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1 | =head1 NAME |
2 | ||
3 | perlnumber - semantics of numbers and numeric operations in Perl | |
4 | ||
5 | =head1 SYNOPSIS | |
6 | ||
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7 | $n = 1234; # decimal integer |
8 | $n = 0b1110011; # binary integer | |
9 | $n = 01234; # octal integer | |
10 | $n = 0x1234; # hexadecimal integer | |
11 | $n = 12.34e-56; # exponential notation | |
12 | $n = "-12.34e56"; # number specified as a string | |
13 | $n = "1234"; # number specified as a string | |
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14 | |
15 | =head1 DESCRIPTION | |
16 | ||
17 | This document describes how Perl internally handles numeric values. | |
18 | ||
19 | Perl's operator overloading facility is completely ignored here. Operator | |
20 | overloading allows user-defined behaviors for numbers, such as operations | |
21 | over arbitrarily large integers, floating points numbers with arbitrary | |
22 | precision, operations over "exotic" numbers such as modular arithmetic or | |
055fd3a9 | 23 | p-adic arithmetic, and so on. See L<overload> for details. |
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24 | |
25 | =head1 Storing numbers | |
26 | ||
b38f6a39 | 27 | Perl can internally represent numbers in 3 different ways: as native |
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28 | integers, as native floating point numbers, and as decimal strings. |
29 | Decimal strings may have an exponential notation part, as in C<"12.34e-56">. | |
30 | I<Native> here means "a format supported by the C compiler which was used | |
31 | to build perl". | |
32 | ||
33 | The term "native" does not mean quite as much when we talk about native | |
34 | integers, as it does when native floating point numbers are involved. | |
35 | The only implication of the term "native" on integers is that the limits for | |
36 | the maximal and the minimal supported true integral quantities are close to | |
85add8c2 | 37 | powers of 2. However, "native" floats have a most fundamental |
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38 | restriction: they may represent only those numbers which have a relatively |
39 | "short" representation when converted to a binary fraction. For example, | |
4375e838 | 40 | 0.9 cannot be represented by a native float, since the binary fraction |
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41 | for 0.9 is infinite: |
42 | ||
43 | binary0.1110011001100... | |
44 | ||
45 | with the sequence C<1100> repeating again and again. In addition to this | |
46 | limitation, the exponent of the binary number is also restricted when it | |
47 | is represented as a floating point number. On typical hardware, floating | |
48 | point values can store numbers with up to 53 binary digits, and with binary | |
49 | exponents between -1024 and 1024. In decimal representation this is close | |
50 | to 16 decimal digits and decimal exponents in the range of -304..304. | |
51 | The upshot of all this is that Perl cannot store a number like | |
52 | 12345678901234567 as a floating point number on such architectures without | |
53 | loss of information. | |
54 | ||
b38f6a39 | 55 | Similarly, decimal strings can represent only those numbers which have a |
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56 | finite decimal expansion. Being strings, and thus of arbitrary length, there |
57 | is no practical limit for the exponent or number of decimal digits for these | |
58 | numbers. (But realize that what we are discussing the rules for just the | |
59 | I<storage> of these numbers. The fact that you can store such "large" numbers | |
106325ad | 60 | does not mean that the I<operations> over these numbers will use all |
ac65edd0 | 61 | of the significant digits. |
4a4eefd0 | 62 | See L<"Numeric operators and numeric conversions"> for details.) |
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63 | |
64 | In fact numbers stored in the native integer format may be stored either | |
65 | in the signed native form, or in the unsigned native form. Thus the limits | |
66 | for Perl numbers stored as native integers would typically be -2**31..2**32-1, | |
67 | with appropriate modifications in the case of 64-bit integers. Again, this | |
68 | does not mean that Perl can do operations only over integers in this range: | |
69 | it is possible to store many more integers in floating point format. | |
70 | ||
71 | Summing up, Perl numeric values can store only those numbers which have | |
72 | a finite decimal expansion or a "short" binary expansion. | |
73 | ||
74 | =head1 Numeric operators and numeric conversions | |
75 | ||
76 | As mentioned earlier, Perl can store a number in any one of three formats, | |
77 | but most operators typically understand only one of those formats. When | |
78 | a numeric value is passed as an argument to such an operator, it will be | |
79 | converted to the format understood by the operator. | |
80 | ||
81 | Six such conversions are possible: | |
82 | ||
83 | native integer --> native floating point (*) | |
84 | native integer --> decimal string | |
85 | native floating_point --> native integer (*) | |
86 | native floating_point --> decimal string (*) | |
87 | decimal string --> native integer | |
88 | decimal string --> native floating point (*) | |
89 | ||
90 | These conversions are governed by the following general rules: | |
91 | ||
13a2d996 | 92 | =over 4 |
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93 | |
94 | =item * | |
95 | ||
