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Bug#22555: STDDEV yields positive result for groups with only one row 

When only one row was present, the subtraction of nearly the same number 
resulted in catastropic cancellation, introducing an error in the 
VARIANCE calculation near 1e-15.  That was sqrt()ed to get STDDEV, the 
error was escallated to near 1e-8.  

The simple fix of testing for a row count of 1 and forcing that to yield 
0.0 is insufficient, as two rows of the same value should also have a
variance of 0.0, yet the error would be about the same.

So, this patch changes the formula that computes the VARIANCE to be one
that is not subject to catastrophic cancellation.

In addition, it now uses only (faster-than-decimal) floating point numbers
to calculate, and renders that to other types on demand.


mysql-test/r/func_group.result:
  Test that the bug is fixed, and that no unexpected behavior arises from the 
  changes.
mysql-test/t/func_group.test:
  Test that the bug is fixed, and that no unexpected behavior arises from the 
  changes.
sql/item_sum.cc:
  Serg's suggestion: Force all VARIANCE calculations to be done with floating-
  point types.  It's faster, and the SQL standard says we may implement these
  functions any way we want.
  
  Additionally, use a form of variance calculation that is not subject to 
  catastrophic cancellation.   
  http://static.flickr.com/108/311308512_5c4e1c0c3d_b.jpg
sql/item_sum.h:
  Remove unused members and add a comment describing the recurrence relation.
pull/374/head
unknown 19 years ago
parent
4f4b46456a
commit
82bd9b6b61
5 changed files with 495 additions and 244 deletions
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  1. 1
      BitKeeper/etc/collapsed
  2. 268
      mysql-test/r/func_group.result
  3. 92
      mysql-test/t/func_group.test
  4. 358
      sql/item_sum.cc
  5. 20
      sql/item_sum.h

1
BitKeeper/etc/collapsed
View File

@ -19,3 +19,4 @@
454f8960jsVT_kMKJtZ9OCgXoba0xQ
4554a95d7txO1DuO9G3nAizI3SkFAA
4554b3722d71SbPiI2Gx-RhbZjmuIQ
45771031yRCoM_ZfONdYchPvVEgLRg

