← All problems Problem 999
Rescaled elliptic divisibility sequence: a_n mod 1234567891. Uses the doubling recurrence for the EDS block (W_{n-3}..W_{n+4}) in O(log n), then rescales by INV_TWO^(n^2/4).
View problem on Project Euler
Performance comparison
Metric Our solution Best known
Time complexity O(n log n)?Space complexity O(1)?Approach Flow solution Not curated Verdict Unknown
Flow source
# Project Euler 999
# Rescaled elliptic divisibility sequence: a_n mod 1234567891.
# Uses the doubling recurrence for the EDS block (W_{n-3}..W_{n+4})
# in O(log n), then rescales by INV_TWO^(n^2/4).
extern {
function malloc(n: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1234567891
const INV_TWO: i64 = 617283946
function norm(x: i64) -> i64 {
let mut r: i64 = x % MOD
if r < 0 { r = r + MOD }
return r
}
function mod_mul(a: i64, b: i64) -> i64 {
return ((norm(a) as i128) * norm(b) % MOD) as i64
}
function mod_sub(a: i64, b: i64) -> i64 {
let mut r: i64 = norm(a) - norm(b)
if r < 0 { r = r + MOD }
return r
}
function mod_pow_generic(base: i64, exp: i128) -> i64 {
let mut b: i64 = norm(base)
let mut result: i64 = 1
let mut e: i128 = exp
while e > 0 {
if (e & 1) != 0 {
result = mod_mul(result, b)
}
b = mod_mul(b, b)
e = e >> 1
}
return result
}
function small_w(index: i64) -> i64 {
if index < 0 { return norm(-small_w(-index)) }
if index == 0 { return norm(0) }
if index == 1 { return norm(1) }
if index == 2 { return norm(2) }
if index == 3 { return norm(-4) }
if index == 4 { return norm(-32) }
if index == 5 { return norm(-192) }
if index == 6 { return norm(3584) }
if index == 7 { return norm(77824) }
return norm(262144)
}
# W_{2*index - 1} from terms around W_index.
function odd_val(s: ptr<i64>, start: i64, index: i64) -> i64 {
let a: i64 = s[index + 1 - start]
let b: i64 = mod_pow_generic(s[index - 1 - start], 3 as i128)
let c: i64 = s[index - 2 - start]
let d: i64 = mod_pow_generic(s[index - start], 3 as i128)
return mod_sub(mod_mul(a, b), mod_mul(c, d))
}
# W_{2*index}; division is only by the fixed W_2 = 2.
function even_val(s: ptr<i64>, start: i64, index: i64) -> i64 {
let a: i64 = s[index - start]
let p1: i64 = mod_pow_generic(s[index - 1 - start], 2 as i128)
let c2: i64 = s[index + 2 - start]
let p2: i64 = mod_pow_generic(s[index + 1 - start], 2 as i128)
let e2: i64 = s[index - 2 - start]
let inner: i64 = mod_sub(mod_mul(c2, p1), mod_mul(e2, p2))
return mod_mul(mod_mul(a, INV_TWO), inner)
}
# Return (W_{n-3}, ..., W_{n+4}) mod MOD as a malloc'd ptr<i64> of size 8.
function eds_block(n: i64) -> ptr<i64> {
let r: ptr<i64> = malloc(64) as ptr<i64>
if n <= 4 {
for i in 0..8 {
r[i] = small_w(n - 3 + (i as i64))
}
return r
}
let middle: i64 = n / 2
let s: ptr<i64> = eds_block(middle)
let start: i64 = middle - 3
if n % 2 == 0 {
r[0] = odd_val(s, start, middle - 1)
r[1] = even_val(s, start, middle - 1)
r[2] = odd_val(s, start, middle)
r[3] = even_val(s, start, middle)
r[4] = odd_val(s, start, middle + 1)
r[5] = even_val(s, start, middle + 1)
r[6] = odd_val(s, start, middle + 2)
r[7] = even_val(s, start, middle + 2)
} else {
r[0] = even_val(s, start, middle - 1)
r[1] = odd_val(s, start, middle)
r[2] = even_val(s, start, middle)
r[3] = odd_val(s, start, middle + 1)
r[4] = even_val(s, start, middle + 1)
r[5] = odd_val(s, start, middle + 2)
r[6] = even_val(s, start, middle + 2)
r[7] = odd_val(s, start, middle + 3)
}
free(s as ptr<void>)
return r
}
function w_mod(n: i64) -> i64 {
if n < 0 { return norm(-w_mod(-n)) }
let blk: ptr<i64> = eds_block(n)
let result: i64 = blk[3]
free(blk as ptr<void>)
return result
}
function a_mod(n: i64) -> i64 {
let rem: i64 = n % 4
let mut sign: i64 = -1
if rem == 1 || rem == 2 { sign = 1 }
