;;;; math-utils-test.scm  -*- Scheme -*-
;;;; Kon Lovett, Oct '22

(import test)

(test-begin "Math Utils")

;;;

(import math-utils)
(import (chicken fixnum) (chicken random))

;;

(define (fibonacci/naive n)
  (case n
    ((0) 0)
    ((1) 1)
    (else (+ (fibonacci/naive (- n 1)) (fibonacci/naive (- n 2)))) ) )

(test-group "seqs"
  (define (fxrand #!optional (rng most-positive-fixnum)) (pseudo-random-integer rng))

  (test "true fib" (fibonacci/naive 10) (fibonacci 10))
  (test "approx fib" (fibonacci/naive 10) (inexact->exact (floor (*fibonacci 10))))

  (test 3628800 (factorial 10))
  ;https://en.wikipedia.org/wiki/Falling_and_rising_factorials
  (let ((thernd (fxrand)))
    (test 1 (factorial- thernd 0))
    (test 1 (factorial+ thernd 0))
    (test thernd (factorial- thernd 1))
    (test thernd (factorial+ thernd 1))
    (test (- (square thernd) thernd) (factorial- thernd 2))
    (test (+ (square thernd) thernd) (factorial+ thernd 2))
    ;quit while ahead
    (test (+ (- (expt thernd 4) (* 6 (cube thernd)))
             (- (* 11 (square thernd)) (* 6 thernd)))
          (factorial- thernd 4))
    (test (+ (expt thernd 4) (* 6 (cube thernd)) (* 11 (square thernd)) (* 6 thernd))
          (factorial+ thernd 4)) )

  (test 137/60 (harmonic 4))
)

(define (approx-points b e pts)
  (map (lambda (c)
         (cons (exact->inexact (car c))
               (exact->inexact (round (+ (* b (car c)) e)))))
       pts))

(test-group "stats"
  (define area-3ln (trapezoid (lambda (x) (* 3 (log x))) 3 4))

  (define some-pts '((0 . 0) (1 . 2) (2 . 4) (3 . 8) (4 . 16)))
  (define data-pts '((1.47 . 52.21) (1.50 . 53.12) (1.52 . 54.48)
                     (1.55 . 55.84) (1.57 . 57.20) (1.60 . 58.57)
                     (1.63 . 59.93) (1.65 . 61.29) (1.68 . 63.11)
                     (1.70 . 64.47) (1.73 . 66.28) (1.75 . 68.10)
                     (1.78 . 69.92) (1.80 . 72.19) (1.83 . 74.46)))
  (define data-pts/exact
          (map (lambda (x) (cons (inexact->exact (car x)) (inexact->exact (cdr x))))
               data-pts))

  (test-assert (procedure? area-3ln))
  (test 3.7478 (area-3ln 10))
  (test 3.7480 (area-3ln 10000))

  (test 1 (average 1))
  (test 2 (average 1 3))
  (test 3 (average 1 3 5))
  (test 9/2 (average 4 5))
  (test 9/2 (average 4 5 4 5))

  (test 70 (binomial 8 4))

  (test-group "Least Squares"
    (define (average-least-squares-error m e pts)
      (/ (foldl (lambda (r pt) (+ r (- (cdr pt) (+ (* m (car pt)) e)))) 0 pts)
         (length pts)) )

    (receive (m e) (least-squares some-pts)
      (test 0 (average-least-squares-error m e some-pts)) )
    (receive (m e) (least-squares data-pts)
      (test 0.0 (average-least-squares-error m e data-pts)) )
  )

  ;https://en.wikipedia.org/wiki/Cross-ratio
  (test-group "Cross Ratio (identity)"
    (let* ((a 1) (b 2) (c 3) (d 4)
           (l (cross-ratio a b c d)))
      (test 4/3 l)
      (test (/ 1 l)       (cross-ratio a b d c))
      (test (/ 1 (- 1 l)) (cross-ratio a c d b))
      (test (- 1 l)       (cross-ratio a c b d))
      (test (/ l (- l 1)) (cross-ratio a d c b))
      (test (/ (- l 1) l) (cross-ratio a d b c)) )
  )
)

(test-group "interest"
  (test 1758.0 (simple-interest 0.043 4 1500))
  (test 1887.0 (simple-interest 0.043 6 1500))

  (test 1780.42 (compound-interest 0.043 6 4 1500))
  (test 1938.84 (compound-interest 0.043 4 6 1500))
)

(test-group "log-with-base"
  (define log256 (log-with-base 256))
  (test-assert (procedure? log256))
  (test "log/base 256" 9 (inexact->exact (round (log256 995972255318008407568))))
)

(test-group "coprime"
  (test-assert (coprime? 2 1))
  (test-assert (coprime? 3 1))
  (test-assert (coprime? 81 19))
  (test-assert (coprime? 1 1))
  (test-assert (not (coprime? 9 3)))
  (test-assert (coprime? (* 3 7) (* 5 19)))
  (test-assert (not (coprime? (* 3 7 5) (* 5 19 2))))
  (test-assert (coprime? 6 10 15))
)

(test-group "pairwise coprime"
  (test-assert (pairwise-coprime? 10 7 33 13))
  (test-assert (not (pairwise-coprime? 10 7 33 14)))
  (test-assert (not (pairwise-coprime? 6 10 15)))
)

(test-group "*coprime"
  (test-assert (fxcoprime? 2 1))
  (test-assert (fxcoprime? 3 1))
  (test-assert (fxcoprime? 81 19))
  (test-assert (fxcoprime? 1 1))
  (test-assert (not (fxcoprime? 9 3)))
  (test-assert (fxcoprime? (* 3 7) (* 5 19)))
  (test-assert (not (fxcoprime? (* 3 7 5) (* 5 19 2))))
)

(test-group "to-places"
  (test 3.141 (to-places 3 (truncate (acos -1))))
  (test 3.0 (to-places 0 (truncate (acos -1))))
  (test 3.14159 (to-places 5 (truncate (acos -1))))
)

;;;

(test-end "Math Utils")

(test-exit)