Reid Augustin > Games-Go-GoPair-1.001 > Games::Go::Erf
Module Version: 0.02

# NAME

Games::Go::Erf - error and scaled and unscaled complementary error functions and their inverses

# SYNOPSIS

`    use Games::Go::Erf qw(erf erfc erfcx erfinv erfcinv erfcxinv);`

Imports all the routines explicitly. Use a subset of the list for the routines you want.

`    use Games::Go::Erf qw(:all);`

Imports all the routines, as well.

# DESCRIPTION

This module implements the error function, `erf`, and its inverse `erfinv`, the complementary error function, `erfc`, and its inverse `erfcinv`, and the scaled complementary error function, `erfcx`, and its inverse `erfcxinv`.

For references and details about the algorithms, see the comments inside this module.

# FUNCTIONS

erf EXPR
erf

Returns the error function evaluated at EXPR. If EXPR is omitted, `\$_` is used. The error function is

`    erf(x) = 2/sqrt(PI) * integral from 0 to x of exp(-t*t) dt`
erfinv EXPR
erfinv

Returns the inverse of the error function evaluated at EXPR. If EXPR is omitted, `\$_` is used.

erfc EXPR
erfc

Returns the complementary error function evaluated at EXPR. If EXPR is omitted, `\$_` is used. The complementary error function is

```    erfc(x) = 2/sqrt(PI) * integral from x to infinity of exp(-t*t) dt
= 1 - erf(x)```

Here is a function returning the lower tail probability of the standard normal distribution function

```    use Games::Go::Erf qw(erfc);

sub ltpnorm (\$) {
erfc( - \$_[0] / sqrt(2) )/2;
}```
erfcinv EXPR
erfcinv

Returns the inverse complementary error function evaluated at EXPR. If EXPR is omitted, `\$_` is used.

Here is a function returning the lower tail quantile of the standard normal distribution function

```    use Games::Go::Erf qw(erfcinv);

sub ltqnorm (\$) {
-sqrt(2) * erfcinv( 2 * \$_[0] );
}```
erfcx EXPR
erfcx

Returns the scaled complementary error function evaluated at EXPR. If EXPR is omitted, `\$_` is used. The scaled complementary error function is

`    erfcx(x) = exp(x*x) * erfc(x)`
erfcxinv EXPR
erfcxinv

Returns the inverse scaled complementary error function evaluated at EXPR. If EXPR is omitted, `\$_` is used.

# HISTORY

Version 0.03

Version 0.02

Minor code tweaking.

Version 0.01

First release.

# AUTHOR

Perl translation by Peter J. Acklam <pjacklam@online.no>

FORTRAN code by W. J. Cody, Argonne National Laboratory, March 19, 1990. FORTRAN code can be found at http://www.netlib.org/specfun/erf