Problem 392

Minimal red area for N=400 enmeshed unit circle grid, 10 decimals.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 392
# Minimal red area for N=400 enmeshed unit circle grid, 10 decimals.

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

function f(x: f64) -> f64 {
    let v: f64 = 1.0 - x * x
    if v < 0.0 { v = 0.0 }
    return sqrt(v)
}

function end_x(m: i32, x1: f64) -> f64 {
    if !(x1 > 0.0 && x1 < 1.0) { return 1.0e300 }
    let mut x_cur: f64 = x1
    let mut g_prev: f64 = 1.0
    let mut k: i32 = 1
    while k < m {
        if x_cur <= 0.0 { return 1.0e300 }
        if x_cur >= 1.0 { return x_cur }
        let g_cur: f64 = f(x_cur)
        let x_next: f64 = x_cur + (g_prev - g_cur) * g_cur / x_cur
        if !(x_cur < x_next) { return 1.0e300 }
        x_cur = x_next
        g_prev = g_cur
        k = k + 1
    }
    return x_cur
}

function solve_quadrant(m: i32) -> f64 {
    let mut lo: f64 = 0.000001
    while end_x(m, lo) >= 1.0 {
        lo = lo * 0.5
        if lo < 1.0e-20 { return 0.0 }
    }
    let mut hi: f64 = 0.9
    while end_x(m, hi) <= 1.0 {
        hi = (hi + 1.0) / 2.0
        if hi >= 1.0 - 1.0e-15 { return 0.0 }
    }
    let mut it: i32 = 0
    while it < 200 {
        let mid: f64 = (lo + hi) / 2.0
        if end_x(m, mid) > 1.0 { hi = mid } else { lo = mid }
        it = it + 1
    }
    let x1: f64 = (lo + hi) / 2.0
    let xs: ptr<f64> = calloc((m + 1) as i64, 8)
    if xs == null { return 0.0 }
    xs[0] = 0.0
    xs[1] = x1
    let mut g_prev: f64 = 1.0
    let mut k: i32 = 1
    while k < m {
        let xk: f64 = xs[k]
        let gk: f64 = f(xk)
        xs[k + 1] = xk + (g_prev - gk) * gk / xk
        g_prev = gk
        k = k + 1
    }
    let mut area_q: f64 = 0.0
    let mut i: i32 = 0
    while i < m {
        let xi: f64 = xs[i]
        area_q = area_q + (xs[i + 1] - xi) * f(xi)
        i = i + 1
    }
    free(xs)
    return area_q
}

function main() -> i32 {
    let N: i32 = 400
    let m: i32 = N / 2 + 1
    let ans: f64 = 4.0 * solve_quadrant(m)
    printf("%.10f\n", ans)
    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 f_f64(double x);
double end_x_i32_f64(int32_t m, double x1);
double solve_quadrant_i32(int32_t m);
int32_t main(void);




double f_f64(double x) {
    double v = (1.0 - (x * x));
    if (v < 0.0) {
        v = 0.0;
    }
    return sqrt(v);
}

double end_x_i32_f64(int32_t m, double x1) {
    if ((!((x1 > 0.0 && x1 < 1.0)))) {
        return 1.0e300;
    }
    double x_cur = x1;
    double g_prev = 1.0;
    int32_t k = 1;
    while (k < m) {
        if (x_cur <= 0.0) {
            return 1.0e300;
        }
        if (x_cur >= 1.0) {
            return x_cur;
        }
        double g_cur = f_f64(x_cur);
        double x_next = (x_cur + (((g_prev - g_cur) * g_cur) / x_cur));
        if ((!(x_cur < x_next))) {
            return 1.0e300;
        }
        x_cur = x_next;
        g_prev = g_cur;
        k = (k + 1);
    }
    return x_cur;
}

double solve_quadrant_i32(int32_t m) {
    double lo = 0.000001;
    while (end_x_i32_f64(m, lo) >= 1.0) {
        lo = (lo * 0.5);
        if (lo < 1.0e-20) {
            return 0.0;
        }
    }
    double hi = 0.9;
    while (end_x_i32_f64(m, hi) <= 1.0) {
        hi = ((hi + 1.0) / 2.0);
        if (hi >= (1.0 - 1.0e-15)) {
            return 0.0;
        }
    }
    int32_t it = 0;
    while (it < 200) {
        double mid = ((lo + hi) / 2.0);
        if (end_x_i32_f64(m, mid) > 1.0) {
            hi = mid;
        } else {
            lo = mid;
        }
        it = (it + 1);
    }
    double x1 = ((lo + hi) / 2.0);
    double* xs = (double*)(calloc(((int64_t)((m + 1))), 8));
    if (xs == NULL) {
        return 0.0;
    }
    xs[0] = 0.0;
    xs[1] = x1;
    double g_prev = 1.0;
    int32_t k = 1;
    while (k < m) {
        double xk = xs[k];
        double gk = f_f64(xk);
        xs[(k + 1)] = (xk + (((g_prev - gk) * gk) / xk));
        g_prev = gk;
        k = (k + 1);
    }
    double area_q = 0.0;
    int32_t i = 0;
    while (i < m) {
        double xi = xs[i];
        area_q = (area_q + ((xs[(i + 1)] - xi) * f_f64(xi)));
        i = (i + 1);
    }
    free(xs);
    return area_q;
}

