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

•   Extreme floating point values

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).

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: *

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:

GNU APL:

∞

Dyalog APL:

1.797693135E308

Argile

Translation of: C

(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

Works with: BBC BASIC for Windows

      *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

Translation of: Java

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

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

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

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)*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

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:

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

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

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

See Delphi

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 10¹⁰⁰⁰ or googol¹⁰ 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

Works with: QBasic version 1.1

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

Works with: Ruby version 1.9.2+

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

Library: Scala

See also

• Extreme_floating_point_values#Scala

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

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 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

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

∞

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

Works with: Visual Basic version 5

Works with: Visual Basic version 6

Works with: VBA version Access 97

Works with: VBA version 6.5

Works with: VBA version 7.1

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).