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{{task|Basic language learning}}
Programming languages have different ways of expressing floating-point literals.
;Task: Show how floating-point literals can be expressed in your language: decimal or other bases, exponential notation, and any other special features.
You may want to include a regular expression or BNF/ABNF/EBNF defining allowable formats for your language.
;Related tasks:
- [[Literals/Integer]]
- [[Extreme floating point values]]
360 Assembly
[[wp:IBM_hexadecimal_floating_point|IBM hexadecimal floating point]]
XS4 DC E'1.23456E-4' short floating-point
XDPI DC D'3.141592653589793' long floating-point
XD1 DC D'0' long floating-point
XD2 DC D'1' long floating-point
XD3 DC D'-1' long floating-point
XD4 DC D'1.2345E-4' long floating-point
XQPI DC L'3.14159265358979323846264338327950' extended
* short floating-point - 32 bits - 4 bytes : 6 decimal digits
* long floating-point - 64 bits - 8 bytes : 16 decimal digits
* extended floating-point - 128 bits - 16 bytes : 33 decimal digits
* absolute approximate range: 5e-79 to 7e75
Ada
Real literals contain decimal point. The exponent part is optional. Underline may be used to separate groups of digits. A literal does not have sign, + or - are unary operations. Examples of real literals:
3.141_592_6
1.0E-12
0.13
Aime
3.14
5.0
8r # without the "r"(eal) suffix, "8" would be an integer
.125
ALGOL 68
# floating point literals are called REAL denotations in Algol 68 #
# They have the following forms: #
# 1: a digit sequence followed by "." followed by a digit sequence #
# 2: a "." followed by a digit sequence #
# 3: forms 1 or 2 followed by "e" followed by an optional sign #
# followed by a digit sequence #
# 4: a digit sequence follows by "e" followed by an optional sign #
# followed by a digit sequence #
# #
# The "e" indicates the following optionally-signed digit sequence is #
# the exponent of the literal. #
# If the implementation allows, a "times ten to the power symbol" #
# can be used to replace "e" - e.g. a subscript "10" character #
# #
# spaces can appear anywhere in the denotation #
# Examples: #
REAL r;
r := 1.234;
r := .987;
r := 4.2e-9;
r := .4e+23;
r := 1e10;
r := 3.142e-23;
r := 1 234 567 . 9 e - 4;
ALGOL W
begin
real r; long real lr;
% floating point literals have the following forms: %
% 1 - a digit sequence followed by "." followed by a digit sequence %
% 2 - a digit sequence followed by "." %
% 3 - "." followed by a digit sequence %
% 4 - one of the above, followed by "'" followed by an optional sign %
% folloed by a digit sequence %
% the literal can be followed by "L", indicating it is long real %
% the literal can be followed by "I", indicating it is imaginary %
% the literal can be followed by "LI" or "IL" indicating it is a long %
% imaginary number %
% an integer literal ( digit sequence ) can also be used where a %
% floating point literal is required %
% non-imaginary examples: %
r := 1.23;
r := 1.;
r := .9;
r := 1.23'5;
r := 1.'+4;
r := .9'-12;
r := 7;
lr := 5.4321L;
end.
Applesoft BASIC
All numeric literals are treated as floating point. (In the Apple II world, Applesoft was sometimes called "floating-point BASIC" to contrast it with [[Integer BASIC]].)
0
19
-3
29.59
-239.4
1E10
1.9E+09
-6.66E-32
Arturo
## AWK
With the One True Awk ([[nawk]]), all numbers are floating-point. A numeric literal consists of one or more digits '0-9', with an optional decimal point '.', followed by an optional exponent. The exponent is a letter 'E' or 'e', then an optional '+' or '-' sign, then one or more digits '0-9'.
```awk
2
2.
.3
45e6
45e+6
78e-9
1.2E34
Other implementations of Awk can differ. They might not use floating-point numbers for integers.
This Awk program will detect whether each line of input contains a valid integer.
/^([0-9]+(\.[0-9]*)?|\.[0-9]+)([Ee][-+]?[0-9]+)?$/ {
print $0 " is a literal number."
next
}
{
print $0 " is not valid."
}
A leading plus or minus sign (as in +23 or -14) is not part of the literal; it is a unary operator. This is easy to check if you know that exponentiation has a higher precedence than unary minus; -14 ** 2 acts like -(14 ** 2), not like (-14) ** 2.
Axe
Axe does not support floating point literals. However, it does support converting floats to integers and vice versa.
123→float{L₁}
float{L₁}→I
Axe does, however, support fixed-point literals.
12.25→A
There are some mathematical operators in Axe that operate specifically on fixed-point numbers.
BBC BASIC
REM Floating-point literal syntax:
REM [-]{digit}[.]{digit}[E[-]{digit}]
REM Examples:
PRINT -123.456E-1
PRINT 1000.0
PRINT 1E-5
REM Valid but non-standard examples:
PRINT 67.
PRINT 8.9E
PRINT .33E-
PRINT -.
'''Output:'''
-12.3456
1000
1E-5
67
8.9
0.33
0
bc
A literal floating point number can be written as .NUMBER, NUMBER. or NUMBER.NUMBER where NUMBER consists of the hexadecimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. If digits in the number are greater than or equal to the current value of ibase (i.e. the input number radix) the behaviour is undefined.
Examples:
12.34 .34 99. ABC.DEF
C
Floating-point numbers can be given in decimal or hexadecimal. Decimal floating-point numbers must have at least one of a decimal point and an exponent part, which is marked by an E:
((\d*\.\d+|\d+\.)([eE][+-]?[0-9]+)?[flFL]?)|([0-9]+[eE][+-]?[0-9]+[flFL]?)
Hexadecimal is similar, but allowing A-F as well as 0-9. They have a binary exponent part marked with a P instead of a decimal exponent:
(0[xX]([0-9a-fA-F]*\.[0-9a-fA-F]+|[0-9a-fA-F]+\.)([pP][+-]?\d+[flFL]?)|(0[xX][0-9a-fA-F]+[pP][+-]?\d+[flFL]?)
