Problem 527

Randomized Binary Search — R(10^10)-B(10^10) to 8 d.p.

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Performance comparison

Flow source

# Project Euler 527
# Randomized Binary Search — R(10^10)-B(10^10) to 8 d.p.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
    function log(x: f64) -> f64
}

const CAP: i64 = 1048576
const EULER_GAMMA: f64 = 0.5772156649015328606

function harmonic(n: i64) -> f64 {
    if n <= 0 { return 0.0 }
    if n < 2000000 {
        let mut s: f64 = 0.0
        let mut k: i64 = 1
        while k <= n {
            s = s + 1.0 / (k as f64)
            k = k + 1
        }
        return s
    }
    let inv: f64 = 1.0 / (n as f64)
    let inv2: f64 = inv * inv
    let inv4: f64 = inv2 * inv2
    let inv6: f64 = inv4 * inv2
    let inv8: f64 = inv4 * inv4
    return log(n as f64) + EULER_GAMMA + 0.5 * inv
        - (1.0 / 12.0) * inv2
        + (1.0 / 120.0) * inv4
        - (1.0 / 252.0) * inv6
        + (1.0 / 240.0) * inv8
}

function R(n: i64) -> f64 {
    let hn: f64 = harmonic(n)
    return 2.0 * ((n + 1) as f64) / (n as f64) * hn - 3.0
}

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 B(n: i64, keys: ptr<i64>, vals: ptr<f64>, used: ptr<i8>) -> f64 {
    if n <= 1 { return n as f64 }
    let s: i64 = hslot(n, keys, used)
    if used[s] == 1 { return vals[s] }
    let g: i64 = (n + 1) / 2
    let left: i64 = g - 1
    let right: i64 = n - g
    let val: f64 = 1.0
        + ((left as f64) / (n as f64)) * B(left, keys, vals, used)
        + ((right as f64) / (n as f64)) * B(right, keys, vals, used)
    used[s] = 1
    keys[s] = n
    vals[s] = val
    return val
}

function main() -> i32 {
    let keys: ptr<i64> = calloc(CAP, 8)
    let vals: ptr<f64> = calloc(CAP, 8)
    let used: ptr<i8> = calloc(CAP, 1)
    if keys == null || vals == null || used == null { return 1 }
    let n: i64 = 10000000000
    let ans: f64 = R(n) - B(n, keys, vals, used)
    printf("%.8f\n", ans)
    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; }

double harmonic_i64(int64_t n);
double R_i64(int64_t n);
int64_t hslot_i64_ptr_i64_ptr_i8(int64_t key, int64_t* keys, int8_t* used);
double B_i64_ptr_i64_ptr_f64_ptr_i8(int64_t n, int64_t* keys, double* vals, int8_t* used);
int32_t main(void);

static const int64_t CAP = 1048576;
static const double EULER_GAMMA = 0.5772156649015328606;




double harmonic_i64(int64_t n) {
    if (n <= 0) {
        return 0.0;
    }
    if (n < 2000000) {
        double s = 0.0;
        int64_t k = 1;
        while (k <= n) {
            s = (s + (1.0 / ((double)(k))));
            k = (k + 1);
        }
        return s;
    }
    double inv = (1.0 / ((double)(n)));
    double inv2 = (inv * inv);
    double inv4 = (inv2 * inv2);
    double inv6 = (inv4 * inv2);
    double inv8 = (inv4 * inv4);
    return ((((((log(((double)(n))) + EULER_GAMMA) + (0.5 * inv)) - ((1.0 / 12.0) * inv2)) + ((1.0 / 120.0) * inv4)) - ((1.0 / 252.0) * inv6)) + ((1.0 / 240.0) * inv8));
}

double R_i64(int64_t n) {
    double hn = harmonic_i64(n);
    return ((((2.0 * ((double)((n + 1)))) / ((double)(n))) * hn) - 3.0);
}

