Problem 064

How many continued fractions for N ≤ 10000 have an odd period?

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 064
# How many continued fractions for N ≤ 10000 have an odd period?

function is_square(n: i64) -> bool {
    let mut r: i64 = 1
    while r * r < n { r = r + 1 }
    return r * r == n
}

function period(n: i64) -> i32 {
    # continued fraction period of sqrt(n)
    let a0: i64 = 0
    let mut r: i64 = 1
    while r * r <= n { r = r + 1 }
    r = r - 1
    # a0 = floor(sqrt(n))
    let mut m: i64 = 0
    let mut d: i64 = 1
    let mut a: i64 = r
    let mut period: i32 = 0
    # repeat until a == 2*a0
    while a != 2 * r {
        m = d * a - m
        d = (n - m * m) / d
        a = (r + m) / d
        period = period + 1
    }
    return period
}

function main() -> i32 {
    let mut count: i64 = 0
    for n in 2..10001 {
        if !is_square(n) {
            if period(n) % 2 == 1 {
                count = count + 1
            }
        }
    }
    printf("%lld\n", count)
    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; }

bool is_square_i64(int64_t n);
int32_t period_i64(int64_t n);
int32_t main(void);

bool is_square_i64(int64_t n) {
    int64_t r = 1;
    while ((r * r) < n) {
        r = (r + 1);
    }
    return (r * r) == n;
}

int32_t period_i64(int64_t n) {
    int64_t a0 = 0;
    int64_t r = 1;
    while ((r * r) <= n) {
        r = (r + 1);
    }
    r = (r - 1);
    int64_t m = 0;
    int64_t d = 1;
    int64_t a = r;
    int32_t period = 0;
    while (a != (2 * r)) {
        m = ((d * a) - m);
        d = FLOW_CHECKED_DIV(((n - (m * m))), (d));
        a = FLOW_CHECKED_DIV(((r + m)), (d));
        period = (period + 1);
    }
    return period;
}

