Integer overflow: Difference between revisions

 

For 32-bit signed integers:

!Expression

!Result that does not fit into a 32-bit signed integer

 

For 64-bit signed integers:

!Expression

!Result that does not fit into a 64-bit signed integer

 

For 32-bit unsigned integers:

!Expression

!Result that does not fit into a 32-bit unsigned integer

 

For 64-bit unsigned integers:

!Expression

!Result that does not fit into a 64-bit unsigned integer

|}

 

<br><br>

 

<br>

If you mask, you can test it in your program:

L 3,=F'1' 1

AR 2,3 add register3 to register2

BO OVERFLOW branch on overflow

....

On the other hand,

you will have the S0C8 system abend code : '''fixed point overflow exception'''

with the same program, if you unmask bit 20 by:

O 1,BITFPO unmask Fixed Overflow

SPM 1 Set Program Mask

...

DS 0F alignment

 

=={{header|Ada}}==

In Ada, both predefined and user-defined integer types are in a given range, between Type'First and Type'Last, inclusive. The range of predefined types is implementation specific. When the result of a computation is out of the type's range, the program <b>does not continue with a wrong result, but</b> instead <b>raises an exception</b>.

 

 

procedure Overflow is

A := A + 1; -- line 49 -- this will later raise a CONSTRAINT_ERROR

end loop;

 

{{out}}

 

Other implementations are at liberty to take any action they wish, including to continue silently with a "wrong" result or to throw a catchable exception (though the latter would require at least one addition to the standard prelude so as to provide the handler routine(s).

print (max int);

print (1+max int)

{{out}}

<pre>+2147483647

Note that, unlike many other languages, there is no presupposition that Algol 68 is running on a binary computer. The second example code below shows that for variables of mode '''long int''' arithmetic is fundamentally decimal in Algol 68 Genie.

 

print (long max int);

print (1+ long max int)

END

 

{{out}}

1

a68g: runtime error: 1: LONG INT value out of bounds (numerical result out of range) (detected in VOID closed-clause starting at "BEGIN" in line 1).</pre>

 

=={{header|AutoHotkey}}==

Since AutoHotkey treats all integers as signed 64-bit, there is no point in demonstrating overflow with other integer types.

A AutoHotkey program does <b>not</b> recognize a signed integer overflow and the program <b>continues with wrong results</b>.

{{out}}

<pre>Testing signed 64-bit integer overflow with AutoHotkey:

Overflow does <b>not</b> trigger an exception (because Axe does not support exceptions). After an overflow the program <b>continues with wrong results</b> (specifically, the value modulo 65536).

 

Disp 40000+40000▶Dec,i

Disp 32767-65535▶Dec,i

 

{{out}}

For those with a finite integer range, though, the most common stack cell size is a 32 bit signed integer, which will usually just wrap when overflowing (as shown in the sample output below). That said, it's not uncommon for the last expression to produce some kind of runtime error or OS exception, frequently even crashing the interpreter itself.

 

v,,,9"="*84 .: ,,"+"*84 .: **:*" }}" ,+55 .-\0-1<

>:+. 55+, ::0\- :. 48*"-",, \:. 48*"="9,,, -. 55v

v.*: ,,,,,999"="*84 .: ,,"*"*84 .: *+8*7"s9" ,+<

 

{{out}}

An overflow for signed integer arithmetic is undefined behavior.

A C program does <b>not</b> recognize a signed integer overflow and the program <b>continues with wrong results</b>.

 

int main (int argc, char *argv[])

printf("%lu\n", 4294967296LU * 4294967296LU);

return 0;

 

{{out}}

The default behavior can be changed with a compiler flag.

 

public class IntegerOverflow

}

{{out}}

<pre>

 

{{works with | g++ | 4.7}}

#include <cstdint>

#include <limits>

<< 4294967296LU * 4294967296LU << '\n';

return 0;

 

{{out}}

 

By default, Clojure throws Exceptions on overflow conditions:

(+ 5000000000000000000 5000000000000000000)

(- -9223372036854775807 9223372036854775807)

{{out}} for all of the above statements:

<pre>ArithmeticException integer overflow clojure.lang.Numbers.throwIntOverflow</pre>

 

If you want to silently overflow, you can set the special *unchecked-math* variable to true or use the special operations, unchecked-add, unchecked-multiply, etc..

(* -1 (dec -9223372036854775807)) ;=> -9223372036854775808

(+ 5000000000000000000 5000000000000000000) ;=> -8446744073709551616

; Note: The following division will currently silently overflow regardless of *unchecked-math*

; See: http://dev.clojure.org/jira/browse/CLJ-1253

 

Clojure supports an arbitrary precision integer, BigInt and alternative math operators suffixed with an apostrophe: +', -', *', inc', and dec'. These operators auto-promote to BigInt upon overflow.

=={{header|COBOL}}==

COBOL uses decimal arithmetic, so the examples given in the specification are not directly relevant. This program declares a variable that can store three decimal digits, and attempts to assign a four-digit number to it. The result is that the number is truncated to fit, with only the three least significant digits actually being stored; and the program then proceeds. This behaviour may sometimes be what we want.

PROGRAM-ID. PROCRUSTES-PROGRAM.

DATA DIVISION.

MOVE 1002 TO X.

DISPLAY X UPON CONSOLE.

{{out}}

<pre>002</pre>

A small example:

 

program-id. overflowing.

 

 

goback.

 

{{out}}

=={{header|Computer/zero Assembly}}==

Arithmetic is performed modulo 256; overflow is not detected. This fragment:

ADD one

 

 

ff: 255

causes the accumulator to adopt the value 0. With a little care, the programmer can exploit this behaviour by treating each eight-bit word as either an unsigned byte or a signed byte using two's complement (although the instruction set does not provide explicit support for negative numbers). On the two's complement interpretation, the code given above would express the computation "–1 + 1 = 0".

 

Additionally, standard functions are available to perform arithmetic on int, long, uint, ulong values that modify a boolean value to signal when an overflow has occurred.

 

import std.stdio;

 

immutable r = muls(46_341, 46_341, overflow);

writeln("\n", r, " ", overflow);

{{out}}

<pre>Signed 32-bit:

 

-2147479015 true</pre>

 

=={{header|Factor}}==

=={{header|FreeBASIC}}==

For the 64-bit integer type a FreeBASIC program does <b>not</b> recognize a signed integer overflow and the program <b>continues with wrong results</b>.

 

 

' The suffixes L, LL, UL and ULL are added to the numbers to make it

Print

Print "Press any key to quit"

 

{{out}}

[http://play.golang.org/p/jsPWC8KGzD Run this in the Go playground].

A Go program does <b>not</b> recognize an integer overflow and the program <b>continues with wrong results</b>.

 

import "fmt"

u64 = 4294967296

fmt.Printf(" %d * %d: %d\n", u64, u64, u64*u64)

{{out}}

<pre>32 bit signed integers

Groovy does not recognize integer overflow in any bounded integral type and the program '''continues with wrong results'''. All bounded integral types use ''2's-complement'' arithmetic.

 

assert -(-2147483647-1) != 2147483648g

println(-(-2147483647-1))

println(3037000500g * 3037000500g)

assert (-9223372036854775807g-1g).intdiv(-1) == 9223372036854775808g

 

Output:

=={{header|Haskell}}==

Haskell supports both fixed sized signed integers (Int) and unbounded integers (Integer). Various sizes of signed and unsigned integers are available in Data.Int and Data.Word, respectively. The Haskell 2010 Language Report explains the following: "The results of exceptional conditions (such as overflow or underflow) on the fixed-precision numeric types are undefined; an implementation may choose error (⊥, semantically), a truncated value, or a special value such as infinity, indefinite, etc" (http://www.haskell.org/definition/haskell2010.pdf Section 6.4 Paragraph 4).

import Data.Word

import Control.Exception

f ((10000000000000000000 + 10000000000000000000) :: Word64)

f ((9223372036854775807 - 18446744073709551615) :: Word64)

{{out}}

<pre>-2147483648

Also, negative numbers do not use - for the negative sign in J (a preceding - means to negate the argument on the right - in some cases this is the same kind of result, but in other cases it's different). Instead, use _ to denote negative numbers. Also, J does not use / for division, instead J uses % for division. With those changes, here's what the results look like in a 32 bit version of J:

 

2.14748e9

2000000000 + 2000000000

_9.22337e18

4294967296 * 4294967296

 

And, here's what it looks like in a 64 bit version of J:

 

2147483648

2000000000 + 2000000000

_9.22337e18

4294967296 * 4294967296

 

That said, note that the above was with default 6 digits of "printing precision". Here's how things look with that limit relaxed:

32 bit J:

 

2147483648

2000000000 + 2000000000

_9223372036854775800

4294967296 * 4294967296

 

64 bit J:

 

2147483648

2000000000 + 2000000000

_9223372036854775800

4294967296 * 4294967296

 

Finally, note that both versions of J support arbitrary precision integers. These are not the default, for performance reasons, but are available for cases where their performance penalty is acceptable.

