← All problems Problem 729
Range of periodic sequences of a_{n+1} = a_n - 1/a_n (the Boole map). Periodic orbits correspond one-to-one with aperiodic binary sign itineraries: the inverse branches g+(y) = (y + sqrt(y*y+4))/2 and g-(y) = -1/g+(y) are contractions, so each binary necklace of length p (mask strictly minimal among its rotations, non-constant) yields one cycle of minimal period p via Newton iteration on the composed inverse map. Each cycle contributes p * (max - min); Kahan-sum S(25), 4dp.
View problem on Project Euler
Performance comparison
Metric Our solution Best known
Time complexity O(n^3)?Space complexity O(1)?Approach Flow solution Not curated Verdict Unknown
Flow source
# Project Euler 729
# Range of periodic sequences of a_{n+1} = a_n - 1/a_n (the Boole map).
# Periodic orbits correspond one-to-one with aperiodic binary sign
# itineraries: the inverse branches g+(y) = (y + sqrt(y*y+4))/2 and
# g-(y) = -1/g+(y) are contractions, so each binary necklace of length p
# (mask strictly minimal among its rotations, non-constant) yields one
# cycle of minimal period p via Newton iteration on the composed inverse
# map. Each cycle contributes p * (max - min); Kahan-sum S(25), 4dp.
extern {
function sqrt(x: f64) -> f64
}
function main() -> i32 {
let big: i64 = 25
let mut total: f64 = 0.0
let mut comp: f64 = 0.0
let mut p: i64 = 2
while p <= big {
let mut pow2p: i64 = 1
let mut j: i64 = 0
while j < p {
pow2p = pow2p * 2
j = j + 1
}
let mut m: i64 = 1
while m < pow2p - 1 {
# keep m only if strictly smaller than all its rotations
let mut ok: i64 = 1
let mut k: i64 = 1
let mut pk: i64 = 2
while k < p && ok == 1 {
let rot: i64 = (m >> k) | ((m % pk) << (p - k))
if rot <= m { ok = 0 }
k = k + 1
pk = pk * 2
}
if ok == 1 {
# contraction warmup from x = 0
let mut x: f64 = 0.0
let mut sweep: i64 = 0
while sweep < 2 {
let mut y: f64 = x
let mut i: i64 = p - 1
while i >= 0 {
let r: f64 = sqrt(y * y + 4.0)
let mut gp: f64 = 0.0
if y >= 0.0 { gp = (y + r) * 0.5 } else { gp = 2.0 / (r - y) }
if ((m >> i) & 1) == 1 { y = gp } else { y = -1.0 / gp }
i = i - 1
}
x = y
sweep = sweep + 1
}
# Newton on G(x) - x, G = composed inverse branches
let mut it: i64 = 0
let mut done: i64 = 0
while done == 0 && it < 60 {
let mut y: f64 = x
let mut d: f64 = 1.0
let mut i: i64 = p - 1
while i >= 0 {
let r: f64 = sqrt(y * y + 4.0)
let mut gp: f64 = 0.0
let mut gpd: f64 = 0.0
if y >= 0.0 {
gp = (y + r) * 0.5
gpd = (r + y) / (2.0 * r)
} else {
gp = 2.0 / (r - y)
gpd = 2.0 / (r * (r - y))
}
if ((m >> i) & 1) == 1 {
y = gp
d = d * gpd
} else {
y = -1.0 / gp
d = d * gpd / (gp * gp)
}
i = i - 1
}
let nx: f64 = x + (y - x) / (1.0 - d)
let mut diff: f64 = nx - x
if diff < 0.0 { diff = -diff }
let mut ax: f64 = nx
if ax < 0.0 { ax = -ax }
x = nx
if diff <= 0.00000000000001 * (1.0 + ax) { done = 1 }
it = it + 1
}
# final backward pass collects the orbit points
let mut y2: f64 = x
let mut mn: f64 = x
let mut mx: f64 = x
let mut i2: i64 = p - 1
while i2 >= 0 {
let r2: f64 = sqrt(y2 * y2 + 4.0)
let mut gp2: f64 = 0.0
if y2 >= 0.0 { gp2 = (y2 + r2) * 0.5 } else { gp2 = 2.0 / (r2 - y2) }
if ((m >> i2) & 1) == 1 { y2 = gp2 } else { y2 = -1.0 / gp2 }