268
mysql-test/r/func_group.result
View File

@ -1029,3 +1029,271 @@ t1 CREATE TABLE `t1` (
`stddev(0)` double(8,4) default NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1
drop table t1;
create table bug22555 (i smallint primary key auto_increment, s1 smallint, s2 smallint, e decimal(30,10), o double);
insert into bug22555 (s1, s2, e, o) values (53, 78, 11.4276528, 6.828112), (17, 78, 5.916793, 1.8502951), (18, 76, 2.679231, 9.17975591), (31, 62, 6.07831, 0.1), (19, 41, 5.37463, 15.1), (83, 73, 14.567426, 7.959222), (92, 53, 6.10151, 13.1856852), (7, 12, 13.92272, 3.442007), (92, 35, 11.95358909, 6.01376678), (38, 84, 2.572, 7.904571);
select std(s1/s2) from bug22555 group by i;
std(s1/s2)
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
select std(e) from bug22555 group by i;
std(e)
0.00000000000000
0.00000000000000
0.00000000000000
0.00000000000000
0.00000000000000
0.00000000000000
0.00000000000000
0.00000000000000
0.00000000000000
0.00000000000000
select std(o) from bug22555 group by i;
std(o)
0
0
0
0
0
0
0
0
0
0
drop table bug22555;
create table bug22555 (i smallint, s1 smallint, s2 smallint, o1 double, o2 double, e1 decimal, e2 decimal);
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
select i, count(*) from bug22555 group by i;
i count(*)
1 1
2 1
3 1
select std(s1/s2) from bug22555 where i=1;
std(s1/s2)
0.00000000
select std(s1/s2) from bug22555 where i=2;
std(s1/s2)
0.00000000
select std(s1/s2) from bug22555 where i=3;
std(s1/s2)
0.00000000
select std(s1/s2) from bug22555 where i=1 group by i;
std(s1/s2)
0.00000000
select std(s1/s2) from bug22555 where i=2 group by i;
std(s1/s2)
0.00000000
select std(s1/s2) from bug22555 where i=3 group by i;
std(s1/s2)
0.00000000
select std(s1/s2) from bug22555 group by i order by i;
std(s1/s2)
0.00000000
0.00000000
0.00000000
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
i count(*) std(o1/o2)
1 1 0
2 1 0
3 1 0
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
i count(*) std(e1/e2)
1 1 0.00000000
2 1 0.00000000
3 1 0.00000000
set @saved_div_precision_increment=@@div_precision_increment;
set div_precision_increment=19;
select i, count(*), variance(s1/s2) from bug22555 group by i order by i;
i count(*) variance(s1/s2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
select i, count(*), variance(o1/o2) from bug22555 group by i order by i;
i count(*) variance(o1/o2)
1 1 0
2 1 0
3 1 0
select i, count(*), variance(e1/e2) from bug22555 group by i order by i;
i count(*) variance(e1/e2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
i count(*) std(s1/s2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
i count(*) std(o1/o2)
1 1 0
2 1 0
3 1 0
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
i count(*) std(e1/e2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
set div_precision_increment=20;
select i, count(*), variance(s1/s2) from bug22555 group by i order by i;
i count(*) variance(s1/s2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
select i, count(*), variance(o1/o2) from bug22555 group by i order by i;
i count(*) variance(o1/o2)
1 1 0
2 1 0
3 1 0
select i, count(*), variance(e1/e2) from bug22555 group by i order by i;
i count(*) variance(e1/e2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
i count(*) std(s1/s2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
i count(*) std(o1/o2)
1 1 0
2 1 0
3 1 0
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
i count(*) std(e1/e2)
1 1 0.000000000000000000000000000000
2 1 0.000000000000000000000000000000
3 1 0.000000000000000000000000000000
set @@div_precision_increment=@saved_div_precision_increment;
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
i count(*) std(s1/s2)
1 4 0.00000000
2 4 0.00000000
3 4 0.00000000
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
i count(*) std(o1/o2)
1 4 0
2 4 0
3 4 0
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
i count(*) std(e1/e2)
1 4 0.00000000
2 4 0.00000000
3 4 0.00000000
select std(s1/s2) from bug22555;
std(s1/s2)
0.21325764
select std(o1/o2) from bug22555;
std(o1/o2)
0.21325763586649
select std(e1/e2) from bug22555;
std(e1/e2)
0.21325764
set @saved_div_precision_increment=@@div_precision_increment;
set div_precision_increment=19;
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
i count(*) std(s1/s2)
1 4 0.000000000000000000000000000000
2 4 0.000000000000000000000000000000
3 4 0.000000000000000000000000000000
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
i count(*) std(o1/o2)
1 4 0
2 4 0
3 4 0
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
i count(*) std(e1/e2)
1 4 0.000000000000000000000000000000
2 4 0.000000000000000000000000000000
3 4 0.000000000000000000000000000000
select std(s1/s2) from bug22555;
std(s1/s2)
0.213257635866493405751853629226
select std(o1/o2) from bug22555;
std(o1/o2)
0.21325763586649
select std(e1/e2) from bug22555;
std(e1/e2)
0.213257635866493405751853629226
set div_precision_increment=20;
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
i count(*) std(s1/s2)
1 4 0.000000000000000000000000000000
2 4 0.000000000000000000000000000000
3 4 0.000000000000000000000000000000
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
i count(*) std(o1/o2)
1 4 0
2 4 0
3 4 0
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
i count(*) std(e1/e2)
1 4 0.000000000000000000000000000000
2 4 0.000000000000000000000000000000
3 4 0.000000000000000000000000000000
select std(s1/s2) from bug22555;
std(s1/s2)
0.213257635866493405751853629226
select std(o1/o2) from bug22555;
std(o1/o2)
0.21325763586649
select std(e1/e2) from bug22555;
std(e1/e2)
0.213257635866493405751853629226
set @@div_precision_increment=@saved_div_precision_increment;
drop table bug22555;
create table bug22555 (s smallint, o double, e decimal);
insert into bug22555 values (1,1,1),(2,2,2),(3,3,3),(6,6,6),(7,7,7);
select var_samp(s), var_pop(s) from bug22555;
var_samp(s) var_pop(s)
6.7000 5.3600
select var_samp(o), var_pop(o) from bug22555;
var_samp(o) var_pop(o)
6.7 5.36
select var_samp(e), var_pop(e) from bug22555;
var_samp(e) var_pop(e)
6.7000 5.3600
drop table bug22555;
create table bug22555 (s smallint, o double, e decimal);
insert into bug22555 values (null,null,null),(null,null,null);
select var_samp(s) as 'null', var_pop(s) as 'null' from bug22555;
null null
NULL NULL
select var_samp(o) as 'null', var_pop(o) as 'null' from bug22555;
null null
NULL NULL
select var_samp(e) as 'null', var_pop(e) as 'null' from bug22555;
null null
NULL NULL
insert into bug22555 values (1,1,1);
select var_samp(s) as 'null', var_pop(s) as '0' from bug22555;
null 0
NULL 0.0000
select var_samp(o) as 'null', var_pop(o) as '0' from bug22555;
null 0
NULL 0
select var_samp(e) as 'null', var_pop(e) as '0' from bug22555;
null 0
NULL 0.0000
insert into bug22555 values (2,2,2);
select var_samp(s) as '0.5', var_pop(s) as '0.25' from bug22555;
0.5 0.25
0.5000 0.2500
select var_samp(o) as '0.5', var_pop(o) as '0.25' from bug22555;
0.5 0.25
0.5 0.25
select var_samp(e) as '0.5', var_pop(e) as '0.25' from bug22555;
0.5 0.25
0.5000 0.2500
drop table bug22555;
End 5.0 tests.

