# Infinity

**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

## 11l

`print(Float.infinity)`

- Output:

inf

## ActionScript

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

```
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

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

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*).

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: *

## APL

For built-in functions, reduction over an empty list returns the identity value for that function.
E.g., `+/⍬`

gives `0`

, and `×/⍬`

gives 1.

The identity value for `⌊`

(minimum) is the largest possible value. For APL implementations
that support infinity, this will be infinity. Otherwise, it will be some large, but finite value.

```
inf ← {⌊/⍬}
```

- Output:

∞

1.797693135E308

## Argile

(simplified)

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

## Arturo

```
print infinity
print neg infinity
```

- Output:

∞ -∞

## AWK

```
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

## BASIC

### BASIC256

```
onerror TratoError
infinity = 1e300*1e300
end
TratoError:
if lasterror = 29 then print lasterrormessage
return
```

### BBC BASIC

```
*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

### bootBASIC

There are no floating point numbers in bootBASIC. All numbers and variables are 2 byte unsigned integers.

The code below can't print anything on the screen, plus the program won't end. No way is currently known to break out of the program.

```
10 print 1/0
```

## BQN

Positive infinity is just ∞:

∞ + 1 ∞ ∞ - 3 ∞ -∞ ¯∞ ∞ - ∞ NaN

## C

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#

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

Output:

```
Infinity
```

## C++

```
#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

Java's floating-point types (float, double) all support infinity. Clojure has literals for infinity:

```
##Inf ;; same as Double/POSITIVE_INFINITY
##-Inf ;; same as Double/NEGATIVE_INFINITY
(Double/isInfinite ##Inf) ;; 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 (1+(1-2^(-52)))*2^1023 or 1.7976931348623157*10^308 (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

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

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.

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

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

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

## Delphi

Delphi defines the following constants in Math:

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

Test for infinite value using:

```
Math.IsInfinite()
```

## Dyalect

Dyalect floating point number support positive infinity:

`func infinityTask() => Float.Infinity`

## E

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

## EasyLang

```
print number "inf"
# or
print 1 / 0
```

## Eiffel

```
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

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

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

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

## F#

```
printfn "%f" (1.0/0.0)
```

- Output:

Infinity

## Factor

```
1/0.
```

## Fantom

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

```
: 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

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

```
' 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)

## FutureBasic

FB has a native definition for infinite floating point types. As demonstrated below, it returns "inf".

```
printf @"%g", INFINITY
HandleEvents
```

- Output:

inf

## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In **this page** you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

**Solution**

Fōrmulæ does not use floating point numbers, but arbitrary-size integers and arbitrary-precision decimal numbers.

Infinity is a predefined expression in Fōrmulæ.

Reduction of certain expressions can produce it:

## GAP

```
# 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

```
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

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

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

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

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

```
inf := 1/0
```

or

```
Number constants inf
```

## IS-BASIC

`PRINT INF`

Output:

9.999999999E62

## J

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

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})*2^{1023} or 1.7976931348623157*10^{308} (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

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)
```

## Joy

`1 1024 ldexp dup neg stack.`

- Output:

[-inf inf]

## jq

Sufficiently recent versions of the C, Go and Rust implementations of jq (jq, gojq, and jaq, respectively) all allow `infinite` as a scalar value in jq programs; jq and gojq display its value as 1.7976931348623157e+308. The C implementation also allows the token `inf` when reading JSON, and stores it as `infinite`.

The C implementation of jq uses IEEE 754 64-bit floating-point arithmetic, and very large real number literals, e.g. 1e1000, are evaluated as IEEE 754 infinity, so 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 jq value is equal to `infinite` or `- infinite`, one can use the built-in filter `isinfinite`. One can also use `==` in the expected manner.

## Julia

Julia uses IEEE floating-point arithmetic and includes a built-in constant `Inf` for (64-bit) floating-point infinity. Inf32 can be used as 32-bit infinity, when avoiding type promotions to Int64.

```
julia> julia> Inf32 == Inf64 == Inf16 == Inf
true
```

## K

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

```
/ 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
```

## Klingphix

```
1e300 dup mult tostr "inf" equal ["Infinity" print] if
" " input
```

## Kotlin

```
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

## Lambdatalk

Lambdatalk is built on Javascript and can inherit lots of its capabilities. For instance:

```
{/ 1 0}
-> Infinity
{/ 1 Infinity}
-> 0
{< {pow 10 100} Infinity}
-> true
{< {pow 10 1000} Infinity}
-> false
```

