Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.soft-sys.math.mathematica > #3597 > unrolled thread

Re: Numerical accuracy/precision - this is a bug or a feature?

Back to article view | Back to comp.soft-sys.math.mathematica

Contents

  Re: Numerical accuracy/precision - this is a bug or a feature? DrMajorBob <btreat1@austin.rr.com> - 2011-07-08 09:09 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-12 11:01 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-13 07:17 +0000

#3597 — Re: Numerical accuracy/precision - this is a bug or a feature?

This happens in EVERY language that converts decimal (real) input to  
binary storage.

Binary storage is not mathematically required, but the result is MUCH  
faster code. Perhaps, at some point, we'll abandon this trade-off when  
computers are so fast that the gain in speed isn't worth the confusion.  
But that day isn't here, yet.

(Well. It is for ME, but not for a lot of other, very impatient people. If  
they can get a result in a second with decimal arithmetic, they'd rather  
have it in a microsecond with binary arithmetic, no matter WHAT the cost  
in confusion factors.)

Bobby

On Thu, 07 Jul 2011 06:31:49 -0500, slawek <slawek@host.pl> wrote:

>
> U=BFytkownik "Kevin J. McCann" <Kevin.McCann@umbc.edu> napisa=B3 w  
> wiadomo=B6ci
> grup dyskusyjnych:iv1a86$sji$1@smc.vnet.net...
>> 2.0 is not an integer nor a rational, it is machine precision. On the
>> other hand 2 is an integer and exact.
>
> The decimal fraction 2.0 is in mathematics (the science) exactly the  
> same as
> the sum 2 + 0/10
>
> The convention that 2.0 is less accurate than 2.00 is applied ONLY in
> Mathematica (the computer program).
>
>
>
>


-- 
DrMajorBob@yahoo.com

[toc] | [next] | [standalone]

#3665

Użytkownik "DrMajorBob" <btreat1@austin.rr.com> napisał w wiadomości grup 
dyskusyjnych:iv6hgo$sch$1@smc.vnet.net...
> Binary storage is not mathematically required, but the result is MUCH
> faster code. Perhaps, at some point, we'll abandon this trade-off when
> computers are so fast that the gain in speed isn't worth the confusion.
> But that day isn't here, yet.

BCD - Binary Coded Decimals. 

[toc] | [prev] | [next] | [standalone]

#3692

On 7/12/2011 4:01 AM, slawek wrote:
> U=BFytkownik "DrMajorBob"<btreat1@austin.rr.com>  napisa=B3 w wiadomo=B6=
ci grup
> dyskusyjnych:iv6hgo$sch$1@smc.vnet.net...
>> Binary storage is not mathematically required, but the result is MUCH
>> faster code. Perhaps, at some point, we'll abandon this trade-off when
>> computers are so fast that the gain in speed isn't worth the confusion=
.
>> But that day isn't here, yet.
>
> BCD - Binary Coded Decimals.
>
>

IEEE 754-2008 is an update to the floating-point standard that not only
includes binary, but decimal arithmetic (and radix-independent).  This
is presumably implemented in hardware, or intended to be implemented in
hardware.

At least one computer algebra system does software arbitrary precision
floats in what looks like decimal.  Though I think it is base 1000 coded
in 1024 bits  or some such thing.
For more reading on IEEE use google or just check out
http://en.wikipedia.org/wiki/IEEE_754-2008

[toc] | [prev] | [standalone]

Back to top | Article view | comp.soft-sys.math.mathematica

csiph-web