|…| (modulus squared) operator

This operator is different from all other operators, because it is not an infix operator (an operator written between its operands, or before the operand in the case of an unary operator), but it is a parenthetic operator. The operand is written between the | characters. This resembles the mathematical notation of the complex modulus operator.

To complicate matters even further, this operator doesn’t even calculate the complex modulus, it calculates the square of the complex modulus, which is defined as:

  |(a, b)| = a*a + b*b    

If you consider the complex operand as a point in the complex plane, the complex modulus is the distance from that point to the origin (the point (0,0)). So this operator calculates the square of that distance.

The reason the squared modulus is returned instead of the modulus itself is that it’s much faster to calculate the squared modulus (no square root operation is necessary). Usually the modulus is compared with another modulus, so in that case it doesn’t matter if they are both squared or not.

When using nested squared modulus operators, overriding parentheses are necessary to let the compiler understand how to translate the expression.

Examples:

  |(3, 4)|             ; 25  |(2, -3)|            ; 13  ||(3,2)| + (2,1)|    ; error!  |(|(3,2)|) + (2,1)|  ; 226    

Notes

• To calculate the complex modulus, use the cabs function.
• Don’t confuse this operator with the || operator.

See Also
Expressions
Types

|…| (modulus squared) operator