# FIXED Fixed point number package Dr. Heinrich Hohl <> Version 1.0.0 - 2016-10-01 ## Introduction This package provides words for convenient handling of fixed point numbers. A fixed point number (f) is an integer number with an implied decimal point at a specified position. Fixed point numbers may be used instead of floating point numbers if only basic arithmetic operations (+, -, \*, /) are required in an application. What does *implied decimal point* mean? Let us assume that your application deals with weight (in kg) and price (in EUR). In this case you would store weights and prices as follows: - Weight: 1 kg = 1.000 kg = 1000 g = 1000 - Price: 1 EUR = 1.00 EUR = 100 ct = 100 Although weight and price are officially shown in kg and EUR, they are internally stored in grams and cents. Before you input or output a fixed point number, you must specify the position of the implied decimal point. In the above example these positions are 3 and 2 digits from the right, respectively. ## Versions The package is available in versions for the following FORTH systems: |System |Standard |Type |Files | |------------------------|---------|------|---------------------------------| |PC/FORTH (LMI) |Forth-83 |16-bit|[fixed\_lmi.txt](fixed_lmi.txt) | |SwiftForth (Forth, Inc.)|ANS Forth|32-bit|[fixed\_sf.f](fixed_sf.f) | |VFX Forth (MPE) |ANS Forth|32-bit|[fixed\_vfx.fth](fixed_vfx.fth) | The package was developed under LMI PC/FORTH in 1992 and published in the German Forth magazine [Vierte Dimension Nr. 2/1992, p.7][1]. The LMI version is included for completeness and because someone might still want to use the package on a 16-bit system. It is also instructive to see how much simpler the code became after rewriting the package for 32-bit systems. The following description will concentrate on the 32-bit versions (SwiftForth, VFX Forth) of the package. ## Installation Use the following commands to install the package: - SwiftForth: `INCLUDE fixed_sf.f` - VFX Forth: `INCLUDE fixed_vfx.fth` This makes the fixed point words available. After loading you still have a standard system. The number conversion routine of the Forth system is not modified by this package. ## Glossary The package adds the following words to the system: PLACES FIXED (F.) F. F.R See [**glossary.md**](glossary.md) for stack comments and descriptions of the defined words. ## Usage Use `PLACES` to specify the number of places behind the decimal point. Input a number (with or without decimal point), immediately followed by `FIXED` which converts the input to a fixed point number. It does this by appending zeros or by truncating excessive digits behind the decimal point as required. The number is now in a well defined format and can be stored, used for calculations, or output. ### Examples 3 PLACES 6 FIXED F. --> 6.000 ok 2.4938 FIXED F. --> 2.493 ok 6 FIXED 2.4938 FIXED + F. --> 8.493 ok 8.493 1 PLACES F. --> 8.4 ok : .WEIGHT ( f -- ) 3 PLACES F. ; : .PRICE ( f -- ) 2 PLACES F. ; ### Important rules 1. Do not put any other words between the number input routine and `FIXED`. Depending on the FORTH system, words such as `.S` may alter the contents of `DPL`. 2. On 32-bit systems, fixed point numbers are represented by single length numbers. 3. Use standard words for storage (`@ ! CONSTANT VALUE VARIABLE`) and for stack manipulation (`DUP DROP SWAP OVER ROT` etc.) 4. Use `+` and `-` to add and subtract two fixed point numbers, respectively. Both operands must be based on the same number of places, and the result will inherit this number of places. 5. Use `*` and `/` to multiply or divide two fixed point numbers. The operands and the result are generally based on different numbers of places. Afterward, you must scale the result by a suitable power of ten. ## Conformance This package largely conforms to Forth-83 (LMI) and ANS Forth (SwiftForth, VFX). Nonstandard words that should be mentioned: - `DPL` contains the decimal point location after an integer number conversion has been performed - `{ ... }` marks block comments in SwiftForth - `(* ... *)` marks block comments in VFX Forth - `PACKAGE PRIVATE PUBLIC END-PACKAGE` are used for information hiding in SwiftForth - `MODULE EXPORT END-MODULE` are used for information hiding in VFX Forth [1]: https://www.forth-ev.de/filemgmt/viewcat.php?cid=2