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
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 for-
mat 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 fundamen-
tal 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 infin-
ite:
binary0.1110011001100...
with the sequence 1100 repeating again and again. In addi-
tion 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
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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 archi-
tectures 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.
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
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representable in the target form, a representation of
the closest limit is used. (Loss of information)
+ If the source number is between two numbers represent-
able 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
"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 for-
mat treat the argument as in modular arithmetic, e.g., "mod
2**32" on a 32-bit 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
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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 "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 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-
read", 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 conver-
sion 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
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