92
mysql-test/t/func_group.test
View File

@ -700,3 +700,95 @@ create table t1 select stddev(0);
show create table t1;
drop table t1;
#
# Bug#22555: STDDEV yields positive result for groups with only one row
#
create table bug22555 (i smallint primary key auto_increment, s1 smallint, s2 smallint, e decimal(30,10), o double);
insert into bug22555 (s1, s2, e, o) values (53, 78, 11.4276528, 6.828112), (17, 78, 5.916793, 1.8502951), (18, 76, 2.679231, 9.17975591), (31, 62, 6.07831, 0.1), (19, 41, 5.37463, 15.1), (83, 73, 14.567426, 7.959222), (92, 53, 6.10151, 13.1856852), (7, 12, 13.92272, 3.442007), (92, 35, 11.95358909, 6.01376678), (38, 84, 2.572, 7.904571);
select std(s1/s2) from bug22555 group by i;
select std(e) from bug22555 group by i;
select std(o) from bug22555 group by i;
drop table bug22555;
create table bug22555 (i smallint, s1 smallint, s2 smallint, o1 double, o2 double, e1 decimal, e2 decimal);
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
select i, count(*) from bug22555 group by i;
select std(s1/s2) from bug22555 where i=1;
select std(s1/s2) from bug22555 where i=2;
select std(s1/s2) from bug22555 where i=3;
select std(s1/s2) from bug22555 where i=1 group by i;
select std(s1/s2) from bug22555 where i=2 group by i;
select std(s1/s2) from bug22555 where i=3 group by i;
select std(s1/s2) from bug22555 group by i order by i;
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
set @saved_div_precision_increment=@@div_precision_increment;
set div_precision_increment=19;
select i, count(*), variance(s1/s2) from bug22555 group by i order by i;
select i, count(*), variance(o1/o2) from bug22555 group by i order by i;
select i, count(*), variance(e1/e2) from bug22555 group by i order by i;
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
set div_precision_increment=20;
select i, count(*), variance(s1/s2) from bug22555 group by i order by i;
select i, count(*), variance(o1/o2) from bug22555 group by i order by i;
select i, count(*), variance(e1/e2) from bug22555 group by i order by i;
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
set @@div_precision_increment=@saved_div_precision_increment;
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
insert into bug22555 values (1,53,78,53,78,53,78),(2,17,78,17,78,17,78),(3,18,76,18,76,18,76);
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
select std(s1/s2) from bug22555;
select std(o1/o2) from bug22555;
select std(e1/e2) from bug22555;
set @saved_div_precision_increment=@@div_precision_increment;
set div_precision_increment=19;
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
select std(s1/s2) from bug22555;
select std(o1/o2) from bug22555;
select std(e1/e2) from bug22555;
set div_precision_increment=20;
select i, count(*), std(s1/s2) from bug22555 group by i order by i;
select i, count(*), std(o1/o2) from bug22555 group by i order by i;
select i, count(*), std(e1/e2) from bug22555 group by i order by i;
select std(s1/s2) from bug22555;
select std(o1/o2) from bug22555;
select std(e1/e2) from bug22555;
set @@div_precision_increment=@saved_div_precision_increment;
drop table bug22555;
create table bug22555 (s smallint, o double, e decimal);
insert into bug22555 values (1,1,1),(2,2,2),(3,3,3),(6,6,6),(7,7,7);
select var_samp(s), var_pop(s) from bug22555;
select var_samp(o), var_pop(o) from bug22555;
select var_samp(e), var_pop(e) from bug22555;
drop table bug22555;
create table bug22555 (s smallint, o double, e decimal);
insert into bug22555 values (null,null,null),(null,null,null);
select var_samp(s) as 'null', var_pop(s) as 'null' from bug22555;
select var_samp(o) as 'null', var_pop(o) as 'null' from bug22555;
select var_samp(e) as 'null', var_pop(e) as 'null' from bug22555;
insert into bug22555 values (1,1,1);
select var_samp(s) as 'null', var_pop(s) as '0' from bug22555;
select var_samp(o) as 'null', var_pop(o) as '0' from bug22555;
select var_samp(e) as 'null', var_pop(e) as '0' from bug22555;
insert into bug22555 values (2,2,2);
select var_samp(s) as '0.5', var_pop(s) as '0.25' from bug22555;
select var_samp(o) as '0.5', var_pop(o) as '0.25' from bug22555;
select var_samp(e) as '0.5', var_pop(e) as '0.25' from bug22555;
drop table bug22555;
###
--echo End 5.0 tests.

