Problem 918

Recursive Sequence Summation a(1)=1; a(2n)=2a(n); a(2n+1)=a(n)-3a(n+1) S(N)=4-a(N/2) (even); 4-3a(N/2+1) (odd). Find S(10^12).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 918
# Recursive Sequence Summation
# a(1)=1; a(2n)=2a(n); a(2n+1)=a(n)-3a(n+1)
# S(N)=4-a(N/2) (even); 4-3a(N/2+1) (odd). Find S(10^12).

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

const CAP: i64 = 1 << 20
let mut keys: ptr<i64> = null
let mut vals: ptr<i64> = null
let mut used: ptr<i8> = null

function hmix(x: i64) -> i64 {
    let mut z: i64 = x + 0x9e3779b97f4a7c15
    z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9
    z = (z ^ (z >> 27)) * 0x94d049bb133111eb
    return z ^ (z >> 31)
}

function memo_get(n: i64) -> i64 {
    let mut i: i64 = hmix(n) & (CAP - 1)
    while used[i] != 0 {
        if keys[i] == n { return vals[i] }
        i = (i + 1) & (CAP - 1)
    }
    return 9223372036854775807
}

function memo_put(n: i64, v: i64) -> void {
    let mut i: i64 = hmix(n) & (CAP - 1)
    while used[i] != 0 {
        if keys[i] == n {
            vals[i] = v
            return
        }
        i = (i + 1) & (CAP - 1)
    }
    used[i] = 1
    keys[i] = n
    vals[i] = v
}

function a(n: i64) -> i64 {
    if n == 1 { return 1 }
    let cached: i64 = memo_get(n)
    if cached != 9223372036854775807 { return cached }
    let mut res: i64 = 0
    if (n & 1) == 0 {
        res = 2 * a(n / 2)
    } else {
        res = a(n / 2) - 3 * a(n / 2 + 1)
    }
    memo_put(n, res)
    return res
}

function S(N: i64) -> i64 {
    if (N & 1) == 0 {
        return 4 - a(N / 2)
    }
    return 4 - 3 * a(N / 2 + 1)
}

function main() -> i32 {
    keys = calloc(CAP, 8)
    vals = calloc(CAP, 8)
    used = calloc(CAP, 1)
    if keys == null || vals == null || used == null { return 1 }
    printf("%lld\n", S(1000000000000))
    free(keys)
    free(vals)
    free(used)
    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 hmix_i64(int64_t x);
int64_t memo_get_i64(int64_t n);
void memo_put_i64_i64(int64_t n, int64_t v);
int64_t a_i64(int64_t n);
int64_t S_i64(int64_t N);
int32_t main(void);

static const int64_t CAP = FLOW_CHECKED_SHL((1), (20));

/* Module statics */
static int64_t* keys = NULL;
static int64_t* vals = NULL;
static int8_t* used = NULL;



int64_t hmix_i64(int64_t x) {
    int64_t z = (x + ((__int128)0x9E3779B97F4A7C15ULL));
    z = ((z ^ FLOW_CHECKED_SHR((z), (30))) * ((__int128)0xBF58476D1CE4E5B9ULL));
    z = ((z ^ FLOW_CHECKED_SHR((z), (27))) * ((__int128)0x94D049BB133111EBULL));
    return (z ^ FLOW_CHECKED_SHR((z), (31)));
}

int64_t memo_get_i64(int64_t n) {
    int64_t i = (hmix_i64(n) & (CAP - 1));
    while (used[i] != 0) {
        if (keys[i] == n) {
            return vals[i];
        }
        i = ((i + 1) & (CAP - 1));
    }
    return 9223372036854775807;
}

void memo_put_i64_i64(int64_t n, int64_t v) {
    int64_t i = (hmix_i64(n) & (CAP - 1));
    while (used[i] != 0) {
        if (keys[i] == n) {
            vals[i] = v;
            return;
        }
        i = ((i + 1) & (CAP - 1));
    }
    used[i] = 1;
    keys[i] = n;
    vals[i] = v;
}

int64_t a_i64(int64_t n) {
    if (n == 1) {
        return 1;
    }
    int64_t cached = memo_get_i64(n);
    if (cached != 9223372036854775807) {
        return cached;
    }
    int64_t res = 0;
    if ((n & 1) == 0) {
        res = (2 * a_i64(FLOW_CHECKED_DIV((n), (2))));
    } else {
        res = (a_i64(FLOW_CHECKED_DIV((n), (2))) - (3 * a_i64((FLOW_CHECKED_DIV((n), (2)) + 1))));
    }
    memo_put_i64_i64(n, res);
    return res;
}

int64_t S_i64(int64_t N) {
    if ((N & 1) == 0) {
        return (4 - a_i64(FLOW_CHECKED_DIV((N), (2))));
    }
    return (4 - (3 * a_i64((FLOW_CHECKED_DIV((N), (2)) + 1))));
}

int32_t main(void) {
    keys = calloc(CAP, 8);
    vals = calloc(CAP, 8);
    used = calloc(CAP, 1);
    if (((keys == NULL || vals == NULL) || used == NULL)) {
        return 1;
    }
    printf("%lld\n", S_i64(1000000000000));
    free(keys);
    free(vals);
    free(used);
    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: CAP
  llvm.mlir.global internal constant @CAP(1048576 : i64) : i64
  // Module static: keys
  llvm.mlir.global internal @keys() {addr_space = 0 : i32} : !llvm.ptr {
    %0 = llvm.mlir.zero : !llvm.ptr
    llvm.return %0 : !llvm.ptr
  }
  // Module static: vals
  llvm.mlir.global internal @vals() {addr_space = 0 : i32} : !llvm.ptr {
    %1 = llvm.mlir.zero : !llvm.ptr
    llvm.return %1 : !llvm.ptr
  }
  // Module static: used
  llvm.mlir.global internal @used() {addr_space = 0 : i32} : !llvm.ptr {
    %2 = llvm.mlir.zero : !llvm.ptr
    llvm.return %2 : !llvm.ptr
  }
  func.func @hmix(%arg0: i64) -> i64 {
    %3 = arith.constant 11400714815028231189 : i32
    %5 = arith.extsi %3 : i32 to i64
    %4 = arith.addi %arg0, %5 : i64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x i64 : (i64) -> !llvm.ptr
    llvm.store %4, %7 : i64, !llvm.ptr
    %8 = llvm.load %7 : !llvm.ptr -> i64
    %9 = llvm.load %7 : !llvm.ptr -> i64
    %10 = arith.constant 30 : i32
    %12 = arith.extsi %10 : i32 to i64
    %11 = arith.shrsi %9, %12 : i64
    %13 = arith.xori %8, %11 : i64
    %14 = arith.constant 13787848788861576633 : i32
    %16 = arith.extsi %14 : i32 to i64
    %15 = arith.muli %13, %16 : i64
    llvm.store %15, %7 : i64, !llvm.ptr
    %17 = llvm.load %7 : !llvm.ptr -> i64
    %18 = llvm.load %7 : !llvm.ptr -> i64
    %19 = arith.constant 27 : i32
    %21 = arith.extsi %19 : i32 to i64
    %20 = arith.shrsi %18, %21 : i64
    %22 = arith.xori %17, %20 : i64
    %23 = arith.constant 10723151776303878635 : i32
    %25 = arith.extsi %23 : i32 to i64
    %24 = arith.muli %22, %25 : i64
    llvm.store %24, %7 : i64, !llvm.ptr
    %26 = llvm.load %7 : !llvm.ptr -> i64
    %27 = llvm.load %7 : !llvm.ptr -> i64
    %28 = arith.constant 31 : i32
    %30 = arith.extsi %28 : i32 to i64
    %29 = arith.shrsi %27, %30 : i64
    %31 = arith.xori %26, %29 : i64
    func.return %31 : i64
  }
  func.func @memo_get(%arg0: i64) -> i64 {
