# LEL Optimization

Performance issues in LEL.

--CASA Developer--

When giving a LEL expression, it is important to keep an eye on performance issues.

## LEL itself will do some optimization:

• As said in the introduction a LEL expression is evaluated in chunks. However, a scalar subexpression is executed only once when getting the first chunk. E.g. in
  lat1 + mean(lat2)

the subexpression mean(lat2) is executed only once and not over and over again when the user gets chunks.
• Often the exponent 2 is used in the pow function (or operator ^). This is optimized by using multiplication instead of using the system pow function.
• When LEL finds a masked-off scalar in a subexpression, it does not evaluate the other operand. Instead it sets the result immediately to a masked-off scalar. Exceptions are the operators AND and OR and function iif, because their masks depend on the operand values.

## The user can optimize by specifying the expression carefully.

• It is strongly recommended to combine scalars into a subexpression to avoid unnecessary scalar-lattice operations. E.g.
  2 * lat1 * pi()

should be written as
  lat1 * (2 * pi())
#or
2 * pi() * lat1

because in that way the scalars form a scalar subexpression which is calculated only once. Note that the subexpression parentheses are needed in the first case, because multiplications are done from left to right.
In the future LEL will be optimized to shuffle the operands when possible and needed.
• It is important to be careful with the automatic data type promotion of single precision lattices. Several scalar functions (e.g. pi) produce a double precision value, so using pi with a single precision lattice causes the lattice to be promoted to double precision. If accuracy allows it, it is much better to convert pi to single precision. E.g. assume lat1 and lat2 are single precision lattices.
  atan2(lat1,lat2) + pi()/2

The result of atan2 is single precision, because both operands are single precision. However, pi is double precision, so the result of atan2 is promoted to double precision to make the addition possible. Specifying the expression as:
  atan2(lat1,lat2) + float(pi())/2

avoids that (expensive) data type promotion.
• POW(LAT,2) or LAT^2 is faster than LAT*LAT, because it accesses lattice LAT only once.
• SQRT(LAT) is faster than LAT^0.5 or POW(LAT,0.5)
• POW(U,2) + POW(V,2) < 1000^2 is considerably faster than
SQRT(SQUARE(U) + SQUARE(V)) < 1000, because it avoids the SQRT function.
• LEL can be used with disk-based lattices and/or memory-based lattices. When used with memory-based lattices it is better to make subexpressions the first operand in another subexpression or a function. E.g.
lat1*lat2 + lat3
is better than
lat3 + lat1*lat2
The reason is that in the first case no copy needs to be made of the lattice data which already reside in memory. All LEL operators and functions try to reference the data of their latter operands instead of making a copy.
In general this optimization does not apply to LEL expression. However, when using the true C++ interface to classes like LatticeExprNode, one can easily use memory-based lattices. In that case it can be advantageous to pay attention to this optimization.