Infinity

From Rosetta Code
Task
Infinity
You are encouraged to solve this task according to the task description, using any language you may know.
Task

Write a function which tests if infinity is supported for floating point numbers (this step should be omitted for languages where the language specification already demands the existence of infinity, e.g. by demanding IEEE numbers), and if so, returns positive infinity.   Otherwise, return the largest possible positive floating point number.

For languages with several floating point types, use the type of the literal constant   1.5   as floating point type.


Related task



ActionScript[edit]

ActionScript has the built in function isFinite() to test if a number is finite or not.

trace(5 / 0); // outputs "Infinity"
trace(isFinite(5 / 0)); // outputs "false"

Ada[edit]

with Ada.Text_IO; use Ada.Text_IO;
 
procedure Infinities is
function Sup return Float is -- Only for predefined types
Result : Float := Float'Last;
begin
if not Float'Machine_Overflows then
Result := Float'Succ (Result);
end if;
return Result;
end Sup;
 
function Inf return Float is -- Only for predefined types
Result : Float := Float'First;
begin
if not Float'Machine_Overflows then
Result := Float'Pred (Result);
end if;
return Result;
end Inf;
begin
Put_Line ("Supremum" & Float'Image (Sup));
Put_Line ("Infimum " & Float'Image (Inf));
end Infinities;

The language-defined attribute Machine_Overflows is defined for each floating-point type. It is true when an overflow or divide-by-zero results in Constraint_Error exception propagation. When the underlying machine type is incapable to implement this semantics the attribute is false. It is to expect that on the machines with IEEE 754 hardware Machine_Overflows is true. The language-defined attributes Succ and Pred yield the value next or previous to the argument, correspondingly.

Sample output on a machine where Float is IEEE 754:

Supremum +Inf*******
Infimum -Inf*******

Note that the code above does not work for user-defined types, which may have range of values narrower than one of the underlying hardware type. This case represents one of the reasons why Ada programmers are advised not to use predefined floating-point types. There is a danger that the implementation of might be IEEE 754, and so the program semantics could be broken.

Here is the code that should work for any type on any machine:

with Ada.Text_IO; use Ada.Text_IO;
 
procedure Infinities is
type Real is digits 5 range -10.0..10.0;
 
function Sup return Real is
Result : Real := Real'Last;
begin
return Real'Succ (Result);
exception
when Constraint_Error =>
return Result;
end Sup;
 
function Inf return Real is
Result : Real := Real'First;
begin
return Real'Pred (Result);
exception
when Constraint_Error =>
return Result;
end Inf;
begin
Put_Line ("Supremum" & Real'Image (Sup));
Put_Line ("Infimum " & Real'Image (Inf));
end Infinities;

Sample output. Note that the compiler is required to generate Constraint_Error even if the hardware is IEEE 754. So the upper and lower bounds are 10.0 and -10.0:

Supremum 1.0000E+01
Infimum -1.0000E+01

Getting rid of IEEE ideals[edit]

There is a simple way to strip IEEE 754 ideals (non-numeric values) from a predefined floating-point type such as Float or Long_Float:

subtype Safe_Float is Float range Float'Range;

The subtype Safe_Float keeps all the range of Float, yet behaves properly upon overflow, underflow and zero-divide.

ALGOL 68[edit]

ALGOL 68R (from Royal Radar Establishment) has an infinity variable as part of the standard prelude, on the ICL 1900 Series mainframes the value of infinity is 5.79860446188₁₀76 (the same as max float).

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny

Note: The underlying hardware may sometimes support an infinity, but the ALGOL 68 standard itself does not, and gives no way of setting a variable to either ±∞.

ALGOL 68 does have some 7 built in exceptions, these might be used to detect exceptions during transput, and so if the underlying hardware does support ∞, then it would be detected with a on value error while printing and if mended would appear as a field full of error char.

printf(($"max int: "gl$,max int));
printf(($"long max int: "gl$,long max int));
printf(($"long long max int: "gl$,long long max int));
printf(($"max real: "gl$,max real));
printf(($"long max real: "gl$,long max real));
printf(($"long long max real: "gl$,long long max real));
printf(($"error char: "gl$,error char))

Output:

max int: +2147483647
long max int: +99999999999999999999999999999999999
long long max int: +9999999999999999999999999999999999999999999999999999999999999999999999
max real: +1.79769313486235e+308
long max real: +1.000000000000000000000000e+999999
long long max real: +1.00000000000000000000000000000000000000000000000000000000000e+999999
error char: *

Argile[edit]

Translation of: C
(simplified)
use std
printf "%f\n" atof "infinity" (: this prints "inf" :)
#extern :atof<text>: -> real

AWK[edit]