    %32 = func.call @hmix(%arg0) : (i64) -> i64
    %33 = llvm.mlir.addressof @CAP : !llvm.ptr
    %34 = llvm.load %33 : !llvm.ptr -> i64
    %35 = arith.constant 1 : i32
    %37 = arith.extsi %35 : i32 to i64
    %36 = arith.subi %34, %37 : i64
    %38 = arith.andi %32, %36 : i64
    %39 = llvm.mlir.constant(1 : i64) : i64
    %40 = llvm.alloca %39 x i64 : (i64) -> !llvm.ptr
    llvm.store %38, %40 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %42 = llvm.mlir.addressof @used : !llvm.ptr
    %43 = llvm.load %42 : !llvm.ptr -> !llvm.ptr
    %44 = llvm.load %40 : !llvm.ptr -> i64
    %45 = llvm.getelementptr %43[%44] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %41 = llvm.load %45 : !llvm.ptr -> i8
    %46 = arith.constant 0 : i32
    %48 = arith.extsi %41 : i8 to i32
    %47 = arith.cmpi ne, %48, %46 : i32
    cf.cond_br %47, ^bb1, ^bb2
    ^bb1:
      %50 = llvm.mlir.addressof @keys : !llvm.ptr
      %51 = llvm.load %50 : !llvm.ptr -> !llvm.ptr
      %52 = llvm.load %40 : !llvm.ptr -> i64
      %53 = llvm.getelementptr %51[%52] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %49 = llvm.load %53 : !llvm.ptr -> i64
      %54 = arith.cmpi eq, %49, %arg0 : i64
      cf.cond_br %54, ^bb3, ^bb4
      ^bb3:
        %56 = llvm.mlir.addressof @vals : !llvm.ptr
        %57 = llvm.load %56 : !llvm.ptr -> !llvm.ptr
        %58 = llvm.load %40 : !llvm.ptr -> i64
        %59 = llvm.getelementptr %57[%58] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %55 = llvm.load %59 : !llvm.ptr -> i64
        func.return %55 : i64
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %60 = llvm.load %40 : !llvm.ptr -> i64
      %61 = arith.constant 1 : i32
      %63 = arith.extsi %61 : i32 to i64
      %62 = arith.addi %60, %63 : i64
      %64 = llvm.mlir.addressof @CAP : !llvm.ptr
      %65 = llvm.load %64 : !llvm.ptr -> i64
      %66 = arith.constant 1 : i32
      %68 = arith.extsi %66 : i32 to i64
      %67 = arith.subi %65, %68 : i64
      %69 = arith.andi %62, %67 : i64
      llvm.store %69, %40 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %70 = arith.constant 9223372032559808511 : i32
    %71 = arith.extsi %70 : i32 to i64
    func.return %71 : i64
  }
  func.func @memo_put(%arg0: i64, %arg1: i64) -> () {
    %72 = func.call @hmix(%arg0) : (i64) -> i64
    %73 = llvm.mlir.addressof @CAP : !llvm.ptr
    %74 = llvm.load %73 : !llvm.ptr -> i64
    %75 = arith.constant 1 : i32
    %77 = arith.extsi %75 : i32 to i64
    %76 = arith.subi %74, %77 : i64
    %78 = arith.andi %72, %76 : i64
    %79 = llvm.mlir.constant(1 : i64) : i64
    %80 = llvm.alloca %79 x i64 : (i64) -> !llvm.ptr
    llvm.store %78, %80 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %82 = llvm.mlir.addressof @used : !llvm.ptr
    %83 = llvm.load %82 : !llvm.ptr -> !llvm.ptr
    %84 = llvm.load %80 : !llvm.ptr -> i64
    %85 = llvm.getelementptr %83[%84] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %81 = llvm.load %85 : !llvm.ptr -> i8
