Question

Is there some way to have a formula that is in both the select and where condition only be calculated once?

I assume mysql must do the calculation twice for each row it the following example.

SELECT z1.id sid1,z2.id sid2,SQRT(POW(ABS(z1.col-z2.col),2) + POW(ABS(z1.row-z2.row),2)) r
    FROM stars z1,stars z2
    WHERE z1.id!=z2.id
    AND SQRT(POW(ABS(z1.col-z2.col),2) + POW(ABS(z1.row-z2.row),2)) <=32
    ORDER BY z1.id,z2.id

Answer 1

You cannot refer to aliases defined in a SELECT clause in a WHERE clause, but you can use them in a HAVING clause. This is because WHERE is evaluated before SELECT as SELECT may contain aggregate functions.

SELECT z1.id sid1,z2.id sid2,SQRT(POW(ABS(z1.col-z2.col),2) + POW(ABS(z1.row-z2.row),2)) r
 FROM stars z1,stars z2
 WHERE z1.id != z2.id
 HAVING r <= 32
 ORDER BY z1.id,z2.id

Beware, though, that the HAVING clause will most likely not be used in indexes. You could provide an approximate term to the WHERE clause for indexing purposes:

SELECT z1.id sid1,z2.id sid2,SQRT(POW(ABS(z1.col-z2.col),2) + POW(ABS(z1.row-z2.row),2)) r
 FROM stars z1,stars z2
 WHERE z1.id != z2.id
 AND (z2.col BETWEEN z1.col-32 AND z1.col+32)
 AND (z2.row BETWEEN z1.row-32 AND z1.row+32)
 HAVING r <= 32
 ORDER BY z1.id,z2.id

Note that the bottleneck is disk access, not arithmetic calculation, so if you are optimising for speed, you may want to stay with WHERE and only optimise the WHERE clause:

note that

• x^2 is the same as abs(x)^2.
• x*x is likely faster than pow(x,2)
• instead of computing the sqrt, you can square the other side.

Try:

SELECT z1.id sid1,z2.id sid2,
  SQRT((z1.col-z2.col)*(z1.col-z2.col) + (z1.row-z2.row)*(z1.row-z2.row)) r
 FROM stars z1,stars z2
 WHERE z1.id != z2.id
 AND (z1.col-z2.col)*(z1.col-z2.col) + (z1.row-z2.row)*(z1.row-z2.row) <= 1024
 ORDER BY z1.id,z2.id