Problem 288

N(61, 10^7) mod 61^10.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 288
# N(61, 10^7) mod 61^10.

function count_factors_t(t: i64, prime: i64) -> i64 {
    let mut result: i64 = 0
    let mut power: i64 = prime
    while power <= t {
        result = result + t / power
        if power > t / prime { break }
        power = power * prime
    }
    return result
}

# valuation of (t * prime^k)! for the prime
function count_factors_pow(t: i64, k: i64, prime: i64) -> i64 {
    if t == 0 { return 0 }
    # sum_{i=1..k} t * prime^{k-i} + count_factors(t)
    let mut result: i64 = 0
    let mut pp: i64 = 1
    let mut j: i64 = 0
    while j < k {
        result = result + t * pp
        pp = pp * prime
        j = j + 1
    }
    return result + count_factors_t(t, prime)
}

function main() -> i32 {
    let prime: i64 = 61
    let iterations: i64 = 10000000
    let exponent: i64 = 10
    let mut modulo: i64 = 1
    let mut e: i64 = 0
    while e < exponent {
        modulo = modulo * prime
        e = e + 1
    }
    let mut k: i64 = 0
    let mut s: i64 = 290797
    let mut result: i64 = 0
    let mut i: i64 = 0
    while i <= iterations {
        let t: i64 = s % prime
        result = (result + count_factors_pow(t, k, prime)) % modulo
        if k < exponent {
            k = k + 1
        }
        s = (s * s) % 50515093
        i = i + 1
    }
    printf("%lld\n", result)
    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 count_factors_t_i64_i64(int64_t t, int64_t prime);
int64_t count_factors_pow_i64_i64_i64(int64_t t, int64_t k, int64_t prime);
int32_t main(void);

int64_t count_factors_t_i64_i64(int64_t t, int64_t prime) {
    int64_t result = 0;
    int64_t power = prime;
    while (power <= t) {
        result = (result + FLOW_CHECKED_DIV((t), (power)));
        if (power > FLOW_CHECKED_DIV((t), (prime))) {
            break;
        }
        power = (power * prime);
    }
    return result;
}

int64_t count_factors_pow_i64_i64_i64(int64_t t, int64_t k, int64_t prime) {
    if (t == 0) {
        return 0;
    }
    int64_t result = 0;
    int64_t pp = 1;
    int64_t j = 0;
    while (j < k) {
        result = (result + (t * pp));
        pp = (pp * prime);
        j = (j + 1);
    }
    return (result + count_factors_t_i64_i64(t, prime));
}