    %86 = arith.constant 0 : i32
    %88 = arith.extsi %81 : i8 to i32
    %87 = arith.cmpi ne, %88, %86 : i32
    cf.cond_br %87, ^bb7, ^bb8
    ^bb7:
      %90 = llvm.mlir.addressof @keys : !llvm.ptr
      %91 = llvm.load %90 : !llvm.ptr -> !llvm.ptr
      %92 = llvm.load %80 : !llvm.ptr -> i64
      %93 = llvm.getelementptr %91[%92] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %89 = llvm.load %93 : !llvm.ptr -> i64
      %94 = arith.cmpi eq, %89, %arg0 : i64
      cf.cond_br %94, ^bb9, ^bb10
      ^bb9:
        %95 = llvm.mlir.addressof @vals : !llvm.ptr
        %96 = llvm.load %95 : !llvm.ptr -> !llvm.ptr
        %97 = llvm.load %80 : !llvm.ptr -> i64
        %98 = llvm.getelementptr %96[%97] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        llvm.store %arg1, %98 : i64, !llvm.ptr
        func.return
      ^bb10:
        cf.br ^bb11
      ^bb11:
      %99 = llvm.load %80 : !llvm.ptr -> i64
      %100 = arith.constant 1 : i32
      %102 = arith.extsi %100 : i32 to i64
      %101 = arith.addi %99, %102 : i64
      %103 = llvm.mlir.addressof @CAP : !llvm.ptr
      %104 = llvm.load %103 : !llvm.ptr -> i64
      %105 = arith.constant 1 : i32
      %107 = arith.extsi %105 : i32 to i64
      %106 = arith.subi %104, %107 : i64
      %108 = arith.andi %101, %106 : i64
      llvm.store %108, %80 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %109 = arith.constant 1 : i32
    %110 = llvm.mlir.addressof @used : !llvm.ptr
    %111 = llvm.load %110 : !llvm.ptr -> !llvm.ptr
    %112 = llvm.load %80 : !llvm.ptr -> i64
    %113 = arith.trunci %109 : i32 to i8
    %114 = llvm.getelementptr %111[%112] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %113, %114 : i8, !llvm.ptr
    %115 = llvm.mlir.addressof @keys : !llvm.ptr
    %116 = llvm.load %115 : !llvm.ptr -> !llvm.ptr
    %117 = llvm.load %80 : !llvm.ptr -> i64
    %118 = llvm.getelementptr %116[%117] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %arg0, %118 : i64, !llvm.ptr
    %119 = llvm.mlir.addressof @vals : !llvm.ptr
    %120 = llvm.load %119 : !llvm.ptr -> !llvm.ptr
    %121 = llvm.load %80 : !llvm.ptr -> i64
    %122 = llvm.getelementptr %120[%121] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %arg1, %122 : i64, !llvm.ptr
    func.return
  }
  func.func @a(%arg0: i64) -> i64 {
    %123 = arith.constant 1 : i32
    %125 = arith.extsi %123 : i32 to i64
    %124 = arith.cmpi eq, %arg0, %125 : i64
    cf.cond_br %124, ^bb12, ^bb13
    ^bb12:
      %126 = arith.constant 1 : i32
      %127 = arith.extsi %126 : i32 to i64
      func.return %127 : i64
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %128 = func.call @memo_get(%arg0) : (i64) -> i64
    %129 = arith.constant 9223372032559808511 : i32
    %131 = arith.extsi %129 : i32 to i64
    %130 = arith.cmpi ne, %128, %131 : i64
    cf.cond_br %130, ^bb15, ^bb16
    ^bb15:
