Fast Automatic Differentiation in C++

//////////////////////////////////////////////////////////////////////////
/// The Reed Library
/// Copyright (c) 2006 Yevgeniy Shatokhin

/// File: util.h
/// Contains some utility stuff.
/// 

/// 
/// Last update: August 29, 2006

#ifndef __UTIL_H__EC89223A_854F_4995_AFE7_974D7057922B_INCLUDED_
#define __UTIL_H__EC89223A_854F_4995_AFE7_974D7057922B_INCLUDED_

#include <cmath>

namespace reed
{
	/// Return the accuracy the argument is stored with. \n
	/// It equals the absolute difference between 'arg' and the representable 
	/// value closest to it but different. (In fact, they differ only in the lower 
	/// bit of their mantissas.)\n
	/// It's assumed that arg is an IEEE-compliant normalized double precision number.
	double derr(double arg);

	/// Compare x and y to see if these numbers are 'approximately' equal (have small
	/// absolute difference.\n
	/// x is assumed to be 'approximately' equal to y if
	/// |x - y| < 2.0 * derr(max(|x|, |y|)). (I chose the 2.0 coefficient quite 
	/// arbitrarily. Perhaps it makes some sense.)
	int dequal(double x, double y);

}	// namespace reed


#endif //__UTIL_H__EC89223A_854F_4995_AFE7_974D7057922B_INCLUDED_