int32_t main(void) {
    int64_t prime = 61;
    int64_t iterations = 10000000;
    int64_t exponent = 10;
    int64_t modulo = 1;
    int64_t e = 0;
    while (e < exponent) {
        modulo = (modulo * prime);
        e = (e + 1);
    }
    int64_t k = 0;
    int64_t s = 290797;
    int64_t result = 0;
    int64_t i = 0;
    while (i <= iterations) {
        int64_t t = FLOW_CHECKED_MOD((s), (prime));
        result = FLOW_CHECKED_MOD(((result + count_factors_pow_i64_i64_i64(t, k, prime))), (modulo));
        if (k < exponent) {
            k = (k + 1);
        }
        s = FLOW_CHECKED_MOD(((s * s)), (50515093));
        i = (i + 1);
    }
    printf("%lld\n", result);
    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 @count_factors_t(%arg0: i64, %arg1: i64) -> i64 {
    %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 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %5 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %6 = llvm.load %5 : !llvm.ptr -> i64
    %7 = arith.cmpi sle, %6, %arg0 : i64
    cf.cond_br %7, ^bb1, ^bb2
    ^bb1:
      %8 = llvm.load %3 : !llvm.ptr -> i64
      %9 = llvm.load %5 : !llvm.ptr -> i64
      %10 = arith.divsi %arg0, %9 : i64
      %11 = arith.addi %8, %10 : i64
      llvm.store %11, %3 : i64, !llvm.ptr
      %12 = llvm.load %5 : !llvm.ptr -> i64
      %13 = arith.divsi %arg0, %arg1 : i64
      %14 = arith.cmpi sgt, %12, %13 : i64
      cf.cond_br %14, ^bb3, ^bb4
      ^bb3:
        cf.br ^bb2
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %15 = llvm.load %5 : !llvm.ptr -> i64
      %16 = arith.muli %15, %arg1 : i64
      llvm.store %16, %5 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %17 = llvm.load %3 : !llvm.ptr -> i64
    func.return %17 : i64
  }
  func.func @count_factors_pow(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
    %18 = arith.constant 0 : i32
    %20 = arith.extsi %18 : i32 to i64
    %19 = arith.cmpi eq, %arg0, %20 : i64
    cf.cond_br %19, ^bb6, ^bb7
    ^bb6:
      %21 = arith.constant 0 : i32
      %22 = arith.extsi %21 : i32 to i64
      func.return %22 : i64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %23 = arith.constant 0 : i32
    %24 = arith.extsi %23 : i32 to i64
    %25 = llvm.mlir.constant(1 : i64) : i64
    %26 = llvm.alloca %25 x i64 : (i64) -> !llvm.ptr
    llvm.store %24, %26 : i64, !llvm.ptr
    %27 = arith.constant 1 : i32
    %28 = arith.extsi %27 : i32 to i64
    %29 = llvm.mlir.constant(1 : i64) : i64
    %30 = llvm.alloca %29 x i64 : (i64) -> !llvm.ptr
    llvm.store %28, %30 : i64, !llvm.ptr
    %31 = arith.constant 0 : i32
    %32 = arith.extsi %31 : i32 to i64
    %33 = llvm.mlir.constant(1 : i64) : i64
    %34 = llvm.alloca %33 x i64 : (i64) -> !llvm.ptr
    llvm.store %32, %34 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %35 = llvm.load %34 : !llvm.ptr -> i64
    %36 = arith.cmpi slt, %35, %arg1 : i64
    cf.cond_br %36, ^bb10, ^bb11
    ^bb10:
      %37 = llvm.load %26 : !llvm.ptr -> i64
      %38 = llvm.load %30 : !llvm.ptr -> i64
      %39 = arith.muli %arg0, %38 : i64
      %40 = arith.addi %37, %39 : i64
      llvm.store %40, %26 : i64, !llvm.ptr
      %41 = llvm.load %30 : !llvm.ptr -> i64
      %42 = arith.muli %41, %arg2 : i64
      llvm.store %42, %30 : i64, !llvm.ptr
      %43 = llvm.load %34 : !llvm.ptr -> i64
      %44 = arith.constant 1 : i32
      %46 = arith.extsi %44 : i32 to i64
      %45 = arith.addi %43, %46 : i64
      llvm.store %45, %34 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %47 = llvm.load %26 : !llvm.ptr -> i64
    %48 = func.call @count_factors_t(%arg0, %arg2) : (i64, i64) -> i64
