#!/usr/bin/env python
# coding: utf-8

# # Floating Point Arithmetic and the Series for the Exponential Function
# 
# Copyright (C) 2010-2020 Luke Olson<br>
# Copyright (C) 2020 Andreas Kloeckner
# 
# <details>
# <summary>MIT License</summary>
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# 
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
# </details>

# In[4]:


import numpy as np
import matplotlib.pyplot as pt


# What this demo does is sum the series
# $$
#   \exp(x) \approx \sum_{i=0}^n \frac{x^i}{i!},
# $$
# for varying $n$, and varying $x$. It then prints the partial sum, the true value, and the final term of the series.

# In[5]:


a = 0.0
x = 1e0 # flip sign
true_f = np.exp(x)
e = []

for i in range(0, 10): # crank up
    d = np.prod(
            np.arange(1, i+1).astype(np.float))

    # series for exp
    a += x**i / d

    print(a, np.exp(x), x**i / d)

    e.append(abs(true_f-a)/true_f)


# In[6]:


pt.semilogy(e)


# In[3]: