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
<lang 11l>print(Float.infinity)</lang>
- Output:
inf
ActionScript
ActionScript has the built in function isFinite() to test if a number is finite or not. <lang actionscript>trace(5 / 0); // outputs "Infinity" trace(isFinite(5 / 0)); // outputs "false"</lang>
Ada
<lang 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;</lang> 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: <lang ada>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;</lang> 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: <lang ada>subtype Safe_Float is Float range Float'Range;</lang> 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.
<lang algol68>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))</lang> 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.
<lang apl>inf ← {⌊/⍬}</lang>
- Output:
∞
1.797693135E308
Argile
(simplified)
<lang Argile>use std printf "%f\n" atof "infinity" (: this prints "inf" :)
- extern :atof<text>: -> real</lang>
AWK
<lang AWK> BEGIN {
k=1; while (2^(k-1) < 2^k) k++; INF = 2^k; print INF; }</lang>
This has been tested with GAWK 3.1.7 and MAWK, both return
inf
BBC BASIC
<lang bbcbasic> *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</lang>
Output:
1.79769313E308
bootBASIC
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. <lang bootBASIC>10 print 1/0</lang>
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.
<lang c>#include <math.h> /* HUGE_VAL */
- include <stdio.h> /* printf() */
double inf(void) {
return HUGE_VAL;
}
int main() {
printf("%g\n", inf()); return 0;
}</lang>
The output from the above program might be "inf", "1.#INF", or something else.
C99 also has a macro for infinity:
<lang c>#define _ISOC99_SOURCE
- include <math.h>
- include <stdio.h>
int main() {
printf("%g\n", INFINITY); return 0;
}</lang>
C#
<lang csharp>using System;
class Program {
static double PositiveInfinity() { return double.PositiveInfinity; }
static void Main() { Console.WriteLine(PositiveInfinity()); }
}</lang> Output: <lang>Infinity</lang>
C++
<lang cpp>#include <limits>
double inf() {
if (std::numeric_limits<double>::has_infinity) return std::numeric_limits<double>::infinity(); else return std::numeric_limits<double>::max();
}</lang>
Clojure
Java's floating-point types (float, double) all support infinity. Clojure has literals for infinity: <lang clojure>##Inf ;; same as Double/POSITIVE_INFINITY
- -Inf ;; same as Double/NEGATIVE_INFINITY
(Double/isInfinite ##Inf) ;; true</lang>
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": <lang coffeescript>Infinity</lang> as well as constants in the Number class: <lang coffeescript>Number.POSITIVE_INFINITY Number.NEGATIVE_INFINITY</lang>
The global isFinite function tests for finiteness: <lang coffeescript>isFinite x</lang>
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
<lang lisp>> (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</lang>
Component Pascal
BlackBox Component Builder <lang oberon2> MODULE Infinity; IMPORT StdLog;
PROCEDURE Do*; VAR x: REAL; BEGIN x := 1 / 0; StdLog.String("x:> ");StdLog.Real(x);StdLog.Ln END Do;
</lang>
Execute: ^Q Infinity.Do
Output:
x:> inf
D
<lang d>auto inf() {
return typeof(1.5).infinity;
}
void main() {}</lang>
Delphi
Delphi defines the following constants in Math: <lang Delphi> Infinity = 1.0 / 0.0;
NegInfinity = -1.0 / 0.0;</lang>
Test for infinite value using: <lang Delphi>Math.IsInfinite()</lang>
Dyalect
Dyalect floating point number support positive infinity:
<lang Dyalect>func infinityTask() {
Float.Inf()
}</lang>
E
<lang e>def infinityTask() {
return Infinity # predefined variable holding positive infinity
}</lang>
Eiffel
<lang 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 </lang>
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: <lang ERRE> 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 </lang>
Euphoria
<lang Euphoria>constant infinity = 1E400
? infinity -- outputs "inf"</lang>
F#
<lang fsharp> printfn "%f" (1.0/0.0) </lang>
- Output:
Infinity
Factor
<lang factor>1/0.</lang>
Fantom
Fantom's Float
data type is an IEEE 754 64-bit floating point type. Positive infinity is represented by the constant posInf
.
