guile/test-suite/tests/numbers.test

;;;; numbers.test --- tests guile's numbers     -*- scheme -*-
;;;; Copyright (C) 2000 Free Software Foundation, Inc.
;;;;
;;;; This program 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 2, or (at your option)
;;;; any later version.
;;;;
;;;; This program 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 this software; see the file COPYING.  If not, write to
;;;; the Free Software Foundation, Inc., 59 Temple Place, Suite 330,
;;;; Boston, MA 02111-1307 USA
;;;;
;;;; As a special exception, the Free Software Foundation gives permission
;;;; for additional uses of the text contained in its release of GUILE.
;;;;
;;;; The exception is that, if you link the GUILE library with other files
;;;; to produce an executable, this does not by itself cause the
;;;; resulting executable to be covered by the GNU General Public License.
;;;; Your use of that executable is in no way restricted on account of
;;;; linking the GUILE library code into it.
;;;;
;;;; This exception does not however invalidate any other reasons why
;;;; the executable file might be covered by the GNU General Public License.
;;;;
;;;; This exception applies only to the code released by the
;;;; Free Software Foundation under the name GUILE.  If you copy
;;;; code from other Free Software Foundation releases into a copy of
;;;; GUILE, as the General Public License permits, the exception does
;;;; not apply to the code that you add in this way.  To avoid misleading
;;;; anyone as to the status of such modified files, you must delete
;;;; this exception notice from them.
;;;;
;;;; If you write modifications of your own for GUILE, it is your choice
;;;; whether to permit this exception to apply to your modifications.
;;;; If you do not wish that, delete this exception notice.

(use-modules (ice-9 documentation))


;;;
;;; miscellaneous
;;;


(define (documented? object)
  (object-documentation object))


(define (make-test-name . args)
  (with-output-to-string
    (lambda ()
      (for-each display args))))


(define bit-widths '(8 16 27 28 29 30 31 32 64 128 256))


(define (2^x-1 x)
  (- (expt 2 x) 1))

(define (2^ x)
  (expt 2 x))

(define (n=2^x-1 x)
  (make-test-name "n = 2^" x " - 1"))

(define (n=-2^x+1 x)
  (make-test-name "n = -2^" x " + 1"))

(define (n=2^ x)
  (make-test-name "n = 2^" x))

(define (n=-2^ x)
  (make-test-name "n = -2^" x))


;;;
;;; exact?
;;;

(with-test-prefix "exact?"

  ;; Is documentation available?

  (pass-if "documented?"
    (documented? exact?))

  ;; Special case:  0

  (pass-if "0"
    (eq? #t (exact? 0)))

  ;; integers:

  (for-each 
   (lambda (x)
     (pass-if (make-test-name "2^" x " - 1")
       (eq? #t (exact? (2^x-1 x))))
     (pass-if (make-test-name "-2^" x " + 1")
       (eq? #t (exact? (- (2^x-1 x)))))
     (pass-if (make-test-name "2^" x)
       (eq? #t (exact? (2^ x))))
     (pass-if (make-test-name "-2^" x)
       (eq? #t (exact? (- (2^ x))))))
   bit-widths)

  ;; floats: (FIXME: need more examples)

  (for-each 
   (lambda (x)
     (pass-if (make-test-name "sqrt((2^" x " - 1)^2 - 1)")
       (eq? #f (exact? (sqrt (- (* (2^x-1 x) (2^x-1 x)) 1)))))
     (pass-if (make-test-name "sqrt((2^" x ")^2 + 1)")
       (eq? #f (exact? (sqrt (+ (* (2^ x) (2^ x)) 1))))))
   bit-widths))

;;;
;;; odd?
;;;


;;;
;;; even?
;;;


;;;
;;; abs
;;;


;;;
;;; quotient
;;;

(with-test-prefix "quotient"

  ;; Is documentation available?

