


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

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
       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
       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:

         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
       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



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       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
       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.

       o   If the source number is outside of the limits
           representable in the target form, a representation of



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           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 zero".)

       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
       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]*\z/" the string increment described



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           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
           strings.

       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
       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
       overload, perlop










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