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NAME    [Toc]    [Back]

       perlnumber - semantics of numbers and numeric operations
       in Perl

SYNOPSIS    [Toc]    [Back]

           $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

DESCRIPTION    [Toc]    [Back]

       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 overload
       for details.

Storing numbers    [Toc]    [Back]

       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 "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 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:


       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 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 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 significant
 digits.  See "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.

Numeric operators and numeric conversions    [Toc]    [Back]

       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

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

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

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

       o   In "native floating point --> native integer" conversions
 the magnitude of the result is less than or
           equal to the magnitude of the source.  ("Rounding to

       o   If the "decimal string --> native integer" conversion
           cannot be done without loss of information, the result
           is compatible with the conversion sequence "decimal_string
 --> native_floating_point --> native_integer".
  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    [Toc]    [Back]

       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
           The binary operators "+" "-" "*" "/" "%" "==" "!=" ">"
           "<" ">=" "<=" and the unary operators "-" "abs" and
           "--" 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.

       ++  "++" behaves as the other operators above, except that
           if it is a string matching the format
           "/^[a-zA-Z]*[0-9]*" 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 argument(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 arguments
 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 operations
 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 "sysread",
 for example.

       Operators which expect a string
           force the argument into the string format.  For example,
 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    [Toc]    [Back]

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

       Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>

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

SEE ALSO    [Toc]    [Back]

       overload, perlop

perl v5.8.5                 2002-11-06                          4
[ Back ]
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