MirOS Manual: perlnumber(1)


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 for-
     mat 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 fundamen-
     tal 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 infin-
     ite:

       binary0.1110011001100...

     with the sequence 1100 repeating again and again.  In addi-
     tion 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

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     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 archi-
     tectures 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:

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

     +   If the source number is outside of the limits

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         representable in the target form, a representation of
         the closest limit is used.  (Loss of information)

     +   If the source number is between two numbers represent-
         able 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 zero".)

     +   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 for-
     mat treat the argument as in modular arithmetic, e.g., "mod
     2**32" on a 32-bit architecture.  "sprintf "%u", -1" there-
     fore 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

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         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 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 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.

     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 conver-
     sion 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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