In some cases, a circuit simulator or computer language lacks a function for the  minimum or maximum of two numbers.   If there is no "if statement" conditional available, the following formulas have been helpful.

MIN( a, b ) = 0.5* ( a + b ) - 0.5* abs( a - b )

MAX( a, b ) = 0.5* ( a + b ) + 0.5* abs( a - b )

Similarly, when the arctangent function alone is insufficient, and the two arguement function atan2 is desired the following formula is helpful.

Atan2( y, x ) = 2* atan( y / ( x + sqrt( x*x + y*y ) ) )

The above Atan2 formula is based on the half-angle  identity:   tan ( theta /2 ) = sin( theta ) / ( 1 + cos( theta ) ).   The formula fails for theta = pi where  the denominator is zero.

Wikipedia on Atan2  here  .