Problem 320

Sum_{i=10..10^6} N(i) mod 10^18 where N(i)! has ≥ 1234567890 trailing zeros in base i.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 320
# Sum_{i=10..10^6} N(i) mod 10^18 where N(i)! has ≥ 1234567890 trailing zeros in base i.

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

function fact_val(n0: i64, p: i64) -> i64 {
    let mut total: i64 = 0
    let mut n: i64 = n0
    while n > 0 {
        n = n / p
        total = total + n
    }
    return total
}

function inv_fact_val(p: i64, target: i64, lower: i64) -> i64 {
    if fact_val(lower, p) >= target { return lower }
    let mut lo: i64 = lower
    let mut step: i64 = p
    let mut hi: i64 = lo + step
    while fact_val(hi, p) < target {
        lo = hi
        step = step * 2
        hi = hi + step
    }
    while hi - lo > 1 {
        let mid: i64 = (lo + hi) / 2
        if fact_val(mid, p) >= target {
            hi = mid
        } else {
            lo = mid
        }
    }
    return hi
}

function main() -> i32 {
    let limit: i64 = 1000000
    let K: i64 = 1234567890
    let MOD: i64 = 1000000000000000000
    let spf: ptr<i32> = calloc(limit + 1, 4)
    let targets: ptr<i64> = calloc(limit + 1, 8)
    let witnesses: ptr<i64> = calloc(limit + 1, 8)
    if spf == null || targets == null || witnesses == null { return 1 }
    let mut i: i64 = 2
    while i <= limit {
        if spf[i] == 0 {
            spf[i] = i as i32
            if i * i <= limit {
                let mut j: i64 = i * i
                while j <= limit {
                    if spf[j] == 0 { spf[j] = i as i32 }
                    j = j + i
                }
            }
        }
        i = i + 1
    }
    let mut current: i64 = 0
    let mut total: i64 = 0
    i = 2
    while i <= limit {
        let mut n: i64 = i
        while n > 1 {
            let p: i64 = spf[n] as i64
            let mut exponent: i64 = 0
            while n % p == 0 {
                n = n / p
                exponent = exponent + 1
            }
            let target: i64 = targets[p] + K * exponent
            targets[p] = target
            if fact_val(current, p) >= target { continue }
            let mut lower: i64 = target * (p - 1)
            if witnesses[p] > lower { lower = witnesses[p] }
            let witness: i64 = inv_fact_val(p, target, lower)
            witnesses[p] = witness
            if witness > current { current = witness }
        }
        if i >= 10 {
            total = (total + current) % MOD
        }
        i = i + 1
    }
    printf("%lld\n", total)
    free(spf); free(targets); free(witnesses)
    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 fact_val_i64_i64(int64_t n0, int64_t p);
int64_t inv_fact_val_i64_i64_i64(int64_t p, int64_t target, int64_t lower);
int32_t main(void);



int64_t fact_val_i64_i64(int64_t n0, int64_t p) {
    int64_t total = 0;
    int64_t n = n0;
    while (n > 0) {
        n = FLOW_CHECKED_DIV((n), (p));
        total = (total + n);
    }
    return total;
}

int64_t inv_fact_val_i64_i64_i64(int64_t p, int64_t target, int64_t lower) {
    if (fact_val_i64_i64(lower, p) >= target) {
        return lower;
    }
    int64_t lo = lower;
    int64_t step = p;