      func.return %128 : i64
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %132 = arith.constant 0 : i32
    %133 = arith.extsi %132 : i32 to i64
    %134 = llvm.mlir.constant(1 : i64) : i64
    %135 = llvm.alloca %134 x i64 : (i64) -> !llvm.ptr
    llvm.store %133, %135 : i64, !llvm.ptr
    %136 = arith.constant 1 : i32
    %138 = arith.extsi %136 : i32 to i64
    %137 = arith.andi %arg0, %138 : i64
    %139 = arith.constant 0 : i32
    %141 = arith.extsi %139 : i32 to i64
    %140 = arith.cmpi eq, %137, %141 : i64
    cf.cond_br %140, ^bb18, ^bb19
    ^bb18:
      %142 = arith.constant 2 : i32
      %144 = arith.constant 2 : i32
      %146 = arith.extsi %144 : i32 to i64
      %145 = arith.divsi %arg0, %146 : i64
      %143 = func.call @a(%145) : (i64) -> i64
      %148 = arith.extsi %142 : i32 to i64
      %147 = arith.muli %148, %143 : i64
      llvm.store %147, %135 : i64, !llvm.ptr
      cf.br ^bb20
    ^bb19:
      %150 = arith.constant 2 : i32
      %152 = arith.extsi %150 : i32 to i64
      %151 = arith.divsi %arg0, %152 : i64
      %149 = func.call @a(%151) : (i64) -> i64
      %153 = arith.constant 3 : i32
      %155 = arith.constant 2 : i32
      %157 = arith.extsi %155 : i32 to i64
      %156 = arith.divsi %arg0, %157 : i64
      %158 = arith.constant 1 : i32
      %160 = arith.extsi %158 : i32 to i64
      %159 = arith.addi %156, %160 : i64
      %154 = func.call @a(%159) : (i64) -> i64
      %162 = arith.extsi %153 : i32 to i64
      %161 = arith.muli %162, %154 : i64
      %163 = arith.subi %149, %161 : i64
      llvm.store %163, %135 : i64, !llvm.ptr
      cf.br ^bb20
    ^bb20:
    %165 = llvm.load %135 : !llvm.ptr -> i64
    func.call @memo_put(%arg0, %165) : (i64, i64) -> ()
    %166 = llvm.load %135 : !llvm.ptr -> i64
    func.return %166 : i64
  }
  func.func @S(%arg0: i64) -> i64 {
    %167 = arith.constant 1 : i32
    %169 = arith.extsi %167 : i32 to i64
    %168 = arith.andi %arg0, %169 : i64
    %170 = arith.constant 0 : i32
    %172 = arith.extsi %170 : i32 to i64
    %171 = arith.cmpi eq, %168, %172 : i64
    cf.cond_br %171, ^bb21, ^bb22
    ^bb21:
      %173 = arith.constant 4 : i32
      %175 = arith.constant 2 : i32
      %177 = arith.extsi %175 : i32 to i64
      %176 = arith.divsi %arg0, %177 : i64
      %174 = func.call @a(%176) : (i64) -> i64
      %179 = arith.extsi %173 : i32 to i64
      %178 = arith.subi %179, %174 : i64
      func.return %178 : i64
    ^bb22:
      cf.br ^bb23
    ^bb23:
    %180 = arith.constant 4 : i32
    %181 = arith.constant 3 : i32
    %183 = arith.constant 2 : i32
    %185 = arith.extsi %183 : i32 to i64
    %184 = arith.divsi %arg0, %185 : i64
    %186 = arith.constant 1 : i32
    %188 = arith.extsi %186 : i32 to i64
    %187 = arith.addi %184, %188 : i64
    %182 = func.call @a(%187) : (i64) -> i64
    %190 = arith.extsi %181 : i32 to i64
    %189 = arith.muli %190, %182 : i64