## Lasso

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

## Lingo

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

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

## M2000 Interpreter

```
Rem : locale 1033
Module CheckIt {
Form 66,40
Cls 5
Pen 14
\\ Ensure True/False for Print boolean (else -1/0)
\\ from m2000 console use statement Switches without Set.
\\ use Monitor statement to see all switches.
Set Switches "+SBL"
IF version<9.4 then exit
IF version=9.4 and revision<25 then exit
Function Infinity(positive=True) {
buffer clear inf as byte*8
m=0x7F
if not positive then m+=128
return inf, 7:=m, 6:=0xF0
=eval(inf, 0 as double)
}
K=Infinity(false)
L=Infinity()
Function TestNegativeInfinity(k) {
=str$(k, 1033) = "-1.#INF"
}
Function TestPositiveInfinity(k) {
=str$(k, 1033) = "1.#INF"
}
Function TestInvalid {
=str$(Number, 1033) = "-1.#IND"
}
Pen 11 {Print " True True"}
Print TestNegativeInfinity(K), TestPositiveInfinity(L)
Pen 11 {Print " -1.#INF 1.#INF -1.#INF 1.#INF -1.#INF 1.#INF"}
Print K, L, K*100, L*100, K+K, L+L
M=K/L
Pen 11 {Print " -1.#IND -1.#IND True True" }
Print K/L, L/K, TestInvalid(M), TestInvalid(K/L)
M=K+L
Pen 11 {Print " -1.#IND -1.#IND -1.#IND True True"}
Print M, K+L, L+K, TestInvalid(M), TestInvalid(K+L)
Pen 11 {Print " -1.#INF 1.#INF"}
Print 1+K+2, 1+L+2
Pen 11 {Print " -1.#INF"}
Print K-L
Pen 11 {Print " 1.#INF"}
Print L-K
}
Checkit
```

## Maple

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

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

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

```
/* 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

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;`

## MiniScript

MiniScript uses IEEE numerics, so:

```
posInfinity = 1/0
print posInfinity
```

- Output:

INF

## Modula-2

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

Producing

```
jan@Beryllium:~/modula/rosetta$ inf
**** RUNTIME ERROR bound check error
Floating point exception
```

## Modula-3

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

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

```
Inf
```

is a predefined constant in Nim:

```
var f = Inf
echo f
```

## NS-HUBASIC

`10 PRINT 1/0`

- Output:

?DZ ERROR is a division by zero error in NS-HUBASIC.

?DZ ERROR IN 10

## OCaml

```
infinity
```

is already a pre-defined value in OCaml.

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

## Oforth

`10 1000.0 powf dup println dup neg println 1 swap / println`

- Output:

1.#INF -1.#INF 0

## Ol

Inexact numbers support can be disabled during recompilation using "-DOLVM_INEXACTS=0" command line argument. Inexact numbers in Ol demands the existence of infinity, by demanding IEEE numbers. There are two signed infinity numbers (as constants) in Ol:

+inf.0 ; positive infinity -inf.0 ; negative infinity

```
(define (infinite? x) (or (equal? x +inf.0) (equal? x -inf.0)))
(infinite? +inf.0) ==> #true
(infinite? -inf.0) ==> #true
(infinite? +nan.0) ==> #false
(infinite? 123456) ==> #false
(infinite? 1/3456) ==> #false
(infinite? 17+28i) ==> #false
```

## OpenEdge/Progress

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

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

```
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

`+oo`

```
infty()={
[1] \\ Used for many functions like intnum
};
```

## Pascal

See Delphi

## PascalABC.NET

```
##
Write(real.PositiveInfinity);
```

- Output:

Infinity

## Perl

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 10^{1000} or googol^{10} or even numbers like this one:

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

which is 10^{10000000000} 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; # N.B. this will consume vast quantities of RAM
```

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;
```

## Phix

with javascript_semantics constant infinity = 1e300*1e300 ? infinity

- Output:

desktop/Phix:

inf

pwa/p2js:

Infinity

## Phixmonti

`1e300 dup * tostr "inf" == if "Infinity" print endif`

## PHP

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.

## PicoLisp

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
```

## PL/I

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

## PostScript

```
/infinity { 9 99 exp } def
```

## PowerShell

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

```
function infinity {
[double]::PositiveInfinity
}
```

## PureBasic

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

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.

## QB64

```
#include<math.h>
//save as inf.h
double inf(void){
return HUGE_VAL;
}
```

```
Declare CustomType Library "inf"
Function inf#
End Declare
Print inf
```

## QBasic

```
DECLARE FUNCTION f! ()
ON ERROR GOTO TratoError
PRINT 0!
PRINT 0 / -1.5
PRINT 1.5 / 0
PRINT 0 / 0
PRINT f
END
TratoError:
PRINT "Error "; ERR; " on line "; ERL; CHR$(9); " --> ";
SELECT CASE ERR
CASE 6
PRINT "Overflow"
RESUME NEXT
CASE 11
PRINT "Division by zero"
RESUME NEXT
CASE ELSE
PRINT "Unexpected error, ending program."
END
END SELECT
FUNCTION f!
f! = -1.5 / 0
END FUNCTION
```

## R