    int64_t hi = (lo + step);
    while (fact_val_i64_i64(hi, p) < target) {
        lo = hi;
        step = (step * 2);
        hi = (hi + step);
    }
    while ((hi - lo) > 1) {
        int64_t mid = FLOW_CHECKED_DIV(((lo + hi)), (2));
        if (fact_val_i64_i64(mid, p) >= target) {
            hi = mid;
        } else {
            lo = mid;
        }
    }
    return hi;
}

int32_t main(void) {
    int64_t limit = 1000000;
    int64_t K = 1234567890;
    int64_t MOD = 1000000000000000000;
    int32_t* spf = (int32_t*)(calloc((limit + 1), 4));
    int64_t* targets = (int64_t*)(calloc((limit + 1), 8));
    int64_t* witnesses = (int64_t*)(calloc((limit + 1), 8));
    if (((spf == NULL || targets == NULL) || witnesses == NULL)) {
        return 1;
    }
    int64_t i = 2;
    while (i <= limit) {
        if (spf[i] == 0) {
            spf[i] = ((int32_t)(i));
            if ((i * i) <= limit) {
                int64_t j = (i * i);
                while (j <= limit) {
                    if (spf[j] == 0) {
                        spf[j] = ((int32_t)(i));
                    }
                    j = (j + i);
                }
            }
        }
        i = (i + 1);
    }
    int64_t current = 0;
    int64_t total = 0;
    i = 2;
    while (i <= limit) {
        int64_t n = i;
        while (n > 1) {
            int64_t p = ((int64_t)(spf[n]));
            int64_t exponent = 0;
            while (FLOW_CHECKED_MOD((n), (p)) == 0) {
                n = FLOW_CHECKED_DIV((n), (p));
                exponent = (exponent + 1);
            }
            int64_t target = (targets[p] + (K * exponent));
            targets[p] = target;
            if (fact_val_i64_i64(current, p) >= target) {
                continue;
            }
            int64_t lower = (target * (p - 1));
            if (witnesses[p] > lower) {
                lower = witnesses[p];
            }
            int64_t witness = inv_fact_val_i64_i64_i64(p, target, lower);
            witnesses[p] = witness;
            if (witness > current) {
                current = witness;
            }
        }
        if (i >= 10) {
            total = FLOW_CHECKED_MOD(((total + current)), (MOD));
        }
        i = (i + 1);
    }
    printf("%lld\n", total);
    free(spf);
    free(targets);
    free(witnesses);
    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 @fact_val(%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 %arg0, %5 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %6 = llvm.load %5 : !llvm.ptr -> i64
    %7 = arith.constant 0 : i32
    %9 = arith.extsi %7 : i32 to i64
    %8 = arith.cmpi sgt, %6, %9 : i64
    cf.cond_br %8, ^bb1, ^bb2
    ^bb1:
      %10 = llvm.load %5 : !llvm.ptr -> i64
      %11 = arith.divsi %10, %arg1 : i64
      llvm.store %11, %5 : i64, !llvm.ptr
      %12 = llvm.load %3 : !llvm.ptr -> i64
      %13 = llvm.load %5 : !llvm.ptr -> i64
      %14 = arith.addi %12, %13 : i64
      llvm.store %14, %3 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %15 = llvm.load %3 : !llvm.ptr -> i64
    func.return %15 : i64
  }
  func.func @inv_fact_val(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
    %16 = func.call @fact_val(%arg2, %arg0) : (i64, i64) -> i64
