Problem 471
Triangle Inscribed in Ellipse — G(10^11) via harmonic closed forms.
View problem on Project Euler
Performance comparison
| Metric | Our solution | Best known |
|---|
| Time complexity | O(1) | O(n^2) |
|---|
| Space complexity | O(1) | O(n^2) |
|---|
| Approach | Flow solution | Bottom-up DP |
|---|
| Verdict | Optimal |
|---|
Flow source
# Project Euler 471
# Triangle Inscribed in Ellipse — G(10^11) via harmonic closed forms.
extern {
function log(x: f64) -> f64
function log10(x: f64) -> f64
function exp(x: f64) -> f64
function floor(x: f64) -> f64
function pow(x: f64, y: f64) -> f64
}
function harmonic(n: i64) -> f64 {
if n <= 0 { return 0.0 }
let N: f64 = n as f64
let inv: f64 = 1.0 / N
let inv2: f64 = inv * inv
let inv4: f64 = inv2 * inv2
let inv6: f64 = inv4 * inv2
let inv8: f64 = inv4 * inv4
let inv10: f64 = inv8 * inv2
let GAMMA: f64 = 0.5772156649015328606
return log(N) + GAMMA + inv / 2.0 - inv2 / 12.0 + inv4 / 120.0 - inv6 / 252.0 + inv8 / 240.0 - inv10 / 132.0
}
function main() -> i32 {
let n: i64 = 100000000000
let ne: i64 = n / 2
let no: i64 = (n - 1) / 2
# P = 3*(T2(ne)-T1(ne)) + 3*T2(no) + 2*T1(no)
let T1ne: f64 = (ne as f64) * ((ne + 1) as f64) / 2.0
let T2ne: f64 = (ne as f64) * ((ne + 1) as f64) * ((2 * ne + 1) as f64) / 6.0
let T1no: f64 = (no as f64) * ((no + 1) as f64) / 2.0
let T2no: f64 = (no as f64) * ((no + 1) as f64) * ((2 * no + 1) as f64) / 6.0
let P: f64 = 3.0 * (T2ne - T1ne) + 3.0 * T2no + 2.0 * T1no
let mA: i64 = n - 1
let HA: f64 = harmonic(mA)
let md: f64 = mA as f64
let S0A: f64 = (md + 1.0) * HA - md
let S1A: f64 = (md * (md + 1.0) / 2.0) * HA - md * (md - 1.0) / 4.0
let S2A: f64 = (md * (md + 1.0) * (2.0 * md + 1.0) / 6.0) * HA - md * (4.0 * md * md - 3.0 * md - 1.0) / 36.0
let A: f64 = S2A + 2.0 * S1A + S0A - 4.0
let m: i64 = ne
let Hm: f64 = harmonic(m)
let m1: i64 = m - 1
let Hm1: f64 = harmonic(m1)
let md1: f64 = m1 as f64
let S0: f64 = (md1 + 1.0) * Hm1 - md1
let S1: f64 = (md1 * (md1 + 1.0) / 2.0) * Hm1 - md1 * (md1 - 1.0) / 4.0
let S2: f64 = (md1 * (md1 + 1.0) * (2.0 * md1 + 1.0) / 6.0) * Hm1 - md1 * (4.0 * md1 * md1 - 3.0 * md1 - 1.0) / 36.0
let B: f64 = 8.0 * S2 + 4.0 * S1 + S0 - 4.0 + (4.0 * (m as f64) * (m as f64)) * Hm
let ans: f64 = P - A + B
let log10e: f64 = log10(exp(1.0))
let log10x: f64 = log(ans) * log10e
let expv: i64 = floor(log10x) as i64
let frac: f64 = log10x - (expv as f64)
let mut mant: f64 = pow(10.0, frac)
let mut mant_r: f64 = floor(mant * 1000000000.0 + 0.5) / 1000000000.0
let mut exp_out: i64 = expv
if mant_r >= 10.0 {
mant_r = mant_r / 10.0
exp_out = exp_out + 1
}
printf("%.9fe%lld\n", mant_r, exp_out)
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);
int32_t main(void);