C#
Floating point suffixes are not case-sensitive.
double d = 1;
d = 1d;
d = 1D;
d = 1.2; //double is the default if there's no suffix
d = 1.2d; //The suffix is redundant here
d = .2;
d = 12e-12;
d = 12E-12;
d = 1_234e-1_2; //digit separators are allowed since C# 7
float f = 1;
f = 1f;
f = 1F;
f = 1.2f;
f = .2f;
f = 12e-12f;
f = 12E-12f;
f = 1_234e-1_2f;
decimal m = 1;
m = 1m;
m = 1m;
m = 1.2m;
m = .2m;
m = 12e-12m;
m = 12E-12m;
m = 1_234e-1_2m;
Clojure
Clojure supports both standard and scientific notation.
user=> 1.
1.0
user=> 1.0
1.0
user=> 3.1415
3.1415
user=> 1.234E-10
1.234E-10
user=> 1e100
1.0E100
user=> (Float/valueOf "1.0f")
1.0
Clojure also supports returning ratios (fractions) if you divide integers. These are not subject to roundoff error. If you do specify a floating point in the division, it will return a floating point value.
user=> (/ 1 3)
1/3
user=> (/ 1.0 3)
0.3333333333333333
Common Lisp
The grammar for floating point literals in EBNF (ISO/IEC 14977):
float = [ sign ], { decimal-digit }, decimal-point, decimal-digit, { decimal-digit }, [exponent]
| [ sign ], decimal-digit, { decimal-digit }, [ decimal-point, { decimal-digit } ], exponent ;
exponent = exponent-marker, [ sign ], decimal-digit, { decimal-digit } ;
sign = "+" | "-" ;
decimal-point = "." ;
decimal-digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
exponent-marker = "e" | "E" | "s" | "S" | "d" | "D" | "f" | "F" | "l" | "L" ;
Common Lisp implementations can provide up to 4 different float subtypes: short-float, single-float, double-float and long-float. The exponent marker specifies the type of the literal. "e"/"E" denotes the default floating point subtype (it is initially single-float but you can set it with the global variable READ-DEFAULT-FLOAT-FORMAT to any of the other subtypes).
The standard only recommends a minimum precision and exponent size for each subtype and an implementation doesn't have to provide all of them:
Format | Minimum Precision | Minimum Exponent Size
--------------------------------------------------
Short (s/S) | 13 bits | 5 bits
Single (f/F) | 24 bits | 8 bits
Double (d/D) | 50 bits | 8 bits
Long (l/L) | 50 bits | 8 bits
Some examples:
> 1.0
1.0
> -.1
-0.1
> -1e-4
-1.0E-4
> 1d2
100.0d0
> .1f3
100.0
> .001l-300
1.0L-303
Note that 123. is not a floating point number but an integer:
> (floatp 123.)
NIL
> (integerp 123.)
T
D
D built-in floating point types include ''float'' (32-bit), ''double'' (64-bit) and ''real'' (machine hardware maximum precision floating point type, 80-bit on x86 machine) and respective complex number types. Here's information for [http://www.d-programming-language.org/lex.html#floatliteral Floating Literals].
Dyalect
Dyalect built-in types include only one floating point number of type ''Float'' (64-bit). Both regular and scientific notations are supported:
var x = 42.02
var y = 0.174e-17
EBNF grammar for the floating point number is as follows:
float = "." digit { digit } [ ("e"|"E") [ "+" | "-" ] digit { digit } ]
| digit { digit }
(
"." digit { digit } [ ( "e" | "E" ) ["+" | "-" ] digit { digit } ]
| ( "e" | "E") ["+" | "-" ] digit { digit }
).
Eiffel
Floating point literals are of the form D.DeSD, where D represents a sequence of decimal digits, and S represents an optional sign. A leading "+" or "-" indicates a unary plus or minus feature and is not considered part of the literal.
'''Examples:'''
1.
1.23
1e-5
.5
1.23E4
Elena
real r := 1;
r := 23.2r;
r := 1.2e+11r;
Elixir
iex(180)> 0.123
0.123
iex(181)> -123.4
-123.4
iex(182)> 1.23e4
1.23e4
iex(183)> 1.2e-3
0.0012
iex(184)> 1.23E4
1.23e4
iex(185)> 10_000.0
1.0e4
iex(186)> .5
** (SyntaxError) iex:186: syntax error before: '.'
iex(186)> 2. + 3
** (CompileError) iex:186: invalid call 2.+(3)
iex(187)> 1e4
** (SyntaxError) iex:187: syntax error before: e4
Erlang
Floating point literal examples: 1.0 , -1.0 , 1.2e3 , 1.2e-3 and 1.2E3 , 1.2E-3 .
Euphoria
printf(1,"Exponential:\t%e, %e, %e, %e\n",{-10.1246,10.2356,16.123456789,64.12})
printf(1,"Floating Point\t%03.3f, %04.3f, %+3.3f, %3.3f\n",{-10.1246,10.2356,16.123456789,64.12})
printf(1,"Floating Point or Exponential: %g, %g, %g, %g\n",{10,16.123456789,64,123456789.123})
{{out}}
Exponential: -1.012460e+001, 1.023560e+001, 1.612346e+001, 6.412000e+001
Floating Point -10.125, 10.236, +16.123, 64.120
Floating Point or Exponential: 10, 16.1235, 64, 1.23457e+008
Factor
3.14 ! basic float
+3.14 ! Optional signs
-3.14
10e5 ! exponents signified by e or E
10E+5 ! with optional signs
+10e-5
1. ! equivalent to 1.0
.5 ! equivalent to 0.5
1/2. ! floating point approximation of a ratio (0.5)
1/3. ! 0.3333333333333333
1/0. ! positive infinity
-1/0. ! negative infinity
0/0. ! not-a-number
! hexadecimal, octal, and binary float literals are supported.
! they require a base 2 exponent expressed as a decimal
! preceded by p or P.