if y2 < mn { mn = y2 }
if y2 > mx { mx = y2 }
i2 = i2 - 1
}
let contrib: f64 = (p as f64) * (mx - mn)
# Kahan summation
let t1: f64 = contrib - comp
let t2: f64 = total + t1
comp = (t2 - total) - t1
total = t2
}
m = m + 1
}
p = p + 1
}
printf("%.4f\n", total)
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; }
int32_t main(void);
int32_t main(void) {
int64_t big = 25;
double total = 0.0;
double comp = 0.0;
int64_t p = 2;
while (p <= big) {
int64_t pow2p = 1;
int64_t j = 0;
while (j < p) {
pow2p = (pow2p * 2);
j = (j + 1);
}
int64_t m = 1;
while (m < (pow2p - 1)) {
int64_t ok = 1;
int64_t k = 1;
int64_t pk = 2;
while ((k < p && ok == 1)) {
int64_t rot = (FLOW_CHECKED_SHR((m), (k)) | FLOW_CHECKED_SHL((FLOW_CHECKED_MOD((m), (pk))), ((p - k))));
if (rot <= m) {
ok = 0;
}
k = (k + 1);
pk = (pk * 2);
}
if (ok == 1) {
double x = 0.0;
int64_t sweep = 0;
while (sweep < 2) {
double y = x;
int64_t i = (p - 1);
while (i >= 0) {
double r = sqrt(((y * y) + 4.0));
double gp = 0.0;
if (y >= 0.0) {
gp = ((y + r) * 0.5);
} else {
gp = (2.0 / (r - y));
}
if ((FLOW_CHECKED_SHR((m), (i)) & 1) == 1) {
y = gp;
} else {
y = ((-1.0) / gp);
}
i = (i - 1);
}
x = y;
sweep = (sweep + 1);
}
int64_t it = 0;
int64_t done = 0;
while ((done == 0 && it < 60)) {
double y = x;
double d = 1.0;
int64_t i = (p - 1);
while (i >= 0) {
double r = sqrt(((y * y) + 4.0));
double gp = 0.0;
double gpd = 0.0;
if (y >= 0.0) {
gp = ((y + r) * 0.5);
gpd = ((r + y) / (2.0 * r));
} else {
gp = (2.0 / (r - y));
gpd = (2.0 / (r * (r - y)));
}
if ((FLOW_CHECKED_SHR((m), (i)) & 1) == 1) {
y = gp;
d = (d * gpd);
} else {
y = ((-1.0) / gp);
d = ((d * gpd) / (gp * gp));
}
i = (i - 1);
}
double nx = (x + ((y - x) / (1.0 - d)));
double diff = (nx - x);
if (diff < 0.0) {
diff = (-diff);
}
double ax = nx;
if (ax < 0.0) {
ax = (-ax);
}
x = nx;
if (diff <= (0.00000000000001 * (1.0 + ax))) {
done = 1;
}
it = (it + 1);
}
double y2 = x;
double mn = x;
double mx = x;
int64_t i2 = (p - 1);
while (i2 >= 0) {
double r2 = sqrt(((y2 * y2) + 4.0));
double gp2 = 0.0;
if (y2 >= 0.0) {
gp2 = ((y2 + r2) * 0.5);
} else {
gp2 = (2.0 / (r2 - y2));
}
if ((FLOW_CHECKED_SHR((m), (i2)) & 1) == 1) {
y2 = gp2;
} else {
y2 = ((-1.0) / gp2);
}
if (y2 < mn) {
mn = y2;
}
if (y2 > mx) {
mx = y2;
}
i2 = (i2 - 1);
}
double contrib = (((double)(p)) * (mx - mn));
double t1 = (contrib - comp);
double t2 = (total + t1);
comp = ((t2 - total) - t1);
total = t2;
}
m = (m + 1);
}
p = (p + 1);
}
printf("%.4f\n", total);
return 0;
}
Generated MLIR
module {
llvm.func @printf(!llvm.ptr, ...) -> i32
llvm.mlir.global internal constant @str_0("%.4f\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
func.func private @sqrt(f64) -> f64
func.func @main() -> i32 {
%0 = arith.constant 25 : i32
%1 = arith.extsi %0 : i32 to i64
%2 = arith.constant 0.0 : f32
%3 = arith.extf %2 : f32 to f64
%4 = llvm.mlir.constant(1 : i64) : i64
%5 = llvm.alloca %4 x f64 : (i64) -> !llvm.ptr
llvm.store %3, %5 : f64, !llvm.ptr
%6 = arith.constant 0.0 : f32
%7 = arith.extf %6 : f32 to f64
%8 = llvm.mlir.constant(1 : i64) : i64
%9 = llvm.alloca %8 x f64 : (i64) -> !llvm.ptr
llvm.store %7, %9 : f64, !llvm.ptr
%10 = arith.constant 2 : i32
%11 = arith.extsi %10 : i32 to i64
%12 = llvm.mlir.constant(1 : i64) : i64
%13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
llvm.store %11, %13 : i64, !llvm.ptr
cf.br ^bb0
^bb0:
%14 = llvm.load %13 : !llvm.ptr -> i64
%15 = arith.cmpi sle, %14, %1 : i64
cf.cond_br %15, ^bb1, ^bb2
^bb1:
%16 = arith.constant 1 : i32
%17 = arith.extsi %16 : i32 to i64
%18 = llvm.mlir.constant(1 : i64) : i64
%19 = llvm.alloca %18 x i64 : (i64) -> !llvm.ptr
llvm.store %17, %19 : i64, !llvm.ptr
%20 = arith.constant 0 : i32
%21 = arith.extsi %20 : i32 to i64
%22 = llvm.mlir.constant(1 : i64) : i64
%23 = llvm.alloca %22 x i64 : (i64) -> !llvm.ptr
llvm.store %21, %23 : i64, !llvm.ptr
cf.br ^bb3
^bb3:
%24 = llvm.load %23 : !llvm.ptr -> i64
%25 = llvm.load %13 : !llvm.ptr -> i64
%26 = arith.cmpi slt, %24, %25 : i64
cf.cond_br %26, ^bb4, ^bb5
^bb4:
%27 = llvm.load %19 : !llvm.ptr -> i64
%28 = arith.constant 2 : i32
%30 = arith.extsi %28 : i32 to i64
%29 = arith.muli %27, %30 : i64
llvm.store %29, %19 : i64, !llvm.ptr
%31 = llvm.load %23 : !llvm.ptr -> i64
%32 = arith.constant 1 : i32
%34 = arith.extsi %32 : i32 to i64
%33 = arith.addi %31, %34 : i64
llvm.store %33, %23 : i64, !llvm.ptr
cf.br ^bb3
^bb5:
%35 = arith.constant 1 : i32
%36 = arith.extsi %35 : i32 to i64
%37 = llvm.mlir.constant(1 : i64) : i64
%38 = llvm.alloca %37 x i64 : (i64) -> !llvm.ptr
llvm.store %36, %38 : i64, !llvm.ptr
cf.br ^bb6
^bb6:
%39 = llvm.load %38 : !llvm.ptr -> i64
%40 = llvm.load %19 : !llvm.ptr -> i64
%41 = arith.constant 1 : i32
%43 = arith.extsi %41 : i32 to i64
%42 = arith.subi %40, %43 : i64
%44 = arith.cmpi slt, %39, %42 : i64
cf.cond_br %44, ^bb7, ^bb8
^bb7:
%45 = arith.constant 1 : i32
%46 = arith.extsi %45 : i32 to i64
%47 = llvm.mlir.constant(1 : i64) : i64
%48 = llvm.alloca %47 x i64 : (i64) -> !llvm.ptr
llvm.store %46, %48 : i64, !llvm.ptr
%49 = arith.constant 1 : i32
%50 = arith.extsi %49 : i32 to i64
%51 = llvm.mlir.constant(1 : i64) : i64
%52 = llvm.alloca %51 x i64 : (i64) -> !llvm.ptr
llvm.store %50, %52 : i64, !llvm.ptr
%53 = arith.constant 2 : i32
%54 = arith.extsi %53 : i32 to i64
%55 = llvm.mlir.constant(1 : i64) : i64
%56 = llvm.alloca %55 x i64 : (i64) -> !llvm.ptr
llvm.store %54, %56 : i64, !llvm.ptr
cf.br ^bb9
^bb9:
%57 = llvm.load %52 : !llvm.ptr -> i64
%58 = llvm.load %13 : !llvm.ptr -> i64
%59 = arith.cmpi slt, %57, %58 : i64
%60 = scf.if %59 -> (i1) {
%61 = llvm.load %48 : !llvm.ptr -> i64
%62 = arith.constant 1 : i32
%64 = arith.extsi %62 : i32 to i64
%63 = arith.cmpi eq, %61, %64 : i64
scf.yield %63 : i1
} else {
%65 = arith.constant false
scf.yield %65 : i1
}
cf.cond_br %60, ^bb10, ^bb11
^bb10:
%66 = llvm.load %38 : !llvm.ptr -> i64
%67 = llvm.load %52 : !llvm.ptr -> i64
%68 = arith.shrsi %66, %67 : i64
%69 = llvm.load %38 : !llvm.ptr -> i64
%70 = llvm.load %56 : !llvm.ptr -> i64
%71 = arith.remsi %69, %70 : i64
%72 = llvm.load %13 : !llvm.ptr -> i64
%73 = llvm.load %52 : !llvm.ptr -> i64
%74 = arith.subi %72, %73 : i64
%75 = arith.shli %71, %74 : i64
%76 = arith.ori %68, %75 : i64
%77 = llvm.load %38 : !llvm.ptr -> i64
%78 = arith.cmpi sle, %76, %77 : i64
cf.cond_br %78, ^bb12, ^bb13
^bb12:
%79 = arith.constant 0 : i32
%80 = arith.extsi %79 : i32 to i64