  (expect-fail "documented?"
    (documented? quotient))

  ;; Special case:  0 / n

  (with-test-prefix "0 / n"

    (pass-if "n = 1"
      (eqv? 0 (quotient 0 1)))

    (pass-if "n = -1"
      (eqv? 0 (quotient 0 -1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (quotient 0 (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (quotient 0 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? 0 (quotient 0 (expt 2 x))))
       (pass-if (n=-2^ x)
	 (eqv? 0 (quotient 0 (- (expt 2 x))))))
     bit-widths))
  
  ;; Special case:  n / 1

  (with-test-prefix "n / 1"

    (pass-if "n = 1"
      (eqv? 1 (quotient 1 1)))

    (pass-if "n = -1"
      (eqv? -1 (quotient -1 1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? (2^x-1 x) (quotient (2^x-1 x) 1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? (- (2^x-1 x)) (quotient (- (2^x-1 x)) 1)))
       (pass-if (n=2^ x)
	 (eqv? (2^ x) (quotient (2^ x) 1)))
       (pass-if (n=-2^ x)
	 (eqv? (- (2^ x)) (quotient (- (2^ x)) 1))))
     bit-widths))

  ;; Special case:  n / -1

  (with-test-prefix "n / -1"

    (pass-if "n = 1"
      (eqv? -1 (quotient 1 -1)))

    (pass-if "n = -1"
      (eqv? 1 (quotient -1 -1)))

    (for-each
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? (- (2^x-1 x)) (quotient (2^x-1 x) -1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? (2^x-1 x) (quotient (- (2^x-1 x)) -1)))
       (pass-if (n=2^ x)
	 (eqv? (- (2^ x)) (quotient (2^ x) -1)))
       (pass-if (n=-2^ x)
	 (eqv? (2^ x) (quotient (- (2^ x)) -1))))
     bit-widths))

  ;; Special case:  n / n

  (with-test-prefix "n / n"

    (for-each
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 1 (quotient (2^x-1 x) (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? 1 (quotient (- (2^x-1 x)) (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? 1 (quotient (2^ x) (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? 1 (quotient (- (2^ x)) (- (2^ x))))))
     bit-widths))
  
  ;; Positive dividend and divisor

  (pass-if "35 / 7"
    (eqv? 5 (quotient 35 7)))

  ;; Negative dividend, positive divisor

  (pass-if "-35 / 7"
    (eqv? -5 (quotient -35 7)))

  ;; Positive dividend, negative divisor

  (pass-if "35 / -7"
    (eqv? -5 (quotient 35 -7)))

  ;; Negative dividend and divisor

  (pass-if "-35 / -7"
    (eqv? 5 (quotient -35 -7)))

  ;; Are numerical overflows detected correctly?

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; remainder
;;;

(with-test-prefix "remainder"

  ;; Is documentation available?

  (expect-fail "documented?"
    (documented? remainder))

  ;; Special case:  0 / n

  (with-test-prefix "0 / n"

    (pass-if "n = 1"
      (eqv? 0 (remainder 0 1)))

    (pass-if "n = -1"
      (eqv? 0 (remainder 0 -1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (remainder 0 (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (remainder 0 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? 0 (remainder 0 (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? 0 (remainder 0 (- (2^ x))))))
     bit-widths))

  ;; Special case:  n / 1

  (with-test-prefix "n / 1"

    (pass-if "n = 1"
      (eqv? 0 (remainder 1 1)))

    (pass-if "n = -1"
      (eqv? 0 (remainder -1 1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (remainder (2^x-1 x) 1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (remainder (- (2^x-1 x)) 1)))
       (pass-if (n=2^ x)
	 (eqv? 0 (remainder (2^ x) 1)))
       (pass-if (n=-2^ x)
	 (eqv? 0 (remainder (- (2^ x)) 1))))
     bit-widths))

  ;; Special case:  n / -1

  (with-test-prefix "n / -1"

    (pass-if "n = 1"
      (eqv? 0 (remainder 1 -1)))

    (pass-if "n = -1"
      (eqv? 0 (remainder -1 -1)))

    (for-each
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (remainder (2^x-1 x) -1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (remainder (- (2^x-1 x)) -1)))
       (pass-if (n=2^ x)
	 (eqv? 0 (remainder (2^ x) -1)))
       (pass-if (n=-2^ x)
	 (eqv? 0 (remainder (- (2^ x)) -1))))
     bit-widths))

  ;; Special case:  n / n

  (with-test-prefix "n / n"

    (for-each
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (remainder (2^x-1 x) (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (remainder (- (2^x-1 x)) (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? 0 (remainder (2^ x) (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? 0 (remainder (- (2^ x)) (- (2^ x))))))
     bit-widths))

  ;; Positive dividend and divisor

  (pass-if "35 / 7"
    (eqv? 0 (remainder 35 7)))

  ;; Negative dividend, positive divisor

  (pass-if "-35 / 7"
    (eqv? 0 (remainder -35 7)))

  ;; Positive dividend, negative divisor

  (pass-if "35 / -7"
    (eqv? 0 (remainder 35 -7)))

  ;; Negative dividend and divisor

  (pass-if "-35 / -7"
    (eqv? 0 (remainder -35 -7)))

  ;; Are numerical overflows detected correctly?