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;
}

double B_i64_ptr_i64_ptr_f64_ptr_i8(int64_t n, int64_t* keys, double* vals, int8_t* used) {
    if (n <= 1) {
        return ((double)(n));
    }
    int64_t s = hslot_i64_ptr_i64_ptr_i8(n, keys, used);
    if (used[s] == 1) {
        return vals[s];
    }
    int64_t g = FLOW_CHECKED_DIV(((n + 1)), (2));
    int64_t left = (g - 1);
    int64_t right = (n - g);
    double val = ((1.0 + ((((double)(left)) / ((double)(n))) * B_i64_ptr_i64_ptr_f64_ptr_i8(left, keys, vals, used))) + ((((double)(right)) / ((double)(n))) * B_i64_ptr_i64_ptr_f64_ptr_i8(right, keys, vals, used)));
    used[s] = 1;
    keys[s] = n;
    vals[s] = val;
    return val;
}

int32_t main(void) {
    int64_t* keys = (int64_t*)(calloc(CAP, 8));
    double* vals = (double*)(calloc(CAP, 8));
    int8_t* used = (int8_t*)(calloc(CAP, 1));
    if (((keys == NULL || vals == NULL) || used == NULL)) {
        return 1;
    }
    int64_t n = 10000000000;
    double ans = (R_i64(n) - B_i64_ptr_i64_ptr_f64_ptr_i8(n, keys, vals, used));
    printf("%.8f\n", ans);
    free(keys);
    free(vals);
    free(used);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.8f\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 private @log(f64) -> f64
  // Constant: CAP
  llvm.mlir.global internal constant @CAP(1048576 : i64) : i64
  // Constant: EULER_GAMMA
  llvm.mlir.global internal constant @EULER_GAMMA(0.5772156649015328606 : f64) : f64
  func.func @harmonic(%arg0: i64) -> f64 {
    %0 = arith.constant 0 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.cmpi sle, %arg0, %2 : i64
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      %3 = arith.constant 0.0 : f32
      %4 = arith.extf %3 : f32 to f64
      func.return %4 : f64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %5 = arith.constant 2000000 : i32
    %7 = arith.extsi %5 : i32 to i64
    %6 = arith.cmpi slt, %arg0, %7 : i64
    cf.cond_br %6, ^bb3, ^bb4
    ^bb3:
      %8 = arith.constant 0.0 : f32
      %9 = arith.extf %8 : f32 to f64
      %10 = llvm.mlir.constant(1 : i64) : i64
      %11 = llvm.alloca %10 x f64 : (i64) -> !llvm.ptr
      llvm.store %9, %11 : f64, !llvm.ptr
      %12 = arith.constant 1 : i32
      %13 = arith.extsi %12 : i32 to i64
      %14 = llvm.mlir.constant(1 : i64) : i64
      %15 = llvm.alloca %14 x i64 : (i64) -> !llvm.ptr
      llvm.store %13, %15 : i64, !llvm.ptr
      cf.br ^bb6
      ^bb6:
      %16 = llvm.load %15 : !llvm.ptr -> i64
      %17 = arith.cmpi sle, %16, %arg0 : i64
      cf.cond_br %17, ^bb7, ^bb8
      ^bb7:
        %18 = llvm.load %11 : !llvm.ptr -> f64
        %19 = arith.constant 1.0 : f32
        %20 = llvm.load %15 : !llvm.ptr -> i64
        %21 = arith.sitofp %20 : i64 to f64
        %23 = arith.extf %19 : f32 to f64
        %22 = arith.divf %23, %21 : f64
        %24 = arith.addf %18, %22 : f64
        llvm.store %24, %11 : f64, !llvm.ptr
        %25 = llvm.load %15 : !llvm.ptr -> i64
        %26 = arith.constant 1 : i32
        %28 = arith.extsi %26 : i32 to i64