  BEGIN { 
k=1;
while (2^(k-1) < 2^k) k++;
INF = 2^k;
print INF;
}

This has been tested with GAWK 3.1.7 and MAWK, both return

 inf 

BBC BASIC[edit]

      *FLOAT 64
PRINT FNinfinity
END
 
DEF FNinfinity
LOCAL supported%, maxpos, prev, inct
supported% = TRUE
ON ERROR LOCAL supported% = FALSE
IF supported% THEN = 1/0
RESTORE ERROR
inct = 1E10
REPEAT
prev = maxpos
inct *= 2
ON ERROR LOCAL inct /= 2
maxpos += inct
RESTORE ERROR
UNTIL maxpos = prev
= maxpos

Output:

1.79769313E308

C[edit]

A previous solution used atof("infinity"), which returned infinity with some C libraries but returned zero with MinGW.

C89 has a macro HUGE_VAL in <math.h>. HUGE_VAL is a double. HUGE_VAL will be infinity if infinity exists, else it will be the largest possible number. HUGE_VAL is a double.

#include <math.h>	/* HUGE_VAL */
#include <stdio.h> /* printf() */
 
double inf(void) {
return HUGE_VAL;
}
 
int main() {
printf("%g\n", inf());
return 0;
}

The output from the above program might be "inf", "1.#INF", or something else.

C99 also has a macro for infinity:

#define _ISOC99_SOURCE
 
#include <math.h>
#include <stdio.h>
 
int main() {
printf("%g\n", INFINITY);
return 0;
}

C#[edit]

using System;
 
class Program
{
static double PositiveInfinity()
{
return double.PositiveInfinity;
}
 
static void Main()
{
Console.WriteLine(PositiveInfinity());
}
}

Output:

Infinity

C++[edit]

#include <limits>
 
double inf()
{
if (std::numeric_limits<double>::has_infinity)
return std::numeric_limits<double>::infinity();
else
return std::numeric_limits<double>::max();
}

Clojure[edit]

Translation of: Java

Java's floating-point types (float, double) all support infinity. You can get infinity from constants in the corresponding wrapper class; for example, Double: (def infinity Double/POSITIVE_INFINITY) ; defined as 1.0/0.0 (Double/isInfinite infinity) ; true

The largest possible number in Java (without using the Big classes) is also in the Double class. (def biggestNumber Double/MAX_VALUE) Its value is (2-2-52)*21023 or 1.7976931348623157*10308 (a.k.a. "big"). Other number classes (Integer, Long, Float, Byte, and Short) have maximum values that can be accessed in the same way.

CoffeeScript[edit]

Translation of: JavaScript

CoffeeScript compiles to JavaScript, and as such it inherits the properties of JavaScript.

JavaScript has a special global property called "Infinity":

Infinity

as well as constants in the Number class:

Number.POSITIVE_INFINITY
Number.NEGATIVE_INFINITY

The global isFinite function tests for finiteness:

isFinite x

Common Lisp[edit]

Common Lisp does not specify an infinity value. Some implementations may have support for IEEE infinity, however. For instance, CMUCL supports IEEE Special Values. Common Lisp does specify that implementations define constants with most (and least) positive (and negative) values. These may vary between implementations.

Works with: LispWorks
5.1.2, Intel, OS X, 32-bit
> (apropos "MOST-POSITIVE" :cl)
MOST-POSITIVE-LONG-FLOAT, value: 1.7976931348623158D308
MOST-POSITIVE-SHORT-FLOAT, value: 3.4028172S38
MOST-POSITIVE-SINGLE-FLOAT, value: 3.4028235E38
MOST-POSITIVE-DOUBLE-FLOAT, value: 1.7976931348623158D308
MOST-POSITIVE-FIXNUM, value: 536870911
 
> (apropos "MOST-NEGATIVE" :cl)
MOST-NEGATIVE-SINGLE-FLOAT, value: -3.4028235E38
MOST-NEGATIVE-LONG-FLOAT, value: -1.7976931348623158D308
MOST-NEGATIVE-SHORT-FLOAT, value: -3.4028172S38
MOST-NEGATIVE-DOUBLE-FLOAT, value: -1.7976931348623158D308
MOST-NEGATIVE-FIXNUM, value: -536870912

Component Pascal[edit]

BlackBox Component Builder

 
MODULE Infinity;
IMPORT StdLog;
 
PROCEDURE Do*;
VAR
x: REAL;
BEGIN
x := 1 / 0;
StdLog.String("x:> ");StdLog.Real(x);StdLog.Ln
END Do;
 
 

Execute: ^Q Infinity.Do
Output:

x:>  inf

D[edit]

auto inf() {
return typeof(1.5).infinity;
}
 
void main() {}

Delphi[edit]