    %17 = arith.cmpi sge, %16, %arg1 : i64
    cf.cond_br %17, ^bb3, ^bb4
    ^bb3:
      func.return %arg2 : i64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %18 = llvm.mlir.constant(1 : i64) : i64
    %19 = llvm.alloca %18 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg2, %19 : i64, !llvm.ptr
    %20 = llvm.mlir.constant(1 : i64) : i64
    %21 = llvm.alloca %20 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %21 : i64, !llvm.ptr
    %22 = llvm.load %19 : !llvm.ptr -> i64
    %23 = llvm.load %21 : !llvm.ptr -> i64
    %24 = arith.addi %22, %23 : i64
    %25 = llvm.mlir.constant(1 : i64) : i64
    %26 = llvm.alloca %25 x i64 : (i64) -> !llvm.ptr
    llvm.store %24, %26 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %28 = llvm.load %26 : !llvm.ptr -> i64
    %27 = func.call @fact_val(%28, %arg0) : (i64, i64) -> i64
    %29 = arith.cmpi slt, %27, %arg1 : i64
    cf.cond_br %29, ^bb7, ^bb8
    ^bb7:
      %30 = llvm.load %26 : !llvm.ptr -> i64
      llvm.store %30, %19 : i64, !llvm.ptr
      %31 = llvm.load %21 : !llvm.ptr -> i64
      %32 = arith.constant 2 : i32
      %34 = arith.extsi %32 : i32 to i64
      %33 = arith.muli %31, %34 : i64
      llvm.store %33, %21 : i64, !llvm.ptr
      %35 = llvm.load %26 : !llvm.ptr -> i64
      %36 = llvm.load %21 : !llvm.ptr -> i64
      %37 = arith.addi %35, %36 : i64
      llvm.store %37, %26 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    cf.br ^bb9
    ^bb9:
    %38 = llvm.load %26 : !llvm.ptr -> i64
    %39 = llvm.load %19 : !llvm.ptr -> i64
    %40 = arith.subi %38, %39 : i64
    %41 = arith.constant 1 : i32
    %43 = arith.extsi %41 : i32 to i64
    %42 = arith.cmpi sgt, %40, %43 : i64
    cf.cond_br %42, ^bb10, ^bb11
    ^bb10:
      %44 = llvm.load %19 : !llvm.ptr -> i64
      %45 = llvm.load %26 : !llvm.ptr -> i64
      %46 = arith.addi %44, %45 : i64
      %47 = arith.constant 2 : i32
      %49 = arith.extsi %47 : i32 to i64
      %48 = arith.divsi %46, %49 : i64
      %50 = func.call @fact_val(%48, %arg0) : (i64, i64) -> i64
      %51 = arith.cmpi sge, %50, %arg1 : i64
      cf.cond_br %51, ^bb12, ^bb13
      ^bb12:
        llvm.store %48, %26 : i64, !llvm.ptr
        cf.br ^bb14
      ^bb13:
        llvm.store %48, %19 : i64, !llvm.ptr
        cf.br ^bb14
      ^bb14:
      cf.br ^bb9
    ^bb11:
    %52 = llvm.load %26 : !llvm.ptr -> i64
    func.return %52 : i64
  }
  func.func @main() -> i32 {
    %53 = arith.constant 1000000 : i32
    %54 = arith.extsi %53 : i32 to i64
    %55 = arith.constant 1234567890 : i32
    %56 = arith.extsi %55 : i32 to i64
    %57 = arith.constant 999999995705032704 : i32
    %58 = arith.extsi %57 : i32 to i64
    %60 = arith.constant 1 : i32
    %62 = arith.extsi %60 : i32 to i64
    %61 = arith.addi %54, %62 : i64
    %63 = arith.constant 4 : i32
    %64 = arith.extsi %63 : i32 to i64
    %59 = func.call @calloc(%61, %64) : (i64, i64) -> !llvm.ptr
    %66 = arith.constant 1 : i32
    %68 = arith.extsi %66 : i32 to i64
    %67 = arith.addi %54, %68 : i64
    %69 = arith.constant 8 : i32
    %70 = arith.extsi %69 : i32 to i64
    %65 = func.call @calloc(%67, %70) : (i64, i64) -> !llvm.ptr