let nn: i128 = (n as i128) * (n as i128)
let exp: i128 = nn / 4
let inverse_scale: i64 = mod_pow_generic(INV_TWO, exp)
let w: i64 = w_mod(n)
let sw: i64 = norm(sign * w)
return mod_mul(sw, inverse_scale)
}
function main() -> i32 {
let result: i64 = a_mod(1000000000000000003)
printf("%lld\n", result)
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 norm_i64(int64_t x);
int64_t mod_mul_i64_i64(int64_t a, int64_t b);
int64_t mod_sub_i64_i64(int64_t a, int64_t b);
int64_t mod_pow_generic_i64_i128(int64_t base, __int128 exp);
int64_t small_w_i64(int64_t index);
int64_t odd_val_ptr_i64_i64_i64(int64_t* s, int64_t start, int64_t index);
int64_t even_val_ptr_i64_i64_i64(int64_t* s, int64_t start, int64_t index);
int64_t* eds_block_i64(int64_t n);
int64_t w_mod_i64(int64_t n);
int64_t a_mod_i64(int64_t n);
int32_t main(void);
static const int64_t MOD = 1234567891;
static const int64_t INV_TWO = 617283946;
int64_t norm_i64(int64_t x) {
int64_t r = FLOW_CHECKED_MOD((x), (MOD));
if (r < 0) {
r = (r + MOD);
}
return r;
}
int64_t mod_mul_i64_i64(int64_t a, int64_t b) {
return ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(norm_i64(a))) * norm_i64(b))), (MOD))));
}
int64_t mod_sub_i64_i64(int64_t a, int64_t b) {
int64_t r = (norm_i64(a) - norm_i64(b));
if (r < 0) {
r = (r + MOD);
}
return r;
}
int64_t mod_pow_generic_i64_i128(int64_t base, __int128 exp) {
int64_t b = norm_i64(base);
int64_t result = 1;
__int128 e = exp;
while (e > 0) {
if ((e & 1) != 0) {
result = mod_mul_i64_i64(result, b);
}
b = mod_mul_i64_i64(b, b);
e = FLOW_CHECKED_SHR((e), (1));
}
return result;
}
int64_t small_w_i64(int64_t index) {
if (index < 0) {
return norm_i64((-small_w_i64((-index))));
}
if (index == 0) {
return norm_i64(0);
}
if (index == 1) {
return norm_i64(1);
}
if (index == 2) {
return norm_i64(2);
}
if (index == 3) {
return norm_i64((-4));
}
if (index == 4) {
return norm_i64((-32));
}
if (index == 5) {
return norm_i64((-192));
}
if (index == 6) {
return norm_i64(3584);
}
if (index == 7) {
return norm_i64(77824);
}
return norm_i64(262144);
}
int64_t odd_val_ptr_i64_i64_i64(int64_t* s, int64_t start, int64_t index) {
int64_t a = s[((index + 1) - start)];
int64_t b = mod_pow_generic_i64_i128(s[((index - 1) - start)], ((__int128)(3)));
int64_t c = s[((index - 2) - start)];
int64_t d = mod_pow_generic_i64_i128(s[(index - start)], ((__int128)(3)));
return mod_sub_i64_i64(mod_mul_i64_i64(a, b), mod_mul_i64_i64(c, d));
}
int64_t even_val_ptr_i64_i64_i64(int64_t* s, int64_t start, int64_t index) {
int64_t a = s[(index - start)];
int64_t p1 = mod_pow_generic_i64_i128(s[((index - 1) - start)], ((__int128)(2)));
int64_t c2 = s[((index + 2) - start)];
int64_t p2 = mod_pow_generic_i64_i128(s[((index + 1) - start)], ((__int128)(2)));
int64_t e2 = s[((index - 2) - start)];
int64_t inner = mod_sub_i64_i64(mod_mul_i64_i64(c2, p1), mod_mul_i64_i64(e2, p2));
return mod_mul_i64_i64(mod_mul_i64_i64(a, INV_TWO), inner);
}
int64_t* eds_block_i64(int64_t n) {
int64_t* r = (int64_t*)(((int64_t*)(malloc(64))));
if (n <= 4) {
int32_t __flow_step_1 = 1;
for (int32_t i = 0; (0 <= 8) ? i < 8 : i > 8; i += (0 <= 8) ? 1 : -1) {
r[i] = small_w_i64(((n - 3) + ((int64_t)(i))));
}
return r;
}
int64_t middle = FLOW_CHECKED_DIV((n), (2));
int64_t* s = (int64_t*)(eds_block_i64(middle));
int64_t start = (middle - 3);
if (FLOW_CHECKED_MOD((n), (2)) == 0) {
r[0] = odd_val_ptr_i64_i64_i64(s, start, (middle - 1));
r[1] = even_val_ptr_i64_i64_i64(s, start, (middle - 1));
r[2] = odd_val_ptr_i64_i64_i64(s, start, middle);
r[3] = even_val_ptr_i64_i64_i64(s, start, middle);
r[4] = odd_val_ptr_i64_i64_i64(s, start, (middle + 1));
r[5] = even_val_ptr_i64_i64_i64(s, start, (middle + 1));
