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;;; calc-tests.el --- tests for calc -*- lexical-binding: t; -*-
;; Copyright (C) 2014-2019 Free Software Foundation, Inc.
;; Author: Leo Liu <sdl.web@gmail.com>
;; Keywords: maint
;; This file is part of GNU Emacs.
;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
;;; Commentary:
;;; Code:
(require 'cl-lib)
(require 'ert)
(require 'calc)
(require 'calc-ext)
(require 'calc-units)
;; XXX The order in which calc libraries (in particular calc-units)
;; are loaded influences whether a calc integer in an expression
;; involving units is represented as a lisp integer or a calc float,
;; see bug#19582. Until this will be fixed the following function can
;; be used to compare such calc expressions.
(defun calc-tests-equal (a b)
"Like `equal' but allow for different representations of numbers.
For example: (calc-tests-equal 10 '(float 1 1)) => t.
A and B should be calc expressions."
(cond ((math-numberp a)
(and (math-numberp b)
(math-equal a b)))
((atom a)
(equal a b))
((consp b)
;; Can't be dotted or circular.
(and (= (length a) (length b))
(equal (car a) (car b))
(cl-every #'calc-tests-equal (cdr a) (cdr b))))))
(defun calc-tests-simple (fun string &rest args)
"Push STRING on the calc stack, then call FUN and return the new top.
The result is a calc (i.e., lisp) expression, not its string representation.
Also pop the entire stack afterwards.
An existing calc stack is reused, otherwise a new one is created."
(calc-eval string 'push)
(prog1
(ignore-errors
(apply fun args)
(calc-top-n 1))
(calc-pop 0)))
;; (ert-deftest test-math-bignum ()
;; ;; bug#17556
;; (let ((n (math-bignum most-negative-fixnum)))
;; (should (math-negp n))
;; (should (cl-notany #'cl-minusp (cdr n)))))
(ert-deftest test-calc-remove-units ()
(should (calc-tests-equal (calc-tests-simple #'calc-remove-units "-1 m") -1)))
(ert-deftest test-calc-extract-units ()
(should (calc-tests-equal (calc-tests-simple #'calc-extract-units "-1 m")
'(var m var-m)))
(should (calc-tests-equal (calc-tests-simple #'calc-extract-units "-1 m*cm")
'(* (float 1 -2) (^ (var m var-m) 2)))))
(ert-deftest test-calc-convert-units ()
;; Used to ask for `(The expression is unitless when simplified) Old Units: '.
(should (calc-tests-equal (calc-tests-simple #'calc-convert-units "-1 m" nil "cm")
'(* -100 (var cm var-cm))))
;; Gave wrong result.
(should (calc-tests-equal (calc-tests-simple #'calc-convert-units "-1 m"
(math-read-expr "1m") "cm")
'(* -100 (var cm var-cm)))))
(ert-deftest calc-imaginary-i ()
"Test `math-imaginary-i' for non-special-const values."
(let ((var-i (calcFunc-polar (calcFunc-sqrt -1))))
(should (math-imaginary-i)))
(let ((var-i (calcFunc-sqrt -1)))
(should (math-imaginary-i))))
(ert-deftest test-calc-23889 ()
"Test for https://debbugs.gnu.org/23889 and 25652."
(skip-unless t) ;; (>= math-bignum-digit-length 9))
(dolist (mode '(deg rad))
(let ((calc-angle-mode mode))
;; If user inputs angle units, then should ignore `calc-angle-mode'.
(should (string= "5253"
(substring
(number-to-string
(nth 1
(math-simplify-units
'(calcFunc-cos (* 45 (var rad var-rad))))))
0 4)))
(should (string= "7071"
(substring
(number-to-string
(nth 1
(math-simplify-units
'(calcFunc-cos (* 45 (var deg var-deg))))))
0 4)))
(should (string= "8939"
(substring
(number-to-string
(nth 1
(math-simplify-units
'(+ (calcFunc-sin (* 90 (var rad var-rad)))
(calcFunc-cos (* 90 (var deg var-deg)))))))
0 4)))
(should (string= "5519"
(substring
(number-to-string
(nth 1
(math-simplify-units
'(+ (calcFunc-sin (* 90 (var deg var-deg)))
(calcFunc-cos (* 90 (var rad var-rad)))))))
0 4)))
;; If user doesn't input units, then must use `calc-angle-mode'.
(should (string= (if (eq calc-angle-mode 'deg)
"9998"
"5403")
(substring
(number-to-string
(nth 1 (calcFunc-cos 1)))
0 4))))))
(ert-deftest calc-test-trig ()
"Trigonometric simplification; bug#33052."
