123.45 - 123 = 0.45

Hello!

On Tue, 15 Dec 1998, Sferacarta Software wrote:

I tried to divide 123.45 by 123.00 but PostgreSQL gives me a wrong
result:

hygea=> select 123.45 - 123.00;
?column?
-----------------
0.450000000000003
(1 row)

I cannot understand anything. You said "to divide" and then "123.45 - 123.00".
Are you trying to divide or to substract?

Oleg.
----
Oleg Broytmann National Research Surgery Centre http://sun.med.ru/~phd/
Programmers don't die, they just GOSUB without RETURN.

Hi all,

I tried to divide 123.45 by 123.00 but PostgreSQL gives me a wrong
result:

hygea=> select 123.45 - 123.00;
?column?
-----------------
0.450000000000003
(1 row)

Wow, I get the same thing here.

Even this doesn't work:

test=> select float8(123.45) - float8(123.00);
?column?
-----------------
0.450000000000003
(1 row)

Now constants are automatically promoted to float8, so I expected the
same results, but what is going on here?

-- 
  Bruce Momjian                        |  http://www.op.net/~candle
  maillist@candle.pha.pa.us            |  (610) 853-3000
  +  If your life is a hard drive,     |  830 Blythe Avenue
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Try this:

#include <stdio.h>

main()
{
double f1 = 123.45;
double f2 = 123.00;
double r;

r = f1 - f2;
printf("%0.15f %0.15f %0.15f\n", f1, f2, r);
}

Internal representation of 123.45 is not exact. In the conversion to
binary, an irrational number is created which is truncated to 64 bits.

Bruce Momjian wrote:

On Tue, 15 Dec 1998, Sferacarta Software wrote:

Hi all,

I tried to divide 123.45 by 123.00 but PostgreSQL gives me a wrong
result:

hygea=> select 123.45 - 123.00;
?column?
-----------------
0.450000000000003
(1 row)

Are you trying to subtract or divide? Your select is subtraction,
your question was division.

Vince.
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Hello Oleg,

marted�, 15 dicembre 98, you wrote:

OB> Hello!

OB> On Tue, 15 Dec 1998, Sferacarta Software wrote:

I tried to divide 123.45 by 123.00 but PostgreSQL gives me a wrong
result:

hygea=> select 123.45 - 123.00;
?column?
-----------------
0.450000000000003
(1 row)

OB> I cannot understand anything. You said "to divide" and then "123.45 - 123.00".
OB> Are you trying to divide or to substract?

Sorry I want to say subtract.

-Jose'-

Try this:

#include <stdio.h>

main()
{
double f1 = 123.45;
double f2 = 123.00;
double r;

r = f1 - f2;
printf("%0.15f %0.15f %0.15f\n", f1, f2, r);
}

Internal representation of 123.45 is not exact. In the conversion to
binary, an irrational number is created which is truncated to 64 bits.

Yes, someone pointed this out to me in private e-mail, and I wrote a C
program to confirm it. I just had never seen such rounding on such
small non-irrational numbers.

-- 
  Bruce Momjian                        |  http://www.op.net/~candle
  maillist@candle.pha.pa.us            |  (610) 853-3000
  +  If your life is a hard drive,     |  830 Blythe Avenue
  +  Christ can be your backup.        |  Drexel Hill, Pennsylvania 19026

Yes, someone pointed this out to me in private e-mail, and I wrote a C
program to confirm it. I just had never seen such rounding on such
small non-irrational numbers.

But, the problem is that it is irrational in base 2 (or at least so many
digits that it won't fit).
-DEJ

Bruce Momjian <maillist@candle.pha.pa.us> writes:

[ 123.45 - 123.00 = 0.450000000000003 ]

Now constants are automatically promoted to float8, so I expected the
same results, but what is going on here?

Plain old, garden-variety, floating point roundoff error. Do the
same calculation in any other program and you'll get the same result
(on the same hardware anyway), if the other program insists on showing
16 digits of precision.

IEEE 64-bit floats only have about 17 decimal digits of accuracy.
So float8(123.45) is good to about 14 digits after the decimal point.
Subtract off the 123, and print what's left with 16 digits, and
by golly you find out that the original number wasn't exactly 123.45,
just an approximation to it. Along about the 15th digit after the
decimal point, you start finding crud.

In short: no surprises here for anyone who's used float math for any
length of time.

Sooner or later we ought to try to implement true fixed-point
arbitrary-precision numeric data types per the SQL spec. That'll be
a lot slower than hardware float math, but its roundoff properties will
be less surprising to novices.

regards, tom lane

Yes, someone pointed this out to me in private e-mail, and I wrote a C
program to confirm it. I just had never seen such rounding on such
small non-irrational numbers.

