Why can't I persist binary(4) computed column? I'm playing with storing and indexing IP addresses.  I'm starting with a simple, stupid table:
CREATE TABLE [dbo].[IP_addresses](
    [IP_as_text] [char](16) NOT NULL,
    [IP]  AS ([dbo].[fnBinaryIPv4]([IP_as_text]))
) ON [PRIMARY]

Where fnBinaryIPv4 is from https://stackoverflow.com/questions/1385552.
CREATE FUNCTION dbo.fnBinaryIPv4(@ip AS VARCHAR(15)) RETURNS BINARY(4)
AS
BEGIN
    DECLARE @bin AS BINARY(4)

    SELECT @bin = CAST( CAST( PARSENAME( @ip, 4 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( PARSENAME( @ip, 3 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( PARSENAME( @ip, 2 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( PARSENAME( @ip, 1 ) AS INTEGER) AS BINARY(1))

    RETURN @bin
END

However, when I try to add PERSISTED to the IP column or use it in an index, I get a message that it is not deterministic.  I've Googled around a bit and that usually has to do with the style passed to CONVERT() for a date but that doesn't seem to apply here.  http://www.sql-server-helper.com/functions/system-functions/index.aspx says CAST() and PARSENAME() are deterministic so I don't see why fnBinaryIPv4() is nondeterministic.  But it turns out that PARSENAME() used to be but is no longer deterministic.  So I rewrote that function:
CREATE FUNCTION [dbo].[fnBinaryIPv4](@ip AS VARCHAR(15)) RETURNS BINARY(4)
WITH SCHEMABINDING
AS
BEGIN
    DECLARE @int_addr AS bigint = 0;
    DECLARE @b CHAR(3);

    DECLARE bCursor CURSOR FOR ( 
        SELECT value FROM STRING_SPLIT(@ip, '.')
    )

    OPEN bCursor

    FETCH NEXT FROM bCursor INTO @b
    WHILE @@FETCH_STATUS = 0
    BEGIN
        SELECT @int_addr = (@int_addr * 256) + CAST(@b AS INTEGER)
        FETCH NEXT FROM bCursor INTO @b
    END

    CLOSE bCursor
    DEALLOCATE bCursor

    RETURN CAST(@int_addr AS BINARY(4))
END

But this version is still nondeterministic.
I'm not sure what &quot;http://www.sql-server-helper.com/&quot; is, but this is from the current, official documentation:

The following built-in functions from other categories are always nondeterministic.
...
PARSENAME

Side note: it looks like PARSENAME was deterministic, at least on SQL Server 2005 (thanks for that link, jpa).  So perhaps that other site just has outdated information on it.
You would need to re-implement this function using only deterministic functions (for instance, SUBSTRING and CHARINDEX).
Just to show that it can be deterministic (note that this implementation doesn't deal with general IP addresses, it's just an example):
CREATE OR ALTER FUNCTION dbo.fnBinaryIPv4(@ip AS VARCHAR(15)) RETURNS BINARY(4)
AS
BEGIN
    DECLARE @bin AS BINARY(4)

    SELECT @bin = CAST( CAST( PARSENAME( @ip, 4 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( PARSENAME( @ip, 3 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( PARSENAME( @ip, 2 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( PARSENAME( @ip, 1 ) AS INTEGER) AS BINARY(1))

    RETURN @bin
END
GO

SELECT OBJECTPROPERTY(OBJECT_ID('dbo.fnBinaryIPv4'), 'IsDeterministic') AS IsDeterministic;
GO

CREATE OR ALTER FUNCTION dbo.fnBinaryIPv4(@ip AS VARCHAR(15)) RETURNS BINARY(4)
WITH SCHEMABINDING
AS
BEGIN
    DECLARE @bin AS BINARY(4)

    SELECT @bin = CAST( CAST( SUBSTRING( @ip, 0, 3 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( SUBSTRING( @ip, 4, 3 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( SUBSTRING( @ip, 8, 3 ) AS INTEGER) AS BINARY(1))
                + CAST( CAST( SUBSTRING( @ip, 12, 3 ) AS INTEGER) AS BINARY(1))

    RETURN @bin
END
GO

SELECT OBJECTPROPERTY(OBJECT_ID('dbo.fnBinaryIPv4'), 'IsDeterministic') AS IsDeterministic;
GO