0x1.0p3 ! 8.0
-0x1.0P-3 ! -0.125
0b1.010001p3 ! 10.125
0o1.21p3 ! 10.125
! comma separators are allowed
1,234.123,456 ! 1234.123456
! normalized hex form ±0x1.MMMMMMMMMMMMMp±EEEE allows any floating-point
! number to be specified precisely according to IEEE 754 representation
+0x1.1234567891234p+0002 ! 4.28444444440952
Forth
Unlike most other languages, floating point literals in Forth are distinguished by their exponent ('E' or 'e') rather than their decimal point ('.' or ','). Numeric literals with just a decimal point are regarded as two-cell double precision integers. From the ANS Forth standards document:
Convertible string := <significand><exponent>
<significand> := [<sign>]<digits>[.<digits0>]
<exponent> := E[<sign>]<digits0>
<sign> := { + | - }
<digits> := <digit><digits0>
<digits0> := <digit>*
<digit> := { 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 }
These are examples of valid representations of floating-point numbers in program source:
1E 1.E 1.E0 +1.23E-1 -1.23E+1
Fortran
Floating-point literals involve a decimal point, otherwise they're integers. The rule is
The status of the sign is delicate, being a matter of context. In a DATA statement or in an assignment such as x = -5.5, the sign is a part of the number, but not in an arithmetic expression such as y = x*-5.5 which has two operators in a row and is rejected. x*(-5.5) is accepted and the sign is a part of the number.
The exponent part signifies a power of ten and if present, has the form
There are also options for specifying constants as hexadecimal sequences, and if assigned to a floating-point variable, then Z"FFFFFFFFFFFFFFFF" will generate a (double precision) NaN value while Z"FFF0000000000000" will generate negative infinity, on cpus supporting such features. Similarly with octal and binary sequences. In these cases, the bit patterns are as they will be in the floating-point format, not as a number expressed in hexadecimal, etc. Thus, pi = Z"40490FDB" or 1000000010010010000111111011011, which is not 11.00100100001111110... at all.
Complex number constants are typically specified as (x,y) where x and y are floating-point literals; there is no provision for complex integers.
FreeBASIC
FreeBASIC has two floating point types : Single (4 bytes) and Double (8 bytes)
Numeric literals of these types can be specified by using the following suffixes:
Single !, f or F : Double #
However, this is not usually necessary as the compiler will automatically infer the type from the context and the two types are implicitly convertible to each other or explicitly convertible using the CSng or CDbl functions. However, conversions from Double to Single may lose precision.
All numeric literals which include a decimal point or exponent (i.e. scientific notation) are considered to be of floating point rather than integral type and are generally of the form:
number[.[fraction]][((D|E) [+|-] exponent)|(D|E)|][suffix]
or
.fraction[((D|E) [+|-] exponent)|(D|E)|][suffix]
Where scientific notation is used, D denotes Double precision and E denotes default precision , though these can be over-ridden by the suffix, if there is one. They can also be used on their own, without a following exponent.
The default precision is Double unless the 'QB' dialect of the language is used (for compatibility with QuickBasic code) where numbers of no more than 7 digits are considered to be Single precision.
Some examples, taken from the language documentation follow:
' FB 1.05.0 Win64 (default dialect)
Dim a As Double = 123.456
Dim b As Double = -123.0
Dim c As Double = -123.0d
Dim d As Double = -123e
Dim e As Double = 743.1e+13
Dim f As Double = 743.1D-13
Dim g As Double = 743.1E13
Dim h As Single = 743D! Rem ! overrides D
Dim i As Single = 3.1!
Dim j As Single = -123.456e-7f
Dim k As Double = 0#
Dim l As Double = 3.141592653589e3#
GAP
-3.14
22.03e4
4.54e-5
gecho
0.0
-1
-1.2
-1.4324
3 4 /
Go
See [http://golang.org/doc/go_spec.html#Floating-point_literals relevant section] of language reference. Basically they are base 10, need either a decimal point or an exponent, and specify no precision or representation. The exponent can be signed, but the mantissa is not. One of the integer part or the fractional part may be elided; one of the decimal point or the exponent may be elided. A leading minus sign would be an operator and not part of the floating point literal. Examples,
0.
0.0
.0
1e3
1e-300
6.02E+23
Groovy
Solution:
println 1.00f // float (IEEE-32)
println 1.00d // double (IEEE-64)
println 1.00 // BigDecimal (scaled BigInteger)
println 1.00g // BigDecimal
println 1.00e0 // BigDecimal
assert 1.00f instanceof Float
assert 1.00d instanceof Double
assert 1.00 instanceof BigDecimal
assert 1.00g instanceof BigDecimal
assert 1.00e0 instanceof BigDecimal
{{out}}
1.0
1.0
1.00
1.00
1.00
Haskell
Haskell supports decimal representation of float literals, with or without an exponent. For more information, see the [http://www.haskell.org/onlinereport/lexemes.html#sect2.5 relevant portion] of the Haskell 98 Report.
main = print [0.1,23.3,35e-1,56E+2,14.67e1]
Output:
[0.1,23.3,3.5,5600.0,146.7]
=={{header|Icon}} and {{header|Unicon}}== Real literals can be represented in two forms by (a) decimal literals, or (b) exponent literals. There is no sign as + and - are unary operators.
The program below shows a full range of valid real literals.
procedure main()
every write( ![ 1., .1, 0.1, 2e10, 2E10, 3e-1, .4e2, 1.41e2, 8.e+3, 3.141e43 ])
end
The function write will cause the real values to be coerced as string constants. Icon/Unicon will format these as it sees fit resorting to exponent forms only where needed. {{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/printf The IPL library routine printf provides a broader range of formatting choices.]
J
This paragraph highlights current implementation specific details of internal types: J has a syntax for specifying numbers, but numeric constants are stored in their most compact implementation; for example, 2.1 is a floating point number, while 2.0 is an integer and 1.0 is a boolean. If the exact type of a value is important, an expression may be used; for example, 1.1-0.1 produces a floating point result.
J's numeric constant mini-language allows the specification of numbers which are not floating point, but as indicated above, numeric type in J is a semantic triviality and not a syntactic feature. (And this pervades the language. For example, 1+1 is 2, despite the result having a different type from both of the arguments. Or, for example, if maxint is the largest value represented using an integer type, maxint+1 will produce a floating point result instead of an error or a wraparound.)