<lang fantom> class Main {
static Float getInfinity () { Float.posInf } public static Void main () { echo (getInfinity ()) }
} </lang>
Forth
<lang 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 ;</lang>
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. <lang fortran>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</lang>
ISO Fortran 90 or later supports a HUGE intrinsic which returns the largest value supported by the data type of the number given. <lang fortran>real :: x real :: huge_real = huge(x)</lang>
FreeBASIC
<lang 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 </lang>
- Output:
1.#INF (String representation of Positive Infinity)
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, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
GAP
<lang 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</lang>
Go
<lang 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
}</lang> 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. <lang groovy>def biggest = { Double.POSITIVE_INFINITY }</lang>
Test program: <lang groovy>println biggest() printf ( "0x%xL \n", Double.doubleToLongBits(biggest()) )</lang>
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:
<lang haskell>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</lang>
Test for the two standard floating point types:
<lang haskell>*Main> infinity :: Float Infinity
- Main> infinity :: Double
Infinity</lang>
Or you can simply use division by 0: <lang haskell>Prelude> 1 / 0 :: Float Infinity Prelude> 1 / 0 :: Double Infinity</lang>
Or use "read" to read the string representation: <lang haskell>Prelude> read "Infinity" :: Float Infinity Prelude> read "Infinity" :: Double Infinity</lang>
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:
<lang idl>print, !Values.f_infinity ;; for normal floats or print, !Values.D_infinity ;; for doubles</lang>
Io
<lang io>inf := 1/0</lang>
or
<lang io>Number constants inf</lang>
IS-BASIC
<lang IS-BASIC>PRINT INF</lang> 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: <lang j>
_ * 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
_ </lang>
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: <lang java>double infinity = Double.POSITIVE_INFINITY; //defined as 1.0/0.0 Double.isInfinite(infinity); //true</lang> As a function: <lang java>public static double getInf(){
return Double.POSITIVE_INFINITY;
}</lang> The largest possible number in Java (without using the Big classes) is also in the Double class. <lang java>double biggestNumber = Double.MAX_VALUE;</lang> 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": <lang javascript>Infinity</lang> as well as constants in the Number class: <lang javascript>Number.POSITIVE_INFINITY Number.NEGATIVE_INFINITY</lang>
The global isFinite() function tests for finiteness: <lang javascript>isFinite(x)</lang>
jq
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:
<lang jq>def infinite: 1e1000;</lang>
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:
<lang jq>def isinfinite: . == infinite;</lang>
Currently, the infinite value prints as though it were a very large floating point number.
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.
<lang Julia> julia> julia> Inf32 == Inf64 == Inf16 == Inf true </lang>
K
K has predefined positive and negative integer and float infinities: -0I, 0I, -0i, 0i. They have following properties:
<lang K> / 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</lang>
Klingphix
<lang Klingphix>1e300 dup mult tostr "inf" equal ["Infinity" print] if
" " input</lang>
Kotlin
<lang scala>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} ${n > 0}") // true false
}</lang>
- Output:
true false false true true false true false
Lambdatalk
Lambdatalk is built on Javascript and can inherit lots of its capabilities. For instance: <lang scheme> {/ 1 0} -> Infinity {/ 1 Infinity} -> 0 {< {pow 10 100} Infinity} -> true {< {pow 10 1000} Infinity} -> false </lang>
Lasso
Lasso supports 64-bit decimals.. This gives Lasso's decimal numbers a range from approximately negative to positive 2x10^300 and with precision down to 2x10^-300. Lasso also supports decimal literals for NaN (not a number) as well and positive and negative infinity.
