Problem 539

Odd Elimination — S(10^18) mod 987654321 via memoized recurrence.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 539
# Odd Elimination — S(10^18) mod 987654321 via memoized recurrence.

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

const MOD: i64 = 987654321
const CAP: i64 = 1048576

function hslot(key: i64, keys: ptr<i64>, used: ptr<i8>) -> i64 {
    let mut h: i64 = key % CAP
    if h < 0 { h = h + CAP }
    while used[h] == 1 && keys[h] != key {
        h = h + 1
        if h == CAP { h = 0 }
    }
    return h
}

function P(n: i64, pk: ptr<i64>, pv: ptr<i64>, pu: ptr<i8>) -> i64 {
    if n == 1 { return 1 }
    let s: i64 = hslot(n, pk, pu)
    if pu[s] == 1 { return pv[s] }
    let val: i64 = 2 * (1 + n / 2 - P(n / 2, pk, pv, pu))
    pu[s] = 1
    pk[s] = n
    pv[s] = val
    return val
}

function S(n: i64, sk: ptr<i64>, sv: ptr<i64>, su: ptr<i8>,
          pk: ptr<i64>, pv: ptr<i64>, pu: ptr<i8>) -> i64 {
    if n <= 0 { return 0 }
    if n == 1 { return 1 }
    let s: i64 = hslot(n, sk, su)
    if su[s] == 1 { return sv[s] }
    let mut val: i64 = 0
    if (n & 1) == 1 {
        let q: i64 = n / 2
        let t: i128 = (1 as i128) + (2 as i128) * (q as i128) * ((q + 3) as i128)
            - (4 as i128) * (S(q, sk, sv, su, pk, pv, pu) as i128)
        val = ((t % (MOD as i128) + (MOD as i128)) % (MOD as i128)) as i64
    } else {
        let q: i64 = n / 2
        let t: i128 = (2 as i128) * (q as i128) * (q as i128) + (4 as i128) * (q as i128) - (1 as i128)
            - (4 as i128) * (S(q - 1, sk, sv, su, pk, pv, pu) as i128)
            - (2 as i128) * ((P(q, pk, pv, pu) % MOD) as i128)
        val = ((t % (MOD as i128) + (MOD as i128)) % (MOD as i128)) as i64
    }
    su[s] = 1
    sk[s] = n
    sv[s] = val
    return val
}

function main() -> i32 {
    let pk: ptr<i64> = calloc(CAP, 8)
    let pv: ptr<i64> = calloc(CAP, 8)
    let pu: ptr<i8> = calloc(CAP, 1)
    let sk: ptr<i64> = calloc(CAP, 8)
    let sv: ptr<i64> = calloc(CAP, 8)
    let su: ptr<i8> = calloc(CAP, 1)
    if pk == null || pv == null || pu == null || sk == null || sv == null || su == null {
        return 1
    }
    let ans: i64 = S(1000000000000000000, sk, sv, su, pk, pv, pu)
    printf("%lld\n", ans)
    free(pk); free(pv); free(pu); free(sk); free(sv); free(su)
    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 hslot_i64_ptr_i64_ptr_i8(int64_t key, int64_t* keys, int8_t* used);
int64_t P_i64_ptr_i64_ptr_i64_ptr_i8(int64_t n, int64_t* pk, int64_t* pv, int8_t* pu);
int64_t S_i64_ptr_i64_ptr_i64_ptr_i8_ptr_i64_ptr_i64_ptr_i8(int64_t n, int64_t* sk, int64_t* sv, int8_t* su, int64_t* pk, int64_t* pv, int8_t* pu);
int32_t main(void);

static const int64_t MOD = 987654321;
static const int64_t CAP = 1048576;



int64_t hslot_i64_ptr_i64_ptr_i8(int64_t key, int64_t* keys, int8_t* used) {
    int64_t h = FLOW_CHECKED_MOD((key), (CAP));
    if (h < 0) {
        h = (h + CAP);
    }
    while ((used[h] == 1 && keys[h] != key)) {
