[erlang-questions] Maths Problem -> 2452.45*100. = 245244.99999999997

Tony Rogvall tony@REDACTED
Wed Nov 27 10:08:39 CET 2013

Always nice with war stories from the dusty past :-)
Does your story imply that the "Maths Problem" can be calculated differently 
still using the standard IEEE representation ?


On 27 nov 2013, at 05:35, Michael Turner <michael.eugene.turner@REDACTED> wrote:

> Gee, now might be a good time to bore everyone with a war story: a
> startup I once worked for independently /pre/-invented the Pentium
> Floating Point Bug, against my strenuous protests. How could this
> happen, I wondered, as I was losing the battle for IEEE-standard
> purity? Maybe, I thought, it's because we're a small company that
> can't afford to hire experts to ratify my opinion?
> We were using Weitek FPU adder and multiplier chips in our hardware,
> and I implemented floating point division the way they said to do it -
> the right way. Tried to, that is. I got overruled.
> Not too many years later, for the Pentium design, Intel acquired
> Weitek's IP. Then they introduced very similar mistakes in floating
> point arithmetic, through no fault of Weitek. Ours, at least, could
> have been patched by sending customers a new ROM to socket. Intel's
> errors went onto a single chip.
> What I learned about IEEE floating point arithmetic is that if you try
> to clean up floating point "errors" one way, you just squeeze the
> errors out some place else.
> What I learned about people is that Size Doesn't Matter.
> The proximate provocation in both cases: somebody didn't like how the
> number printed. I first saw "errors" like when I was in high school,
> programming in Dartmouth BASIC. I was told, "floating point is like
> that - if it weren't that, it would be something worse." So I was
> prepared. But lots of people now graduate with C.S. degrees who aren't
> prepared.
> Regards,
> Michael Turner
> Executive Director
> Project Persephone
> K-1 bldg 3F
> 7-2-6 Nishishinjuku
> Shinjuku-ku Tokyo 160-0023
> Tel: +81 (3) 6890-1140
> Fax: +81 (3) 6890-1158
> Mobile: +81 (90) 5203-8682
> turner@REDACTED
> http://www.projectpersephone.org/
> "Love does not consist in gazing at each other, but in looking outward
> together in the same direction." -- Antoine de Saint-Exupéry
> On Wed, Nov 27, 2013 at 12:28 PM, Richard A. O'Keefe <ok@REDACTED> wrote:
>> On 27/11/2013, at 3:01 PM, Sanath Prasanna wrote:
>>> I accepted your comment. But generally we expected full value. I did same in another scripting language like php. It is given correct result.
>> Wrong.  It *calculated* the same number as Erlang did,
>> but then it *displayed* a different number, a rounded version.
>> m% cat >foo.php
>> <?php
>> $a = 2452.45*100;
>> echo $a; echo "\n";
>> $a = $a - 245245.0;
>> echo $a; echo "\n";
>> exit;
>> ?>
>> <EOF>
>> m% php foo.php
>> 245245
>> -2.9103830456734E-11
>> We see from this that while the number *displays as*
>> 245245, it is not *equal to* 245245.
>> As I said, PHP computed *exactly* the same answer as Erlang.
>> Who is this "we" who "expect full value"?
>> This is floating-point arithmetic, not rational arithmetic.
>> (Our 2nd year students are taught this stuff, but it doesn't
>> really take.  In 3rd year they have an exercise they have to
>> do where they start to really understand that floating point
>> arithmetic is *not* arithmetic on the mathematical real
>> numbers, but a different mathematical system which sort of
>> approximates the algebra of the reals.  They learn that
>> adding up an array of numbers from left to right generally
>> gives you a different answer from adding up from right to
>> left, for example.)
>> Numbers in IEEE floating point arithmetic are precise,
>> but are bounded in their precision, and arithmetic operations
>> on them (including conversion between decimal and binary)
>> have to round their answers to something that is representable.
>> There's a rounding in the conversion of 2452.45 to binary,
>> and then the multiplication incurs another rounding.
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