Обсуждение: 123.45 - 123 = 0.45
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) -Jose'-
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 justGOSUB 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 + Christ can be your backup. | Drexel Hill, Pennsylvania19026
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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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:
> > 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
> + Christ can be your backup. | Drexel Hill, Pennsylvania 19026
Hello Oleg, martedì, 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,
Pennsylvania19026
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
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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> 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