I noticed the storage format for the numeric type is rather inefficient: 

typedef struct NumericData
{
    int32       varlen;         /* Variable size        */
    int16       n_weight;       /* Weight of 1st digit  */
    uint16      n_rscale;       /* Result scale         */
    uint16      n_sign_dscale;  /* Sign + display scale */
    unsigned char n_data[1];    /* Digit data (2 decimal digits/byte) */
} NumericData;
typedef NumericData *Numeric;

Oracle uses a similar variable length format for all numeric types, and they
document its storage requirement as 2 + (sig digits/2) bytes.  One byte is
used for the column length, one byte for the exponent, a variable number of
bytes for the significant digits. 

A zero value uses two bytes total in Oracle, where in the current version of
PostgreSQL it uses ten bytes.  Given the pending demise of the money type, the
remaining alternative is rather wasteful for use in large financial
applications.

Is there a reason why varlen has to be an int32?  uint8 would be more than
enough.  The other three fields could be int8 as well.  I do not understand
why we need four header fields - a much more efficient decimal type could be
implemented as follows:

typedef struct DecimalData
{
 int8 varlen;                /* variable size */
 int8 d_sign_exponent;       /* 1 bit sign, 7 bit exponent */
 int8 d_mantissa[1];         /* variable precision binary integer mantissa */
};

Value represented is (-1 ^ sign)*(mantissa)*(10 ^ exponent).

This would be more space efficient than Oracle and would support precisions up
to DECIMAL(63).  Having a reasonable maximum precision would allow a fixed
length internal representation which make processing *much* faster* by using
binary arithmetic and eliminating the necessity to palloc() buffers for every
temporary result.  

(Aside: Doesn't the current numeric type use up memory in a hurry in a large
sum(numeric_column) query? - Or are all those digitbuf_free()'s actually being
cleaned up? And shouldn't the type operator calling convention be changed to
pass a result buffer so these palloc()'s could be mostly avoided? )

As an even faster, lower max precision alternative:

typedef struct FastDecimalData 
{
 int64 fd_mantissa;  
 int8  fd_sign;
 int8  fd_exponent;
};

Value represented is (-1 ^ sign)*(mantissa)*(10 ^ exponent).

This would support precisions up to DECIMAL(18).   Intermediate results could
be stored using a 128 bit format to avoid loss of precision.

Any comments?

  - Mark Butler

Thu, 12 Apr 2001 23:13:16 -0600
Mark Butler <butlerm@middle.net>
NUMERIC type efficiency problem
Mark Butler <butlerm@middle.net> writes:
> I noticed the storage format for the numeric type is rather inefficient: 
> ...
> A zero value uses two bytes total in Oracle, where in the current version of
> PostgreSQL it uses ten bytes.

Yawn ... given row overhead, alignment padding, etc, this is not nearly
as big a deal as you make it ...

> Is there a reason why varlen has to be an int32?

Yes.  That's what all varlena types use.

> The other three fields could be int8 as well.

If we were willing to restrict numeric values to a much tighter range,
perhaps so.  I rather like a numeric type that can handle ranges wider
than double precision, however.

> Having a reasonable maximum precision would allow a fixed
> length internal representation which make processing *much* faster* by using
> binary arithmetic and eliminating the necessity to palloc() buffers for every
> temporary result.  

I don't have any objection in principle to an additional datatype "small
numeric", or some such name, with a different representation.  I do
object to emasculating the type we have.

A more significant point is that you have presented no evidence to back
up your claim that this would be materially faster than the existing
type.  I doubt that the extra pallocs are all that expensive.  (I think
it'd be far more helpful to reimplement numeric using base-10000
representation --- four decimal digits per int16 --- and then eliminate
the distinction between storage format and computation format.  See past
discussions in the pghackers archives.)

			regards, tom lane

Fri, 13 Apr 2001 02:57:26 -0400
Tom Lane <tgl@sss.pgh.pa.us>
Re: NUMERIC type efficiency problem 
Tom Lane wrote:

> Yawn ... given row overhead, alignment padding, etc, this is not nearly
> as big a deal as you make it ...

For a table with ten decimal columns with an average of 5 significant digits
apiece, each row could be reduced from ~170 bytes to about ~90 bytes, which
could be rather significant, I would think.  (In Oracle such a row takes ~55
bytes.)

By the way, is alignment padding really a good use of disk space?  Surely
storage efficiency trumps minor CPU overhead in any I/O bound database.  Or
are there other considerations? (like processor portability perhaps?)
 
> I don't have any objection in principle to an additional datatype "small
> numeric", or some such name, with a different representation.  I do
> object to emasculating the type we have.

Surely we can't get rid of it, but it might be a good idea to make NUMERIC(p)
map to multiple representations, given that it is a ANSI standard data-type.

I suggest using a system like the FLOAT(p) -> float4 / float8 mapping. 
Columns declared with precisions higher than 16 or so could map to the current
unrestricted representation, and columns with more typical precisions could
map to a more efficient fixed length representation.
 
> A more significant point is that you have presented no evidence to back
> up your claim that this would be materially faster than the existing
> type.  I doubt that the extra pallocs are all that expensive.  (I think
> it'd be far more helpful to reimplement numeric using base-10000
> representation --- four decimal digits per int16 --- and then eliminate
> the distinction between storage format and computation format.  See past
> discussions in the pghackers archives.)

That sounds like it would help a lot.  I certainly don't have any hard
evidence yet.  Thanks for the pointer.

- Mark Butler

Fri, 13 Apr 2001 03:21:24 -0600
Mark Butler <butlerm@middle.net>
Re: NUMERIC type efficiency problem
Mark Butler <butlerm@middle.net> writes:
> By the way, is alignment padding really a good use of disk space?  Surely
> storage efficiency trumps minor CPU overhead in any I/O bound database.

Weren't you just complaining about excess palloc's ;-) ?  Seriously,
I have no idea about the costs/benefits of aligning data on disk.
That decision was made way back in the Berkeley days, and hasn't been
questioned since then AFAIK.  Feel free to experiment if you are
interested.

> I suggest using a system like the FLOAT(p) -> float4 / float8 mapping.
> Columns declared with precisions higher than 16 or so could map to the
> current unrestricted representation, and columns with more typical
> precisions could map to a more efficient fixed length representation.

Given that the "more efficient representation" would only be internal to
calculation subroutines, it seems easier to exploit preallocation at
runtime.  This is already done in a number of places in Postgres.
It'd look something like

	{
		digit	*tmp;
		digit	 tmpbuf[MAX_FIXED_DIGITS];

		if (digits_needed > MAX_FIXED_DIGITS)
			tmp = palloc(...);
		else
			tmp = tmpbuf;

		// use tmp here

		if (tmp != tmpbuf)
			pfree(tmp);
	}

Ugly, but most of the ugliness could be hidden inside a couple of
macros.

Again, though, I wouldn't bother with this until I had some profiles
proving that the palloc overhead is worth worrying about.

			regards, tom lane

Fri, 13 Apr 2001 11:26:39 -0400
Tom Lane <tgl@sss.pgh.pa.us>
Re: NUMERIC type efficiency problem 
Tom Lane wrote:

> A more significant point is that you have presented no evidence to back
> up your claim that this would be materially faster than the existing
> type.  I doubt that the extra pallocs are all that expensive.  (I think
> it'd be far more helpful to reimplement numeric using base-10000
> representation --- four decimal digits per int16 --- and then eliminate
> the distinction between storage format and computation format.  See past
> discussions in the pghackers archives.)


I did several tests with functions designed to sum the number 12345 a million
times.  The results are as follows (Pentium II 450, Redhat 6.2):

Postgres PL/PGSQL original numeric:    14.8 seconds
Postgres PL/PGSQL modified numeric:    11.0 seconds  
Postgres PL/PGSQL float8:              10.7 seconds
GNU AWK:                                2.5 seconds
Oracle PL/SQL number:                   2.0 seconds

The modified Postgres numeric type is the original source code modified to use
a 32 digit NumericVar attribute digit buffer that eliminates palloc()/pfree()
calls when ndigits < 32.

Surely those are performance differences worth considering...

- Mark Butler


Note: The functions are as follows, all called with 12345 as a parameter,
except for the awk program, which has it hard coded:

PostgreSQL
==========


create function test_f1(float8) returns float8 as '
declare
  i integer;
  val float8;
begin
 
  val := 0;
  
  for i in 1 .. 1000000 loop
     val := val + $1;
  end loop;

  return val;
end;'
language 'plpgsql';

create function test_f2(numeric) returns numeric as '
declare
  i integer;
  val numeric;
begin
 
  val := 0;
  
  for i in 1 .. 1000000 loop
     val := val + $1;
  end loop;

  return val;
end;'
language 'plpgsql';


Awk
===

BEGIN {
  val = 0;
  p = 12345;
  for(i = 1; i <= 1000000; i++)
    { 
     val = val + p;
    }
  printf("%20f\n", val);
}