358
sql/item_sum.cc
View File

@ -1098,7 +1098,7 @@ Field *Item_sum_avg::create_tmp_field(bool group, TABLE *table,
{
/*
We must store both value and counter in the temporary table in one field.
The easyest way is to do this is to store both value in a string
The easiest way is to do this is to store both value in a string
and unpack on access.
*/
return new Field_string(((hybrid_type == DECIMAL_RESULT) ?
@ -1172,8 +1172,9 @@ String *Item_sum_avg::val_str(String *str)
double Item_sum_std::val_real()
{
DBUG_ASSERT(fixed == 1);
double tmp= Item_sum_variance::val_real();
return tmp <= 0.0 ? 0.0 : sqrt(tmp);
double nr= Item_sum_variance::val_real();
DBUG_ASSERT(nr >= 0.0);
return sqrt(nr);
}
Item *Item_sum_std::copy_or_same(THD* thd)
@ -1187,40 +1188,77 @@ Item *Item_sum_std::copy_or_same(THD* thd)
*/
Item_sum_variance::Item_sum_variance(THD *thd, Item_sum_variance *item):
Item_sum_num(thd, item), hybrid_type(item->hybrid_type),
cur_dec(item->cur_dec), count(item->count), sample(item->sample),
prec_increment(item->prec_increment)
/**
Variance implementation for floating-point implementations, without
catastrophic cancellation, from Knuth's _TAoCP_, 3rd ed, volume 2, pg232.
This alters the value at m, s, and increments count.
*/
/*
These two functions are used by the Item_sum_variance and the
Item_variance_field classes, which are unrelated, and each need to calculate
variance. The difference between the two classes is that the first is used
for a mundane SELECT, while the latter is used in a GROUPing SELECT.
*/
static void variance_fp_recurrence_next(double *m, double *s, ulonglong *count, double nr)
{
if (hybrid_type == DECIMAL_RESULT)
*count += 1;
if (*count == 1)
{
memcpy(dec_sum, item->dec_sum, sizeof(item->dec_sum));
memcpy(dec_sqr, item->dec_sqr, sizeof(item->dec_sqr));
for (int i=0; i<2; i++)
{
dec_sum[i].fix_buffer_pointer();
dec_sqr[i].fix_buffer_pointer();
}
*m= nr;
*s= 0;
}
else
{
sum= item->sum;
sum_sqr= item->sum_sqr;
double m_kminusone= *m;
*m= m_kminusone + (nr - m_kminusone) / (double) *count;
*s= *s + (nr - m_kminusone) * (nr - *m);
}
}
static double variance_fp_recurrence_result(double s, ulonglong count, bool is_sample_variance)
{
if (count == 1)
return 0.0;
if (is_sample_variance)
return s / (count - 1);
/* else, is a population variance */
return s / count;
}
Item_sum_variance::Item_sum_variance(THD *thd, Item_sum_variance *item):
Item_sum_num(thd, item), hybrid_type(item->hybrid_type),
count(item->count), sample(item->sample),
prec_increment(item->prec_increment)
{
recurrence_m= item->recurrence_m;
recurrence_s= item->recurrence_s;
}
void Item_sum_variance::fix_length_and_dec()
{
DBUG_ENTER("Item_sum_variance::fix_length_and_dec");
maybe_null= null_value= 1;
prec_increment= current_thd->variables.div_precincrement;
/*
According to the SQL2003 standard (Part 2, Foundations; sec 10.9,
aggregate function; paragraph 7h of Syntax Rules), "the declared
type of the result is an implementation-defined aproximate numeric
type.
*/
hybrid_type= REAL_RESULT;
switch (args[0]->result_type()) {
case REAL_RESULT:
case STRING_RESULT:
decimals= min(args[0]->decimals + 4, NOT_FIXED_DEC);
hybrid_type= REAL_RESULT;
sum= 0.0;
break;
case INT_RESULT:
case DECIMAL_RESULT:
@ -1229,37 +1267,14 @@ void Item_sum_variance::fix_length_and_dec()
decimals= min(args[0]->decimals + prec_increment, DECIMAL_MAX_SCALE);
max_length= my_decimal_precision_to_length(precision, decimals,
unsigned_flag);
cur_dec= 0;
hybrid_type= DECIMAL_RESULT;
my_decimal_set_zero(dec_sum);