Delphi defines the following constants in Math:

  Infinity    =  1.0 / 0.0;
NegInfinity = -1.0 / 0.0;

Test for infinite value using:

Math.IsInfinite()

E[edit]

def infinityTask() {
return Infinity # predefined variable holding positive infinity
}


Eiffel[edit]

 
class
APPLICATION
inherit
ARGUMENTS
create
make
feature {NONE} -- Initialization
number:REAL_64
make
-- Run application.
do
number := 2^2000
print(number)
print("%N")
print(number.is_positive_infinity)
print("%N")
end
end
 

Output:

Infinity
True

Erlang[edit]

No infinity available. Largest floating point number is supposed to be 1.80e308 (IEEE 754-1985 double precision 64 bits) but that did not work. However 1.79e308 is fine, so max float is somewhere close to 1.80e308.

ERRE[edit]

Every type has its "infinity" constant: MAXINT for 16-bit integer, MAXREAL for single precision floating and MAXLONGREAL for double precision floating. An infinity test can be achieved with an EXCEPTION:

 
PROGRAM INFINITY
 
EXCEPTION
PRINT("INFINITY")
ESCI%=TRUE
END EXCEPTION
 
BEGIN
ESCI%=FALSE
K=1
WHILE 2^K>0 DO
EXIT IF ESCI%
K+=1
END WHILE
END PROGRAM
 

Euphoria[edit]

constant infinity = 1E400
 
? infinity -- outputs "inf"

Factor[edit]

1/0.

Fantom[edit]

Fantom's Float data type is an IEEE 754 64-bit floating point type. Positive infinity is represented by the constant posInf.

 
class Main
{
static Float getInfinity () { Float.posInf }
public static Void main () { echo (getInfinity ()) }
}
 

Forth[edit]

: inf ( -- f ) 1e 0e f/ ;
inf f. \ implementation specific. GNU Forth will output "inf"
 
: inf? ( f -- ? ) s" MAX-FLOAT" environment? drop f> ;
\ IEEE infinity is the only value for which this will return true
 
: has-inf ( -- ? ) ['] inf catch if false else inf? then ;

Fortran[edit]

ISO Fortran 2003 or later supports an IEEE_ARITHMETIC module which defines a wide range of intrinsic functions and types in support of IEEE floating point formats and arithmetic rules.

program to_f_the_ineffable
use, intrinsic :: ieee_arithmetic
integer :: i
real dimension(2) :: y, x = (/ 30, ieee_value(y,ieee_positive_inf) /)
 
do i = 1, 2
if (ieee_support_datatype(x(i))) then
if (ieee_is_finite(x(i))) then
print *, 'x(',i,') is finite'
else
print *, 'x(',i,') is infinite'
end if
 
else
print *, 'x(',i,') is not in an IEEE-supported format'
end if
end do
end program to_f_the_ineffable

ISO Fortran 90 or later supports a HUGE intrinsic which returns the largest value supported by the data type of the number given.

real :: x
real :: huge_real = huge(x)

FreeBASIC[edit]

' FB 1.05.0 Win64
 
#Include "crt/math.bi"
#Print Typeof(1.5) ' Prints DOUBLE at compile time
 
Dim d As Typeof(1.5) = INFINITY
Print d; " (String representation of Positive Infinity)"
Sleep
 
Output:
 1.#INF (String representation of Positive Infinity)

GAP[edit]

# Floating point infinity
inf := FLOAT_INT(1) / FLOAT_INT(0);
 
IS_FLOAT(inf);
#true;
 
# GAP has also a formal ''infinity'' value
infinity in Cyclotomics;
# true

Go[edit]

package main
 
import (
"fmt"
"math"
)
 
// function called for by task
func posInf() float64 {
return math.Inf(1) // argument specifies positive infinity
}
 
func main() {
x := 1.5 // type of x determined by literal
// that this compiles demonstrates that PosInf returns same type as x,
// the type specified by the task.
x = posInf() // test function
fmt.Println(x, math.IsInf(x, 1)) // demonstrate result
}

Output:

+Inf true

Groovy[edit]

Groovy, like Java, requires full support for IEEE 32-bit (Float) and 64-bit (Double) formats. So the solution function would simply return either the Float or Double constant encoded as IEEE infinity.

def biggest = { Double.POSITIVE_INFINITY }

Test program:

println biggest()
printf ( "0x%xL \n", Double.doubleToLongBits(biggest()) )

Output:

Infinity
0x7ff0000000000000L

Haskell[edit]

The Haskell 98 standard does not require full IEEE numbers, and the required operations on floating point numbers leave some degree of freedom to the implementation. Also, it's not possible to use the type of the literal 1.0 to decide which concrete type to use, because Haskell number literals are automatically converted.

