1*0Sstevel@tonic-gate=head1 NAME 2*0Sstevel@tonic-gate 3*0Sstevel@tonic-gateperlnumber - semantics of numbers and numeric operations in Perl 4*0Sstevel@tonic-gate 5*0Sstevel@tonic-gate=head1 SYNOPSIS 6*0Sstevel@tonic-gate 7*0Sstevel@tonic-gate $n = 1234; # decimal integer 8*0Sstevel@tonic-gate $n = 0b1110011; # binary integer 9*0Sstevel@tonic-gate $n = 01234; # octal integer 10*0Sstevel@tonic-gate $n = 0x1234; # hexadecimal integer 11*0Sstevel@tonic-gate $n = 12.34e-56; # exponential notation 12*0Sstevel@tonic-gate $n = "-12.34e56"; # number specified as a string 13*0Sstevel@tonic-gate $n = "1234"; # number specified as a string 14*0Sstevel@tonic-gate 15*0Sstevel@tonic-gate=head1 DESCRIPTION 16*0Sstevel@tonic-gate 17*0Sstevel@tonic-gateThis document describes how Perl internally handles numeric values. 18*0Sstevel@tonic-gate 19*0Sstevel@tonic-gatePerl's operator overloading facility is completely ignored here. Operator 20*0Sstevel@tonic-gateoverloading allows user-defined behaviors for numbers, such as operations 21*0Sstevel@tonic-gateover arbitrarily large integers, floating points numbers with arbitrary 22*0Sstevel@tonic-gateprecision, operations over "exotic" numbers such as modular arithmetic or 23*0Sstevel@tonic-gatep-adic arithmetic, and so on. See L<overload> for details. 24*0Sstevel@tonic-gate 25*0Sstevel@tonic-gate=head1 Storing numbers 26*0Sstevel@tonic-gate 27*0Sstevel@tonic-gatePerl can internally represent numbers in 3 different ways: as native 28*0Sstevel@tonic-gateintegers, as native floating point numbers, and as decimal strings. 29*0Sstevel@tonic-gateDecimal strings may have an exponential notation part, as in C<"12.34e-56">. 30*0Sstevel@tonic-gateI<Native> here means "a format supported by the C compiler which was used 31*0Sstevel@tonic-gateto build perl". 32*0Sstevel@tonic-gate 33*0Sstevel@tonic-gateThe term "native" does not mean quite as much when we talk about native 34*0Sstevel@tonic-gateintegers, as it does when native floating point numbers are involved. 35*0Sstevel@tonic-gateThe only implication of the term "native" on integers is that the limits for 36*0Sstevel@tonic-gatethe maximal and the minimal supported true integral quantities are close to 37*0Sstevel@tonic-gatepowers of 2. However, "native" floats have a most fundamental 38*0Sstevel@tonic-gaterestriction: they may represent only those numbers which have a relatively 39*0Sstevel@tonic-gate"short" representation when converted to a binary fraction. For example, 40*0Sstevel@tonic-gate0.9 cannot be represented by a native float, since the binary fraction 41*0Sstevel@tonic-gatefor 0.9 is infinite: 42*0Sstevel@tonic-gate 43*0Sstevel@tonic-gate binary0.1110011001100... 44*0Sstevel@tonic-gate 45*0Sstevel@tonic-gatewith the sequence C<1100> repeating again and again. In addition to this 46*0Sstevel@tonic-gatelimitation, the exponent of the binary number is also restricted when it 47*0Sstevel@tonic-gateis represented as a floating point number. On typical hardware, floating 48*0Sstevel@tonic-gatepoint values can store numbers with up to 53 binary digits, and with binary 49*0Sstevel@tonic-gateexponents between -1024 and 1024. In decimal representation this is close 50*0Sstevel@tonic-gateto 16 decimal digits and decimal exponents in the range of -304..304. 51*0Sstevel@tonic-gateThe upshot of all this is that Perl cannot store a number like 52*0Sstevel@tonic-gate12345678901234567 as a floating point number on such architectures without 53*0Sstevel@tonic-gateloss of information. 54*0Sstevel@tonic-gate 55*0Sstevel@tonic-gateSimilarly, decimal strings can represent only those numbers which have a 56*0Sstevel@tonic-gatefinite decimal expansion. Being strings, and thus of arbitrary length, there 57*0Sstevel@tonic-gateis no practical limit for the exponent or number of decimal digits for these 58*0Sstevel@tonic-gatenumbers. (But realize that what we are discussing the rules for just the 59*0Sstevel@tonic-gateI<storage> of these numbers. The fact that you can store such "large" numbers 60*0Sstevel@tonic-gatedoes not mean that the I<operations> over these numbers will use all 61*0Sstevel@tonic-gateof the significant digits. 62*0Sstevel@tonic-gateSee L<"Numeric operators and numeric conversions"> for details.) 