my_decimal_set_zero(dec_sqr);
/*
The maxium value to usable for variance is DECIMAL_MAX_LENGTH/2
becasue we need to be able to calculate in dec_bin_size1
column_value * column_value
*/
f_scale0= args[0]->decimals;
f_precision0= min(args[0]->decimal_precision() + DECIMAL_LONGLONG_DIGITS,
DECIMAL_MAX_PRECISION);
f_scale1= min(args[0]->decimals * 2, DECIMAL_MAX_SCALE);
f_precision1= min(args[0]->decimal_precision()*2 + DECIMAL_LONGLONG_DIGITS,
DECIMAL_MAX_PRECISION);
dec_bin_size0= my_decimal_get_binary_size(f_precision0, f_scale0);
dec_bin_size1= my_decimal_get_binary_size(f_precision1, f_scale1);
break;
}
case ROW_RESULT:
default:
DBUG_ASSERT(0);
}
DBUG_PRINT("info", ("Type: %s (%d, %d)",
(hybrid_type == REAL_RESULT ? "REAL_RESULT" :
hybrid_type == DECIMAL_RESULT ? "DECIMAL_RESULT" :
hybrid_type == INT_RESULT ? "INT_RESULT" :
"--ILLEGAL!!!--"),
max_length,
(int)decimals));
DBUG_PRINT("info", ("Type: REAL_RESULT (%d, %d)", max_length, (int)decimals));
DBUG_VOID_RETURN;
}
@ -1270,6 +1285,11 @@ Item *Item_sum_variance::copy_or_same(THD* thd)
}
/**
Create a new field to match the type of value we're expected to yield.
If we're grouping, then we need some space to serialize variables into, to
pass around.
*/
Field *Item_sum_variance::create_tmp_field(bool group, TABLE *table,
uint convert_blob_len)
{
@ -1277,13 +1297,10 @@ Field *Item_sum_variance::create_tmp_field(bool group, TABLE *table,
{
/*
We must store both value and counter in the temporary table in one field.
The easyest way is to do this is to store both value in a string
The easiest way is to do this is to store both value in a string
and unpack on access.
*/
return new Field_string(((hybrid_type == DECIMAL_RESULT) ?
dec_bin_size0 + dec_bin_size1 :
sizeof(double)*2) + sizeof(longlong),
0, name, table, &my_charset_bin);
return new Field_string(sizeof(double)*2 + sizeof(longlong), 0, name, table, &my_charset_bin);
}
return new Field_double(max_length, maybe_null,name,table,decimals);
}
@ -1291,90 +1308,51 @@ Field *Item_sum_variance::create_tmp_field(bool group, TABLE *table,
void Item_sum_variance::clear()
{
if (hybrid_type == DECIMAL_RESULT)
{
my_decimal_set_zero(dec_sum);
my_decimal_set_zero(dec_sqr);
cur_dec= 0;
}
else
sum=sum_sqr=0.0;
count=0;
count= 0;
}
bool Item_sum_variance::add()
{
if (hybrid_type == DECIMAL_RESULT)
{
my_decimal dec_buf, *dec= args[0]->val_decimal(&dec_buf);
my_decimal sqr_buf;
if (!args[0]->null_value)
{
count++;
int next_dec= cur_dec ^ 1;
my_decimal_mul(E_DEC_FATAL_ERROR, &sqr_buf, dec, dec);
my_decimal_add(E_DEC_FATAL_ERROR, dec_sqr+next_dec,
dec_sqr+cur_dec, &sqr_buf);
my_decimal_add(E_DEC_FATAL_ERROR, dec_sum+next_dec,
dec_sum+cur_dec, dec);
cur_dec= next_dec;
}
}
else
{
double nr= args[0]->val_real();
if (!args[0]->null_value)
{
sum+=nr;
sum_sqr+=nr*nr;
count++;
}
}
/*
Why use a temporary variable? We don't know if it is null until we
evaluate it, which has the side-effect of setting null_value .
*/
double nr= args[0]->val_real();
if (!args[0]->null_value)
variance_fp_recurrence_next(&recurrence_m, &recurrence_s, &count, nr);
return 0;
}
double Item_sum_variance::val_real()
{
DBUG_ASSERT(fixed == 1);
if (hybrid_type == DECIMAL_RESULT)
return val_real_from_decimal();
/*
'sample' is a 1/0 boolean value. If it is 1/true, id est this is a sample
variance call, then we should set nullness when the count of the items
is one or zero. If it's zero, i.e. a population variance, then we only
set nullness when the count is zero.
Another way to read it is that 'sample' is the numerical threshhold, at and