Here is an informal bnf for J's numeric constant language. Note, however, that the implementation may disallow some unusual cases -- cases which are not treated as exceptional here (for example, the [http://jsoftware.com/help/dictionary/dcons.htm language specification] allows 1.2e3.4 but the current implementation does not support fractional powers of 10 in numeric constants):
numeric-constant ::= number-constant | number-constant whitespace numeric-constant
whitespace ::= whitespacecharacter | whitespacecharacter whitespace
whitespacecharacter ::= ' ' | TAB
TAB is ascii 9
number-constant ::= arbitrary-constant | arbitrary-constant base-token base-constant
base-token ::= 'b' | 'b-'
base-constant ::= base-digits | base-digits '.' base-digits
base-digits ::= base-digit | base-digit base-digits
base-digit ::= digit | alpha1 | alpha2
alpha1 ::= 'a'|'b'|'c'|'d'|'e'|'f'|'g'|'h'|'i'|'j'|'k'|'l'|'m'
alpha2 ::= 'n'|'o'|'p'|'q'|'r'|'s'|'t'|'u'|'v'|'w'|'x'|'y'|'z'
arbitrary-constant ::= complex-constant | pi-constant | euler-constant | extended-constant
pi-constant ::= complex-constant 'p' complex-constant
euler-constant ::= complex-constant 'x' complex-constant
extended-constant ::= signed-digits 'x' | signed-digits 'r' signed-digits
complex-constant ::= exponential-constant | exponential-constant complex-token exponential-constant
complex-token ::= 'ad' | 'ar' | 'j'
exponential-constant ::= signed-constant | signed-constant 'e' signed-constant
signed-constant ::= decimal-constant | '_' decimal-constant
decimal-constant ::= digits | digits '.' digits
signed-digits ::= digits | '_' digits
digits ::= digit | digit digits
digit ::= '0'|'1'|'2'|'3'|'4'|'5'|'6'|'7'|'8'|'9'
e indicates exponential or scientific notation (number on left multiplied by 10 raised to power indicated by number on right)
ad, ar and j are used to describe complex numbers (angle in degrees, in radians, and rectangular form)
p and infix x are analogous to e except the base is pi or the base of natural logarithms
r and x are also used for arbitrary precision numbers, r indication a ration and a trailing x indicating an extended precision integer.
b is used for arbitrary bases, and letters a-z indicate digit values 10 through 35 when they follow a b
Floating point examples:
0 1 _2 3.4 3e4 3p4 3x4
0 1 _2 3.4 30000 292.227 163.794
16bcafe.babe _16b_cafe.babe _10b11
51966.7 46818.7 _9
Note that all the values in an array are the same type, thus the 0, 1 and 2 in the above example are floating point because they do not appear by themselves. Note also that by default J displays no more than six significant digits of floating point values.
jq
jq floating point literals are identical to JSON floating point literals. However, when jq parses a floating point or integer literal, conversion to IEEE 754 numbers takes place, which may result in a loss of accuracy and/or an apparent change of type, as illustrated by the following sequence of input => output pairs:
1
1.2 => 1.2
1e10 => 10000000000
1e100 => 1e+100
1e1234 => 1.7976931348623157e+308
.1 => 0.1
.1e1 => 1
Java
1. //double equal to 1.0
1.0 //double
2432311.7567374 //double
1.234E-10 //double
1.234e-10 //double
758832d //double
728832f //float
1.0f //float
758832D //double
728832F //float
1.0F //float
1 / 2. //double
1 / 2 //int equal to 0
Values that are outside the bounds of a type will give compiler errors when trying to force them to that type.
Julia
{{works with|Julia|0.6}}
0.1
.1
1.
1e-1 # scientific notation
1e+10
1e-10
0x01p-1 # hex float
Kotlin
val d: Double = 1.0
val d2: Double = 1.234e-10
val f: Float = 728832f
val f2: Float = 728832F
Lasso
0.0
0.1
-0.1
1.2e3
1.3e+3
1.2e-3
Lingo
put 0.23
-- 0.2300
-- activate higher printing precision
the floatPrecision = 8
put -.23
-- -0.23000000
put 9.00719925474099e15
-- 9.00719925474099e15
-- result is NOT a float
put 2/3
-- 0
-- casting integer to float
put float(2)/3
-- 0.66666667
-- casting string to float
put float("0.23")
-- 0.23000000
Lua
3.14159
314.159E-2
M2000 Interpreter
We can use Decimal using @ and Currency using # (no exponent part, both types)
Def ExpType$(x)=Type$(x)
Print ExpType$(-12)="Double", -12
Print ExpType$(12.)="Double", 12.
Print ExpType$(12.e-5)="Double", 12.e-5
Print ExpType$(.1)="Double", .1
Print ExpType$(-12~)="Single", -12~
Print ExpType$(12.~)="Single", 12.~
Print ExpType$(12.e-5~)="Single", 12.e-5~
Print ExpType$(.1~)="Single", .1~
Maple
Maple distinguishes "software floats" (of arbitrary precision) and "hardware floats" (of machine precision). To get the latter, use the "HFloat" constructor.
> 123.456; # decimal notation
123.456
> 1.23456e2; # scientific notation
123.456
> Float( 23, -2 ); # float constructor notation, by mantissa and exponent
0.23
> Float( .123456, 3 ); # again
123.456
> Float( 1.23456, 2 ); # again
123.456
> Float( 12.3456, 1 ); # again
123.456
> HFloat( 1.23456, 2 ); # hardware float constructor
123.456000000000
> HFloat( 123.456 ); # again
123.456000000000
> 2.3^30; # large floats are printed using scientific notation
11
0.7109434879 10
> 2/3; # NOT a float!
2/3
> evalf( 2/3 ); # but you can get one
0.6666666667
> 0.0; # zero
0.
> -0.0; # negative zero
-0.