        h = (h + 1);
        if (h == CAP) {
            h = 0;
        }
    }
    return h;
}

int64_t P_i64_ptr_i64_ptr_i64_ptr_i8(int64_t n, int64_t* pk, int64_t* pv, int8_t* pu) {
    if (n == 1) {
        return 1;
    }
    int64_t s = hslot_i64_ptr_i64_ptr_i8(n, pk, pu);
    if (pu[s] == 1) {
        return pv[s];
    }
    int64_t val = (2 * ((1 + FLOW_CHECKED_DIV((n), (2))) - P_i64_ptr_i64_ptr_i64_ptr_i8(FLOW_CHECKED_DIV((n), (2)), pk, pv, pu)));
    pu[s] = 1;
    pk[s] = n;
    pv[s] = val;
    return val;
}

int64_t S_i64_ptr_i64_ptr_i64_ptr_i8_ptr_i64_ptr_i64_ptr_i8(int64_t n, int64_t* sk, int64_t* sv, int8_t* su, int64_t* pk, int64_t* pv, int8_t* pu) {
    if (n <= 0) {
        return 0;
    }
    if (n == 1) {
        return 1;
    }
    int64_t s = hslot_i64_ptr_i64_ptr_i8(n, sk, su);
    if (su[s] == 1) {
        return sv[s];
    }
    int64_t val = 0;
    if ((n & 1) == 1) {
        int64_t q = FLOW_CHECKED_DIV((n), (2));
        __int128 t = ((((__int128)(1)) + ((((__int128)(2)) * ((__int128)(q))) * ((__int128)((q + 3))))) - (((__int128)(4)) * ((__int128)(S_i64_ptr_i64_ptr_i64_ptr_i8_ptr_i64_ptr_i64_ptr_i8(q, sk, sv, su, pk, pv, pu)))));
        val = ((int64_t)(FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD((t), (((__int128)(MOD)))) + ((__int128)(MOD)))), (((__int128)(MOD))))));
    } else {
        int64_t q = FLOW_CHECKED_DIV((n), (2));
        __int128 t = ((((((((__int128)(2)) * ((__int128)(q))) * ((__int128)(q))) + (((__int128)(4)) * ((__int128)(q)))) - ((__int128)(1))) - (((__int128)(4)) * ((__int128)(S_i64_ptr_i64_ptr_i64_ptr_i8_ptr_i64_ptr_i64_ptr_i8((q - 1), sk, sv, su, pk, pv, pu))))) - (((__int128)(2)) * ((__int128)(FLOW_CHECKED_MOD((P_i64_ptr_i64_ptr_i64_ptr_i8(q, pk, pv, pu)), (MOD))))));
        val = ((int64_t)(FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD((t), (((__int128)(MOD)))) + ((__int128)(MOD)))), (((__int128)(MOD))))));
    }
    su[s] = 1;
    sk[s] = n;
    sv[s] = val;
    return val;
}

int32_t main(void) {
    int64_t* pk = (int64_t*)(calloc(CAP, 8));
    int64_t* pv = (int64_t*)(calloc(CAP, 8));
    int8_t* pu = (int8_t*)(calloc(CAP, 1));
    int64_t* sk = (int64_t*)(calloc(CAP, 8));
    int64_t* sv = (int64_t*)(calloc(CAP, 8));
    int8_t* su = (int8_t*)(calloc(CAP, 1));
    if ((((((pk == NULL || pv == NULL) || pu == NULL) || sk == NULL) || sv == NULL) || su == NULL)) {
        return 1;
    }
    int64_t ans = S_i64_ptr_i64_ptr_i64_ptr_i8_ptr_i64_ptr_i64_ptr_i8(1000000000000000000, sk, sv, su, pk, pv, pu);
    printf("%lld\n", ans);
    free(pk);
    free(pv);
    free(pu);
    free(sk);
    free(sv);
    free(su);
    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) -> ()
  // Constant: MOD
  llvm.mlir.global internal constant @MOD(987654321 : i64) : i64
  // Constant: CAP
  llvm.mlir.global internal constant @CAP(1048576 : i64) : i64
  func.func @hslot(%arg0: i64, %arg1: !llvm.ptr, %arg2: !llvm.ptr) -> i64 {
    %0 = llvm.mlir.addressof @CAP : !llvm.ptr
