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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 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 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 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
perl v5.26.3                      2018-03-23                     PERLNUMBER(1)