Continued Fraction Evaluation

• Write a tail-recursive version of function continued_fraction (or continuedFraction) we worked on in an earlier topic of recursion and define it as continued_fraction_tail (or continuedFractionTail)
• It takes:
  • a 64-bit floating point number $a$, and
  • an integer $n$ (you may assume $n \ge 1$), and returns the value of the following nested expression:

$$ \frac{1}{a + \frac{1}{a + \frac{1}{a + \cdots}}} $$ where the expression contains $n$ occurrences of $a$.

• Boilerplate source files {go,jl,ml,rs}/continued_fraction.{go,jl,ml,rs} containing the test code is generated and shown below.

• Edit the source files either by opening them in a text editor (e.g., vscode), or editing the cells below and executing them.

1. AI tutor

1-1. Prepare

• Your personal AI tutor is provided for questions and feedback
• Execute the following cell before you use it

import heytutor

1-2. Examples

1-2-1. A general question

%%hey
How to write a function in Go?

1-2-2. A hint on this specific problem

%%hey
Give me a hint on this problem for Rust

1-2-3. NEW: A few builtin variables

• {file:FILENAME} is the content of FILE
• {bash[-1]} is the output of the last %%bash_ cell, {bash[-2]} that of the second last %%bash_ cell, etc.
• {problem} is the content of the file you specified by %%hey problem_file=foo.md
• {answer} is the content of the file you specified by %%hey answer_file=go/foo.go

1-2-4. Help when you struggle

%%hey answer_file=go/foo.go
I get this error when I compile it. What's wrong?"

My program:
{answer}

Error message:
{bash[-1]}

1-2-5. Ask feedback

• You are encouraged to ask a feedback once you think you are done with the problem, to know if there is a better answer. You can do so by something like:

%%hey problem_file=foo.md answer_file=go/foo.md
Give me a feedback to my answer.

Problem:
{problem}

My Answer:
{answer}

2. Go

2-1. Baseline code

import heytutor

%%writefile_ go/continued_fraction.go
package main
import "math"
import "fmt"

/** begin my answer */

func continuedFractionTailRec(a float64, m int, xm float64, n int) float64 {
	if m == n  {
		return xm
	} else {
		xm_1 := 1.0 / (a + xm)
		return continuedFractionTailRec(a, m + 1, xm_1, n)
	}
}

func continuedFractionTail(a float64, n int) float64 {
	return continuedFractionTailRec(a, 0, 1.0, n)
}
/** end my answer */

func main() {
	if !(math.Abs(continuedFractionTail(2.0, 100) - 0.4142136) < 1.0e-6) { panic("wrong") }
	if !(math.Abs(continuedFractionTail(3.0, 100) - 0.3027756) < 1.0e-6) { panic("wrong") }
	if !(math.Abs(continuedFractionTail(4.0, 100) - 0.2360680) < 1.0e-6) { panic("wrong") }
	fmt.Println("OK")
}

2-2. Compile

%%bash_
export PATH=${PATH}:~/.local/go/bin:~/go/bin
go build -o go/continued_fraction go/continued_fraction.go

• Note: when you run go or other Go commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/go/bin)
• You may consider adding that line in your ~/.bash_profile

2-3. Run

%%bash_
go/continued_fraction

2-4. Ask Questions or Get Feedback

%%hey problem_file=continued_fraction.md answer_file=go/continued_fraction.go

Problem:
{problem}
My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.

3. Julia

3-1. Baseline code

import heytutor

%%writefile_ jl/continued_fraction.jl
### begin my answer

function continued_fraction_tail_rec(a, m, xm, n)
    if m == n
        xm
    else
        xm_1 = 1 / (a + xm)
        continued_fraction_tail_rec(a, m + 1, xm_1, n)
    end
end

continued_fraction_tail(a, n) = continued_fraction_tail_rec(a, 0, 1.0, n)

### end my answer

function main()
    @assert abs(continued_fraction_tail(2.0, 100) - 0.4142136) < 1.0e-6
    @assert abs(continued_fraction_tail(3.0, 100) - 0.3027756) < 1.0e-6
    @assert abs(continued_fraction_tail(4.0, 100) - 0.2360680) < 1.0e-6
    println("OK")
end

main()

