Everything2
Near Matches
Ignore Exact
Full Text
Everything2

1+1=1.99999999486

created by PaSTE

(idea) by PaSTE (3.1 y) (print)   ?   (I like it!) Sat Nov 13 1999 at 14:23:30

One of the most famous expressions used in the average kindergarten classroom made a bit more confusing by Intel. Seeing as computers never make mathmatical errors, I guess 1+1=1.99999999486 after all.

In the early days of the 8086 architecture, in order to make certain routines as efficient as possible, Intel programmed a pretty good Floating Point Number (FPN) addition routine. Unfortunately, they didn't test the chip out properly and found that the processor understood FPN 1 plus FPN 1 equals FPN 1.9999999486. This ovbiously sucked, and since the 8086, Intel has corrected the error and made it more efficient.

(idea) by everyone (3.1 mon) (print)   ?   (I like it!) 1 C! Sun Sep 17 2000 at 20:22:05

Actually, the bug was in the 586 (Pentium)'s floating point division. Unless you're talking about something much older, in which case I've never heard of it. Either way, Intel CPUs didn't have FPUs until the 486DX, which came much after the 8086.

Hardly anyone understands this bug anyway, they all just like to laugh like idiots at equations like "1+1=1.999999486". Most of them are Mac users. Go figure.

(idea) by Potatoswatter (2 mon) (print)   ?   (I like it!) 1 C! Wed Jun 26 2002 at 3:33:22

Doubtful this floating point arithmetic mistake has ever been made, even by Intel.

FPUs represent real numbers as a binary number (the mantissa) times a power of 2 (the exponent). 1 would be represented as a mantissa of 1 and an exponent of 0. (Internally, it's a mantissa of 0 and an exponent of 127 for IEEE 754 single precision, but that's beside the point.)

This means that no accuracy is lost in the translations of the two numbers to binary form. The process of adding is then easy. Since the exponents are the same, the exponent of the result is one more than that of the addends, and the mantissa of the result is just the sum of the addends bit-shifted right by 1. The addends and the answers are infinitely precise.

An FPU with zero bits of precision would still get 1+1 right.

Well, addition is easy. Division is hard.


printable version
chaos

2+2=5 brown-paper-bag bug That's not a bug, that's a feature! Intel Pentium FDIV bug
qualitative comparison of assembly language and unprotected sex The "Romeo and Juliet" Comparison mantissa One equals point nine repeating
Mac PowerPC Generating random numbers with a Poisson distribution Existentialism
floating point addiction infinitely precise Floating point Mac users are less likely to believe in God
FDIV IEEE 754 586 Intel
floating-point comparison kindergarten Pablo Escobar F00F
Y'know, if you log in, you can write something here, or contact authors directly on the site. Create a New User if you don't already have an account.
  Epicenter
Login
Password

password reminder
register

Everything2 Help

Cool Staff Picks
Nodes to live by:
Why the Borg have such terrible fashion sense
Everything Quests: Film Reviews
Granny shot
The Whiz-Bang Atlanta E2 Party
a case for lowercase
Jaguar
A duck meets God at a bar
Under normal circumstances, the Jewish community does not seek converts
The next revolution in music has not yet arrived
Ghost Dance
Kaspar Hauser
The Texas Chain Saw Massacre
colcannon
New Writeups
Glowing Fish
Tualatin River(place)
The Jacket
Words of Advice(idea)
keepinitreal
Why buy the cow when you can get the milk for free?(idea)
John_Fox
Good Intentions Gone Wrong(person)
Cuckowski
Slavonic Princess(poetry)
Heitah
Posthumous Oscar(thing)
ignis_glaciesque
University of South Florida(place)
ignis_glaciesque
Flogstaskriket(idea)
liveforever
Caesar's last breath(idea)
dagnyswaggart
she wants to believe(personal)
antigravpussy
he doesn't know, but her eyes widen too far(thing)
dagnyswaggart
Wild tides guard her secrets(poetry)
Lord Brawl
Caesar's last breath(poetry)
locke baron
Forgotten things in space(fiction)
sitaraika
Colours(idea)
Everything 2 is brought to you by the letter C and The Everything Development Company