Comments on: Apple Flunks First Grade Math

By: Imf

Imf — Tue, 24 Aug 2010 11:51:54 +0000

So stupid. There has to be a way to do this with software. Maybe something that handles both sides of the decimal separately? Then it wouldn’t need to calculate the decimal points as fractions. Regardless of the reason, it’s absolutely, 100.00000000000002% inexcusable.

By: Bob D

Bob D — Fri, 16 Oct 2009 13:20:26 +0000

Can anyone tell me how to do the following?

Using Calculator, with input a real number between 0 and 1 for example, how do I get the angle for which the sin equals that real number?

That is, how do I enter arcsin (or any other arc-trig) to determine the angle? Thanks.

Bob

By: David K

David K — Fri, 26 Sep 2008 18:17:08 +0000

Here is the problem I am having with the Apple Calculator. I can’t get it to display numbers in the format I would like.

Here is what its is doing if calculate 13.5 / 1539 it shows me 8.7719e-03

While that is technically a correct answer I think I want tit to display it in the format I have become accustomed to like .0087719

What do I need to do to get it from this format 8.7719e-03 to this format .0087719

Right now I have OSX 10.4.11, Calculator version 4.0.6 but I have the same problem with Leopard too

David

By: sesli

sesli — Tue, 08 Jul 2008 22:28:08 +0000

Jeff, you forget one crucial thing: we programmers are lazy. The standard math operations in any language are based on the basic integer and floating point operations as they are

By: steve

steve — Wed, 28 May 2008 03:29:41 +0000

On the Mac bug site they wrote:

Additional information

For an advanced discussion of why this happens, see “What Every Computer Scientist Should Know About Floating-Point Arithmetic”

Interesting though that the computer scientists at Apple do not know this, and that they even point out what they should know, but don’t, on their help site.

By: Heike Childs

Heike Childs — Mon, 17 Dec 2007 00:23:53 +0000

Today’s calculator version 4.0.6. solved the addition problem of “1938 + 65″ to equate 2000. After selection show paper tape and then pushing recalculate it came up with the correct answer 2003. What an embarrassment for Apple’s math team. I’m running the Operating system 10.4.11

By: bwold

bwold — Mon, 26 Nov 2007 05:55:23 +0000

try

sin 360

(degree mode)

the answer should be zero but the calc shows -2.449293598294706e-16

os x 10.3.9

By: Janne Kalliola

Janne Kalliola — Wed, 30 Nov -0001 00:00:00 +0000

This error is most probably due to the way computers store floating point numbers. As computers do not think with decimals but with binary numbers, these rounding mistakes do happen.

There are exact number storing formats available, but they are much more cumbersome to use and coders of simple applications as calculators do not generally bother.

By: Mike D.

Mike D. — Wed, 30 Nov -0001 00:00:00 +0000

Janne,

Sounds plausible, but that is setting the bar extremely low, don’t you think? I mean, the bar is pretty much just laying on the ground at that point.

I would think any calculator would use a number-storing format which could produce 100% accurate results on simple two-decimal arithmetic. When I think of rounding errors, I think more of legitimate repeating decimals like the square root of 2 or something.

By: Shaun Inman

Shaun Inman — Wed, 30 Nov -0001 00:00:00 +0000

Didn’t Netscape’s JavaScript engine have this same problem?

By: Kim

Kim — Wed, 30 Nov -0001 00:00:00 +0000

Yes, it is to do with floating point precision.

If you want an explanation check this out.

It can be solved by using integer math rather than floating point. Windows had the same problem with its calculator, but it was upgraded in XP which fixed the problem.

Oh, and I am really really surprised your software “engineer” did not know this. It is really basic introductory computer science stuff.

By: AkaXakA Watson

AkaXakA Watson — Wed, 30 Nov -0001 00:00:00 +0000

Thing is, if even this math is wrong, how can we trust the rest?

By: David Schontzler

David Schontzler — Wed, 30 Nov -0001 00:00:00 +0000

Sounds like someone needs a new principal software engineer. I find it hard that he doesn’t know much about floating point arithmetic operations.

And “precision” isn’t a misnomer at all.

By: Doc Griffin

Doc Griffin — Wed, 30 Nov -0001 00:00:00 +0000

This situation is not limited to the Macintosh calculator program. It occurs on any system using floating point precision, including handheld calculators. The culprit here is the number 0.1. A perfectly straightforward decimal number, in binary it has an infinite repeating representation. In base two floating-point arithmetic, the number 0.1 lies strictly between two floating-point numbers and is exactly representable by neither of them.

By: Mike D.

Mike D. — Wed, 30 Nov -0001 00:00:00 +0000

Shaun,

Funny you should mention Netscape, because I actually thought of their frame sizing algorithm when I was thinking about this bug. I know it’s probably unrelated but it just reminded me of it. Basically, if you are using a frameset and you specify your frame dimensions in pixels, Netscape (at least up through version 4) would convert your pixels to a window size percentage, and then convert it back to pixels resulting in rounding errors all the time.

Kim and David,

Thanks for the Sun link. It looks like it explains floating points pretty thoroughly, but sheesh, 105 pages of engineer-speak. All I know is that even if this problem is legitimate, these errors should never make it to the consumer. As for our principal software engineer, I’m pretty sure his astonishment had more to do with not knowing how a calculator which had been around since 1984 could suddenly have this bug, as opposed to not knowing what floating point operations are. I mean, what could have possibly changed in Panther that would have introduced such a bug in the calculator? That is more the question…