    %1 = llvm.load %0 : !llvm.ptr -> i64
    %2 = arith.remsi %arg0, %1 : i64
    %3 = llvm.mlir.constant(1 : i64) : i64
    %4 = llvm.alloca %3 x i64 : (i64) -> !llvm.ptr
    llvm.store %2, %4 : i64, !llvm.ptr
    %5 = llvm.load %4 : !llvm.ptr -> i64
    %6 = arith.constant 0 : i32
    %8 = arith.extsi %6 : i32 to i64
    %7 = arith.cmpi slt, %5, %8 : i64
    cf.cond_br %7, ^bb0, ^bb1
    ^bb0:
      %9 = llvm.load %4 : !llvm.ptr -> i64
      %10 = llvm.mlir.addressof @CAP : !llvm.ptr
      %11 = llvm.load %10 : !llvm.ptr -> i64
      %12 = arith.addi %9, %11 : i64
      llvm.store %12, %4 : i64, !llvm.ptr
      cf.br ^bb2
    ^bb1:
      cf.br ^bb2
    ^bb2:
    cf.br ^bb3
    ^bb3:
    %14 = llvm.load %4 : !llvm.ptr -> i64
    %15 = llvm.getelementptr %arg2[%14] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %13 = llvm.load %15 : !llvm.ptr -> i8
    %16 = arith.constant 1 : i32
    %18 = arith.extsi %13 : i8 to i32
    %17 = arith.cmpi eq, %18, %16 : i32
    %19 = scf.if %17 -> (i1) {
      %21 = llvm.load %4 : !llvm.ptr -> i64
      %22 = llvm.getelementptr %arg1[%21] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %20 = llvm.load %22 : !llvm.ptr -> i64
      %23 = arith.cmpi ne, %20, %arg0 : i64
      scf.yield %23 : i1
    } else {
      %24 = arith.constant false
      scf.yield %24 : i1
    }
    cf.cond_br %19, ^bb4, ^bb5
    ^bb4:
      %25 = llvm.load %4 : !llvm.ptr -> i64
      %26 = arith.constant 1 : i32
      %28 = arith.extsi %26 : i32 to i64
      %27 = arith.addi %25, %28 : i64
      llvm.store %27, %4 : i64, !llvm.ptr
      %29 = llvm.load %4 : !llvm.ptr -> i64
      %30 = llvm.mlir.addressof @CAP : !llvm.ptr
      %31 = llvm.load %30 : !llvm.ptr -> i64
      %32 = arith.cmpi eq, %29, %31 : i64
      cf.cond_br %32, ^bb6, ^bb7
      ^bb6:
        %33 = arith.constant 0 : i32
        %34 = arith.extsi %33 : i32 to i64
        llvm.store %34, %4 : i64, !llvm.ptr
        cf.br ^bb8
      ^bb7:
        cf.br ^bb8
      ^bb8:
      cf.br ^bb3
    ^bb5:
    %35 = llvm.load %4 : !llvm.ptr -> i64
    func.return %35 : i64
  }
  func.func @P(%arg0: i64, %arg1: !llvm.ptr, %arg2: !llvm.ptr, %arg3: !llvm.ptr) -> i64 {
    %36 = arith.constant 1 : i32
    %38 = arith.extsi %36 : i32 to i64
    %37 = arith.cmpi eq, %arg0, %38 : i64
    cf.cond_br %37, ^bb9, ^bb10
    ^bb9:
      %39 = arith.constant 1 : i32
      %40 = arith.extsi %39 : i32 to i64
      func.return %40 : i64
    ^bb10:
      cf.br ^bb11
    ^bb11:
    %41 = func.call @hslot(%arg0, %arg1, %arg3) : (i64, !llvm.ptr, !llvm.ptr) -> i64
    %43 = llvm.getelementptr %arg3[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %42 = llvm.load %43 : !llvm.ptr -> i8
    %44 = arith.constant 1 : i32
    %46 = arith.extsi %42 : i8 to i32
    %45 = arith.cmpi eq, %46, %44 : i32
    cf.cond_br %45, ^bb12, ^bb13
    ^bb12:
      %48 = llvm.getelementptr %arg2[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %47 = llvm.load %48 : !llvm.ptr -> i64
