BUG in postgres mathematic

This problem is not specific to Postgres. If you play around with a little C
program like:

#include <stdio.h>

int main(int argc, char * argv[])
{
float f = 27.81;
int i = 5;
int l = 100;

int ii = i*f*l;
long ll = l*f*i;
float ff = i*f*l;

printf("%i\n", ii);
printf("%li\n", ll);
printf("%.5f\n", ff);
printf("%i\n", (int) ff);
}

It prints:

13904
13904
13905.00000
13905

There is probably a good explanation for this. gcc 2.95 and egcs 2.91.66 do
this. Maybe a rounding problem.

On Thursday 25 January 2001 05:34, Max Vaschenko wrote:

Postgres-7.0.3-2
RedHat-6.2

SELECT int8(5*27.81*100);
13904

SELECT int4(5*27.81*100);
13905

SELECT int8(27.81*100*5);
13905

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"Robert B. Easter" <reaster@comptechnews.com> writes:

This problem is not specific to Postgres.

The fact that 5*27.81*100 != 27.81*100*5 is certainly a garden-variety
floating-point roundoff error. However, I think Max has a fair
complaint here: it seems float-to-int8 conversion is truncating, not
rounding like the other conversions to integer do.

regression=# select 4.7::float8::int4;
?column?
----------
5
(1 row)

regression=# select 4.7::float8::int8;
?column?
----------
4
(1 row)

Seems to me this is a bug we should fix.

regards, tom lane

On Thursday 25 January 2001 22:52, Tom Lane wrote:

"Robert B. Easter" <reaster@comptechnews.com> writes:

This problem is not specific to Postgres.

The fact that 5*27.81*100 != 27.81*100*5 is certainly a garden-variety
floating-point roundoff error. However, I think Max has a fair
complaint here: it seems float-to-int8 conversion is truncating, not
rounding like the other conversions to integer do.

regression=# select 4.7::float8::int4;
?column?
----------
5
(1 row)

regression=# select 4.7::float8::int8;
?column?
----------
4
(1 row)

Seems to me this is a bug we should fix.

regards, tom lane

Yeah, I agree. It isn't right that it truncates and that is something C does
appearently. The fix is to pass the float through a rounding something like
(long)(f + 0.5) or else C just truncates it off. This must already be
happening for the int4 conversion or C would do the same thing to it. I
didn't look at the Postgres sources yet, but it is probably one of those very
easy things to fix. :)

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The fact that 5*27.81*100 != 27.81*100*5 is certainly a garden-variety
floating-point roundoff error. However, I think Max has a fair
complaint here: it seems float-to-int8 conversion is truncating, not
rounding like the other conversions to integer do.

I have changed float8-to-int8 to start with an rint() call, the same as
float8-to-int4 and float8-to-int2. This should give the same roundoff
behavior as the other cases, including round-to-nearest-even if your
hardware supports IEEE-compliant float math.

Curiously, this change exposed what I take to be a platform dependency
in the int8 regress test. It was computing
int8(float8(4567890123456789::int8)) and expecting to get back exactly
4567890123456789. However, that value is 53 bits long and so there is
no margin for error in a standard IEEE float8 value. I find that at
least on HP hardware, rint() treats the value as inexact and rounds to
nearest even:

regression=# select round(4567890123456788::float8) - 4567890123456780::float8;
?column?
----------
8
(1 row)

regression=# select round(4567890123456789::float8) - 4567890123456780::float8;
?column?
----------
8
(1 row)

regression=# select round(4567890123456790::float8) - 4567890123456780::float8;
?column?
----------
10
(1 row)

regression=#

Whether this is a bug in rint or spec-compliant behavior is unclear, but
I'll bet HP's hardware is not the only platform that behaves this way.
Since I'm not eager to try to develop a new set of platform-specific
int8 expected files at this late hour, I just diked out that test
instead...

regards, tom lane

On Friday 26 January 2001 18:07, Tom Lane wrote:

Curiously, this change exposed what I take to be a platform dependency
in the int8 regress test. It was computing
int8(float8(4567890123456789::int8)) and expecting to get back exactly
4567890123456789. However, that value is 53 bits long and so there is
no margin for error in a standard IEEE float8 value. I find that at
least on HP hardware, rint() treats the value as inexact and rounds to
nearest even:

regression=# select round(4567890123456788::float8) -
4567890123456780::float8; ?column?
----------
8
(1 row)

regression=# select round(4567890123456789::float8) -
4567890123456780::float8; ?column?
----------
8
(1 row)

regression=# select round(4567890123456790::float8) -
4567890123456780::float8; ?column?
----------
10
(1 row)

regression=#

Whether this is a bug in rint or spec-compliant behavior is unclear, but
I'll bet HP's hardware is not the only platform that behaves this way.
Since I'm not eager to try to develop a new set of platform-specific
int8 expected files at this late hour, I just diked out that test
instead...

Here is what I get on Linux (PIII):

reaster=# select round(4567890123456788::float8) - 4567890123456780::float8;
?column?
----------
8
(1 row)

reaster=# select round(4567890123456789::float8) - 4567890123456780::float8;
?column?
----------
9
(1 row)

reaster=# select round(4567890123456790::float8) - 4567890123456780::float8;
?column?
----------
10
(1 row)

I'm not sure what the problem is either. The PIII has an 80-bit FPU but not
sure that matters. When there is no exponent, maybe only 52 bits are really
in the mantissa. If you try rounding numbers <= 4503599627370495 (2^52 - 1),
maybe you'll get expected results. The hidden bit is 0. Could be that round
or rint (whatever it is) always makes the hidden bit 1 when I think it should
only be 1 when the exponent is nonzero. I'm no float expert! :) Feel free
to correct me.

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