Problem 455

Powers with Trailing Digits — sum f(n) for n=2..10^6, f = fixed point of x↦n^x mod 10^9.

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Performance comparison

Flow source

# Project Euler 455
# Powers with Trailing Digits — sum f(n) for n=2..10^6, f = fixed point of x↦n^x mod 10^9.

function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
    let mut r: i64 = 1
    let mut b: i64 = base0 % mod
    let mut e: i64 = exp0
    while e > 0 {
        if e % 2 == 1 {
            let t: i128 = (r as i128) * (b as i128) % (mod as i128)
            r = t as i64
        }
        let t2: i128 = (b as i128) * (b as i128) % (mod as i128)
        b = t2 as i64
        e = e / 2
    }
    return r
}

function f_n(n: i64, modulo: i64) -> i64 {
    let mut exponent: i64 = n
    let mut guard: i32 = 0
    while guard < 64 {
        let next_value: i64 = modpow(n, exponent, modulo)
        if next_value == 0 || next_value == exponent {
            return next_value
        }
        exponent = next_value
        guard = guard + 1
    }
    return 0
}

function main() -> i32 {
    let limit: i64 = 1000000
    let modulo: i64 = 1000000000
    let mut total: i64 = 0
    let mut i: i64 = 2
    while i <= limit {
        total = total + f_n(i, modulo)
        i = i + 1
    }
    printf("%lld\n", total)
    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 f_n_i64_i64(int64_t n, int64_t modulo);
int32_t main(void);

int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
    int64_t r = 1;
    int64_t b = FLOW_CHECKED_MOD((base0), (mod));
    int64_t e = exp0;
    while (e > 0) {
        if (FLOW_CHECKED_MOD((e), (2)) == 1) {
            __int128 t = FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))));
            r = ((int64_t)(t));
        }
        __int128 t2 = FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))));
        b = ((int64_t)(t2));
        e = FLOW_CHECKED_DIV((e), (2));
    }
    return r;
}

int64_t f_n_i64_i64(int64_t n, int64_t modulo) {
    int64_t exponent = n;
    int32_t guard = 0;
    while (guard < 64) {
        int64_t next_value = modpow_i64_i64_i64(n, exponent, modulo);
        if ((next_value == 0 || next_value == exponent)) {
            return next_value;
        }
        exponent = next_value;
        guard = (guard + 1);
    }
    return 0;
}

int32_t main(void) {
    int64_t limit = 1000000;
    int64_t modulo = 1000000000;
    int64_t total = 0;
    int64_t i = 2;
    while (i <= limit) {
        total = (total + f_n_i64_i64(i, modulo));
        i = (i + 1);
    }
    printf("%lld\n", total);
    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
    %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.remsi %arg0, %arg2 : i64
    %5 = llvm.mlir.constant(1 : i64) : i64
    %6 = llvm.alloca %5 x i64 : (i64) -> !llvm.ptr
    llvm.store %4, %6 : i64, !llvm.ptr
    %7 = llvm.mlir.constant(1 : i64) : i64
    %8 = llvm.alloca %7 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %8 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %9 = llvm.load %8 : !llvm.ptr -> i64
    %10 = arith.constant 0 : i32
    %12 = arith.extsi %10 : i32 to i64
    %11 = arith.cmpi sgt, %9, %12 : i64
    cf.cond_br %11, ^bb1, ^bb2
    ^bb1:
      %13 = llvm.load %8 : !llvm.ptr -> i64
      %14 = arith.constant 2 : i32
      %16 = arith.extsi %14 : i32 to i64
      %15 = arith.remsi %13, %16 : i64
      %17 = arith.constant 1 : i32
      %19 = arith.extsi %17 : i32 to i64
      %18 = arith.cmpi eq, %15, %19 : i64
      cf.cond_br %18, ^bb3, ^bb4
      ^bb3:
        %20 = llvm.load %3 : !llvm.ptr -> i64
        %21 = arith.extsi %20 : i64 to i128
        %22 = llvm.load %6 : !llvm.ptr -> i64
        %23 = arith.extsi %22 : i64 to i128
        %25 = arith.trunci %21 : i128 to i64
        %26 = arith.trunci %23 : i128 to i64
        %24 = arith.muli %25, %26 : i64
        %27 = arith.extsi %arg2 : i64 to i128
        %29 = arith.trunci %27 : i128 to i64
        %28 = arith.remsi %24, %29 : i64
        %30 = arith.extsi %28 : i64 to i128
        %31 = arith.trunci %30 : i128 to i64
        llvm.store %31, %3 : i64, !llvm.ptr
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %32 = llvm.load %6 : !llvm.ptr -> i64
      %33 = arith.extsi %32 : i64 to i128
      %34 = llvm.load %6 : !llvm.ptr -> i64
      %35 = arith.extsi %34 : i64 to i128
      %37 = arith.trunci %33 : i128 to i64
      %38 = arith.trunci %35 : i128 to i64
      %36 = arith.muli %37, %38 : i64
      %39 = arith.extsi %arg2 : i64 to i128
      %41 = arith.trunci %39 : i128 to i64
      %40 = arith.remsi %36, %41 : i64
      %42 = arith.extsi %40 : i64 to i128
      %43 = arith.trunci %42 : i128 to i64
      llvm.store %43, %6 : i64, !llvm.ptr
      %44 = llvm.load %8 : !llvm.ptr -> i64
      %45 = arith.constant 2 : i32
      %47 = arith.extsi %45 : i32 to i64
      %46 = arith.divsi %44, %47 : i64
      llvm.store %46, %8 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %48 = llvm.load %3 : !llvm.ptr -> i64
    func.return %48 : i64
  }
  func.func @f_n(%arg0: i64, %arg1: i64) -> i64 {
    %49 = llvm.mlir.constant(1 : i64) : i64
    %50 = llvm.alloca %49 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %50 : i64, !llvm.ptr
    %51 = arith.constant 0 : i32
    %52 = llvm.mlir.constant(1 : i64) : i64
    %53 = llvm.alloca %52 x i32 : (i64) -> !llvm.ptr
    llvm.store %51, %53 : i32, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %54 = llvm.load %53 : !llvm.ptr -> i32
    %55 = arith.constant 64 : i32
    %56 = arith.cmpi slt, %54, %55 : i32
    cf.cond_br %56, ^bb7, ^bb8
    ^bb7:
      %58 = llvm.load %50 : !llvm.ptr -> i64
      %57 = func.call @modpow(%arg0, %58, %arg1) : (i64, i64, i64) -> i64
      %59 = arith.constant 0 : i32
      %61 = arith.extsi %59 : i32 to i64
      %60 = arith.cmpi eq, %57, %61 : i64
      %62 = scf.if %60 -> (i1) {
        %63 = arith.constant true
        scf.yield %63 : i1
      } else {
        %64 = llvm.load %50 : !llvm.ptr -> i64
        %65 = arith.cmpi eq, %57, %64 : i64
        scf.yield %65 : i1
      }
      cf.cond_br %62, ^bb9, ^bb10
      ^bb9:
        func.return %57 : i64
      ^bb10:
        cf.br ^bb11
      ^bb11:
      llvm.store %57, %50 : i64, !llvm.ptr
      %66 = llvm.load %53 : !llvm.ptr -> i32
      %67 = arith.constant 1 : i32
      %68 = arith.addi %66, %67 : i32
      llvm.store %68, %53 : i32, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %69 = arith.constant 0 : i32
    %70 = arith.extsi %69 : i32 to i64
    func.return %70 : i64
  }
  func.func @main() -> i32 {
    %71 = arith.constant 1000000 : i32
    %72 = arith.extsi %71 : i32 to i64
    %73 = arith.constant 1000000000 : i32
    %74 = arith.extsi %73 : i32 to i64
    %75 = arith.constant 0 : 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 2 : 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 ^bb12
    ^bb12:
    %83 = llvm.load %82 : !llvm.ptr -> i64
    %84 = arith.cmpi sle, %83, %72 : i64
    cf.cond_br %84, ^bb13, ^bb14
    ^bb13:
      %85 = llvm.load %78 : !llvm.ptr -> i64
      %87 = llvm.load %82 : !llvm.ptr -> i64
      %86 = func.call @f_n(%87, %74) : (i64, i64) -> i64
      %88 = arith.addi %85, %86 : i64
      llvm.store %88, %78 : i64, !llvm.ptr
      %89 = llvm.load %82 : !llvm.ptr -> i64
      %90 = arith.constant 1 : i32
      %92 = arith.extsi %90 : i32 to i64
      %91 = arith.addi %89, %92 : i64
      llvm.store %91, %82 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %93 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %94 = llvm.load %78 : !llvm.ptr -> i64
    %95 = llvm.call @printf(%93, %94) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %96 = arith.constant 0 : i32
    func.return %96 : i32
  }
}