      func.return %47 : i64
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %49 = arith.constant 2 : i32
    %50 = arith.constant 1 : i32
    %51 = arith.constant 2 : i32
    %53 = arith.extsi %51 : i32 to i64
    %52 = arith.divsi %arg0, %53 : i64
    %55 = arith.extsi %50 : i32 to i64
    %54 = arith.addi %55, %52 : i64
    %57 = arith.constant 2 : i32
    %59 = arith.extsi %57 : i32 to i64
    %58 = arith.divsi %arg0, %59 : i64
    %56 = func.call @P(%58, %arg1, %arg2, %arg3) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> i64
    %60 = arith.subi %54, %56 : i64
    %62 = arith.extsi %49 : i32 to i64
    %61 = arith.muli %62, %60 : i64
    %63 = arith.constant 1 : i32
    %64 = arith.trunci %63 : i32 to i8
    %65 = llvm.getelementptr %arg3[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %64, %65 : i8, !llvm.ptr
    %66 = llvm.getelementptr %arg1[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %arg0, %66 : i64, !llvm.ptr
    %67 = llvm.getelementptr %arg2[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %61, %67 : i64, !llvm.ptr
    func.return %61 : i64
  }
  func.func @S(%arg0: i64, %arg1: !llvm.ptr, %arg2: !llvm.ptr, %arg3: !llvm.ptr, %arg4: !llvm.ptr, %arg5: !llvm.ptr, %arg6: !llvm.ptr) -> i64 {
    %68 = arith.constant 0 : i32
    %70 = arith.extsi %68 : i32 to i64
    %69 = arith.cmpi sle, %arg0, %70 : i64
    cf.cond_br %69, ^bb15, ^bb16
    ^bb15:
      %71 = arith.constant 0 : i32
      %72 = arith.extsi %71 : i32 to i64
      func.return %72 : i64
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %73 = arith.constant 1 : i32
    %75 = arith.extsi %73 : i32 to i64
    %74 = arith.cmpi eq, %arg0, %75 : i64
    cf.cond_br %74, ^bb18, ^bb19
    ^bb18:
      %76 = arith.constant 1 : i32
      %77 = arith.extsi %76 : i32 to i64
      func.return %77 : i64
    ^bb19:
      cf.br ^bb20
    ^bb20:
    %78 = func.call @hslot(%arg0, %arg1, %arg3) : (i64, !llvm.ptr, !llvm.ptr) -> i64
    %80 = llvm.getelementptr %arg3[%78] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %79 = llvm.load %80 : !llvm.ptr -> i8
    %81 = arith.constant 1 : i32
    %83 = arith.extsi %79 : i8 to i32
    %82 = arith.cmpi eq, %83, %81 : i32
    cf.cond_br %82, ^bb21, ^bb22
    ^bb21:
      %85 = llvm.getelementptr %arg2[%78] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %84 = llvm.load %85 : !llvm.ptr -> i64
      func.return %84 : i64
    ^bb22:
      cf.br ^bb23
    ^bb23:
    %86 = arith.constant 0 : i32
    %87 = arith.extsi %86 : i32 to i64
    %88 = llvm.mlir.constant(1 : i64) : i64
    %89 = llvm.alloca %88 x i64 : (i64) -> !llvm.ptr
    llvm.store %87, %89 : i64, !llvm.ptr
    %90 = arith.constant 1 : i32
    %92 = arith.extsi %90 : i32 to i64
    %91 = arith.andi %arg0, %92 : i64
    %93 = arith.constant 1 : i32
    %95 = arith.extsi %93 : i32 to i64
    %94 = arith.cmpi eq, %91, %95 : i64
    cf.cond_br %94, ^bb24, ^bb25
    ^bb24:
      %96 = arith.constant 2 : i32
      %98 = arith.extsi %96 : i32 to i64