3-2. Compile

• Julia code is compiled "just in time" (compiled upon executed), so does not need a specific action for compilation before you run

3-3. Run

%%bash_
export PATH=${PATH}:~/.juliaup/bin
julia jl/continued_fraction.jl

• Note: when you run julia or other Julia commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/.juliaup/bin)
• You may consider adding that line in your ~/.bash_profile

3-4. Interactive execution

• julia command also serves is an interactive command for Julia programs

• You can run a source code and continue interaction

$ julia -i jl/continued_fraction.jl

• For trial and error, you may also consider creating a Julia notebook

3-5. Ask Questions or Get Feedback

%%hey problem_file=continued_fraction.md answer_file=jl/continued_fraction.jl

Problem:
{problem}

My Answer (between ### begin my answer and ### end my answer):
{answer}

Give me a feedback to my answer.

4. OCaml

4-1. Baseline code

import heytutor

%%writefile_ ml/continued_fraction.ml
(** begin my answer *)

let rec continued_fraction_tail_rec a m xm n =
  if m = n then
    xm
  else
    let xm_1 = 1.0 /. (a +. xm) in
    continued_fraction_tail_rec a (m + 1) xm_1 n

let rec continued_fraction_tail a n = continued_fraction_tail_rec a 0 1.0 n
(** end my answer *)


let main () =
  assert (Float.abs (continued_fraction_tail 2.0 100 -. 0.4142136) < 1.0e-6);
  assert (Float.abs (continued_fraction_tail 3.0 100 -. 0.3027756) < 1.0e-6);
  assert (Float.abs (continued_fraction_tail 4.0 100 -. 0.2360680) < 1.0e-6);
  Printf.printf "OK\n"
;;

main()

4-2. Compile

%%bash_
eval $(opam env)
ocamlc ml/continued_fraction.ml -o ml/continued_fraction

• Note: when you run ocamlc or other OCaml commands (see below) in a terminal (SSH or Jupyter terminal), you need to execute the first line (eval $(opam env))
• You may consider adding that line in your ~/.bash_profile

4-3. Run

%%bash_
ml/continued_fraction

4-4. Interactive execution

• ocaml command is an interactive command for OCaml programs

• In terminal (Jupyter or SSH), you can directly run a source code

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml ml/continued_fraction.ml

• You can run a source code and continue interaction

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml -init ml/continued_fraction.ml

• For trial and error, you may also consider creating an OCaml notebook

4-5. Ask Questions or Get Feedback

%%hey problem_file=continued_fraction.md answer_file=ml/continued_fraction.ml

Problem:
{problem}

My Answer (between (** begin my answer *) and (** end my answer *)):
{answer}

Give me a feedback to my answer.

5. Rust

5-1. Baseline code

import heytutor

%%writefile_ rs/continued_fraction.rs
/** begin my answer */

fn continued_fraction_tail_rec(a: f64, m: i64, xm: f64, n: i64) -> f64 {
    if m == n {
        xm
    } else {
	let xm_1 = 1.0 / (a + xm);
        continued_fraction_tail_rec(a, m + 1, xm_1, n)
    }
}

fn continued_fraction_tail(a: f64, n: i64) -> f64 {
    continued_fraction_tail_rec(a, 0, 1.0, n)
}
/** end my answer */

fn main() {
    assert!((continued_fraction_tail(2.0, 100) - 0.4142136).abs() < 1.0e-6);
    assert!((continued_fraction_tail(3.0, 100) - 0.3027756).abs() < 1.0e-6);
    assert!((continued_fraction_tail(4.0, 100) - 0.2360680).abs() < 1.0e-6);
    println!("OK");
}

5-2. Compile

%%bash_
. ~/.cargo/env
rustc rs/continued_fraction.rs -o rs/continued_fraction

• Note: when you run rustc or other Rust commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (. ~/.cargo/env)
• You may consider adding that line in your ~/.bash_profile

5-3. Run

%%bash_
rs/continued_fraction

5-4. Ask Questions or Get Feedback

%%hey problem_file=continued_fraction.md answer_file=rs/continued_fraction.rs

Problem:
{problem}

My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.