int32_t main(void) {
    int32_t N = 400;
    int32_t m = (FLOW_CHECKED_DIV((N), (2)) + 1);
    double ans = (4.0 * solve_quadrant_i32(m));
    printf("%.10f\n", ans);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.10f\n\00") {addr_space = 0 : i32} : !llvm.array<7 x i8>
  func.func private @sqrt(f64) -> f64
  func.func private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func @f(%arg0: f64) -> f64 {
    %0 = arith.constant 1.0 : f32
    %1 = arith.mulf %arg0, %arg0 : f64
    %3 = arith.extf %0 : f32 to f64
    %2 = arith.subf %3, %1 : f64
    %4 = arith.constant 0.0 : f32
    %6 = arith.extf %4 : f32 to f64
    %5 = arith.cmpf olt, %2, %6 : f64
    %7 = scf.if %5 -> (f64) {
      %8 = arith.constant 0.0 : f32
      %9 = arith.extf %8 : f32 to f64
      scf.yield %9 : f64
    } else {
      scf.yield %2 : f64
    }
    %10 = math.sqrt %7 : f64
    func.return %10 : f64
  }
  func.func @end_x(%arg0: i32, %arg1: f64) -> f64 {
    %11 = arith.constant 0.0 : f32
    %13 = arith.extf %11 : f32 to f64
    %12 = arith.cmpf ogt, %arg1, %13 : f64
    %14 = scf.if %12 -> (i1) {
      %15 = arith.constant 1.0 : f32
      %17 = arith.extf %15 : f32 to f64
      %16 = arith.cmpf olt, %arg1, %17 : f64
      scf.yield %16 : i1
    } else {
      %18 = arith.constant false
      scf.yield %18 : i1
    }
    %20 = arith.constant 1 : i1
    %19 = arith.xori %14, %20 : i1
    cf.cond_br %19, ^bb0, ^bb1
    ^bb0:
      %22 = arith.constant 1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704443832883878176942523235360430575644792184786706982848387200926575803737830233794788090059368953234970799945081119038967640880074652742780142494579258788820056842838115669472196386865459400540160 : f32
      %23 = arith.extf %22 : f32 to f64
      func.return %23 : f64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %24 = llvm.mlir.constant(1 : i64) : i64
    %25 = llvm.alloca %24 x f64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %25 : f64, !llvm.ptr
    %26 = arith.constant 1.0 : f32
    %27 = arith.extf %26 : f32 to f64
    %28 = llvm.mlir.constant(1 : i64) : i64
    %29 = llvm.alloca %28 x f64 : (i64) -> !llvm.ptr
    llvm.store %27, %29 : f64, !llvm.ptr
    %30 = arith.constant 1 : i32
    %31 = llvm.mlir.constant(1 : i64) : i64
    %32 = llvm.alloca %31 x i32 : (i64) -> !llvm.ptr
    llvm.store %30, %32 : i32, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %33 = llvm.load %32 : !llvm.ptr -> i32
    %34 = arith.cmpi slt, %33, %arg0 : i32
    cf.cond_br %34, ^bb4, ^bb5
    ^bb4:
      %35 = llvm.load %25 : !llvm.ptr -> f64
      %36 = arith.constant 0.0 : f32
      %38 = arith.extf %36 : f32 to f64
      %37 = arith.cmpf ole, %35, %38 : f64
      cf.cond_br %37, ^bb6, ^bb7
      ^bb6:
        %39 = arith.constant 1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704443832883878176942523235360430575644792184786706982848387200926575803737830233794788090059368953234970799945081119038967640880074652742780142494579258788820056842838115669472196386865459400540160 : f32
        %40 = arith.extf %39 : f32 to f64
        func.return %40 : f64
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %41 = llvm.load %25 : !llvm.ptr -> f64
      %42 = arith.constant 1.0 : f32
      %44 = arith.extf %42 : f32 to f64
      %43 = arith.cmpf oge, %41, %44 : f64
      cf.cond_br %43, ^bb9, ^bb10
      ^bb9:
        %45 = llvm.load %25 : !llvm.ptr -> f64
        func.return %45 : f64