> Float(infinity); # positive infinity
Float(infinity)
> Float(-infinity); # minus infinity
Float(-infinity)
> Float(undefined); # "NaN", not-a-number
Float(undefined)
Whether a given float is a software or hardware float can be determined by using "type".
> type( 2.3, 'hfloat' );
false
> type( HFloat( 2.3 ), 'hfloat' );
true
(There is also a type "sfloat" for software floats, and the type "float", which covers both.)
Mathematica
These numbers are given in the default output format. Large numbers are given in scientific notation.
{6.7^-4,6.7^6,6.7^8}
{0.00049625,90458.4,4.06068*10^6}
This gives all numbers in scientific notation.
ScientificForm[%]
{4.9625*10^(-4),9.04584*10^(4),4.06068*10^(6)}
This gives the numbers in engineering notation, with exponents arranged to be multiples of three.
EngineeringForm[%]
{496.25*10^(-6),90.4584*10^(3),4.06068*10^(6)}
In accounting form, negative numbers are given in parentheses, and scientific notation is never used.
AccountingForm[{5.6,-6.7,10.^7}]
{5.6,(6.7),10000000.}
Maxima
/* Maxima has machine floating point (usually double precision IEEE 754), and
arbitrary length "big floats" */
/* Here are ordinary floats */
3.14159
2.718e0
1.2345d10
1.2345e10
1.2345f10
/* And big floats (always with a "b" for the exponent) */
3.14159b0
2.718b0
1.2345b10
/* Before computing with big float, one must set precision to some value (default is 16 decimal digits) */
fpprec: 40$
bfloat(%pi);
3.141592653589793238462643383279502884197b0
Nemerle
3.14f // float literal
3.14d, 3.14 // double literal
3.14m // decimal literal
Formally (from the [http://nemerle.org/wiki/index.php?title=Lexical_structure_%28ref%29 Reference Manual]):
<floating_point_literal> ::=
[ <digits_> ] '.' <digits_> [ <exponent> ] [ <suffix> ]
| <digits_> <exponent> [ <suffix> ]
| <digits_> <suffix>
<exponent> ::=
<exponential_marker> [ <sign> ] <digits>
<digits> ::=
{ <digit> }
<digits_> ::=
<digits> [ { '_' <digits> } ]
<exponential_marker> ::=
'e'
| 'E'
<sign> ::=
'+'
| '-'
<digit> ::=
<decimal_digit>
<suffix> ::=
<floating_point_suffix>
<floating_point_suffix> ::=
'f'
| 'd'
| 'm'
NetRexx
NetRexx supports ''decimal'' and ''exponential'' notation for floating point constants. A number in ''exponential notation'' is a simple number followed immediately by the sequence "E" (or "e"), followed immediately by a sign ("+" or "-"), followed immediately by one or more digits.
NetRexx supports floating point number notation in the primitive ''float'' and ''double'' types, it's built in ''Rexx'' object and any other Java object that supports floating point numbers.
/* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 40 -- make lots of space for big numbers
numeric form scientific -- set output form for exponential notation
say 'Sample using objects of type "Rexx" (default):'
fv = 1.5; say '1.5'.right(20) '==' normalize(fv).right(20) -- 1.5
fv = -1.5; say '-1.5'.right(20) '==' normalize(fv).right(20) -- -1.5
fv = 15e-1; say '15e-1'.right(20) '==' normalize(fv).right(20) -- 1.5
fv = 3e-12; say '3e-12'.right(20) '==' normalize(fv).right(20) -- 3E-12
fv = 3e+12; say '3e+12'.right(20) '==' normalize(fv).right(20) -- 3000000000000
fv = 17.3E-12; say '17.3E-12'.right(20) '==' normalize(fv).right(20) -- 1.73E-11
fv = 17.3E+12; say '17.3E+12'.right(20) '==' normalize(fv).right(20) -- 17300000000000
fv = 17.3E+40; say '17.3E+40'.right(20) '==' normalize(fv).right(20) -- 1.73E+41
fv = 0.033e+9; say '0.033e+9'.right(20) '==' normalize(fv).right(20) -- 33000000
fv = 0.033e-9; say '0.033e-9'.right(20) '==' normalize(fv).right(20) -- 3.3E-11
say
say 'Sample using primitive type "float":'
ff = float
ff = float 15e-1; say '15e-1'.right(20) '==' normalize(ff).right(20) -- 1.5
ff = float 17.3E-12; say '17.3E-12'.right(20) '==' normalize(ff).right(20) -- 1.73E-11
ff = float 17.3E+12; say '17.3E+12'.right(20) '==' normalize(ff).right(20) -- 17300000000000
ff = float 0.033E+9; say '0.033E+9'.right(20) '==' normalize(ff).right(20) -- 33000000
ff = float 0.033E-9; say '0.033E-9'.right(20) '==' normalize(ff).right(20) -- 3.3E-11
say
say 'Sample using primitive type "double":'
fd = double
fd = 15e-1; say '15e-1'.right(20) '==' normalize(fd).right(20) -- 1.5
fd = 17.3E-12; say '17.3E-12'.right(20) '==' normalize(fd).right(20) -- 1.73E-11
fd = 17.3E+12; say '17.3E+12'.right(20) '==' normalize(fd).right(20) -- 17300000000000
fd = 17.3E+40; say '17.3E+40'.right(20) '==' normalize(fd).right(20) -- 1.73E+41
fd = 0.033E+9; say '0.033E+9'.right(20) '==' normalize(fd).right(20) -- 33000000
fd = 0.033E-9; say '0.033E-9'.right(20) '==' normalize(fd).right(20) -- 3.3E-11
say
return
/**
* Convert input to a Rexx object and add zero to the value which forces NetRexx to change its internal representation
*
* @param fv a Rexx object containing the floating point value
* @return a Rexx object which allows NetRexx string manipulation methods to act on it
*/
method normalize(fv) private constant
return fv + 0
'''Output:'''