double harmonic_i64(int64_t n) {
if (n <= 0) {
return 0.0;
}
double N = ((double)(n));
double inv = (1.0 / N);
double inv2 = (inv * inv);
double inv4 = (inv2 * inv2);
double inv6 = (inv4 * inv2);
double inv8 = (inv4 * inv4);
double inv10 = (inv8 * inv2);
double GAMMA = 0.5772156649015328606;
return (((((((log(N) + GAMMA) + (inv / 2.0)) - (inv2 / 12.0)) + (inv4 / 120.0)) - (inv6 / 252.0)) + (inv8 / 240.0)) - (inv10 / 132.0));
}
int32_t main(void) {
int64_t n = 100000000000;
int64_t ne = FLOW_CHECKED_DIV((n), (2));
int64_t no = FLOW_CHECKED_DIV(((n - 1)), (2));
double T1ne = ((((double)(ne)) * ((double)((ne + 1)))) / 2.0);
double T2ne = (((((double)(ne)) * ((double)((ne + 1)))) * ((double)(((2 * ne) + 1)))) / 6.0);
double T1no = ((((double)(no)) * ((double)((no + 1)))) / 2.0);
double T2no = (((((double)(no)) * ((double)((no + 1)))) * ((double)(((2 * no) + 1)))) / 6.0);
double P = (((3.0 * (T2ne - T1ne)) + (3.0 * T2no)) + (2.0 * T1no));
int64_t mA = (n - 1);
double HA = harmonic_i64(mA);
double md = ((double)(mA));
double S0A = (((md + 1.0) * HA) - md);
double S1A = ((((md * (md + 1.0)) / 2.0) * HA) - ((md * (md - 1.0)) / 4.0));
double S2A = (((((md * (md + 1.0)) * ((2.0 * md) + 1.0)) / 6.0) * HA) - ((md * ((((4.0 * md) * md) - (3.0 * md)) - 1.0)) / 36.0));
double A = (((S2A + (2.0 * S1A)) + S0A) - 4.0);
int64_t m = ne;
double Hm = harmonic_i64(m);
int64_t m1 = (m - 1);
double Hm1 = harmonic_i64(m1);
double md1 = ((double)(m1));
double S0 = (((md1 + 1.0) * Hm1) - md1);
double S1 = ((((md1 * (md1 + 1.0)) / 2.0) * Hm1) - ((md1 * (md1 - 1.0)) / 4.0));
double S2 = (((((md1 * (md1 + 1.0)) * ((2.0 * md1) + 1.0)) / 6.0) * Hm1) - ((md1 * ((((4.0 * md1) * md1) - (3.0 * md1)) - 1.0)) / 36.0));
double B = (((((8.0 * S2) + (4.0 * S1)) + S0) - 4.0) + (((4.0 * ((double)(m))) * ((double)(m))) * Hm));
double ans = ((P - A) + B);
double log10e = log10(exp(1.0));
double log10x = (log(ans) * log10e);
int64_t expv = ((int64_t)(floor(log10x)));
double frac = (log10x - ((double)(expv)));
double mant = pow(10.0, frac);
double mant_r = (floor(((mant * 1000000000.0) + 0.5)) / 1000000000.0);
int64_t exp_out = expv;
if (mant_r >= 10.0) {
mant_r = (mant_r / 10.0);
exp_out = (exp_out + 1);
}
printf("%.9fe%lld\n", mant_r, exp_out);
return 0;
}
Generated MLIR
module {
llvm.func @printf(!llvm.ptr, ...) -> i32
llvm.mlir.global internal constant @str_0("%.9fe%lld\n\00") {addr_space = 0 : i32} : !llvm.array<11 x i8>
func.func private @log(f64) -> f64
func.func private @log10(f64) -> f64
func.func private @exp(f64) -> f64
func.func private @floor(f64) -> f64
func.func private @pow(f64, 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.sitofp %arg0 : i64 to f64
%6 = arith.constant 1.0 : f32
