith.constant 1 : i32
      %90 = llvm.mlir.constant(1 : i64) : i64
      %91 = llvm.alloca %90 x i32 : (i64) -> !llvm.ptr
      llvm.store %89, %91 : i32, !llvm.ptr
      cf.br ^bb15
      ^bb15:
      %92 = llvm.load %91 : !llvm.ptr -> i32
      %93 = arith.constant 40 : i32
      %94 = arith.cmpi sle, %92, %93 : i32
      cf.cond_br %94, ^bb16, ^bb17
      ^bb16:
        %96 = llvm.load %88 : !llvm.ptr -> i32
        %97 = llvm.load %65 : !llvm.ptr -> i64
        %95 = func.call @mul_small(%51, %96, %97) : (!llvm.ptr, i32, i64) -> i32
        llvm.store %95, %88 : i32, !llvm.ptr
        %98 = llvm.load %88 : !llvm.ptr -> i32
        %99 = llvm.load %91 : !llvm.ptr -> i32
        %100 = arith.cmpi eq, %98, %99 : i32
        cf.cond_br %100, ^bb18, ^bb19
        ^bb18:
          %101 = llvm.load %61 : !llvm.ptr -> i64
          %102 = arith.constant 1 : i32
          %104 = arith.extsi %102 : i32 to i64
          %103 = arith.addi %101, %104 : i64
          llvm.store %103, %61 : i64, !llvm.ptr
          cf.br ^bb20
        ^bb19:
          cf.br ^bb20
        ^bb20:
        %105 = llvm.load %88 : !llvm.ptr -> i32
        %106 = llvm.load %91 : !llvm.ptr -> i32
        %107 = arith.cmpi sgt, %105, %106 : i32
        cf.cond_br %107, ^bb21, ^bb22
        ^bb21:
          cf.br ^bb17
        ^bb22:
          cf.br ^bb23
        ^bb23:
        %108 = llvm.load %91 : !llvm.ptr -> i32
        %109 = arith.constant 1 : i32
        %110 = arith.addi %108, %109 : i32
        llvm.store %110, %91 : i32, !llvm.ptr
        cf.br ^bb15
      ^bb17:
      %111 = llvm.load %65 : !llvm.ptr -> i64
      %112 = arith.constant 1 : i32
      %114 = arith.extsi %112 : i32 to i64
      %113 = arith.addi %111, %114 : i64
      llvm.store %113, %65 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %115 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %116 = llvm.load %61 : !llvm.ptr -> i64
    %117 = llvm.call @printf(%115, %116) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%51) : (!llvm.ptr) -> ()
    %119 = arith.constant 0 : i32
    func.return %119 : i32
  }
}