phpman > perldoc > number(n)

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
    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:

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

    *   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*)

    *   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*)

    *   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".*)

    *   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 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 AT math.edu"

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

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

SEE ALSO
    overload, perlop