r[6] = odd_val_ptr_i64_i64_i64(s, start, (middle + 2));
r[7] = even_val_ptr_i64_i64_i64(s, start, (middle + 2));
} else {
r[0] = even_val_ptr_i64_i64_i64(s, start, (middle - 1));
r[1] = odd_val_ptr_i64_i64_i64(s, start, middle);
r[2] = even_val_ptr_i64_i64_i64(s, start, middle);
r[3] = odd_val_ptr_i64_i64_i64(s, start, (middle + 1));
r[4] = even_val_ptr_i64_i64_i64(s, start, (middle + 1));
r[5] = odd_val_ptr_i64_i64_i64(s, start, (middle + 2));
r[6] = even_val_ptr_i64_i64_i64(s, start, (middle + 2));
r[7] = odd_val_ptr_i64_i64_i64(s, start, (middle + 3));
}
free(((void*)(s)));
return r;
}
int64_t w_mod_i64(int64_t n) {
if (n < 0) {
return norm_i64((-w_mod_i64((-n))));
}
int64_t* blk = (int64_t*)(eds_block_i64(n));
int64_t result = blk[3];
free(((void*)(blk)));
return result;
}
int64_t a_mod_i64(int64_t n) {
int64_t rem = FLOW_CHECKED_MOD((n), (4));
int64_t sign = (-1);
if ((rem == 1 || rem == 2)) {
sign = 1;
}
__int128 nn = (((__int128)(n)) * ((__int128)(n)));
__int128 exp = FLOW_CHECKED_DIV((nn), (4));
int64_t inverse_scale = mod_pow_generic_i64_i128(INV_TWO, exp);
int64_t w = w_mod_i64(n);
int64_t sw = norm_i64((sign * w));
return mod_mul_i64_i64(sw, inverse_scale);
}
int32_t main(void) {
int64_t result = a_mod_i64(1000000000000000003);
printf("%lld\n", result);
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 @malloc(i64) -> !llvm.ptr
func.func private @free(!llvm.ptr) -> ()
// Constant: MOD
llvm.mlir.global internal constant @MOD(1234567891 : i64) : i64
// Constant: INV_TWO
llvm.mlir.global internal constant @INV_TWO(617283946 : i64) : i64
func.func @norm(%arg0: i64) -> i64 {
%0 = llvm.mlir.addressof @MOD : !llvm.ptr
%1 = llvm.load %0 : !llvm.ptr -> i64
%2 = arith.remsi %arg0, %1 : i64
%3 = llvm.mlir.constant(1 : i64) : i64
%4 = llvm.alloca %3 x i64 : (i64) -> !llvm.ptr
llvm.store %2, %4 : i64, !llvm.ptr
%5 = llvm.load %4 : !llvm.ptr -> i64
%6 = arith.constant 0 : i32
%8 = arith.extsi %6 : i32 to i64
%7 = arith.cmpi slt, %5, %8 : i64
cf.cond_br %7, ^bb0, ^bb1
^bb0:
%9 = llvm.load %4 : !llvm.ptr -> i64
%10 = llvm.mlir.addressof @MOD : !llvm.ptr
%11 = llvm.load %10 : !llvm.ptr -> i64
%12 = arith.addi %9, %11 : i64
llvm.store %12, %4 : i64, !llvm.ptr
cf.br ^bb2
^bb1:
cf.br ^bb2
^bb2:
%13 = llvm.load %4 : !llvm.ptr -> i64
func.return %13 : i64
}
func.func @mod_mul(%arg0: i64, %arg1: i64) -> i64 {
%14 = func.call @norm(%arg0) : (i64) -> i64
%15 = arith.extsi %14 : i64 to i128
%16 = func.call @norm(%arg1) : (i64) -> i64
%18 = arith.trunci %15 : i128 to i64
%17 = arith.muli %18, %16 : i64
%19 = llvm.mlir.addressof @MOD : !llvm.ptr
%20 = llvm.load %19 : !llvm.ptr -> i64
%21 = arith.remsi %17, %20 : i64
func.return %21 : i64
}
func.func @mod_sub(%arg0: i64, %arg1: i64) -> i64 {
%22 = func.call @norm(%arg0) : (i64) -> i64
%23 = func.call @norm(%arg1) : (i64) -> i64
%24 = arith.subi %22, %23 : i64
%25 = llvm.mlir.constant(1 : i64) : i64
%26 = llvm.alloca %25 x i64 : (i64) -> !llvm.ptr
llvm.store %24, %26 : i64, !llvm.ptr
%27 = llvm.load %26 : !llvm.ptr -> i64
%28 = arith.constant 0 : i32
%30 = arith.extsi %28 : i32 to i64
%29 = arith.cmpi slt, %27, %30 : i64
cf.cond_br %29, ^bb3, ^bb4
^bb3:
%31 = llvm.load %26 : !llvm.ptr -> i64
%32 = llvm.mlir.addressof @MOD : !llvm.ptr
%33 = llvm.load %32 : !llvm.ptr -> i64
%34 = arith.addi %31, %33 : i64
llvm.store %34, %26 : i64, !llvm.ptr
cf.br ^bb5
^bb4:
cf.br ^bb5
^bb5:
%35 = llvm.load %26 : !llvm.ptr -> i64
func.return %35 : i64
}
func.func @mod_pow_generic(%arg0: i64, %arg1: i128) -> i64 {
%36 = func.call @norm(%arg0) : (i64) -> i64
%37 = llvm.mlir.constant(1 : i64) : i64
%38 = llvm.alloca %37 x i64 : (i64) -> !llvm.ptr
llvm.store %36, %38 : i64, !llvm.ptr
%39 = arith.constant 1 : i32