The type int is a signed 32-bit integer and the type long is a 64-bit integer.

A Java program does <b>not</b> recognize an integer overflow and the program <b>continues with wrong results</b>.

public static void main(String[] args) {

System.out.println("Signed 32-bit:");

System.out.println(2000000000 + 2000000000);

System.out.println(-2147483647 - 2147483647);

System.out.println(46341 * 46341);

System.out.println("Signed 64-bit:");

System.out.println(-9223372036854775807L - 9223372036854775807L);

System.out.println(3037000500L * 3037000500L);

}

 

{{out}}

-9223372036854775808

</pre>

 

=={{header|Julia}}==

'''Plain Integer Types and Their Limits'''

S = subtypes(Signed)

U = subtypes(Unsigned)

@printf("%8s: [%s, %s]\n", s, typemin(s), typemax(s))

@printf("%8s: [%s, %s]\n", u, typemin(u), typemax(u))

{{out}}

<pre>Integer limits:

Julia does not throw an explicit error on integer overflow.

 

for t in S

over = typemax(t) + one(t)

@printf("%8s → %-25s (%s)\n", t, over, typeof(over))

 

{{out}}

A Kotlin program does <b>not</b> recognize a signed integer overflow and the program <b>continues with wrong results</b>.

 

 

@Suppress("INTEGER_OVERFLOW")

println("*** Signed 32 bit integers ***\n")

println(-(-2147483647 - 1))

println(3037000500 * 3037000500)

println((-9223372036854775807 - 1) / -1)

println("\n*** Unsigned 32 bit integers ***\n")

 

{{out}}

2147483648

131073

</pre>

 

Lingo uses 32-bit signed integers.

A Lingo program does <b>not</b> recognize a signed integer overflow and the program <b>continues with wrong results</b>.

 

-- -2147483648

 

 

put (-2147483647-1) / -1

 

=={{header|M2000 Interpreter}}==

Long A

Try ok {

Print Hex$(Eval(DataMem, 0!b))="BBBBAAAA"

Print Eval(DataMem, 0!b)=Eval(DataMem, 0!a2)*0x10000+Eval(DataMem, 0!a1)

 

 

=={{header|Nim}}==

 

 

 

 

 

 

 

 

 

 

 

 

{{out}}

 

=={{header|Oforth}}==

 

=={{header|PARI/GP}}==

{{out}}

<pre>%1 = Vecsmall([1])

 

Of course PARI can use the same techniques as [[#C|C]].

 

=={{header|Perl}}==

Using Perl 5.18 on 64-bit Linux with use integer:

The Perl 5 program below does <b>not</b> recognize a signed integer overflow and the program <b>continues with wrong results</b>.

 

use strict;

use warnings;

say(3037000500 * 3037000500);

say((-9223372036854775807-1) / -1);

{{out}}

<pre>

 

=={{header|Phix}}==

Phix has both 32 and 64 bit implementations. Integers are signed and limited to 31 (or 63) bits, ie

-1,073,741,824 to +1,073,741,823 (-#40000000 to #3FFFFFFF) on 32 bit, whereas on

Integer overflow is handled by automatic promotion to atom (an IEEE float, 64/80 bit for the 32/64 bit implementations respectively),

which triggers a run-time type check if stored in a variable declared as integer, eg:

{{out}}

<pre>

</pre>

The <b>overflow is automatically caught</b> and the program <b>does not continue</b> with the wrong results. You are always given the exact source file and line number that the error occurs on, and several editors, including Edita which is bundled with the compiler, will automatically jump to the source code line at fault. Alternatively you may declare a variable as atom and get the same performance for small integers, with seamless conversion to floats (with 53 or 64 bits of precision) as needed. Phix has no concept of unsigned numbers, except as user defined types that trigger errors when negative values are detected, but otherwise have the same ranges as above.

 

=={{header|PicoLisp}}==

=={{header|Pike}}==

Pike transparently promotes int to bignum when needed, so integer overflows do not occur.