<lang Lasso>infinity
'
'
infinity -> type</lang>
-> inf
decimal
Lingo
Lingo stores floats using IEEE 754 double-precision (64-bit) format. INF is not a constant that can be used programmatically, but only a special return value. <lang lingo>x = (1-power(2, -53)) * power(2, 1023) * 2 put ilk(x), x -- #float 1.79769313486232e308
x = (1-power(2, -53)) * power(2, 1023) * 3 put ilk(x), x, -x -- #float INF -INF</lang>
Lua
<lang lua> function infinity()
return 1/0 --lua uses unboxed C floats for all numbers
end </lang>
M2000 Interpreter
<lang M2000 Interpreter> Rem : locale 1033 Module CheckIt {
Form 66,40 Cls 5 Pen 14 \\ Ensure True/False for Print boolean (else -1/0) \\ from m2000 console use statement Switches without Set. \\ use Monitor statement to see all switches. Set Switches "+SBL" IF version<9.4 then exit IF version=9.4 and revision<25 then exit Function Infinity(positive=True) { buffer clear inf as byte*8 m=0x7F if not positive then m+=128 return inf, 7:=m, 6:=0xF0 =eval(inf, 0 as double) } K=Infinity(false) L=Infinity() Function TestNegativeInfinity(k) { =str$(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 </lang>
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. <lang Maple> > proc() Float(infinity) end();
Float(infinity)
</lang> 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. <lang Maple> > proc() HFloat(infinity) end();
HFloat(infinity)
</lang>
Mathematica / Wolfram Language
Mathematica has infinity built-in as a symbol. Which can be used throughout the software: <lang Mathematica>Sum[1/n^2,{n,Infinity}] 1/Infinity Integrate[Exp[-x^2], {x, -Infinity, Infinity}] 10^100 < Infinity</lang> 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]]: <lang Mathematica>Integrate[Exp[-x^2]/(x^2 - 1), {x, 0, DirectedInfinity[Exp[I Pi/4]]}]</lang> 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.
<lang Matlab>a = +Inf; isinf(a) </lang>
Returns:
ans = 1
Maxima
<lang 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); */</lang>
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
<lang metafont>infinity := 4095.99998;</lang>
MiniScript
MiniScript uses IEEE numerics, so:
<lang MiniScript>posInfinity = 1/0 print posInfinity</lang>
- Output:
INF
Modula-2
<lang Modula-2>MODULE inf;
IMPORT InOut;
BEGIN
InOut.WriteReal (1.0 / 0.0, 12, 12); InOut.WriteLn
END inf.</lang> Producing <lang Modula-2>jan@Beryllium:~/modula/rosetta$ inf
- RUNTIME ERROR bound check error
Floating point exception</lang>
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). <lang modula3>MODULE Inf EXPORTS Main;
IMPORT IO, IEEESpecial;
BEGIN
IO.PutReal(IEEESpecial.RealPosInf); IO.Put("\n");
END Inf.</lang>
Output:
Infinity
Nemerle
Both single and double precision floating point numbers support PositiveInfinity, NegativeInfinity and NaN. <lang Nemerle>def posinf = double.PositiveInfinity; def a = IsInfinity(posinf); // a = true def b = IsNegativeInfinity(posinf); // b = false def c = IsPositiveInfinity(posinf); // c = true</lang>
Nim
<lang nim>Inf</lang> is a predefined constant in Nim: <lang nim>var f = Inf echo f</lang>
NS-HUBASIC
<lang NS-HUBASIC>10 PRINT 1/0</lang>
- Output:
?DZ ERROR is a division by zero error in NS-HUBASIC.
?DZ ERROR IN 10
OCaml
<lang ocaml>infinity</lang> is already a pre-defined value in OCaml.
# infinity;; - : float = infinity # 1.0 /. 0.0;; - : float = infinity
Oforth
<lang Oforth>10 1000.0 powf dup println dup neg println 1 swap / println</lang>
- 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
<lang scheme> (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 </lang>
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.
<lang progress>MESSAGE
1.0 / 0.0 SKIP -1.0 / 0.0 SKIP(1) ( 1.0 / 0.0 ) = ( -1.0 / 0.0 )
VIEW-AS ALERT-BOX.</lang>
Output
--------------------------- Message (Press HELP to view stack trace) --------------------------- ? ? yes --------------------------- OK Help ---------------------------
OxygenBasic
Using double precision floats: <lang oxygenbasic> 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 </lang>
Oz
<lang 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</lang>
PARI/GP
<lang parigp>+oo</lang>
<lang parigp>infty()={
[1] \\ Used for many functions like intnum
};</lang>
Pascal
See Delphi
Perl
Positive infinity:
<lang perl>my $x = 0 + "inf";
my $y = 0 + "+inf";</lang>
Negative infinity:
<lang perl>my $x = 0 - "inf";
my $y = 0 + "-inf";</lang>
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:
<lang perl>my $x = "inf";</lang>
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:
<lang perl>my $x = 1e1000;</lang>
which is 101000 or googol10 or even numbers like this one:
<lang perl>my $y = 10**10**10;</lang>
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:
<lang perl>use bigint;
my $x = 1e1000;
my $y = 10**10**10; # N.B. this will consume vast quantities of RAM</lang>
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:
<lang perl>use bigint;
my $x = inf;
my $y = -inf;</lang>
Phix
with javascript_semantics constant infinity = 1e300*1e300 ? infinity
- Output:
desktop/Phix:
inf
pwa/p2js:
Infinity
Phixmonti
<lang Phixmonti>1e300 dup * tostr "inf" == if "Infinity" print endif</lang>
PHP
This is how you get infinity: <lang php>INF</lang> Unfortunately, "1.0 / 0.0" doesn't evaluate to infinity; but instead seems to evaluate to False, which is more like 0 than infinity.
