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           $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


       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 overload
       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:


       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 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

       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

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

       ·   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)

       ·   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)

       ·   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

       ·   If the "decimal string --> native integer" conversion
           cannot be done without loss of information, the result

       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 pre­
           cision, 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 argu­
           ment(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 argu­
           ments to floating point format.

       Bitwise operators
           Arguments are forced into the integer format if not

       Bitwise operators during "use integer"
           forces arguments to integer format. Also shift opera­
           tions 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 "sys­
           read", for example.

       Editorial adjustments by Gurusamy Sarathy <gsar@ActiveS­

       Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org>


       overload, perlop

perl v5.8.1                 2003-09-02              PERLNUMBER(1)

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