Modulo operation

In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus).

Given two positive numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n. For instance, the expression "5 mod 2" would evaluate to 1 because 5 divided by 2 leaves a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and leaves a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3. (Note that doing the division with a calculator will not show the result referred to here by this operation; the quotient will be expressed as a decimal fraction.)

Although typically performed with a and n both being integers, many computing systems allow other types of numeric operands. The range of numbers for an integer modulo of n is 0 to n − 1. (n mod 1 is always 0; n mod 0 is undefined, possibly resulting in a division by zero error in computer programming languages.) See modular arithmetic for an older and related convention applied in number theory.

Null coalescing operator

The null coalescing operator (called the Logical Defined-Or operator in Perl) is a binary operator that is part of the syntax for a basic conditional expression in several programming languages, including C#,Perl as of version 5.10,Swift, and PHP 7.0.0.

In contrast to the ternary conditional if operator used as x ? x : y, but like the binary Elvis operator used as x ?: y, the null coalescing operator is a binary operator and thus evaluates its operands at most once, which is significant if the evaluation of x has side-effects.

C#

In C#, the null coalescing operator is ??. It is most often used to simplify null expressions as follows:

For example, if one wishes to implement some C# code to give a page a default title if none is present, one may use the following statement:

instead of the more verbose

or

The three forms are logically equivalent.

The operator can also be used multiple times in the same expression:

Once a non-null value is assigned to number, or it reaches the final value (which may or may not be null), the expression is completed.

Liberman (album)

Liberman is the fifth studio album by American singer-songwriter Vanessa Carlton, released on October 23, 2015, through Dine Alone Records. It is the follow up to Carlton's 2011 album Rabbits on the Run and marks her first release since signing with Dine Alone Records. The title of the album comes from an oil painting made by Carlton's late grandfather, whose given surname was Liberman.

Background and writing

Following the 2011 release Rabbits on the Run, Carlton took time off to get married, start a family and write another album. She tells CBS News that these changes in her life are reflected in Liberman's songs and that she "wanted the whole album to feel like an escape type of album, where you put it on and you feel like you're in this dreamy state."

To avoid preconceived notions, demos recorded were sent to Dine Alone Records without Carlton's name attached. Label president Joel Carriere recalls hearing the demos and tells The Toronto Star, "The songs were amazing, it was atmospheric, it kind of fit into what we’re all into ... and we never would have guessed it was Vanessa Carlton because her voice has developed so much since her pop songs 14 years ago and the songwriting had obviously changed. We were, like: 'Yeah, we want to do this. But what is it we’re doing?'"