Re: Adding a generic mathematical library

[Emanuel Berg]

Philip Kaludercic wrote:

>> Someone™ should propose a concrete suggestion.
>
> I've rename the thread to get some more attention, and also
> wanted to mention, that if we do so, I think putting some
> thought into the design wouldn't be bad. Including an
> infix-notation macro and perhaps even overloaded operator
> support ala APL would be a nice thing to have. We'd have to
> weigh the cost of this kind of flexibility with performance,
> unless someone were to write a specialised byte-compiler.

Yeah, I've pushed for a math library for a long time.

I have several files that are very close to that (for stats,
time, permutations and so on) but I also have a math.el which
I yank below if any of it can be used.

I'd love to stay in the loop and read more on this!

;;; -*- lexical-binding: t -*-
;;
;; this file:
;;   https://dataswamp.org/~incal/emacs-init/math.el

(require 'cl-lib)

(require 'dwim) ; https://dataswamp.org/~incal/emacs-init/dwim.el
(require 'perm) ; https://dataswamp.org/~incal/emacs-init/perm.el

(defun nand (&rest conditions)
  (when (member nil conditions)
    t) )

;; (nand)           ; nil
;; (nand 1 2 3)     ; nil
;; (nand nil)       ; t
;; (nand 1 2 nil 3) ; t

;; (not (and))           ; nil
;; (not (and 1 2 3))     ; nil
;; (not (and nil))       ; t
;; (not (and 1 2 nil 3)) ; t

(defalias '**   #'expt)
(defalias 'ceil #'ceiling)

(defun percent-change (from to)
  (if (= from to)
      0
    (/ (- to from) (abs from) 0.01)))

;; (percent-change  1  2) ;  100
;; (percent-change  1  1) ;    0
;; (percent-change  1  0) ; -100
;; (percent-change  1 -1) ; -200
;;
;; (percent-change  0  1) ;  1.0e+INF
;; (percent-change  0  0) ;  0
;; (percent-change  0 -1) ; -1.0e+INF
;;
;; (percent-change -1  1) ;  200
;; (percent-change -1  0) ;  100
;; (percent-change -1 -1) ;    0
;; (percent-change -1 -2) ; -100

(defun distance-point (min max)
  (+ min (/ (- max min) 2.0)) )

;; (distance-point  1   5) ; 3
;; (distance-point  1  10) ; 5.5
;; (distance-point 60 100) ; 80

(defun // (nom denom)
  (/ nom denom 1.0) )

;; (/  8 256) ; 0
;; (// 8 256) ; 0.03125

(defun arith-sum (n)
  (cl-loop
    with sum = 0
    for i from 1 to (1- n)
    do (cl-incf sum i)
    finally return sum) )

(defun digs (n)
  (* n (1- n)) )

(defun mean-value (vs)
  (let*((sum  (apply #'+ vs))
        (mean (/ sum (length vs) 1.0)) )
    mean) )

(defun mean-str (strs)
  (mean-value (cl-map 'list #'length strs)) )

(defun faster (old new)
  (format "%.1f%%" (* 100 (1- (/ new old 1.0)))) )

;; (faster 0.2  0.5)  ; 150.0%
;; (faster 1.35 0.84) ; -37.8%
;; (faster  200  400) ; 100.0%
;; (faster 1000 1000) ;   0.0%
;; (faster 1000  100) ; -90.0%

(defun percent (nom &optional denom str)
  (or denom (setq denom 1))
  (let ((perc (/ nom denom 0.01)))
    (if str
        (format "%.1f%%" perc)
      perc)))

;; (percent 0.25)           ; 25.0
;; (percent 50 75)          ; 66.66 ...
;; (percent (// 1 2) nil t) ; 50.0%
;; (percent 1019 22 t)      ; 4631.8%

(let ((min-def 0)
      (max-def 9)
      (inc-def 1) )
  (defun interval (&optional min max inc)
    (interactive `(,(read-number "min: " min-def)
                   ,(read-number "max: " max-def)
                   ,(read-number "inc: " inc-def)) )
    (or min (setq min min-def))
    (or max (setq max max-def))
    (or inc (setq inc inc-def))
    (unless (<= min max)
      (error "Bogus interval") )
    (unless (> inc 0)
      (error "Bogus increment") )
    (cl-loop
      for i from min to max by inc
      collect i) )
  (declare-function interval nil) )

