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Perl version 5.10.0 documentation - perlnumber
NAME
perlnumber - semantics of numbers and numeric operations in Perl
SYNOPSIS
$n
$n
$n
$n
$n
$n
$n
=
=
=
=
=
=
=
1234;
# decimal integer
0b1110011;
# binary integer
01234;
# octal integer
0x1234;
# hexadecimal integer
12.34e-56;
# exponential notation
"-12.34e56";
# number specified as a string
"1234";
# number specified as a string
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 precision, operations over "exotic" numbers such as modular arithmetic or
p-adic 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
"12.34e-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 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:
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 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
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**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.
http://perldoc.perl.org
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Perl version 5.10.0 documentation - perlnumber
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 integer
native floating_point
native floating_point
decimal string
decimal string
-->
-->
-->
-->
-->
-->
native floating
decimal string
native integer
decimal string
native integer
native floating
point (*)
(*)
(*)
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 information)
If the source number is between two numbers representable in the target form, a
representation of one of these numbers is used. (Loss
of information)
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.
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
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
/^[a-zA-Z]*[0-9]*\z/
the string increment described in
perlop
is used.
Arithmetic operators during
use integer
http://perldoc.perl.org
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Perl version 5.10.0 documentation - perlnumber
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
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 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.
AUTHOR
Ilya Zakharevich
ilya@math.ohio-state.edu
Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org>
SEE ALSO
overload, perlop
http://perldoc.perl.org
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