below which a 'count' number of items is called NULL.
*/
DBUG_ASSERT((sample == 0) || (sample == 1));
if (count <= sample)
{
null_value=1;
return 0.0;
}
null_value=0;
/* Avoid problems when the precision isn't good enough */
double tmp=ulonglong2double(count);
double tmp2= (sum_sqr - sum*sum/tmp)/(tmp - (double)sample);
return tmp2 <= 0.0 ? 0.0 : tmp2;
return variance_fp_recurrence_result(recurrence_s, count, sample);
}
my_decimal *Item_sum_variance::val_decimal(my_decimal *dec_buf)
{
my_decimal count_buf, count1_buf, sum_sqr_buf;
DBUG_ASSERT(fixed ==1 );
if (hybrid_type == REAL_RESULT)
return val_decimal_from_real(dec_buf);
if (count <= sample)
{
null_value= 1;
return 0;
}
null_value= 0;
int2my_decimal(E_DEC_FATAL_ERROR, count, 0, &count_buf);
int2my_decimal(E_DEC_FATAL_ERROR, count-sample, 0, &count1_buf);
my_decimal_mul(E_DEC_FATAL_ERROR, &sum_sqr_buf,
dec_sum+cur_dec, dec_sum+cur_dec);
my_decimal_div(E_DEC_FATAL_ERROR, dec_buf,
&sum_sqr_buf, &count_buf, prec_increment);
my_decimal_sub(E_DEC_FATAL_ERROR, &sum_sqr_buf, dec_sqr+cur_dec, dec_buf);
my_decimal_div(E_DEC_FATAL_ERROR, dec_buf,
&sum_sqr_buf, &count1_buf, prec_increment);
return dec_buf;
DBUG_ASSERT(fixed == 1);
return val_decimal_from_real(dec_buf);
}
@ -1383,89 +1361,44 @@ void Item_sum_variance::reset_field()
double nr;
char *res= result_field->ptr;
if (hybrid_type == DECIMAL_RESULT)
{
my_decimal value, *arg_dec, *arg2_dec;
longlong tmp;
arg_dec= args[0]->val_decimal(&value);
if (args[0]->null_value)
{
arg_dec= arg2_dec= &decimal_zero;
tmp= 0;
}
else
{
my_decimal_mul(E_DEC_FATAL_ERROR, dec_sum, arg_dec, arg_dec);
arg2_dec= dec_sum;
tmp= 1;
}
my_decimal2binary(E_DEC_FATAL_ERROR, arg_dec,
res, f_precision0, f_scale0);
my_decimal2binary(E_DEC_FATAL_ERROR, arg2_dec,
res+dec_bin_size0, f_precision1, f_scale1);
res+= dec_bin_size0 + dec_bin_size1;
int8store(res,tmp);
return;
}
nr= args[0]->val_real();
nr= args[0]->val_real(); /* sets null_value as side-effect */
if (args[0]->null_value)
bzero(res,sizeof(double)*2+sizeof(longlong));
else
{
longlong tmp;
float8store(res,nr);
nr*=nr;
float8store(res+sizeof(double),nr);
tmp= 1;
int8store(res+sizeof(double)*2,tmp);
/* Serialize format is (double)m, (double)s, (longlong)count */
ulonglong tmp_count;
double tmp_s;
float8store(res, nr); /* recurrence variable m */
tmp_s= 0.0;
float8store(res + sizeof(double), tmp_s);
tmp_count= 1;
int8store(res + sizeof(double)*2, tmp_count);
}
}
void Item_sum_variance::update_field()
{
longlong field_count;
ulonglong field_count;
char *res=result_field->ptr;
if (hybrid_type == DECIMAL_RESULT)
{
my_decimal value, *arg_val= args[0]->val_decimal(&value);
if (!args[0]->null_value)
{
binary2my_decimal(E_DEC_FATAL_ERROR, res,
dec_sum+1, f_precision0, f_scale0);
binary2my_decimal(E_DEC_FATAL_ERROR, res+dec_bin_size0,
dec_sqr+1, f_precision1, f_scale1);
field_count= sint8korr(res + (dec_bin_size0 + dec_bin_size1));
my_decimal_add(E_DEC_FATAL_ERROR, dec_sum, arg_val, dec_sum+1);
my_decimal_mul(E_DEC_FATAL_ERROR, dec_sum+1, arg_val, arg_val);
my_decimal_add(E_DEC_FATAL_ERROR, dec_sqr, dec_sqr+1, dec_sum+1);
field_count++;
my_decimal2binary(E_DEC_FATAL_ERROR, dec_sum,
res, f_precision0, f_scale0);
my_decimal2binary(E_DEC_FATAL_ERROR, dec_sqr,
res+dec_bin_size0, f_precision1, f_scale1);
res+= dec_bin_size0 + dec_bin_size1;
int8store(res, field_count);
}
double nr= args[0]->val_real(); /* sets null_value as side-effect */
if (args[0]->null_value)
return;
}
double nr,old_nr,old_sqr;
float8get(old_nr, res);
float8get(old_sqr, res+sizeof(double));
