
[The original thread
< http://groups.google.com/group/comp....se_frm/thread/
b495b4898808fde0>
is more than one month old  this may pose problem for posting over
some news servers. This is why I'm starting a new one]
I'd still like to finish this rounding mess. As a startup lemma we can
take that VK is the worst programmer of all times and places: let's
move from here forward please.
The usability of any program depends on exact behavior description.
This way it is a must to know i) what argument we can feed into and
ii) what results to expect.
The usability of the current FAQ code in this aspect is zero. "take
power of x, extract y" and similar is not a behavior description  it
is a description of the formal algorithm. It is the same as instead
remote control manual provide a detailed electronic schema of the
control. Obviously a reference to some other formal algorithm ("in
accordance with ECMA262 section...") doesn't add any usability.
So first it has to be defined what common rules (behavior) are used
for rounding.
The key points are:
1) how to round with losses (when some signs have to be dropped)
2) how to round equipoint (in decimal system it will be 5)
3) how to round negative
As milestone values used everywhere further are
1) 1.033
2) 1.035
3) 1.035
IEEE754/IEEE754r define five methods of rounding for numeral string
representation:
(the specification order is changed, the implemented methods moved
atop)
1) Biased round to nearest, ties away from zero
Implemented by IE's toFixed method. Overall the most known as studied
at the school
toFixed(2)
1.033 = 1.03
1.035 = 1.04 (equipoint ties away zero, so to positive infinity
for positive values)
1.035 =1.04 (equipoint ties away zero, so to negative infinity
for negative values)
2) Biased towards zero
Implemented by Gecko and Opera toFixed method.
toFixed(2)
1.033 = 1.03
1.035 = 1.03 (equipoint ties towards zero)
1.035 =1.03 (equipoint ties towards zero)
3) Biased towards positive infinity
No known ECMAScript implementations (?)
toFixed(2)
1.033 = 1.03
1.035 = 1.04 (equipoint ties towards positive infinity)
1.035 =1.03 (equipoint ties towards positive infinity)
4) Biased towards negative infinity
No known ECMAScript implementations (?)
toFixed(2)
1.033 = 1.03
1.035 = 1.03 (equipoint ties towards negative infinity)
1.035 =1.04 (equipoint ties towards negative infinity)
This is as far as IEEE754 currently goes. As it was pointed by some
posters, rounding is not some "natural" feature coming out of numbers
themselves. It is merely a contract behavior: "let's make it as
this...". This way it can be a rule combining two or more rules from
IEEE or even all separate custom algorithm. In the latter case of
course any appellations to "standards" and "bug fixes" must be
dropped. In any case exact behavior description has to be given.
This way I am insistently asking to explain what rounding rule is
considered correct by FAQ maintainer:
1) Biased round to nearest, ties away from zero (IE)  thus Gecko
needs a fix
2) Biased towards zero (Gecko, Opera)  thus IE needs a fix
3) some third  thus everyone needs a fix
In the 3rd case what this rounding rule is?  
Share:

VK wrote in message
news:11**********************@q2g2000cwa.googlegro ups.com...
[The original thread
<http://groups.google.com/group/comp....se_frm/thread/
b495b4898808fde0>
is more than one month old  this may pose problem for posting
over some news servers. This is why I'm starting a new one]
Is it? Or is it more a matter of the code you posted in that thread being
so selfevidently inept that you would rather distract attention away
form it, and the harm it would have done to your credibility, if you had
any to start with.
I'd still like to finish this rounding mess.
Maybe, but you have demonstrated that it is beyond your comprehension.
As a startup lemma we can take that VK is the worst
programmer of all times and places:
Not a programmer at all. A programmer would not response to having the
faults in their code pointed out by stating that they "don't care about
that situation", as you did.
let's move from here forward please.
What is the point of this appeal? You are so far behind everyone else
that you have a couple of years learning the basics to go before you
would become qualified to participate in this discussion.
<snip>
As milestone values used everywhere further are
1) 1.033
2) 1.035
3) 1.035
<snip>
So you have still not understood that javascript's numeric type cannot
represent certain numbers, so instead it uses a number that is the
nearest approximation of the original number that it can represent.
Richard.   
On Jan 28, 11:30 pm, "Richard Cornford" <Rich...@litotes.demon.co.uk>
wrote:
<snip>As milestone values used everywhere further are
1) 1.033
2) 1.035
3) 1.035<snip>
So you have still not understood that javascript's numeric type cannot
represent certain numbers, so instead it uses a number that is the
nearest approximation of the original number that it can represent.
As I once asked prior: please be nasty, sarcastic and so on  but
please don't be silly. The choice of the "nearest approximation" for
these three numbers (can be any other triplet of course) defines the
rounding mechanics in use. I spelled all four from IEEE754, I
explained which one is chosen by IE and by Gecko.
Now I'm asking which one of four should be _really_ used by "selected
people"'s opinion. If no one but something fifth then please spell
it. If the IEEE official terms put too much of challenge then simply
give the rounding results with two numerals after comma which are
considered correct by you:
correctToFixed(2)
1.033 =?
1.035 =?
1.035 =?
This would easily show what rounding method are you bearing in your
mind.   
VK wrote:
Richard Cornford wrote:
><snip>As milestone values used everywhere further are
1) 1.033
2) 1.035
3) 1.035<snip>
So you have still not understood that javascript's numeric type cannot represent certain numbers, so instead it uses a number that is the nearest approximation of the original number that it can represent.
As I once asked prior: please be nasty, sarcastic and so
on  but please don't be silly.
Whatever you may perceive as silly here is of no concern to me. You don't
comprehend the subject and instead of doing something about finding out
you are wasting time with misdirecting yourself.
The choice of the "nearest approximation" for
these three numbers (can be any other triplet of course)
defines the rounding mechanics in use.
Bullshit. You are failing to grasp that a numeric literal in source code
will result in a value of numeric type (following ECMA 262 specified
rules) but that numeric value will not necessarily be the number that may
be expected from reading the numeric literal's text.
The rounding used is specified, but has no more than a coincidental
bearing on any other rounding performed by the language.
I spelled all four from IEEE754,
And again you were looking in the wrong place and so not seeing the
pertinent information.
I explained which one is chosen by IE and by Gecko.
No you did not. What you did was drivel on about what you misperceived
based upon another of your misconceptions.
Now I'm asking which one of four should be _really_ used
by "selected people"'s opinion.
Your question starts from a false premise. The behaviour of  toFixed 
implementations imply nothing beyond the nature of the implementations
of  toFixed  methods.
If no one but something fifth then please spell
it.
Gibberish.
If the IEEE official terms put too much of challenge
then simply give the rounding results with two numerals
after comma which are considered correct by you:
correctToFixed(2)
1.033 =?
1.035 =?
1.035 =?
Are you asking which results the  toFixed  method of Number objects
would return? There is a specified algorithm for  toFixed , so its
correct output is output that would be produced by applying the algorithm
to the input.
On the other hand, as you have repeatedly been told, there is no value of
the numeric type in javascript that precisely represents 1.035, and so
that value _can_not_ be the input value for the  toFixed  algorithm.
This would easily show what rounding method are you bearing
in your mind.
Differing rounding methods are suited to different applications. Given
that you are limited in your perceptions by some concept of a single
correct "school rounding" (that is itself apparently too complex for you
to implement in javascript yourself) you are incapable of seeing the
worthlessness of your insisting that there be some single absolute answer
to your question.
Richard.   
Richard Cornford wrote:
>
>If the IEEE official terms put too much of challenge then simply give the rounding results with two numerals after comma which are considered correct by you: correctToFixed(2) 1.033 =? 1.035 =? 1.035 =?
Are you asking which results the  toFixed  method of Number objects
would return? There is a specified algorithm for  toFixed , so its
correct output is output that would be produced by applying the algorithm
to the input.
On the other hand, as you have repeatedly been told, there is no value of
the numeric type in javascript that precisely represents 1.035, and so
that value _can_not_ be the input value for the  toFixed  algorithm.
VK,
Just try to imagine how many bits you have to store a piece of information,
when thinking about precision and representation and what it means.
You can only store 256 values in 8 bits. Clear, isn't it?
Same goes for floating points. If you have 4 bytes, or 8, or whatever, to
store a floating point number, is should be clear you cannot store ANY
floating point number excactly in it.
Some rounding is always needed. The amount of rounding (=error when storing
floating point numbers) depends on the number of bytes allocated to a
variable, but since you don't have an unlimitted amount of bytes available,
you will always have rounding in the real world.
So if you are talking about 1.035 and want to store that in a variable,
wonder how much bytes JavaScript has to represent the number.