(let ((calc-angle-mode 'rad))
(let ((calc-symbolic-mode t))
(should (equal (math-simplify '(calcFunc-sin (/ (var pi var-pi) 4)))
'(/ (calcFunc-sqrt 2) 2)))
(should (equal (math-simplify '(calcFunc-cos (/ (var pi var-pi) 4)))
'(/ (calcFunc-sqrt 2) 2)))
(should (equal (math-simplify '(calcFunc-sec (/ (var pi var-pi) 4)))
'(calcFunc-sqrt 2)))
(should (equal (math-simplify '(calcFunc-csc (/ (var pi var-pi) 4)))
'(calcFunc-sqrt 2)))
(should (equal (math-simplify '(calcFunc-tan (/ (var pi var-pi) 3)))
'(calcFunc-sqrt 3)))
(should (equal (math-simplify '(calcFunc-cot (/ (var pi var-pi) 3)))
'(/ (calcFunc-sqrt 3) 3))))
(let ((calc-symbolic-mode nil))
(should (equal (math-simplify '(calcFunc-sin (/ (var pi var-pi) 4)))
'(calcFunc-sin (/ (var pi var-pi) 4))))
(should (equal (math-simplify '(calcFunc-cos (/ (var pi var-pi) 4)))
'(calcFunc-cos (/ (var pi var-pi) 4))))
(should (equal (math-simplify '(calcFunc-sec (/ (var pi var-pi) 4)))
'(calcFunc-sec (/ (var pi var-pi) 4))))
(should (equal (math-simplify '(calcFunc-csc (/ (var pi var-pi) 4)))
'(calcFunc-csc (/ (var pi var-pi) 4))))
(should (equal (math-simplify '(calcFunc-tan (/ (var pi var-pi) 3)))
'(calcFunc-tan (/ (var pi var-pi) 3))))
(should (equal (math-simplify '(calcFunc-cot (/ (var pi var-pi) 3)))
'(calcFunc-cot (/ (var pi var-pi) 3)))))))
(ert-deftest calc-test-format-radix ()
"Test integer formatting (bug#36689)."
(let ((calc-group-digits nil))
(let ((calc-number-radix 10))
(should (equal (math-format-number 12345678901) "12345678901")))
(let ((calc-number-radix 2))
(should (equal (math-format-number 12345) "2#11000000111001")))
(let ((calc-number-radix 8))
(should (equal (math-format-number 12345678901) "8#133767016065")))
(let ((calc-number-radix 16))
(should (equal (math-format-number 12345678901) "16#2DFDC1C35")))
(let ((calc-number-radix 36))
(should (equal (math-format-number 12345678901) "36#5O6AQT1"))))
(let ((calc-group-digits t))
(let ((calc-number-radix 10))
(should (equal (math-format-number 12345678901) "12,345,678,901")))
(let ((calc-number-radix 2))
(should (equal (math-format-number 12345) "2#11,0000,0011,1001")))
(let ((calc-number-radix 8))
(should (equal (math-format-number 12345678901) "8#133,767,016,065")))
(let ((calc-number-radix 16))
(should (equal (math-format-number 12345678901) "16#2,DFDC,1C35")))
(let ((calc-number-radix 36))
(should (equal (math-format-number 12345678901) "36#5,O6A,QT1")))))
(ert-deftest calc-test-calendar ()
"Test calendar conversions (bug#36822)."
(should (equal (calcFunc-julian (math-parse-date "2019-07-27")) 2458692))
(should (equal (math-parse-date "2019-07-27") '(date 737267)))
(should (equal (calcFunc-julian '(date 0)) 1721425))
(should (equal (math-date-to-gregorian-dt 1) '(1 1 1)))
(should (equal (math-date-to-gregorian-dt 0) '(-1 12 31)))
(should (equal (math-date-to-gregorian-dt -1721425) '(-4714 11 24)))
(should (equal (math-absolute-from-gregorian-dt 2019 7 27) 737267))
(should (equal (math-absolute-from-gregorian-dt 1 1 1) 1))
(should (equal (math-absolute-from-gregorian-dt -1 12 31) 0))
(should (equal (math-absolute-from-gregorian-dt -99 12 31) -35795))
(should (equal (math-absolute-from-gregorian-dt -4714 11 24) -1721425))
(should (equal (calcFunc-julian '(date -1721425)) 0))
(should (equal (math-date-to-julian-dt 1) '(1 1 3)))
(should (equal (math-date-to-julian-dt -1721425) '(-4713 1 1)))
(should (equal (math-absolute-from-julian-dt 2019 1 1) 737073))
(should (equal (math-absolute-from-julian-dt 1 1 3) 1))
(should (equal (math-absolute-from-julian-dt -101 1 1) -36892))
(should (equal (math-absolute-from-julian-dt -101 3 1) -36832))
(should (equal (math-absolute-from-julian-dt -4713 1 1) -1721425)))
(ert-deftest calc-test-solve-linear-system ()
"Test linear system solving (bug#35374)."
;; x + y = 3
;; 2x - 3y = -4
;; with the unique solution x=1, y=2
(should (equal
(calcFunc-solve
'(vec
(calcFunc-eq (+ (var x var-x) (var y var-y)) 3)
(calcFunc-eq (- (* 2 (var x var-x)) (* 3 (var y var-y))) -4))
'(vec (var x var-x) (var y var-y)))
'(vec (calcFunc-eq (var x var-x) 1)
(calcFunc-eq (var y var-y) 2))))
;; x + y = 1
;; x + y = 2
;; has no solution
(should (equal
(calcFunc-solve
'(vec
(calcFunc-eq (+ (var x var-x) (var y var-y)) 1)
(calcFunc-eq (+ (var x var-x) (var y var-y)) 2))
'(vec (var x var-x) (var y var-y)))
'(calcFunc-solve
(vec
(calcFunc-eq (+ (var x var-x) (var y var-y)) 1)
(calcFunc-eq (+ (var x var-x) (var y var-y)) 2))
(vec (var x var-x) (var y var-y)))))
;; x - y = 1
;; x + y = 1
;; with the unique solution x=1, y=0
(should (equal
(calcFunc-solve
'(vec
(calcFunc-eq (- (var x var-x) (var y var-y)) 1)
(calcFunc-eq (+ (var x var-x) (var y var-y)) 1))
'(vec (var x var-x) (var y var-y)))
'(vec (calcFunc-eq (var x var-x) 1)
(calcFunc-eq (var y var-y) 0))))
;; 2x - 3y + z = 5
;; x + y - 2z = 0
;; -x + 2y + 3z = -3
;; with the unique solution x=1, y=-1, z=0
(should (equal
(calcFunc-solve
'(vec
(calcFunc-eq
(+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z))
5)
(calcFunc-eq
(- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z)))
0)
(calcFunc-eq
(+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z)))
-3))
'(vec (var x var-x) (var y var-y) (var z var-z)))
;; The `float' forms in the result are just artefacts of Calc's
;; current solver; it should be fixed to produce exact (integral)
;; results in this case.
'(vec (calcFunc-eq (var x var-x) (float 1 0))
(calcFunc-eq (var y var-y) (float -1 0))
(calcFunc-eq (var z var-z) 0))))
;; x = y + 1
;; x = y
;; has no solution
(should (equal
(calcFunc-solve
'(vec
(calcFunc-eq (var x var-x) (+ (var y var-y) 1))
(calcFunc-eq (var x var-x) (var y var-y)))
'(vec (var x var-x) (var y var-y)))
'(calcFunc-solve
(vec
(calcFunc-eq (var x var-x) (+ (var y var-y) 1))
(calcFunc-eq (var x var-x) (var y var-y)))
(vec (var x var-x) (var y var-y)))))
;; x + y + z = 6
;; x + y = 3
;; x - y = 1
;; with the unique solution x=2, y=1, z=3
(should (equal
(calcFunc-solve
'(vec
(calcFunc-eq (+ (+ (var x var-x) (var y var-y)) (var z var-z)) 6)
(calcFunc-eq (+ (var x var-x) (var y var-y)) 3)
(calcFunc-eq (- (var x var-x) (var y var-y)) 1))
'(vec (var x var-x) (var y var-y) (var z var-z)))
'(vec
(calcFunc-eq (var x var-x) 2)
(calcFunc-eq (var y var-y) 1)
(calcFunc-eq (var z var-z) 3))))
;; x = 3
;; x + 4y^2 = 3 (ok, so this one isn't linear)
;; with the unique (double) solution x=3, y=0
(should (equal
(calcFunc-solve
'(vec
(calcFunc-eq (var x var-x) 3)
(calcFunc-eq (+ (var x var-x) (* 4 (^ (var y var-y) 2))) 3))
'(vec (var x var-x) (var y var-y)))
'(vec (calcFunc-eq (var x var-x) 3)
(calcFunc-eq (var y var-y) 0)))))
(provide 'calc-tests)
;;; calc-tests.el ends here
;; Local Variables:
;; bug-reference-url-format: "https://debbugs.gnu.org/%s"
;; End:
|
