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
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.
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:
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.
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:
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.
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".
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.
Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
Updates for 5.8.0 by Nicholas Clark <firstname.lastname@example.org>
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