perlnumber - semantics of numbers and numeric operations in Perl
$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
This document describes how Perl internally handles numeric values.
Perl's operator overloading facility is completely ignored here. Operator
overloading allows user-defined behaviors for numbers, such as operations over
arbitrarily large integers, floating points numbers with arbitrary precision,
operations over "exotic" numbers such as modular arithmetic or
p-adic arithmetic, and so on. See overload for details.
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 exponential notation part, as in "12.34e-56". Native
here means "a format supported by the C compiler which was used to build
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 maximal 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" representation 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:
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 digits, 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 upshot
of all this is that Perl cannot store a number like 12345678901234567 as a
floating point number on such architectures without loss of information.
Similarly, decimal strings can represent only those numbers which have a finite
decimal expansion. Being strings, and thus of arbitrary length, there is no
practical limit for the exponent or number of decimal digits for these
numbers. (But realize that what we are discussing the rules for just the
of these numbers. The fact that you can store such
"large" numbers does not mean that the operations
numbers will use all of the significant digits. See "Numeric operators
and numeric conversions" for details.)
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 numbers 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 representable in the target
form, a representation of the closest limit is used. ( Loss of
- If the source number is between two numbers representable in the target
form, a representation of one of these numbers is used. ( Loss of
- In "native floating point --> native integer" conversions 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 is compatible with the
conversion sequence "decimal_string --> native_floating_point
--> native_integer". In particular, rounding is strongly biased to
0, though a number like "0.99999999999999999999" has a chance of
being rounded to 1.
: The conversions marked with "(*)" above involve
steps performed by the C compiler. In particular, bugs/features of the
compiler used may lead to breakage of some of the above rules.
Flavors of Perl numeric operations¶
Perl operations which take a numeric argument treat that argument in one of four
different ways: they may force it 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 precision, 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
- "++" 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 argument(s) into integer format,
and return an integer result. The exceptions, "abs",
"++" and "--", do not change their behavior with
- Other mathematical operators
- Operators such as "**", "sin" and "exp"
force arguments 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 operations 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 "sysread", for example.
- Operators which expect a string
- force the argument into the string format. For example, this is applicable
to "printf "%s", $value".
Though forcing an argument into a particular form does not change the stored
number, Perl remembers the result of such conversions. In particular, though
the first such conversion may be time-consuming, repeated operations will not
need to redo the conversion.
Ilya Zakharevich "firstname.lastname@example.org"
Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
Updates for 5.8.0 by Nicholas Clark <email@example.com>