What number would require 22 bytes for Oracle to store? - oracle

Question

In Oracle 19c, using both DUMP and block dumps I have been able to store NUMBER values as large as to require 21 bytes (when negative). Any higher rounds off significant digits and allows numbers up to 125 digits but never uses more than 21 bytes. So if 21 is the greatest # of bytes that Oracle will ever use to store a number, why does dba_tab_cols and the official docs all say the maximum size is 22 bytes? What number would actually require 22 bytes?
If someone can do it, please provide DUMP output to show a 22-byte number, and what number it was.
Update: I inserted a single row with two NUMBER columns of -9+E38 each. Per block dump, they supposedly are stored this way:
But block dumps are interpreted for human consumption. So, I did an octal dump (od) on the datafile itself. The following octal dump shows that the size of the field is being stored first (0x15 = 21 bytes) adjacent to the first value by (0x2c), followed by 20 more value bytes ending with 0x6602. The next number then repeats the same thing. So, I guess one could say it does require 22 bytes to store a maximally precise number, if we count the size byte. But this is also true of all other datatypes, so it doesn't make sense that they would count this toward the "22" for numbers and not for other datatypes.

Answer 1

It's unclear why 22 bytes are allowed, and documented. Possibly some ancient history and the size has survived.
The 10gR2 documentation and Oracle support document 1031902.6 give different formulas for working out the length required to store a number; both are based on the precision (but not scale) and sign of the value, and both give a maximum value - for precision of 38 - of 21 bytes, not 22.
So it seems there can be no number which requires or can utilise all 22 bytes.
The Oracle Call Interface Programmer's Guide also says that the maximum internal storage for NUMBER is 21 bytes. The explanation of the NUMBER datatype in that document also explains the storage, probably better than the support document:
Oracle Database stores values of the NUMBER data type in a variable-length format. The first byte is the exponent and is followed by 1 to 20 mantissa bytes.
and as it's an OCI reference it also mentions "The output variable should be a 21-byte array to accommodate the largest possible number", but earlier says not to use it.
But it does also talk about the VARNUM datatype for which it says "Reserve 22 bytes to receive the longest possible VARNUM", which may be related to why 22 bytes are available, or may be a coincidence.

Answer 2

A partial answer of there does not appear to be one (but trying all values would take too long).
Starting from the reverse premise of can I force a 22-byte value into a number:
CREATE FUNCTION createNumber(hex VARCHAR2)
RETURN NUMBER DETERMINISTIC
IS
n NUMBER;
BEGIN
DBMS_OUTPUT.PUT_LINE( hex );
DBMS_STATS.CONVERT_RAW_VALUE( HEXTORAW( hex ), n );
RETURN n;
END;
/
Then:
CREATE TABLE table_name (value number);
INSERT INTO table_name (value)
SELECT createNumber(
LPAD(LEVEL - 1, 44, LEVEL - 1)
)
FROM DUAL
CONNECT BY LEVEL <= 10;
INSERT INTO table_name (value)
SELECT createNumber(
LPAD(CHR(96+LEVEL), 44, CHR(96+LEVEL))
)
FROM DUAL
CONNECT BY LEVEL <= 6;
Should insert 22-byte values into the table. However:
SELECT value, DUMP(value, 16) FROM table_name;
Outputs:
VALUE
DUMP(VALUE,16)
-~
Typ=2 Len=21: 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
-84848484848484848484848484848484848484840000000000000000000000000000000000000000000000000000
Typ=2 Len=21: 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11
-6767676767676767676767676767676767676767000000000000000000
Typ=2 Len=21: 22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22
-505050505050505050505050.505050505050505
Typ=2 Len=21: 33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33,33
-.00000000003333333333333333333333333333333333333333
Typ=2 Len=21: 44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44
-.000000000000000000000000000000000000000000001616161616161616161616161616161616161616
Typ=2 Len=21: 55,55,55,55,55,55,55,55,55,55,55,55,55,55,55,55,55,55,55,55,55
null
Typ=2 Len=21: 66,66,66,66,66,66,66,66,66,66,66,66,66,66,66,66,66,66,66,66,66
null
Typ=2 Len=21: 77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77
null
Typ=2 Len=21: 88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88
null
Typ=2 Len=21: 99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99
null
Typ=2 Len=21: aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa
null
Typ=2 Len=21: bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb,bb
null
Typ=2 Len=21: cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc,cc
null
Typ=2 Len=21: dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd,dd
null
Typ=2 Len=21: ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee,ee
null
Typ=2 Len=21: ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff,ff
Which are all 21 bytes.
fiddle