### Description

Floating-point Comparison With Epsilon

Kon Lovett

### Version

• 0.1 Initial release

### Usage

(require-extension fpfz)

fpfz.egg

• miscmacros

### 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.

```Copyright (c) 2006, Kon Lovett.  All rights reserved.

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The above copyright notice and this permission notice shall be included
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THE SOFTWARE IS PROVIDED ASIS, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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