Nevertheless, the following may come close to the task description:

maxRealFloat :: RealFloat a => a -> a
maxRealFloat x = encodeFloat b (e-1) `asTypeOf` x where
b = floatRadix x - 1
(_,e) = floatRange x
 
infinity :: RealFloat a => a
infinity = if isInfinite inf then inf else maxRealFloat 1.0 where
inf = 1/0

Test for the two standard floating point types:

*Main> infinity :: Float
Infinity
*Main> infinity :: Double
Infinity

Or you can simply use division by 0:

Prelude> 1 / 0 :: Float
Infinity
Prelude> 1 / 0 :: Double
Infinity

Or use "read" to read the string representation:

Prelude> read "Infinity" :: Float
Infinity
Prelude> read "Infinity" :: Double
Infinity

Icon and Unicon[edit]

Icon and Unicon have no infinity value (or defined maximum or minimum values). Reals are implemented as C doubles and the behavior could vary somewhat from platform to platform. Both explicitly check for divide by zero and treat it as a runtime error (201), so it's not clear how you could produce one with the possible exception of externally called code.

IDL[edit]

IDL provides the standard IEEE values for _inf and _NaN in the !Values system structure:

print, !Values.f_infinity             ;; for normal floats or
print, !Values.D_infinity ;; for doubles

Io[edit]

inf := 1/0

or

Number constants inf

J[edit]

Positive infinity is produced by the primary constant function _: .
It is also represented directly as a numeric value by an underscore, used alone.

Example:

 
_ * 5 NB. multiplying infinity to 5 results in infinity
_
5 % _ NB. dividing 5 by infinity results in 0
0
5 % 0 NB. dividing 5 by 0 results in infinity
_
 

Java[edit]

Java's floating-point types (float, double) all support infinity. You can get infinity from constants in the corresponding wrapper class; for example, Double:

double infinity = Double.POSITIVE_INFINITY; //defined as 1.0/0.0
Double.isInfinite(infinity); //true

As a function:

public static double getInf(){
return Double.POSITIVE_INFINITY;
}

The largest possible number in Java (without using the Big classes) is also in the Double class.

double biggestNumber = Double.MAX_VALUE;

Its value is (2-2-52)*21023 or 1.7976931348623157*10308 (a.k.a. "big"). Other number classes (Integer, Long, Float, Byte, and Short) have maximum values that can be accessed in the same way.

JavaScript[edit]

JavaScript has a special global property called "Infinity":

Infinity

as well as constants in the Number class:

Number.POSITIVE_INFINITY
Number.NEGATIVE_INFINITY

The global isFinite() function tests for finiteness:

isFinite(x)

jq[edit]

jq uses IEEE 754 64-bit floating-point arithmetic, and very large number literals, e.g. 1e1000, are evaluated as IEEE 754 infinity. If your version of jq does not include `infinite` as a built-in, you could therefore define it as follows:

def infinite: 1e1000;

To test whether a JSON entity is equal to `infinite`, one can simply use `==` in the expected manner. Thus, assuming `infinite` has been defined, one could define a predicate, isinfinite, as follows:

def isinfinite: . == infinite;

Currently, the infinite value prints as though it were a very large floating point number.

Julia[edit]

Julia uses IEEE floating-point arithmetic and includes a built-in constant `Inf` for (64-bit) floating-point infinity.

 
infinity() = Inf
 

There is actually a built-in function that does returns infinity in various types, called inf, which takes as its argument the type to return infinity for.

 
inf(Float64) # 64-bit Inf
inf(Float32) # 32-bit Inf32
inf(BigFloat) # infinity for arbitrary-precision floating-point arithmetic
 

Lingo[edit]

Lingo stores floats using IEEE 754 double-precision (64-bit) format. INF is not a constant that can be used programmatically, but only a special return value.

x = (1-power(2, -53)) * power(2, 1023) * 2
put ilk(x), x
-- #float 1.79769313486232e308
 
x = (1-power(2, -53)) * power(2, 1023) * 3
put ilk(x), x, -x
-- #float INF -INF

Lua[edit]

 
function infinity()
return 1/0 --lua uses unboxed C floats for all numbers
end
 

K[edit]

K has predefined positive and negative integer and float infinities: -0I, 0I, -0i, 0i. They have following properties:

Works with: Kona
   / Integer infinities
/ 0I is just 2147483647
/ -0I is just -2147483647
/ -2147483648 is a special "null integer"(NaN) 0N
0I*0I
1
0I-0I
0
0I+1
0N
0I+2
-0I
0I+3 / -0I+1
-2147483646
0I-1
2147483646
0I%0I
1
0I^2
4.611686e+18
0I^0I
0i
0I^-0I
0.0
1%0
0I
0%0
0
0i^2
0i
0i^0i
0i
 
