;;;; numbers.test --- tests guile's numbers     -*- scheme -*-
;;;; Copyright (C) 2000, 2001 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.
;;;;
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;;;; 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
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(use-modules (ice-9 documentation))


;;;
;;; miscellaneous
;;;

(define exception:numerical-overflow
  (cons 'numerical-overflow "^Numerical overflow"))

(define (documented? object)
  (not (not (object-documentation object))))

(define fixnum-bit
  (inexact->exact (+ (/ (log (+ most-positive-fixnum 1)) (log 2)) 1)))

(define fixnum-min most-negative-fixnum)
(define fixnum-max most-positive-fixnum)


;;;
;;; exact?
;;;

(with-test-prefix "exact?"

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

  (with-test-prefix "integers"

    (pass-if "0"
      (exact? 0))

    (pass-if "fixnum-max"
      (exact? fixnum-max))

    (pass-if "fixnum-max + 1"
      (exact? (+ fixnum-max 1)))

    (pass-if "fixnum-min"
      (exact? fixnum-min))

    (pass-if "fixnum-min - 1"
      (exact? (- fixnum-min 1))))

  (with-test-prefix "reals"

    ;; (FIXME: need better examples.)

    (pass-if "sqrt (fixnum-max^2 - 1)"
      (eq? #f (exact? (sqrt (- (expt fixnum-max 2) 1)))))

    (pass-if "sqrt ((fixnum-max+1)^2 - 1)"
      (eq? #f (exact? (sqrt (- (expt (+ fixnum-max 1) 2) 1)))))))

;;;
;;; odd?
;;;


;;;
;;; even?
;;;


;;;
;;; abs
;;;


;;;
;;; quotient
;;;

(with-test-prefix "quotient"

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

  (with-test-prefix "0 / n"

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

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

    (pass-if "n = 2"
      (eqv? 0 (quotient 0 2)))

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

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

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

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

  (with-test-prefix "1 / n"

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

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

    (pass-if "n = 2"
      (eqv? 0 (quotient 1 2)))

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

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

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

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

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

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

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

    (pass-if "n = 2"
      (eqv? 0 (quotient -1 2)))

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

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

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

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

  (with-test-prefix "fixnum-max / n"

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

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

    (pass-if "n = 2"
      (eqv? fixnum-max (+ (* (quotient fixnum-max 2) 2) 1)))

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

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

    (pass-if "n = fixnum-min"
      (eqv? 0 (quotient fixnum-max fixnum-min)))

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

  (with-test-prefix "(fixnum-max + 1) / n"

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

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

    (pass-if "n = 2"
      (eqv? (+ fixnum-max 1) (* (quotient (+ fixnum-max 1) 2) 2)))

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

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

    (pass-if "n = fixnum-min"
      (eqv? -1 (quotient (+ fixnum-max 1) fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (eqv? 0 (quotient (+ fixnum-max 1) (- fixnum-min 1)))))

  (with-test-prefix "fixnum-min / n"

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

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

    (pass-if "n = 2"
      (eqv? fixnum-min (* (quotient fixnum-min 2) 2)))

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

    (pass-if "n = fixnum-max + 1"
      (eqv? -1 (quotient fixnum-min (+ fixnum-max 1))))

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

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

  (with-test-prefix "(fixnum-min - 1) / n"

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

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

    (pass-if "n = 2"
      (eqv? fixnum-min (* (quotient (- fixnum-min 1) 2) 2)))

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

    (pass-if "n = fixnum-max + 1"
      (eqv? -1 (quotient (- fixnum-min 1) (+ fixnum-max 1))))

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

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

  (with-test-prefix "division by zero"

    (pass-if-exception "(quotient 1 0)"
      exception:numerical-overflow
      (quotient 1 0))

    (pass-if-exception "(quotient bignum 0)"
      exception:numerical-overflow
      (quotient (+ fixnum-max 1) 0)))

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; remainder
;;;

(with-test-prefix "remainder"

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

  (with-test-prefix "0 / n"

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

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

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

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

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

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

  (with-test-prefix "1 / n"

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? 1 (remainder 1 (+ fixnum-max 1))))

