declares function Number::*add()* for addition, and method *muas()* in
the "class" `Number`

(or one of its base classes)
for the assignment form `*=`

of multiplication. Legal values of this
hash array are values legal inside `&{ ... }`

call, so the name of a
subroutine, a reference to a subroutine, or an anonymous subroutine
will all work.

The subroutine

will be called to execute **$OVERLOAD**{"+"}

if **$a**+**$b****$a**
is a reference to an object blessed into the package `Number`

, or **$a** is
not an object from a package with defined mathemagic addition, but **$b** is a
reference to a `Number`

. It can be called also in other situations, like

, or **$a**+=7

. See
**$a**++*MAGIC AUTOGENERATION*
. (Mathemagical
methods refer to methods triggered by an overloaded mathematical
operator.)

`7+`**$a**

, the order of arguments is interchanged.
Most probably it does not matter for implementation of the addition
method, but whether the arguments are reversed is vital for the
subtraction method. The subroutine can query this information by
examining the third argument, which can take three different values:

**FALSE**- the order of arguments is as in the current operation.
**TRUE**- the arguments are reversed.
**undef**-
the current operation is an assignment variant (as in

), but the usual function is called instead. This additional information can be used to generate some optimizations.**$a**+=7

**$OVERLOAD**{"++"}

is called with
arguments `(`**$a**,undef,'')

when

******Arithmetic operations*-
"+", "+=", "-", "-=", "*", "*=", "/", "/=", "%", "%=",
"**", "**=", "<<", "<<=", >>", >>=", "x", "x=", ".", ".=",
For these operations a substituted non-assignment variant can be called if the assignment variant is not available. Methods for operations "

`+`

", "`-`

", "`+=`

", and "`-=`

" can be called to automatically generate increment and decrement methods. The operations "`-`

" can be used to autogenerate missing methods for unary minus or abs . *** Comparison operations**-
<", <=", ">", ">=", "==", "!=", <=>",
"lt", "le", "gt", "ge", "eq", "ne", "cmp",
If the corresponding "spaceship" variant is available, it can be used to substitute for the missing operation. During sort ing arrays,

`cmp`

is used to compare values subject to**%OVERLOAD**. ******Bit operations*-
"&", "^", "|", "&=", "^=", "|=", "neg", "!", "~",
"

`neg`

" stands for unary minus. If the method for`neg`

is not specified, it can be autogenerated using on the method for subtraction. *** Increment and decrement**-
"++", "--",
If undefined, addition and subtraction methods can be used instead. These operations are called both in prefix and postfix form.

******Transcendental functions*-
"atan2", "cos", "sin", "exp", "abs", "log", "sqrt",
If abs is unavailable, it can be autogenerated using methods for <" or <=>" combined with either unary minus or subtraction.

******Boolean, string and numeric conversion*-
"bool", "\"\"", "0+",
If one or two of these operations are unavailable, the remaining ones can be used instead.

`bool`

is used in the flow control operators (like`while`

) and for the ternary "`?:`

" operation. These functions can return any arbitrary Perl value. If the corresponding operation for this value is overloaded too, that operation will be called again with this value. ******Special*- "nomethod", "fallback", "=",

**$OVERLOAD**{"nomethod"}

is a reference to a function of four parameters.
If defined, it is called when the overloading mechanism cannot find a
method for some operation. The first three arguments of this function
coincide with arguments for the corresponding method if it were found, the
fourth argument is the key of `1-`**$a**

can be equivalent to

If some operation cannot be resolved, and there is no

, then an exception will be raised
via
die()
-- unless **$OVERLOAD**{"nomethod"}

is true.
**$OVERLOAD**{"fallback"}

**$OVERLOAD**{"fallback"}

governs what to do if a method for a particular
operation is not found. Three different cases are possible depending on
value of **$OVERLOAD**{"fallback"}

:

*** undef**-
Perl tries to use a
substituted method (see
*MAGIC AUTOGENERATION*). If this fails, it then tries to calls

; if missing, an exception will be raised.**$OVERLOAD**{"nomethod"} ** TRUE*-
The same as for the
undef
value, but no exception is raised. Instead,
it silently reverts to what it would have done were there no
**%OVERLOAD**is present. ** defined, but FALSE*-
No autogeneration is tried. Perl tries to call