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; modulo
;;;

(with-test-prefix "modulo"

  ;; Is documentation available?

  (expect-fail "documented?"
    (documented? modulo))

  ;; Special case:  0 % n

  (with-test-prefix "0 % n"

    (pass-if "n = 1"
      (eqv? 0 (modulo 0 1)))

    (pass-if "n = -1"
      (eqv? 0 (modulo 0 -1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (modulo 0 (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (modulo 0 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? 0 (modulo 0 (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? 0 (modulo 0 (- (2^ x))))))
     bit-widths))

  ;; Special case:  n % 1

  (with-test-prefix "n % 1"

    (pass-if "n = 1"
      (eqv? 0 (modulo 1 1)))

    (pass-if "n = -1"
      (eqv? 0 (modulo -1 1)))

    (for-each
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (modulo (2^x-1 x) 1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (modulo (- (2^x-1 x)) 1)))
       (pass-if (n=2^ x)
	 (eqv? 0 (modulo (2^ x) 1)))
       (pass-if (n=-2^ x)
	 (eqv? 0 (modulo (- (2^ x)) 1))))
     bit-widths))

  ;; Special case:  n % -1

  (with-test-prefix "n % -1"

    (pass-if "n = 1"
      (eqv? 0 (modulo 1 -1)))

    (pass-if "n = -1"
      (eqv? 0 (modulo -1 -1)))

    (for-each
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 0 (modulo (2^x-1 x) -1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? 0 (modulo (- (2^x-1 x)) -1)))
       (pass-if (n=2^ x)
	 (eqv? 0 (modulo (2^ x) -1)))
       (pass-if (n=-2^ x)
	 (eqv? 0 (modulo (- (2^ x)) -1))))
     bit-widths))

  ;; Special case:  n % n

  (with-test-prefix "n % n"

  (for-each
   (lambda (x)
     (pass-if (n=2^x-1 x)
       (eqv? 0 (modulo (2^x-1 x) (2^x-1 x))))
     (pass-if (n=-2^x+1 x)
       (eqv? 0 (modulo (- (2^x-1 x)) (- (2^x-1 x)))))
     (pass-if (n=2^ x)
       (eqv? 0 (modulo (2^ x) (2^ x))))
     (pass-if (n=-2^ x)
       (eqv? 0 (modulo (- (2^ x)) (- (2^ x))))))
   bit-widths))

  ;; Positive dividend and divisor

  (pass-if "13 % 4"
    (eqv? 1 (modulo 13 4)))

  (pass-if "2177452800 % 86400"
    (eqv? 0 (modulo 2177452800 86400)))

  ;; Negative dividend, positive divisor

  (pass-if "-13 % 4"
    (eqv? 3 (modulo -13 4)))

  (pass-if "-2177452800 % 86400"
    (eqv? 0 (modulo -2177452800 86400)))

  ;; Positive dividend, negative divisor

  (pass-if "13 % -4"
    (eqv? -3 (modulo 13 -4)))

  (pass-if "2177452800 % -86400"
    (eqv? 0 (modulo 2177452800 -86400)))

  ;; Negative dividend and divisor

  (pass-if "-13 % -4"
    (eqv? -1 (modulo -13 -4)))

  (pass-if "-2177452800 % -86400"
    (eqv? 0 (modulo -2177452800 -86400)))

  ;; Are numerical overflows detected correctly?

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; gcd
;;;

(with-test-prefix "gcd"

  ;; Is documentation available?

