Changes between Version 1 and Version 2 of doc/maths/remez/tutorial-exponential Tweet

Timestamp:

Dec 28, 2011, 11:17:19 PM (11 years ago)

Author:

sam

Comment:

--

doc/maths/remez/tutorial-exponential

@@ -1 +1 @@
 = Remez tutorial first example: exp(x) =
 
-This section is a hands-on example of the Lol Remez toolkit.
+In this section we are going to approximate the ''exp(x)'' function using a polynomial.
+
+This should be a hands-on example of the Lol Remez toolkit.
 
 == Source code ==
@@ -31 +33 @@
 == Compilation ==
 
+If you are using LolRemez, just put the above source code in `remez.cpp` and type:
+
+{{{
+make
+}}}
+
+== Execution ==
+
+To launch the test, type:
+
+{{{
+./remez
+}}}
+
 After all the iterations the output should be as follows:
 
-
-Let’s say we want to approximate the following function:
-
 {{{
-#!latex
-\[f(x) = \e^x\]
+Final error: 5.462771976237482581009771665937582411463e-4
+Polynomial estimate:
+x**0*1.000090756764725753887362987792025308996
++x**1*9.973086551667860566788019540269306006270e-1
++x**2*4.988332174505582284710918757571761729419e-1
++x**3*1.773462612793916519454714108029230813767e-1
++x**4*4.415666059995979611944324860870682575219e-2
 }}}
 
+== Using the results ==
+
+The above results can be used in a C++ implementation:
+ 
+{{{
+#!cpp
+double fastexp(double x)
+{
+    const double a0 = 1.000090756764725753887362987792025308996;
+    const double a1 = 9.973086551667860566788019540269306006270e-1;
+    const double a2 = 4.988332174505582284710918757571761729419e-1;
+    const double a3 = 1.773462612793916519454714108029230813767e-1;
+    const double a4 = 4.415666059995979611944324860870682575219e-2;
+
+    return a0 + x * (a1 + x * (a2 + x * (a3 + x * a4)));
+}
+}}}
+
+== Analysing the results ==
+
+Plotting the real exponential function and our `fastexp` function gives the following curves:
+
+[[Image(fastexp.png, nolink)]]
+