PHP has functions is_finite() and is_infinite() to test for infiniteness.
PicoLisp
The symbol 'T' is used to represent infinite values, e.g. for the length of circular lists, and is greater than any other value in comparisons. PicoLisp has only very limited floating point support (scaled bignum arithmetics), but some functions return 'T' for infinite results. <lang PicoLisp>(load "@lib/math.l")
- (exp 1000.0)
-> T</lang>
PL/I
<lang PL/I> declare x float, y float (15), z float (18);
put skip list (huge(x), huge(y), huge(z)); </lang>
PostScript
<lang postscript>/infinity { 9 99 exp } def</lang>
PowerShell
A .NET floating-point number representing infinity is available. <lang powershell>function infinity {
[double]::PositiveInfinity
}</lang>
PureBasic
PureBasic uses IEEE 754 coding for float types. PureBasic also includes the function Infinity() that return the positive value for infinity and the boolean function IsInfinite(value.f) that returns true if the floating point value is either positive or negative infinity.
<lang PureBasic>If OpenConsole()
Define.d a, b b = 0 ;positive infinity PrintN(StrD(Infinity())) ;returns the value for positive infinity from builtin function a = 1.0 PrintN(StrD(a / b)) ;calculation results in the value of positive infinity ;negative infinity PrintN(StrD(-Infinity())) ;returns the value for negative infinity from builtin function a = -1.0 PrintN(StrD(a / b)) ;calculation results in the value of negative infinity Print(#crlf$ + #crlf$ + "Press ENTER to exit"): Input() CloseConsole()
EndIf </lang>
Outputs
+Infinity +Infinity -Infinity -Infinity
Python
This is how you get infinity:
<lang python>>>> float('infinity')
inf</lang>
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: <lang python>>>> 1.0 / 0.0 Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: float division</lang>
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
<lang c++>#include<math.h> //save as inf.h double inf(void){ return HUGE_VAL; }</lang> <lang vb>Declare CustomType Library "inf"
Function inf#
End Declare
Print inf</lang>
R
<lang 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</lang>
Racket
as in Scheme:
<lang Racket>#lang racket
+inf.0 ; positive infinity (define (finite? x) (< -inf.0 x +inf.0)) (define (infinite? x) (not (finite? x)))</lang>
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. <lang perl6>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'</lang>
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
<lang RLaB> >> x = inf()
inf
>> isinf(x)
1
>> inf() > 10
1
>> -inf() > 10
0
</lang>
Ruby
Infinity is a Float value <lang ruby>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</lang>
<lang ruby>a = Float::INFINITY # => Infinity</lang>
Rust
Rust has builtin function for floating types which returns infinity. This program outputs 'inf'. <lang rust>fn main() {
let inf = f32::INFINITY; println!("{}", inf);
}</lang>
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: <lang Scala>val inf = Double.PositiveInfinity //defined as 1.0/0.0 inf.isInfinite; //true</lang> The largest possible number in Scala (without using the Big classes) is also in the Double class. <lang Scala>val biggestNumber = Double.MaxValue</lang>
REPL session: <lang scala>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</lang>
Scheme
<lang scheme>+inf.0 ; positive infinity (define (finite? x) (< -inf.0 x +inf.0)) (define (infinite? x) (not (finite? x)))</lang>
Seed7
Seed7s floating-point type (float) supports infinity. The library float.s7i defines the constant Infinity as: <lang seed7>const float: Infinity is 1.0 / 0.0;</lang> Checks for infinity can be done by comparing with this constant.
