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```

```

## SYNOPSIS

```           \$n = 1234;              # decimal integer
\$n = 0b1110011;         # binary integer
\$n = 01234;             # octal integer
\$n = 0x1234;            # hexadecimal integer
\$n = 12.34e-56;         # exponential notation
\$n = "-12.34e56";       # number specified as a string
\$n = "1234";            # number specified as a string

```

## DESCRIPTION

```       This document describes how Perl internally handles
numeric values.

for numbers, such as operations over arbitrarily large
integers, floating points numbers with arbitrary preci­
sion, operations over "exotic" numbers such as modular
for details.

```

## Storing numbers

```       Perl can internally represent numbers in 3 different ways:
as native integers, as native floating point numbers, and
as decimal strings.  Decimal strings may have an exponen­
tial notation part, as in "12.34e-56".  Native here means
"a format supported by the C compiler which was used to
build perl".

The term "native" does not mean quite as much when we talk
about native integers, as it does when native floating
point numbers are involved.  The only implication of the
term "native" on integers is that the limits for the maxi­
mal and the minimal supported true integral quantities are
close to powers of 2.  However, "native" floats have a
most fundamental restriction: they may represent only
those numbers which have a relatively "short" representa­
tion when converted to a binary fraction.  For example,
0.9 cannot be represented by a native float, since the
binary fraction for 0.9 is infinite:

binary0.1110011001100...

with the sequence 1100 repeating again and again.  In
addition to this limitation,  the exponent of the binary
number is also restricted when it is represented as a
floating point number.  On typical hardware, floating
point values can store numbers with up to 53 binary dig­
its, and with binary exponents between -1024 and 1024.  In
decimal representation this is close to 16 decimal digits
and decimal exponents in the range of -304..304.  The

In fact numbers stored in the native integer format may be
stored either in the signed native form, or in the
unsigned native form.  Thus the limits for Perl numbers
stored as native integers would typically be
-2**31..2**32-1, with appropriate modifications in the
case of 64-bit integers.  Again, this does not mean that
Perl can do operations only over integers in this range:
it is possible to store many more integers in floating
point format.

Summing up, Perl numeric values can store only those num­
bers which have a finite decimal expansion or a "short"
binary expansion.

```

## Numeric operators and numeric conversions

```       As mentioned earlier, Perl can store a number in any one
of three formats, but most operators typically understand
only one of those formats.  When a numeric value is passed
as an argument to such an operator, it will be converted
to the format understood by the operator.

Six such conversions are possible:

native integer        --> native floating point       (*)
native integer        --> decimal string
native floating_point --> native integer              (*)
native floating_point --> decimal string              (*)
decimal string        --> native integer
decimal string        --> native floating point       (*)

These conversions are governed by the following general
rules:

·   If the source number can be represented in the target
form, that representation is used.

·   If the source number is outside of the limits repre­
sentable in the target form, a representation of the
closest limit is used.  (Loss of information)

·   If the source number is between two numbers repre­
sentable in the target form, a representation of one
of these numbers is used.  (Loss of information)

·   In "native floating point --> native integer" conver­
sions the magnitude of the result is less than or
equal to the magnitude of the source.  ("Rounding to
zero".)

·   If the "decimal string --> native integer" conversion
cannot be done without loss of information, the result

to one of the integer/floating/ string formats, or they
may behave differently depending on the format of the
operand.  Forcing a numeric value to a particular format
does not change the number stored in the value.

All the operators which need an argument in the integer
format treat the argument as in modular arithmetic, e.g.,
"mod 2**32" on a 32-bit architecture.  "sprintf "%u", -1"
therefore provides the same result as "sprintf "%u", ~0".

Arithmetic operators
The binary operators "+" "-" "*" "/" "%" "==" "!=" ">"
"<" ">=" "<=" and the unary operators "-" "abs" and
"--" will attempt to convert arguments to integers.
If both conversions are possible without loss of pre­
cision, and the operation can be performed without
loss of precision then the integer result is used.
Otherwise arguments are converted to floating point
format and the floating point result is used.  The
caching of conversions (as described above) means that
the integer conversion does not throw away fractional
parts on floating point numbers.

++  "++" behaves as the other operators above, except that
if it is a string matching the format
"/^[a-zA-Z]*[0-9]*\z/" the string increment described
in perlop is used.

Arithmetic operators during "use integer"
In scopes where "use integer;" is in force, nearly all
the operators listed above will force their argu­
ment(s) into integer format, and return an integer
result.  The exceptions, "abs", "++" and "--", do not
change their behavior with "use integer;"

Other mathematical operators
Operators such as "**", "sin" and "exp" force argu­
ments to floating point format.

Bitwise operators
Arguments are forced into the integer format if not
strings.

Bitwise operators during "use integer"
forces arguments to integer format. Also shift opera­
tions internally use signed integers rather than the
default unsigned.

Operators which expect an integer
force the argument into the integer format.  This is
applicable to the third and fourth arguments of "sys­

Editorial adjustments by Gurusamy Sarathy <gsar@ActiveS­
tate.com>

Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org>

```

```       overload, perlop

perl v5.8.1                 2003-09-02              PERLNUMBER(1)
```

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