      %97 = arith.divsi %arg0, %98 : i64
      %99 = arith.constant 1 : i32
      %100 = arith.extsi %99 : i32 to i128
      %101 = arith.constant 2 : i32
      %102 = arith.extsi %101 : i32 to i128
      %103 = arith.extsi %97 : i64 to i128
      %105 = arith.trunci %102 : i128 to i64
      %106 = arith.trunci %103 : i128 to i64
      %104 = arith.muli %105, %106 : i64
      %107 = arith.constant 3 : i32
      %109 = arith.extsi %107 : i32 to i64
      %108 = arith.addi %97, %109 : i64
      %110 = arith.extsi %108 : i64 to i128
      %112 = arith.trunci %110 : i128 to i64
      %111 = arith.muli %104, %112 : i64
      %114 = arith.trunci %100 : i128 to i64
      %113 = arith.addi %114, %111 : i64
      %115 = arith.constant 4 : i32
      %116 = arith.extsi %115 : i32 to i128
      %117 = func.call @S(%97, %arg1, %arg2, %arg3, %arg4, %arg5, %arg6) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> i64
      %118 = arith.extsi %117 : i64 to i128
      %120 = arith.trunci %116 : i128 to i64
      %121 = arith.trunci %118 : i128 to i64
      %119 = arith.muli %120, %121 : i64
      %122 = arith.subi %113, %119 : i64
      %123 = arith.extsi %122 : i64 to i128
      %124 = llvm.mlir.addressof @MOD : !llvm.ptr
      %125 = llvm.load %124 : !llvm.ptr -> i64
      %126 = arith.extsi %125 : i64 to i128
      %128 = arith.trunci %123 : i128 to i64
      %129 = arith.trunci %126 : i128 to i64
      %127 = arith.remsi %128, %129 : i64
      %130 = llvm.mlir.addressof @MOD : !llvm.ptr
      %131 = llvm.load %130 : !llvm.ptr -> i64
      %132 = arith.extsi %131 : i64 to i128
      %134 = arith.trunci %132 : i128 to i64
      %133 = arith.addi %127, %134 : i64
      %135 = llvm.mlir.addressof @MOD : !llvm.ptr
      %136 = llvm.load %135 : !llvm.ptr -> i64
      %137 = arith.extsi %136 : i64 to i128
      %139 = arith.trunci %137 : i128 to i64
      %138 = arith.remsi %133, %139 : i64
      llvm.store %138, %89 : i64, !llvm.ptr
      cf.br ^bb26
    ^bb25:
      %140 = arith.constant 2 : i32
      %142 = arith.extsi %140 : i32 to i64
      %141 = arith.divsi %arg0, %142 : i64
      %143 = arith.constant 2 : i32
      %144 = arith.extsi %143 : i32 to i128
      %145 = arith.extsi %141 : i64 to i128
      %147 = arith.trunci %144 : i128 to i64
      %148 = arith.trunci %145 : i128 to i64
      %146 = arith.muli %147, %148 : i64
      %149 = arith.extsi %141 : i64 to i128
      %151 = arith.trunci %149 : i128 to i64
      %150 = arith.muli %146, %151 : i64
      %152 = arith.constant 4 : i32
      %153 = arith.extsi %152 : i32 to i128
      %154 = arith.extsi %141 : i64 to i128
      %156 = arith.trunci %153 : i128 to i64
      %157 = arith.trunci %154 : i128 to i64
      %155 = arith.muli %156, %157 : i64
      %158 = arith.addi %150, %155 : i64
      %159 = arith.constant 1 : i32
      %160 = arith.extsi %159 : i32 to i128
      %162 = arith.trunci %160 : i128 to i64
      %161 = arith.subi %158, %162 : i64
      %163 = arith.constant 4 : i32
