zaccone@rigel.bucknell.edu (Rick Zaccone) (05/23/89)
The following program produces incorrect results in LSP 2.01:
program test (input, output);
var
a, out: real;
begin
a := 16807.0;
out := a * a;
writeln(out : 10 : 0);
end.
The program prints 282475264 instead of the correct 282475249. If I
type "a*a" in the observe window, I can see that a*a is being computed
correctly. The error occurs when the assignment is made to out. Can
anyone else reproduce this? Am I missing something obvious?
I am running on a Mac Plus with Finder 6.1, and System 6.0.2.
Rick Zaccone
--
zaccone@bknlvms.bitnet
zaccone@rigel.bucknell.eduksitze@nmsu.edu (Kevin Sitze) (05/23/89)
In article: <zaccone@rigel.bucknell.edu's message of 23 May 89 01:19:53 GMT> Rick Zaccone writes: >The following program produces incorrect results in LSP 2.01: > >program test (input, output); >var > a, out: real; >begin > a := 16807.0; > out := a * a; > writeln(out : 10 : 0); >end. > >The program prints 282475264 instead of the correct 282475249. If I >type "a*a" in the observe window, I can see that a*a is being computed >correctly. The error occurs when the assignment is made to out. Can >anyone else reproduce this? Am I missing something obvious? Your missing something obvious. If you look at Apple's numerics manual (SANE manual) you'll find that real numbers have an definite accuracy of only _6_ digits. Anything else you see is affected by remaining bit patterns in the real number that may or may not be accurate. When a*a is used in the observe window, LSP converts the reals to extended format (as it does in the program as well) and then prints out the answer using the _extended_ result. The difference lies in assigning the answer to 'out'. The result has to be converted back into single precision and stored in 'out' (loosing several digits of accuracy as it's converted). If you had done something like this: ... a := 16807.0 writeln(a*a:10:0); ... you'd get the correct answer. If you need that precision inside a variable then just change your variable declaration to: var a : real; out : extended; and everything should work fine and dandy. Remember, floating point numbers by the virtue of being represented by a finite number of bits can _never_ represent the entirety (?sp?) of all real numbers. Enjoy the limited world of computer programming... -Kelesi -- ------------------------------------+------------------------------- From the Macintosh of: Kevin Sitze | Disclamer: Who the heck needs | a disclamer? After all, Dan EMail: ksitze%NMSU.edu | Quayle doesn't. SMail: 601 S. Melendres +------------------------------- Las Cruces, NM 88005 | "We have the answers, the ------------------------------------+ trouble lies in finding the "The difference between intelligence| questions..." and stupidity is that intelligence | "The information is there, has a limit." - anonymous | finding it is another story." The dolt confuses you -- more -- | - Any consultant ------------------------------------+-------------------------------
ksitze@nmsu.edu (Kevin Sitze) (05/23/89)
I write: >accuracy of only _6_ digits. Anything else you see is affected by >remaining bit patterns in the real number that may or may not be >accurate. When a*a is used in the observe window, LSP converts the Uh, must be early still... Wanted to say: Anything else you see is affected by remander bit patterns in the real number that may or may not be accurate. (During string to number conversions SANE does some multiplications, etc) -- ------------------------------------+------------------------------- From the Macintosh of: Kevin Sitze | Disclamer: Who the heck needs | a disclamer? After all, Dan EMail: ksitze%NMSU.edu | Quayle doesn't. SMail: 601 S. Melendres +------------------------------- Las Cruces, NM 88005 | "We have the answers, the ------------------------------------+ trouble lies in finding the "The difference between intelligence| questions..." and stupidity is that intelligence | "The information is there, has a limit." - anonymous | finding it is another story." The dolt confuses you -- more -- | - Any consultant ------------------------------------+-------------------------------
siegel@endor.harvard.edu (Rich Siegel) (05/23/89)
I think the bug is in the output routines, not in the arithmetic. I'll look into it. In the meantime, use "Extended" instead of "Real", and everything should work OK. --Rich ~~~~~~~~~~~~~~~ Rich Siegel Staff Software Developer Symantec Corporation, Language Products Group Internet: siegel@endor.harvard.edu UUCP: ..harvard!endor!siegel "She told me to make myself comfortable, so I pulled down my pants and sat in the pudding." -Emo Phillips ~~~~~~~~~~~~~~~