;; (interval 10 5)        ; Bogus interval
;; (interval 1 3 -1)      ; Bogus increment
;; (interval 5 10)        ; (5 6 7 8 9 10)
;; (interval 1.8 2.0 0.1) ; (1.8 1.9 2.0)
;; (interval)             ; (0 1 2 3 4 5 6 7 8 9)
;; (interval 19 99)       ; (19 20 21 ... 97 98 99)

(defun digits-sum (&optional beg end)
  (interactive (use-region))
  (or beg (setq beg (point-min)))
  (or end (setq end (point-max)))
  (let ((sum 0))
    (goto-char beg)
    (while (re-search-forward " [[:digit:].]+ " end t)
      (cl-incf sum (string-to-number (match-string-no-properties 0))) )
    (prog1
        sum
      (message "sum: %.1f" sum) )))

(defalias 'di #'digits-sum)

(defun film-mean ()
  (interactive)
  (let ((scores)
        (beg (point-min))
        (end (point-max)) )
    (save-excursion
      (goto-char beg)
      (while (re-search-forward "[[:digit:]]" end t)
        (when (= (current-column) 73)
          (push (string-to-number (match-string-no-properties 0)) scores) )))
    (when scores
      (message (format "%.3f" (mean-value scores))) )))

(defun positive-integer-p (n)
  (and
    (integerp n)
    (< 0 n) ))

;; (positive-integer-p  1.5) ; nil
;; (positive-integer-p  1)   ; t
;; (positive-integer-p  0)   ; nil
;; (positive-integer-p -1)   ; nil

(defun string-to-number-number (str)
  (let ((s (string-trim str)))
    (when (string-match-p
           "\\`[+-]?\\([[:digit:]]+\\|[[:digit:]]*\\.[[:digit:]]+\\)\\'" s)
      (string-to-number s) )))

(defun string-to-number-number-test ()
  (cl-map 'list (lambda (e)
                  (pcase-let ((`(,a ,b) e))
                    (if (and a b)
                        (= a b)
                      (eq a b) )))
          (list
           (list (string-to-number-number " 10")                   10)
           (list (string-to-number-number "  1.5")                 1.5)
           (list (string-to-number-number " +0")                   0)
           (list (string-to-number-number "  0")                   0)
           (list (string-to-number-number " -0.0")                 -0.0)
           (list (string-to-number-number " -1.5")                -1.5)
           (list (string-to-number-number "-10")                  -10)
           (list (string-to-number-number "123this used to work")  nil)
           (list (string-to-number-number "NAN")                   nil) )))

;; (string-to-number-number-test)

(defun read-integer ()
  (let ((str)
        (str-number)
        (n) )
    (cl-loop until (progn
                     (setq str (read-string "integer: "))
                     (if (string= str "0")
                         (setq n 0)
                       (setq str-number (string-to-number str))
                       (unless (= str-number 0)
                         (setq n str-number) ))
                     (integerp n)) )
    n) )

;; (read-integer)

(defun compare (old new)
  (format "%.2f%%" (* 100 (/ (- old new)
                             (* old 1.0) ))))
;; (compare 185 80) ; 56.76%

(defun hypotenuse (c1 c2)
  (sqrt (+ (* c1 c1) (* c2 c2))) )

(defun speed (hour minute second km)
  (let*((s   (+ second (* 60 minute) (* 60 60 hour)))
        (m   (* 1000 km))
        (mps (/ m s)) )
    (* 3.6 mps) ))

;; (speed 04 44 10  42.195) ;  8.909208211143694
;; (speed 02 01 39  42.195) ; 20.811344019728732
;; (speed 19 04 00 168    ) ;  7.2

(defun binom (n k)
  (/ (cl-factorial n)
     (* (cl-factorial k)
        (cl-factorial (- n k)) )))

(defun product (l)
  (cl-loop with prod = 1
    for i in l do
    (setq prod (* prod i))
    finally return prod) )

;; (product '(1 2 3 4)) ; 24

(defun tau-ceti (speed)
  (let*((dist       (* 11.8 9.46 (expt 10 12)))
        (time       (/ dist speed) )
        (days       (/ time 24))
        (whole-days (round days)) )
    (format-seconds "%y years"
                    (- (float-time (encode-time 0 0 0 whole-days 0 0))
                       (float-time (encode-time 0 0 0 0 0 0)) ))))

;; (tau-ceti 5000) ; 2 548 584 years

(provide 'math)

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