llvm.store %80, %48 : i64, !llvm.ptr
cf.br ^bb14
^bb13:
cf.br ^bb14
^bb14:
%81 = llvm.load %52 : !llvm.ptr -> i64
%82 = arith.constant 1 : i32
%84 = arith.extsi %82 : i32 to i64
%83 = arith.addi %81, %84 : i64
llvm.store %83, %52 : i64, !llvm.ptr
%85 = llvm.load %56 : !llvm.ptr -> i64
%86 = arith.constant 2 : i32
%88 = arith.extsi %86 : i32 to i64
%87 = arith.muli %85, %88 : i64
llvm.store %87, %56 : i64, !llvm.ptr
cf.br ^bb9
^bb11:
%89 = llvm.load %48 : !llvm.ptr -> i64
%90 = arith.constant 1 : i32
%92 = arith.extsi %90 : i32 to i64
%91 = arith.cmpi eq, %89, %92 : i64
cf.cond_br %91, ^bb15, ^bb16
^bb15:
%93 = arith.constant 0.0 : f32
%94 = arith.extf %93 : f32 to f64
%95 = llvm.mlir.constant(1 : i64) : i64
%96 = llvm.alloca %95 x f64 : (i64) -> !llvm.ptr
llvm.store %94, %96 : f64, !llvm.ptr
%97 = arith.constant 0 : i32
%98 = arith.extsi %97 : i32 to i64
%99 = llvm.mlir.constant(1 : i64) : i64
%100 = llvm.alloca %99 x i64 : (i64) -> !llvm.ptr
llvm.store %98, %100 : i64, !llvm.ptr
cf.br ^bb18
^bb18:
%101 = llvm.load %100 : !llvm.ptr -> i64
%102 = arith.constant 2 : i32
%104 = arith.extsi %102 : i32 to i64
%103 = arith.cmpi slt, %101, %104 : i64
cf.cond_br %103, ^bb19, ^bb20
^bb19:
%105 = llvm.load %96 : !llvm.ptr -> f64
%106 = llvm.mlir.constant(1 : i64) : i64
%107 = llvm.alloca %106 x f64 : (i64) -> !llvm.ptr
llvm.store %105, %107 : f64, !llvm.ptr
%108 = llvm.load %13 : !llvm.ptr -> i64
%109 = arith.constant 1 : i32
%111 = arith.extsi %109 : i32 to i64
%110 = arith.subi %108, %111 : i64
%112 = llvm.mlir.constant(1 : i64) : i64
%113 = llvm.alloca %112 x i64 : (i64) -> !llvm.ptr
llvm.store %110, %113 : i64, !llvm.ptr
cf.br ^bb21
^bb21:
%114 = llvm.load %113 : !llvm.ptr -> i64
%115 = arith.constant 0 : i32
%117 = arith.extsi %115 : i32 to i64
%116 = arith.cmpi sge, %114, %117 : i64
cf.cond_br %116, ^bb22, ^bb23
^bb22:
%118 = llvm.load %107 : !llvm.ptr -> f64
%119 = llvm.load %107 : !llvm.ptr -> f64
%120 = arith.mulf %118, %119 : f64
%121 = arith.constant 4.0 : f32
%123 = arith.extf %121 : f32 to f64
%122 = arith.addf %120, %123 : f64
%124 = math.sqrt %122 : f64
%125 = arith.constant 0.0 : f32
%126 = arith.extf %125 : f32 to f64
%127 = llvm.mlir.constant(1 : i64) : i64
%128 = llvm.alloca %127 x f64 : (i64) -> !llvm.ptr
llvm.store %126, %128 : f64, !llvm.ptr
%129 = llvm.load %107 : !llvm.ptr -> f64
%130 = arith.constant 0.0 : f32
%132 = arith.extf %130 : f32 to f64
%131 = arith.cmpf oge, %129, %132 : f64
cf.cond_br %131, ^bb24, ^bb25
^bb24:
%133 = llvm.load %107 : !llvm.ptr -> f64
%134 = arith.addf %133, %124 : f64
%135 = arith.constant 0.5 : f32
%137 = arith.extf %135 : f32 to f64
%136 = arith.mulf %134, %137 : f64
llvm.store %136, %128 : f64, !llvm.ptr
cf.br ^bb26
^bb25:
%138 = arith.constant 2.0 : f32
%139 = llvm.load %107 : !llvm.ptr -> f64
%140 = arith.subf %124, %139 : f64
%142 = arith.extf %138 : f32 to f64
%141 = arith.divf %142, %140 : f64
llvm.store %141, %128 : f64, !llvm.ptr
cf.br ^bb26
^bb26:
%143 = llvm.load %38 : !llvm.ptr -> i64
%144 = llvm.load %113 : !llvm.ptr -> i64
%145 = arith.shrsi %143, %144 : i64
%146 = arith.constant 1 : i32
%148 = arith.extsi %146 : i32 to i64
%147 = arith.andi %145, %148 : i64