But, the problem is that it is irrational in base 2 (or at least so many
digits that it won't fit).

Ah, I figured that out after I sent the message.

-- 
  Bruce Momjian                        |  http://www.op.net/~candle
  maillist@candle.pha.pa.us            |  (610) 853-3000
  +  If your life is a hard drive,     |  830 Blythe Avenue
  +  Christ can be your backup.        |  Drexel Hill, Pennsylvania 19026

Tom Lane wrote:

Sooner or later we ought to try to implement true fixed-point
arbitrary-precision numeric data types per the SQL spec. That'll be
a lot slower than hardware float math, but its roundoff properties will
be less surprising to novices.

I think the string math done in bc(1) could be a good point
to start from. In the old version (1.3 if I remember right)
of the minix sources (yepp - still have them), there are the
algorithm's to get sine, logarithm and the like in any
precision as bc functions. Internally, only the four base
operations, (think think) pow() and sqrt() are implemented in
C. Anything else is done with them on the higher level.

We need to define what the precision of a result should be,
if it is not assigned to a column (where the precision can be
the atttypmod). Is there any standard defined for? If not,
what about this:

Internal representation holds different precision for DISPLAY
and CALC.

On any operation, the DISPLAY precision is set to the higher
of the two operands.

On add/subtract, the CALC precision becomes the higher of the
two.

On multiply, the CALC precision is adjusted to hold the exact
result up to a (variable settable?) maximum.

On divide, the CALC precision is set to max and after it to
the number of used digits.

If the result get's assigned to an attribute, it is rounded
to it's atttypmod and both precisions set to that.

The types output function rounds it to the DISPLAY precision.

The input function sets both precisions to the number of
digits present after decimal point.

Needless to say that there will be special functions to round
explicitly and set the precisions.

Jan

--

#======================================================================#
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# Let's break this rule - forgive me. #
#======================================== jwieck@debis.com (Jan Wieck) #

"Jackson, DeJuan" <djackson@cpsgroup.com> writes:

But, the problem is that it is irrational in base 2 (or at least so many
digits that it won't fit).

It's not irrational in any base. 123.45 = 12345/100 is a ratio of
integers, ie, rational. The problem is that the exact representation
of this number as a base-2 fraction is longer than the 52 or so bits
available in float8 format. (I think it's an infinite repeating
fraction, in the same way that 1/9 = 0.111111111111111111111111111...
is a repeating fraction in base 10. But even a terminating fraction
will get rounded off as a float8 if it takes more than 52 bits.)

Irrational numbers are those which are not expressible as the ratio of
any two integers, eg, square root of 2. (The ancient Greeks became
*very* unhappy when they realized that there were such things.) A
subcategory is transcendentals, which are not expressible as the
solution of any algebraic equation, eg, pi.

Rational numbers have either terminating or repeating expansions in
any base you care to use; irrationals never do.

Sorry, I'll get off my math-pedant soapbox now. Just tend to get
annoyed when people misuse technical terms.

regards, tom lane

Rational numbers have either terminating or repeating expansions in
any base you care to use; irrationals never do.

Sorry, I'll get off my math-pedant soapbox now. Just tend to get
annoyed when people misuse technical terms.

And I was a math minor in college. I am embarassed at what I have
forgotten.

-- 
  Bruce Momjian                        |  http://www.op.net/~candle
  maillist@candle.pha.pa.us            |  (610) 853-3000
  +  If your life is a hard drive,     |  830 Blythe Avenue
  +  Christ can be your backup.        |  Drexel Hill, Pennsylvania 19026

We need to define what the precision of a result should be,
if it is not assigned to a column (where the precision can be
the atttypmod). Is there any standard defined for? If not,
what about this:

Internal representation holds different precision for DISPLAY
and CALC.

On any operation, the DISPLAY precision is set to the higher
of the two operands.

On add/subtract, the CALC precision becomes the higher of the
two.

On multiply, the CALC precision is adjusted to hold the exact
result up to a (variable settable?) maximum.

On divide, the CALC precision is set to max and after it to
the number of used digits.

If the result get's assigned to an attribute, it is rounded
to it's atttypmod and both precisions set to that.

The types output function rounds it to the DISPLAY precision.

The input function sets both precisions to the number of
digits present after decimal point.

Needless to say that there will be special functions to round
explicitly and set the precisions.

I have a routine that does the necessary rounding on 8 byte floating points to a
precision up to 8 decimal places. Not exactly based on higher math but it
does the job in many financial applications on all assignments, comparisons
and when displayed.

I never use it on arithmetic operations.

The interface is as follows

double RoundDouble(double value, int decimals);

I am happy to submit it for use in the postgres code.

Regards
Theo