Re: Some comments on the ansi test suite

>>>>> "Peter" == Peter Van Eynde <[email protected]> writes:

    Peter> On Tue, Jul 09, 2002 at 09:38:28AM -0400, Raymond Toy wrote:
    Peter> These are part of the less useful history of ansi-test. It came from an
    Peter> implementation that seems to have had its share of numeric bugs. So
    Peter> there are a lot of simple tests like this. Of course they fall on their
    Peter> face the moment you change fp format... 
    >> 
    >> What do you propose?  Leave them?  Remove them?  Change them to be be
    >> an approximately equal type of test instead of equality?

    Peter> Replace them with a better test would be nice. As most of them are fp
    Peter> problems we should (IMHO) replace them with "zero knowledge" tests or
    Peter> remove them.

Hmm, I seem not to have sent my proposals to this list.  Here they
are:

;; sin(8*pi/2) = sin(4*pi) = 0.  Assume that our pi is a bit off.  Say
;; pi*(1+eps).  Then sin(8*pi*(1+eps)/2) = sin(4*pi + 4*pi*eps) =
;; sin(4*pi*eps) ~= 4*pi*eps.  Test for this, but allow a fudge factor
;; of 2.
(check-for-bug :alltest-legacy-1045
  (let ((y (sin (* 8 (/ pi 2))))
	(fudge 2))
    (< (abs y) (* fudge (* 4 pi long-float-epsilon))))
  t)

;; As in 1045, cos(pi*(1+eps)/2) = cos(pi/2+pi*eps/2) = -sin(pi*eps/2)
;; ~= -pi*eps/2.  Check that we are close enough.
(check-for-bug :alltest-legacy-1061
  (let ((y (cos (/ pi 2)))
	(fudge 2))
    (< (abs y) (* fudge (* pi long-float-epsilon 1/2))))
  t)

;; As in 1045, tan(x) = sin(x)/cos(x).  When x = pi/2+pi*eps/2, sin(x)
;; is essentially 1, but cos(x) is about pi/2*eps.  So tan(x) =
;; 1/cos(x).  So we have 1/tan(x) = cos(x).  But from 1061, we know
;; that cos(x) ~= -pi*eps/2.  So our check is |1/tan(x) - cos(x)| is
;; close enough to zero.
(check-for-bug :alltest-legacy-1073
  (let* ((fudge 2)
	 (val (tan (/ pi 2)))
	 (ref (cos (/ pi 2)))
	 (rel-err (abs (/ (- (/ val) ref) ref))))
    (< rel-err (* fudge long-float-epsilon)))
  t)

Note that Clisp fails test 1073 because, strangely, 1/tan(x) gives
a quite different value from cos(x) here.

Ray


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