%149 = arith.constant 1 : i32
%151 = arith.extsi %149 : i32 to i64
%150 = arith.cmpi eq, %147, %151 : i64
cf.cond_br %150, ^bb27, ^bb28
^bb27:
%152 = llvm.load %128 : !llvm.ptr -> f64
llvm.store %152, %107 : f64, !llvm.ptr
cf.br ^bb29
^bb28:
%153 = arith.constant 1.0 : f32
%154 = arith.negf %153 : f32
%155 = llvm.load %128 : !llvm.ptr -> f64
%157 = arith.extf %154 : f32 to f64
%156 = arith.divf %157, %155 : f64
llvm.store %156, %107 : f64, !llvm.ptr
cf.br ^bb29
^bb29:
%158 = llvm.load %113 : !llvm.ptr -> i64
%159 = arith.constant 1 : i32
%161 = arith.extsi %159 : i32 to i64
%160 = arith.subi %158, %161 : i64
llvm.store %160, %113 : i64, !llvm.ptr
cf.br ^bb21
^bb23:
%162 = llvm.load %107 : !llvm.ptr -> f64
llvm.store %162, %96 : f64, !llvm.ptr
%163 = llvm.load %100 : !llvm.ptr -> i64
%164 = arith.constant 1 : i32
%166 = arith.extsi %164 : i32 to i64
%165 = arith.addi %163, %166 : i64
llvm.store %165, %100 : i64, !llvm.ptr
cf.br ^bb18
^bb20:
%167 = arith.constant 0 : i32
%168 = arith.extsi %167 : i32 to i64
%169 = llvm.mlir.constant(1 : i64) : i64
%170 = llvm.alloca %169 x i64 : (i64) -> !llvm.ptr
llvm.store %168, %170 : i64, !llvm.ptr
%171 = arith.constant 0 : i32
%172 = arith.extsi %171 : i32 to i64
%173 = llvm.mlir.constant(1 : i64) : i64
%174 = llvm.alloca %173 x i64 : (i64) -> !llvm.ptr
llvm.store %172, %174 : i64, !llvm.ptr
cf.br ^bb30
^bb30:
%175 = llvm.load %174 : !llvm.ptr -> i64
%176 = arith.constant 0 : i32
%178 = arith.extsi %176 : i32 to i64
%177 = arith.cmpi eq, %175, %178 : i64
%179 = scf.if %177 -> (i1) {
%180 = llvm.load %170 : !llvm.ptr -> i64
%181 = arith.constant 60 : i32
%183 = arith.extsi %181 : i32 to i64
%182 = arith.cmpi slt, %180, %183 : i64
scf.yield %182 : i1
} else {
%184 = arith.constant false
scf.yield %184 : i1
}
cf.cond_br %179, ^bb31, ^bb32
^bb31:
%185 = llvm.load %96 : !llvm.ptr -> f64
%186 = llvm.mlir.constant(1 : i64) : i64
%187 = llvm.alloca %186 x f64 : (i64) -> !llvm.ptr
llvm.store %185, %187 : f64, !llvm.ptr
%188 = arith.constant 1.0 : f32
%189 = arith.extf %188 : f32 to f64
%190 = llvm.mlir.constant(1 : i64) : i64
%191 = llvm.alloca %190 x f64 : (i64) -> !llvm.ptr
llvm.store %189, %191 : f64, !llvm.ptr
%192 = llvm.load %13 : !llvm.ptr -> i64
%193 = arith.constant 1 : i32
%195 = arith.extsi %193 : i32 to i64
%194 = arith.subi %192, %195 : i64
%196 = llvm.mlir.constant(1 : i64) : i64
%197 = llvm.alloca %196 x i64 : (i64) -> !llvm.ptr
llvm.store %194, %197 : i64, !llvm.ptr
cf.br ^bb33
^bb33:
%198 = llvm.load %197 : !llvm.ptr -> i64
%199 = arith.constant 0 : i32
%201 = arith.extsi %199 : i32 to i64
%200 = arith.cmpi sge, %198, %201 : i64
cf.cond_br %200, ^bb34, ^bb35
^bb34:
%202 = llvm.load %187 : !llvm.ptr -> f64
%203 = llvm.load %187 : !llvm.ptr -> f64
%204 = arith.mulf %202, %203 : f64
%205 = arith.constant 4.0 : f32
%207 = arith.extf %205 : f32 to f64
%206 = arith.addf %204, %207 : f64
%208 = math.sqrt %206 : f64
%209 = arith.constant 0.0 : f32
%210 = arith.extf %209 : f32 to f64
%211 = llvm.mlir.constant(1 : i64) : i64
%212 = llvm.alloca %211 x f64 : (i64) -> !llvm.ptr
llvm.store %210, %212 : f64, !llvm.ptr
%213 = arith.constant 0.0 : f32
%214 = arith.extf %213 : f32 to f64
%215 = llvm.mlir.constant(1 : i64) : i64
%216 = llvm.alloca %215 x f64 : (i64) -> !llvm.ptr
llvm.store %214, %216 : f64, !llvm.ptr
%217 = llvm.load %187 : !llvm.ptr -> f64
%218 = arith.constant 0.0 : f32
%220 = arith.extf %218 : f32 to f64
%219 = arith.cmpf oge, %217, %220 : f64
cf.cond_br %219, ^bb36, ^bb37
^bb36:
%221 = llvm.load %187 : !llvm.ptr -> f64
%222 = arith.addf %221, %208 : f64
%223 = arith.constant 0.5 : f32
%225 = arith.extf %223 : f32 to f64
%224 = arith.mulf %222, %225 : f64
llvm.store %224, %212 : f64, !llvm.ptr
%226 = llvm.load %187 : !llvm.ptr -> f64
%227 = arith.addf %208, %226 : f64
%228 = arith.constant 2.0 : f32
%230 = arith.extf %228 : f32 to f64
%229 = arith.mulf %230, %208 : f64
%231 = arith.divf %227, %229 : f64
llvm.store %231, %216 : f64, !llvm.ptr
cf.br ^bb38
^bb37:
%232 = arith.constant 2.0 : f32
%233 = llvm.load %187 : !llvm.ptr -> f64
%234 = arith.subf %208, %233 : f64
%236 = arith.extf %232 : f32 to f64
%235 = arith.divf %236, %234 : f64
llvm.store %235, %212 : f64, !llvm.ptr
%237 = arith.constant 2.0 : f32
%238 = llvm.load %187 : !llvm.ptr -> f64
%239 = arith.subf %208, %238 : f64
%240 = arith.mulf %208, %239 : f64
%242 = arith.extf %237 : f32 to f64
%241 = arith.divf %242, %240 : f64
llvm.store %241, %216 : f64, !llvm.ptr
cf.br ^bb38
^bb38:
%243 = llvm.load %38 : !llvm.ptr -> i64
%244 = llvm.load %197 : !llvm.ptr -> i64
%245 = arith.shrsi %243, %244 : i64
%246 = arith.constant 1 : i32
%248 = arith.extsi %246 : i32 to i64
%247 = arith.andi %245, %248 : i64
%249 = arith.constant 1 : i32
%251 = arith.extsi %249 : i32 to i64
%250 = arith.cmpi eq, %247, %251 : i64
cf.cond_br %250, ^bb39, ^bb40
^bb39:
%252 = llvm.load %212 : !llvm.ptr -> f64
llvm.store %252, %187 : f64, !llvm.ptr
%253 = llvm.load %191 : !llvm.ptr -> f64
%254 = llvm.load %216 : !llvm.ptr -> f64
%255 = arith.mulf %253, %254 : f64
llvm.store %255, %191 : f64, !llvm.ptr
cf.br ^bb41
^bb40:
%256 = arith.constant 1.0 : f32
%257 = arith.negf %256 : f32
%258 = llvm.load %212 : !llvm.ptr -> f64
%260 = arith.extf %257 : f32 to f64
%259 = arith.divf %260, %258 : f64
llvm.store %259, %187 : f64, !llvm.ptr
%261 = llvm.load %191 : !llvm.ptr -> f64
%262 = llvm.load %216 : !llvm.ptr -> f64
%263 = arith.mulf %261, %262 : f64
%264 = llvm.load %212 : !llvm.ptr -> f64
%265 = llvm.load %212 : !llvm.ptr -> f64
%266 = arith.mulf %264, %265 : f64
%267 = arith.divf %263, %266 : f64
llvm.store %267, %191 : f64, !llvm.ptr
cf.br ^bb41
^bb41:
%268 = llvm.load %197 : !llvm.ptr -> i64
%269 = arith.constant 1 : i32
%271 = arith.extsi %269 : i32 to i64
%270 = arith.subi %268, %271 : i64
llvm.store %270, %197 : i64, !llvm.ptr
cf.br ^bb33
^bb35:
%272 = llvm.load %96 : !llvm.ptr -> f64
%273 = llvm.load %187 : !llvm.ptr -> f64
%274 = llvm.load %96 : !llvm.ptr -> f64
%275 = arith.subf %273, %274 : f64
%276 = arith.constant 1.0 : f32
%277 = llvm.load %191 : !llvm.ptr -> f64
%279 = arith.extf %276 : f32 to f64
%278 = arith.subf %279, %277 : f64
%280 = arith.divf %275, %278 : f64
%281 = arith.addf %272, %280 : f64
%282 = llvm.load %96 : !llvm.ptr -> f64
%283 = arith.subf %281, %282 : f64
%284 = llvm.mlir.constant(1 : i64) : i64
%285 = llvm.alloca %284 x f64 : (i64) -> !llvm.ptr
llvm.store %283, %285 : f64, !llvm.ptr
%286 = llvm.load %285 : !llvm.ptr -> f64
%287 = arith.constant 0.0 : f32
%289 = arith.extf %287 : f32 to f64
%288 = arith.cmpf olt, %286, %289 : f64
cf.cond_br %288, ^bb42, ^bb43
^bb42:
%290 = llvm.load %285 : !llvm.ptr -> f64
%291 = arith.negf %290 : f64
llvm.store %291, %285 : f64, !llvm.ptr
cf.br ^bb44
^bb43:
cf.br ^bb44
^bb44:
%292 = llvm.mlir.constant(1 : i64) : i64
%293 = llvm.alloca %292 x f64 : (i64) -> !llvm.ptr
llvm.store %281, %293 : f64, !llvm.ptr
%294 = llvm.load %293 : !llvm.ptr -> f64
%295 = arith.constant 0.0 : f32
%297 = arith.extf %295 : f32 to f64
%296 = arith.cmpf olt, %294, %297 : f64
cf.cond_br %296, ^bb45, ^bb46
^bb45:
%298 = llvm.load %293 : !llvm.ptr -> f64
%299 = arith.negf %298 : f64
llvm.store %299, %293 : f64, !llvm.ptr
cf.br ^bb47
^bb46:
cf.br ^bb47
^bb47:
llvm.store %281, %96 : f64, !llvm.ptr
%300 = llvm.load %285 : !llvm.ptr -> f64
%301 = arith.constant 0.00000000000001 : f32
%302 = arith.constant 1.0 : f32
%303 = llvm.load %293 : !llvm.ptr -> f64
%305 = arith.extf %302 : f32 to f64
%304 = arith.addf %305, %303 : f64
%307 = arith.extf %301 : f32 to f64
%306 = arith.mulf %307, %304 : f64
%308 = arith.cmpf ole, %300, %306 : f64
cf.cond_br %308, ^bb48, ^bb49
^bb48:
%309 = arith.constant 1 : i32
%310 = arith.extsi %309 : i32 to i64
llvm.store %310, %174 : i64, !llvm.ptr
cf.br ^bb50
^bb49:
cf.br ^bb50
^bb50:
%311 = llvm.load %170 : !llvm.ptr -> i64
%312 = arith.constant 1 : i32
%314 = arith.extsi %312 : i32 to i64
%313 = arith.addi %311, %314 : i64
llvm.store %313, %170 : i64, !llvm.ptr
cf.br ^bb30
^bb32:
%315 = llvm.load %96 : !llvm.ptr -> f64
%316 = llvm.mlir.constant(1 : i64) : i64
%317 = llvm.alloca %316 x f64 : (i64) -> !llvm.ptr
llvm.store %315, %317 : f64, !llvm.ptr
%318 = llvm.load %96 : !llvm.ptr -> f64
%319 = llvm.mlir.constant(1 : i64) : i64
%320 = llvm.alloca %319 x f64 : (i64) -> !llvm.ptr
llvm.store %318, %320 : f64, !llvm.ptr
%321 = llvm.load %96 : !llvm.ptr -> f64
%322 = llvm.mlir.constant(1 : i64) : i64
%323 = llvm.alloca %322 x f64 : (i64) -> !llvm.ptr
llvm.store %321, %323 : f64, !llvm.ptr
%324 = llvm.load %13 : !llvm.ptr -> i64
%325 = arith.constant 1 : i32
%327 = arith.extsi %325 : i32 to i64
%326 = arith.subi %324, %327 : i64
%328 = llvm.mlir.constant(1 : i64) : i64
%329 = llvm.alloca %328 x i64 : (i64) -> !llvm.ptr
llvm.store %326, %329 : i64, !llvm.ptr
cf.br ^bb51
^bb51:
%330 = llvm.load %329 : !llvm.ptr -> i64
%331 = arith.constant 0 : i32
%333 = arith.extsi %331 : i32 to i64
%332 = arith.cmpi sge, %330, %333 : i64
cf.cond_br %332, ^bb52, ^bb53
^bb52:
%334 = llvm.load %317 : !llvm.ptr -> f64
%335 = llvm.load %317 : !llvm.ptr -> f64
%336 = arith.mulf %334, %335 : f64
%337 = arith.constant 4.0 : f32
%339 = arith.extf %337 : f32 to f64
%338 = arith.addf %336, %339 : f64
%340 = math.sqrt %338 : f64
%341 = arith.constant 0.0 : f32
%342 = arith.extf %341 : f32 to f64
%343 = llvm.mlir.constant(1 : i64) : i64
%344 = llvm.alloca %343 x f64 : (i64) -> !llvm.ptr
llvm.store %342, %344 : f64, !llvm.ptr
%345 = llvm.load %317 : !llvm.ptr -> f64
%346 = arith.constant 0.0 : f32
%348 = arith.extf %346 : f32 to f64
%347 = arith.cmpf oge, %345, %348 : f64