%40 = arith.extsi %39 : i32 to i64
%41 = llvm.mlir.constant(1 : i64) : i64
%42 = llvm.alloca %41 x i64 : (i64) -> !llvm.ptr
llvm.store %40, %42 : i64, !llvm.ptr
%43 = llvm.mlir.constant(1 : i64) : i64
%44 = llvm.alloca %43 x i128 : (i64) -> !llvm.ptr
llvm.store %arg1, %44 : i128, !llvm.ptr
cf.br ^bb6
^bb6:
%45 = llvm.load %44 : !llvm.ptr -> i128
%46 = arith.constant 0 : i32
%48 = arith.trunci %45 : i128 to i64
%49 = arith.extsi %46 : i32 to i64
%47 = arith.cmpi sgt, %48, %49 : i64
cf.cond_br %47, ^bb7, ^bb8
^bb7:
%50 = llvm.load %44 : !llvm.ptr -> i128
%51 = arith.constant 1 : i32
%53 = arith.trunci %50 : i128 to i64
%54 = arith.extsi %51 : i32 to i64
%52 = arith.andi %53, %54 : i64
%55 = arith.constant 0 : i32
%57 = arith.extsi %55 : i32 to i64
%56 = arith.cmpi ne, %52, %57 : i64
cf.cond_br %56, ^bb9, ^bb10
^bb9:
%59 = llvm.load %42 : !llvm.ptr -> i64
%60 = llvm.load %38 : !llvm.ptr -> i64
%58 = func.call @mod_mul(%59, %60) : (i64, i64) -> i64
llvm.store %58, %42 : i64, !llvm.ptr
cf.br ^bb11
^bb10:
cf.br ^bb11
^bb11:
%62 = llvm.load %38 : !llvm.ptr -> i64
%63 = llvm.load %38 : !llvm.ptr -> i64
%61 = func.call @mod_mul(%62, %63) : (i64, i64) -> i64
llvm.store %61, %38 : i64, !llvm.ptr
%64 = llvm.load %44 : !llvm.ptr -> i128
%65 = arith.constant 1 : i32
%67 = arith.trunci %64 : i128 to i64
%68 = arith.extsi %65 : i32 to i64
%66 = arith.shrsi %67, %68 : i64
%69 = arith.extsi %66 : i64 to i128
llvm.store %69, %44 : i128, !llvm.ptr
cf.br ^bb6
^bb8:
%70 = llvm.load %42 : !llvm.ptr -> i64
func.return %70 : i64
}
func.func @small_w(%arg0: i64) -> i64 {
%71 = arith.constant 0 : i32
%73 = arith.extsi %71 : i32 to i64
%72 = arith.cmpi slt, %arg0, %73 : i64
cf.cond_br %72, ^bb12, ^bb13
^bb12:
%77 = arith.constant 0 : i64
%76 = arith.subi %77, %arg0 : i64
%75 = func.call @small_w(%76) : (i64) -> i64
%79 = arith.constant 0 : i64
%78 = arith.subi %79, %75 : i64
%74 = func.call @norm(%78) : (i64) -> i64
func.return %74 : i64
^bb13:
cf.br ^bb14
^bb14:
%80 = arith.constant 0 : i32
%82 = arith.extsi %80 : i32 to i64
%81 = arith.cmpi eq, %arg0, %82 : i64
cf.cond_br %81, ^bb15, ^bb16
^bb15:
%84 = arith.constant 0 : i32
%85 = arith.extsi %84 : i32 to i64
%83 = func.call @norm(%85) : (i64) -> i64
func.return %83 : i64
^bb16:
cf.br ^bb17
^bb17:
%86 = arith.constant 1 : i32
%88 = arith.extsi %86 : i32 to i64
%87 = arith.cmpi eq, %arg0, %88 : i64
cf.cond_br %87, ^bb18, ^bb19
^bb18:
%90 = arith.constant 1 : i32
%91 = arith.extsi %90 : i32 to i64
%89 = func.call @norm(%91) : (i64) -> i64
func.return %89 : i64
^bb19:
cf.br ^bb20
^bb20:
%92 = arith.constant 2 : i32
%94 = arith.extsi %92 : i32 to i64
%93 = arith.cmpi eq, %arg0, %94 : i64
cf.cond_br %93, ^bb21, ^bb22
^bb21:
%96 = arith.constant 2 : i32
%97 = arith.extsi %96 : i32 to i64
%95 = func.call @norm(%97) : (i64) -> i64
func.return %95 : i64
^bb22:
cf.br ^bb23
^bb23:
%98 = arith.constant 3 : i32
%100 = arith.extsi %98 : i32 to i64
%99 = arith.cmpi eq, %arg0, %100 : i64
cf.cond_br %99, ^bb24, ^bb25
^bb24:
%102 = arith.constant 4 : i32
%104 = arith.constant 0 : i32
%103 = arith.subi %104, %102 : i32
%105 = arith.extsi %103 : i32 to i64
%101 = func.call @norm(%105) : (i64) -> i64
func.return %101 : i64
^bb25:
cf.br ^bb26
^bb26:
%106 = arith.constant 4 : i32
%108 = arith.extsi %106 : i32 to i64
%107 = arith.cmpi eq, %arg0, %108 : i64
cf.cond_br %107, ^bb27, ^bb28
^bb27:
%110 = arith.constant 32 : i32
%112 = arith.constant 0 : i32
%111 = arith.subi %112, %110 : i32
%113 = arith.extsi %111 : i32 to i64
%109 = func.call @norm(%113) : (i64) -> i64
func.return %109 : i64
^bb28:
cf.br ^bb29
^bb29:
%114 = arith.constant 5 : i32
%116 = arith.extsi %114 : i32 to i64
%115 = arith.cmpi eq, %arg0, %116 : i64
cf.cond_br %115, ^bb30, ^bb31
^bb30:
%118 = arith.constant 192 : i32
%120 = arith.constant 0 : i32
%119 = arith.subi %120, %118 : i32
%121 = arith.extsi %119 : i32 to i64
%117 = func.call @norm(%121) : (i64) -> i64
func.return %117 : i64
^bb31:
cf.br ^bb32
^bb32:
%122 = arith.constant 6 : i32
%124 = arith.extsi %122 : i32 to i64
%123 = arith.cmpi eq, %arg0, %124 : i64
cf.cond_br %123, ^bb33, ^bb34
^bb33:
%126 = arith.constant 3584 : i32
%127 = arith.extsi %126 : i32 to i64
%125 = func.call @norm(%127) : (i64) -> i64
func.return %125 : i64
^bb34:
cf.br ^bb35
^bb35:
%128 = arith.constant 7 : i32
%130 = arith.extsi %128 : i32 to i64
%129 = arith.cmpi eq, %arg0, %130 : i64
cf.cond_br %129, ^bb36, ^bb37
^bb36:
%132 = arith.constant 77824 : i32
%133 = arith.extsi %132 : i32 to i64
%131 = func.call @norm(%133) : (i64) -> i64
func.return %131 : i64
^bb37:
cf.br ^bb38
^bb38:
%135 = arith.constant 262144 : i32
%136 = arith.extsi %135 : i32 to i64
%134 = func.call @norm(%136) : (i64) -> i64
func.return %134 : i64
}
func.func @odd_val(%arg0: !llvm.ptr, %arg1: i64, %arg2: i64) -> i64 {
%138 = arith.constant 1 : i32
%140 = arith.extsi %138 : i32 to i64
%139 = arith.addi %arg2, %140 : i64
%141 = arith.subi %139, %arg1 : i64
%142 = llvm.getelementptr %arg0[%141] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%137 = llvm.load %142 : !llvm.ptr -> i64
%145 = arith.constant 1 : i32
%147 = arith.extsi %145 : i32 to i64
%146 = arith.subi %arg2, %147 : i64
%148 = arith.subi %146, %arg1 : i64
%149 = llvm.getelementptr %arg0[%148] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%144 = llvm.load %149 : !llvm.ptr -> i64
%150 = arith.constant 3 : i32
%151 = arith.extsi %150 : i32 to i128
%143 = func.call @mod_pow_generic(%144, %151) : (i64, i128) -> i64
%153 = arith.constant 2 : i32
%155 = arith.extsi %153 : i32 to i64
%154 = arith.subi %arg2, %155 : i64
%156 = arith.subi %154, %arg1 : i64
%157 = llvm.getelementptr %arg0[%156] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%152 = llvm.load %157 : !llvm.ptr -> i64
%160 = arith.subi %arg2, %arg1 : i64
%161 = llvm.getelementptr %arg0[%160] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%159 = llvm.load %161 : !llvm.ptr -> i64
%162 = arith.constant 3 : i32
%163 = arith.extsi %162 : i32 to i128
%158 = func.call @mod_pow_generic(%159, %163) : (i64, i128) -> i64
%165 = func.call @mod_mul(%137, %143) : (i64, i64) -> i64
%166 = func.call @mod_mul(%152, %158) : (i64, i64) -> i64
%164 = func.call @mod_sub(%165, %166) : (i64, i64) -> i64
func.return %164 : i64
}
func.func @even_val(%arg0: !llvm.ptr, %arg1: i64, %arg2: i64) -> i64 {
%168 = arith.subi %arg2, %arg1 : i64
%169 = llvm.getelementptr %arg0[%168] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%167 = llvm.load %169 : !llvm.ptr -> i64
%172 = arith.constant 1 : i32
%174 = arith.extsi %172 : i32 to i64
%173 = arith.subi %arg2, %174 : i64
%175 = arith.subi %173, %arg1 : i64
%176 = llvm.getelementptr %arg0[%175] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%171 = llvm.load %176 : !llvm.ptr -> i64
%177 = arith.constant 2 : i32
%178 = arith.extsi %177 : i32 to i128
%170 = func.call @mod_pow_generic(%171, %178) : (i64, i128) -> i64
%180 = arith.constant 2 : i32
%182 = arith.extsi %180 : i32 to i64
%181 = arith.addi %arg2, %182 : i64
%183 = arith.subi %181, %arg1 : i64
%184 = llvm.getelementptr %arg0[%183] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%179 = llvm.load %184 : !llvm.ptr -> i64
%187 = arith.constant 1 : i32
%189 = arith.extsi %187 : i32 to i64
%188 = arith.addi %arg2, %189 : i64
%190 = arith.subi %188, %arg1 : i64
%191 = llvm.getelementptr %arg0[%190] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%186 = llvm.load %191 : !llvm.ptr -> i64
