Problem 078

Least n such that p(n) is divisible by one million (pentagonal recurrence).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 078
# Least n such that p(n) is divisible by one million (pentagonal recurrence).

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
}

function main() -> i32 {
    let mod: i64 = 1000000
    let maxn: i32 = 100000
    let p: ptr<i64> = calloc((maxn + 1) as i64, 8)
    if p == null { return 1 }
    p[0] = 1

    let mut n: i32 = 1
    let mut ans: i64 = 0
    while n <= maxn {
        let mut s: i64 = 0
        let mut k: i32 = 1
        while true {
            let g1: i32 = k * (3 * k - 1) / 2
            let g2: i32 = k * (3 * k + 1) / 2
            if g1 > n {
                break
            }
            # generalized pentagonals for ±k share sign (-1)^{k-1}
            let mut sign: i64 = 1
            if k % 2 == 0 {
                sign = 0 - 1
            }
            s = s + sign * p[n - g1]
            if g2 <= n {
                s = s + sign * p[n - g2]
            }
            k = k + 1
        }
        s = s % mod
        if s < 0 {
            s = s + mod
        }
        p[n] = s
        if s == 0 {
            ans = n as i64
            break
        }
        n = n + 1
    }
    printf("%lld\n", ans)
    free(p)
    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 mod = 1000000;
    int32_t maxn = 100000;
    int64_t* p = (int64_t*)(calloc(((int64_t)((maxn + 1))), 8));
    if (p == NULL) {
        return 1;
    }
    p[0] = 1;
    int32_t n = 1;
    int64_t ans = 0;
    while (n <= maxn) {
        int64_t s = 0;
        int32_t k = 1;
        while (1) {
            int32_t g1 = FLOW_CHECKED_DIV(((k * ((3 * k) - 1))), (2));
            int32_t g2 = FLOW_CHECKED_DIV(((k * ((3 * k) + 1))), (2));
            if (g1 > n) {
                break;
            }
            int64_t sign = 1;
            if (FLOW_CHECKED_MOD((k), (2)) == 0) {
                sign = (0 - 1);
            }
            s = (s + (sign * p[(n - g1)]));
            if (g2 <= n) {
                s = (s + (sign * p[(n - g2)]));
            }
            k = (k + 1);
        }
        s = FLOW_CHECKED_MOD((s), (mod));
        if (s < 0) {
            s = (s + mod);
        }
        p[n] = s;
        if (s == 0) {
            ans = ((int64_t)(n));
            break;
        }
        n = (n + 1);
    }
    printf("%lld\n", ans);
    free(p);
    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 @main() -> i32 {
    %0 = arith.constant 1000000 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = arith.constant 100000 : i32
    %4 = arith.constant 1 : i32
    %5 = arith.addi %2, %4 : i32
    %6 = arith.extsi %5 : i32 to i64
    %7 = arith.constant 8 : i32
    %8 = arith.extsi %7 : i32 to i64
    %3 = func.call @calloc(%6, %8) : (i64, i64) -> !llvm.ptr
    %9 = llvm.mlir.zero : !llvm.ptr
    %10 = llvm.icmp "eq" %3, %9 : !llvm.ptr
    cf.cond_br %10, ^bb0, ^bb1
    ^bb0:
      %11 = arith.constant 1 : i32
      func.return %11 : i32
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %12 = arith.constant 1 : i32
    %13 = arith.constant 0 : i32
    %14 = arith.extsi %12 : i32 to i64
    %15 = arith.extsi %13 : i32 to i64
    %16 = llvm.getelementptr %3[%15] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %14, %16 : i64, !llvm.ptr
    %17 = arith.constant 1 : i32
    %18 = llvm.mlir.constant(1 : i64) : i64
    %19 = llvm.alloca %18 x i32 : (i64) -> !llvm.ptr
    llvm.store %17, %19 : i32, !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 %19 : !llvm.ptr -> i32
    %25 = arith.cmpi sle, %24, %2 : i32
    cf.cond_br %25, ^bb4, ^bb5
    ^bb4:
      %26 = arith.constant 0 : i32
      %27 = arith.extsi %26 : i32 to i64
      %28 = llvm.mlir.constant(1 : i64) : i64
      %29 = llvm.alloca %28 x i64 : (i64) -> !llvm.ptr
      llvm.store %27, %29 : i64, !llvm.ptr
      %30 = arith.constant 1 : i32
      %31 = llvm.mlir.constant(1 : i64) : i64
      %32 = llvm.alloca %31 x i32 : (i64) -> !llvm.ptr
      llvm.store %30, %32 : i32, !llvm.ptr
      cf.br ^bb6
      ^bb6:
      %33 = arith.constant 1 : i1
      cf.cond_br %33, ^bb7, ^bb8
      ^bb7:
        %34 = llvm.load %32 : !llvm.ptr -> i32
        %35 = arith.constant 3 : i32
        %36 = llvm.load %32 : !llvm.ptr -> i32
        %37 = arith.muli %35, %36 : i32
        %38 = arith.constant 1 : i32
        %39 = arith.subi %37, %38 : i32
