Problem 647

Linear transforms of polygonal numbers: S(10^12).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 647
# Linear transforms of polygonal numbers: S(10^12).

function F(k: i64, N: i64) -> i64 {
    let mut total: i64 = 0
    let mut i: i64 = 1
    while true {
        let a: i64 = 2 * (k - 2) * i + 1
        let b: i64 = (4 - k) * i
        let A: i64 = a * a
        let B: i64 = ((k - 2) * b * b + (4 - k) * b) / 2
        let mx: i64 = A
        if B > mx { mx = B }
        if mx > N { break }
        total = total + A + B
        i = i + 1
    }
    return total
}

function S(N: i64) -> i64 {
    let mut total: i64 = 0
    let mut k: i64 = 3
    while true {
        let t: i64 = F(k, N)
        if t == 0 { break }
        total = total + t
        k = k + 2
    }
    return total
}

function main() -> i32 {
    printf("%lld\n", S(1000000000000))
    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 F_i64_i64(int64_t k, int64_t N);
int64_t S_i64(int64_t N);
int32_t main(void);

int64_t F_i64_i64(int64_t k, int64_t N) {
    int64_t total = 0;
    int64_t i = 1;
    while (1) {
        int64_t a = (((2 * (k - 2)) * i) + 1);
        int64_t b = ((4 - k) * i);
        int64_t A = (a * a);
        int64_t B = FLOW_CHECKED_DIV((((((k - 2) * b) * b) + ((4 - k) * b))), (2));
        int64_t mx = A;
        if (B > mx) {
            mx = B;
        }
        if (mx > N) {
            break;
        }
        total = ((total + A) + B);
        i = (i + 1);
    }
    return total;
}

int64_t S_i64(int64_t N) {
    int64_t total = 0;
    int64_t k = 3;
    while (1) {
        int64_t t = F_i64_i64(k, N);
        if (t == 0) {
            break;
        }
        total = (total + t);
        k = (k + 2);
    }
    return total;
}

int32_t main(void) {
    printf("%lld\n", S_i64(1000000000000));
    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 @F(%arg0: i64, %arg1: i64) -> i64 {
    %0 = arith.constant 0 : 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.constant 1 : i32
    %5 = arith.extsi %4 : i32 to i64
    %6 = llvm.mlir.constant(1 : i64) : i64
    %7 = llvm.alloca %6 x i64 : (i64) -> !llvm.ptr
    llvm.store %5, %7 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %8 = arith.constant 1 : i1
    cf.cond_br %8, ^bb1, ^bb2
    ^bb1:
      %9 = arith.constant 2 : i32
      %10 = arith.constant 2 : i32
      %12 = arith.extsi %10 : i32 to i64
      %11 = arith.subi %arg0, %12 : i64
      %14 = arith.extsi %9 : i32 to i64
      %13 = arith.muli %14, %11 : i64
      %15 = llvm.load %7 : !llvm.ptr -> i64
      %16 = arith.muli %13, %15 : i64
      %17 = arith.constant 1 : i32
      %19 = arith.extsi %17 : i32 to i64
      %18 = arith.addi %16, %19 : i64
      %20 = arith.constant 4 : i32
      %22 = arith.extsi %20 : i32 to i64
      %21 = arith.subi %22, %arg0 : i64
      %23 = llvm.load %7 : !llvm.ptr -> i64
      %24 = arith.muli %21, %23 : i64
      %25 = arith.muli %18, %18 : i64
      %26 = arith.constant 2 : i32
      %28 = arith.extsi %26 : i32 to i64
      %27 = arith.subi %arg0, %28 : i64
      %29 = arith.muli %27, %24 : i64
      %30 = arith.muli %29, %24 : i64
      %31 = arith.constant 4 : i32
      %33 = arith.extsi %31 : i32 to i64
      %32 = arith.subi %33, %arg0 : i64
      %34 = arith.muli %32, %24 : i64
      %35 = arith.addi %30, %34 : i64
      %36 = arith.constant 2 : i32
      %38 = arith.extsi %36 : i32 to i64
      %37 = arith.divsi %35, %38 : i64
      %39 = arith.cmpi sgt, %37, %25 : i64
      %40 = scf.if %39 -> (i64) {
        scf.yield %37 : i64
      } else {
        scf.yield %25 : i64
      }
      %41 = arith.cmpi sgt, %40, %arg1 : i64
      cf.cond_br %41, ^bb3, ^bb4
      ^bb3:
        cf.br ^bb2
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %42 = llvm.load %3 : !llvm.ptr -> i64
      %43 = arith.addi %42, %25 : i64
      %44 = arith.addi %43, %37 : i64
      llvm.store %44, %3 : i64, !llvm.ptr
      %45 = llvm.load %7 : !llvm.ptr -> i64
      %46 = arith.constant 1 : i32
      %48 = arith.extsi %46 : i32 to i64
      %47 = arith.addi %45, %48 : i64
      llvm.store %47, %7 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %49 = llvm.load %3 : !llvm.ptr -> i64
    func.return %49 : i64
  }
  func.func @S(%arg0: i64) -> i64 {
    %50 = arith.constant 0 : i32
    %51 = arith.extsi %50 : i32 to i64
    %52 = llvm.mlir.constant(1 : i64) : i64
    %53 = llvm.alloca %52 x i64 : (i64) -> !llvm.ptr
    llvm.store %51, %53 : i64, !llvm.ptr
    %54 = arith.constant 3 : i32
    %55 = arith.extsi %54 : i32 to i64
    %56 = llvm.mlir.constant(1 : i64) : i64
    %57 = llvm.alloca %56 x i64 : (i64) -> !llvm.ptr
    llvm.store %55, %57 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %58 = arith.constant 1 : i1
    cf.cond_br %58, ^bb7, ^bb8
    ^bb7:
      %60 = llvm.load %57 : !llvm.ptr -> i64
      %59 = func.call @F(%60, %arg0) : (i64, i64) -> i64
      %61 = arith.constant 0 : i32
      %63 = arith.extsi %61 : i32 to i64
      %62 = arith.cmpi eq, %59, %63 : i64
      cf.cond_br %62, ^bb9, ^bb10
      ^bb9:
        cf.br ^bb8
      ^bb10:
        cf.br ^bb11
      ^bb11:
      %64 = llvm.load %53 : !llvm.ptr -> i64
      %65 = arith.addi %64, %59 : i64
      llvm.store %65, %53 : i64, !llvm.ptr
      %66 = llvm.load %57 : !llvm.ptr -> i64
      %67 = arith.constant 2 : i32
      %69 = arith.extsi %67 : i32 to i64
      %68 = arith.addi %66, %69 : i64
      llvm.store %68, %57 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %70 = llvm.load %53 : !llvm.ptr -> i64
    func.return %70 : i64
  }
  func.func @main() -> i32 {
    %71 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %73 = arith.constant 995705032704 : i32
    %74 = arith.extsi %73 : i32 to i64
    %72 = func.call @S(%74) : (i64) -> i64
    %75 = llvm.call @printf(%71, %72) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %76 = arith.constant 0 : i32
    func.return %76 : i32
  }
}