  (expect-fail "documented?"
    (documented? gcd))

  ;; Special case:  gcd 0 n

  (with-test-prefix "(0 n)"

    (pass-if "n = 1"
      (eqv? 1 (gcd 0 1)))

    (pass-if "n = -1"
      (eqv? 1 (gcd 0 -1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? (2^x-1 x) (gcd 0 (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? (2^x-1 x) (gcd 0 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? (2^ x) (gcd 0 (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? (2^ x) (gcd 0 (- (2^ x))))))
     bit-widths))

  ;; Special case:  gcd n 0

  (with-test-prefix "(n 0)"

    (pass-if "n = 1"
      (eqv? 1 (gcd 1 0)))

    (pass-if "n = -1"
      (eqv? 1 (gcd -1 0)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? (2^x-1 x) (gcd (2^x-1 x) 0)))
       (pass-if (n=-2^x+1 x)
	 (eqv? (2^x-1 x) (gcd (- (2^x-1 x)) 0)))
       (pass-if (n=2^ x)
	 (eqv? (2^ x) (gcd (2^ x) 0)))
       (pass-if (n=-2^ x)
	 (eqv? (2^ x) (gcd (- (2^ x)) 0))))
     bit-widths))

  ;; Special case:  gcd 1 n

  (with-test-prefix "(1 n)"

    (pass-if "n = 1"
      (eqv? 1 (gcd 1 1)))

    (pass-if "n = -1"
      (eqv? 1 (gcd 1 -1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 1 (gcd 1 (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? 1 (gcd 1 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? 1 (gcd 1 (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? 1 (gcd 1 (- (2^ x))))))
     bit-widths))

  ;; Special case:  gcd n 1

  (with-test-prefix "(n 1)"

    (pass-if "n = -1"
      (eqv? 1 (gcd -1 1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 1 (gcd (2^x-1 x) 1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? 1 (gcd (- (2^x-1 x)) 1)))
       (pass-if (n=2^ x)
	 (eqv? 1 (gcd (2^ x) 1)))
       (pass-if (n=-2^ x)
	 (eqv? 1 (gcd (- (2^ x)) 1))))
     bit-widths))

  ;; Special case:  gcd -1 n

  (with-test-prefix "(-1 n)"

    (pass-if "n = -1"
      (eqv? 1 (gcd -1 -1)))

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 1 (gcd -1 (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? 1 (gcd -1 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? 1 (gcd -1 (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? 1 (gcd -1 (- (2^ x))))))
     bit-widths))

  ;; Special case:  gcd n -1

  (with-test-prefix "(n -1)"

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? 1 (gcd (2^x-1 x) -1)))
       (pass-if (n=-2^x+1 x)
	 (eqv? 1 (gcd (- (2^x-1 x)) -1)))
       (pass-if (n=2^ x)
	 (eqv? 1 (gcd (2^ x) -1)))
       (pass-if (n=-2^ x)
	 (eqv? 1 (gcd (- (2^ x)) -1))))
     bit-widths))

  ;; Special case:  gcd n n

  (with-test-prefix "(n n)"

    (for-each 
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (eqv? (2^x-1 x) (gcd (2^x-1 x) (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (eqv? (2^x-1 x) (gcd (- (2^x-1 x)) (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (eqv? (2^ x) (gcd (2^ x) (2^ x))))
       (pass-if (n=-2^ x)
	 (eqv? (2^ x) (gcd (- (2^ x)) (- (2^ x))))))
     bit-widths))

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; <
;;;

(with-test-prefix "<"

  ;; Is documentation available?

  (expect-fail "documented?"
    (documented? <))

  ;; Special case:  0 < n

  (with-test-prefix "(< 0 n)"
    
    (pass-if "n = 0"
      (not (< 0 0)))
    
    (pass-if "n = 0.0"
      (not (< 0 0.0)))
    
    (pass-if "n = 1"
      (< 0 1))
    
    (pass-if "n = 1.0"
      (< 0 1.0))
    
    (pass-if "n = -1"
      (not (< 0 -1)))
    
    (pass-if "n = -1.0"
      (not (< 0 -1.0)))
    
    (for-each ;; FIXME: compare agains floats.
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (< 0 (2^x-1 x)))
       (pass-if (n=-2^x+1 x)
	 (not (< 0 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (< 0 (2^ x)))
       (pass-if (n=-2^ x)
	 (not (< 0 (- (2^ x))))))
     bit-widths))
  
  ;; Special case:  0.0 < n

  (with-test-prefix "(< 0.0 n)"
    
    (pass-if "n = 0"
      (not (< 0.0 0)))
    
    (pass-if "n = 0.0"
      (not (< 0.0 0.0)))
    
    (pass-if "n = 1"
      (< 0.0 1))
    
    (pass-if "n = 1.0"
      (< 0.0 1.0))
    
    (pass-if "n = -1"
      (not (< 0.0 -1)))
    
    (pass-if "n = -1.0"
      (not (< 0.0 -1.0)))
    