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

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

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

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? -1 (remainder -1 (+ fixnum-max 1))))

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

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

  (with-test-prefix "fixnum-max / n"

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? fixnum-max (remainder fixnum-max (+ fixnum-max 1))))

    (pass-if "n = fixnum-min"
      (eqv? fixnum-max (remainder fixnum-max fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (eqv? fixnum-max (remainder fixnum-max (- fixnum-min 1)))))

  (with-test-prefix "(fixnum-max + 1) / n"

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

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

    (pass-if "n = fixnum-max"
      (eqv? 1 (remainder (+ fixnum-max 1) fixnum-max)))

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

    (pass-if "n = fixnum-min"
      (eqv? 0 (remainder (+ fixnum-max 1) fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (eqv? (+ fixnum-max 1) (remainder (+ fixnum-max 1) (- fixnum-min 1)))))

  (with-test-prefix "fixnum-min / n"

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

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

    (pass-if "n = fixnum-max"
      (eqv? -1 (remainder fixnum-min fixnum-max)))

    (pass-if "n = fixnum-max + 1"
      (eqv? 0 (remainder fixnum-min (+ fixnum-max 1))))

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

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

  (with-test-prefix "(fixnum-min - 1) / n"

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

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

    (pass-if "n = fixnum-max"
      (eqv? -2 (remainder (- fixnum-min 1) fixnum-max)))

    (pass-if "n = fixnum-max + 1"
      (eqv? -1 (remainder (- fixnum-min 1) (+ fixnum-max 1))))

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

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

  ;; 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?

  (with-test-prefix "division by zero"

    (pass-if-exception "(remainder 1 0)"
      exception:numerical-overflow
      (remainder 1 0))

    (pass-if-exception "(remainder bignum 0)"
      exception:numerical-overflow
      (remainder (+ fixnum-max 1) 0)))

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; modulo
;;;

(with-test-prefix "modulo"

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

  (with-test-prefix "0 % n"

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

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

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

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

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

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

  (with-test-prefix "1 % n"

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? 1 (modulo 1 (+ fixnum-max 1))))

    (pass-if "n = fixnum-min"
      (eqv? (+ fixnum-min 1) (modulo 1 fixnum-min)))

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

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

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? fixnum-max (modulo -1 (+ fixnum-max 1))))

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

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

  (with-test-prefix "fixnum-max % n"

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? fixnum-max (modulo fixnum-max (+ fixnum-max 1))))

    (pass-if "n = fixnum-min"
      (eqv? -1 (modulo fixnum-max fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (eqv? -2 (modulo fixnum-max (- fixnum-min 1)))))

  (with-test-prefix "(fixnum-max + 1) % n"

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

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

    (pass-if "n = fixnum-max"
      (eqv? 1 (modulo (+ fixnum-max 1) fixnum-max)))

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

    (pass-if "n = fixnum-min"
      (eqv? 0 (modulo (+ fixnum-max 1) fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (eqv? -1 (modulo (+ fixnum-max 1) (- fixnum-min 1)))))

  (with-test-prefix "fixnum-min % n"

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

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

    (pass-if "n = fixnum-max"
      (eqv? (- fixnum-max 1) (modulo fixnum-min fixnum-max)))

    (pass-if "n = fixnum-max + 1"
      (eqv? 0 (modulo fixnum-min (+ fixnum-max 1))))

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

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

  (with-test-prefix "(fixnum-min - 1) % n"

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

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

    (pass-if "n = fixnum-max"
      (eqv? (- fixnum-max 2) (modulo (- fixnum-min 1) fixnum-max)))

    (pass-if "n = fixnum-max + 1"
      (eqv? fixnum-max (modulo (- fixnum-min 1) (+ fixnum-max 1))))

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

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

  ;; 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?