A simple example:
var val1 = 1.12345;
var val2 = 1.123456;
var val3 = (val1val2);
alert (val3);
This might be a good startingpoint to get an idea of what Richard is
reffering to: http://en.wikipedia.org/wiki/Roundoff_error http://en.wikipedia.org/wiki/Machine_epsilon http://en.wikipedia.org/wiki/Floating_point_arithmetic
Regards,
Erwin Moller   
On Jan 29, 2:01 am, "Richard Cornford" <Rich...@litotes.demon.co.uk>
wrote:
<snip irrelevant>
If the IEEE official terms put too much of challenge
then simply give the rounding results with two numerals
after comma which are considered correct by you:
correctToFixed(2)
1.033 =?
1.035 =?
1.035 =?
Are you asking which results the  toFixed  method of Number objects
would return? There is a specified algorithm for  toFixed , so its
correct output is output that would be produced by applying the algorithm
to the input.
That was my original suspicion, thank you for confirming it and it's
good I decided to take care of this FAQ. So basically the position is:
"We don't know what rounding results will be produced for a particular
number  until it's actually rounded. But whatever rounding result
will be  it will be the correct one, and anything else wrong".
34 years ago I would decide that I'm talking with a mentally
inadequate person, but now I accustomed a bit to clj regulars'
specifics.
Still you had to make some rounding testing I guess to conclude that
native toFixed on say IE or Gecko do not "predict the feature" in the
same way as your algorithm does. What was these series?
Of course you may add some fun by stating that the current algorithm
is so correct that anything else is wrong by definition without any
extra testing needed.
P.S. The current rounding question is based on the common default of
people lacking any real knowledge but pretending to have such by
quickly reading some serious sources. Usually they miss the whole
picture but fixate on one or two points they managed to understand. In
this case you grabbed the internal unbiased round to nearest ties to
even rule. In my post I said "five rounding rules" but I named only
four and I was waiting you ask for the fifth. Here is it: the default
internal unbiased round to nearest ties to even. It was not listed as
an option because it is internal  you cannot get on it unless gaining
system level access to the engine or unless making the entire
calculation on BigMath (with string values). "5 is uncertain" you are
repeating  but not grasping its real sense  is from there. On
equipoint resolution the system will move to the nearest even, with
overall destribution 50/50 But again it is internal mechanics you have
no access nor business.
P.P.S. As it is pretty much confirmed that no one can tell what
rounding rule is the most "ECMAScript correct" I guess that biased
ties away from zero will be the such, as I initially decided. It is
the most publically known and the most implemented in javascript
engines (IE, 85%95% of visitors).   
On Jan 29, 2:23 pm, Erwin Moller
So if you are talking about 1.035 and want to store that in a variable,
wonder how much bytes JavaScript has to represent the number.
A simple example:
var val1 = 1.12345;
var val2 = 1.123456;
var val3 = (val1val2);
alert (val3);
This might be a good startingpoint to get an idea of what Richard is
reffering to:
Erwin, the FAQ in question is "How do I convert a Number into a String
with exactly 2 decimal places?"  this is the startingpoint. There are
4 official rules for that, we can come with 5th, 6th etc.  as long as
it provides predictable results.
The limitations of IEEE754 floating point are known to me better then
Richard could imagine. Unfortunately fixed point systems on current 32
bit machines impose too narrow range of numbers to be universally
usable. IEEE754 floating point still remains as the most usable
compromise for PCs (personal computers).
But internal unbiased rounding algorithm of IEEE754 based systems is
irrelevant to this FAQ. Yes, we cannot represent exactly 2^52+1, 1/3,
PI etc. etc.
But we have to say exactly what will be 1.035 or 1.035 converted into
a string with exactly 2 decimal places after comma. All four official
rules are giving exact answer on it.
Both IE and Geck toFixed give the exact answer as well: but they are
using different rules so these answers will be different.
So the task is to decide who is right: IE, Gecko, no one; based on
this decision a program has to be provided to ensure unifirmed results
by fixing IE, or Gecko or both.   
VK wrote:
On Jan 29, 2:23 pm, Erwin Moller
>So if you are talking about 1.035 and want to store that in a variable, wonder how much bytes JavaScript has to represent the number.
