update doc

tcaduser · tcaduser · commit 232aa7006abb · 2024-08-04T13:28:37.000-05:00
diff --git a/devsim_docs/TCADdocs.pdf b/devsim_docs/TCADdocs.pdf
diff --git a/devsim_docs/source/changes.rst b/devsim_docs/source/changes.rst
@@ -2,6 +2,11 @@
 Changes
 -------
 
+Version 0.0.3
+~~~~~~~~~~~~~
+
+    Add new method for Bernoulli function evaluation in :ref:`sec_bernoulli_new`.
+
 Version 0.0.2
 ~~~~~~~~~~~~~
 
diff --git a/devsim_docs/source/sg.rst b/devsim_docs/source/sg.rst
@@ -165,6 +165,36 @@ or
 Evaluate Bernoulli
 ~~~~~~~~~~~~~~~~~~
 
+.. _sec_bernoulli_new:
+
+New Method
+^^^^^^^^^^
+
+The C++ standard library provides the ``expm1`` function
+
+.. math::
+
+  \text{expm1}(x) = \exp(x) - 1
+
+which is more accurate than subtracting ``1`` from ``exp(x)``.
+
+A sample implementation is:
+
+.. code::
+
+  def B(x):
+    y = expm1(x)
+    if x != y:
+      b = 1.0/y
+    else:
+      b = 1.0 / (1. + 0.5*x)
+    return b
+
+Note that the check for ``x != y`` prevents a bad result when ``x == 0``.
+
+Old Method
+^^^^^^^^^^
+
 This requires an expansion near :math:`0` and use of :eq:`hf4`.
 
 .. math::