%8 = arith.extf %6 : f32 to f64
%7 = arith.divf %8, %5 : f64
%9 = arith.mulf %7, %7 : f64
%10 = arith.mulf %9, %9 : f64
%11 = arith.mulf %10, %9 : f64
%12 = arith.mulf %10, %10 : f64
%13 = arith.mulf %12, %9 : f64
%14 = arith.constant 0.5772156649015328606 : f32
%15 = arith.extf %14 : f32 to f64
%16 = math.log %5 : f64
%17 = arith.addf %16, %15 : f64
%18 = arith.constant 2.0 : f32
%20 = arith.extf %18 : f32 to f64
%19 = arith.divf %7, %20 : f64
%21 = arith.addf %17, %19 : f64
%22 = arith.constant 12.0 : f32
%24 = arith.extf %22 : f32 to f64
%23 = arith.divf %9, %24 : f64
%25 = arith.subf %21, %23 : f64
%26 = arith.constant 120.0 : f32
%28 = arith.extf %26 : f32 to f64
%27 = arith.divf %10, %28 : f64
%29 = arith.addf %25, %27 : f64
%30 = arith.constant 252.0 : f32
%32 = arith.extf %30 : f32 to f64
%31 = arith.divf %11, %32 : f64
%33 = arith.subf %29, %31 : f64
%34 = arith.constant 240.0 : f32
%36 = arith.extf %34 : f32 to f64
%35 = arith.divf %12, %36 : f64
%37 = arith.addf %33, %35 : f64
%38 = arith.constant 132.0 : f32
%40 = arith.extf %38 : f32 to f64
%39 = arith.divf %13, %40 : f64
%41 = arith.subf %37, %39 : f64
func.return %41 : f64
}
func.func @main() -> i32 {
%42 = arith.constant 95705032704 : i32
%43 = arith.extsi %42 : i32 to i64
%44 = arith.constant 2 : i32
%46 = arith.extsi %44 : i32 to i64
%45 = arith.divsi %43, %46 : i64
%47 = arith.constant 1 : i32
%49 = arith.extsi %47 : i32 to i64
%48 = arith.subi %43, %49 : i64
%50 = arith.constant 2 : i32
%52 = arith.extsi %50 : i32 to i64
%51 = arith.divsi %48, %52 : i64
%53 = arith.sitofp %45 : i64 to f64
%54 = arith.constant 1 : i32
%56 = arith.extsi %54 : i32 to i64
%55 = arith.addi %45, %56 : i64
%57 = arith.sitofp %55 : i64 to f64
%58 = arith.mulf %53, %57 : f64
%59 = arith.constant 2.0 : f32
%61 = arith.extf %59 : f32 to f64
%60 = arith.divf %58, %61 : f64
%62 = arith.sitofp %45 : i64 to f64
%63 = arith.constant 1 : i32
%65 = arith.extsi %63 : i32 to i64
%64 = arith.addi %45, %65 : i64
%66 = arith.sitofp %64 : i64 to f64
%67 = arith.mulf %62, %66 : f64
%68 = arith.constant 2 : i32
%70 = arith.extsi %68 : i32 to i64
%69 = arith.muli %70, %45 : i64
%71 = arith.constant 1 : i32
%73 = arith.extsi %71 : i32 to i64
%72 = arith.addi %69, %73 : i64
%74 = arith.sitofp %72 : i64 to f64
%75 = arith.mulf %67, %74 : f64
%76 = arith.constant 6.0 : f32
%78 = arith.extf %76 : f32 to f64
%77 = arith.divf %75, %78 : f64
%79 = arith.sitofp %51 : i64 to f64
%80 = arith.constant 1 : i32
%82 = arith.extsi %80 : i32 to i64
%81 = arith.addi %51, %82 : i64
%83 = arith.sitofp %81 : i64 to f64
%84 = arith.mulf %79, %83 : f64
%85 = arith.constant 2.0 : f32
%87 = arith.extf %85 : f32 to f64
%86 = arith.divf %84, %87 : f64
%88 = arith.sitofp %51 : i64 to f64
