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+;;; number.el --- Functions for working with numbers -*- lexical-binding: t -*-
+;; Author: William Carroll <wpcarro@gmail.com>
+
+;;; Commentary:
+;;
+;; Classifications of numbers:
+;; - Natural: (a.k.a positive integers, counting numbers); {1, 2, 3, ... }
+;;
+;; - Whole: Natural Numbers, plus zero; {0, 1, 2, 3, ...}
+;;
+;; - Integers: Whole numbers plus all the negatives of the natural numbers;
+;;   {... , -2, -1, 0, 1, 2, ...}
+;;
+;; - Rational numbers: (a.k.a. fractions) where the top and bottom numbers are
+;;   integers; e.g., 1/2, 3/4, 7/2, ⁻4/3, 4/1.  Note: The denominator cannot be
+;;   0, but the numerator can be.
+;;
+;; - Real numbers: All numbers that can be written as a decimal.  This includes
+;;   fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or
+;;   2.142857. It also includes all the irrational numbers such as π, √2 etc.
+;;   Every real number corresponds to a point on the number line.
+;;
+;; The functions defined herein attempt to capture the mathematical definitions
+;; of numbers and their classifications as defined above.
+
+;;; Code:
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Dependencies
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+(require 'prelude)
+(require 'dash)
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Library
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+(defconst number/test? t
+  "When t, run the test suite defined herein.")
+
+;; TODO: What about int.el?
+
+;; TODO: How do we handle a number typeclass?
+
+(defun number/positive? (x)
+  "Return t if `X' is a positive number."
+  (> x 0))
+
+(defun number/negative? (x)
+  "Return t if `X' is a positive number."
+  (< x 0))
+
+;; TODO: Don't rely on this. Need to have 10.0 and 10 behave similarly.
+(defun number/float? (x)
+  "Return t if `X' is a floating point number."
+  (floatp x))
+
+(defun number/natural? (x)
+  "Return t if `X' is a natural number."
+  (and (number/positive? x)
+       (not (number/float? x))))
+
+(defun number/whole? (x)
+  "Return t if `X' is a whole number."
+  (or (= 0 x)
+      (number/natural? x)))
+
+(defun number/integer? (x)
+  "Return t if `X' is an integer."
+  (or (number/whole? x)
+      (number/natural? (- x))))
+
+;; TODO: How defensive should these guards be?  Should we assert that the inputs
+;; are integers before checking evenness or oddness?
+
+;; TODO: Look up Runar (from Unison) definition of handling zero as even or odd.
+
+;; TODO: How should rational numbers be handled? Lisp is supposedly famous for
+;; its handling of rational numbers.
+;; TODO: `calc-mode' supports rational numbers as "1:2" meaning "1/2"
+;; (defun number/rational? (x))
+
+;; TODO: Can or should I support real numbers?
+;; (defun number/real? (x))
+
+(defun number/even? (x)
+  "Return t if `X' is an even number."
+  (or (= 0 x)
+      (= 0 (mod x 2))))
+
+(defun number/odd? (x)
+  "Return t if `X' is an odd number."
+  (not (number/even? x)))
+
+(defun number/dec (x)
+  "Subtract one from `X'.
+While this function is undeniably trivial, I have unintentionally done (- 1 x)
+  when in fact I meant to do (- x 1) that I figure it's better for this function
+  to exist, and for me to train myself to reach for it and its inc counterpart."
+  (- x 1))
+
+(defun number/inc (x)
+  "Add one to `X'."
+  (+ x 1))
+
+;; TODO: Does this belong in a math module?  Is math too vague?  Or is number
+;; too vague?
+(defun number/factorial (x)
+  "Return factorial of `X'."
+  (cond
+   ((number/negative? x) (error "Will not take factorial of negative numbers"))
+   ((= 0 x) 1)
+   ;; NOTE: Using `series/range' introduces a circular dependency because:
+   ;; series -> number -> series.  Conceptually, however, this should be
+   ;; perfectly acceptable.
+   (t (->> (series/range 1 x)
+           (list/reduce 1 #'*)))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Tests
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+(when number/test?
+  (prelude/assert
+   (number/positive? 10))
+  (prelude/assert
+   (number/natural? 10))
+  (prelude/assert
+   (number/whole? 10))
+  (prelude/assert
+   (number/whole? 0))
+  (prelude/assert
+   (number/integer? 10))
+  (prelude/assert
+   (= 120 (number/factorial 5)))
+  (prelude/assert
+   (number/even? 6))
+  (prelude/refute
+   (number/odd? 6))
+  (prelude/refute
+   (number/positive? -10))
+  (prelude/refute
+   (number/natural? 10.0))
+  (prelude/refute
+   (number/natural? -10))
+  (prelude/refute
+   (number/natural? -10.0)))
+
+(provide 'number)
+;;; number.el ends here