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database/perl/lib/pods/perlnumber.pod

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+=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>