%192 = arith.constant 2 : i32
%193 = arith.extsi %192 : i32 to i128
%185 = func.call @mod_pow_generic(%186, %193) : (i64, i128) -> i64
%195 = arith.constant 2 : i32
%197 = arith.extsi %195 : i32 to i64
%196 = arith.subi %arg2, %197 : i64
%198 = arith.subi %196, %arg1 : i64
%199 = llvm.getelementptr %arg0[%198] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%194 = llvm.load %199 : !llvm.ptr -> i64
%201 = func.call @mod_mul(%179, %170) : (i64, i64) -> i64
%202 = func.call @mod_mul(%194, %185) : (i64, i64) -> i64
%200 = func.call @mod_sub(%201, %202) : (i64, i64) -> i64
%205 = llvm.mlir.addressof @INV_TWO : !llvm.ptr
%206 = llvm.load %205 : !llvm.ptr -> i64
%204 = func.call @mod_mul(%167, %206) : (i64, i64) -> i64
%203 = func.call @mod_mul(%204, %200) : (i64, i64) -> i64
func.return %203 : i64
}
func.func @eds_block(%arg0: i64) -> !llvm.ptr {
%208 = arith.constant 64 : i32
%209 = arith.extsi %208 : i32 to i64
%207 = func.call @malloc(%209) : (i64) -> !llvm.ptr
%210 = arith.constant 4 : i32
%212 = arith.extsi %210 : i32 to i64
%211 = arith.cmpi sle, %arg0, %212 : i64
cf.cond_br %211, ^bb39, ^bb40
^bb39:
%213 = arith.constant 0 : i32
%214 = arith.constant 8 : i32
%215 = arith.index_cast %213 : i32 to index
%216 = arith.index_cast %214 : i32 to index
%218 = arith.constant 1 : index
%219 = arith.constant -1 : index
%220 = arith.cmpi sle, %215, %216 : index
%217 = arith.select %220, %218, %219 : index
cf.br ^bb42(%215 : index)
^bb42(%221: index):
%222 = arith.cmpi slt, %221, %216 : index
%223 = arith.cmpi sgt, %221, %216 : index
%224 = arith.select %220, %222, %223 : i1
cf.cond_br %224, ^bb43(%221 : index), ^bb44(%221 : index)
^bb43(%225: index):
%227 = arith.constant 3 : i32
%229 = arith.extsi %227 : i32 to i64
%228 = arith.subi %arg0, %229 : i64
%230 = arith.index_cast %225 : index to i64
%231 = arith.addi %228, %230 : i64
%226 = func.call @small_w(%231) : (i64) -> i64
%232 = arith.index_cast %225 : index to i64
%233 = llvm.getelementptr %207[%232] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %226, %233 : i64, !llvm.ptr
%234 = arith.addi %225, %217 : index
cf.br ^bb42(%234 : index)
^bb44(%235: index):
func.return %207 : !llvm.ptr
^bb40:
cf.br ^bb41
^bb41:
%236 = arith.constant 2 : i32
%238 = arith.extsi %236 : i32 to i64
%237 = arith.divsi %arg0, %238 : i64
%239 = func.call @eds_block(%237) : (i64) -> !llvm.ptr
%240 = arith.constant 3 : i32
%242 = arith.extsi %240 : i32 to i64
%241 = arith.subi %237, %242 : i64
%243 = arith.constant 2 : i32
%245 = arith.extsi %243 : i32 to i64
%244 = arith.remsi %arg0, %245 : i64
%246 = arith.constant 0 : i32
%248 = arith.extsi %246 : i32 to i64
%247 = arith.cmpi eq, %244, %248 : i64
cf.cond_br %247, ^bb45, ^bb46
^bb45:
%250 = arith.constant 1 : i32
%252 = arith.extsi %250 : i32 to i64
%251 = arith.subi %237, %252 : i64
%249 = func.call @odd_val(%239, %241, %251) : (!llvm.ptr, i64, i64) -> i64
%253 = arith.constant 0 : i32
%254 = arith.extsi %253 : i32 to i64
%255 = llvm.getelementptr %207[%254] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %249, %255 : i64, !llvm.ptr
%257 = arith.constant 1 : i32
%259 = arith.extsi %257 : i32 to i64
%258 = arith.subi %237, %259 : i64
%256 = func.call @even_val(%239, %241, %258) : (!llvm.ptr, i64, i64) -> i64
%260 = arith.constant 1 : i32
%261 = arith.extsi %260 : i32 to i64
%262 = llvm.getelementptr %207[%261] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %256, %262 : i64, !llvm.ptr
%263 = func.call @odd_val(%239, %241, %237) : (!llvm.ptr, i64, i64) -> i64
%264 = arith.constant 2 : i32
%265 = arith.extsi %264 : i32 to i64
%266 = llvm.getelementptr %207[%265] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %263, %266 : i64, !llvm.ptr
