Myujth

I have the following table in an SQLite database

CREATE TABLE `log` (
 `time` REAL NOT NULL DEFAULT CURRENT_TIMESTAMP,
 `data` BLOB NOT NULL
) WITHOUT ROWID;

CREATE INDEX `time_index` ON `log`(`time`);

The index is created because the most frequent query is going to be

SELECT * FROM `log` WHERE `time` BETWEEN ? AND ?

Since the time is going to be always the current time when the new record is added, the index is not really required here. So I would like to "tell" the SQLite engine something like "The lines are going to be added with the 'time' column always having increasing value (similar to AUTO_INCREMENT), and if something goes wrong I will take all responsibility".

Is it possible at all?

You don't want a separate index. You want to declare the column to be the primary key:

CREATE TABLE `log` (
 `time` REAL NOT NULL DEFAULT CURRENT_TIMESTAMP PRIMARY KEY,
 `data` BLOB NOT NULL
) WITHOUT ROWID;

This creates a single b-tree index for the log based on the primary key. In other databases, this structure would be called a "clustered index". You have probably already read the documentation but I'm referencing it anyway.

You would have an issue, or not depending upon how you consider that you cannot use :-

CREATE TABLE `log` (
 `time` REAL NOT NULL DEFAULT CURRENT_TIMESTAMP,
 `data` BLOB NOT NULL
) WITHOUT ROWID;

because :-

Every WITHOUT ROWID table must have a PRIMARY KEY. An error is raised
if a CREATE TABLE statement with the WITHOUT ROWID clause lacks a
PRIMARY KEY.
Clustered Indexes and the WITHOUT ROWID Optimization

So you might as well make the time column the PRIMARY KEY.

but the problem is that the precision of REAL is not enough to handle
microsecond resolution, and thus two adjacent records may have the
same time value which would violate the PRIMARY KEY constraint.

Then you could use a composite PRIMARY KEY where the precision required is satisfied by multiple columns (a second column would likely more than suffice) perhaps along the lines of :-

CREATE TABLE log (
 time_datepart INTEGER, 
 time_microsecondpart, 
 data BLOB NOt NULL, 
 PRIMARY KEY (time_datepart,time_microsecondpart)
) WITHOUT ROWID;

The time_microsecondpart column needn't necessarily be microseconds it could be a counter derived from another table similar to how the sqlite_sequence table is utilised when AUTOINCREMENT is utilised (less the need for the column that holds the name of the table that a row is attached to).