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## lognum

### Introduction

A logarithmic number system (LNS) is an arithmetic system for representing real numbers. In LNS, a number X, is represented by the logarithm L of its absolute value:

X -> { s, L = \log_b(|X|) }

where `s` denotes the sign of `X` (`s = 1` if `X > 0` and `s = -1` if `X < 0`).

### Requires

### Library procedures

*[procedure]*

`{{lognum?:: X -> BOOL}}`

*[procedure]*

`{{lognum-sign:: X -> INTEGER}}`

*[procedure]*

`{{lognum-value:: X -> NUMBER}}`

*[procedure]*

`{{number->lognum:: NUMBER -> LOGNUM}}`

*[procedure]*

`{{lognum->number:: LOGNUM -> NUMBER}}`

*[procedure]*

`{{lognum+:: A * B -> X}}`

*[procedure]*

`{{lognum-:: A * B -> X}}`

*[procedure]*

`{{lognum*:: A * B -> X}}`

*[procedure]*

`{{lognum/:: A * B -> X}}`

*[procedure]*

`{{lognum-neg:: A -> B}}`

*[procedure]*

`{{lognum-abs:: A -> B}}`

*[procedure]*

`{{lognum-signum:: A -> B}}`

*[procedure]*

`{{lognum-recip:: A -> B}}`

### Authors

Ivan Raikov

### Version

- 1.0
- Initial version

### License

Copyright 2009 Ivan Raikov and the Okinawa Institute of Science and Technology.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>.