/ Floating point infinities in K are something like
/ IEEE 754 values
/ Also there is floating point NaN -- 0n
0i+1
0i
0i*0i
0i
0i-0i
0n
0i%0i
0n
0i%0n
0n
/ but
0.0%0.0
0.0

Kotlin[edit]

fun main(args: Array<String>) {
val p = Double.POSITIVE_INFINITY // +∞
println(p.isInfinite()) // true
println(p.isFinite()) // false
println("${p < 0} ${p > 0}") // false true
 
val n = Double.NEGATIVE_INFINITY // -∞
println(n.isInfinite()) // true
println(n.isFinite()) // false
println("${n < 0} ${n > 0}") // true false
}
Output:
true
false
false true
true
false
true false

Lasso[edit]

Lasso supports 64-bit decimals.. This gives Lasso's decimal numbers a range from approximately negative to positive 2x10^300 and with precision down to 2x10^-300. Lasso also supports decimal literals for NaN (not a number) as well and positive and negative infinity.

infinity
'<br />'
infinity -> type

-> inf

decimal

Maple[edit]

Maple's floating point numerics are a strict extension of IEEE/754 and IEEE/854 so there is already a built-in infinity. (In fact, there are several.) The following procedure just returns the floating point (positive) infinity directly.

 
> proc() Float(infinity) end();
Float(infinity)
 

There is also an exact infinity ("infinity"), a negative float infinity ("Float(-infinity)" or "-Float(infinity)") and a suite of complex infinities. The next procedure returns a boxed machine (double precision) float infinity.

 
> proc() HFloat(infinity) end();
HFloat(infinity)
 

Mathematica / Wolfram Language[edit]

Mathematica has infinity built-in as a symbol. Which can be used throughout the software:

Sum[1/n^2,{n,Infinity}]
1/Infinity
Integrate[Exp[-x^2], {x, -Infinity, Infinity}]
10^100 < Infinity

gives back:

Pi^2/6
0
Sqrt[Pi]
True

Moreover Mathematica has 2 other variables that represent 'infinity': DirectedInfinity[r] and ComplexInfinity. DirectInfinity[r] represents an infinite quantity with complex direction r. ComplexInfinity represents an infinite quantity with an undetermined direction; like 1/0. Which has infinite size but undetermined direction. So the general infinity is DirectedInfinity, however if the direction is unknown it will turn to ComplexInfinity, DirectedInfinity[-1] will return -infinity and DirectedInfinity[1] will return infinity. Directed infinity can, for example, be used to integrate over an infinite domain with a given complex direction: one might want to integrate Exp[-x^2]/(x^2-1) from 0 to DirectedInfinity[Exp[I Pi/4]]:

Integrate[Exp[-x^2]/(x^2 - 1), {x, 0, DirectedInfinity[Exp[I Pi/4]]}]

gives back:

-((Pi (I+Erfi[1]))/(2 E))

MATLAB / Octave[edit]

MATLAB implements the IEEE 754 floating point standard as the default for all numeric data types. +Inf and -Inf are by default implemented and supported by MATLAB. To check if a variable has the value +/-Inf, one can use the built-in function "isinf()" which will return a Boolean 1 if the number is +/-inf.

a = +Inf;
isinf(a)
 

Returns:

ans =
     1

Maxima[edit]

/* Maxima has inf (positive infinity) and minf (negative infinity) */
 
declare(x, real)$
 
is(x < inf);
/* true */
 
is(x > minf);
/* true */
 
/* However, it is an error to try to divide by zero, even with floating-point numbers */
1.0/0.0;
/* expt: undefined: 0 to a negative exponent.
-- an error. To debug this try: debugmode(true); */

Metafont[edit]

Metafont numbers are a little bit odd (it uses fixed binary arithmetic). For Metafont, the biggest number (and so the one which is also considered to be infinity) is 4095.99998. In fact, in the basic set of macros for Metafont, we can read

infinity := 4095.99998;

Modula-2[edit]

MODULE inf;
 
IMPORT InOut;
 
BEGIN
InOut.WriteReal (1.0 / 0.0, 12, 12);
InOut.WriteLn
END inf.

Producing

[email protected]:~/modula/rosetta$ inf
 
**** RUNTIME ERROR bound check error
Floating point exception

Modula-3[edit]

IEEESpecial contains 3 variables defining negative infinity, positive infinity, and NaN for all 3 floating point types in Modula-3 (REAL, LONGREAL, and EXTENDED).

If the implementation doesn't support IEEE floats, the program prints arbitrary values (Critical Mass Modula-3 implementation does support IEEE floats).

MODULE Inf EXPORTS Main;
 
IMPORT IO, IEEESpecial;
 
BEGIN
IO.PutReal(IEEESpecial.RealPosInf);
IO.Put("\n");
END Inf.

Output:

Infinity

Nemerle[edit]

Both single and double precision floating point numbers support PositiveInfinity, NegativeInfinity and NaN.

def posinf = double.PositiveInfinity;
def a = IsInfinity(posinf); // a = true
def b = IsNegativeInfinity(posinf); // b = false
def c = IsPositiveInfinity(posinf); // c = true

Nim[edit]

Inf

is a predefined constant in Nim:

var f = Inf
echo f

OCaml[edit]

infinity

is already a pre-defined value in OCaml.

# infinity;;
- : float = infinity
# 1.0 /. 0.0;;
- : float = infinity


Oforth[edit]

10 1000.0 powf dup println dup neg println 1 swap / println
Output:
1.#INF
-1.#INF
0

OpenEdge/Progress[edit]

The unknown value (represented by a question mark) can be considered to equal infinity. There is no difference between positive and negative infinity but the unknown value sometimes sorts low and sometimes sorts high when used in queries.

MESSAGE
1.0 / 0.0 SKIP
-1.0 / 0.0 SKIP(1)
( 1.0 / 0.0 ) = ( -1.0 / 0.0 )
VIEW-AS ALERT-BOX.

Output

---------------------------
Message (Press HELP to view stack trace)
---------------------------
? 
? 

yes
---------------------------
OK   Help   
---------------------------

OxygenBasic[edit]

Using double precision floats:

 
print 1.5e-400 '0
 
print 1.5e400 '#INF
 
print -1.5e400 '#-INF
 
print 0/-1.5 '-0
 
print 1.5/0 '#INF
 
print -1.5/0 '#-INF
 
print 0/0 '#qNAN
 
 
function f() as double
return -1.5/0
end function
 
print f '#-INF
 

Oz[edit]

declare
PosInf = 1./0.
NegInf = ~1./0.
in
{Show PosInf}
{Show NegInf}
 
%% some assertion
42. / PosInf = 0.
42. / NegInf = 0.
PosInf * PosInf = PosInf
PosInf * NegInf = NegInf
NegInf * NegInf = PosInf

PARI/GP[edit]

Works with: PARI/GP version version 2.8.0 and higher
+oo
Works with: PARI/GP version version 2.2.9 to 2.7.0
infty()={
[1] \\ Used for many functions like intnum
};

Pascal[edit]

See Delphi

Perl[edit]

Positive infinity:

my $x = 0 + "inf";
my $y = 0 + "+inf";

Negative infinity:

my $x = 0 - "inf";
my $y = 0 + "-inf";

The "0 + ..." is used here to make sure that the variable stores a value that is actually an infinitive number instead of just a string "inf" but in practice one can use just:

my $x = "inf";

and $x while originally holding a string will get converted to an infinite number when it is first used as a number.

Some programmers use expressions that overflow the IEEE floating point numbers such as:

my $x = 1e1000;

which is 101000 or googol10 or even numbers like this one:

my $y = 10**10**10;

which is 1010000000000 but it has to make some assumptions about the underlying hardware format and its size. Furthermore, using such literals in the scope of some pragmas such as bigint, bignum or bigrat would actually compute those numbers:

use bigint;
my $x = 1e1000;
my $y = 10**10**10;

Here the $x and $y when printed would give 1001 and 10000000001-digit numbers respectively, the latter taking no less than 10GB of space to just output.

Under those pragmas, however, there is a simpler way to use infinite values, thanks to the inf symbol being exported into the namespace by default:

use bigint;
my $x = inf;
my $y = -inf;

Perl 6[edit]

Inf support is required by language spec on all abstract Numeric types (in the absence of subset constraints) including Num, Rat and Int types. Native integers cannot support Inf, so attempting to assign Inf will result in an exception; native floats are expected to follow IEEE standards including +/- Inf and NaN.

Phix[edit]

constant infinity = 1e300*1e300
? infinity
Output:
inf

PHP[edit]

This is how you get infinity:

INF

Unfortunately, "1.0 / 0.0" doesn't evaluate to infinity; but instead seems to evaluate to False, which is more like 0 than infinity.

PHP has functions is_finite() and is_infinite() to test for infiniteness.

PL/I[edit]

 
declare x float, y float (15), z float (18);
 
put skip list (huge(x), huge(y), huge(z));
 

PicoLisp[edit]

The symbol 'T' is used to represent infinite values, e.g. for the length of circular lists, and is greater than any other value in comparisons. PicoLisp has only very limited floating point support (scaled bignum arithmetics), but some functions return 'T' for infinite results.

(load "@lib/math.l")
 
: (exp 1000.0)
-> T

PostScript[edit]

/infinity { 9 99 exp } def

PowerShell[edit]

A .NET floating-point number representing infinity is available.

function infinity {
[double]::PositiveInfinity
}

PureBasic[edit]

PureBasic uses IEEE 754 coding for float types. PureBasic also includes the function Infinity() that return the positive value for infinity and the boolean function IsInfinite(value.f) that returns true if the floating point value is either positive or negative infinity.

If OpenConsole()
Define.d a, b
b = 0
 
;positive infinity
PrintN(StrD(Infinity())) ;returns the value for positive infinity from builtin function
 
a = 1.0
PrintN(StrD(a / b)) ;calculation results in the value of positive infinity
 
;negative infinity
PrintN(StrD(-Infinity())) ;returns the value for negative infinity from builtin function
 
a = -1.0
PrintN(StrD(a / b)) ;calculation results in the value of negative infinity
 
Print(#crlf$ + #crlf$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf
 

Outputs

+Infinity
+Infinity
-Infinity
-Infinity

Python[edit]

This is how you get infinity:

>>> float('infinity')
inf

Note: When passing in a string to float(), values for NaN and Infinity may be returned, depending on the underlying C library. The specific set of strings accepted which cause these values to be returned depends entirely on the underlying C library used to compile Python itself, and is known to vary.
The Decimal module explicitly supports +/-infinity Nan, +/-0.0, etc without exception.

Floating-point division by 0 doesn't give you infinity, it raises an exception:

>>> 1.0 / 0.0
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: float division

If float('infinity') doesn't work on your platform, you could use this trick:

>>> 1e999
1.#INF

It works by trying to create a float bigger than the machine can handle.

R[edit]

 Inf                    #positive infinity
-Inf #negative infinity
.Machine$double.xmax # largest finite floating-point number
is.finite # function to test to see if a number is finite
 
# function that returns the input if it is finite, otherwise returns (plus or minus) the largest finite floating-point number
forcefinite <- function(x) ifelse(is.finite(x), x, sign(x)*.Machine$double.xmax)
 
forcefinite(c(1, -1, 0, .Machine$double.xmax, -.Machine$double.xmax, Inf, -Inf))
# [1] 1.000000e+00 -1.000000e+00 0.000000e+00 1.797693e+308
# [5] -1.797693e+308 1.797693e+308 -1.797693e+308

Racket[edit]

as in Scheme:

#lang racket
 
+inf.0 ; positive infinity
(define (finite? x) (< -inf.0 x +inf.0))
(define (infinite? x) (not (finite? x)))

REXX[edit]

The language specifications for REXX are rather open-ended when it comes to language limits.

Limits on numbers are expressed as: The REXX interpreter has to at least handle exponents up to nine (decimal) digits.

So it's up to the writers of the REXX interpreter to decide what limits are to be implemented or enforced.

For the default setting of

               NUMERIC DIGITS 9

the biggest number that can be used is  (for the Regina REXX  and  R4  REXX interpreters):

.999999999e+999999999
For a setting of

              NUMERIC DIGITS 100

the biggest number that can be used is:


(for the Regina REXX interpreter)

.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999e+999999999


(for the R4 REXX interpreter)

.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999e+9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999



... and so on with larger  NUMERIC DIGITS

For most REXX interpreters, the maximum number of digits is only limited by virtual storage,
but the pratical limit would be a little less than half of available virtual storage,
which would (realistically) be around one billion digits. Other interpreters have a limitation of roughly 8 million digits.

RLaB[edit]

 
>> x = inf()
inf
>> isinf(x)
1
>> inf() > 10
1
>> -inf() > 10
0
 


Ruby[edit]

Infinity is a Float value

a = 1.0/0       # => Infinity
a.finite? # => false
a.infinite? # => 1
 
a = -1/0.0 # => -Infinity
a.infinite? # => -1
 
a = Float::MAX # => 1.79769313486232e+308
a.finite? # => true
a.infinite? # => nil
Works with: Ruby version 1.9.2+
a = Float::INFINITY       # => Infinity

Rust[edit]

Rust has builtin function for floating types which returns infinity. This program outputs 'inf'.

fn main() {
let inf = std::f32::INFINITY;
println!("{}", inf);
}

Scala[edit]

Library: Scala

See also

In order to be compliant with IEEE-754, Scala has all support for infinity on its floating-point types (float, double). You can get infinity from constants in the corresponding wrapper class; for example, Double:

val inf = Double.PositiveInfinity //defined as 1.0/0.0
inf.isInfinite; //true

The largest possible number in Scala (without using the Big classes) is also in the Double class.

val biggestNumber = Double.MaxValue

REPL session:

scala> 1 / 0.
res2: Double = Infinity
 
scala> -1 / 0.
res3: Double = -Infinity
 
scala> 1 / Double.PositiveInfinity
res4: Double = 0.0
 
scala> 1 / Double.NegativeInfinity
res5: Double = -0.0

Scheme[edit]

+inf.0 ; positive infinity
(define (finite? x) (< -inf.0 x +inf.0))
(define (infinite? x) (not (finite? x)))

Seed7[edit]

Seed7s floating-point type (float) supports infinity. The library float.s7i defines the constant Infinity as:

const float: Infinity is 1.0 / 0.0;

Checks for infinity can be done by comparing with this constant.

Sidef[edit]

var a = 1.5/0        # Inf
say a.is_inf # true
say a.is_pos # true
 
var b = -1.5/0 # -Inf
say b.is_ninf # true
say b.is_neg # true
 
var inf = Inf
var ninf = -Inf
say (inf == -ninf) # true

Slate[edit]

PositiveInfinity

Smalltalk[edit]

Works with: GNU Smalltalk

Each of the finite-precision Float classes (FloatE, FloatD, FloatQ), have an "infinity" method that returns infinity in that type.

st> FloatD infinity
Inf
st> 1.0 / 0.0
Inf
Works with: Smalltalk/X

The class names are different (Float, ShortFloat and LongFloat); for sourcecode compatibility, you can do "Smalltalk at:#FloatQ put:LongFloat". The behavior is slightly different, in that an exception is raised:

Float infinity -> INF
1.0 / 0.0 -> "ZeroDivide exception"

but we can simulate the other behavior with:

[
1.0 / 0.0
] on: ZeroDivide do:[:ex |
ex proceedWith: (Float infinity)
]
-> INF

Standard ML[edit]

Real.posInf
- Real.posInf;
val it = inf : real
- 1.0 / 0.0;
val it = inf : real

Swift[edit]

Swift's floating-point types (Float, Double, and any other type that conforms to the FloatingPointNumber protocol) all support infinity. You can get infinity from the infinity class property in the type:

let inf = Double.infinity
inf.isInfinite //true

As a function:

func getInf() -> Double {
return Double.infinity
}

Tcl[edit]

Works with: Tcl version 8.5

Tcl 8.5 has Infinite as a floating point value, not an integer value

package require Tcl 8.5
 
expr {1.0 / 0} ;# ==> Inf
expr {-1.0 / 0} ;# ==> -Inf
expr {inf} ;# ==> Inf
expr {1 / 0} ;# ==> "divide by zero" error; Inf not part of range of integer division

A maximal integer is not easy to find, as Tcl switches to unbounded integers when a 64-bit integer is about to roll over:

% format %lx -1      ;# all bits set
ffffffffffffffff
 
% regsub f 0x[format %lx -1] 7 ;# unset the sign bit for positive
0x7fffffffffffffff
 
% set ii [expr [regsub f 0x[format %lx -1] 7]] ;# show as decimal
9223372036854775807
 
% incr ii
9223372036854775808 ;# silently upgrade to unbounded integer, still positive

A theoretical MAXINT, though very impractical, could be

string repeat 9 [expr 2**32-1]

TI-89 BASIC[edit]

TorqueScript[edit]

function infinity()
{
return 1/0;
}

Trith[edit]

The following functions are included as part of the core operators:

 
: inf 1.0 0.0 / ;
: -inf inf neg ;
: inf? abs inf = ;
 

Ursa[edit]

Infinity is a defined value in Ursa.

decl double d
set d Infinity

Ursala[edit]

IEEE double precision floating point numbers are a primitive type in Ursala. This function returns IEEE double precision infinity when applied to any argument, using the value inf, which is declared as a constant in the flo library.


#import flo
 
infinity = inf!

Visual Basic[edit]

Works with: Visual Basic version 6

Positive infinity, negative infinity and indefinite number (usable as NaN?) can be generated by deliberately dividing by zero under the influence of On Error Resume Next:

Dim PlusInfinity as Double
Dim MinusInfinity as Double
Dim IndefiniteNumber as Double
On Error Resume Next
PlusInfinity = 1 / 0
MinusInfinity = -1 / 0
IndefiniteNumber = 0 / 0

The results of the above are stored internally as:

1.#INF
-1.#INF
-1.#IND

zkl[edit]

zkl doesn't like INF, NaN, etc but sorta knows about them:

1.5/0
Output:
Exception thrown: MathError(INF (number is infinite))