\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

azmul

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Absolute Zero Multiplication

Syntax

z = azmul ( x , y )

Purpose

Evaluates multiplication with an absolute zero for any of the possible types listed below. The result is given by

\[\begin{split}z = \left\{ \begin{array}{ll} 0 & {\rm if} \; x = 0 \\ x \cdot y & {\rm otherwise} \end{array} \right.\end{split}\]

Note if x is zero and y is infinity, ieee multiplication would result in not a number whereas z would be zero.

Base

If Base satisfies the base type requirements and arguments x , y have prototypes

      const Base & x

      const Base & y

then the result z has prototype

Base z

AD<Base>

If the arguments x , y have prototype

      const AD < Base >& x

      const AD < Base >& y

then the result z has prototype

AD < Base > z

VecAD<Base>

If the arguments x , y have prototype

      const VecAD < Base >:: reference& x

      const VecAD < Base >:: reference& y

then the result z has prototype

AD < Base > z

Example

The file azmul.cpp is an examples and tests of this function.