        %27 = arith.addi %25, %28 : i64
        llvm.store %27, %15 : i64, !llvm.ptr
        cf.br ^bb6
      ^bb8:
      %29 = llvm.load %11 : !llvm.ptr -> f64
      func.return %29 : f64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %30 = arith.constant 1.0 : f32
    %31 = arith.sitofp %arg0 : i64 to f64
    %33 = arith.extf %30 : f32 to f64
    %32 = arith.divf %33, %31 : f64
    %34 = arith.mulf %32, %32 : f64
    %35 = arith.mulf %34, %34 : f64
    %36 = arith.mulf %35, %34 : f64
    %37 = arith.mulf %35, %35 : f64
    %38 = arith.sitofp %arg0 : i64 to f64
    %39 = math.log %38 : f64
    %40 = llvm.mlir.addressof @EULER_GAMMA : !llvm.ptr
    %41 = llvm.load %40 : !llvm.ptr -> f64
    %42 = arith.addf %39, %41 : f64
    %43 = arith.constant 0.5 : f32
    %45 = arith.extf %43 : f32 to f64
    %44 = arith.mulf %45, %32 : f64
    %46 = arith.addf %42, %44 : f64
    %47 = arith.constant 1.0 : f32
    %48 = arith.constant 12.0 : f32
    %49 = arith.divf %47, %48 : f32
    %51 = arith.extf %49 : f32 to f64
    %50 = arith.mulf %51, %34 : f64
    %52 = arith.subf %46, %50 : f64
    %53 = arith.constant 1.0 : f32
    %54 = arith.constant 120.0 : f32
    %55 = arith.divf %53, %54 : f32
    %57 = arith.extf %55 : f32 to f64
    %56 = arith.mulf %57, %35 : f64
    %58 = arith.addf %52, %56 : f64
    %59 = arith.constant 1.0 : f32
    %60 = arith.constant 252.0 : f32
    %61 = arith.divf %59, %60 : f32
    %63 = arith.extf %61 : f32 to f64
    %62 = arith.mulf %63, %36 : f64
    %64 = arith.subf %58, %62 : f64
    %65 = arith.constant 1.0 : f32
    %66 = arith.constant 240.0 : f32
    %67 = arith.divf %65, %66 : f32
    %69 = arith.extf %67 : f32 to f64
    %68 = arith.mulf %69, %37 : f64
    %70 = arith.addf %64, %68 : f64
    func.return %70 : f64
  }
  func.func @R(%arg0: i64) -> f64 {
    %71 = func.call @harmonic(%arg0) : (i64) -> f64
    %72 = arith.constant 2.0 : f32
    %73 = arith.constant 1 : i32
    %75 = arith.extsi %73 : i32 to i64
    %74 = arith.addi %arg0, %75 : i64
    %76 = arith.sitofp %74 : i64 to f64
    %78 = arith.extf %72 : f32 to f64
    %77 = arith.mulf %78, %76 : f64
    %79 = arith.sitofp %arg0 : i64 to f64
    %80 = arith.divf %77, %79 : f64
    %81 = arith.mulf %80, %71 : f64
    %82 = arith.constant 3.0 : f32
    %84 = arith.extf %82 : f32 to f64
    %83 = arith.subf %81, %84 : f64
    func.return %83 : f64
  }
  func.func @hslot(%arg0: i64, %arg1: !llvm.ptr, %arg2: !llvm.ptr) -> i64 {
    %85 = llvm.mlir.addressof @CAP : !llvm.ptr
    %86 = llvm.load %85 : !llvm.ptr -> i64
    %87 = arith.remsi %arg0, %86 : 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 = llvm.load %89 : !llvm.ptr -> i64
    %91 = arith.constant 0 : i32
    %93 = arith.extsi %91 : i32 to i64
    %92 = arith.cmpi slt, %90, %93 : i64
    cf.cond_br %92, ^bb9, ^bb10
    ^bb9:
      %94 = llvm.load %89 : !llvm.ptr -> i64
      %95 = llvm.mlir.addressof @CAP : !llvm.ptr
      %96 = llvm.load %95 : !llvm.ptr -> i64
      %97 = arith.addi %94, %96 : i64
      llvm.store %97, %89 : i64, !llvm.ptr
      cf.br ^bb11
    ^bb10:
      cf.br ^bb11
    ^bb11:
    cf.br ^bb12
    ^bb12:
    %99 = llvm.load %89 : !llvm.ptr -> i64
    %100 = llvm.getelementptr %arg2[%99] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %98 = llvm.load %100 : !llvm.ptr -> i8
    %101 = arith.constant 1 : i32
    %103 = arith.extsi %98 : i8 to i32
    %102 = arith.cmpi eq, %103, %101 : i32
    %104 = scf.if %102 -> (i1) {
      %106 = llvm.load %89 : !llvm.ptr -> i64
      %107 = llvm.getelementptr %arg1[%106] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %105 = llvm.load %107 : !llvm.ptr -> i64
      %108 = arith.cmpi ne, %105, %arg0 : i64
      scf.yield %108 : i1
    } else {
      %109 = arith.constant false
      scf.yield %109 : i1
    }
    cf.cond_br %104, ^bb13, ^bb14
    ^bb13:
      %110 = llvm.load %89 : !llvm.ptr -> i64
      %111 = arith.constant 1 : i32
      %113 = arith.extsi %111 : i32 to i64
      %112 = arith.addi %110, %113 : i64
      llvm.store %112, %89 : i64, !llvm.ptr
      %114 = llvm.load %89 : !llvm.ptr -> i64
      %115 = llvm.mlir.addressof @CAP : !llvm.ptr
      %116 = llvm.load %115 : !llvm.ptr -> i64
      %117 = arith.cmpi eq, %114, %116 : i64
      cf.cond_br %117, ^bb15, ^bb16
      ^bb15:
        %118 = arith.constant 0 : i32
        %119 = arith.extsi %118 : i32 to i64
        llvm.store %119, %89 : i64, !llvm.ptr
        cf.br ^bb17
      ^bb16:
        cf.br ^bb17
      ^bb17:
      cf.br ^bb12
    ^bb14:
    %120 = llvm.load %89 : !llvm.ptr -> i64
    func.return %120 : i64
  }
  func.func @B(%arg0: i64, %arg1: !llvm.ptr, %arg2: !llvm.ptr, %arg3: !llvm.ptr) -> f64 {
    %121 = arith.constant 1 : i32
    %123 = arith.extsi %121 : i32 to i64
    %122 = arith.cmpi sle, %arg0, %123 : i64
    cf.cond_br %122, ^bb18, ^bb19
    ^bb18:
      %124 = arith.sitofp %arg0 : i64 to f64
      func.return %124 : f64
    ^bb19:
      cf.br ^bb20
    ^bb20:
    %125 = func.call @hslot(%arg0, %arg1, %arg3) : (i64, !llvm.ptr, !llvm.ptr) -> i64
    %127 = llvm.getelementptr %arg3[%125] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    %126 = llvm.load %127 : !llvm.ptr -> i8
    %128 = arith.constant 1 : i32
    %130 = arith.extsi %126 : i8 to i32
    %129 = arith.cmpi eq, %130, %128 : i32
    cf.cond_br %129, ^bb21, ^bb22
    ^bb21:
      %132 = llvm.getelementptr %arg2[%125] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %131 = llvm.load %132 : !llvm.ptr -> f64
      func.return %131 : f64
    ^bb22:
      cf.br ^bb23
    ^bb23:
    %133 = arith.constant 1 : i32
    %135 = arith.extsi %133 : i32 to i64
    %134 = arith.addi %arg0, %135 : i64
    %136 = arith.constant 2 : i32
    %138 = arith.extsi %136 : i32 to i64
    %137 = arith.divsi %134, %138 : i64
    %139 = arith.constant 1 : i32
    %141 = arith.extsi %139 : i32 to i64
    %140 = arith.subi %137, %141 : i64
    %142 = arith.subi %arg0, %137 : i64
    %143 = arith.constant 1.0 : f32
    %144 = arith.sitofp %140 : i64 to f64
    %145 = arith.sitofp %arg0 : i64 to f64
    %146 = arith.divf %144, %145 : f64