Sample using objects of type "Rexx" (default):
1.5 == 1.5
-1.5 == -1.5
15e-1 == 1.5
3e-12 == 3E-12
3e+12 == 3000000000000
17.3E-12 == 1.73E-11
17.3E+12 == 17300000000000
17.3E+40 == 1.73E+41
0.033e+9 == 33000000
0.033e-9 == 3.3E-11
Sample using primitive type "float":
15e-1 == 1.5
17.3E-12 == 1.73E-11
17.3E+12 == 17300000000000
0.033E+9 == 33000000
0.033E-9 == 3.3E-11
Sample using primitive type "double":
15e-1 == 1.5
17.3E-12 == 1.73E-11
17.3E+12 == 17300000000000
17.3E+40 == 1.73E+41
0.033E+9 == 33000000
0.033E-9 == 3.3E-11
Nim
var x: float
x = 2.3
x = 2.0
x = 0.3
x = 123_456_789.000_000_1
x = 2e10
x = 2.5e10
x = 2.523_123E10
x = 5.2e-10
var y = 2'f32 # Automatically a float32
var z = 2'f64 # Automatically a float64
Objeck
3 + .14159
3.14159
314.159E-2
OCaml
In the OCaml manual, the chapter '''lexical conventions''' describes [http://caml.inria.fr/pub/docs/manual-ocaml/lex.html#float-literal floating-point literals], which are:
float-literal ::= [-] (0…9) { 0…9∣ _ } [. { 0…9∣ _ }] [(e∣ E) [+∣ -] (0…9) { 0…9∣ _ }]
Here are some examples:
0.5
1.0
1. (* it is not possible to write only "1" because OCaml is strongly typed,
and this would be interpreted as an integer *)
1e-10
3.14159_26535_89793
Oforth
A literal floating point number is written with a . and with or without an exponential notation :
3.14
1.0e-12
0.13
1000.0
.22
PARI/GP
Similar to C, but allowing only decimal. Also, GP allows a trailing decimal point:
[+-]?((\d*\.\d+\b)|(\d+(\.\d*)?[Ee][+-]?\d+\b)|-?(\.\d+[Ee][+-]?\d+\b)|(\d+\.))
PARI t_REAL numbers have a maximum value of
{|class="wikitable" ! 32-bit |
| 161,614,249 decimal digits |
|---|
| ! 64-bit |
| 694,127,911,065,419,642 decimal digits |
| } |
| where is the machine epsilon at the selected precision. The minimum value is the opposite of the maximum value (reverse the sign bit). |
0.0
0. \\ == 0.0
.0 \\ == 0.0
. \\ == 0.0
2e2
6.02e23
-2e48
1e-9
1e0
Pascal
1.345
-0.5345
5.34e-34
Perl
# Standard notations:
.5;
0.5;
1.23345e10;
1.23445e-10;
# The numbers can be grouped:
100_000_000; # equals to 100000000
Perl 6
Floating point numbers (the Num type) are written in the standard 'e' scientific notation:
2e2 # same as 200e0, 2e2, 200.0e0 and 2.0e2
6.02e23
-2e48
1e-9
1e0
A number like 3.1416 is specifically not floating point, but rational (the Rat type), equivalent to 3927/1250. On the other hand, Num(3.1416) would be considered a floating literal though by virtue of mandatory constant folding.
Phix
Phix does not require any distinction between integers and floats: 5 and 5.0 are exactly the same. A variable declared as atom can hold an integer or a floating point value.
Division and other operators do what a sensible language should, eg 1/3 is 0.333333, not 0. [for the latter use floor(1/3)]
Floats cannot be expressed in any base other than decimal. They may optinally include a sign for mantissa and/or exponent.
It is not necessary for a digit to precede a decimal point, but one must follow it. Upper or lower e/g may be used.
In the 32-bit version, integers outside -1,073,741,824 to +1,073,741,823 must be stored as atoms. In the 64-bit version the limits of integers are -4,611,686,018,427,387,904 to +4,611,686,018,427,387,903.
On a 32-bit architecture floats can range from approximately -1e308 to +1e308 with 15 decimal digits, and on a 64-bit architecture they can range from approximately -1e4932 to +1e4932 with 19 decimal digits.
The included bigatom library allows working with extremely large integers and floats with arbitrary precision. In the following, '?x' is the Phix shorthand for 'print(1,x)', plus \n
?1e+12 -- (same as 1e12)
?1e-12
?5 -- (same as 5.0)
--?1. -- (illegal, use 1 or 1.0)
?.1 -- (same as 0.1)
?1/3 -- 0.333333
printf(1,"%g %G\n",1e-30)
{{out}}
1e+12
1e-12
5
0.1
0.3333333333
1e-30 1E-30
PHP
More [http://php.net/manual/en/language.types.float.php information] about floating point numbers in PHP.
.12
0.1234
1.2e3
7E-10
Formal representation:
LNUM [0-9]+
DNUM ([0-9]*[\.]{LNUM}) | ({LNUM}[\.][0-9]*)
EXPONENT_DNUM [+-]?(({LNUM} | {DNUM}) [eE][+-]? {LNUM})
PicoLisp
PicoLisp does not support floating point literals in the base language, only fixed point (scaled) decimal integers of unlimited size and precision. See [http://software-lab.de/doc/ref.html#num-io Numbers] in the reference.
PL/I
1.2345e-4 decimal floating-point
7e5 decimal floating-point
1.234_567_89e0 decimal floating-point.
1.0s0 decimal floating-point (single precision)
1.0d0 decimal floating-point (double precision)
1.34q0 decimal floating-point (quadruple/extended precision)
111.0101e7b binary floating-point equals 111.0101 * 2**7
or 7.3125 * 2**7
1e5b binary floating-point equals 1 * 2**5
PureBasic
Floating point literals do not need a decimal point if an exponent is used. They may also include a sign for the number or exponent.
-1.0 1.0 1.0E2 1.0E+2 1.0E-2 -1E2
Python
{{works with|Python|2.3.3}}
This is an excerpt of an ANTLR grammar for python obtained from [http://www.antlr.org/grammar/1200715779785/Python.g here].