    %72 = arith.constant 1 : i32
    %74 = arith.extsi %72 : i32 to i64
    %73 = arith.addi %54, %74 : i64
    %75 = arith.constant 8 : i32
    %76 = arith.extsi %75 : i32 to i64
    %71 = func.call @calloc(%73, %76) : (i64, i64) -> !llvm.ptr
    %77 = llvm.mlir.zero : !llvm.ptr
    %78 = llvm.icmp "eq" %59, %77 : !llvm.ptr
    %79 = scf.if %78 -> (i1) {
      %80 = arith.constant true
      scf.yield %80 : i1
    } else {
      %81 = llvm.mlir.zero : !llvm.ptr
      %82 = llvm.icmp "eq" %65, %81 : !llvm.ptr
      scf.yield %82 : i1
    }
    %83 = scf.if %79 -> (i1) {
      %84 = arith.constant true
      scf.yield %84 : i1
    } else {
      %85 = llvm.mlir.zero : !llvm.ptr
      %86 = llvm.icmp "eq" %71, %85 : !llvm.ptr
      scf.yield %86 : i1
    }
    cf.cond_br %83, ^bb15, ^bb16
    ^bb15:
      %87 = arith.constant 1 : i32
      func.return %87 : i32
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %88 = arith.constant 2 : i32
    %89 = arith.extsi %88 : i32 to i64
    %90 = llvm.mlir.constant(1 : i64) : i64
    %91 = llvm.alloca %90 x i64 : (i64) -> !llvm.ptr
    llvm.store %89, %91 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %92 = llvm.load %91 : !llvm.ptr -> i64
    %93 = arith.cmpi sle, %92, %54 : i64
    cf.cond_br %93, ^bb19, ^bb20
    ^bb19:
      %95 = llvm.load %91 : !llvm.ptr -> i64
      %96 = llvm.getelementptr %59[%95] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %94 = llvm.load %96 : !llvm.ptr -> i32
      %97 = arith.constant 0 : i32
      %98 = arith.cmpi eq, %94, %97 : i32
      cf.cond_br %98, ^bb21, ^bb22
      ^bb21:
        %99 = llvm.load %91 : !llvm.ptr -> i64
        %100 = arith.trunci %99 : i64 to i32
        %101 = llvm.load %91 : !llvm.ptr -> i64
        %102 = llvm.getelementptr %59[%101] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        llvm.store %100, %102 : i32, !llvm.ptr
        %103 = llvm.load %91 : !llvm.ptr -> i64
        %104 = llvm.load %91 : !llvm.ptr -> i64
        %105 = arith.muli %103, %104 : i64
        %106 = arith.cmpi sle, %105, %54 : i64
        cf.cond_br %106, ^bb24, ^bb25
        ^bb24:
          %107 = llvm.load %91 : !llvm.ptr -> i64
          %108 = llvm.load %91 : !llvm.ptr -> i64
          %109 = arith.muli %107, %108 : i64
          %110 = llvm.mlir.constant(1 : i64) : i64
          %111 = llvm.alloca %110 x i64 : (i64) -> !llvm.ptr
          llvm.store %109, %111 : i64, !llvm.ptr
          cf.br ^bb27
          ^bb27:
          %112 = llvm.load %111 : !llvm.ptr -> i64
          %113 = arith.cmpi sle, %112, %54 : i64
          cf.cond_br %113, ^bb28, ^bb29
          ^bb28:
            %115 = llvm.load %111 : !llvm.ptr -> i64
            %116 = llvm.getelementptr %59[%115] : (!llvm.ptr, i64) -> !llvm.ptr, i32
            %114 = llvm.load %116 : !llvm.ptr -> i32
            %117 = arith.constant 0 : i32
            %118 = arith.cmpi eq, %114, %117 : i32
            cf.cond_br %118, ^bb30, ^bb31
            ^bb30:
              %119 = llvm.load %91 : !llvm.ptr -> i64
              %120 = arith.trunci %119 : i64 to i32
              %121 = llvm.load %111 : !llvm.ptr -> i64
              %122 = llvm.getelementptr %59[%121] : (!llvm.ptr, i64) -> !llvm.ptr, i32