/* Serialize format is (double)m, (double)s, (longlong)count */
double field_recurrence_m, field_recurrence_s;
float8get(field_recurrence_m, res);
float8get(field_recurrence_s, res + sizeof(double));
field_count=sint8korr(res+sizeof(double)*2);
nr= args[0]->val_real();
if (!args[0]->null_value)
{
old_nr+=nr;
old_sqr+=nr*nr;
field_count++;
}
float8store(res,old_nr);
float8store(res+sizeof(double),old_sqr);
variance_fp_recurrence_next(&field_recurrence_m, &field_recurrence_s, &field_count, nr);
float8store(res, field_recurrence_m);
float8store(res + sizeof(double), field_recurrence_s);
res+= sizeof(double)*2;
int8store(res,field_count);
}
@ -2295,25 +2228,9 @@ double Item_std_field::val_real()
{
double nr;
// fix_fields() never calls for this Item
if (hybrid_type == REAL_RESULT)
{
/*
We can't call Item_variance_field::val_real() on a DECIMAL_RESULT
as this would call Item_std_field::val_decimal() and we would
calculate sqrt() twice
*/
nr= Item_variance_field::val_real();
}
else
{
my_decimal dec_buf,*dec;
dec= Item_variance_field::val_decimal(&dec_buf);
if (!dec)
nr= 0.0; // NULL; Return 0.0
else
my_decimal2double(E_DEC_FATAL_ERROR, dec, &nr);
}
return nr <= 0.0 ? 0.0 : sqrt(nr);
nr= Item_variance_field::val_real();
DBUG_ASSERT(nr >= 0.0);
return sqrt(nr);
}
@ -2327,11 +2244,13 @@ my_decimal *Item_std_field::val_decimal(my_decimal *dec_buf)
double nr;
if (hybrid_type == REAL_RESULT)
return val_decimal_from_real(dec_buf);
dec= Item_variance_field::val_decimal(dec_buf);
if (!dec)
return 0;
my_decimal2double(E_DEC_FATAL_ERROR, dec, &nr);
nr= nr <= 0.0 ? 0.0 : sqrt(nr);
DBUG_ASSERT(nr >= 0.0);
nr= sqrt(nr);
double2my_decimal(E_DEC_FATAL_ERROR, nr, &tmp_dec);
my_decimal_round(E_DEC_FATAL_ERROR, &tmp_dec, decimals, FALSE, dec_buf);
return dec_buf;
@ -2366,52 +2285,15 @@ double Item_variance_field::val_real()
if (hybrid_type == DECIMAL_RESULT)
return val_real_from_decimal();
double sum,sum_sqr;
longlong count;
float8get(sum,field->ptr);
float8get(sum_sqr,(field->ptr+sizeof(double)));
double recurrence_s;
ulonglong count;
float8get(recurrence_s, (field->ptr + sizeof(double)));
count=sint8korr(field->ptr+sizeof(double)*2);
if ((null_value= (count <= sample)))
return 0.0;
double tmp= (double) count;
double tmp2= (sum_sqr - sum*sum/tmp)/(tmp - (double)sample);
return tmp2 <= 0.0 ? 0.0 : tmp2;
}
String *Item_variance_field::val_str(String *str)
{
if (hybrid_type == DECIMAL_RESULT)
return val_string_from_decimal(str);
return val_string_from_real(str);
}
my_decimal *Item_variance_field::val_decimal(my_decimal *dec_buf)
{
// fix_fields() never calls for this Item
if (hybrid_type == REAL_RESULT)
return val_decimal_from_real(dec_buf);
longlong count= sint8korr(field->ptr+dec_bin_size0+dec_bin_size1);
if ((null_value= (count <= sample)))
return 0;
my_decimal dec_count, dec1_count, dec_sum, dec_sqr, tmp;
int2my_decimal(E_DEC_FATAL_ERROR, count, 0, &dec_count);
int2my_decimal(E_DEC_FATAL_ERROR, count-sample, 0, &dec1_count);
binary2my_decimal(E_DEC_FATAL_ERROR, field->ptr,
&dec_sum, f_precision0, f_scale0);
binary2my_decimal(E_DEC_FATAL_ERROR, field->ptr+dec_bin_size0,
&dec_sqr, f_precision1, f_scale1);
my_decimal_mul(E_DEC_FATAL_ERROR, &tmp, &dec_sum, &dec_sum);
my_decimal_div(E_DEC_FATAL_ERROR, dec_buf, &tmp, &dec_count, prec_increment);
my_decimal_sub(E_DEC_FATAL_ERROR, &dec_sum, &dec_sqr, dec_buf);
my_decimal_div(E_DEC_FATAL_ERROR, dec_buf,
&dec_sum, &dec1_count, prec_increment);
return dec_buf;
return variance_fp_recurrence_result(recurrence_s, count, sample);
}