%89 = arith.constant 1 : i32
%91 = arith.extsi %89 : i32 to i64
%90 = arith.addi %51, %91 : i64
%92 = arith.sitofp %90 : i64 to f64
%93 = arith.mulf %88, %92 : f64
%94 = arith.constant 2 : i32
%96 = arith.extsi %94 : i32 to i64
%95 = arith.muli %96, %51 : i64
%97 = arith.constant 1 : i32
%99 = arith.extsi %97 : i32 to i64
%98 = arith.addi %95, %99 : i64
%100 = arith.sitofp %98 : i64 to f64
%101 = arith.mulf %93, %100 : f64
%102 = arith.constant 6.0 : f32
%104 = arith.extf %102 : f32 to f64
%103 = arith.divf %101, %104 : f64
%105 = arith.constant 3.0 : f32
%106 = arith.subf %77, %60 : f64
%108 = arith.extf %105 : f32 to f64
%107 = arith.mulf %108, %106 : f64
%109 = arith.constant 3.0 : f32
%111 = arith.extf %109 : f32 to f64
%110 = arith.mulf %111, %103 : f64
%112 = arith.addf %107, %110 : f64
%113 = arith.constant 2.0 : f32
%115 = arith.extf %113 : f32 to f64
%114 = arith.mulf %115, %86 : f64
%116 = arith.addf %112, %114 : f64
%117 = arith.constant 1 : i32
%119 = arith.extsi %117 : i32 to i64
%118 = arith.subi %43, %119 : i64
%120 = func.call @harmonic(%118) : (i64) -> f64
%121 = arith.sitofp %118 : i64 to f64
%122 = arith.constant 1.0 : f32
%124 = arith.extf %122 : f32 to f64
%123 = arith.addf %121, %124 : f64
%125 = arith.mulf %123, %120 : f64
%126 = arith.subf %125, %121 : f64
%127 = arith.constant 1.0 : f32
%129 = arith.extf %127 : f32 to f64
%128 = arith.addf %121, %129 : f64
%130 = arith.mulf %121, %128 : f64
%131 = arith.constant 2.0 : f32
%133 = arith.extf %131 : f32 to f64
%132 = arith.divf %130, %133 : f64
%134 = arith.mulf %132, %120 : f64
%135 = arith.constant 1.0 : f32
%137 = arith.extf %135 : f32 to f64
%136 = arith.subf %121, %137 : f64
%138 = arith.mulf %121, %136 : f64
%139 = arith.constant 4.0 : f32
%141 = arith.extf %139 : f32 to f64
%140 = arith.divf %138, %141 : f64
%142 = arith.subf %134, %140 : f64
%143 = arith.constant 1.0 : f32
%145 = arith.extf %143 : f32 to f64
%144 = arith.addf %121, %145 : f64
%146 = arith.mulf %121, %144 : f64
%147 = arith.constant 2.0 : f32
%149 = arith.extf %147 : f32 to f64
%148 = arith.mulf %149, %121 : f64
%150 = arith.constant 1.0 : f32
%152 = arith.extf %150 : f32 to f64
%151 = arith.addf %148, %152 : f64
%153 = arith.mulf %146, %151 : f64
%154 = arith.constant 6.0 : f32
%156 = arith.extf %154 : f32 to f64
%155 = arith.divf %153, %156 : f64
%157 = arith.mulf %155, %120 : f64
%158 = arith.constant 4.0 : f32
%160 = arith.extf %158 : f32 to f64
%159 = arith.mulf %160, %121 : f64
%161 = arith.mulf %159, %121 : f64
%162 = arith.constant 3.0 : f32
%164 = arith.extf %162 : f32 to f64
%163 = arith.mulf %164, %121 : f64
%165 = arith.subf %161, %163 : f64
%166 = arith.constant 1.0 : f32
%168 = arith.extf %166 : f32 to f64