              llvm.store %120, %122 : i32, !llvm.ptr
              cf.br ^bb32
            ^bb31:
              cf.br ^bb32
            ^bb32:
            %123 = llvm.load %111 : !llvm.ptr -> i64
            %124 = llvm.load %91 : !llvm.ptr -> i64
            %125 = arith.addi %123, %124 : i64
            llvm.store %125, %111 : i64, !llvm.ptr
            cf.br ^bb27
          ^bb29:
          cf.br ^bb26
        ^bb25:
          cf.br ^bb26
        ^bb26:
        cf.br ^bb23
      ^bb22:
        cf.br ^bb23
      ^bb23:
      %126 = llvm.load %91 : !llvm.ptr -> i64
      %127 = arith.constant 1 : i32
      %129 = arith.extsi %127 : i32 to i64
      %128 = arith.addi %126, %129 : i64
      llvm.store %128, %91 : i64, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %130 = arith.constant 0 : i32
    %131 = arith.extsi %130 : i32 to i64
    %132 = llvm.mlir.constant(1 : i64) : i64
    %133 = llvm.alloca %132 x i64 : (i64) -> !llvm.ptr
    llvm.store %131, %133 : i64, !llvm.ptr
    %134 = arith.constant 0 : i32
    %135 = arith.extsi %134 : i32 to i64
    %136 = llvm.mlir.constant(1 : i64) : i64
    %137 = llvm.alloca %136 x i64 : (i64) -> !llvm.ptr
    llvm.store %135, %137 : i64, !llvm.ptr
    %138 = arith.constant 2 : i32
    %139 = arith.extsi %138 : i32 to i64
    llvm.store %139, %91 : i64, !llvm.ptr
    cf.br ^bb33
    ^bb33:
    %140 = llvm.load %91 : !llvm.ptr -> i64
    %141 = arith.cmpi sle, %140, %54 : i64
    cf.cond_br %141, ^bb34, ^bb35
    ^bb34:
      %142 = llvm.load %91 : !llvm.ptr -> i64
      %143 = llvm.mlir.constant(1 : i64) : i64
      %144 = llvm.alloca %143 x i64 : (i64) -> !llvm.ptr
      llvm.store %142, %144 : i64, !llvm.ptr
      cf.br ^bb36
      ^bb36:
      %145 = llvm.load %144 : !llvm.ptr -> i64
      %146 = arith.constant 1 : i32
      %148 = arith.extsi %146 : i32 to i64
      %147 = arith.cmpi sgt, %145, %148 : i64
      cf.cond_br %147, ^bb37, ^bb38
      ^bb37:
        %150 = llvm.load %144 : !llvm.ptr -> i64
        %151 = llvm.getelementptr %59[%150] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %149 = llvm.load %151 : !llvm.ptr -> i32
        %152 = arith.extsi %149 : i32 to i64
        %153 = arith.constant 0 : i32
        %154 = arith.extsi %153 : i32 to i64
        %155 = llvm.mlir.constant(1 : i64) : i64
        %156 = llvm.alloca %155 x i64 : (i64) -> !llvm.ptr
        llvm.store %154, %156 : i64, !llvm.ptr
        cf.br ^bb39
        ^bb39:
        %157 = llvm.load %144 : !llvm.ptr -> i64
        %158 = arith.remsi %157, %152 : i64
        %159 = arith.constant 0 : i32
        %161 = arith.extsi %159 : i32 to i64
        %160 = arith.cmpi eq, %158, %161 : i64
        cf.cond_br %160, ^bb40, ^bb41
        ^bb40:
          %162 = llvm.load %144 : !llvm.ptr -> i64
          %163 = arith.divsi %162, %152 : i64
          llvm.store %163, %144 : i64, !llvm.ptr
          %164 = llvm.load %156 : !llvm.ptr -> i64
          %165 = arith.constant 1 : i32
          %167 = arith.extsi %165 : i32 to i64
          %166 = arith.addi %164, %167 : i64
          llvm.store %166, %156 : i64, !llvm.ptr
          cf.br ^bb39
        ^bb41:
        %169 = llvm.getelementptr %65[%152] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %168 = llvm.load %169 : !llvm.ptr -> i64