      %164 = arith.extsi %163 : i32 to i128
      %166 = arith.constant 1 : i32
      %168 = arith.extsi %166 : i32 to i64
      %167 = arith.subi %141, %168 : i64
      %165 = func.call @S(%167, %arg1, %arg2, %arg3, %arg4, %arg5, %arg6) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> i64
      %169 = arith.extsi %165 : i64 to i128
      %171 = arith.trunci %164 : i128 to i64
      %172 = arith.trunci %169 : i128 to i64
      %170 = arith.muli %171, %172 : i64
      %173 = arith.subi %161, %170 : i64
      %174 = arith.constant 2 : i32
      %175 = arith.extsi %174 : i32 to i128
      %176 = func.call @P(%141, %arg4, %arg5, %arg6) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> i64
      %177 = llvm.mlir.addressof @MOD : !llvm.ptr
      %178 = llvm.load %177 : !llvm.ptr -> i64
      %179 = arith.remsi %176, %178 : i64
      %180 = arith.extsi %179 : i64 to i128
      %182 = arith.trunci %175 : i128 to i64
      %183 = arith.trunci %180 : i128 to i64
      %181 = arith.muli %182, %183 : i64
      %184 = arith.subi %173, %181 : i64
      %185 = arith.extsi %184 : i64 to i128
      %186 = llvm.mlir.addressof @MOD : !llvm.ptr
      %187 = llvm.load %186 : !llvm.ptr -> i64
      %188 = arith.extsi %187 : i64 to i128
      %190 = arith.trunci %185 : i128 to i64
      %191 = arith.trunci %188 : i128 to i64
      %189 = arith.remsi %190, %191 : i64
      %192 = llvm.mlir.addressof @MOD : !llvm.ptr
      %193 = llvm.load %192 : !llvm.ptr -> i64
      %194 = arith.extsi %193 : i64 to i128
      %196 = arith.trunci %194 : i128 to i64
      %195 = arith.addi %189, %196 : i64
      %197 = llvm.mlir.addressof @MOD : !llvm.ptr
      %198 = llvm.load %197 : !llvm.ptr -> i64
      %199 = arith.extsi %198 : i64 to i128
      %201 = arith.trunci %199 : i128 to i64
      %200 = arith.remsi %195, %201 : i64
      llvm.store %200, %89 : i64, !llvm.ptr
      cf.br ^bb26
    ^bb26:
    %202 = arith.constant 1 : i32
    %203 = arith.trunci %202 : i32 to i8
    %204 = llvm.getelementptr %arg3[%78] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %203, %204 : i8, !llvm.ptr
    %205 = llvm.getelementptr %arg1[%78] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %arg0, %205 : i64, !llvm.ptr
    %206 = llvm.load %89 : !llvm.ptr -> i64
    %207 = llvm.getelementptr %arg2[%78] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %206, %207 : i64, !llvm.ptr
    %208 = llvm.load %89 : !llvm.ptr -> i64
    func.return %208 : i64
  }
  func.func @main() -> i32 {
    %210 = llvm.mlir.addressof @CAP : !llvm.ptr
    %211 = llvm.load %210 : !llvm.ptr -> i64
    %212 = arith.constant 8 : i32
    %213 = arith.extsi %212 : i32 to i64
    %209 = func.call @calloc(%211, %213) : (i64, i64) -> !llvm.ptr
    %215 = llvm.mlir.addressof @CAP : !llvm.ptr
    %216 = llvm.load %215 : !llvm.ptr -> i64
    %217 = arith.constant 8 : i32
    %218 = arith.extsi %217 : i32 to i64
    %214 = func.call @calloc(%216, %218) : (i64, i64) -> !llvm.ptr