A simple example: var val1 = 1.12345; var val2 = 1.123456; var val3 = (val1val2); alert (val3);
This might be a good startingpoint to get an idea of what Richard is reffering to:
Erwin, the FAQ in question is "How do I convert a Number into a String
with exactly 2 decimal places?"  this is the startingpoint. There are
4 official rules for that, we can come with 5th, 6th etc.  as long as
it provides predictable results.
The limitations of IEEE754 floating point are known to me better then
Richard could imagine. Unfortunately fixed point systems on current 32
bit machines impose too narrow range of numbers to be universally
usable. IEEE754 floating point still remains as the most usable
compromise for PCs (personal computers).
But internal unbiased rounding algorithm of IEEE754 based systems is
irrelevant to this FAQ. Yes, we cannot represent exactly 2^52+1, 1/3,
PI etc. etc.
But we have to say exactly what will be 1.035 or 1.035 converted into
a string with exactly 2 decimal places after comma. All four official
rules are giving exact answer on it.
Both IE and Geck toFixed give the exact answer as well: but they are
using different rules so these answers will be different.
So the task is to decide who is right: IE, Gecko, no one; based on
this decision a program has to be provided to ensure unifirmed results
by fixing IE, or Gecko or both.
Ok VK,
I happened to be reading that piece on wikipedia, and thought it might be
relevant to the discussion.
But if you all know it allready, I better shut up. :)
Regards,
Erwin Moller   
On Jan 29, 3:21 pm, Erwin Moller
I happened to be reading that piece on wikipedia, and thought it might be
relevant to the discussion.
But if you all know it allready, I better shut up. :)
Why? It is a public discussion  anyone's opinion is welcome. Say what
would you personally expect from 1.035.toFixed(2) : 1.03 (Gecko) or
1.04 (IE) ? And from 1.035.toFixed(2) : 1.03 or 1.04
Either is "correct"  thus in accordance with one of official rounding
rules  but what would you expect first?   
On Jan 29, 11:33 am, "VK" <schools_r...@yahoo.comwrote:
On Jan 29, 2:01 am, Richard Cornford wrote:
<snip irrelevant>
If you cannot differentiate between what is relevant and what is not
then you will never understand this subject.
>>If the IEEE official terms put too much of challenge then simply give the rounding results with two numerals after comma which are considered correct by you: correctToFixed(2) 1.033 =? 1.035 =? 1.035 =?
Are you asking which results the  toFixed  method of Number objects would return? There is a specified algorithm for  toFixed , so its correct output is output that would be produced by applying the algorithm to the input.
That was my original suspicion, thank you for confirming it and it's
good I decided to take care of this FAQ.
Confirming what? The algorithm for the  toFixed  method of numbers
has no implications beyond determining the correct behaviour for the 
toFixed method of number objects.
So basically the position is:
"We don't know what rounding results will be produced for a particular
number  until it's actually rounded. But whatever rounding result
will be  it will be the correct one, and anything else wrong".
How does that follow from the observation that there is a specified
algorithm for the  toFixed  method and so the correct output of the
 toFiexed  method can be determined from its input?
34 years ago I would decide that I'm talking with a mentally
inadequate person, but now I accustomed a bit to clj regulars'
specifics.
You certainly should be getting familiar with experiencing discussions
in this group going right over your head by now.
Still you had to make some rounding testing I guess to conclude that
native toFixed on say IE or Gecko do not "predict the feature" in the
same way as your algorithm does.
I can certainly state that IE's  toFiexed  method is not implemented
in accordance with the specification.
What was these series?
What was what "series"?
Of course you may add some fun by stating that the current algorithm
is so correct that anything else is wrong by definition without any
extra testing needed.
The specified algorithm is the specified algorithm. It states how the
 toFiexed  method of number objects should behave. It is completely
irrelevant to the wider subject of rounding numeric values to strings,
unless the type of rounding perceived as appropriate for any given
application happens to correspond with what the  toFiexed  method
does (and the environment does not include buggy implementations like
that in JScript).
P.S. The current rounding question is based on the common default of
people lacking any real knowledge but pretending to have such by
quickly reading some serious sources. Usually they miss the whole
picture but fixate on one or two points they managed to understand.
You are describing yourself? You certainly seem to be fixating on
numerous irrelevancies (the  toFiexed  methods and the rounding
specified in the IEEE standard) and failing to see what is relevant to
the subject.
In this case you grabbed the internal unbiased round to nearest
ties to even rule.
Who garbled it? And why does it have any relevance? And, what happened
to your insistence on "school rounding" (whatever that was intended to
mean) being the one true rounding?