, and if this is missing, raises an exception.**$OVERLOAD**{"nomethod"}

**$OVERLOAD**{"="}

is a reference to a function with three arguments,
i.e., it looks like a usual value of

To make this change to **$a** and not to change **$b**, a freshly made copy of
```
$$
a
```

is made, and **$a** is assigned a reference to this object. This
operation is executed during

, (so before this **$a**++```
$$
a
```

coincides
with ```
$$
b
```

), and only if `++`

is expressed via

or
**$OPERATOR**{'++'}

. Note that if this operation is expressed via '**$OPERATOR**{'+='}`+`

',
i.e., as

then ```
$$
a
```

and ```
$$
b
```

do not appear as lvalues.

If the copy constructor is required during execution of some mutator, but

is missing, it can be autogenerated as a string
copy if an object of
the package is a plain scalar.
**$OPERATOR**{'='}

**$OVERLOAD**{"fallback"}

is
TRUE or undefined, Perl tries to to autogenerate a substitute method for
the missing operation based on defined operations. Autogenerated method
substitutions are possible for the following operations:

**Assignment forms of arithmetic operations**-

can use the**$a**=+**$b**

method if**$OVERLOAD**{"+"}

is not defined.**$OVERLOAD**{"+="} **Conversion operations**- String, numeric, and boolean conversion are calculated in terms of one another if not all of them are defined.
**Increment and decrement**-
The
`++`

operation can be expressed in terms of**$a**

or**$a**+=1

, and**$a**+1

in terms of**$a**--

and**$a**-=1

.**$a**-1 **abs(****$a**)-
can be expressed in terms of

and**$a**<0`-`

(or**$a**`0-`

).**$a** **Unary minus**- can be expressed in terms of subtraction.
**Concatenation**- can be expressed in terms of string conversion.
**Comparison operations**-
can be expressed in terms of its "spaceship" counterpart: either
`<=>`

or`cmp`

: <, >,<=, >=, ==, != in terms of<=> lt, gt, le, ge, eq, ne in terms of cmp **Copy operator**- can be expressed in terms of assignment to the dereferenced value, if this value is scalar but not a reference.

`cmp`

' should return a reference to a blessed object, the
autogenerated ``lt`

'
function will produce only a standard logical value based on the
numerical value of the result of ``cmp`

'. In particular, a working
numeric conversion is needed in this case (possibly expressed in terms of
other conversions).
Similarly, `.=`

and `x=`

operators lose their mathemagical properties
if the string conversion substitution is applied.

When you chop() a mathemagical object, it becomes promoted to a string first, and its mathemagical qualities is lost. The same can happen with other operations as well.

(Every SVish thing has a magic queue, and a magic is an entry in that queue.
This is how a single variable may participate in multiple forms of magic
simultaneously. For instance, environment variables regularly have two
forms at once: their **%ENV** magic and their taint magic.)

If an object belongs to a package with **%OVERLOAD**, it carries a special
flag. Thus the only speed penalty during arithmetic operations without
overload is the check of this flag.

In fact, if no **%OVERLOAD** is ever accessed, there is almost no overhead for
overloadable operations, so most programs should not suffer measurable
performance penalties. Considerable effort was made minimize overhead
when **%OVERLOAD** is accessed and the current operation is overloadable but
the arguments in question do not belong to packages with **%OVERLOAD**. When
in doubt, test your speed with **%OVERLOAD** and without it. So far there
have been no reports of substantial speed degradation if Perl is compiled
with optimization turned on.

There is no size penalty for data if there is no **%OVERLOAD**.

The copying like

is shallow; however, a one-level-deep
copying is
carried out before any operation that can imply an assignment to the
object **$a**=**$b****$b** (or **$a**) refers to, like

. You can override this
behavior by defining your copy constructor (see
**$b**++*Copy Constructor*
).

It is expected that arguments to methods that are not explicitly supposed to be changed are constant (but this is not enforced).

As shipped, **%OVERLOAD** is not inherited via the **@ISA** tree. A patch for
this is available from the author.

This document is confusing.