    %220 = llvm.mlir.addressof @CAP : !llvm.ptr
    %221 = llvm.load %220 : !llvm.ptr -> i64
    %222 = arith.constant 1 : i32
    %223 = arith.extsi %222 : i32 to i64
    %219 = func.call @calloc(%221, %223) : (i64, i64) -> !llvm.ptr
    %225 = llvm.mlir.addressof @CAP : !llvm.ptr
    %226 = llvm.load %225 : !llvm.ptr -> i64
    %227 = arith.constant 8 : i32
    %228 = arith.extsi %227 : i32 to i64
    %224 = func.call @calloc(%226, %228) : (i64, i64) -> !llvm.ptr
    %230 = llvm.mlir.addressof @CAP : !llvm.ptr
    %231 = llvm.load %230 : !llvm.ptr -> i64
    %232 = arith.constant 8 : i32
    %233 = arith.extsi %232 : i32 to i64
    %229 = func.call @calloc(%231, %233) : (i64, i64) -> !llvm.ptr
    %235 = llvm.mlir.addressof @CAP : !llvm.ptr
    %236 = llvm.load %235 : !llvm.ptr -> i64
    %237 = arith.constant 1 : i32
    %238 = arith.extsi %237 : i32 to i64
    %234 = func.call @calloc(%236, %238) : (i64, i64) -> !llvm.ptr
    %239 = llvm.mlir.zero : !llvm.ptr
    %240 = llvm.icmp "eq" %209, %239 : !llvm.ptr
    %241 = scf.if %240 -> (i1) {
      %242 = arith.constant true
      scf.yield %242 : i1
    } else {
      %243 = llvm.mlir.zero : !llvm.ptr
      %244 = llvm.icmp "eq" %214, %243 : !llvm.ptr
      scf.yield %244 : i1
    }
    %245 = scf.if %241 -> (i1) {
      %246 = arith.constant true
      scf.yield %246 : i1
    } else {
      %247 = llvm.mlir.zero : !llvm.ptr
      %248 = llvm.icmp "eq" %219, %247 : !llvm.ptr
      scf.yield %248 : i1
    }
    %249 = scf.if %245 -> (i1) {
      %250 = arith.constant true
      scf.yield %250 : i1
    } else {
      %251 = llvm.mlir.zero : !llvm.ptr
      %252 = llvm.icmp "eq" %224, %251 : !llvm.ptr
      scf.yield %252 : i1
    }
    %253 = scf.if %249 -> (i1) {
      %254 = arith.constant true
      scf.yield %254 : i1
    } else {
      %255 = llvm.mlir.zero : !llvm.ptr
      %256 = llvm.icmp "eq" %229, %255 : !llvm.ptr
      scf.yield %256 : i1
    }
    %257 = scf.if %253 -> (i1) {
      %258 = arith.constant true
      scf.yield %258 : i1
    } else {
      %259 = llvm.mlir.zero : !llvm.ptr
      %260 = llvm.icmp "eq" %234, %259 : !llvm.ptr
      scf.yield %260 : i1
    }
    cf.cond_br %257, ^bb27, ^bb28
    ^bb27:
      %261 = arith.constant 1 : i32
      func.return %261 : i32
    ^bb28:
      cf.br ^bb29
    ^bb29:
    %263 = arith.constant 999999995705032704 : i32
    %264 = arith.extsi %263 : i32 to i64
    %262 = func.call @S(%264, %224, %229, %234, %209, %214, %219) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> i64
    %265 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %266 = llvm.call @printf(%265, %262) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%209) : (!llvm.ptr) -> ()
    func.call @free(%214) : (!llvm.ptr) -> ()
    func.call @free(%219) : (!llvm.ptr) -> ()
    func.call @free(%224) : (!llvm.ptr) -> ()
    func.call @free(%229) : (!llvm.ptr) -> ()
    func.call @free(%234) : (!llvm.ptr) -> ()
    %273 = arith.constant 0 : i32
    func.return %273 : i32
  }
}