        %170 = llvm.load %156 : !llvm.ptr -> i64
        %171 = arith.muli %56, %170 : i64
        %172 = arith.addi %168, %171 : i64
        %173 = llvm.getelementptr %65[%152] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        llvm.store %172, %173 : i64, !llvm.ptr
        %175 = llvm.load %133 : !llvm.ptr -> i64
        %174 = func.call @fact_val(%175, %152) : (i64, i64) -> i64
        %176 = arith.cmpi sge, %174, %172 : i64
        cf.cond_br %176, ^bb42, ^bb43
        ^bb42:
          cf.br ^bb36
        ^bb43:
          cf.br ^bb44
        ^bb44:
        %177 = arith.constant 1 : i32
        %179 = arith.extsi %177 : i32 to i64
        %178 = arith.subi %152, %179 : i64
        %180 = arith.muli %172, %178 : i64
        %181 = llvm.mlir.constant(1 : i64) : i64
        %182 = llvm.alloca %181 x i64 : (i64) -> !llvm.ptr
        llvm.store %180, %182 : i64, !llvm.ptr
        %184 = llvm.getelementptr %71[%152] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %183 = llvm.load %184 : !llvm.ptr -> i64
        %185 = llvm.load %182 : !llvm.ptr -> i64
        %186 = arith.cmpi sgt, %183, %185 : i64
        cf.cond_br %186, ^bb45, ^bb46
        ^bb45:
          %188 = llvm.getelementptr %71[%152] : (!llvm.ptr, i64) -> !llvm.ptr, i64
          %187 = llvm.load %188 : !llvm.ptr -> i64
          llvm.store %187, %182 : i64, !llvm.ptr
          cf.br ^bb47
        ^bb46:
          cf.br ^bb47
        ^bb47:
        %190 = llvm.load %182 : !llvm.ptr -> i64
        %189 = func.call @inv_fact_val(%152, %172, %190) : (i64, i64, i64) -> i64
        %191 = llvm.getelementptr %71[%152] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        llvm.store %189, %191 : i64, !llvm.ptr
        %192 = llvm.load %133 : !llvm.ptr -> i64
        %193 = arith.cmpi sgt, %189, %192 : i64
        cf.cond_br %193, ^bb48, ^bb49
        ^bb48:
          llvm.store %189, %133 : i64, !llvm.ptr
          cf.br ^bb50
        ^bb49:
          cf.br ^bb50
        ^bb50:
        cf.br ^bb36
      ^bb38:
      %194 = llvm.load %91 : !llvm.ptr -> i64
      %195 = arith.constant 10 : i32
      %197 = arith.extsi %195 : i32 to i64
      %196 = arith.cmpi sge, %194, %197 : i64
      cf.cond_br %196, ^bb51, ^bb52
      ^bb51:
        %198 = llvm.load %137 : !llvm.ptr -> i64
        %199 = llvm.load %133 : !llvm.ptr -> i64
        %200 = arith.addi %198, %199 : i64
        %201 = arith.remsi %200, %58 : i64
        llvm.store %201, %137 : i64, !llvm.ptr
        cf.br ^bb53
      ^bb52:
        cf.br ^bb53
      ^bb53:
      %202 = llvm.load %91 : !llvm.ptr -> i64
      %203 = arith.constant 1 : i32
      %205 = arith.extsi %203 : i32 to i64
      %204 = arith.addi %202, %205 : i64
      llvm.store %204, %91 : i64, !llvm.ptr
      cf.br ^bb33
    ^bb35:
    %206 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %207 = llvm.load %137 : !llvm.ptr -> i64
    %208 = llvm.call @printf(%206, %207) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%59) : (!llvm.ptr) -> ()
    func.call @free(%65) : (!llvm.ptr) -> ()
    func.call @free(%71) : (!llvm.ptr) -> ()
    %212 = arith.constant 0 : i32
    func.return %212 : i32
  }
}