In my post I said "five rounding rules" but I named only
four and I was waiting you ask for the fifth.
Why would anyone ask you to elaborate on an irrelevance?
<snip>
P.P.S. As it is pretty much confirmed that no one can tell what
rounding rule is the most "ECMAScript correct"
<snip>
Where ECMAScript requires rounding the specification precisely states
what rounding will happen and how it will happen. Rounding for an
application context is determined by the context. For any given
situation there are appropriate rounding strategies, which may be
provided by features of the language or may need to be implemented
with the language. It simply makes no sense to be talking of "what
rounding rule is the most ECMAScript correct".
Richard.   
VK wrote:
On Jan 29, 2:23 pm, Erwin Moller
>So if you are talking about 1.035 and want to store that in a variable, wonder how much bytes JavaScript has to represent the number.
A simple example: var val1 = 1.12345; var val2 = 1.123456; var val3 = (val1val2); alert (val3);
This might be a good startingpoint to get an idea of what Richard is reffering to:
Erwin, the FAQ in question is "How do I convert a Number into a String
with exactly 2 decimal places?"  this is the startingpoint. There are
4 official rules for that,
Are there? You have mentioned how IEEE 754 mandates rounding be
performed when it is necessary in operations using IEEE 754 double
precision floating point numbers, but that does not make those into "4
official rules" for converting a number into a string with exactly 2
decimal places.
we can come with 5th, 6th etc.  as long as
it provides predictable results.
Given your public record on implementing rounding algorithms "we can
come up with" seems a little optimistic.
The limitations of IEEE754 floating point are known to me better then
Richard could imagine.
Don't put money on it. You still do not appear to have comprehended
that if 1.035 cannot ever be an IEEE 754 floating point number then it
can also never be the number in "How do I convert a Number into a
String with exactly 2 decimal places". Your continued obsession with
that number is telling in this regard.
Unfortunately fixed point systems on current 32
bit machines impose too narrow range of numbers to be
universally usable.
Bullshit. And you have been told why often enough by now.
IEEE754 floating point still remains as the most usable
compromise for PCs (personal computers).
Nonsense.
But internal unbiased rounding algorithm of IEEE754 based systems is
irrelevant to this FAQ. Yes, we cannot represent exactly 2^52+1, 1/3,
PI etc. etc.
But we have to say exactly what will be 1.035 or 1.035 converted into
a string with exactly 2 decimal places after comma.
If 1.035 cannot be an IEEE 754 double precision floating point number
then we can say with certainty that such a number can never be
converted into a string with exactly 2 decimal places.
All four official rules are giving exact answer on it.
Not is the number cannot exist to start with.
Both IE and Geck toFixed give the exact answer as well: but they are
using different rules so these answers will be different.
So the task is to decide who is right: IE, Gecko, no one; based on
this decision a program has to be provided to ensure unifirmed results
by fixing IE, or Gecko or both.
Nobody misses the point quite so relentlessly as you do.
Richard.   
On Jan 29, 5:10 pm, "Richard Cornford" <Rich...@litotes.demon.co.uk>
wrote:
Are you asking which results the  toFixed  method of Number objects
would return? There is a specified algorithm for  toFixed , so its
correct output is output that would be produced by applying the algorithm
to the input.
var n1 = 2.070;
var n2 = n1/2;
alert(n2 === 1.035); // true
// but by Cornford's lemma:
// 1.035.toFixed(2) is impossible
// so futile to impose any rules
So what you saying is: "I cannot predict any consistent behavior for
the program, moreover it is silly to expect any consistent behavior
out of it; but whatever it will output  it will be correct to take
without questioning."
Splendid! :) Science and religion working together to unveil secrets
of universe and stuff... :)
I can certainly state that IE's  toFixed  method is not implemented
in accordance with the specification.
A fire angel visited you to deliver this message or did you actually
test it with a series of numbers? In the first case I have nothing but
take your statement, as it is, in the second case what are these
numbers?
What was what "series"?
The series of numbers you tried to round using native toFixed method
to conclude that this method is buggy. Please past below in form
"number"/"correct result"/"actual result". In case if no testing was
made or if any empiric results are irrelevant by the definition of the
matter then simply type in "fire angel" below.