%267 = func.call @even_val(%239, %241, %237) : (!llvm.ptr, i64, i64) -> i64
%268 = arith.constant 3 : i32
%269 = arith.extsi %268 : i32 to i64
%270 = llvm.getelementptr %207[%269] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %267, %270 : i64, !llvm.ptr
%272 = arith.constant 1 : i32
%274 = arith.extsi %272 : i32 to i64
%273 = arith.addi %237, %274 : i64
%271 = func.call @odd_val(%239, %241, %273) : (!llvm.ptr, i64, i64) -> i64
%275 = arith.constant 4 : i32
%276 = arith.extsi %275 : i32 to i64
%277 = llvm.getelementptr %207[%276] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %271, %277 : i64, !llvm.ptr
%279 = arith.constant 1 : i32
%281 = arith.extsi %279 : i32 to i64
%280 = arith.addi %237, %281 : i64
%278 = func.call @even_val(%239, %241, %280) : (!llvm.ptr, i64, i64) -> i64
%282 = arith.constant 5 : i32
%283 = arith.extsi %282 : i32 to i64
%284 = llvm.getelementptr %207[%283] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %278, %284 : i64, !llvm.ptr
%286 = arith.constant 2 : i32
%288 = arith.extsi %286 : i32 to i64
%287 = arith.addi %237, %288 : i64
%285 = func.call @odd_val(%239, %241, %287) : (!llvm.ptr, i64, i64) -> i64
%289 = arith.constant 6 : i32
%290 = arith.extsi %289 : i32 to i64
%291 = llvm.getelementptr %207[%290] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %285, %291 : i64, !llvm.ptr
%293 = arith.constant 2 : i32
%295 = arith.extsi %293 : i32 to i64
%294 = arith.addi %237, %295 : i64
%292 = func.call @even_val(%239, %241, %294) : (!llvm.ptr, i64, i64) -> i64
%296 = arith.constant 7 : i32
%297 = arith.extsi %296 : i32 to i64
%298 = llvm.getelementptr %207[%297] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %292, %298 : i64, !llvm.ptr
cf.br ^bb47
^bb46:
%300 = arith.constant 1 : i32
%302 = arith.extsi %300 : i32 to i64
%301 = arith.subi %237, %302 : i64
%299 = func.call @even_val(%239, %241, %301) : (!llvm.ptr, i64, i64) -> i64
%303 = arith.constant 0 : i32
%304 = arith.extsi %303 : i32 to i64
%305 = llvm.getelementptr %207[%304] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %299, %305 : i64, !llvm.ptr
%306 = func.call @odd_val(%239, %241, %237) : (!llvm.ptr, i64, i64) -> i64
%307 = arith.constant 1 : i32
%308 = arith.extsi %307 : i32 to i64
%309 = llvm.getelementptr %207[%308] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %306, %309 : i64, !llvm.ptr
%310 = func.call @even_val(%239, %241, %237) : (!llvm.ptr, i64, i64) -> i64
%311 = arith.constant 2 : i32
%312 = arith.extsi %311 : i32 to i64
%313 = llvm.getelementptr %207[%312] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %310, %313 : i64, !llvm.ptr
%315 = arith.constant 1 : i32
%317 = arith.extsi %315 : i32 to i64
%316 = arith.addi %237, %317 : i64
%314 = func.call @odd_val(%239, %241, %316) : (!llvm.ptr, i64, i64) -> i64
%318 = arith.constant 3 : i32
%319 = arith.extsi %318 : i32 to i64
%320 = llvm.getelementptr %207[%319] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %314, %320 : i64, !llvm.ptr
%322 = arith.constant 1 : i32
%324 = arith.extsi %322 : i32 to i64
%323 = arith.addi %237, %324 : i64
%321 = func.call @even_val(%239, %241, %323) : (!llvm.ptr, i64, i64) -> i64
%325 = arith.constant 4 : i32
%326 = arith.extsi %325 : i32 to i64
%327 = llvm.getelementptr %207[%326] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %321, %327 : i64, !llvm.ptr
%329 = arith.constant 2 : i32
%331 = arith.extsi %329 : i32 to i64
%330 = arith.addi %237, %331 : i64
%328 = func.call @odd_val(%239, %241, %330) : (!llvm.ptr, i64, i64) -> i64
%332 = arith.constant 5 : i32
%333 = arith.extsi %332 : i32 to i64
%334 = llvm.getelementptr %207[%333] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %328, %334 : i64, !llvm.ptr