  (with-test-prefix "division by zero"

    (pass-if-exception "(modulo 1 0)"
      exception:numerical-overflow
      (modulo 1 0))

    (pass-if-exception "(modulo bignum 0)"
      exception:numerical-overflow
      (modulo (+ fixnum-max 1) 0)))

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; gcd
;;;

(with-test-prefix "gcd"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    (pass-if "n = fixnum-max"
      (eqv? fixnum-max (gcd fixnum-max fixnum-max)))

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

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

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

  (with-test-prefix "((+ fixnum-max 1) n)"

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

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

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

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

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

    (pass-if "n = fixnum-min"
      (eqv? (+ fixnum-max 1) (gcd (+ fixnum-max 1) fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (eqv? 1 (gcd (+ fixnum-max 1) (- fixnum-min 1)))))

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

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

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? (+ fixnum-max 1) (gcd fixnum-min (+ fixnum-max 1))))

    (pass-if "n = fixnum-min"
      (eqv? (- fixnum-min) (gcd fixnum-min fixnum-min)))

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

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

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

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

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

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

    (pass-if "n = fixnum-max + 1"
      (eqv? 1 (gcd (- fixnum-min 1) (+ fixnum-max 1))))

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

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

  ;; Are wrong type arguments detected correctly?

  )

;;;
;;; lcm
;;;

;;;
;;; number->string
;;;

;;;
;;; string->number
;;;

(with-test-prefix "string->number"

  (pass-if "string->number"
    (documented? string->number))

  (pass-if "non number strings"
    (for-each (lambda (x) (if (string->number x) (throw 'fail)))
	      '("" "q" "1q" "6+7iq" "8+9q" "10+11" "13+" "18@19q" "20@q" "23@"
		"+25iq" "26i" "-q" "-iq" "i" "5#.0" "8/" "10#11" ".#" "."
		"#o.2" "3.4q" "15.16e17q" "18.19e+q" ".q" ".17#18" "10q" "#b2"
		"#b3" "#b4" "#b5" "#b6" "#b7" "#b8" "#b9" "#ba" "#bb" "#bc"
		"#bd" "#be" "#bf" "#q" "#b#b1" "#o#o1" "#d#d1" "#x#x1" "#e#e1"
		"#i#i1" "12@12+0i"))
    #t)

  (pass-if "valid number strings"
    (for-each (lambda (couple)
                (apply
                 (lambda (x y)
                   (let ((x (string->number x)))
                     (if (or (eq? x #f) (not (eqv? x y))) (throw 'fail))))
                 couple))
              `(;; Radix:
                ("#b0" 0) ("#B0" 0) ("#b1" 1) ("#B1" 1) ("#o0" 0) ("#O0" 0)
                ("#o1" 1) ("#O1" 1) ("#o2" 2) ("#O2" 2) ("#o3" 3) ("#O3" 3)
                ("#o4" 4) ("#O4" 4) ("#o5" 5) ("#O5" 5) ("#o6" 6) ("#O6" 6)
                ("#o7" 7) ("#O7" 7) ("#d0" 0) ("#D0" 0) ("#d1" 1) ("#D1" 1)
                ("#d2" 2) ("#D2" 2) ("#d3" 3) ("#D3" 3) ("#d4" 4) ("#D4" 4)
                ("#d5" 5) ("#D5" 5) ("#d6" 6) ("#D6" 6) ("#d7" 7) ("#D7" 7)
                ("#d8" 8) ("#D8" 8) ("#d9" 9) ("#D9" 9)
                ("#xa" 10) ("#Xa" 10) ("#xb" 11) ("#Xb" 11)
                ("#xc" 12) ("#Xc" 12) ("#xd" 13) ("#Xd" 13)
                ("#xe" 14) ("#Xe" 14) ("#xf" 15) ("#Xf" 15)
                ("#b1010" 10)
                ("#o12345670" 2739128)
                ("#d1234567890" 1234567890)
                ("#x1234567890abcdef" 1311768467294899695)
                ;; Exactness:
                ("#e1" 1) ("#e1.2" 1) ("#i1.1" 1.1) ("#i1" 1.0)
                ;; Integers:
                ("1" ,(1+ 0)) ("23" ,(+ 9 9 5)) ("-1" ,(- 0 1)) 
                ("-45" ,(- 0 45)) ("2#" 20.0) ("2##" 200.0) ("12##" 1200.0)
                ("#b#i100" 4.0)
                ;; Rationals:
                ("1/1" 1) ("1/2" 0.5) ("-1/2" -0.5) ("1#/1" 10.0)
                ("10/1#" 1.0) ("1#/1#" 1.0) ("#e9/10" 1) ("#e10/1#" 1)
                ("#i6/8" 0.75) ("#i1/1" 1.0)
                ;; Decimal numbers:
                ;; * <uinteger 10> <suffix>
                ("1e2" 100.0) ("1E2" 100.0) ("1s2" 100.0) ("1S2" 100.0)
                ("1f2" 100.0) ("1F2" 100.0) ("1d2" 100.0) ("1D2" 100.0)
                ("1l2" 100.0) ("1L2" 100.0) ("1e+2" 100.0) ("1e-2" 0.01)
                ;; * . <digit 10>+ #* <suffix>
                (".1" .1) (".0123456789" 123456789e-10) (".16#" 0.16)
                (".0123456789e10" 123456789.0) (".16#e3" 160.0) ("#d.3" 0.3)
                ;; * <digit 10>+ . <digit 10>* #* <suffix>
                ("3." ,(exact->inexact 3)) ("3.e0" ,(exact->inexact 3))
                ("3.1" ,(exact->inexact 31/10)) ("3.1e0" 3.1) ("3.1#" 3.1)
                ("3.1#e0" 3.1)
                ;; * <digit 10>+ #+ . #* <suffix>
                ("3#." 30.0) ("3#.e0" 30.0) ("3#.#" 30.0) ("3#.#e0" 30.0)
                ;; Complex:
                ("1@0" 1.0) ("1@+0" 1.0) ("1@-0" 1.0)
                ("2+3i" ,(+ 2 (* 3 +i))) ("4-5i" ,(- 4 (* 5 +i)))
                ("1+i" 1+1i) ("1-i" 1-1i) ("+1i" 0+1i) ("-1i" 0-1i)
                ("+i" +1i) ("-i" -1i)))
    #t)

