


PERLNUMBER(1)    Perl Programmers Reference Guide   PERLNUMBER(1)


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


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 preci-
       sion, operations over "exotic" numbers such as modular
       arithmetic or p-adic arithmetic, and so on.  See the over-
       load manpage 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 exponen-
       tial 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 maxi-
       mal 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" representa-
       tion 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 "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



2001-05-24                 perl v5.6.1                          1





PERLNUMBER(1)    Perl Programmers Reference Guide   PERLNUMBER(1)


       point values can store numbers with up to 53 binary dig-
       its, 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 num-
       bers which have a finite decimal expansion.  Being
       strings, and thus of arbitrary length, there is no practi-
       cal 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 sig-
       nificant digits.  See the section on "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 num-
       bers 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:

       o   If the source number can be represented in the target
           form, that representation is used.



2001-05-24                 perl v5.6.1                          2





PERLNUMBER(1)    Perl Programmers Reference Guide   PERLNUMBER(1)


       o   If the source number is outside of the limits repre-
           sentable in the target form, a representation of the
           closest limit is used.  (Loss of information)

       o   If the source number is between two numbers repre-
           sentable in the target form, a representation of one
           of these numbers is used.  (Loss of information)

       o   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".)

       o   If the "decimal string --> native integer" conversion
           cannot be done without loss of information, the result
           is compatible with the conversion sequence "deci-
           mal_string --> native_floating_point --> native_inte-
           ger".  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
       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 except, ""no integer""
           force the argument into the floating point format.

       Arithmetic operators except, ""use integer""
       Bitwise operators, ""no integer""
           force the argument into the integer format if it is
           not a string.

       Bitwise operators, ""use integer""
           force the argument into the integer format

       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.



2001-05-24                 perl v5.6.1                          3





PERLNUMBER(1)    Perl Programmers Reference Guide   PERLNUMBER(1)


       Operators which expect a string
           force the argument into the string format.  For exam-
           ple, 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.

AUTHOR
       Ilya Zakharevich "ilya@math.ohio-state.edu"

       Editorial adjustments by Gurusamy Sarathy <gsar@ActiveS-
       tate.com>

SEE ALSO
       the overload manpage







































2001-05-24                 perl v5.6.1                          4


