Probability Value Library

	Peter N. Yianilos and Eric Sven Ristad

	The pr_t package provides an abstraction for probability
	values.  The principal benefit of using this abstraction is to
	avoid underflow in time series modeling.  This package
	provides a direct and elegant solution to this problem.  All
	work necessary to support a sufficiently large exponent range
	is swept into the routines associated with the pr_t data type.

	This software was first described in a 1994 Princeton University Computer
	Science Technical Report.
	
Description of Files:
				
	Makefile

		If you have gcc installed, you should be able to simply
		type make.  Otherwise you will need to edit this file.
		If you run into problems running pr_test.c below, consider
		removing "-DNDEBUG".  This will enable many asserts() which
		may help locate the problem, but slow things down by a 
		a factor of 2-3.
	
	pr.c
		The source code for all pr_t functions.

	pr.h
		Defines the interface to pr_t.
		
	pr_bench.c

		Run this program "pr_bench" to benchmark the pr_t
		functions on your system in comparison with other
		approaches.  We provide runbench.csh described below
		to perform a complete series.

	pr_test.c
		
		Run this after making the software.  You should get
		13 or more digits of precision for all tests.

	pr_t.3			

		A man page which may installed in section 3.

	runbench.csh

		Run this shell file to measure pr_t performance -- and
		for comparison that of plain double operations, and
		logarithmic operations as well.	 Five times are reported, 
		all for addition operations:
		
		1) Standard double addition

		2) pr_t (macro form).  This is not actually part of the pr_t
		   library, but represents what one might expect from inline
		   implementation.

		3) pr_t (pointer form).  Here the pr_t routines are passed
		   pointers to their arguments.

		4) pr_t (functional form).  These routines lead to cleaner code
		   at the cost of performance.

		5) Logarithmic computation:  Here, exp() and log() are used to
		   emulate a system which represents probabilities using logs,
		   and uses the standard math functions to convert back and forth.
		   Using table lookup techniques one could certainly improve on
		   these times.
			
		The most important comparisons are between (1) and (3),(4).