# Maxima by Example, Chapter 9: Bigfloats and High Accuracy Quadrature

### Ted Woollett

##
A valuable feature of a computer algebra system is the ability to
do arithmetic with high precision. Chapter 9 presents four
methods of high accuracy quadrature, including examples and test integrals.

- --mbe9bfloat.pdf : May 30, 2016, Maxima 5.36.1, 40 pages
- --mbe9bfloat.tex : May 30, 2016, Latex code file
- --mbe9code.txt : Copy and Paste Code: May 30, 2016, Maxima 5.36.1
- --bfloat.mac : May 30, 2016, Maxima 5.36.1
- --quad-maxima.lisp : May 30, 2016, Maxima 5.36.1
- --quad_de.mac : May 30, 2016, Maxima 5.36.1
- --quad_ts.mac : May 30, 2016, Maxima 5.36.1
- --quad_gs.mac : May 30, 2016, Maxima 5.36.1

Chapter 9 Topics

- The Use of Bigfloat Numbers in Maxima,

- Bigfloat Numbers Using bfloat, fpprec, and fpprintprec.

- Using print and printf with Bigfloats,

- Adding Bigfloats having Differing Accuracy,

- Highly Accurate Roots of Polynomials using bfallroots,

- Highly Accurate Roots using bf_find_root,

- Bigfloat Number Gaps and Binary Arithmetic,

- Effect of Floating Point Precision on Function Evaluation,

- High Accuracy Quadrature with Maxima,

- Using bromberg for High Accuracy Quadrature,

- A Double Exponential Quadrature Method for a <= x < inf,

- The tanh-sinh Quadrature Method for a <= x <= b,

- The Gauss-Legendre Quadrature Method for a <= x <= b

The text files bfloat.mac, quad_de.mac, quad_ts.mac, and quad_gs.mac
are free software: you can redistribute them and/or modify
them under the terms of the GNU GENERAL PUBLIC LICENSE, Version 2, June 1991,
as published by the Free Software Foundation. For more information see
the license information at the top of the files.