PERLNUMBER(1) Perl Programmers Reference Guide PERLNUMBER(1)NAMEperlnumber - 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 = 12.34e-56; # 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 user-defined behaviors
for numbers, such as operations over arbitrarily large
integers, floating points numbers with arbitrary preci
sion, operations over "exotic" numbers such as modular
arithmetic or p-adic arithmetic, and so on. See the over
load manpage 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
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 num
bers which have a finite decimal expansion. Being
strings, and thus of arbitrary length, there is no practi
cal 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 sig
nificant digits. See the section on "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 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
is compatible with the conversion sequence "deci
mal_string --> native_floating_point --> native_inte
ger". 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 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 except, ""no integer""
force the argument into the floating point format.
Arithmetic operators except, ""use integer""
Bitwise operators, ""no integer""
force the argument into the integer format if it is
not a string.
Bitwise operators, ""use integer""
force the argument into the integer format
Operators which expect an integer
force the argument into the integer format. This is
applicable to the third and fourth arguments of "sys
read", for example.
Operators which expect a string
force the argument into the string format. For exam
ple, 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.
AUTHOR
Ilya Zakharevich "ilya@math.ohio-state.edu"
Editorial adjustments by Gurusamy Sarathy <gsar@ActiveS
tate.com>
SEE ALSO
the overload manpage
2001-03-18 perl v5.6.1 PERLNUMBER(1)
