
PERLNUMBER(1) Perl Programmers Reference Guide PERLNUMBER(1)
NAME
perlnumber  semantics of numbers and numeric operations in Perl
SYNOPSIS
$n = 1234; # decimal integer
$n = 0b1110011; # binary integer
$n = 01234; # octal integer
$n = 0x1234; # hexadecimal integer
$n = 12.34e56; # exponential notation
$n = "12.34e56"; # number specified as a string
$n = "1234"; # number specified as a string
$n = v49.50.51.52; # number specified as a string, which in
# turn is specified in terms of numbers :)
DESCRIPTION
This document describes how Perl internally handles numeric values.
Perl's operator overloading facility is completely ignored here. Operator overloading
allows userdefined behaviors for numbers, such as operations over arbitrarily large inte
gers, floating points numbers with arbitrary precision, operations over "exotic" numbers
such as modular arithmetic or padic arithmetic, and so on. See overload 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 exponential
notation part, as in "12.34e56". 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 maximal and the minimal supported true
integral quantities are close to powers of 2. However, "native" floats have a most funda
mental 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 repre
sented 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 digits, and with binary exponents between 1024 and 1024. In decimal representa
tion 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 storage of these numbers. The fact that you can store
such "large" numbers does not mean that the operations over these 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**321, with appropriate modifications in the
case of 64bit 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 for
mat.
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 opera
tors 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 opera
tor.
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:
o If the source number can be represented in the target form, that representation is
used.
o If the source number is outside of the limits representable in the target form, a rep
resentation of the closest limit is used. (Loss of information)
o If the source number is between two numbers representable in the target form, a repre
sentation of one of these numbers is used. (Loss of information)
o 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".)
o 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.
RESTRICTION: The conversions marked with "(*)" above involve steps performed by the C com
piler. 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 particu
lar 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 32bit architecture. "sprintf "%u", 1" there
fore 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 numbers.
++ "++" behaves as the other operators above, except that if it is a string matching the
format "/^[azAZ]*[09]*\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 excep
tions, "abs", "++" and "", do not change their behavior with "use integer;"
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 inte
gers 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 timeconsuming, repeated operations will not need to redo the conversion.
AUTHOR
Ilya Zakharevich "ilya@math.ohiostate.edu"
Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org>
SEE ALSO
overload, perlop
perl v5.8.0 20030218 PERLNUMBER(1) 
