What does this line of code mean in non-code speak?

if (div4 & ~( xor(div100, div400)))

div4 div100 and div400 are given by:

div4 = ((year/4) == floor (year/4));
div100 = ((year/100) == floor (year/100));
div400 = ((year/400) == floor (year/400));

Answer 1

[Wayne King]

div4, div100, and div400 are all logical variables, 1 or 0.

 if (div4 & ~(xor(div100,div400)))

says "if div4 is true (1) and div100 and div400 are both false or both are true, do something"

~xor(div100,div400)

equals 1 (true) only if both div100 and div400 are false or both are true

[per isakson]

xor(A,B) is true if one of A and B is true, else false

[Wayne King]

right, ~xor(A,B) is true only if both are false or both are true (I forgot the both are true condition)

~xor(1,0)
~xor(0,1)
~xor(1,1)
~xor(0,0)

[per isakson]

Yes,

    not( [ xor(1,0), xor(0,1), xor(1,1), xor(0,0) ] )

returns

    ans =
         0     0     1     1

[J]

Many thanks. Couldn't wrap my head around the latter part of it.

Answer 2

[Roger Stafford]

In other words, this logical statement is true when 'year' is to be a leap year under the Gregorian calendar. They could just as well have written

 if div4&(div100==div400)

or, given the definitions of these quantities,

 if div4&(div100<=div400)

or, again given their definitions, even this

 if div400|(div4~=div100)

Answer 3

[Andrei Bobrov]

~rem(year,4)&rem(year,100)|~rem(year,400)