  (pass-if-exception "exponent too big"
    exception:out-of-range
    (string->number "12.13e141414")))

;;;
;;; number?
;;;

;;;
;;; complex?
;;;

;;;
;;; real?
;;;

;;;
;;; rational?
;;;

;;;
;;; integer?
;;;

;;;
;;; inexact?
;;;

;;;
;;; =
;;;

;;;
;;; <
;;;

(with-test-prefix "<"

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

  (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)))
    
    (pass-if "n = fixnum-max"
      (< 0 fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< 0 (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< 0 fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< 0 (- fixnum-min 1)))))
  
  (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)))
    
    (pass-if "n = fixnum-max"
      (< 0.0 fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< 0.0 (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< 0.0 fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< 0.0 (- fixnum-min 1)))))
  
  (with-test-prefix "(< 1 n)"
    
    (pass-if "n = 0"
      (not (< 1 0)))
    
    (pass-if "n = 0.0"
      (not (< 1 0.0)))
    
    (pass-if "n = 1"
      (not (< 1 1)))
    
    (pass-if "n = 1.0"
      (not (< 1 1.0)))
    
    (pass-if "n = -1"
      (not (< 1 -1)))
    
    (pass-if "n = -1.0"
      (not (< 1 -1.0)))
    
    (pass-if "n = fixnum-max"
      (< 1 fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< 1 (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< 1 fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< 1 (- fixnum-min 1)))))

  (with-test-prefix "(< 1.0 n)"
    
    (pass-if "n = 0"
      (not (< 1.0 0)))
    
    (pass-if "n = 0.0"
      (not (< 1.0 0.0)))
    
    (pass-if "n = 1"
      (not (< 1.0 1)))
    
    (pass-if "n = 1.0"
      (not (< 1.0 1.0)))
    
    (pass-if "n = -1"
      (not (< 1.0 -1)))
    
    (pass-if "n = -1.0"
      (not (< 1.0 -1.0)))
    
    (pass-if "n = fixnum-max"
      (< 1.0 fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< 1.0 (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< 1.0 fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< 1.0 (- fixnum-min 1)))))
  
  (with-test-prefix "(< -1 n)"
    