Oracle
======

create or replace function test_f2(p number) return number is
  i number;
  val number;
begin
 
  val := 0;
  
  for i in 1 .. 1000000 loop
     val := val + p;
  end loop;

  return val;
end;
/

Fri, 13 Apr 2001 15:16:58 -0600
Mark Butler <butlerm@middle.net>
NUMERIC type benchmarks
Mark Butler wrote:

> I did several tests with functions designed to sum the number 12345 a million
> times.  The results are as follows (Pentium II 450, Redhat 6.2):
> 
> Postgres PL/PGSQL original numeric:    14.8 seconds
> Postgres PL/PGSQL modified numeric:    11.0 seconds
> Postgres PL/PGSQL float8:              10.7 seconds
> GNU AWK:                                2.5 seconds
> Oracle PL/SQL number:                   2.0 seconds

I have a new result:

  Postgres PL/PGSQL integer:              7.5 seconds

I do not know what to attribute the large difference between float8 and int to
other than pg_alloc overhead used in the calling convention for float8. 
Commments?

- Mark Butler

Fri, 13 Apr 2001 17:47:12 -0600
Mark Butler <butlerm@middle.net>
Re: New benchmark result
Am Freitag, 13. April 2001 23:16 schrieben Sie:
> Tom Lane wrote:
> > A more significant point is that you have presented no evidence to back
> > up your claim that this would be materially faster than the existing
> > type.  I doubt that the extra pallocs are all that expensive.  (I think
> > it'd be far more helpful to reimplement numeric using base-10000
> > representation --- four decimal digits per int16 --- and then eliminate
> > the distinction between storage format and computation format.  See past
> > discussions in the pghackers archives.)
>
> I did several tests with functions designed to sum the number 12345 a
> million times.  The results are as follows (Pentium II 450, Redhat 6.2):
>
> Postgres PL/PGSQL original numeric:    14.8 seconds
> Postgres PL/PGSQL modified numeric:    11.0 seconds
> Postgres PL/PGSQL float8:              10.7 seconds
> GNU AWK:                                2.5 seconds
> Oracle PL/SQL number:                   2.0 seconds
>
> The modified Postgres numeric type is the original source code modified to
> use a 32 digit NumericVar attribute digit buffer that eliminates
> palloc()/pfree() calls when ndigits < 32.
>
> Surely those are performance differences worth considering...

I tested that on a similar configuration (P-III 450) and got the same 
results. When the addition is removed from the loop and replaced with a 
simple assignment, the total execution time goes down to ~6.5 seconds. That 
means that the modified numeric is nearly twice as fast, sure worth 
considering that.

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Sun, 15 Apr 2001 10:42:19 +0200
Mario Weilguni <mweilguni@sime.com>
Re: NUMERIC type benchmarks
Mario Weilguni wrote:

> I tested that on a similar configuration (P-III 450) and got the same
> results. When the addition is removed from the loop and replaced with a
> simple assignment, the total execution time goes down to ~6.5 seconds. That
> means that the modified numeric is nearly twice as fast, sure worth
> considering that.

I am embarrassed to admit I had an undeleted overloaded function that caused
me to time the wrong function.  The correct numbers should be:

Postgres PL/PGSQL original numeric:    14.8 seconds
Postgres PL/PGSQL modified numeric:    14.0 seconds
Postgres PL/PGSQL float8:              10.7 seconds
GNU AWK:                                2.5 seconds
Oracle PL/SQL number:                   2.0 seconds

This means that Tom Lane was absolutely right - for the current numeric type
implementation, palloc() overhead is not a dominant concern.  A serious
solution needs to change the internal format to use a larger base, as Tom
suggested.

- Mark Butler

Sun, 15 Apr 2001 18:26:43 -0600
Mark Butler <butlerm@middle.net>
Re: NUMERIC type benchmarks - CORRECTED
Mark Butler <butlerm@middle.net> writes:
> ... The correct numbers should be:

> Postgres PL/PGSQL original numeric:    14.8 seconds
> Postgres PL/PGSQL modified numeric:    14.0 seconds
> Postgres PL/PGSQL float8:              10.7 seconds
> GNU AWK:                                2.5 seconds
> Oracle PL/SQL number:                   2.0 seconds

> This means that Tom Lane was absolutely right - for the current numeric type
> implementation, palloc() overhead is not a dominant concern.  A serious
> solution needs to change the internal format to use a larger base, as Tom
> suggested.

What do you get if you use int4 in PL/PGSQL?  The above numbers look to
me like the real problem may be PL/PGSQL interpretation overhead, and
not the datatype at all...

			regards, tom lane

Sun, 15 Apr 2001 21:28:09 -0400
Tom Lane <tgl@sss.pgh.pa.us>
Re: NUMERIC type benchmarks - CORRECTED 