Class GenFn

java.lang.Object
  GenFn

public class GenFn
extends java.lang.Object

Class GenFn computes approximations to a function λ(z) to be used in Theorem 3.3, for a specified transition function file, and then computes the corresponding bounds on γ.
In the comments in the code, the notation APPROX(e,n), where e is some expression and n is an integer, denotes the statement that the ratio between the computed numerical value of e and the exact value the expression e would have if all arithmetic were exact (starting with the given value of z and the computed values of v) lies in (ρ^-n,ρⁿ), where ρ=1+2^-52.

Field Summary

(package private) int	h The history length.
(package private) double	maxRatio The maximum ratio by which any component of v increases this iteration.
(package private) double	minRatio The minimum ratio by which any component of v increases this iteration.
(package private) int	numberOfAcceptingStates The number of states, not including the rejecting state
static double	TOLERANCE The factor controlling how close the ratios between elements of two successive vectors must be before we stop iterating.
(package private) double[]	v The last approximation to an eigenvector of Az; see Section 3.1 in the paper.
(package private) static int	verbosity This controls the level of output.
(package private) double[]	vNew The next approximation to an eigenvector of Az.
(package private) double[]	wmuz wmuz is computed in method lambda by wmuz[h+i] = wμ,z(Tc,i), where wμ,z is as defined in Section 3.1, and μ and Tc,i are as defined in the overview of the code.

Constructor Summary

GenFn(java.lang.String filename)
Initialize the structure to compute λ values corresponding to the transition function represented in file filename.

Method Summary

void	dumpEigen(double z) Dump the current approximation to the eigenvector to the file eigen<h>.bin.
void	iterate() Carry out one iteration: multiply Az and v, and rescale.
double	lambda(double z) Compute a numerical approximation to the λ(z) in Theorem 3.3, using the machine encoded in the file filename.
static void	logbase(double x, double b, double eb, int denom) Compute and print an integer value p such that logbx≤p/denom, attempting to make p as small as possible so that the round-off error verification described in Section 3.2.2 can be performed.
static void	main(java.lang.String[] args) The main program is used with the command GenFn <filename> <z0> <z1> <zdelta> For each z in the range z0 to z1, with a step size of zdelta, it computes lambda(z) and the resulting upper bound on γ, using the transition function stored in ./data/filename.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

verbosity

static int verbosity

This controls the level of output.

• 0 gives the least output.
• 1 shows the ratios by which table entries increase at each iteration.
• 2 also shows details of the iterations.
• 3 also shows details of the log calculations.

TOLERANCE

public static final double TOLERANCE

The factor controlling how close the ratios between elements of two successive vectors must be before we stop iterating.

See Also:

Constant Field Values

h

int h

The history length.

numberOfAcceptingStates

int numberOfAcceptingStates

The number of states, not including the rejecting state

v

double[] v

The last approximation to an eigenvector of A_z; see Section 3.1 in the paper. This vector is indexed by the accepting states.

vNew

double[] vNew

The next approximation to an eigenvector of A_z. It is computed by multiplying A_z and v.

minRatio

double minRatio

The minimum ratio by which any component of v increases this iteration.

maxRatio

double maxRatio

The maximum ratio by which any component of v increases this iteration.

wmuz

double[] wmuz

wmuz is computed in method lambda by wmuz[h+i] = w_μ,z(T_c,i), where w_μ,z is as defined in Section 3.1, and μ and T_c,i are as defined in the overview of the code.

Constructor Detail

GenFn

public GenFn(java.lang.String filename)
      throws java.io.IOException

Initialize the structure to compute λ values corresponding to the transition function represented in file filename.

Throws:

java.io.IOException

Method Detail

lambda

public double lambda(double z)
              throws java.io.IOException

Compute a numerical approximation to the λ(z) in Theorem 3.3, using the machine encoded in the file filename.

Throws:

java.io.IOException

iterate

public void iterate()
             throws java.io.IOException

Carry out one iteration: multiply A_z and v, and rescale. Set minRatio (resp. maxRatio) to the minimum (resp. maximum) ratio by which any entry in v increases under this multiplication.

Throws:

java.io.IOException

logbase

public static void logbase(double x,
                           double b,
                           double eb,
                           int denom)

Compute and print an integer value p such that log_bx≤p/denom, attempting to make p as small as possible so that the round-off error verification described in Section 3.2.2 can be performed. Parameter b and eb must be satisfy APPROX(b,eb); parameter x is assumed to be exact.

dumpEigen

public void dumpEigen(double z)
               throws java.io.IOException

Dump the current approximation to the eigenvector to the file eigen<h>.bin.

Throws:

java.io.IOException

main

public static void main(java.lang.String[] args)
                 throws java.io.IOException

The main program is used with the command
GenFn <filename> <z0> <z1> <zdelta>
For each z in the range z0 to z1, with a step size of zdelta, it computes lambda(z) and the resulting upper bound on γ, using the transition function stored in ./data/filename.

Throws:

java.io.IOException