    (for-each ;; FIXME: compare agains floats.
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (< 0.0 (2^x-1 x)))
       (pass-if (n=-2^x+1 x)
	 (not (< 0.0 (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (< 0.0 (2^ x)))
       (pass-if (n=-2^ x)
	 (not (< 0.0 (- (2^ x))))))
     bit-widths))
  
  ;; Special case:  n < 0

  (with-test-prefix "(< n 0)"
    
    (pass-if "n = 1"
      (not (< 1 0)))
    
    (pass-if "n = 1.0"
      (not (< 1.0 0)))
    
    (pass-if "n = -1"
      (< -1 0))
    
    (pass-if "n = -1.0"
      (< -1.0 0))
    
    (for-each ;; FIXME: compare agains floats.
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (not (< (2^x-1 x) 0)))
       (pass-if (n=-2^x+1 x)
	 (< (- (2^x-1 x)) 0))
       (pass-if (n=2^ x)
	 (not (< (2^ x) 0)))
       (pass-if (n=-2^ x)
	 (< (- (2^ x)) 0)))
     bit-widths))
  
  ;; Special case:  n < 0.0

  (with-test-prefix "(< n 0.0)"
    
    (pass-if "n = 1"
      (not (< 1 0.0)))
    
    (pass-if "n = 1.0"
      (not (< 1.0 0.0)))
    
    (pass-if "n = -1"
      (< -1 0.0))
    
    (pass-if "n = -1.0"
      (< -1.0 0.0))
    
    (for-each ;; FIXME: compare agains floats.
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (not (< (2^x-1 x) 0.0)))
       (pass-if (n=-2^x+1 x)
	 (< (- (2^x-1 x)) 0.0))
       (pass-if (n=2^ x)
	 (not (< (2^ x) 0.0)))
       (pass-if (n=-2^ x)
	 (< (- (2^ x)) 0.0)))
     bit-widths))
  
  ;; Special case:  n < n

  (with-test-prefix "(< n n)"
    
    (pass-if "n = 1"
      (not (< 1 1)))
    
    (pass-if "n = 1.0"
      (not (< 1.0 1.0)))
    
    (pass-if "n = -1"
      (not (< -1 -1)))
    
    (pass-if "n = -1.0"
      (not (< -1.0 -1.0)))
    
    (for-each ;; FIXME: compare agains floats.
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (not (< (2^x-1 x) (2^x-1 x))))
       (pass-if (n=-2^x+1 x)
	 (not (< (- (2^x-1 x)) (- (2^x-1 x)))))
       (pass-if (n=2^ x)
	 (not (< (2^ x) (2^ x))))
       (pass-if (n=-2^ x)
	 (not (< (- (2^ x)) (- (2^ x))))))
     bit-widths))

  ;; Special case:  n < n + 1

  (with-test-prefix "(< n (+ n 1))"
    
    (pass-if "n = 1"
      (< 1 2))
    
    (pass-if "n = 1.0"
      (< 1.0 2.0))
    
    (pass-if "n = -1"
      (< -1 0))
    
    (pass-if "n = -1.0"
      (< -1.0 0.0))
    
    (for-each ;; FIXME: compare agains floats.
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (< (2^x-1 x) (+ (2^x-1 x) 1)))
       (pass-if (n=-2^x+1 x)
	 (< (- (2^x-1 x)) (+ (- (2^x-1 x)) 1)))
       (pass-if (n=2^ x)
	 (< (2^ x) (+ (2^ x) 1)))
       (pass-if (n=-2^ x)
	 (< (- (2^ x)) (+ (- (2^ x)) 1))))
     bit-widths))

  ;; Special case:  n < n - 1

  (with-test-prefix "(< n (- n 1))"
    
    (pass-if "n = -1"
      (not (< -1 -2)))
    
    (pass-if "n = -1.0"
      (not (< -1.0 -2.0)))
    
    (for-each ;; FIXME: compare agains floats.
     (lambda (x)
       (pass-if (n=2^x-1 x)
	 (not (< (2^x-1 x) (- (2^x-1 x) 1))))
       (pass-if (n=-2^x+1 x)
	 (not (< (- (2^x-1 x)) (- (- (2^x-1 x)) 1))))
       (pass-if (n=2^ x)
	 (not (< (2^ x) (- (2^ x) 1))))
       (pass-if (n=-2^ x)
	 (not (< (- (2^ x)) (- (- (2^ x)) 1)))))
     bit-widths))

  ;; Special case:  

  )