63*0Sstevel@tonic-gate 64*0Sstevel@tonic-gateIn fact numbers stored in the native integer format may be stored either 65*0Sstevel@tonic-gatein the signed native form, or in the unsigned native form. Thus the limits 66*0Sstevel@tonic-gatefor Perl numbers stored as native integers would typically be -2**31..2**32-1, 67*0Sstevel@tonic-gatewith appropriate modifications in the case of 64-bit integers. Again, this 68*0Sstevel@tonic-gatedoes not mean that Perl can do operations only over integers in this range: 69*0Sstevel@tonic-gateit is possible to store many more integers in floating point format. 70*0Sstevel@tonic-gate 71*0Sstevel@tonic-gateSumming up, Perl numeric values can store only those numbers which have 72*0Sstevel@tonic-gatea finite decimal expansion or a "short" binary expansion. 73*0Sstevel@tonic-gate 74*0Sstevel@tonic-gate=head1 Numeric operators and numeric conversions 75*0Sstevel@tonic-gate 76*0Sstevel@tonic-gateAs mentioned earlier, Perl can store a number in any one of three formats, 77*0Sstevel@tonic-gatebut most operators typically understand only one of those formats. When 78*0Sstevel@tonic-gatea numeric value is passed as an argument to such an operator, it will be 79*0Sstevel@tonic-gateconverted to the format understood by the operator. 80*0Sstevel@tonic-gate 81*0Sstevel@tonic-gateSix such conversions are possible: 82*0Sstevel@tonic-gate 83*0Sstevel@tonic-gate native integer --> native floating point (*) 84*0Sstevel@tonic-gate native integer --> decimal string 85*0Sstevel@tonic-gate native floating_point --> native integer (*) 86*0Sstevel@tonic-gate native floating_point --> decimal string (*) 87*0Sstevel@tonic-gate decimal string --> native integer 88*0Sstevel@tonic-gate decimal string --> native floating point (*) 89*0Sstevel@tonic-gate 90*0Sstevel@tonic-gateThese conversions are governed by the following general rules: 91*0Sstevel@tonic-gate 92*0Sstevel@tonic-gate=over 4 93*0Sstevel@tonic-gate 94*0Sstevel@tonic-gate=item * 95*0Sstevel@tonic-gate 96*0Sstevel@tonic-gateIf the source number can be represented in the target form, that 97*0Sstevel@tonic-gaterepresentation is used. 98*0Sstevel@tonic-gate 99*0Sstevel@tonic-gate=item * 100*0Sstevel@tonic-gate 101*0Sstevel@tonic-gateIf the source number is outside of the limits representable in the target form, 102*0Sstevel@tonic-gatea representation of the closest limit is used. (I<Loss of information>) 103*0Sstevel@tonic-gate 104*0Sstevel@tonic-gate=item * 105*0Sstevel@tonic-gate 106*0Sstevel@tonic-gateIf the source number is between two numbers representable in the target form, 107*0Sstevel@tonic-gatea representation of one of these numbers is used. (I<Loss of information>) 108*0Sstevel@tonic-gate 109*0Sstevel@tonic-gate=item * 110*0Sstevel@tonic-gate 111*0Sstevel@tonic-gateIn C<< native floating point --> native integer >> conversions the magnitude 112*0Sstevel@tonic-gateof the result is less than or equal to the magnitude of the source. 113*0Sstevel@tonic-gate(I<"Rounding to zero".>) 114*0Sstevel@tonic-gate 115*0Sstevel@tonic-gate=item * 116*0Sstevel@tonic-gate 117*0Sstevel@tonic-gateIf the C<< decimal string --> native integer >> conversion cannot be done 118*0Sstevel@tonic-gatewithout loss of information, the result is compatible with the conversion 119*0Sstevel@tonic-gatesequence C<< decimal_string --> native_floating_point --> native_integer >>. 120*0Sstevel@tonic-gateIn particular, rounding is strongly biased to 0, though a number like 121*0Sstevel@tonic-gateC<"0.99999999999999999999"> has a chance of being rounded to 1. 122*0Sstevel@tonic-gate 123*0Sstevel@tonic-gate=back 124*0Sstevel@tonic-gate 125*0Sstevel@tonic-gateB<RESTRICTION>: The conversions marked with C<(*)> above involve steps 126*0Sstevel@tonic-gateperformed by the C compiler. In particular, bugs/features of the compiler 127*0Sstevel@tonic-gateused may lead to breakage of some of the above rules. 128*0Sstevel@tonic-gate 129*0Sstevel@tonic-gate=head1 Flavors of Perl numeric operations 130*0Sstevel@tonic-gate 131*0Sstevel@tonic-gatePerl operations which take a numeric argument treat that argument in one 132*0Sstevel@tonic-gateof four different ways: they may force it to one of the integer/floating/ 133*0Sstevel@tonic-gatestring formats, or they may behave differently depending on the format of 134*0Sstevel@tonic-gatethe operand. Forcing a numeric value to a particular format does not 135*0Sstevel@tonic-gatechange the number stored in the value. 