NAME
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
$n = v49.50.51.52; # number specified as a string, which in
# turn is specified in terms of numbers :-)
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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 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:
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.
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 (*)
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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.
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
- 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.
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>
overload, perlop
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