Where ECMAScript requires rounding the specification precisely states
what rounding will happen and how it will happen. Rounding for an
application context is determined by the context. For any given
situation there are appropriate rounding strategies, which may be
provided by features of the language or may need to be implemented
with the language. It simply makes no sense to be talking of "what
rounding rule is the most ECMAScript correct".
But it does make sense to define what rounding result is correct and
what is wrong? "bugs in IE toFixed implementation" FAQ says. An
interesting approach. :)
That's getting like beating down a baby, really... But for all nasties
you wrote before I can allow myself this little pleasure.
Before posting I looked for some IEEE rounding online source suitable
for junior school students  thus hopefully not hard enough for
Mr.Crockford: obviously IEEE754 specs in their pure form are beyond
the level.
<http://mathforum.org/library/drmath/view/63989.htmlmaybe?
P.S. By the middle of the week I'm expecting some free time to write a
normal rounding proc for the FAQ, so the current eschatological
guessing machine could be finally removed. I think the best is to
profide a switch as an optional argument for the method call so either
of four roundings could be used  with default round to nearest ties
away from zero.   
On Jan 29, 7:58 pm, "VK" <schools_r...@yahoo.comwrote:
not hard enough for Mr.Crockford
Cruze / Kruse
Cornford / Crockford
clj is really a challenge for dislexic people like I am :)
_Mr. Cornford_ I meant   
In comp.lang.javascript message <ep*******************@news.demon.co.uk>
, Sun, 28 Jan 2007 23:01:31, Richard Cornford
<Ri*****@litotes.demon.co.ukposted:
> Bullshit. You are failing to grasp that a numeric literal in source code will result in a value of numeric type (following ECMA 262 specified rules) but that numeric value will not necessarily be the number that may be expected from reading the numeric literal's text.
OTOH, if you follow the link in the FAQ you can see that a quantity
supplied as "1.035" and converted by unary + to a Number of exact value
1.034999999999999920063942226988729089498519897460 9375 can be rounded
(traditional or Bankers') or truncated without undue difficulty (except
by the VK standard) *as* *if* *it* *had* *been* *stored* *exactly*, in
two quite distinct ways.

(c) John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v6.05 MIME.
Web <URL:http://www.merlyn.demon.co.uk/ FAQish topics, acronyms, & links.
For more on our news hierarchy news:uk.*, see newsgroups news:uk.answers and
news:uk.net.news.*, and <URL:http://www.usenet.org.uk/>.   
On Jan 29, 4:58 pm, "VK" <schools_r...@yahoo.comwrote:
On Jan 29, 5:10 pm, Richard Cornford wrote:
>>>Are you asking which results the  toFixed  method of Number objects would return? There is a specified algorithm for  toFixed , so its correct output is output that would be produced by applying the algorithm to the input.
var n1 = 2.070;
var n2 = n1/2;
alert(n2 === 1.035); // true
What do you imagine that is attempting to demonstrate?
// but by Cornford's lemma:
// 1.035.toFixed(2) is impossible
// so futile to impose any rules
I did not say that was impossible. There is no problem writing that
code, it is understanding what it means that you are having trouble
with.
I said that it was imposable for  toFixed  to act upon a Number
object with the value 1.035, because no numeric value in javascript
can have the value 1.035.
So what you saying is: "I cannot predict any consistent behavior for
the program, moreover it is silly to expect any consistent behavior
out of it; but whatever it will output  it will be correct to take
without questioning."
No, I am saying that I can precisely predict the outcome of 
1.035.toFixed(2)  in any ECMAScript implementation that does not
suffer from bugs in the related areas. However, in making that
prediction I would have to take the numeric literal source code
"1.035" and transform it into an IEEE 754 double precision floating
point number following the rules in ECMA 262 3rd Ed. section 7.8.3.
The result of that process will _not_ be 1.035, but it is still the
value of the Number object upon which the  toFixed  method will be
called, and so the real input value for the  toFixed  algorithm.
The question of how the  toFixed  method handles the number 1.035 is
a nonsense because it is never presented with any number that cannot
be precisely represented as an IEEE 754 double precision floating
point number.
Splendid! :) Science and religion working together to unveil
secrets of universe and stuff... :)
? Is it really too much trouble to read the specification for the
language you insist in babbling on about?
>I can certainly state that IE's  toFixed  method is not implemented in accordance with the specification.
A fire angel visited you to deliver this message or did you actually
test it with a series of numbers? In the first case I have nothing but
take your statement, as it is, in the second case what are these
numbers?
