1PERLNUMBER(1)          Perl Programmers Reference Guide          PERLNUMBER(1)
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NAME

6       perlnumber - semantics of numbers and numeric operations in Perl
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SYNOPSIS

9           $n = 1234;              # decimal integer
10           $n = 0b1110011;         # binary integer
11           $n = 01234;             # octal integer
12           $n = 0x1234;            # hexadecimal integer
13           $n = 12.34e-56;         # exponential notation
14           $n = "-12.34e56";       # number specified as a string
15           $n = "1234";            # number specified as a string
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DESCRIPTION

18       This document describes how Perl internally handles numeric values.
19
20       Perl's operator overloading facility is completely ignored here.
21       Operator overloading allows user-defined behaviors for numbers, such as
22       operations over arbitrarily large integers, floating points numbers
23       with arbitrary precision, operations over "exotic" numbers such as
24       modular arithmetic or p-adic arithmetic, and so on.  See overload for
25       details.
26

Storing numbers

28       Perl can internally represent numbers in 3 different ways: as native
29       integers, as native floating point numbers, and as decimal strings.
30       Decimal strings may have an exponential notation part, as in
31       "12.34e-56".  Native here means "a format supported by the C compiler
32       which was used to build perl".
33
34       The term "native" does not mean quite as much when we talk about native
35       integers, as it does when native floating point numbers are involved.
36       The only implication of the term "native" on integers is that the
37       limits for the maximal and the minimal supported true integral
38       quantities are close to powers of 2.  However, "native" floats have a
39       most fundamental restriction: they may represent only those numbers
40       which have a relatively "short" representation when converted to a
41       binary fraction.  For example, 0.9 cannot be represented by a native
42       float, since the binary fraction for 0.9 is infinite:
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44         binary0.1110011001100...
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46       with the sequence 1100 repeating again and again.  In addition to this
47       limitation,  the exponent of the binary number is also restricted when
48       it is represented as a floating point number.  On typical hardware,
49       floating point values can store numbers with up to 53 binary digits,
50       and with binary exponents between -1024 and 1024.  In decimal
51       representation this is close to 16 decimal digits and decimal exponents
52       in the range of -304..304.  The upshot of all this is that Perl cannot
53       store a number like 12345678901234567 as a floating point number on
54       such architectures without loss of information.
55
56       Similarly, decimal strings can represent only those numbers which have
57       a finite decimal expansion.  Being strings, and thus of arbitrary
58       length, there is no practical limit for the exponent or number of
59       decimal digits for these numbers.  (But realize that what we are
60       discussing the rules for just the storage of these numbers.  The fact
61       that you can store such "large" numbers does not mean that the
62       operations over these numbers will use all of the significant digits.
63       See "Numeric operators and numeric conversions" for details.)
64
65       In fact numbers stored in the native integer format may be stored
66       either in the signed native form, or in the unsigned native form.  Thus
67       the limits for Perl numbers stored as native integers would typically
68       be -2**31..2**32-1, with appropriate modifications in the case of
69       64-bit integers.  Again, this does not mean that Perl can do operations
70       only over integers in this range: it is possible to store many more
71       integers in floating point format.
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73       Summing up, Perl numeric values can store only those numbers which have
74       a finite decimal expansion or a "short" binary expansion.
75

Numeric operators and numeric conversions

77       As mentioned earlier, Perl can store a number in any one of three
78       formats, but most operators typically understand only one of those
79       formats.  When a numeric value is passed as an argument to such an
80       operator, it will be converted to the format understood by the
81       operator.
82
83       Six such conversions are possible:
84
85         native integer        --> native floating point       (*)
86         native integer        --> decimal string
87         native floating_point --> native integer              (*)
88         native floating_point --> decimal string              (*)
89         decimal string        --> native integer
90         decimal string        --> native floating point       (*)
91
92       These conversions are governed by the following general rules:
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94       •   If the source number can be represented in the target form, that
95           representation is used.
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97       •   If the source number is outside of the limits representable in the
98           target form, a representation of the closest limit is used.  (Loss
99           of information)
100
101       •   If the source number is between two numbers representable in the
102           target form, a representation of one of these numbers is used.
103           (Loss of information)
104
105       •   In "native floating point --> native integer" conversions the
106           magnitude of the result is less than or equal to the magnitude of
107           the source.  ("Rounding to zero".)
108
109       •   If the "decimal string --> native integer" conversion cannot be
110           done without loss of information, the result is compatible with the
111           conversion sequence "decimal_string --> native_floating_point -->
112           native_integer".  In particular, rounding is strongly biased to 0,
113           though a number like "0.99999999999999999999" has a chance of being
114           rounded to 1.
115
116       RESTRICTION: The conversions marked with "(*)" above involve steps
117       performed by the C compiler.  In particular, bugs/features of the
118       compiler used may lead to breakage of some of the above rules.
119

Flavors of Perl numeric operations

121       Perl operations which take a numeric argument treat that argument in
122       one of four different ways: they may force it to one of the integer,
123       floating, or string formats; or they may behave differently depending
124       on the format of the operand.  Forcing a numeric value to a particular
125       format does not change the number stored in the value.
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127       All the operators which need an argument in the integer format treat
128       the argument as in modular arithmetic, e.g., "mod 2**32" on a 32-bit
129       architecture.  "sprintf "%u", -1" therefore provides the same result as
130       "sprintf "%u", ~0".
131
132       Arithmetic operators
133           The binary operators "+" "-" "*" "/" "%" "==" "!=" ">" "<" ">="
134           "<=" and the unary operators "-" "abs" and "--" will attempt to
135           convert arguments to integers.  If both conversions are possible
136           without loss of precision, and the operation can be performed
137           without loss of precision then the integer result is used.
138           Otherwise arguments are converted to floating point format and the
139           floating point result is used.  The caching of conversions (as
140           described above) means that the integer conversion does not throw
141           away fractional parts on floating point numbers.
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143       ++  "++" behaves as the other operators above, except that if it is a
144           string matching the format "/^[a-zA-Z]*[0-9]*\z/" the string
145           increment described in perlop is used.
146
147       Arithmetic operators during "use integer"
148           In scopes where "use integer;" is in force, nearly all the
149           operators listed above will force their argument(s) into integer
150           format, and return an integer result.  The exceptions, "abs", "++"
151           and "--", do not change their behavior with "use integer;"
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153       Other mathematical operators
154           Operators such as "**", "sin" and "exp" force arguments to floating
155           point format.
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157       Bitwise operators
158           Arguments are forced into the integer format if not strings.
159
160       Bitwise operators during "use integer"
161           forces arguments to integer format. Also shift operations
162           internally use signed integers rather than the default unsigned.
163
164       Operators which expect an integer
165           force the argument into the integer format.  This is applicable to
166           the third and fourth arguments of "sysread", for example.
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168       Operators which expect a string
169           force the argument into the string format.  For example, this is
170           applicable to "printf "%s", $value".
171
172       Though forcing an argument into a particular form does not change the
173       stored number, Perl remembers the result of such conversions.  In
174       particular, though the first such conversion may be time-consuming,
175       repeated operations will not need to redo the conversion.
176

AUTHOR

178       Ilya Zakharevich "ilya@math.ohio-state.edu"
179
180       Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com>
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182       Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org>
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SEE ALSO

185       overload, perlop
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189perl v5.36.0                      2022-08-30                     PERLNUMBER(1)
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