← All problems Problem 274
Sum of divisibility multipliers m for primes p < 10^7, p != 2,5.
View problem on Project Euler
Performance comparison
Metric Our solution Best known
Time complexity O(n^2)O(n log log n)Space complexity O(n)O(n)Approach Flow solution Sieve-based computation Verdict Suboptimal
Flow source
# Project Euler 274
# Sum of divisibility multipliers m for primes p < 10^7, p != 2,5.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function mod_pow(base0: i64, exp0: i64, mod: i64) -> i64 {
let mut result: i64 = 1
let mut base: i64 = base0 % mod
let mut exp: i64 = exp0
while exp > 0 {
if exp % 2 == 1 {
result = (result * base) % mod
}
base = (base * base) % mod
exp = exp / 2
}
return result
}
function main() -> i32 {
let limit: i64 = 10000000
let sieve: ptr<i8> = calloc(limit, 1)
if sieve == null { return 1 }
let mut i: i64 = 0
while i < limit {
sieve[i] = 1
i = i + 1
}
sieve[0] = 0
sieve[1] = 0
let mut p: i64 = 2
while p * p < limit {
if sieve[p] == 1 {
let mut m: i64 = p * p
while m < limit {
sieve[m] = 0
m = m + p
}
}
p = p + 1
}
let mut total: i64 = 0
let mut n: i64 = 3
while n < limit {
if sieve[n] == 1 && n != 5 {
let last_digit: i64 = n % 10
let first_digits: i64 = n / 10
if last_digit != 7 {
total = total + (n - first_digits) / last_digit
} else {
total = total + mod_pow(10, n - 2, n)
}
}
n = n + 2
}
printf("%lld\n", total)
free(sieve)
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 mod_pow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int32_t main(void);
int64_t mod_pow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
int64_t result = 1;
int64_t base = FLOW_CHECKED_MOD((base0), (mod));
int64_t exp = exp0;
while (exp > 0) {
if (FLOW_CHECKED_MOD((exp), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result * base)), (mod));
}
base = FLOW_CHECKED_MOD(((base * base)), (mod));
exp = FLOW_CHECKED_DIV((exp), (2));
}
return result;
}
int32_t main(void) {
int64_t limit = 10000000;
int8_t* sieve = (int8_t*)(calloc(limit, 1));
if (sieve == NULL) {
return 1;
}
int64_t i = 0;
while (i < limit) {
sieve[i] = 1;
i = (i + 1);
}
sieve[0] = 0;
sieve[1] = 0;
int64_t p = 2;
while ((p * p) < limit) {
if (sieve[p] == 1) {
int64_t m = (p * p);
while (m < limit) {
sieve[m] = 0;
m = (m + p);
}
}
p = (p + 1);
}
int64_t total = 0;
int64_t n = 3;
while (n < limit) {
if ((sieve[n] == 1 && n != 5)) {
int64_t last_digit = FLOW_CHECKED_MOD((n), (10));
int64_t first_digits = FLOW_CHECKED_DIV((n), (10));
if (last_digit != 7) {
total = (total + FLOW_CHECKED_DIV(((n - first_digits)), (last_digit)));
} else {
total = (total + mod_pow_i64_i64_i64(10, (n - 2), n));
}
}
n = (n + 2);
}
printf("%lld\n", total);
free(sieve);
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 @calloc(i64, i64) -> !llvm.ptr
func.func private @free(!llvm.ptr) -> ()
func.func @mod_pow(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
%0 = arith.constant 1 : i32
%1 = arith.extsi %0 : i32 to i64
%2 = llvm.mlir.constant(1 : i64) : i64
%3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
llvm.store %1, %3 : i64, !llvm.ptr
%4 = arith.remsi %arg0, %arg2 : i64
%5 = llvm.mlir.constant(1 : i64) : i64
%6 = llvm.alloca %5 x i64 : (i64) -> !llvm.ptr
llvm.store %4, %6 : i64, !llvm.ptr
%7 = llvm.mlir.constant(1 : i64) : i64
%8 = llvm.alloca %7 x i64 : (i64) -> !llvm.ptr
llvm.store %arg1, %8 : i64, !llvm.ptr
cf.br ^bb0
^bb0:
%9 = llvm.load %8 : !llvm.ptr -> i64
%10 = arith.constant 0 : i32