Some of these numbers (and there are many) are:
(0.94).toFixed(0)
(0.88).toFixed(0)
(0.77).toFixed(0)
(0.66).toFixed(0)
(0.55).toFixed(0)
 which all result in the string: "0"
(0.94).toFixed(0)
(0.88).toFixed(0)
(0.77).toFixed(0)
(0.66).toFixed(0)
(0.55).toFixed(0)
 which all result in the string: "0"
(0.094).toFixed(1)
(0.088).toFixed(1)
(0.077).toFixed(1)
(0.066).toFixed(1)
(0.055).toFixed(1)
 which all result in the string: "0.0"
(0.0094).toFixed(2)
(0.0088).toFixed(2)
(0.0077).toFixed(2)
(0.0066).toFixed(2)
(0.0055).toFixed(2)
 which all result in the string: "0.00"
(0.000000000000000064).toFixed(16)
 which results in the string: "0.0000000000000000"
None of these are results in accordance with the algorithm specified
in ECMA 262 3rd Ed.
>What was what "series"?
>The series of numbers you tried to round using native toFixed
method to conclude that this method is buggy.
One single erroneous result is sufficient to conclude that any
function/method is buggy.
Please past below in form "number"/"correct result"/"actual
result". In case if no testing was made or if any empiric results
are irrelevant by the definition of the matter then simply type in
"fire angel" below.
The correct output from  (0.000000000000000064).toFixed(16)  is
"0.0000000000000001", while IE outputs "0.0000000000000000".
>Where ECMAScript requires rounding the specification precisely states what rounding will happen and how it will happen. Rounding for an application context is determined by the context. For any given situation there are appropriate rounding strategies, which may be provided by features of the language or may need to be implemented with the language. It simply makes no sense to be talking of "what rounding rule is the most ECMAScript correct".
But it does make sense to define what rounding result is correct and
what is wrong?
Not really. Various forms of rounding would produce results that
disagree, yet all have valid application in some context or another.
"bugs in IE toFixed implementation" FAQ says. An
interesting approach. :)
There are bugs in IE's  toFixed  implementation, hence the obviously
dubious results it outputs for so many values.
That's getting like beating down a baby, really... But for all nasties
you wrote before I can allow myself this little pleasure.
Before posting I looked for some IEEE rounding online source suitable
for junior school students  thus hopefully not hard enough for
Mr.Crockford: obviously IEEE754 specs in their pure form are beyond
the level.
<http://mathforum.org/library/drmath/view/63989.htmlmaybe?
Do you intend stating what relevance you think that has?
P.S. By the middle of the week I'm expecting some free time
to write a normal rounding proc for the FAQ,
Are you really willing to take that risk? After the sorry excuse for a
method you posted last time you attempted that, and given your
inability to verify whether your own code actually does what you thing
it may be doing, don't you think you are likely to just post another
embarrassing f**kup?
so the current eschatological
guessing machine could be finally removed.
Apart form you, who is guessing?
I think the best is to profide a switch as an optional argument
for the method call so either of four roundings could be used
 with default round to nearest ties away from zero.
You don't think you might be safer only attempting one rounding
algorithm at a time, given how poorly you failed last time you
attempted one?
Richard.   
VK wrote:
On Jan 29, 7:58 pm, VK wrote:
not hard enough for Mr.Crockford
Cruze / Kruse
Cornford / Crockford
clj is really a challenge for dislexic people like I am :)
I don't have that much trouble, but then I am not arrogant enough to
believe that I could not make a mistake and so would go and check the
spelling of someone's name.
_Mr. Cornford_ I meant
This mistake is just another symptom of your delusion that you know
what you are doing. It will keep you arguing this subject on and on
until someone eventually manages to make you see that you have been
utterly wrong from the outset.
Richard.   
In comp.lang.javascript message <11*********************@l53g2000cwa.goo
glegroups.com>, Mon, 29 Jan 2007 04:14:55, VK <sc**********@yahoo.com>
posted:
>On Jan 29, 2:23 pm, Erwin Moller
>So if you are talking about 1.035 and want to store that in a variable, wonder how much bytes JavaScript has to represent the number.
A simple example: var val1 = 1.12345; var val2 = 1.123456; var val3 = (val1val2); alert (val3);
This might be a good startingpoint to get an idea of what Richard is reffering to:
Erwin, the FAQ in question is "How do I convert a Number into a String with exactly 2 decimal places?"