int32_t main(void) {
    int64_t count = 0;
    int32_t __flow_step_1 = 1;
    for (int32_t n = 2; (2 <= 10001) ? n < 10001 : n > 10001; n += (2 <= 10001) ? 1 : -1) {
        if ((!(is_square_i64(n)))) {
            if (FLOW_CHECKED_MOD((period_i64(n)), (2)) == 1) {
                count = (count + 1);
            }
        }
    }
    printf("%lld\n", count);
    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 @is_square(%arg0: i64) -> i1 {
    %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
    cf.br ^bb0
    ^bb0:
    %4 = llvm.load %3 : !llvm.ptr -> i64
    %5 = llvm.load %3 : !llvm.ptr -> i64
    %6 = arith.muli %4, %5 : i64
    %7 = arith.cmpi slt, %6, %arg0 : i64
    cf.cond_br %7, ^bb1, ^bb2
    ^bb1:
      %8 = llvm.load %3 : !llvm.ptr -> i64
      %9 = arith.constant 1 : i32
      %11 = arith.extsi %9 : i32 to i64
      %10 = arith.addi %8, %11 : i64
      llvm.store %10, %3 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %12 = llvm.load %3 : !llvm.ptr -> i64
    %13 = llvm.load %3 : !llvm.ptr -> i64
    %14 = arith.muli %12, %13 : i64
    %15 = arith.cmpi eq, %14, %arg0 : i64
    func.return %15 : i1
  }
  func.func @period(%arg0: i64) -> i32 {
    %16 = arith.constant 0 : i32
    %17 = arith.extsi %16 : i32 to i64
    %18 = arith.constant 1 : i32
    %19 = arith.extsi %18 : i32 to i64
    %20 = llvm.mlir.constant(1 : i64) : i64
    %21 = llvm.alloca %20 x i64 : (i64) -> !llvm.ptr
    llvm.store %19, %21 : i64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %22 = llvm.load %21 : !llvm.ptr -> i64
    %23 = llvm.load %21 : !llvm.ptr -> i64
    %24 = arith.muli %22, %23 : i64
    %25 = arith.cmpi sle, %24, %arg0 : i64
    cf.cond_br %25, ^bb4, ^bb5
    ^bb4:
      %26 = llvm.load %21 : !llvm.ptr -> i64
      %27 = arith.constant 1 : i32
      %29 = arith.extsi %27 : i32 to i64
      %28 = arith.addi %26, %29 : i64
      llvm.store %28, %21 : i64, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %30 = llvm.load %21 : !llvm.ptr -> i64
    %31 = arith.constant 1 : i32
    %33 = arith.extsi %31 : i32 to i64
    %32 = arith.subi %30, %33 : i64
    llvm.store %32, %21 : i64, !llvm.ptr
    %34 = arith.constant 0 : i32
    %35 = arith.extsi %34 : i32 to i64
    %36 = llvm.mlir.constant(1 : i64) : i64
    %37 = llvm.alloca %36 x i64 : (i64) -> !llvm.ptr
    llvm.store %35, %37 : i64, !llvm.ptr
    %38 = arith.constant 1 : i32
    %39 = arith.extsi %38 : i32 to i64
    %40 = llvm.mlir.constant(1 : i64) : i64
    %41 = llvm.alloca %40 x i64 : (i64) -> !llvm.ptr
    llvm.store %39, %41 : i64, !llvm.ptr
    %42 = llvm.load %21 : !llvm.ptr -> i64
    %43 = llvm.mlir.constant(1 : i64) : i64
    %44 = llvm.alloca %43 x i64 : (i64) -> !llvm.ptr
    llvm.store %42, %44 : i64, !llvm.ptr
    %45 = arith.constant 0 : i32
    %46 = llvm.mlir.constant(1 : i64) : i64
    %47 = llvm.alloca %46 x i32 : (i64) -> !llvm.ptr
    llvm.store %45, %47 : i32, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %48 = llvm.load %44 : !llvm.ptr -> i64
    %49 = arith.constant 2 : i32
    %50 = llvm.load %21 : !llvm.ptr -> i64
    %52 = arith.extsi %49 : i32 to i64
    %51 = arith.muli %52, %50 : i64
    %53 = arith.cmpi ne, %48, %51 : i64
    cf.cond_br %53, ^bb7, ^bb8
    ^bb7:
      %54 = llvm.load %41 : !llvm.ptr -> i64
      %55 = llvm.load %44 : !llvm.ptr -> i64
      %56 = arith.muli %54, %55 : i64
      %57 = llvm.load %37 : !llvm.ptr -> i64
      %58 = arith.subi %56, %57 : i64
      llvm.store %58, %37 : i64, !llvm.ptr
      %59 = llvm.load %37 : !llvm.ptr -> i64
      %60 = llvm.load %37 : !llvm.ptr -> i64
      %61 = arith.muli %59, %60 : i64
      %62 = arith.subi %arg0, %61 : i64
      %63 = llvm.load %41 : !llvm.ptr -> i64
      %64 = arith.divsi %62, %63 : i64
      llvm.store %64, %41 : i64, !llvm.ptr
      %65 = llvm.load %21 : !llvm.ptr -> i64
      %66 = llvm.load %37 : !llvm.ptr -> i64
      %67 = arith.addi %65, %66 : i64
      %68 = llvm.load %41 : !llvm.ptr -> i64
      %69 = arith.divsi %67, %68 : i64
      llvm.store %69, %44 : i64, !llvm.ptr
      %70 = llvm.load %47 : !llvm.ptr -> i32
      %71 = arith.constant 1 : i32
      %72 = arith.addi %70, %71 : i32
      llvm.store %72, %47 : i32, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %73 = llvm.load %47 : !llvm.ptr -> i32
    func.return %73 : i32
  }
  func.func @main() -> i32 {
    %74 = arith.constant 0 : i32
    %75 = arith.extsi %74 : i32 to i64
    %76 = llvm.mlir.constant(1 : i64) : i64
    %77 = llvm.alloca %76 x i64 : (i64) -> !llvm.ptr
    llvm.store %75, %77 : i64, !llvm.ptr
    %78 = arith.constant 2 : i32
    %79 = arith.constant 10001 : i32
    %80 = arith.index_cast %78 : i32 to index
    %81 = arith.index_cast %79 : i32 to index
    %83 = arith.constant 1 : index
    %84 = arith.constant -1 : index
    %85 = arith.cmpi sle, %80, %81 : index
    %82 = arith.select %85, %83, %84 : index
    cf.br ^bb9(%80 : index)
    ^bb9(%86: index):
    %87 = arith.cmpi slt, %86, %81 : index
    %88 = arith.cmpi sgt, %86, %81 : index
    %89 = arith.select %85, %87, %88 : i1
    cf.cond_br %89, ^bb10(%86 : index), ^bb11(%86 : index)
    ^bb10(%90: index):
      %92 = arith.index_cast %90 : index to i64
      %91 = func.call @is_square(%92) : (i64) -> i1
      %94 = arith.constant 1 : i1
      %93 = arith.xori %91, %94 : i1
      cf.cond_br %93, ^bb12, ^bb13
      ^bb12:
        %97 = arith.index_cast %90 : index to i64
        %96 = func.call @period(%97) : (i64) -> i32
        %98 = arith.constant 2 : i32
        %99 = arith.remsi %96, %98 : i32
        %100 = arith.constant 1 : i32
        %101 = arith.cmpi eq, %99, %100 : i32
        cf.cond_br %101, ^bb15, ^bb16
        ^bb15:
          %102 = llvm.load %77 : !llvm.ptr -> i64
          %103 = arith.constant 1 : i32
          %105 = arith.extsi %103 : i32 to i64
          %104 = arith.addi %102, %105 : i64
          llvm.store %104, %77 : i64, !llvm.ptr
          cf.br ^bb17
        ^bb16:
          cf.br ^bb17
        ^bb17:
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %106 = arith.addi %90, %82 : index
      cf.br ^bb9(%106 : index)
    ^bb11(%107: index):
    %108 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %109 = llvm.load %77 : !llvm.ptr -> i64
    %110 = llvm.call @printf(%108, %109) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %111 = arith.constant 0 : i32
    func.return %111 : i32
  }
}