%167 = arith.subf %165, %168 : f64
%169 = arith.mulf %121, %167 : f64
%170 = arith.constant 36.0 : f32
%172 = arith.extf %170 : f32 to f64
%171 = arith.divf %169, %172 : f64
%173 = arith.subf %157, %171 : f64
%174 = arith.constant 2.0 : f32
%176 = arith.extf %174 : f32 to f64
%175 = arith.mulf %176, %142 : f64
%177 = arith.addf %173, %175 : f64
%178 = arith.addf %177, %126 : f64
%179 = arith.constant 4.0 : f32
%181 = arith.extf %179 : f32 to f64
%180 = arith.subf %178, %181 : f64
%182 = func.call @harmonic(%45) : (i64) -> f64
%183 = arith.constant 1 : i32
%185 = arith.extsi %183 : i32 to i64
%184 = arith.subi %45, %185 : i64
%186 = func.call @harmonic(%184) : (i64) -> f64
%187 = arith.sitofp %184 : i64 to f64
%188 = arith.constant 1.0 : f32
%190 = arith.extf %188 : f32 to f64
%189 = arith.addf %187, %190 : f64
%191 = arith.mulf %189, %186 : f64
%192 = arith.subf %191, %187 : f64
%193 = arith.constant 1.0 : f32
%195 = arith.extf %193 : f32 to f64
%194 = arith.addf %187, %195 : f64
%196 = arith.mulf %187, %194 : f64
%197 = arith.constant 2.0 : f32
%199 = arith.extf %197 : f32 to f64
%198 = arith.divf %196, %199 : f64
%200 = arith.mulf %198, %186 : f64
%201 = arith.constant 1.0 : f32
%203 = arith.extf %201 : f32 to f64
%202 = arith.subf %187, %203 : f64
%204 = arith.mulf %187, %202 : f64
%205 = arith.constant 4.0 : f32
%207 = arith.extf %205 : f32 to f64
%206 = arith.divf %204, %207 : f64
%208 = arith.subf %200, %206 : f64
%209 = arith.constant 1.0 : f32
%211 = arith.extf %209 : f32 to f64
%210 = arith.addf %187, %211 : f64
%212 = arith.mulf %187, %210 : f64
%213 = arith.constant 2.0 : f32
%215 = arith.extf %213 : f32 to f64
%214 = arith.mulf %215, %187 : f64
%216 = arith.constant 1.0 : f32
%218 = arith.extf %216 : f32 to f64
%217 = arith.addf %214, %218 : f64
%219 = arith.mulf %212, %217 : f64
%220 = arith.constant 6.0 : f32
%222 = arith.extf %220 : f32 to f64
%221 = arith.divf %219, %222 : f64
%223 = arith.mulf %221, %186 : f64
%224 = arith.constant 4.0 : f32
%226 = arith.extf %224 : f32 to f64
%225 = arith.mulf %226, %187 : f64
%227 = arith.mulf %225, %187 : f64
%228 = arith.constant 3.0 : f32
%230 = arith.extf %228 : f32 to f64
%229 = arith.mulf %230, %187 : f64
%231 = arith.subf %227, %229 : f64
%232 = arith.constant 1.0 : f32
%234 = arith.extf %232 : f32 to f64
%233 = arith.subf %231, %234 : f64
%235 = arith.mulf %187, %233 : f64
%236 = arith.constant 36.0 : f32
%238 = arith.extf %236 : f32 to f64
%237 = arith.divf %235, %238 : f64
%239 = arith.subf %223, %237 : f64
%240 = arith.constant 8.0 : f32
%242 = arith.extf %240 : f32 to f64
%241 = arith.mulf %242, %239 : f64
%243 = arith.constant 4.0 : f32
%245 = arith.extf %243 : f32 to f64