        %40 = arith.muli %34, %39 : i32
        %41 = arith.constant 2 : i32
        %42 = arith.divsi %40, %41 : i32
        %43 = llvm.load %32 : !llvm.ptr -> i32
        %44 = arith.constant 3 : i32
        %45 = llvm.load %32 : !llvm.ptr -> i32
        %46 = arith.muli %44, %45 : i32
        %47 = arith.constant 1 : i32
        %48 = arith.addi %46, %47 : i32
        %49 = arith.muli %43, %48 : i32
        %50 = arith.constant 2 : i32
        %51 = arith.divsi %49, %50 : i32
        %52 = llvm.load %19 : !llvm.ptr -> i32
        %53 = arith.cmpi sgt, %42, %52 : i32
        cf.cond_br %53, ^bb9, ^bb10
        ^bb9:
          cf.br ^bb8
        ^bb10:
          cf.br ^bb11
        ^bb11:
        %54 = arith.constant 1 : 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
        %58 = llvm.load %32 : !llvm.ptr -> i32
        %59 = arith.constant 2 : i32
        %60 = arith.remsi %58, %59 : i32
        %61 = arith.constant 0 : i32
        %62 = arith.cmpi eq, %60, %61 : i32
        cf.cond_br %62, ^bb12, ^bb13
        ^bb12:
          %63 = arith.constant 0 : i32
          %64 = arith.constant 1 : i32
          %65 = arith.subi %63, %64 : i32
          %66 = arith.extsi %65 : i32 to i64
          llvm.store %66, %57 : i64, !llvm.ptr
          cf.br ^bb14
        ^bb13:
          cf.br ^bb14
        ^bb14:
        %67 = llvm.load %29 : !llvm.ptr -> i64
        %68 = llvm.load %57 : !llvm.ptr -> i64
        %70 = llvm.load %19 : !llvm.ptr -> i32
        %71 = arith.subi %70, %42 : i32
        %72 = arith.extsi %71 : i32 to i64
        %73 = llvm.getelementptr %3[%72] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %69 = llvm.load %73 : !llvm.ptr -> i64
        %74 = arith.muli %68, %69 : i64
        %75 = arith.addi %67, %74 : i64
        llvm.store %75, %29 : i64, !llvm.ptr
        %76 = llvm.load %19 : !llvm.ptr -> i32
        %77 = arith.cmpi sle, %51, %76 : i32
        cf.cond_br %77, ^bb15, ^bb16
        ^bb15:
          %78 = llvm.load %29 : !llvm.ptr -> i64
          %79 = llvm.load %57 : !llvm.ptr -> i64
          %81 = llvm.load %19 : !llvm.ptr -> i32
          %82 = arith.subi %81, %51 : i32
          %83 = arith.extsi %82 : i32 to i64
          %84 = llvm.getelementptr %3[%83] : (!llvm.ptr, i64) -> !llvm.ptr, i64
          %80 = llvm.load %84 : !llvm.ptr -> i64
          %85 = arith.muli %79, %80 : i64
          %86 = arith.addi %78, %85 : i64
          llvm.store %86, %29 : i64, !llvm.ptr
          cf.br ^bb17
        ^bb16:
          cf.br ^bb17
        ^bb17:
        %87 = llvm.load %32 : !llvm.ptr -> i32
        %88 = arith.constant 1 : i32
        %89 = arith.addi %87, %88 : i32
        llvm.store %89, %32 : i32, !llvm.ptr
        cf.br ^bb6
      ^bb8:
      %90 = llvm.load %29 : !llvm.ptr -> i64
      %91 = arith.remsi %90, %1 : i64
      llvm.store %91, %29 : i64, !llvm.ptr
      %92 = llvm.load %29 : !llvm.ptr -> i64
      %93 = arith.constant 0 : i32
      %95 = arith.extsi %93 : i32 to i64
      %94 = arith.cmpi slt, %92, %95 : i64
      cf.cond_br %94, ^bb18, ^bb19
      ^bb18:
        %96 = llvm.load %29 : !llvm.ptr -> i64
        %97 = arith.addi %96, %1 : i64
        llvm.store %97, %29 : i64, !llvm.ptr
        cf.br ^bb20
      ^bb19:
        cf.br ^bb20
      ^bb20:
      %98 = llvm.load %29 : !llvm.ptr -> i64
      %99 = llvm.load %19 : !llvm.ptr -> i32
      %100 = arith.extsi %99 : i32 to i64
      %101 = llvm.getelementptr %3[%100] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %98, %101 : i64, !llvm.ptr
      %102 = llvm.load %29 : !llvm.ptr -> i64
      %103 = arith.constant 0 : i32
      %105 = arith.extsi %103 : i32 to i64
      %104 = arith.cmpi eq, %102, %105 : i64
      cf.cond_br %104, ^bb21, ^bb22
      ^bb21:
        %106 = llvm.load %19 : !llvm.ptr -> i32
        %107 = arith.extsi %106 : i32 to i64
        llvm.store %107, %23 : i64, !llvm.ptr
        cf.br ^bb5
      ^bb22:
        cf.br ^bb23
      ^bb23:
      %108 = llvm.load %19 : !llvm.ptr -> i32
      %109 = arith.constant 1 : i32
      %110 = arith.addi %108, %109 : i32
      llvm.store %110, %19 : i32, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %111 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %112 = llvm.load %23 : !llvm.ptr -> i64
    %113 = llvm.call @printf(%111, %112) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%3) : (!llvm.ptr) -> ()
    %115 = arith.constant 0 : i32
    func.return %115 : i32
  }
}