FM / pod

/usr/share/perl5/pod

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perl.pod	16270	0644	edit dl rm
perl56delta.pod	107201	0644	edit dl rm
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perl561delta.pod	124713	0644	edit dl rm
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perlaix.pod	20437	0644	edit dl rm
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perlandroid.pod	7871	0644	edit dl rm
perlapi.pod	443535	0644	edit dl rm
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perlartistic.pod	7010	0644	edit dl rm
perlbook.pod	8338	0644	edit dl rm
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perlbs2000.pod	8058	0644	edit dl rm
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perlce.pod	14602	0644	edit dl rm
perlcheat.pod	4481	0644	edit dl rm
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perlcn.pod	4691	0644	edit dl rm
perlcommunity.pod	7217	0644	edit dl rm
perlcygwin.pod	27199	0644	edit dl rm
perldata.pod	46743	0644	edit dl rm
perldbmfilter.pod	4981	0644	edit dl rm
perldebguts.pod	38535	0644	edit dl rm
perldebtut.pod	22152	0644	edit dl rm
perldebug.pod	39258	0644	edit dl rm
perldelta.pod	7063	0644	edit dl rm
perldeprecation.pod	18169	0644	edit dl rm
perldiag.pod	284572	0644	edit dl rm
perldos.pod	10522	0644	edit dl rm
perldsc.pod	25614	0644	edit dl rm
perldtrace.pod	7958	0644	edit dl rm
perlebcdic.pod	84233	0644	edit dl rm
perlembed.pod	37196	0644	edit dl rm
perlexperiment.pod	7195	0644	edit dl rm
perlfork.pod	13355	0644	edit dl rm
perlform.pod	16608	0644	edit dl rm
perlfreebsd.pod	1610	0644	edit dl rm
perlfunc.pod	392957	0644	edit dl rm
perlgit.pod	33509	0644	edit dl rm
perlgpl.pod	13815	0644	edit dl rm
perlguts.pod	139329	0644	edit dl rm
perlhack.pod	40445	0644	edit dl rm
perlhacktips.pod	55509	0644	edit dl rm
perlhacktut.pod	6153	0644	edit dl rm
perlhaiku.pod	1508	0644	edit dl rm
perlhist.pod	53546	0644	edit dl rm
perlhpux.pod	30509	0644	edit dl rm
perlhurd.pod	1993	0644	edit dl rm
perlintern.pod	54572	0644	edit dl rm
perlinterp.pod	33687	0644	edit dl rm
perlintro.pod	22119	0644	edit dl rm
perliol.pod	34185	0644	edit dl rm
perlipc.pod	70829	0644	edit dl rm
perlirix.pod	4395	0644	edit dl rm
perljp.pod	7521	0644	edit dl rm
perlko.pod	12259	0644	edit dl rm
perllexwarn.pod	355	0644	edit dl rm
perllinux.pod	1488	0644	edit dl rm
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perlmacos.pod	1001	0644	edit dl rm
perlmacosx.pod	12060	0644	edit dl rm
perlmod.pod	26250	0644	edit dl rm
perlmodinstall.pod	12792	0644	edit dl rm
perlmodlib.pod	76482	0644	edit dl rm
perlmodstyle.pod	22575	0644	edit dl rm
perlmroapi.pod	3212	0644	edit dl rm
perlnetware.pod	6648	0644	edit dl rm
perlnewmod.pod	11036	0644	edit dl rm
perlnumber.pod	8353	0644	edit dl rm
perlobj.pod	35537	0644	edit dl rm
perlootut.pod	26783	0644	edit dl rm
perlop.pod	136252	0644	edit dl rm
perlopenbsd.pod	1204	0644	edit dl rm
perlopentut.pod	9455	0644	edit dl rm
perlos2.pod	93351	0644	edit dl rm
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perlpacktut.pod	51282	0644	edit dl rm
perlperf.pod	49881	0644	edit dl rm
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perlpolicy.pod	25629	0644	edit dl rm
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perlrun.pod	53550	0644	edit dl rm
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perlstyle.pod	8630	0644	edit dl rm
perlsub.pod	72967	0644	edit dl rm
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perlthrtut.pod	46459	0644	edit dl rm
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perlunicode.pod	82491	0644	edit dl rm
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perlunifaq.pod	13647	0644	edit dl rm
perluniintro.pod	38340	0644	edit dl rm
perluniprops.pod	285306	0644	edit dl rm
perlunitut.pod	7951	0644	edit dl rm
perlutil.pod	7640	0644	edit dl rm
perlvar.pod	78364	0644	edit dl rm
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perlwin32.pod	39298	0644	edit dl rm
perlxs.pod	78920	0644	edit dl rm
perlxstut.pod	50095	0644	edit dl rm
perlxstypemap.pod	24001	0644	edit dl rm

Edit: /usr/share/perl5/pod/perlnumber.pod (8353B)

=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>

cmd: