OBERON FOR MS-DOS

System 3 

This file contains all the changes made for the current release.

14. 6. 93
 Version 1.2
 Improved real arithmetic (see below)
 Start of this file.


AN IMPROVED IMPLEMENTATION OF THE FLOATING-POINT CONVERSION

The floating-point handling has been improved in the Oberon implementation 
that is shipped with this note. The original version of Oberon, as published 
in [1] suffer from the following deficiencies:

1) The floating-point numbers from a source file which are scanned by the 
   compiler and floating-point numbers read in from a text file by Texts.Scan 
   are not necessarily identical. The bit pattern differs in the least 
   significant part. Furthermore, the decimal-to-binary conversion is 
   inaccurate.

2) The trap handler prints fewer decimal digits of REALs and LONGREALs than 
   significant.

3) The two least significant digits (7-8 for REALs and 15-16 for LONGREALs) 
   are often wrong.

4) The procedure Texts.WriteRealFix has the same deficiencies as 
   Texts.WriteReal; moreover it traps for some parameters.

5) For floating-point numbers with certain binary exponents (listed 
   subsequently), the decimal exponent printed is wrong by one decimal unit!
   For example: all floating-point numbers x with 2^-103 <= x < 2^-102 are 
   printed with a wrong exponent.

   REALs:
	       wrong          correct
   2^-103  9.8607620E-31   9.8607613E-32
   2^-113  9.6296500E-34   9.6296497E-35
   2^-123  9.4039550E-37   9.4039548E-38

   LONGREALs: (totally 132 cases)
		   wrong                  correct
   2^-103  9.860761315262652D-031  9.860761315262648D-032
   2^-113  9.629649721936183D-034  9.629649721936179D-035
   2^-123  9.403954806578305D-037  9.403954806578299D-038
   ...
   2^-1017  7.120236347223050D-306 7.120236347223044D-307
   2^-1020  8.900295434028810D-307 8.900295434028805D-308


All errors mentioned above are avoided by the new implementation. Since 
IEEE error codes and denormalized numbers are not always supported, all 
error codes are printed as "NaN" (Not-a-Number) and denormalized numbers 
are flushed to zero. Besides, the functionality of the WriteRealFix has 
been redesigned, and WriteLongRealFix has been added:

Description:

 PROCEDURE WriteLongRealFix* (VAR W: Writer; x: LONGREAL; n, f, D: LONGINT);

 The parameters are:

 W       a Texts.Writer
 x       the LONGREAL number to be printed
 n       the overall field length available for the output
 f       the number of fraction digits following the decimal point
 D       the fixed exponent (printed only when D # 0)


Example:  The following program excerpt

 e:= -310;
 WHILE e <= -277 DO
  Texts.WriteInt(W, e, 2);
  Texts.WriteLongRealFix(W, -1.234567898765432D-300,30,5,e);
  Texts.WriteLn(W);
  INC(e)
 END

	delivers the following output:

	-310                           NaN
	-309                           NaN
	-308 -***********************D-308
	-307 -***********************D-307
	-306 -***********************D-306
	-305 -***********************D-305
	-304 -***********************D-304
	-303 -***********************D-303
	-302 -***********************D-302
	-301 -***********************D-301
	-300 -1.234567898765431000000D-300
	-299 -0.123456789876543100000D-299
	-298 -0.012345678987654310000D-298
	-297 -0.001234567898765431000D-297
	-296 -0.000123456789876543100D-296
	-295 -0.000012345678987654310D-295
	-294 -0.000001234567898765432D-294
	-293 -0.000000123456789876543D-293
	-292 -0.000000012345678987654D-292
	-291 -0.000000001234567898765D-291
	-290 -0.000000000123456789877D-290
	-289 -0.000000000012345678988D-289
	-288 -0.000000000001234567899D-288
	-287 -0.000000000000123456790D-287
	-286 -0.000000000000012345679D-286
	-285 -0.000000000000001234568D-285
	-284 -0.000000000000000123457D-284
	-283 -0.000000000000000012346D-283
	-282 -0.000000000000000001235D-282
	-281 -0.000000000000000000123D-281
	-280 -0.000000000000000000012D-280
	-279 -0.000000000000000000001D-279
	-278 -0.000000000000000000000D-278
	-277 -0.000000000000000000000D-277

The least significant non zero digit (in this example: 1 resp. 2 when 
D >= -300) has an error of at most 2 decimal units caused by the rounding 
error in the least significant bit of 10^D and the subsequent 
multiplication with the mantissa.

All the computations in the floating-point units are done correctly. The 
testing of the modules Math and MathL is in progress.

For further information or remarks please contact either the corresponding
implementor at the 

	Institut fr Computersysteme ETH, 8092 Zrich, Switzerland,
	Telephone (1)254 7311, Facsimile (1)262 3973

or the author of this note.


Reference

[1] N. Wirth and J. Gutknecht: Project Oberon. The Design of an Operating 
	System and Compiler. Addison Wesley, 1992, ISBN 0-201-54428-8.
	Program listings with explanations for the whole Oberon system, 
	including the compiler for NS32000.


Bernd Moesli
moesli@sam.math.ethz.ch
Seminar for Applied Mathematics
Swiss Federal Institute of Technology Zurich
ETH-Zentrum
Fliederstr. 23
CH-8092 Zuerich, Switzerland


BM      1993.3.15       Copyright 1993