186 lines
7.1 KiB
Plaintext
186 lines
7.1 KiB
Plaintext
=head1 NAME
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perlnumber - semantics of numbers and numeric operations in Perl
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=head1 SYNOPSIS
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$n = 1234; # decimal integer
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$n = 0b1110011; # binary integer
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$n = 01234; # octal integer
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$n = 0x1234; # hexadecimal integer
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$n = 12.34e-56; # exponential notation
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$n = "-12.34e56"; # number specified as a string
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$n = "1234"; # number specified as a string
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$n = v49.50.51.52; # number specified as a string, which in
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# turn is specified in terms of numbers :-)
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=head1 DESCRIPTION
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This document describes how Perl internally handles numeric values.
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Perl's operator overloading facility is completely ignored here. Operator
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overloading allows user-defined behaviors for numbers, such as operations
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over arbitrarily large integers, floating points numbers with arbitrary
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precision, operations over "exotic" numbers such as modular arithmetic or
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p-adic arithmetic, and so on. See L<overload> for details.
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=head1 Storing numbers
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Perl can internally represent numbers in 3 different ways: as native
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integers, as native floating point numbers, and as decimal strings.
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Decimal strings may have an exponential notation part, as in C<"12.34e-56">.
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I<Native> here means "a format supported by the C compiler which was used
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to build perl".
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The term "native" does not mean quite as much when we talk about native
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integers, as it does when native floating point numbers are involved.
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The only implication of the term "native" on integers is that the limits for
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the maximal and the minimal supported true integral quantities are close to
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powers of 2. However, "native" floats have a most fundamental
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restriction: they may represent only those numbers which have a relatively
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"short" representation when converted to a binary fraction. For example,
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0.9 cannot be respresented by a native float, since the binary fraction
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for 0.9 is infinite:
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binary0.1110011001100...
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with the sequence C<1100> repeating again and again. In addition to this
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limitation, the exponent of the binary number is also restricted when it
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is represented as a floating point number. On typical hardware, floating
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point values can store numbers with up to 53 binary digits, and with binary
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exponents between -1024 and 1024. In decimal representation this is close
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to 16 decimal digits and decimal exponents in the range of -304..304.
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The upshot of all this is that Perl cannot store a number like
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12345678901234567 as a floating point number on such architectures without
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loss of information.
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Similarly, decimal strings can represent only those numbers which have a
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finite decimal expansion. Being strings, and thus of arbitrary length, there
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is no practical limit for the exponent or number of decimal digits for these
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numbers. (But realize that what we are discussing the rules for just the
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I<storage> of these numbers. The fact that you can store such "large" numbers
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does not mean that that the I<operations> over these numbers will use all
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of the significant digits.
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See L<"Numeric operators and numeric conversions"> for details.)
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In fact numbers stored in the native integer format may be stored either
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in the signed native form, or in the unsigned native form. Thus the limits
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for Perl numbers stored as native integers would typically be -2**31..2**32-1,
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with appropriate modifications in the case of 64-bit integers. Again, this
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does not mean that Perl can do operations only over integers in this range:
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it is possible to store many more integers in floating point format.
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Summing up, Perl numeric values can store only those numbers which have
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a finite decimal expansion or a "short" binary expansion.
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=head1 Numeric operators and numeric conversions
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As mentioned earlier, Perl can store a number in any one of three formats,
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but most operators typically understand only one of those formats. When
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a numeric value is passed as an argument to such an operator, it will be
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converted to the format understood by the operator.
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Six such conversions are possible:
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native integer --> native floating point (*)
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native integer --> decimal string
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native floating_point --> native integer (*)
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native floating_point --> decimal string (*)
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decimal string --> native integer
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decimal string --> native floating point (*)
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These conversions are governed by the following general rules:
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=over
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=item *
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If the source number can be represented in the target form, that
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representation is used.
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=item *
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If the source number is outside of the limits representable in the target form,
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a representation of the closest limit is used. (I<Loss of information>)
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=item *
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If the source number is between two numbers representable in the target form,
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a representation of one of these numbers is used. (I<Loss of information>)
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=item *
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In C<< native floating point --> native integer >> conversions the magnitude
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of the result is less than or equal to the magnitude of the source.
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(I<"Rounding to zero".>)
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=item *
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If the C<< decimal string --> native integer >> conversion cannot be done
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without loss of information, the result is compatible with the conversion
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sequence C<< decimal_string --> native_floating_point --> native_integer >>.
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In particular, rounding is strongly biased to 0, though a number like
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C<"0.99999999999999999999"> has a chance of being rounded to 1.
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=back
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B<RESTRICTION>: The conversions marked with C<(*)> above involve steps
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performed by the C compiler. In particular, bugs/features of the compiler
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used may lead to breakage of some of the above rules.
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=head1 Flavors of Perl numeric operations
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Perl operations which take a numeric argument treat that argument in one
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of four different ways: they may force it to one of the integer/floating/
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string formats, or they may behave differently depending on the format of
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the operand. Forcing a numeric value to a particular format does not
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change the number stored in the value.
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All the operators which need an argument in the integer format treat the
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argument as in modular arithmetic, e.g., C<mod 2**32> on a 32-bit
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architecture. C<sprintf "%u", -1> therefore provides the same result as
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C<sprintf "%u", ~0>.
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=over
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=item Arithmetic operators except, C<no integer>
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force the argument into the floating point format.
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=item Arithmetic operators except, C<use integer>
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=item Bitwise operators, C<no integer>
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force the argument into the integer format if it is not a string.
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=item Bitwise operators, C<use integer>
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force the argument into the integer format
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=item Operators which expect an integer
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force the argument into the integer format. This is applicable
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to the third and fourth arguments of C<sysread>, for example.
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=item Operators which expect a string
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force the argument into the string format. For example, this is
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applicable to C<printf "%s", $value>.
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=back
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Though forcing an argument into a particular form does not change the
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stored number, Perl remembers the result of such conversions. In
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particular, though the first such conversion may be time-consuming,
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repeated operations will not need to redo the conversion.
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=head1 AUTHOR
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Ilya Zakharevich C<ilya@math.ohio-state.edu>
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Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
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=head1 SEE ALSO
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L<overload>
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