--- a/scripts/general/quadl.m	Thu Aug 25 04:07:11 2011 -0500
+++ b/scripts/general/quadl.m	Thu Aug 25 09:51:27 2011 -0700
@@ -62,14 +62,12 @@
 ##   * replace global variable terminate2 with local function need_warning
 ##   * add paper ref to docs
 
-function q = quadl (f, a, b, tol, trace, varargin)
-  need_warning (1);
-  if (nargin < 4)
-    tol = [];
+function q = quadl (f, a, b, tol = [], trace = false, varargin)
+
+  if (nargin < 3)
+    print_usage ();
   endif
-  if (nargin < 5)
-    trace = [];
-  endif
+
   if (isa (a, "single") || isa (b, "single"))
     myeps = eps ("single");
   else
@@ -79,16 +77,23 @@
     tol = myeps;
   endif
   if (isempty (trace))
-    trace = 0;
+    trace = false;
   endif
   if (tol < myeps)
     tol = myeps;
   endif
 
+  ## Track whether recursion has occurred
+  global __quadl_recurse_done__;
+  __quadl_recurse_done__ = false;
+  ## Track whether warning about machine precision has been issued
+  global __quadl_need_warning__;
+  __quadl_need_warning__ = true;
+
   m = (a+b)/2;
   h = (b-a)/2;
-  alpha = sqrt(2/3);
-  beta = 1/sqrt(5);
+  alpha = sqrt (2/3);
+  beta = 1/sqrt (5);
 
   x1 = .942882415695480;
   x2 = .641853342345781;
@@ -104,12 +109,12 @@
 
   i2 = (h/6)*(y(1) + y(13) + 5*(y(5)+y(9)));
 
-  i1 = (h/1470)*(77*(y(1)+y(13))
+  i1 = (h/1470)*(   77*(y(1)+y(13))
                  + 432*(y(3)+y(11))
                  + 625*(y(5)+y(9))
                  + 672*y(7));
 
-  is = h*(.0158271919734802*(y(1)+y(13))
+  is = h*( .0158271919734802*(y(1)+y(13))
           +.0942738402188500*(y(2)+y(12))
           + .155071987336585*(y(3)+y(11))
           + .188821573960182*(y(4)+y(10))
@@ -117,102 +122,96 @@
           + .224926465333340*(y(6)+y(8))
           + .242611071901408*y(7));
 
-  s = sign(is);
-
+  s = sign (is);
   if (s == 0)
     s = 1;
   endif
-  erri1 = abs(i1-is);
-  erri2 = abs(i2-is);
-  R = 1;
+  erri1 = abs (i1-is);
+  erri2 = abs (i2-is);
   if (erri2 != 0)
     R = erri1/erri2;
+  else
+    R = 1;
   endif
   if (R > 0 && R < 1)
     tol = tol/R;
   endif
-  is = s*abs(is)*tol/myeps;
+  is = s * abs(is) * tol/myeps;
   if (is == 0)
     is = b-a;
   endif
+
   q = adaptlobstp (f, a, b, fa, fb, is, trace, varargin{:});
+
 endfunction
 
 ## ADAPTLOBSTP  Recursive function used by QUADL.
 ##
 ##   Q = ADAPTLOBSTP('F', A, B, FA, FB, IS, TRACE) tries to
 ##   approximate the integral of F(X) from A to B to
-##   an appropriate relative error. The argument 'F' is
+##   an appropriate relative error.  The argument 'F' is
 ##   a string containing the name of f.  The remaining
 ##   arguments are generated by ADAPTLOB or by recursion.
 ##
 ##   Walter Gautschi, 08/03/98
 
 function q = adaptlobstp (f, a, b, fa, fb, is, trace, varargin)
+  global __quadl_recurse_done__;
+  global __quadl_need_warning__;
+
   h = (b-a)/2;
   m = (a+b)/2;
-  alpha = sqrt(2/3);
-  beta = 1/sqrt(5);
+  alpha = sqrt (2/3);
+  beta = 1 / sqrt(5);
   mll = m-alpha*h;
-  ml = m-beta*h;
-  mr = m+beta*h;
+  ml  = m-beta*h;
+  mr  = m+beta*h;
   mrr = m+alpha*h;
   x = [mll, ml, m, mr, mrr];
-  y = feval(f, x, varargin{:});
+  y = feval (f, x, varargin{:});
   fmll = y(1);
-  fml = y(2);
-  fm = y(3);
-  fmr = y(4);
+  fml  = y(2);
+  fm   = y(3);
+  fmr  = y(4);
   fmrr = y(5);
   i2 = (h/6)*(fa + fb + 5*(fml+fmr));
   i1 = (h/1470)*(77*(fa+fb) + 432*(fmll+fmrr) + 625*(fml+fmr) + 672*fm);
-  if (is+(i1-i2) == is || mll <= a || b <= mrr)
-    if ((m <= a || b <= m) && need_warning ())
+  if ((is+(i1-i2) == is || mll <= a || b <= mrr) && __quadl_recurse_done__)
+    if ((m <= a || b <= m) && __quadl_need_warning__)
       warning ("quadl: interval contains no more machine number");
       warning ("quadl: required tolerance may not be met");
-      need_warning (0);
+      __quadl_need_warning__ = false;
     endif
     q = i1;
     if (trace)
       disp ([a, b-a, q]);
     endif
   else
-    q = (adaptlobstp (f, a, mll, fa, fmll, is, trace, varargin{:})
-         + adaptlobstp (f, mll, ml, fmll, fml, is, trace, varargin{:})
-         + adaptlobstp (f, ml, m, fml, fm, is, trace, varargin{:})
-         + adaptlobstp (f, m, mr, fm, fmr, is, trace, varargin{:})
-         + adaptlobstp (f, mr, mrr, fmr, fmrr, is, trace, varargin{:})
-         + adaptlobstp (f, mrr, b, fmrr, fb, is, trace, varargin{:}));
-  endif
-endfunction
-
-function r = need_warning (v)
-  persistent w = [];
-  if (nargin == 0)
-    r = w;
-  else
-    w = v;
+    __quadl_recurse_done__ = true;
+    q = (  adaptlobstp (f, a  , mll, fa  , fmll, is, trace, varargin{:})
+         + adaptlobstp (f, mll, ml , fmll, fml , is, trace, varargin{:})
+         + adaptlobstp (f, ml , m  , fml , fm  , is, trace, varargin{:})
+         + adaptlobstp (f, m  , mr , fm  , fmr , is, trace, varargin{:})
+         + adaptlobstp (f, mr , mrr, fmr , fmrr, is, trace, varargin{:})
+         + adaptlobstp (f, mrr, b  , fmrr, fb  , is, trace, varargin{:}));
   endif
 endfunction
 
 
 ## basic functionality
-%!assert( quadl (@(x) sin (x), 0, pi, [], []), 2, -3e-16)
+%!assert (quadl (@(x) sin (x), 0, pi, [], []), 2, -3e-16)
 
 ## the values here are very high so it may be unavoidable that this fails
-%!assert ( quadl (@(x) sin (3*x).*cosh (x).*sinh (x),10,15),
+%!assert (quadl (@(x) sin (3*x).*cosh (x).*sinh (x),10,15),
 %!         2.588424538641647e+10, -9e-15)
 
 ## extra parameters
 %!assert (quadl (@(x,a,b) sin (a + b*x), 0, 1, [], [], 2, 3),
 %!        cos(2)/3 - cos(5)/3, - 3e-16)
 
-## test different tolerances. This test currently fails for a very high
-## tolerances.
-%!assert ( quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.3, []),
+## test different tolerances. 
+%!assert (quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.3, []),
 %!        (60 + sin(4) - sin(64))/12, -0.3)
+%!assert (quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.1, []),
+%!        (60 + sin(4) - sin(64))/12, -0.1)
 
-
-## for lower tolerances the test passes.
-%!assert ( quadl (@(x) sin (2 + 3*x).^2, 0, 10, 0.1, []),
-%!        (60 + sin(4) - sin(64))/12, -0.1)
\ No newline at end of file