20
sql/item_sum.h
View File

@ -665,8 +665,10 @@ public:
double val_real();
longlong val_int()
{ /* can't be fix_fields()ed */ return (longlong) rint(val_real()); }
String *val_str(String*);
my_decimal *val_decimal(my_decimal *);
String *val_str(String *str)
{ return val_string_from_real(str); }
my_decimal *val_decimal(my_decimal *dec_buf)
{ return val_decimal_from_real(dec_buf); }
bool is_null() { (void) val_int(); return null_value; }
enum_field_types field_type() const
{
@ -688,6 +690,14 @@ public:
= (sum(ai^2) - 2*sum(a)*sum(a)/count(a) + count(a)*sum(a)^2/count(a)^2 )/count(a) =
= (sum(ai^2) - 2*sum(a)^2/count(a) + sum(a)^2/count(a) )/count(a) =
= (sum(ai^2) - sum(a)^2/count(a))/count(a)
But, this falls prey to catastrophic cancellation. Instead, use the recurrence formulas
M_{1} = x_{1}, ~ M_{k} = M_{k-1} + (x_{k} - M_{k-1}) / k newline
S_{1} = 0, ~ S_{k} = S_{k-1} + (x_{k} - M_{k-1}) times (x_{k} - M_{k}) newline
for 2 <= k <= n newline
ital variance = S_{n} / (n-1)
*/
class Item_sum_variance : public Item_sum_num
@ -696,9 +706,8 @@ class Item_sum_variance : public Item_sum_num
public:
Item_result hybrid_type;
double sum, sum_sqr;
my_decimal dec_sum[2], dec_sqr[2];
int cur_dec;
double recurrence_m, recurrence_s; /* Used in recurrence relation. */
ulonglong count;
uint f_precision0, f_scale0;
uint f_precision1, f_scale1;
@ -707,7 +716,7 @@ public:
uint prec_increment;
Item_sum_variance(Item *item_par, uint sample_arg) :Item_sum_num(item_par),
hybrid_type(REAL_RESULT), cur_dec(0), count(0), sample(sample_arg)
hybrid_type(REAL_RESULT), count(0), sample(sample_arg)
{}
Item_sum_variance(THD *thd, Item_sum_variance *item);
enum Sumfunctype sum_func () const { return VARIANCE_FUNC; }
@ -727,7 +736,6 @@ public:
enum Item_result result_type () const { return REAL_RESULT; }
void cleanup()
{
cur_dec= 0;
count= 0;
Item_sum_num::cleanup();
}

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