### Интерактивная система просмотра системных руководств (man-ов)

 Тема Набор Категория Solaris man FreeBSD man Разные man Русские man Linux man POSIX man All 1 2 3 4 5 6 7 8 9 [Cписок руководств | Печать]
perlnumber ()
• >> perlnumber (1) ( Solaris man: Команды и прикладные программы пользовательского уровня )
• perlnumber (1) ( Разные man: Команды и прикладные программы пользовательского уровня )
• ```

```

## 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
\$n = v49.50.51.52;          # number specified as a string, which in
# turn is specified in terms of numbers :-)

DESCRIPTION     This document describes how Perl internally handles numeric
values.

for numbers, such as operations over arbitrarily large
integers, floating points numbers with arbitrary precision,
operations over "exotic" numbers such as modular arithmetic
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
respresented 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 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
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 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

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@math.ohio-state.edu'

<gsar@ActiveState.com>

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