%336 = arith.constant 2 : i32
%338 = arith.extsi %336 : i32 to i64
%337 = arith.addi %237, %338 : i64
%335 = func.call @even_val(%239, %241, %337) : (!llvm.ptr, i64, i64) -> i64
%339 = arith.constant 6 : i32
%340 = arith.extsi %339 : i32 to i64
%341 = llvm.getelementptr %207[%340] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %335, %341 : i64, !llvm.ptr
%343 = arith.constant 3 : i32
%345 = arith.extsi %343 : i32 to i64
%344 = arith.addi %237, %345 : i64
%342 = func.call @odd_val(%239, %241, %344) : (!llvm.ptr, i64, i64) -> i64
%346 = arith.constant 7 : i32
%347 = arith.extsi %346 : i32 to i64
%348 = llvm.getelementptr %207[%347] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %342, %348 : i64, !llvm.ptr
cf.br ^bb47
^bb47:
func.call @free(%239) : (!llvm.ptr) -> ()
func.return %207 : !llvm.ptr
}
func.func @w_mod(%arg0: i64) -> i64 {
%350 = arith.constant 0 : i32
%352 = arith.extsi %350 : i32 to i64
%351 = arith.cmpi slt, %arg0, %352 : i64
cf.cond_br %351, ^bb48, ^bb49
^bb48:
%356 = arith.constant 0 : i64
%355 = arith.subi %356, %arg0 : i64
%354 = func.call @w_mod(%355) : (i64) -> i64
%358 = arith.constant 0 : i64
%357 = arith.subi %358, %354 : i64
%353 = func.call @norm(%357) : (i64) -> i64
func.return %353 : i64
^bb49:
cf.br ^bb50
^bb50:
%359 = func.call @eds_block(%arg0) : (i64) -> !llvm.ptr
%361 = arith.constant 3 : i32
%362 = arith.extsi %361 : i32 to i64
%363 = llvm.getelementptr %359[%362] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%360 = llvm.load %363 : !llvm.ptr -> i64
func.call @free(%359) : (!llvm.ptr) -> ()
func.return %360 : i64
}
func.func @a_mod(%arg0: i64) -> i64 {
%365 = arith.constant 4 : i32
%367 = arith.extsi %365 : i32 to i64
%366 = arith.remsi %arg0, %367 : i64
%368 = arith.constant 1 : i32
%370 = arith.constant 0 : i32
%369 = arith.subi %370, %368 : i32
%371 = arith.extsi %369 : i32 to i64
%372 = llvm.mlir.constant(1 : i64) : i64
%373 = llvm.alloca %372 x i64 : (i64) -> !llvm.ptr
llvm.store %371, %373 : i64, !llvm.ptr
%374 = arith.constant 1 : i32
%376 = arith.extsi %374 : i32 to i64
%375 = arith.cmpi eq, %366, %376 : i64
%377 = scf.if %375 -> (i1) {
%378 = arith.constant true
scf.yield %378 : i1
} else {
%379 = arith.constant 2 : i32
%381 = arith.extsi %379 : i32 to i64
%380 = arith.cmpi eq, %366, %381 : i64
scf.yield %380 : i1
}
cf.cond_br %377, ^bb51, ^bb52
^bb51:
%382 = arith.constant 1 : i32
%383 = arith.extsi %382 : i32 to i64
llvm.store %383, %373 : i64, !llvm.ptr
cf.br ^bb53
^bb52:
cf.br ^bb53
^bb53:
%384 = arith.extsi %arg0 : i64 to i128
%385 = arith.extsi %arg0 : i64 to i128
%387 = arith.trunci %384 : i128 to i64
%388 = arith.trunci %385 : i128 to i64
%386 = arith.muli %387, %388 : i64
%389 = arith.extsi %386 : i64 to i128
%390 = arith.constant 4 : i32
%392 = arith.trunci %389 : i128 to i64
%393 = arith.extsi %390 : i32 to i64
%391 = arith.divsi %392, %393 : i64
%394 = arith.extsi %391 : i64 to i128
%396 = llvm.mlir.addressof @INV_TWO : !llvm.ptr
%397 = llvm.load %396 : !llvm.ptr -> i64
%395 = func.call @mod_pow_generic(%397, %394) : (i64, i128) -> i64
%398 = func.call @w_mod(%arg0) : (i64) -> i64
%400 = llvm.load %373 : !llvm.ptr -> i64
%401 = arith.muli %400, %398 : i64
%399 = func.call @norm(%401) : (i64) -> i64
%402 = func.call @mod_mul(%399, %395) : (i64, i64) -> i64
func.return %402 : i64
}
func.func @main() -> i32 {
%404 = arith.constant 999999995705032707 : i32
%405 = arith.extsi %404 : i32 to i64
%403 = func.call @a_mod(%405) : (i64) -> i64
%406 = llvm.mlir.addressof @str_0 : !llvm.ptr
%407 = llvm.call @printf(%406, %403) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
%408 = arith.constant 0 : i32
func.return %408 : i32
}
}