    %192 = arith.extsi %180 : i32 to i64
    %191 = arith.subi %192, %189 : i64
    func.return %191 : i64
  }
  func.func @main() -> i32 {
    %194 = llvm.mlir.addressof @CAP : !llvm.ptr
    %195 = llvm.load %194 : !llvm.ptr -> i64
    %196 = arith.constant 8 : i32
    %197 = arith.extsi %196 : i32 to i64
    %193 = func.call @calloc(%195, %197) : (i64, i64) -> !llvm.ptr
    %198 = llvm.mlir.addressof @keys : !llvm.ptr
    llvm.store %193, %198 : !llvm.ptr, !llvm.ptr
    %200 = llvm.mlir.addressof @CAP : !llvm.ptr
    %201 = llvm.load %200 : !llvm.ptr -> i64
    %202 = arith.constant 8 : i32
    %203 = arith.extsi %202 : i32 to i64
    %199 = func.call @calloc(%201, %203) : (i64, i64) -> !llvm.ptr
    %204 = llvm.mlir.addressof @vals : !llvm.ptr
    llvm.store %199, %204 : !llvm.ptr, !llvm.ptr
    %206 = llvm.mlir.addressof @CAP : !llvm.ptr
    %207 = llvm.load %206 : !llvm.ptr -> i64
    %208 = arith.constant 1 : i32
    %209 = arith.extsi %208 : i32 to i64
    %205 = func.call @calloc(%207, %209) : (i64, i64) -> !llvm.ptr
    %210 = llvm.mlir.addressof @used : !llvm.ptr
    llvm.store %205, %210 : !llvm.ptr, !llvm.ptr
    %211 = llvm.mlir.addressof @keys : !llvm.ptr
    %212 = llvm.load %211 : !llvm.ptr -> !llvm.ptr
    %213 = llvm.mlir.zero : !llvm.ptr
    %214 = llvm.icmp "eq" %212, %213 : !llvm.ptr
    %215 = scf.if %214 -> (i1) {
      %216 = arith.constant true
      scf.yield %216 : i1
    } else {
      %217 = llvm.mlir.addressof @vals : !llvm.ptr
      %218 = llvm.load %217 : !llvm.ptr -> !llvm.ptr
      %219 = llvm.mlir.zero : !llvm.ptr
      %220 = llvm.icmp "eq" %218, %219 : !llvm.ptr
      scf.yield %220 : i1
    }
    %221 = scf.if %215 -> (i1) {
      %222 = arith.constant true
      scf.yield %222 : i1
    } else {
      %223 = llvm.mlir.addressof @used : !llvm.ptr
      %224 = llvm.load %223 : !llvm.ptr -> !llvm.ptr
      %225 = llvm.mlir.zero : !llvm.ptr
      %226 = llvm.icmp "eq" %224, %225 : !llvm.ptr
      scf.yield %226 : i1
    }
    cf.cond_br %221, ^bb24, ^bb25
    ^bb24:
      %227 = arith.constant 1 : i32
      func.return %227 : i32
    ^bb25:
      cf.br ^bb26
    ^bb26:
    %228 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %230 = arith.constant 995705032704 : i32
    %231 = arith.extsi %230 : i32 to i64
    %229 = func.call @S(%231) : (i64) -> i64
    %232 = llvm.call @printf(%228, %229) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %234 = llvm.mlir.addressof @keys : !llvm.ptr
    %235 = llvm.load %234 : !llvm.ptr -> !llvm.ptr
    func.call @free(%235) : (!llvm.ptr) -> ()
    %237 = llvm.mlir.addressof @vals : !llvm.ptr
    %238 = llvm.load %237 : !llvm.ptr -> !llvm.ptr
    func.call @free(%238) : (!llvm.ptr) -> ()
    %240 = llvm.mlir.addressof @used : !llvm.ptr
    %241 = llvm.load %240 : !llvm.ptr -> !llvm.ptr
    func.call @free(%241) : (!llvm.ptr) -> ()
    %242 = arith.constant 0 : i32
    func.return %242 : i32
  }
}