FLOAT
: '.' DIGITS (Exponent)?
| DIGITS '.' Exponent
| DIGITS ('.' (DIGITS (Exponent)?)? | Exponent)
;
DIGITS : ( '0' .. '9' )+ ;
Exponent
: ('e' | 'E') ( '+' | '-' )? DIGITS
;
Examples
2.3 # 2.2999999999999998
.3 # 0.29999999999999999
.3e4 # 3000.0
.3e+34 # 2.9999999999999998e+33
.3e-34 # 2.9999999999999999e-35
2.e34 # 1.9999999999999999e+34
Racket
#lang racket
.2
2.
2.+0i ; zero imaginary part
2e0
#x10.8 ; hex float
#o1e2 ; oct float
2.0f0 ; single float
1.0t0 ; extended 80-bit float (when available on platform)
Output:
0.2
2.0
2.0
2.0
16.5
64.0
2.0f0
1.0t0
REXX
All values in REXX are character strings, so a value could hold such things as these (decimal) numbers:
something = 127
something = '127' /*exactly the same as the above. */
something = 1.27e2
something = 1.27E2
something = 1.27E+2
something = ' + 0001.27e+00000000000000002 '
To forcibly express a value in exponential notation, REXX has a built-in function '''format''' that can be used.
Note that a value of '''0''' (zero) in any form is always converted to
0
by the '''format''' BIF.
something = -.00478
say something
say format(something,,,,0)
'''output'''
-0.00478
-4.78E-3
The last invocation of '''format''' (above, with the 5th parameter equal to zero) forces exponential notation, unless the exponent is '''0''' (zero), then exponential notation won't be used.
There are other options for the '''format''' BIF to force any number of digits before and/or after the decimal point, and/or specifying the number of digits in the exponent.
Ruby
A Float literal is an optional sign followed by one or more digits and a dot, one or more digits and an optional exponent (e or E followed by an optional sign and one or more digits). Unlike many languages .1 is not a valid float.
Underscores can be used for clarity: 1_000_000_000.01
Rust
The fractional part may be elided (so 1. is valid) but the integer part may not (so .0 is not valid).
2.3 // Normal floating point literal
3. // Equivalent to 3.0 (3 would be interpreted as an integer)
2f64 // The type (in this case f64, a 64-bit floating point number) may be appended to the value
1_000.2_f32 // Underscores may appear anywhere in the number for clarity.
Scala
{{libheader|Scala}} As all values in Scala, values are boxed with wrapper classes. The compiler will unbox them to primitive types for run-time execution.
1. //Double equal to 1.0
1.0 //Double, a 64-bit IEEE-754 floating point number (equivalent to Java's double primitive type)
2432311.7567374 //Double
1.234E-10 //Double
1.234e-10 //Double
758832d //Double
728832f //32-bit IEEE-754 floating point number (equivalent to Java's float primitive type)
1.0f //Float
758832D //Double
728832F //Float
1.0F //Float
1 / 2. //Double
1 / 2 //Int equal to 0
// Constants
Float.MinPositiveValue
Float.NaN
Float.PositiveInfinity
Float.NegativeInfinity
Double.MinPositiveValue
Double.NaN
Double.PositiveInfinity
Double.NegativeInfinity
Values that are outside the bounds of a type will give compiler-time errors when trying to force them to that type.
Scheme
.2 ; 0.2
2. ; 2.0
2e3 ; 2000
2.+3.i ; complex floating-point number
; in Scheme, floating-point numbers are inexact numbers
(inexact? 2.)
; #t
(inexact? 2)
; #f
Seed7
The type [http://seed7.sourceforge.net/libraries/float.htm float] consists of single precision floating point numbers. Float literals are base 10 and contain a decimal point. There must be at least one digit before and after the decimal point. An exponent part, which is introduced with E or e, is optional. The exponent can be signed, but the mantissa is not. A literal does not have a sign, + or - are unary operations. Examples of float literals are:
3.14159265358979
1.0E-12
0.1234
The functions [http://seed7.sourceforge.net/libraries/float.htm#str%28ref_float%29 str] and the operators [http://seed7.sourceforge.net/libraries/float.htm#%28ref_float%29digits%28ref_integer%29 digits] and [http://seed7.sourceforge.net/libraries/float.htm#%28attr_float%29parse%28in_string%29 parse] create and accept float literals with sign.
Original source: [http://seed7.sourceforge.net/manual/types.htm#float]
Sidef
say 1.234;
say .1234;
say 1234e-5;
say 12.34e5;
{{out}}
1.234
0.1234
0.01234
1234000
Smalltalk
2.0
45e6
45e+6
78e-9
1.2E34
base 2 mantissa:
2r1010.0 -> 10.0
2r0.01 -> 0.25
2r1010e5 -> 320.0
base 2 mantissa and base 2 exponent:
2r1010e2r0101 -> 320.0
Stata
Only decimal floating-point are supported, computations are done in double precision (but storage can be made in integer or single floating-point as well).
Examples:
.3
1.5
-1.5e10
3.15e-100
Swift
let double = 1.0 as Double // Double precision
let float = 1.0 as Float // Single precision
let scientific = 1.0E-12
// Swift does not feature type coercion for explicit type declaration
let sum = double + float // Error
let div = 1.1 / 2 // Double
let div1 = 1 / 2 // 0
Tcl
Floating point literals in Tcl always contain either “.” or “e” (of any case), if not both, or are references to either one of the IEEE infinities or NaN. Formally, they are values that (case-insensitively) match one these regular expressions:
;Normal values
:[-+]?[0-9]*.[0-9]+(e[-+]?[0-9]+)?
:[-+]?[0-9]+.?e[-+]?[0-9]+
;Infinite values
:[-+]?inf(inity)?
;NaN values
:[-+]?nan(([0-9a-f]+))?
Note also that NaN values usually result in checked exceptions; they are supported mainly so that they can be handled when parsing and generating external binary data. All other floating-point literals are fully legal values. (Also note that this excludes the definition of integer literals; for details see [http://www.tcl.tk/cgi-bin/tct/tip/249.html this TIP document], which explains the whole state machine.)
Ursa
Cygnus/X Ursa (the standard Ursa interpreter) is written in Java and supports Java style floating-point literals.
