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perlnumber (1)
  • >> perlnumber (1) ( Solaris man: Команды и прикладные программы пользовательского уровня )
  • perlnumber (1) ( Разные man: Команды и прикладные программы пользовательского уровня )


         perlnumber - semantics of numbers and numeric operations in


             $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 :-)


         This document describes how Perl internally handles numeric
         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 the overload 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 exponential
         notation part, as in `"12.34e-56"'.  Native here means "a
         format supported by the C compiler which was used to build
         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
         respresented 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 that the operations
         over these numbers will use all of the significant 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 numbers
         which have a finite decimal expansion or a "short" binary

    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
         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

         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
             `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.


         Ilya Zakharevich `'
         Editorial adjustments by Gurusamy Sarathy


         the overload manpage

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