    (pass-if "n = 0"
      (< -1 0))
    
    (pass-if "n = 0.0"
      (< -1 0.0))
    
    (pass-if "n = 1"
      (< -1 1))
    
    (pass-if "n = 1.0"
      (< -1 1.0))
    
    (pass-if "n = -1"
      (not (< -1 -1)))
    
    (pass-if "n = -1.0"
      (not (< -1 -1.0)))
    
    (pass-if "n = fixnum-max"
      (< -1 fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< -1 (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< -1 fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< -1 (- fixnum-min 1)))))

  (with-test-prefix "(< -1.0 n)"
    
    (pass-if "n = 0"
      (< -1.0 0))
    
    (pass-if "n = 0.0"
      (< -1.0 0.0))
    
    (pass-if "n = 1"
      (< -1.0 1))
    
    (pass-if "n = 1.0"
      (< -1.0 1.0))
    
    (pass-if "n = -1"
      (not (< -1.0 -1)))
    
    (pass-if "n = -1.0"
      (not (< -1.0 -1.0)))
    
    (pass-if "n = fixnum-max"
      (< -1.0 fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< -1.0 (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< -1.0 fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< -1.0 (- fixnum-min 1)))))

  (with-test-prefix "(< fixnum-max n)"
    
    (pass-if "n = 0"
      (not (< fixnum-max 0)))
    
    (pass-if "n = 0.0"
      (not (< fixnum-max 0.0)))
    
    (pass-if "n = 1"
      (not (< fixnum-max 1)))
    
    (pass-if "n = 1.0"
      (not (< fixnum-max 1.0)))
    
    (pass-if "n = -1"
      (not (< fixnum-max -1)))
    
    (pass-if "n = -1.0"
      (not (< fixnum-max -1.0)))
    
    (pass-if "n = fixnum-max"
      (not (< fixnum-max fixnum-max)))

    (pass-if "n = fixnum-max + 1"
      (< fixnum-max (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< fixnum-max fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< fixnum-max (- fixnum-min 1)))))

  (with-test-prefix "(< (+ fixnum-max 1) n)"
    
    (pass-if "n = 0"
      (not (< (+ fixnum-max 1) 0)))
    
    (pass-if "n = 0.0"
      (not (< (+ fixnum-max 1) 0.0)))
    
    (pass-if "n = 1"
      (not (< (+ fixnum-max 1) 1)))
    
    (pass-if "n = 1.0"
      (not (< (+ fixnum-max 1) 1.0)))
    
    (pass-if "n = -1"
      (not (< (+ fixnum-max 1) -1)))
    
    (pass-if "n = -1.0"
      (not (< (+ fixnum-max 1) -1.0)))
    
    (pass-if "n = fixnum-max"
      (not (< (+ fixnum-max 1) fixnum-max)))

    (pass-if "n = fixnum-max + 1"
      (not (< (+ fixnum-max 1) (+ fixnum-max 1))))

    (pass-if "n = fixnum-min"
      (not (< (+ fixnum-max 1) fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< (+ fixnum-max 1) (- fixnum-min 1)))))

  (with-test-prefix "(< fixnum-min n)"
    
    (pass-if "n = 0"
      (< fixnum-min 0))
    
    (pass-if "n = 0.0"
      (< fixnum-min 0.0))
    
    (pass-if "n = 1"
      (< fixnum-min 1))
    
    (pass-if "n = 1.0"
      (< fixnum-min 1.0))
    
    (pass-if "n = -1"
      (< fixnum-min -1))
    
    (pass-if "n = -1.0"
      (< fixnum-min -1.0))
    
    (pass-if "n = fixnum-max"
      (< fixnum-min fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< fixnum-min (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (not (< fixnum-min fixnum-min)))

    (pass-if "n = fixnum-min - 1"
      (not (< fixnum-min (- fixnum-min 1)))))

  (with-test-prefix "(< (- fixnum-min 1) n)"
    
    (pass-if "n = 0"
      (< (- fixnum-min 1) 0))
    
    (pass-if "n = 0.0"
      (< (- fixnum-min 1) 0.0))
    
    (pass-if "n = 1"
      (< (- fixnum-min 1) 1))
    
    (pass-if "n = 1.0"
      (< (- fixnum-min 1) 1.0))
    
    (pass-if "n = -1"
      (< (- fixnum-min 1) -1))
    
    (pass-if "n = -1.0"
      (< (- fixnum-min 1) -1.0))
    
    (pass-if "n = fixnum-max"
      (< (- fixnum-min 1) fixnum-max))

    (pass-if "n = fixnum-max + 1"
      (< (- fixnum-min 1) (+ fixnum-max 1)))

    (pass-if "n = fixnum-min"
      (< (- fixnum-min 1) fixnum-min))

    (pass-if "n = fixnum-min - 1"
      (not (< (- fixnum-min 1) (- fixnum-min 1))))))

;;;
;;; >
;;;

;;;
;;; <=
;;;

;;;
;;; >=
;;;

;;;
;;; zero?
;;;

;;;
;;; positive?
;;;

;;;
;;; negative?
;;;

;;;
;;; max
;;;

;;;
;;; min
;;;

;;;
;;; +
;;;

(with-test-prefix "+"

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

  (with-test-prefix "wrong type argument"

    (pass-if-exception "1st argument string"
      exception:wrong-type-arg
      (+ "1" 2))

    (pass-if-exception "2nd argument bool"
      exception:wrong-type-arg
      (+ 1 #f))))
;;;
;;; -
;;;

;;;
;;; *
;;;

;;;
;;; /
;;;

(with-test-prefix "/"

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

  (with-test-prefix "division by zero"

    (pass-if-exception "(/ 0)"
      exception:numerical-overflow
      (/ 0))

    (pass-if-exception "(/ 0.0)"
      exception:numerical-overflow
      (/ 0.0))

    (pass-if-exception "(/ 1 0)"
      exception:numerical-overflow
      (/ 1 0))

    (pass-if-exception "(/ 1 0.0)"
      exception:numerical-overflow
      (/ 1 0.0))

    (pass-if-exception "(/ bignum 0)"
      exception:numerical-overflow
      (/ (+ fixnum-max 1) 0))

    (pass-if-exception "(/ bignum 0.0)"
      exception:numerical-overflow
      (/ (+ fixnum-max 1) 0.0))

    (pass-if-exception "(/ 1.0 0)"
      exception:numerical-overflow
      (/ 1.0 0))

    (pass-if-exception "(/ 1.0 0.0)"
      exception:numerical-overflow
      (/ 1.0 0.0))

    (pass-if-exception "(/ +i 0)"
      exception:numerical-overflow
      (/ +i 0))

    (pass-if-exception "(/ +i 0.0)"
      exception:numerical-overflow
      (/ +i 0.0)))

  (with-test-prefix "complex division"

    (pass-if "(/ 3+4i)"
      (= (/ 3+4i) 0.12-0.16i))

    (pass-if "(/ 4+3i)"
      (= (/ 4+3i) 0.16-0.12i))

    (pass-if "(/ 25+125i 3+4i)"
      (= (/ 25+125i 3+4i) 23.0+11.0i))

    (pass-if "(/ 25+125i 4+3i)"
      (= (/ 25+125i 4+3i) 19.0+17.0i))

    (pass-if "(/ 25 3+4i)"
      (= (/ 25 3+4i) 3.0-4.0i))

    (pass-if "(/ 25 4+3i)"
      (= (/ 25 4+3i) 4.0-3.0i))

    (pass-if "(/ 1e200+1e200i)"
      (= (/ 1e200+1e200i) 5.0e-201-5.0e-201i))))

;;;
;;; truncate
;;;

;;;
;;; round
;;;

;;;
;;; exact->inexact
;;;

;;;
;;; floor
;;;

;;;
;;; ceiling
;;;

;;;
;;; make-rectangular
;;;

;;;
;;; make-polar
;;;

;;;
;;; real-part
;;;

;;;
;;; imag-part
;;;

;;;
;;; magnitude
;;;

;;;
;;; angle
;;;

;;;
;;; inexact->exact
;;;