1.
1.0
2432311.7567374
1.234E-10
1.234e-10
758832d
728832f
1.0f
758832D
728832F
1.0F
Verbexx
// Floating-point Literals:
//
// If present,the exponent must be of the form:
//
// eNNN...N
// ENNN...N
// e-NNN...N
// E-NNN...N
// e+NNN...N
// E+NNN...N
//
// If present, length suffix must be:
//
// f F (FLOAT64_T)
// f32 F32 (FLOAT32_T)
// f64 F64 (FLOAT64_T)
// fd Fd fD FD (FLOATD_T) -- boost::multiprecision::
// cpp_dec_float<100, int64_t>
//
// The presence of "." "E" "e" "F" or "f" indicates a floating point literal.
//
// A literal can start with "-" "." or a decimal digit, but not "+" or "_".
// There must be at least one digit, so forms like ".F" ".e+11_f32" or just "."
// are not recognized as floating point literals.
//
// Floating-point literal examples:
@SAY 0. .0 0.0 1. .1 123.123 ;// FLOAT64_T
@SAY -0. -.0 -0.0 -1. -.1 -123.123 ;// FLOAT64_T
@SAY -0.E1 .0e0 0.0E6 -1.e6 -.1E8 12.12e44 -0E0 1e20 ;// FLOAT64_T
@SAY -0.e+1 .0E+0 0.0e+6 -1.E+6 -.1e+8 12.12E+44 -0e+0 1E+20 ;// FLOAT64_T
@SAY -0.E-1 .0e-0 0.0E-6 -1.e-6 -.1E-8 12.12e-44 -0E-0 1e-20 ;// FLOAT64_T
@SAY -0E9999999999999999 .0e+9999999999 0.E-999999999999999999 ;// FLOAT64_T
@SAY -8e0000000000000299 .6E+0000000299 5.e-000000000000000299 ;// FLOAT64_T
@SAY 0f -0f 0F -0f .0F -1234f 12.F 12.34f ;// FLOAT64_T
@SAY 0F32 -0f32 0f32 -0f32 .0f32 -1234F32 12.f32 12.34F32 ;// FLOAT32_T
@SAY 0f64 -0f64 0F64 -0f64 .0F64 -1234f64 12.F64 12.34f64 ;// FLOAT64_T
@SAY 0fD -0fd 0FD -0fd .0Fd -1234fD 12.FD 12.34fD ;// FLOATD_T
@SAY -0.E1f .0e0F 0.0E6f64 -1.e6F64 -.1E8f 12.12e44f64 -0E0F 1e20f64 ;// FLOAT64_T
@SAY -0.e+1f32 .0E+0F32 0.0e+6f32 -1.E+6F32 -.1e+8f32 12.12E+34F32 -0e+0f32 1E+20F32;// FLOAT32_T
@SAY -0.E-1fd .0e-0fD 0.0E-6Fd -1.e-6FD -.1E-8fd 12.12e-44fD -0E-0Fd 1e-20FD ;// FLOATD_T
@SAY -0E9999999999999999f32 .0e+9999999999F32 0.E-999999999999999999f32 ;// FLOAT32_T
@SAY -8e0000000000000299f .6E+0000000299f64 5.e-00000000000000000000299F64 ;// FLOAT64_T
@SAY -8e9999999999999999fD .6E+99999999999fD 5.e-12345678987654321FD ;// FLOATD_T
// note: _ (underscores) can appear in the main numeric part of the literal
// after the first digit and before any length suffix:
@SAY -10_000__f 1__0._55__ -1__.__ .0___44 1_._2__E-23F32 debug:;
// Underscores can also appear in the exponent, after the first digit:
@SAY -1_E-0__2_f32 1.e+0___5_5____ -1.0_E123_456_789_987_654_321__fD debug:;
Vim Script
There are two ways to write floating point literals:
[-+]?[0-9]+.[0-9]+[-+]?[0-9]+.[0-9]+[eE][-+]?[0-9]+
Examples: 12.34 +0.34 -1.0 12.34e5 0.99e-2 -1.0E+4
Note that there must always be at least one digit before and after the period (and for the exponent).
Visual Basic
{{works with|Visual Basic|5}} {{works with|Visual Basic|6}} {{works with|VBA|Access 97}} {{works with|VBA|6.5}} {{works with|VBA|7.1}}
Sub Main()
Dim d As Double ' 8 Bytes, type specifier = #
Dim s As Single ' 4 Bytes, type specifier = !
d = -12.3456
d = 1000#
d = 0.00001
d = 67#
d = 8.9
d = 0.33
d = 0#
d = 2# * 10 ^ 3
d = 2E+50
d = 2E-50
s = -12.3456!
s = 1000!
s = 0.00001!
s = 67!
s = 8.9!
s = 0.33!
s = 0!
s = 2! * 10 ^ 3
End Sub
There is no built-in support for not-a-number, but here's a way to handle that anyway:
Option Explicit
Public Declare Function RtlCompareMemory Lib "ntdll.dll" _
(ByRef Source1 As Any, ByRef Source2 As Any, ByVal Length As Long) As Long
Public Function IsNAN(ByRef d As Double) As Boolean
Dim d1 As Double
d1 = NaN()
IsNAN = (RtlCompareMemory(d, d1, 8) = 8)
End Function
Public Function NaN() As Double
On Error Resume Next ' ignore the error
NaN = 0 / 0
End Function
Sub Main()
Dim d1 As Double
Dim d2 As Double
d1 = NaN()
d2 = d1
Debug.Assert IsNAN(d2)
Debug.Print CStr(d2)
End Sub
{{out}}
-1,#IND
XPL0
0.
.1
1e3
123.456E-300
-123_456_789e+123
zkl
zkl requires something on both sides of the dot for a thing to be a float
1.0, 0.1, 3.1415, 1.e-100, 1.2e100, -1e10, -1e+10, 123.456E-300
{{omit from|Integer BASIC|You see the word "Integer" in the name, right? :-)}} {{omit from|ML/I}} {{omit from|Retro|No floating point support in the standard VM}}