      ^bb10:
        cf.br ^bb11
      ^bb11:
      %47 = llvm.load %25 : !llvm.ptr -> f64
      %46 = func.call @f(%47) : (f64) -> f64
      %48 = llvm.load %25 : !llvm.ptr -> f64
      %49 = llvm.load %29 : !llvm.ptr -> f64
      %50 = arith.subf %49, %46 : f64
      %51 = arith.mulf %50, %46 : f64
      %52 = llvm.load %25 : !llvm.ptr -> f64
      %53 = arith.divf %51, %52 : f64
      %54 = arith.addf %48, %53 : f64
      %55 = llvm.load %25 : !llvm.ptr -> f64
      %56 = arith.cmpf olt, %55, %54 : f64
      %58 = arith.constant 1 : i1
      %57 = arith.xori %56, %58 : i1
      cf.cond_br %57, ^bb12, ^bb13
      ^bb12:
        %60 = arith.constant 1000000000000000052504760255204420248704468581108159154915854115511802457988908195786371375080447864043704443832883878176942523235360430575644792184786706982848387200926575803737830233794788090059368953234970799945081119038967640880074652742780142494579258788820056842838115669472196386865459400540160 : f32
        %61 = arith.extf %60 : f32 to f64
        func.return %61 : f64
      ^bb13:
        cf.br ^bb14
      ^bb14:
      llvm.store %54, %25 : f64, !llvm.ptr
      llvm.store %46, %29 : f64, !llvm.ptr
      %62 = llvm.load %32 : !llvm.ptr -> i32
      %63 = arith.constant 1 : i32
      %64 = arith.addi %62, %63 : i32
      llvm.store %64, %32 : i32, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %65 = llvm.load %25 : !llvm.ptr -> f64
    func.return %65 : f64
  }
  func.func @solve_quadrant(%arg0: i32) -> f64 {
    %66 = arith.constant 0.000001 : f32
    %67 = arith.extf %66 : f32 to f64
    %68 = llvm.mlir.constant(1 : i64) : i64
    %69 = llvm.alloca %68 x f64 : (i64) -> !llvm.ptr
    llvm.store %67, %69 : f64, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %71 = llvm.load %69 : !llvm.ptr -> f64
    %70 = func.call @end_x(%arg0, %71) : (i32, f64) -> f64
    %72 = arith.constant 1.0 : f32
    %74 = arith.extf %72 : f32 to f64
    %73 = arith.cmpf oge, %70, %74 : f64
    cf.cond_br %73, ^bb16, ^bb17
    ^bb16:
      %75 = llvm.load %69 : !llvm.ptr -> f64
      %76 = arith.constant 0.5 : f32
      %78 = arith.extf %76 : f32 to f64
      %77 = arith.mulf %75, %78 : f64
      llvm.store %77, %69 : f64, !llvm.ptr
      %79 = llvm.load %69 : !llvm.ptr -> f64
      %80 = arith.constant 0 : f32
      %82 = arith.extf %80 : f32 to f64
      %81 = arith.cmpf olt, %79, %82 : f64
      cf.cond_br %81, ^bb18, ^bb19
      ^bb18:
        %83 = arith.constant 0.0 : f32
        %84 = arith.extf %83 : f32 to f64
        func.return %84 : f64
      ^bb19:
        cf.br ^bb20
      ^bb20:
      cf.br ^bb15
    ^bb17:
    %85 = arith.constant 0.9 : f32
    %86 = arith.extf %85 : f32 to f64
    %87 = llvm.mlir.constant(1 : i64) : i64
    %88 = llvm.alloca %87 x f64 : (i64) -> !llvm.ptr
    llvm.store %86, %88 : f64, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %90 = llvm.load %88 : !llvm.ptr -> f64
    %89 = func.call @end_x(%arg0, %90) : (i32, f64) -> f64
    %91 = arith.constant 1.0 : f32
    %93 = arith.extf %91 : f32 to f64
    %92 = arith.cmpf ole, %89, %93 : f64
    cf.cond_br %92, ^bb22, ^bb23
    ^bb22:
      %94 = llvm.load %88 : !llvm.ptr -> f64
      %95 = arith.constant 1.0 : f32
      %97 = arith.extf %95 : f32 to f64
      %96 = arith.addf %94, %97 : f64
      %98 = arith.constant 2.0 : f32
      %100 = arith.extf %98 : f32 to f64
      %99 = arith.divf %96, %100 : f64