Sidef
<lang ruby>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</lang>
Slate
<lang slate>PositiveInfinity</lang>
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: <lang smalltalk>FloatD infinity -> INF 1.0 / 0.0 -> "ZeroDivide exception"</lang> but we can simulate the other behavior with: <lang smalltalk>[
1.0 / 0.0
] on: ZeroDivide do:[:ex |
ex proceedWith: (FloatD infinity)
] -> INF</lang>
Standard ML
<lang sml>Real.posInf</lang>
- 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: <lang swift>let inf = Double.infinity inf.isInfinite //true</lang> As a function: <lang swift>func getInf() -> Double {
return Double.infinity
}</lang>
Tcl
Tcl 8.5 has Infinite as a floating point value, not an integer value <lang tcl>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</lang>
A maximal integer is not easy to find, as Tcl switches to unbounded integers when a 64-bit integer is about to roll over: <lang Tcl>% 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</lang> A theoretical MAXINT, though very impractical, could be
string repeat 9 [expr 2**32-1]
TI-89 BASIC
<lang ti89b>∞</lang>
TorqueScript
<lang TorqueScript>function infinity() {
return 1/0;
}</lang>
Trith
The following functions are included as part of the core operators: <lang trith>
- inf 1.0 0.0 / ;
- -inf inf neg ;
- inf? abs inf = ;
</lang>
Ursa
Infinity is a defined value in Ursa. <lang ursa>decl double d set d Infinity</lang>
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.
<lang Ursala>#import flo
infinity = inf!</lang>
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
:
<lang vb>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</lang>
- Output:
PlusInfinity = 1,#INF (7FF0000000000000)MinusInfinity = -1,#INF (FFF0000000000000) IndefiniteNumber = -1,#IND (FFF8000000000000)
Wren
Wren certainly supports infinity for floating point numbers as we already have a method Num.isInfinity to test for it. <lang ecmascript>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)")</lang>
- Output:
x = 1.5 y = infinity 'x' is infinite? false 'y' is infinite? true
XPL0
The IEEE 754 floating point standard is used. <lang XPL0>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):= $7FEF_FFFF; RlOut(0, X); \display it ]</lang>
- Output:
1.797693134862320E+308
Yabasic
<lang Yabasic>infinity = 1e300*1e300 if str$(infinity) = "inf" print "Infinity"</lang>
Zig
<lang zig>const std = @import("std");
const debug = std.debug; const math = std.math;
test "infinity" {
const infinite_f16 = math.inf(f16); const infinite_f32 = math.inf(f32); const infinite_f64 = math.inf(f64); const infinite_f128 = math.inf(f128);
// Any other types besides these four floating types are not implemented.
debug.assert(math.isInf(infinite_f16)); debug.assert(math.isInf(infinite_f32)); debug.assert(math.isInf(infinite_f64)); debug.assert(math.isInf(infinite_f128));
debug.assert(math.isPositiveInf(infinite_f16)); debug.assert(math.isPositiveInf(infinite_f32)); debug.assert(math.isPositiveInf(infinite_f64)); debug.assert(math.isPositiveInf(infinite_f128));
debug.assert(math.isNegativeInf(-infinite_f16)); debug.assert(math.isNegativeInf(-infinite_f32)); debug.assert(math.isNegativeInf(-infinite_f64)); debug.assert(math.isNegativeInf(-infinite_f128));
debug.assert(!math.isFinite(infinite_f16)); debug.assert(!math.isFinite(infinite_f32)); debug.assert(!math.isFinite(infinite_f64)); // isFinite(f128) is not implemented. //debug.assert(!math.isFinite(infinite_f128));
}</lang>
zkl
zkl doesn't like INF, NaN, etc but sorta knows about them: <lang zkl>1.5/0</lang>
- Output:
Exception thrown: MathError(INF (number is infinite))
ZX Spectrum Basic
ZX Spectrum BASIC has no infinity handling; <lang zxbasic>PRINT 1/0</lang> will be met with
6 Number too big, 0:1
A quick doubling loop will get you halfway to the maximum floating point value: <lang zxbasic>10 LET z=1 20 PRINT z 30 LET z=z*2 40 GO TO 20</lang>
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).
- Programming Tasks
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