96 | If the source number can be represented in the target form, that | |
97 | representation is used. | |
98 | ||
99 | =item * | |
100 | ||
101 | If the source number is outside of the limits representable in the target form, | |
102 | a representation of the closest limit is used. (I<Loss of information>) | |
103 | ||
104 | =item * | |
105 | ||
106 | If the source number is between two numbers representable in the target form, | |
107 | a representation of one of these numbers is used. (I<Loss of information>) | |
108 | ||
109 | =item * | |
110 | ||
111 | In C<< native floating point --> native integer >> conversions the magnitude | |
112 | of the result is less than or equal to the magnitude of the source. | |
113 | (I<"Rounding to zero".>) | |
114 | ||
115 | =item * | |
116 | ||
117 | If the C<< decimal string --> native integer >> conversion cannot be done | |
118 | without loss of information, the result is compatible with the conversion | |
119 | sequence C<< decimal_string --> native_floating_point --> native_integer >>. | |
120 | In particular, rounding is strongly biased to 0, though a number like | |
121 | C<"0.99999999999999999999"> has a chance of being rounded to 1. | |
122 | ||
123 | =back | |
124 | ||
125 | B<RESTRICTION>: The conversions marked with C<(*)> above involve steps | |
126 | performed by the C compiler. In particular, bugs/features of the compiler | |
127 | used may lead to breakage of some of the above rules. | |
128 | ||
129 | =head1 Flavors of Perl numeric operations | |
130 | ||
131 | Perl operations which take a numeric argument treat that argument in one | |
132 | of four different ways: they may force it to one of the integer/floating/ | |
133 | string formats, or they may behave differently depending on the format of | |
134 | the operand. Forcing a numeric value to a particular format does not | |
135 | change the number stored in the value. | |
136 | ||
137 | All the operators which need an argument in the integer format treat the | |
138 | argument as in modular arithmetic, e.g., C<mod 2**32> on a 32-bit | |
139 | architecture. C<sprintf "%u", -1> therefore provides the same result as | |
140 | C<sprintf "%u", ~0>. | |
141 | ||
13a2d996 | 142 | =over 4 |
ac65edd0 | 143 | |
78594626 | 144 | =item Arithmetic operators |
ac65edd0 | 145 | |
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146 | The binary operators C<+> C<-> C<*> C</> C<%> C<==> C<!=> C<E<gt>> C<E<lt>> |
147 | C<E<gt>=> C<E<lt>=> and the unary operators C<-> C<abs> and C<--> will | |
148 | attempt to convert arguments to integers. If both conversions are possible | |
149 | without loss of precision, and the operation can be performed without | |
150 | loss of precision then the integer result is used. Otherwise arguments are | |
151 | converted to floating point format and the floating point result is used. | |
152 | The caching of conversions (as described above) means that the integer | |
153 | conversion does not throw away fractional parts on floating point numbers. | |
ac65edd0 | 154 | |
78594626 | 155 | =item ++ |
ac65edd0 | 156 | |
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157 | C<++> behaves as the other operators above, except that if it is a string |
158 | matching the format C</^[a-zA-Z]*[0-9]*\z/> the string increment described | |
159 | in L<perlop> is used. | |
ac65edd0 | 160 | |
78594626 | 161 | =item Arithmetic operators during C<use integer> |
ac65edd0 | 162 | |
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163 | In scopes where C<use integer;> is in force, nearly all the operators listed |
164 | above will force their argument(s) into integer format, and return an integer | |
165 | result. The exceptions, C<abs>, C<++> and C<-->, do not change their | |
166 | behavior with C<use integer;> | |
ac65edd0 | 167 | |
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168 | =item Other mathematical operators |
169 | ||
170 | Operators such as C<**>, C<sin> and C<exp> force arguments to floating point | |
171 | format. | |
172 | ||
173 | =item Bitwise operators | |
174 | ||
175 | Arguments are forced into the integer format if not strings. | |
176 | ||
177 | =item Bitwise operators during C<use integer> | |
178 | ||
179 | forces arguments to integer format. Also shift operations internally use | |
180 | signed integers rather than the default unsigned. | |
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181 | |
182 | =item Operators which expect an integer | |
183 | ||
184 | force the argument into the integer format. This is applicable | |
185 | to the third and fourth arguments of C<sysread>, for example. | |
186 | ||
187 | =item Operators which expect a string | |
188 | ||
189 | force the argument into the string format. For example, this is | |
190 | applicable to C<printf "%s", $value>. | |
191 | ||
192 | =back | |
193 | ||
194 | Though forcing an argument into a particular form does not change the | |
195 | stored number, Perl remembers the result of such conversions. In | |
196 | particular, though the first such conversion may be time-consuming, | |
197 | repeated operations will not need to redo the conversion. | |
198 | ||
199 | =head1 AUTHOR | |
200 | ||
201 | Ilya Zakharevich C<ilya@math.ohio-state.edu> | |
202 | ||
203 | Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com> | |
204 | ||
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205 | Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org> |
206 | ||
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207 | =head1 SEE ALSO |
208 | ||
78594626 | 209 | L<overload>, L<perlop> |