      llvm.store %99, %88 : f64, !llvm.ptr
      %101 = llvm.load %88 : !llvm.ptr -> f64
      %102 = arith.constant 1.0 : f32
      %103 = arith.constant 0 : f32
      %104 = arith.subf %102, %103 : f32
      %106 = arith.extf %104 : f32 to f64
      %105 = arith.cmpf oge, %101, %106 : f64
      cf.cond_br %105, ^bb24, ^bb25
      ^bb24:
        %107 = arith.constant 0.0 : f32
        %108 = arith.extf %107 : f32 to f64
        func.return %108 : f64
      ^bb25:
        cf.br ^bb26
      ^bb26:
      cf.br ^bb21
    ^bb23:
    %109 = arith.constant 0 : i32
    %110 = llvm.mlir.constant(1 : i64) : i64
    %111 = llvm.alloca %110 x i32 : (i64) -> !llvm.ptr
    llvm.store %109, %111 : i32, !llvm.ptr
    cf.br ^bb27
    ^bb27:
    %112 = llvm.load %111 : !llvm.ptr -> i32
    %113 = arith.constant 200 : i32
    %114 = arith.cmpi slt, %112, %113 : i32
    cf.cond_br %114, ^bb28, ^bb29
    ^bb28:
      %115 = llvm.load %69 : !llvm.ptr -> f64
      %116 = llvm.load %88 : !llvm.ptr -> f64
      %117 = arith.addf %115, %116 : f64
      %118 = arith.constant 2.0 : f32
      %120 = arith.extf %118 : f32 to f64
      %119 = arith.divf %117, %120 : f64
      %121 = func.call @end_x(%arg0, %119) : (i32, f64) -> f64
      %122 = arith.constant 1.0 : f32
      %124 = arith.extf %122 : f32 to f64
      %123 = arith.cmpf ogt, %121, %124 : f64
      cf.cond_br %123, ^bb30, ^bb31
      ^bb30:
        llvm.store %119, %88 : f64, !llvm.ptr
        cf.br ^bb32
      ^bb31:
        llvm.store %119, %69 : f64, !llvm.ptr
        cf.br ^bb32
      ^bb32:
      %125 = llvm.load %111 : !llvm.ptr -> i32
      %126 = arith.constant 1 : i32
      %127 = arith.addi %125, %126 : i32
      llvm.store %127, %111 : i32, !llvm.ptr
      cf.br ^bb27
    ^bb29:
    %128 = llvm.load %69 : !llvm.ptr -> f64
    %129 = llvm.load %88 : !llvm.ptr -> f64
    %130 = arith.addf %128, %129 : f64
    %131 = arith.constant 2.0 : f32
    %133 = arith.extf %131 : f32 to f64
    %132 = arith.divf %130, %133 : f64
    %135 = arith.constant 1 : i32
    %136 = arith.addi %arg0, %135 : i32
    %137 = arith.extsi %136 : i32 to i64
    %138 = arith.constant 8 : i32
    %139 = arith.extsi %138 : i32 to i64
    %134 = func.call @calloc(%137, %139) : (i64, i64) -> !llvm.ptr
    %140 = llvm.mlir.zero : !llvm.ptr
    %141 = llvm.icmp "eq" %134, %140 : !llvm.ptr
    cf.cond_br %141, ^bb33, ^bb34
    ^bb33:
      %142 = arith.constant 0.0 : f32
      %143 = arith.extf %142 : f32 to f64
      func.return %143 : f64
    ^bb34:
      cf.br ^bb35
    ^bb35:
    %144 = arith.constant 0.0 : f32
    %145 = arith.constant 0 : i32
    %146 = arith.extf %144 : f32 to f64
    %147 = arith.extsi %145 : i32 to i64
    %148 = llvm.getelementptr %134[%147] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %146, %148 : f64, !llvm.ptr
    %149 = arith.constant 1 : i32
    %150 = arith.extsi %149 : i32 to i64
    %151 = llvm.getelementptr %134[%150] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %132, %151 : f64, !llvm.ptr
    %152 = arith.constant 1.0 : f32
    %153 = arith.extf %152 : f32 to f64
    %154 = llvm.mlir.constant(1 : i64) : i64
    %155 = llvm.alloca %154 x f64 : (i64) -> !llvm.ptr
    llvm.store %153, %155 : f64, !llvm.ptr
    %156 = arith.constant 1 : i32
    %157 = llvm.mlir.constant(1 : i64) : i64
    %158 = llvm.alloca %157 x i32 : (i64) -> !llvm.ptr
    llvm.store %156, %158 : i32, !llvm.ptr
    cf.br ^bb36
    ^bb36:
    %159 = llvm.load %158 : !llvm.ptr -> i32
    %160 = arith.cmpi slt, %159, %arg0 : i32
    cf.cond_br %160, ^bb37, ^bb38
    ^bb37:
      %162 = llvm.load %158 : !llvm.ptr -> i32
      %163 = arith.extsi %162 : i32 to i64
      %164 = llvm.getelementptr %134[%163] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %161 = llvm.load %164 : !llvm.ptr -> f64
      %165 = func.call @f(%161) : (f64) -> f64
      %166 = llvm.load %155 : !llvm.ptr -> f64
      %167 = arith.subf %166, %165 : f64
      %168 = arith.mulf %167, %165 : f64
      %169 = arith.divf %168, %161 : f64
      %170 = arith.addf %161, %169 : f64
      %171 = llvm.load %158 : !llvm.ptr -> i32
      %172 = arith.constant 1 : i32
      %173 = arith.addi %171, %172 : i32
      %174 = arith.extsi %173 : i32 to i64
      %175 = llvm.getelementptr %134[%174] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      llvm.store %170, %175 : f64, !llvm.ptr
      llvm.store %165, %155 : f64, !llvm.ptr
      %176 = llvm.load %158 : !llvm.ptr -> i32
      %177 = arith.constant 1 : i32
      %178 = arith.addi %176, %177 : i32
      llvm.store %178, %158 : i32, !llvm.ptr
      cf.br ^bb36
    ^bb38:
    %179 = arith.constant 0.0 : f32
    %180 = arith.extf %179 : f32 to f64
    %181 = llvm.mlir.constant(1 : i64) : i64
    %182 = llvm.alloca %181 x f64 : (i64) -> !llvm.ptr
    llvm.store %180, %182 : f64, !llvm.ptr
    %183 = arith.constant 0 : i32
    %184 = llvm.mlir.constant(1 : i64) : i64
    %185 = llvm.alloca %184 x i32 : (i64) -> !llvm.ptr
    llvm.store %183, %185 : i32, !llvm.ptr
    cf.br ^bb39
    ^bb39:
    %186 = llvm.load %185 : !llvm.ptr -> i32
    %187 = arith.cmpi slt, %186, %arg0 : i32
    cf.cond_br %187, ^bb40, ^bb41
    ^bb40:
      %189 = llvm.load %185 : !llvm.ptr -> i32
      %190 = arith.extsi %189 : i32 to i64
      %191 = llvm.getelementptr %134[%190] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %188 = llvm.load %191 : !llvm.ptr -> f64
      %192 = llvm.load %182 : !llvm.ptr -> f64
      %194 = llvm.load %185 : !llvm.ptr -> i32
      %195 = arith.constant 1 : i32
      %196 = arith.addi %194, %195 : i32
      %197 = arith.extsi %196 : i32 to i64
      %198 = llvm.getelementptr %134[%197] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %193 = llvm.load %198 : !llvm.ptr -> f64
      %199 = arith.subf %193, %188 : f64
      %200 = func.call @f(%188) : (f64) -> f64
      %201 = arith.mulf %199, %200 : f64
      %202 = arith.addf %192, %201 : f64
      llvm.store %202, %182 : f64, !llvm.ptr
      %203 = llvm.load %185 : !llvm.ptr -> i32
      %204 = arith.constant 1 : i32
      %205 = arith.addi %203, %204 : i32
      llvm.store %205, %185 : i32, !llvm.ptr
      cf.br ^bb39
    ^bb41:
    func.call @free(%134) : (!llvm.ptr) -> ()
    %207 = llvm.load %182 : !llvm.ptr -> f64
    func.return %207 : f64
  }
  func.func @main() -> i32 {
    %208 = arith.constant 400 : i32
    %209 = arith.constant 2 : i32
    %210 = arith.divsi %208, %209 : i32
    %211 = arith.constant 1 : i32
    %212 = arith.addi %210, %211 : i32
    %213 = arith.constant 4.0 : f32
    %214 = func.call @solve_quadrant(%212) : (i32) -> f64
    %216 = arith.extf %213 : f32 to f64
    %215 = arith.mulf %216, %214 : f64
    %217 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %218 = llvm.call @printf(%217, %215) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %219 = arith.constant 0 : i32
    func.return %219 : i32
  }
}