210 lines
8.2 KiB
Plaintext
210 lines
8.2 KiB
Plaintext
=head1 NAME
|
|
|
|
perlnumber - semantics of numbers and numeric operations in Perl
|
|
|
|
=head1 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
|
|
|
|
=head1 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 L<overload> for details.
|
|
|
|
=head1 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 C<"12.34e-56">.
|
|
I<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 C<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
|
|
I<storage> of these numbers. The fact that you can store such "large" numbers
|
|
does not mean that the I<operations> over these numbers will use all
|
|
of the significant digits.
|
|
See L</"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.
|
|
|
|
=head1 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:
|
|
|
|
=over 4
|
|
|
|
=item *
|
|
|
|
If the source number can be represented in the target form, that
|
|
representation is used.
|
|
|
|
=item *
|
|
|
|
If the source number is outside of the limits representable in the target form,
|
|
a representation of the closest limit is used. (I<Loss of information>)
|
|
|
|
=item *
|
|
|
|
If the source number is between two numbers representable in the target form,
|
|
a representation of one of these numbers is used. (I<Loss of information>)
|
|
|
|
=item *
|
|
|
|
In C<< native floating point --> native integer >> conversions the magnitude
|
|
of the result is less than or equal to the magnitude of the source.
|
|
(I<"Rounding to zero".>)
|
|
|
|
=item *
|
|
|
|
If the C<< decimal string --> native integer >> conversion cannot be done
|
|
without loss of information, the result is compatible with the conversion
|
|
sequence C<< decimal_string --> native_floating_point --> native_integer >>.
|
|
In particular, rounding is strongly biased to 0, though a number like
|
|
C<"0.99999999999999999999"> has a chance of being rounded to 1.
|
|
|
|
=back
|
|
|
|
B<RESTRICTION>: The conversions marked with C<(*)> 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.
|
|
|
|
=head1 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., C<mod 2**32> on a 32-bit
|
|
architecture. C<sprintf "%u", -1> therefore provides the same result as
|
|
C<sprintf "%u", ~0>.
|
|
|
|
=over 4
|
|
|
|
=item Arithmetic operators
|
|
|
|
The binary operators C<+> C<-> C<*> C</> C<%> C<==> C<!=> C<E<gt>> C<E<lt>>
|
|
C<E<gt>=> C<E<lt>=> and the unary operators C<-> C<abs> and C<--> 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.
|
|
|
|
=item ++
|
|
|
|
C<++> behaves as the other operators above, except that if it is a string
|
|
matching the format C</^[a-zA-Z]*[0-9]*\z/> the string increment described
|
|
in L<perlop> is used.
|
|
|
|
=item Arithmetic operators during C<use integer>
|
|
|
|
In scopes where C<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, C<abs>, C<++> and C<-->, do not change their
|
|
behavior with C<use integer;>
|
|
|
|
=item Other mathematical operators
|
|
|
|
Operators such as C<**>, C<sin> and C<exp> force arguments to floating point
|
|
format.
|
|
|
|
=item Bitwise operators
|
|
|
|
Arguments are forced into the integer format if not strings.
|
|
|
|
=item Bitwise operators during C<use integer>
|
|
|
|
forces arguments to integer format. Also shift operations internally use
|
|
signed integers rather than the default unsigned.
|
|
|
|
=item Operators which expect an integer
|
|
|
|
force the argument into the integer format. This is applicable
|
|
to the third and fourth arguments of C<sysread>, for example.
|
|
|
|
=item Operators which expect a string
|
|
|
|
force the argument into the string format. For example, this is
|
|
applicable to C<printf "%s", $value>.
|
|
|
|
=back
|
|
|
|
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.
|
|
|
|
=head1 AUTHOR
|
|
|
|
Ilya Zakharevich C<ilya@math.ohio-state.edu>
|
|
|
|
Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
|
|
|
|
Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org>
|
|
|
|
=head1 SEE ALSO
|
|
|
|
L<overload>, L<perlop>
|