|Perl Language Reference Manual|
by Larry Wall and others
Paperback (6"x9"), 724 pages
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6.1 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
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:
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 to 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 6.2 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 to 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.
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