%12 = arith.extsi %10 : i32 to i64
%11 = arith.cmpi sgt, %9, %12 : i64
cf.cond_br %11, ^bb1, ^bb2
^bb1:
%13 = llvm.load %8 : !llvm.ptr -> i64
%14 = arith.constant 2 : i32
%16 = arith.extsi %14 : i32 to i64
%15 = arith.remsi %13, %16 : i64
%17 = arith.constant 1 : i32
%19 = arith.extsi %17 : i32 to i64
%18 = arith.cmpi eq, %15, %19 : i64
cf.cond_br %18, ^bb3, ^bb4
^bb3:
%20 = llvm.load %3 : !llvm.ptr -> i64
%21 = llvm.load %6 : !llvm.ptr -> i64
%22 = arith.muli %20, %21 : i64
%23 = arith.remsi %22, %arg2 : i64
llvm.store %23, %3 : i64, !llvm.ptr
cf.br ^bb5
^bb4:
cf.br ^bb5
^bb5:
%24 = llvm.load %6 : !llvm.ptr -> i64
%25 = llvm.load %6 : !llvm.ptr -> i64
%26 = arith.muli %24, %25 : i64
%27 = arith.remsi %26, %arg2 : i64
llvm.store %27, %6 : i64, !llvm.ptr
%28 = llvm.load %8 : !llvm.ptr -> i64
%29 = arith.constant 2 : i32
%31 = arith.extsi %29 : i32 to i64
%30 = arith.divsi %28, %31 : i64
llvm.store %30, %8 : i64, !llvm.ptr
cf.br ^bb0
^bb2:
%32 = llvm.load %3 : !llvm.ptr -> i64
func.return %32 : i64
}
func.func @main() -> i32 {
%33 = arith.constant 10000000 : i32
%34 = arith.extsi %33 : i32 to i64
%36 = arith.constant 1 : i32
%37 = arith.extsi %36 : i32 to i64
%35 = func.call @calloc(%34, %37) : (i64, i64) -> !llvm.ptr
%38 = llvm.mlir.zero : !llvm.ptr
%39 = llvm.icmp "eq" %35, %38 : !llvm.ptr
cf.cond_br %39, ^bb6, ^bb7
^bb6:
%40 = arith.constant 1 : i32
func.return %40 : i32
^bb7:
cf.br ^bb8
^bb8:
%41 = arith.constant 0 : i32
%42 = arith.extsi %41 : i32 to i64
%43 = llvm.mlir.constant(1 : i64) : i64
%44 = llvm.alloca %43 x i64 : (i64) -> !llvm.ptr
llvm.store %42, %44 : i64, !llvm.ptr
cf.br ^bb9
^bb9:
%45 = llvm.load %44 : !llvm.ptr -> i64
%46 = arith.cmpi slt, %45, %34 : i64
cf.cond_br %46, ^bb10, ^bb11
^bb10:
%47 = arith.constant 1 : i32
%48 = llvm.load %44 : !llvm.ptr -> i64
%49 = arith.trunci %47 : i32 to i8
%50 = llvm.getelementptr %35[%48] : (!llvm.ptr, i64) -> !llvm.ptr, i8
llvm.store %49, %50 : i8, !llvm.ptr
%51 = llvm.load %44 : !llvm.ptr -> i64
%52 = arith.constant 1 : i32
%54 = arith.extsi %52 : i32 to i64
%53 = arith.addi %51, %54 : i64
llvm.store %53, %44 : i64, !llvm.ptr
cf.br ^bb9
^bb11:
%55 = arith.constant 0 : i32
%56 = arith.constant 0 : i32
%57 = arith.trunci %55 : i32 to i8
%58 = arith.extsi %56 : i32 to i64
%59 = llvm.getelementptr %35[%58] : (!llvm.ptr, i64) -> !llvm.ptr, i8
llvm.store %57, %59 : i8, !llvm.ptr
%60 = arith.constant 0 : i32
%61 = arith.constant 1 : i32
%62 = arith.trunci %60 : i32 to i8
%63 = arith.extsi %61 : i32 to i64
%64 = llvm.getelementptr %35[%63] : (!llvm.ptr, i64) -> !llvm.ptr, i8
llvm.store %62, %64 : i8, !llvm.ptr
%65 = arith.constant 2 : i32
%66 = arith.extsi %65 : i32 to i64
%67 = llvm.mlir.constant(1 : i64) : i64
%68 = llvm.alloca %67 x i64 : (i64) -> !llvm.ptr
llvm.store %66, %68 : i64, !llvm.ptr
cf.br ^bb12
^bb12:
%69 = llvm.load %68 : !llvm.ptr -> i64
%70 = llvm.load %68 : !llvm.ptr -> i64
%71 = arith.muli %69, %70 : i64
%72 = arith.cmpi slt, %71, %34 : i64
cf.cond_br %72, ^bb13, ^bb14
^bb13:
%74 = llvm.load %68 : !llvm.ptr -> i64
%75 = llvm.getelementptr %35[%74] : (!llvm.ptr, i64) -> !llvm.ptr, i8
%73 = llvm.load %75 : !llvm.ptr -> i8
%76 = arith.constant 1 : i32
%78 = arith.extsi %73 : i8 to i32
%77 = arith.cmpi eq, %78, %76 : i32
cf.cond_br %77, ^bb15, ^bb16
^bb15:
%79 = llvm.load %68 : !llvm.ptr -> i64
%80 = llvm.load %68 : !llvm.ptr -> i64
%81 = arith.muli %79, %80 : i64
%82 = llvm.mlir.constant(1 : i64) : i64
