From 07141fb72a9b9b7f7291dd0ad3ea747e665bd167 Mon Sep 17 00:00:00 2001
From: Thomas Baruchel <baruchel@sdf.org>
Date: Tue, 4 Oct 2022 18:29:50 +0200
Subject: [PATCH] Update

---
 thiele.lisp | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/thiele.lisp b/thiele.lisp
index 08184e4..7775224 100644
--- a/thiele.lisp
+++ b/thiele.lisp
@@ -31,6 +31,27 @@
 
 ; Thiele's interpolation formula
 ; ==============================
+; 
+;   In the following example, we use Thiele's interpolation formula
+;   for computing the inverse cos function cos^(-1) from 32 points
+;   given by the cos function itself.
+; 
+;   We create two vectors:
+;     * the vector 'a' contains regularly spaced points in [0..1.55]
+;     * the vector 'b' contains cos(x) for each x in vector 'a'
+; 
+;   We set the keepfloat flag to true in order to prevent Maxima
+;   to replace the values with rational approximations.
+; 
+;   Then we compute the inverse function by using thiele(b,a);
+;   we evaluate this interpolation at 0.5 expecting some value
+;   close to pi/3.
+; 
+; (%i1) a:makelist(0.05*i,i,0,31)$
+; (%i2) b:makelist(float(cos(0.05*i)),i,0,31)$
+; (%i3) keepfloat:true$
+; (%i4) subst(x=0.5, thiele(b,a))*3;
+; (%o4)                         3.14159265357928
 
 (defun $thiele (u v)
   (loop for rh on