cf.cond_br %347, ^bb54, ^bb55
^bb54:
%349 = llvm.load %317 : !llvm.ptr -> f64
%350 = arith.addf %349, %340 : f64
%351 = arith.constant 0.5 : f32
%353 = arith.extf %351 : f32 to f64
%352 = arith.mulf %350, %353 : f64
llvm.store %352, %344 : f64, !llvm.ptr
cf.br ^bb56
^bb55:
%354 = arith.constant 2.0 : f32
%355 = llvm.load %317 : !llvm.ptr -> f64
%356 = arith.subf %340, %355 : f64
%358 = arith.extf %354 : f32 to f64
%357 = arith.divf %358, %356 : f64
llvm.store %357, %344 : f64, !llvm.ptr
cf.br ^bb56
^bb56:
%359 = llvm.load %38 : !llvm.ptr -> i64
%360 = llvm.load %329 : !llvm.ptr -> i64
%361 = arith.shrsi %359, %360 : i64
%362 = arith.constant 1 : i32
%364 = arith.extsi %362 : i32 to i64
%363 = arith.andi %361, %364 : i64
%365 = arith.constant 1 : i32
%367 = arith.extsi %365 : i32 to i64
%366 = arith.cmpi eq, %363, %367 : i64
cf.cond_br %366, ^bb57, ^bb58
^bb57:
%368 = llvm.load %344 : !llvm.ptr -> f64
llvm.store %368, %317 : f64, !llvm.ptr
cf.br ^bb59
^bb58:
%369 = arith.constant 1.0 : f32
%370 = arith.negf %369 : f32
%371 = llvm.load %344 : !llvm.ptr -> f64
%373 = arith.extf %370 : f32 to f64
%372 = arith.divf %373, %371 : f64
llvm.store %372, %317 : f64, !llvm.ptr
cf.br ^bb59
^bb59:
%374 = llvm.load %317 : !llvm.ptr -> f64
%375 = llvm.load %320 : !llvm.ptr -> f64
%376 = arith.cmpf olt, %374, %375 : f64
cf.cond_br %376, ^bb60, ^bb61
^bb60:
%377 = llvm.load %317 : !llvm.ptr -> f64
llvm.store %377, %320 : f64, !llvm.ptr
cf.br ^bb62
^bb61:
cf.br ^bb62
^bb62:
%378 = llvm.load %317 : !llvm.ptr -> f64
%379 = llvm.load %323 : !llvm.ptr -> f64
%380 = arith.cmpf ogt, %378, %379 : f64
cf.cond_br %380, ^bb63, ^bb64
^bb63:
%381 = llvm.load %317 : !llvm.ptr -> f64
llvm.store %381, %323 : f64, !llvm.ptr
cf.br ^bb65
^bb64:
cf.br ^bb65
^bb65:
%382 = llvm.load %329 : !llvm.ptr -> i64
%383 = arith.constant 1 : i32
%385 = arith.extsi %383 : i32 to i64
%384 = arith.subi %382, %385 : i64
llvm.store %384, %329 : i64, !llvm.ptr
cf.br ^bb51
^bb53:
%386 = llvm.load %13 : !llvm.ptr -> i64
%387 = arith.sitofp %386 : i64 to f64
%388 = llvm.load %323 : !llvm.ptr -> f64
%389 = llvm.load %320 : !llvm.ptr -> f64
%390 = arith.subf %388, %389 : f64
%391 = arith.mulf %387, %390 : f64
%392 = llvm.load %9 : !llvm.ptr -> f64
%393 = arith.subf %391, %392 : f64
%394 = llvm.load %5 : !llvm.ptr -> f64
%395 = arith.addf %394, %393 : f64
%396 = llvm.load %5 : !llvm.ptr -> f64
%397 = arith.subf %395, %396 : f64
%398 = arith.subf %397, %393 : f64
llvm.store %398, %9 : f64, !llvm.ptr
llvm.store %395, %5 : f64, !llvm.ptr
cf.br ^bb17
^bb16:
cf.br ^bb17
^bb17:
%399 = llvm.load %38 : !llvm.ptr -> i64
%400 = arith.constant 1 : i32
%402 = arith.extsi %400 : i32 to i64
%401 = arith.addi %399, %402 : i64
llvm.store %401, %38 : i64, !llvm.ptr
cf.br ^bb6
^bb8:
%403 = llvm.load %13 : !llvm.ptr -> i64
%404 = arith.constant 1 : i32
%406 = arith.extsi %404 : i32 to i64
%405 = arith.addi %403, %406 : i64
llvm.store %405, %13 : i64, !llvm.ptr
cf.br ^bb0
^bb2:
%407 = llvm.mlir.addressof @str_0 : !llvm.ptr
%408 = llvm.load %5 : !llvm.ptr -> f64
%409 = llvm.call @printf(%407, %408) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
%410 = arith.constant 0 : i32
func.return %410 : i32
}
}