(ns main
  (:gen-class)
  (:require [clojure.test :refer :all]))


(defn get_trapezoid [func]
  (letfn [(step [] 0.5)
          (next [x] (+ x (step)))
          (trapezoid [x] (* (/ (+ (func x) (func (- x (step)))) 2.0) (step)))
          (integrate [mesh_x acc x] (if (> mesh_x x) acc (recur (next mesh_x) (+ acc (trapezoid mesh_x)) x)))]
    (partial integrate (step) 0)
    )
  )


(defn get_trapezoid_memo [func]
  (let [step 0.1
        to_point (fn [x] (* x step))
        trapezoid (fn [x] (* (/ (+ (func (to_point x)) (func (- (to_point x) step))) 2.0) step))
        integrate (memoize (fn [recfunc mesh_x] (println mesh_x) (if (< (dec mesh_x) 0) 0.0 (+ (trapezoid mesh_x) (recfunc recfunc (dec mesh_x))))))]
    (fn [x] (integrate integrate (Math/floor (/ x step))))))


(defn get_trapezoid_memo_with_part [func]
  (let [step 0.1
        to_point (fn [x] (* x step))
        trapezoid (fn [x delta] (* (/ (+ (func (to_point x)) (func (- (to_point x) delta))) 2.0) delta))
        integrate (memoize (fn [recfunc mesh_x] (if (< (dec mesh_x) 0) 0.0 (+ (trapezoid mesh_x step) (recfunc recfunc (dec mesh_x))))))]
    (fn [x] (+ (integrate integrate (Math/floor (/ x step))) (trapezoid x (- x (to_point (Math/floor (/ x step)))))))))


(defn get_trapezoid_stream [func]
  (letfn [(step [] 0.5)
          (trapezoid [x] (* (/ (+ (func x) (func (+ x (step)))) 2.0) (step)))
          (to_point [x] (* x (step)))
          ]
    (fn [x] (let [limit (quot x (step))]
              (->> (range)
                   (map to_point)
                   (map trapezoid)
                   (take limit)
                   (reduce +))))
    ))


(defn get_trapezoid_stream_2 [func]
  (letfn [(step [] 0.5)
          (trapezoid [x] (* (/ (+ (func x) (func (+ x (step)))) 2.0) (step)))
          (next_point [x] (+ x (step)))
          (next_step [[x, integral]] (println x) [(next_point x) (+ (trapezoid x) integral)])]
    (let
      [seq_pair (iterate next_step [0 0])]
      (fn [x] (nth (map last seq_pair) (quot x (step)))))
    ))


(let [linear #(* % 2)
      integral_tail (get_trapezoid linear)
      integral_stream (get_trapezoid_stream linear)
      integral_stream_2 (get_trapezoid_stream_2 linear)
      integral_memo_part (get_trapezoid_memo_with_part linear)
      integral_memo (get_trapezoid_memo linear)]
  ;(println (time (integral_memo 17)))
  ;(println (time (integral_memo 15)))
  ;(println (time (integral_memo 15.1)))
  ;(println (time (integral_memo 20)))
  ;(println (time (integral_memo 100)))
  ;(println (time (integral_memo 100)))
  ;(println "------------------")
  ;(println (time (integral_tail 17)))
  ;(println (time (integral_tail 15)))
  ;(println (time (integral_tail 10)))
  ;(println (time (integral_tail 20)))
  ;(println (time (integral_tail 25)))
  ;(println (time (integral_tail 2500)))
  ;(println "------------------")
  ;(println (time (integral_stream 17)))
  ;(println (time (integral_stream 15)))
  ;(println (time (integral_stream 10)))
  ;(println (time (integral_stream 20)))
  ;(println (time (integral_stream 25)))
  ;(println (time (integral_stream 2500)))
  (println "------------------")
  (println (time (integral_stream_2 15)))
  (println (time (integral_stream_2 16)))
  ;(println (time (integral_stream_2 17)))
  ;(println (time (integral_stream_2 18)))
  ;(println (time (integral_stream_2 19)))
  ;(println (time (integral_stream_2 2500)))
  (println "------------------")
  ;(println (time (integral_memo_part 15)))
  ;(println (time (integral_memo_part 15.25)))
  ;(println (time (integral_memo_part 16)))
  ;(println (time (integral_memo_part 17)))
  ;(println (time (integral_memo_part 18)))
  ;(println (time (integral_memo_part 19)))
  )

((deftest generator_tests
   (testing "3*x^2 => x^3"
     (let [quad #(* (Math/pow % 2) 3)
           integral (get_trapezoid quad)]
       (is (< (Math/abs (- (integral 4) 64)) 1))
       (is (< (Math/abs (- (integral 5) 125)) 1))
       (is (< (Math/abs (- (integral 6) 216)) 1))
       )
     )
   (testing "2*x => x^2"
     (let [linear #(* % 2)
           integral (get_trapezoid linear)]
       (is (< (- (integral 3) 9) 1))
       (is (< (- (integral 25) 625) 1))
       (is (= (integral -1) 0))
       )
     )
   ))

;(run-tests 'main)