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;;; floatfns-tests.el --- tests for floating point operations
;; Copyright 2017-2019 Free Software Foundation, Inc.
;; 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/>.
(require 'ert)
(ert-deftest divide-extreme-sign ()
(should (= (ceiling most-negative-fixnum -1.0) (- most-negative-fixnum)))
(should (= (floor most-negative-fixnum -1.0) (- most-negative-fixnum)))
(should (= (round most-negative-fixnum -1.0) (- most-negative-fixnum)))
(should (= (truncate most-negative-fixnum -1.0) (- most-negative-fixnum))))
(ert-deftest logb-extreme-fixnum ()
(should (= (logb most-negative-fixnum) (1+ (logb most-positive-fixnum)))))
(ert-deftest fround-fixnum ()
(should-error (ffloor 0) :type 'wrong-type-argument)
(should-error (fceiling 0) :type 'wrong-type-argument)
(should-error (ftruncate 0) :type 'wrong-type-argument)
(should-error (fround 0) :type 'wrong-type-argument))
(ert-deftest bignum-to-float ()
;; 122 because we want to go as big as possible to provoke a rounding error,
;; but not too big: 2**122 < 10**37 < 2**123, and the C standard says
;; 10**37 <= DBL_MAX so 2**122 cannot overflow as a double.
(let ((a (1- (ash 1 122))))
(should (or (eql a (1- (floor (float a))))
(eql a (floor (float a))))))
(should (eql (float (+ most-positive-fixnum 1))
(+ (float most-positive-fixnum) 1))))
(ert-deftest bignum-abs ()
(should (= most-positive-fixnum
(- (abs most-negative-fixnum) 1))))
(ert-deftest bignum-expt ()
(dolist (n (list most-positive-fixnum (1+ most-positive-fixnum)
most-negative-fixnum (1- most-negative-fixnum)
(* 5 most-negative-fixnum)
(* 5 (1+ most-positive-fixnum))
-2 -1 0 1 2))
(should (or (<= n 0) (= (expt 0 n) 0)))
(should (= (expt 1 n) 1))
(should (or (< n 0) (= (expt -1 n) (if (zerop (logand n 1)) 1 -1))))
(should (= (expt n 0) 1))
(should (= (expt n 1) n))
(should (= (expt n 2) (* n n)))
(should (= (expt n 3) (* n n n)))))
(ert-deftest bignum-logb ()
(should (= (+ (logb most-positive-fixnum) 1)
(logb (+ most-positive-fixnum 1)))))
(ert-deftest bignum-mod ()
(should (= 0 (mod (1+ most-positive-fixnum) 2.0))))
(ert-deftest bignum-round ()
(let ((ns (list (* most-positive-fixnum most-negative-fixnum)
(1- most-negative-fixnum) most-negative-fixnum
(1+ most-negative-fixnum) -2 1 1 2
(1- most-positive-fixnum) most-positive-fixnum
(1+ most-positive-fixnum)
(* most-positive-fixnum most-positive-fixnum))))
(dolist (n ns)
(should (= n (ceiling n)))
(should (= n (floor n)))
(should (= n (round n)))
(should (= n (truncate n)))
(let ((-n (- n))
(f (float n))
(-f (- (float n))))
(should (= 1 (round n f) (round -n -f) (round f n) (round -f -n)))
(should (= -1 (round -n f) (round n -f) (round f -n) (round -f n))))
(dolist (d ns)
(let ((q (/ n d))
(r (% n d))
(same-sign (eq (< n 0) (< d 0))))
(should (= (ceiling n d)
(+ q (if (and same-sign (not (zerop r))) 1 0))))
(should (= (floor n d)
(- q (if (and (not same-sign) (not (zerop r))) 1 0))))
(should (= (truncate n d) q))
(let ((cdelta (abs (- n (* d (ceiling n d)))))
(fdelta (abs (- n (* d (floor n d)))))
(rdelta (abs (- n (* d (round n d))))))
(should (<= rdelta cdelta))
(should (<= rdelta fdelta))
(should (if (zerop r)
(= 0 cdelta fdelta rdelta)
(or (/= cdelta fdelta)
(zerop (% (round n d) 2)))))))))))
(ert-deftest special-round ()
(dolist (f '(ceiling floor round truncate))
(let ((ns '(-1e+INF 1e+INF -1 -0.0 0.0 0 1 -1e+NaN 1e+NaN)))
(dolist (n ns)
(if (not (<= (abs n) 1))
(should-error (funcall f n))
(should (= n (funcall f n)))
(dolist (d '(-1e+INF 1e+INF))
(should (eq 0 (funcall f n d)))))
(dolist (d ns)
(when (or (zerop d) (= (abs n) 1e+INF) (not (= n n)) (not (= d d)))
(should-error (funcall f n d))))))))
(ert-deftest big-round ()
(should (= (floor 54043195528445955 3)
(floor 54043195528445955 3.0)))
(should (= (floor 1.7976931348623157e+308 5e-324)
(ash (1- (ash 1 53)) 2045))))
(provide 'floatfns-tests)
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