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AD Binary Arithmetic Operators

Syntax
z = x Op y

Purpose
Performs arithmetic operations where either x or y has type AD<Base> or VecAD<Base>::reference .

Op
The operator Op is one of the following
Op Meaning
+ z is x plus y
- z is x minus y
* z is x times y
/ z is x divided by y

Base
The type Base is determined by the operand that has type AD<Base> or VecAD<Base>::reference.

x
The operand x has the following prototype
     const 
Type &x
where Type is VecAD<Base>::reference, AD<Base>, Base, or double.

y
The operand y has the following prototype
     const 
Type &y
where Type is VecAD<Base>::reference, AD<Base>, Base, or double.

z
The result z has the following prototype
     
Type z
where Type is AD<Base>.

Operation Sequence
This is an atomic AD of Base operation and hence it is part of the current AD of Base operation sequence .

Example
The following files contain examples and tests of these functions. Each test returns true if it succeeds and false otherwise.
Add.cpp AD Binary Addition: Example and Test
Sub.cpp AD Binary Subtraction: Example and Test
Mul.cpp AD Binary Multiplication: Example and Test
Div.cpp AD Binary Division: Example and Test

Derivative
If  f and  g are Base functions

Addition
 \[
     \D{[ f(x) + g(x) ]}{x} = \D{f(x)}{x} + \D{g(x)}{x}
\] 


Subtraction
 \[
     \D{[ f(x) - g(x) ]}{x} = \D{f(x)}{x} - \D{g(x)}{x}
\] 


Multiplication
 \[
     \D{[ f(x) * g(x) ]}{x} = g(x) * \D{f(x)}{x} + f(x) * \D{g(x)}{x}
\] 


Division
 \[
     \D{[ f(x) / g(x) ]}{x} = 
          [1/g(x)] * \D{f(x)}{x} - [f(x)/g(x)^2] * \D{g(x)}{x}
\] 

Input File: cppad/local/ad_binary.hpp