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## perlnumber(1) - perlnumber - semantics of numbers and numeric operations in Perl - man 1 perlnumber

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```PERLNUMBER(1)          Perl Programmers Reference Guide          PERLNUMBER(1)

NAME
perlnumber - semantics of numbers and numeric operations in(1,8) 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(3,n)
\$n = "1234";            # number specified as a string(3,n)

DESCRIPTION
This document describes how Perl internally handles numeric values.

Perl's operator overloading facility is completely ignored here.  Oper-
ator 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 mod-
ular arithmetic or p-adic arithmetic, and so on.  See overload for
details.

Storing numbers
Perl can internally represent numbers in(1,8) 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(1,8)
"12.34e-56".  Native here means "a format supported by the C compiler
which was used to build perl".

The term(5,7) "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(5,7) "native" on integers is that the lim-
its for the maximal and the minimal supported true integral quantities
are close(2,7,n) to powers of 2.  However, "native" floats have a most funda-
mental 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 represen-
tation this is close(2,7,n) to 16 decimal digits and decimal exponents in(1,8) 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 deci-
mal 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(1,8) the native integer format may be stored
either in(1,8) the signed native form, or in(1,8) 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(1,8) the case of
64-bit integers.  Again, this does not mean that Perl can do operations
only over integers in(1,8) this range: it is possible to store many more
integers in(1,8) 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(1,8) any one of three for-
mats, but most operators typically understand only one of those for-
mats.  When a numeric value is passed as an argument to such an opera-
tor, 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(3,n)
native floating_point --> native integer              (*)
native floating_point --> decimal string(3,n)              (*)
decimal string(3,n)        --> native integer
decimal string(3,n)        --> native floating point       (*)

These conversions are governed by the following general rules:

If the source number can be represented in(1,8) the target form, that
representation is used.

If the source number is outside of the limits representable in(1,8) the
target form, a representation of the closest limit is used.  (Loss
of information)

If the source number is between two numbers representable in(1,8) the
target form, a representation of one of these numbers is used.
(Loss of information)

In "native floating point --> native integer" conversions the mag-
nitude of the result is less(1,3) than or equal to the magnitude of the
source.  ("Rounding to zero".)

If the "decimal string(3,n) --> 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 per-
formed 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(1,8)
one of four different ways: they may force it to one of the inte-
ger/floating/ string(3,n) 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(1,8) the value.

All the operators which need an argument in(1,8) the integer format treat
the argument as in(1,8) 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 with-
out 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 frac-
tional parts on floating point numbers.

++  "++" behaves as the other operators above, except that if(3,n) it is a
string(3,n) matching the format "/^[a-zA-Z]*[0-9]*\z/" the string(3,n) incre-
ment described in(1,8) perlop is used.

Arithmetic operators during "use integer"
In scopes where "use integer;" is in(1,8) force, nearly all the opera-
tors 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(3,n) not strings.

Bitwise operators during "use integer"
forces arguments to integer format. Also shift operations inter-
nally 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(3,n)
force the argument into the string(3,n) format.  For example, this is
applicable to "printf(1,3,1 builtins) "%s", \$value".

Though forcing an argument into a particular form does not change the
stored number, Perl remembers the result of such conversions.  In par-
ticular, 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

perl v5.8.5                       2004-04-23                     PERLNUMBER(1)
```