```
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

as in Scheme:

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

## Raku

(formerly Perl 6) 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.

```
my $x = 1.5/0; # Failure: catchable error, if evaluated will return: "Attempt to divide by zero ...
my $y = (1.5/0).Num; # assigns 'Inf'
```

## REXX

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

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

## RPL

- Input:

MAXR →NUM

- Output:

1: 1.7976931348E+308

## Ruby

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
```

```
a = Float::INFINITY # => Infinity
```

## Rust

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

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

## 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

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

## Seed7

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

```
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

`PositiveInfinity`

## 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

The behavior is slightly different, in that an exception is raised if you divide by zero:

```
FloatD 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: (FloatD infinity)
]
-> INF
```

## Standard ML

```
Real.posInf
```

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

## Swift

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

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

`∞`

## TorqueScript

```
function infinity()
{
return 1/0;
}
```

## Trith

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

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

## Ursa

Infinity is a defined value in Ursa.

```
decl double d
set d Infinity
```

## Ursala

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

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`

:

```
Option Explicit
Private Declare Sub GetMem8 Lib "msvbvm60.dll" _
(ByVal SrcAddr As Long, ByVal TarAddr As Long)
Sub Main()
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
Debug.Print "PlusInfinity = " & CStr(PlusInfinity) _
& " (" & DoubleAsHex(PlusInfinity) & ")"
Debug.Print "MinusInfinity = " & CStr(MinusInfinity) _
& " (" & DoubleAsHex(MinusInfinity) & ")"
Debug.Print "IndefiniteNumber = " & CStr(IndefiniteNumber) _
& " (" & DoubleAsHex(IndefiniteNumber) & ")"
End Sub
Function DoubleAsHex(ByVal d As Double) As String
Dim l(0 To 1) As Long
GetMem8 VarPtr(d), VarPtr(l(0))
DoubleAsHex = Right$(String$(8, "0") & Hex$(l(1)), 8) _
& Right$(String$(8, "0") & Hex$(l(0)), 8)
End Function
```

- Output:

PlusInfinity = 1,#INF (7FF0000000000000)MinusInfinity = -1,#INF (FFF0000000000000) IndefiniteNumber = -1,#IND (FFF8000000000000)

## V (Vlang)

```
import math
fn main() {
mut 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 = math.inf(1)
println('$x ${math.is_inf(x, 1)}') // demonstrate result
}
```

## Wren

Wren certainly supports infinity for floating point numbers as we already have a method *Num.isInfinity* to test for it.

```
var x = 1.5
var y = x / 0
System.print("x = %(x)")
System.print("y = %(y)")
System.print("'x' is infinite? %(x.isInfinity)")
System.print("'y' is infinite? %(y.isInfinity)")
```

- Output:

x = 1.5 y = infinity 'x' is infinite? false 'y' is infinite? true

## XPL0

The IEEE 754 floating point standard is used.

```
int A;
real X;
[Format(0, 15); \output in scientific notation
A:= addr X; \get address of (pointer to) X
A(0):= $FFFF_FFFF; \stuff in largest possible value
A(1):= $7FEF_FFFF;
RlOut(0, X); \display it
]
```

- Output:

1.797693134862320E+308

## Yabasic

```
infinity = 1e300*1e300
if str$(infinity) = "inf" print "Infinity"
```

## Zig

**Works with:** 0.10.x, 0.11.x, 0.12.0-dev.1577+9ad03b628

Assumes that defaul float optimization mode was not changed via @setFloatMode (performed in Strict mode, not Optimized, latter is equivalent to -ffast-math).

```
const std = @import("std");
const math = std.math;
test "infinity" {
const expect = std.testing.expect;
const float_types = [_]type{ f16, f32, f64, f80, f128, c_longdouble };
inline for (float_types) |T| {
const infinite_value: T = comptime std.math.inf(T);
try expect(math.isInf(infinite_value));
try expect(math.isPositiveInf(infinite_value));
try expect(!math.isNegativeInf(infinite_value));
try expect(!math.isFinite(infinite_value));
}
}
```

- Output:

$ zig test src/infinity_float.zig All 1 tests passed.

## zkl

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

`1.5/0`

- Output:

Exception thrown: MathError(INF (number is infinite))

## ZX Spectrum Basic

ZX Spectrum BASIC has no infinity handling;

`PRINT 1/0`

will be met with

6 Number too big, 0:1

A quick doubling loop will get you halfway to the maximum floating point value:

```
10 LET z=1
20 PRINT z
30 LET z=z*2
40 GO TO 20
```

Output will end with:

4.2535296E+37 8.5070592E+37 6 Number too big, 30:1

Precision has been lost by this stage through the loop, but one more manual double and subtract 1 will get you the true displayable maximum of 1.7014118E+38 (or 2^127-1).

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