It seems that you have failed to notice that, in the Subject lines of
FAQ Section 4 entries, words do not generally start with capital
letters.
<FAQENTRY bug in Subject 4.31 ! </FAQENTRY>
<FAQENTRY Subject 4.30 : should be lastModified or LastModified
But in 4.6 Subject, Number starts with a capital letter. That indicates
that we are not dealing with any old number, such as onethird or pi or
e or 1.035  we are dealing with the content of a javascript variable of
type Number.
Since an IEEE Double is 64 bits, it can have at most 2^64 values (in
javascript, it effectively has fewer, because (in spite of the result of
NaN == NaN being false ) all NaNs are indistinguishable). Exactly
NONE of those values is 1.035. 100*Number("1.035") produces
approximately 103.49999999999998 which correctly rounds to 103.

(c) John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v6.05 MIME.
Web <URL:http://www.merlyn.demon.co.uk/ FAQish topics, acronyms, & links.
Proper <= 4line sig. separator as above, a line exactly " " (SonOfRFC1036)
Do not Mail News to me. Before a reply, quote with ">" or "" (SonOfRFC1036)   
Dr J R Stockton said the following on 1/29/2007 2:22 PM:
<snip>
<FAQENTRY bug in Subject 4.31 ! </FAQENTRY>
Why are my Rollovers so slow?
What is the bug and a proposed correction? The bug is that it doesn't
even come close to answering the question. I did change it to rollover
vice Rollover locally. Will get the minor corrections uploaded later today.
<FAQENTRY Subject 4.30 : should be lastModified or LastModified
Changed to:
How do I format the LastModified date with javascript?
Although I think it should say LastModified Date of a document with
javascript.

Randy
Chance Favors The Prepared Mind
comp.lang.javascript FAQ  http://jibbering.com/faq/index.html
Javascript Best Practices  http://www.JavascriptToolbox.com/bestpractices/   
In comp.lang.javascript message <11*********************@q2g2000cwa.goog
legroups.com>, Mon, 29 Jan 2007 10:34:01, Richard Cornford
<Ri*****@litotes.demon.co.ukposted:
> There are bugs in IE's  toFixed  implementation, hence the obviously dubious results it outputs for so many values.
Be aware that DA posted, in news:m.p.s.j 20031106, javascript code said
to follow ECMA262s specification step by step. It's in my Rounding 1.
IMHO, it's less than ideal, since null and undefined are converted to
"0.00" and "NaN"  but that may be what ECMA wants.

(c) John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v6.05 IE 6
news:comp.lang.javascript FAQ <URL:http://www.jibbering.com/faq/index.html>.
<URL:http://www.merlyn.demon.co.uk/jsindex.htmjscr maths, dates, sources.
<URL:http://www.merlyn.demon.co.uk/TP/BP/Delphi/jscr/&c, FAQ items, links.   
In comp.lang.javascript message <K********************@telcove.net>,
Tue, 30 Jan 2007 07:55:08, Randy Webb <Hi************@aol.composted:
>Dr J R Stockton said the following on 1/29/2007 2:22 PM:
<snip>
> <FAQENTRY bug in Subject 4.31 ! </FAQENTRY>
Why are my Rollovers so slow?
What is the bug and a proposed correction?
The bug in the Subject is the capital R. As a correction, I suggest a
lowercase r.
> <FAQENTRY Subject 4.30 : should be lastModified or LastModified
Changed to:
How do I format the LastModified date with javascript?
On rereading the body of the section : the word "it" refers to the
grammatical object in the Subject, and so lastModified or
document.lastModified is needed.
If that part of the system had been intelligently specified, the
javascript lastModified string would have been a copy of the header
LastModified, thereby not losing any information  and the whole
problem would reduce to converting RFC format  "Tue, 15 Nov 1994
12:45:26 GMT"  into whatever the page designer fancied.
And if the RFC format had been well designed, it would be as "19941115
12:45:26 GMT", for easy comparison.

(c) John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v6.05 IE 6.
Web <URL:http://www.merlyn.demon.co.uk/ w. FAQish topics, links, acronyms
PAS EXE etc : <URL:http://www.merlyn.demon.co.uk/programs/ see 00index.htm
Dates  miscdate.htm moredate.htm jsdates.htm pastime.htm critdate.htm etc.   This discussion thread is closed Replies have been disabled for this discussion. Similar topics
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