### Description

Floating-point Comparison With Epsilon

### Usage

`(require-extension fpfz)`
### Documentation

Routines to perform floating-point operations with an error
bound. These routines are not some cure-all for floating-point
anomalies, but useful anyway.

#### Parameters

**parameter:** (current-fpfz-epsilon [#])
Sets or returns the error bound.

#### Predicates

The formula below are for exposition only; they are not the
actual test.

**macro:** (fpfz= A B [EPSILON (current-fpfz-epsilon)])
|a - b| <= E.

**macro:** (fpfz<> A B [EPSILON (current-fpfz-epsilon)])
|a - b| > E.

**macro:** (fpfz> A B [EPSILON (current-fpfz-epsilon)])
|a - b| > E.

**macro:** (fpfz< A B [EPSILON (current-fpfz-epsilon)])
|a - b| < E.

**macro:** (fpfz>= A B [EPSILON (current-fpfz-epsilon)])
|a - b| >= E.

**macro:** (fpfz<= A B [EPSILON (current-fpfz-epsilon)])
|a - b| <= E.

#### Operations

**macro:** (roundn N [ND])
Nearest number within a given precision, the number of
decimal digits in the fraction `ND`. When precision
missing normal 'round' is performed.

**macro:** (fpfzroundn N [ND])
Nearest number within a given precision, the number of
decimal digits in the fraction `ND`, & epsilon. When
precision missing normal 'round' is performed.

**macro:** (fpfzceil N)
Smallest integer number that is tolerably larger than
the given value.

**procedure:** (fpfzfloor N)
Smallest integer number that is tolerably smaller than
the given value.

**macro:** (fpmaxabs A B)
Mininum of the absolute value of the arguments.

**procedure:** (calculate-fpfz-epsilon [FEPS 3.0])
Returns the system epsilon to within a factor of the real
epsilon.

### License

Copyright (c) 2006, Kon Lovett. All rights reserved.
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the Software),
to deal in the Software without restriction, including without limitation
the rights to use, copy, modify, merge, publish, distribute, sublicense,
and/or sell copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED ASIS, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.