Boost.Real: Optimizing internal representation of operation and improving math functions

Boost.Real aims to provide a data-type that can represent all types of computable real numbers and provides the flexibility of performing arbitrary precision arithmetic. I propose to optimize the space and time by reducing the dag structure and by various arithmetic optimizations in operation. I propose to optimize space and time in addition and multiplication operations by making adjustments to Karatsuba multiplication and other helper functions. I propose to improve the Champernowne Irrational number and pi's digit computation and add e and golden ratio to irrationals as well. I propose to optimize mathematical functions like exponent, logarithm, trigonometric and add inverse trigonometric functions. After this, Boost.Real may be ready for peer review.