perlnumber - semantics of numbers and numeric operations
in Perl
$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
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.
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 [Toc] [Back] 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 [Toc] [Back] 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]*" 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.
Ilya Zakharevich "[email protected]"
Editorial adjustments by Gurusamy Sarathy <[email protected]>
Updates for 5.8.0 by Nicholas Clark <[email protected]>
overload, perlop
perl v5.8.5 2002-11-06 4 [ Back ] |