    %49 = arith.addi %47, %48 : i64
    func.return %49 : i64
  }
  func.func @main() -> i32 {
    %50 = arith.constant 61 : i32
    %51 = arith.extsi %50 : i32 to i64
    %52 = arith.constant 10000000 : i32
    %53 = arith.extsi %52 : i32 to i64
    %54 = arith.constant 10 : i32
    %55 = arith.extsi %54 : i32 to i64
    %56 = arith.constant 1 : i32
    %57 = arith.extsi %56 : i32 to i64
    %58 = llvm.mlir.constant(1 : i64) : i64
    %59 = llvm.alloca %58 x i64 : (i64) -> !llvm.ptr
    llvm.store %57, %59 : i64, !llvm.ptr
    %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
    cf.br ^bb12
    ^bb12:
    %64 = llvm.load %63 : !llvm.ptr -> i64
    %65 = arith.cmpi slt, %64, %55 : i64
    cf.cond_br %65, ^bb13, ^bb14
    ^bb13:
      %66 = llvm.load %59 : !llvm.ptr -> i64
      %67 = arith.muli %66, %51 : i64
      llvm.store %67, %59 : i64, !llvm.ptr
      %68 = llvm.load %63 : !llvm.ptr -> i64
      %69 = arith.constant 1 : i32
      %71 = arith.extsi %69 : i32 to i64
      %70 = arith.addi %68, %71 : i64
      llvm.store %70, %63 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %72 = arith.constant 0 : i32
    %73 = arith.extsi %72 : i32 to i64
    %74 = llvm.mlir.constant(1 : i64) : i64
    %75 = llvm.alloca %74 x i64 : (i64) -> !llvm.ptr
    llvm.store %73, %75 : i64, !llvm.ptr
    %76 = arith.constant 290797 : i32
    %77 = arith.extsi %76 : i32 to i64
    %78 = llvm.mlir.constant(1 : i64) : i64
    %79 = llvm.alloca %78 x i64 : (i64) -> !llvm.ptr
    llvm.store %77, %79 : i64, !llvm.ptr
    %80 = arith.constant 0 : i32
    %81 = arith.extsi %80 : i32 to i64
    %82 = llvm.mlir.constant(1 : i64) : i64
    %83 = llvm.alloca %82 x i64 : (i64) -> !llvm.ptr
    llvm.store %81, %83 : i64, !llvm.ptr
    %84 = arith.constant 0 : 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
    cf.br ^bb15
    ^bb15:
    %88 = llvm.load %87 : !llvm.ptr -> i64
    %89 = arith.cmpi sle, %88, %53 : i64
    cf.cond_br %89, ^bb16, ^bb17
    ^bb16:
      %90 = llvm.load %79 : !llvm.ptr -> i64
      %91 = arith.remsi %90, %51 : i64
      %92 = llvm.load %83 : !llvm.ptr -> i64
      %94 = llvm.load %75 : !llvm.ptr -> i64
      %93 = func.call @count_factors_pow(%91, %94, %51) : (i64, i64, i64) -> i64
      %95 = arith.addi %92, %93 : i64
      %96 = llvm.load %59 : !llvm.ptr -> i64
      %97 = arith.remsi %95, %96 : i64
      llvm.store %97, %83 : i64, !llvm.ptr
      %98 = llvm.load %75 : !llvm.ptr -> i64
      %99 = arith.cmpi slt, %98, %55 : i64
      cf.cond_br %99, ^bb18, ^bb19
      ^bb18:
        %100 = llvm.load %75 : !llvm.ptr -> i64
        %101 = arith.constant 1 : i32
        %103 = arith.extsi %101 : i32 to i64
        %102 = arith.addi %100, %103 : i64
        llvm.store %102, %75 : i64, !llvm.ptr
        cf.br ^bb20
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %104 = llvm.load %79 : !llvm.ptr -> i64
      %105 = llvm.load %79 : !llvm.ptr -> i64
      %106 = arith.muli %104, %105 : i64
      %107 = arith.constant 50515093 : i32
      %109 = arith.extsi %107 : i32 to i64
      %108 = arith.remsi %106, %109 : i64
      llvm.store %108, %79 : i64, !llvm.ptr
      %110 = llvm.load %87 : !llvm.ptr -> i64
      %111 = arith.constant 1 : i32
      %113 = arith.extsi %111 : i32 to i64
      %112 = arith.addi %110, %113 : i64
      llvm.store %112, %87 : i64, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %114 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %115 = llvm.load %83 : !llvm.ptr -> i64
    %116 = llvm.call @printf(%114, %115) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %117 = arith.constant 0 : i32
    func.return %117 : i32
  }
}