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<h4 class="subsection">D.7.1 <code>gslint</code> input parameters</h4>

<p>The library functions <code>qng</code> and <code>qagx</code> take an
argument of the form <code>(</code><var>f</var><code>,(</code><var>a</var><code>,</code><var>b</var><code>))</code>, where <var>f</var>
is a function to be integrated, <var>a</var> is the lower limit, and
<var>b</var> is the upper limit, both limits being floating point numbers
as in <a href="math.html#math">math</a>.

   <p>The <code>qng_tol</code> and <code>qagx_tol</code> functions take an argument of
<a name="index-tolerance-727"></a>the form <code>((</code><var>f</var><code>,</code><var>t</var><code>),(</code><var>a</var><code>,</code><var>b</var><code>))</code>, where <var>f</var>,
<var>a</var>, and <var>b</var> are as above, and <var>t</var> is a specified
tolerance.

   <p>The <code>qagp</code> and <code>qagp_tol</code> functions take arguments of
the form <code>(</code><var>f</var><code>,</code><var>p</var><code>)</code> and
<code>((</code><var>f</var><code>,</code><var>t</var><code>),</code><var>p</var><code>)</code>, respectively, where <var>f</var> and
<var>t</var> are as above, and <var>p</var> is an ordered list of real numbers
specifying the limits of integration along with arbitrarily many
intervening breakpoints.

   <p>The integrand <var>f</var> is expressed in virtual machine code, and takes a
single real argument to a real result. The argument and result of
<var>f</var> are required to be floating point numbers as described in
<a href="math.html#math">math</a>. Any expressible function of this type is acceptable, even
one defined in terms of other integrals, so that a double or triple
integral can be expressed easily, albeit a costly computation. 
However, a constant overhead in stack space is required for each
nested library function call, and there is currently no mechanism to
<a name="index-segmentation-fault-728"></a>prevent segmentation faults due to a stack overflow.

   <p>When no tolerance is specified, as with <code>qng</code>, <code>qagx</code>, and
<code>qagp</code>, the tightest attainable tolerance is chosen by default,
currently <code>2e-14</code>, in order find the most accurate result
possible. A selection of progressively looser tolerances is tried
automatically if the tightest one is not successful, stopping when
either a solution is found or ten orders of magnitude are covered.

   <p>If a tolerance is explicitly specified, as with <code>qng_tol</code>,
<code>qagx_tol</code> or <code>qagp_tol</code>, only that tolerance is tried.

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