%83 = llvm.alloca %82 x i64 : (i64) -> !llvm.ptr
llvm.store %81, %83 : i64, !llvm.ptr
cf.br ^bb18
^bb18:
%84 = llvm.load %83 : !llvm.ptr -> i64
%85 = arith.cmpi slt, %84, %34 : i64
cf.cond_br %85, ^bb19, ^bb20
^bb19:
%86 = arith.constant 0 : i32
%87 = llvm.load %83 : !llvm.ptr -> i64
%88 = arith.trunci %86 : i32 to i8
%89 = llvm.getelementptr %35[%87] : (!llvm.ptr, i64) -> !llvm.ptr, i8
llvm.store %88, %89 : i8, !llvm.ptr
%90 = llvm.load %83 : !llvm.ptr -> i64
%91 = llvm.load %68 : !llvm.ptr -> i64
%92 = arith.addi %90, %91 : i64
llvm.store %92, %83 : i64, !llvm.ptr
cf.br ^bb18
^bb20:
cf.br ^bb17
^bb16:
cf.br ^bb17
^bb17:
%93 = llvm.load %68 : !llvm.ptr -> i64
%94 = arith.constant 1 : i32
%96 = arith.extsi %94 : i32 to i64
%95 = arith.addi %93, %96 : i64
llvm.store %95, %68 : i64, !llvm.ptr
cf.br ^bb12
^bb14:
%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
%101 = arith.constant 3 : i32
%102 = arith.extsi %101 : i32 to i64
%103 = llvm.mlir.constant(1 : i64) : i64
%104 = llvm.alloca %103 x i64 : (i64) -> !llvm.ptr
llvm.store %102, %104 : i64, !llvm.ptr
cf.br ^bb21
^bb21:
%105 = llvm.load %104 : !llvm.ptr -> i64
%106 = arith.cmpi slt, %105, %34 : i64
cf.cond_br %106, ^bb22, ^bb23
^bb22:
%108 = llvm.load %104 : !llvm.ptr -> i64
%109 = llvm.getelementptr %35[%108] : (!llvm.ptr, i64) -> !llvm.ptr, i8
%107 = llvm.load %109 : !llvm.ptr -> i8
%110 = arith.constant 1 : i32
%112 = arith.extsi %107 : i8 to i32
%111 = arith.cmpi eq, %112, %110 : i32
%113 = scf.if %111 -> (i1) {
%114 = llvm.load %104 : !llvm.ptr -> i64
%115 = arith.constant 5 : i32
%117 = arith.extsi %115 : i32 to i64
%116 = arith.cmpi ne, %114, %117 : i64
scf.yield %116 : i1
} else {
%118 = arith.constant false
scf.yield %118 : i1
}
cf.cond_br %113, ^bb24, ^bb25
^bb24:
%119 = llvm.load %104 : !llvm.ptr -> i64
%120 = arith.constant 10 : i32
%122 = arith.extsi %120 : i32 to i64
%121 = arith.remsi %119, %122 : i64
%123 = llvm.load %104 : !llvm.ptr -> i64
%124 = arith.constant 10 : i32
%126 = arith.extsi %124 : i32 to i64
%125 = arith.divsi %123, %126 : i64
%127 = arith.constant 7 : i32
%129 = arith.extsi %127 : i32 to i64
%128 = arith.cmpi ne, %121, %129 : i64
cf.cond_br %128, ^bb27, ^bb28
^bb27:
%130 = llvm.load %100 : !llvm.ptr -> i64
%131 = llvm.load %104 : !llvm.ptr -> i64
%132 = arith.subi %131, %125 : i64
%133 = arith.divsi %132, %121 : i64
%134 = arith.addi %130, %133 : i64
llvm.store %134, %100 : i64, !llvm.ptr
cf.br ^bb29
^bb28:
%135 = llvm.load %100 : !llvm.ptr -> i64
%137 = arith.constant 10 : i32
%138 = llvm.load %104 : !llvm.ptr -> i64
%139 = arith.constant 2 : i32
%141 = arith.extsi %139 : i32 to i64
%140 = arith.subi %138, %141 : i64
%142 = llvm.load %104 : !llvm.ptr -> i64
%143 = arith.extsi %137 : i32 to i64
%136 = func.call @mod_pow(%143, %140, %142) : (i64, i64, i64) -> i64
%144 = arith.addi %135, %136 : i64
llvm.store %144, %100 : i64, !llvm.ptr
cf.br ^bb29
^bb29:
cf.br ^bb26
^bb25:
cf.br ^bb26
^bb26:
%145 = llvm.load %104 : !llvm.ptr -> i64
%146 = arith.constant 2 : i32
%148 = arith.extsi %146 : i32 to i64
%147 = arith.addi %145, %148 : i64
llvm.store %147, %104 : i64, !llvm.ptr
cf.br ^bb21
^bb23:
%149 = llvm.mlir.addressof @str_0 : !llvm.ptr
%150 = llvm.load %100 : !llvm.ptr -> i64
%151 = llvm.call @printf(%149, %150) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
func.call @free(%35) : (!llvm.ptr) -> ()
%153 = arith.constant 0 : i32
func.return %153 : i32
}
}