136*0Sstevel@tonic-gate 137*0Sstevel@tonic-gateAll the operators which need an argument in the integer format treat the 138*0Sstevel@tonic-gateargument as in modular arithmetic, e.g., C<mod 2**32> on a 32-bit 139*0Sstevel@tonic-gatearchitecture. C<sprintf "%u", -1> therefore provides the same result as 140*0Sstevel@tonic-gateC<sprintf "%u", ~0>. 141*0Sstevel@tonic-gate 142*0Sstevel@tonic-gate=over 4 143*0Sstevel@tonic-gate 144*0Sstevel@tonic-gate=item Arithmetic operators 145*0Sstevel@tonic-gate 146*0Sstevel@tonic-gateThe binary operators C<+> C<-> C<*> C</> C<%> C<==> C<!=> C<E<gt>> C<E<lt>> 147*0Sstevel@tonic-gateC<E<gt>=> C<E<lt>=> and the unary operators C<-> C<abs> and C<--> will 148*0Sstevel@tonic-gateattempt to convert arguments to integers. If both conversions are possible 149*0Sstevel@tonic-gatewithout loss of precision, and the operation can be performed without 150*0Sstevel@tonic-gateloss of precision then the integer result is used. Otherwise arguments are 151*0Sstevel@tonic-gateconverted to floating point format and the floating point result is used. 152*0Sstevel@tonic-gateThe caching of conversions (as described above) means that the integer 153*0Sstevel@tonic-gateconversion does not throw away fractional parts on floating point numbers. 154*0Sstevel@tonic-gate 155*0Sstevel@tonic-gate=item ++ 156*0Sstevel@tonic-gate 157*0Sstevel@tonic-gateC<++> behaves as the other operators above, except that if it is a string 158*0Sstevel@tonic-gatematching the format C</^[a-zA-Z]*[0-9]*\z/> the string increment described 159*0Sstevel@tonic-gatein L<perlop> is used. 160*0Sstevel@tonic-gate 161*0Sstevel@tonic-gate=item Arithmetic operators during C<use integer> 162*0Sstevel@tonic-gate 163*0Sstevel@tonic-gateIn scopes where C<use integer;> is in force, nearly all the operators listed 164*0Sstevel@tonic-gateabove will force their argument(s) into integer format, and return an integer 165*0Sstevel@tonic-gateresult. The exceptions, C<abs>, C<++> and C<-->, do not change their 166*0Sstevel@tonic-gatebehavior with C<use integer;> 167*0Sstevel@tonic-gate 168*0Sstevel@tonic-gate=item Other mathematical operators 169*0Sstevel@tonic-gate 170*0Sstevel@tonic-gateOperators such as C<**>, C<sin> and C<exp> force arguments to floating point 171*0Sstevel@tonic-gateformat. 172*0Sstevel@tonic-gate 173*0Sstevel@tonic-gate=item Bitwise operators 174*0Sstevel@tonic-gate 175*0Sstevel@tonic-gateArguments are forced into the integer format if not strings. 176*0Sstevel@tonic-gate 177*0Sstevel@tonic-gate=item Bitwise operators during C<use integer> 178*0Sstevel@tonic-gate 179*0Sstevel@tonic-gateforces arguments to integer format. Also shift operations internally use 180*0Sstevel@tonic-gatesigned integers rather than the default unsigned. 181*0Sstevel@tonic-gate 182*0Sstevel@tonic-gate=item Operators which expect an integer 183*0Sstevel@tonic-gate 184*0Sstevel@tonic-gateforce the argument into the integer format. This is applicable 185*0Sstevel@tonic-gateto the third and fourth arguments of C<sysread>, for example. 186*0Sstevel@tonic-gate 187*0Sstevel@tonic-gate=item Operators which expect a string 188*0Sstevel@tonic-gate 189*0Sstevel@tonic-gateforce the argument into the string format. For example, this is 190*0Sstevel@tonic-gateapplicable to C<printf "%s", $value>. 191*0Sstevel@tonic-gate 192*0Sstevel@tonic-gate=back 193*0Sstevel@tonic-gate 194*0Sstevel@tonic-gateThough forcing an argument into a particular form does not change the 195*0Sstevel@tonic-gatestored number, Perl remembers the result of such conversions. In 196*0Sstevel@tonic-gateparticular, though the first such conversion may be time-consuming, 197*0Sstevel@tonic-gaterepeated operations will not need to redo the conversion. 198*0Sstevel@tonic-gate 199*0Sstevel@tonic-gate=head1 AUTHOR 200*0Sstevel@tonic-gate 201*0Sstevel@tonic-gateIlya Zakharevich C<ilya@math.ohio-state.edu> 202*0Sstevel@tonic-gate 203*0Sstevel@tonic-gateEditorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com> 204*0Sstevel@tonic-gate 205*0Sstevel@tonic-gateUpdates for 5.8.0 by Nicholas Clark <nick@ccl4.org> 206*0Sstevel@tonic-gate 207*0Sstevel@tonic-gate=head1 SEE ALSO 208*0Sstevel@tonic-gate 209*0Sstevel@tonic-gateL<overload>, L<perlop> 210