%244 = arith.mulf %245, %208 : f64
%246 = arith.addf %241, %244 : f64
%247 = arith.addf %246, %192 : f64
%248 = arith.constant 4.0 : f32
%250 = arith.extf %248 : f32 to f64
%249 = arith.subf %247, %250 : f64
%251 = arith.constant 4.0 : f32
%252 = arith.sitofp %45 : i64 to f64
%254 = arith.extf %251 : f32 to f64
%253 = arith.mulf %254, %252 : f64
%255 = arith.sitofp %45 : i64 to f64
%256 = arith.mulf %253, %255 : f64
%257 = arith.mulf %256, %182 : f64
%258 = arith.addf %249, %257 : f64
%259 = arith.subf %116, %180 : f64
%260 = arith.addf %259, %258 : f64
%262 = arith.constant 1.0 : f32
%263 = math.exp %262 : f32
%264 = arith.extf %263 : f32 to f64
%261 = func.call @log10(%264) : (f64) -> f64
%265 = math.log %260 : f64
%266 = arith.mulf %265, %261 : f64
%267 = func.call @floor(%266) : (f64) -> f64
%268 = arith.fptosi %267 : f64 to i64
%269 = arith.sitofp %268 : i64 to f64
%270 = arith.subf %266, %269 : f64
%272 = arith.constant 10.0 : f32
%273 = arith.extf %272 : f32 to f64
%271 = func.call @pow(%273, %270) : (f64, f64) -> f64
%274 = llvm.mlir.constant(1 : i64) : i64
%275 = llvm.alloca %274 x f64 : (i64) -> !llvm.ptr
llvm.store %271, %275 : f64, !llvm.ptr
%277 = llvm.load %275 : !llvm.ptr -> f64
%278 = arith.constant 1000000000.0 : f32
%280 = arith.extf %278 : f32 to f64
%279 = arith.mulf %277, %280 : f64
%281 = arith.constant 0.5 : f32
%283 = arith.extf %281 : f32 to f64
%282 = arith.addf %279, %283 : f64
%276 = func.call @floor(%282) : (f64) -> f64
%284 = arith.constant 1000000000.0 : f32
%286 = arith.extf %284 : f32 to f64
%285 = arith.divf %276, %286 : f64
%287 = llvm.mlir.constant(1 : i64) : i64
%288 = llvm.alloca %287 x f64 : (i64) -> !llvm.ptr
llvm.store %285, %288 : f64, !llvm.ptr
%289 = llvm.mlir.constant(1 : i64) : i64
%290 = llvm.alloca %289 x i64 : (i64) -> !llvm.ptr
llvm.store %268, %290 : i64, !llvm.ptr
%291 = llvm.load %288 : !llvm.ptr -> f64
%292 = arith.constant 10.0 : f32
%294 = arith.extf %292 : f32 to f64
%293 = arith.cmpf oge, %291, %294 : f64
cf.cond_br %293, ^bb3, ^bb4
^bb3:
%295 = llvm.load %288 : !llvm.ptr -> f64
%296 = arith.constant 10.0 : f32
%298 = arith.extf %296 : f32 to f64
%297 = arith.divf %295, %298 : f64
llvm.store %297, %288 : f64, !llvm.ptr
%299 = llvm.load %290 : !llvm.ptr -> i64
%300 = arith.constant 1 : i32
%302 = arith.extsi %300 : i32 to i64
%301 = arith.addi %299, %302 : i64
llvm.store %301, %290 : i64, !llvm.ptr
cf.br ^bb5
^bb4:
cf.br ^bb5
^bb5:
%303 = llvm.mlir.addressof @str_0 : !llvm.ptr
%304 = llvm.load %288 : !llvm.ptr -> f64
%305 = llvm.load %290 : !llvm.ptr -> i64
%306 = llvm.call @printf(%303, %304, %305) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64, i64) -> i32
%307 = arith.constant 0 : i32
func.return %307 : i32
}
}