    %147 = func.call @B(%140, %arg1, %arg2, %arg3) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> f64
    %148 = arith.mulf %146, %147 : f64
    %150 = arith.extf %143 : f32 to f64
    %149 = arith.addf %150, %148 : f64
    %151 = arith.sitofp %142 : i64 to f64
    %152 = arith.sitofp %arg0 : i64 to f64
    %153 = arith.divf %151, %152 : f64
    %154 = func.call @B(%142, %arg1, %arg2, %arg3) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> f64
    %155 = arith.mulf %153, %154 : f64
    %156 = arith.addf %149, %155 : f64
    %157 = arith.constant 1 : i32
    %158 = arith.trunci %157 : i32 to i8
    %159 = llvm.getelementptr %arg3[%125] : (!llvm.ptr, i64) -> !llvm.ptr, i8
    llvm.store %158, %159 : i8, !llvm.ptr
    %160 = llvm.getelementptr %arg1[%125] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %arg0, %160 : i64, !llvm.ptr
    %161 = llvm.getelementptr %arg2[%125] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %156, %161 : f64, !llvm.ptr
    func.return %156 : f64
  }
  func.func @main() -> i32 {
    %163 = llvm.mlir.addressof @CAP : !llvm.ptr
    %164 = llvm.load %163 : !llvm.ptr -> i64
    %165 = arith.constant 8 : i32
    %166 = arith.extsi %165 : i32 to i64
    %162 = func.call @calloc(%164, %166) : (i64, i64) -> !llvm.ptr
    %168 = llvm.mlir.addressof @CAP : !llvm.ptr
    %169 = llvm.load %168 : !llvm.ptr -> i64
    %170 = arith.constant 8 : i32
    %171 = arith.extsi %170 : i32 to i64
    %167 = func.call @calloc(%169, %171) : (i64, i64) -> !llvm.ptr
    %173 = llvm.mlir.addressof @CAP : !llvm.ptr
    %174 = llvm.load %173 : !llvm.ptr -> i64
    %175 = arith.constant 1 : i32
    %176 = arith.extsi %175 : i32 to i64
    %172 = func.call @calloc(%174, %176) : (i64, i64) -> !llvm.ptr
    %177 = llvm.mlir.zero : !llvm.ptr
    %178 = llvm.icmp "eq" %162, %177 : !llvm.ptr
    %179 = scf.if %178 -> (i1) {
      %180 = arith.constant true
      scf.yield %180 : i1
    } else {
      %181 = llvm.mlir.zero : !llvm.ptr
      %182 = llvm.icmp "eq" %167, %181 : !llvm.ptr
      scf.yield %182 : i1
    }
    %183 = scf.if %179 -> (i1) {
      %184 = arith.constant true
      scf.yield %184 : i1
    } else {
      %185 = llvm.mlir.zero : !llvm.ptr
      %186 = llvm.icmp "eq" %172, %185 : !llvm.ptr
      scf.yield %186 : i1
    }
    cf.cond_br %183, ^bb24, ^bb25
    ^bb24:
      %187 = arith.constant 1 : i32
      func.return %187 : i32
    ^bb25:
      cf.br ^bb26
    ^bb26:
    %188 = arith.constant 5705032704 : i32
    %189 = arith.extsi %188 : i32 to i64
    %190 = func.call @R(%189) : (i64) -> f64
    %191 = func.call @B(%189, %162, %167, %172) : (i64, !llvm.ptr, !llvm.ptr, !llvm.ptr) -> f64
    %192 = arith.subf %190, %191 : f64
    %193 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %194 = llvm.call @printf(%193, %192) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    func.call @free(%162) : (!llvm.ptr) -> ()
    func.call @free(%167) : (!llvm.ptr) -> ()
    func.call @free(%172) : (!llvm.ptr) -> ()
    %198 = arith.constant 0 : i32
    func.return %198 : i32
  }
}