 

=={{header|PowerShell}}==

https://docs.microsoft.com/en-us/dotnet/api/system.decimal?view=netframework-4.8#remarks

 

try {

# All of these raise an exception, which is caught below.

$Error.Exception

}

 

=={{header|PureBasic}}==

CPU=x64, OS=Windows7

 

#MAX_ASCII=255 ;=MAX_CHAR Ascii-Mode

say("Quad",q1,q2,SizeOf(q1))

 

{{out}}

<pre>

Python 2.X has a 32 bit signed integer type called 'int' that automatically converts to type 'long' on overflow. Type long is of arbitrary precision adjusting its precision up to computer limits, as needed.

 

Type "copyright", "credits" or "license()" for more information.

>>> for calc in ''' -(-2147483647-1)

Expression: '46341 * 46341' evaluates to 2147488281 of type <type 'long'>

Expression: '(-2147483647-1) / -1' evaluates to 2147483648 of type <type 'long'>

 

===Python 3.x===

Python 3.X has the one 'int' type that is of arbitrary precision. Implementations ''may'' use 32 bit integers for speed and silently shift to arbitrary precision to avoid overflow.

Type "copyright", "credits" or "license()" for more information.

>>> for calc in ''' -(-2147483647-1)

Expression: '46341 * 46341' evaluates to 2147488281 of type <class 'int'>

Expression: '(-2147483647-1) / -1' evaluates to 2147483648.0 of type <class 'float'>

 

Note: In Python 3.X the division operator used between two ints returns a floating point result, (as this was seen as most often required and expected in the Python community). Use <code>//</code> to get integer division.

 

=={{header|Racket}}==

The unsafe operations expects fixnums in the arguments, and that the result is also a fixnum. They don't autopromote the result. They are faster but they should be used only in special cases, where the values known to be bounded. We can use them to see the behavior after an overflow. In case of a overflow they have undefined behaviour, so they may give different results or change without warning in future versions. (I don't expect that they will change soon, but there is no official guaranty.)

 

(require racket/unsafe/ops)

 

 

(/ -1073741824 -1) ;==> 1073741824

 

The 64-bit version is similar. The fixnum are effectively 63-bits signed integers.

The Raku program below does <b>not</b> recognize a signed integer overflow and the program <b>continues with wrong results</b>.

 

{{out}}

<pre>-9223372036854775808

For newer versions of REXX, the &nbsp; '''signal on lostDigits''' &nbsp; statement can be used to accomplish the same results &nbsp;

<br>(for detecting a loss of significance [digits]).

numeric digits 9 /*the REXX default is 9 decimal digits.*/

call showResult( 999999997 + 1 )

else _=' [underflow]' /*did it underflow? */

say right(x, 20) _ /*show the result. */

'''output''' &nbsp; using the default input(s): <br><br>

Output note: &nbsp; (as it happens, all of the results below are numerically correct)

-1.00000000E+9 [underflow]

-1.50000000E+9 [underflow]

</pre>

 

Bignum objects are created automatically when integer calculations would otherwise overflow a Fixnum.

When a calculation involving Bignum objects returns a result that will fit in a Fixnum, the result is automatically converted.

=> 4611686018427387903

2.1.1 :002 > a.class

2.1.1 :004 > (b-1).class

=> Fixnum

Since Ruby 2.4 these different classes have disappeared: all numbers in above code are of class Integer.

 

The following code will always panic when run in any mode

 

// The following will panic!

let i32_1 : i32 = -(-2_147_483_647 - 1);

let i64_4 : i64 = 3_037_000_500 * 3_037_000_500;

let i64_5 : i64 = (-9_223_372_036_854_775_807 - 1) / -1;

 

In order to declare overflow/underflow behaviour as intended (and, thus, valid in both debug and release modes), Rust provides two mechanisms:

<br>

 

// The following will never panic!

println!("{:?}", 65_537u32.checked_mul(65_537)); // None

println!("{:?}", 65_537i32.saturating_mul(65_537)); // 2147483647

println!("{:?}", 65_537i32.wrapping_mul(-65_537)); // -131073

 

Second, a generic <code>Wrapping<T></code> one-element tuple type is provided which implements the same basic operations as the <code>wrapping_...</code> methods, but allows you to use normal operators and then use the <code>.0</code> field accessor to retrieve the value once you are finished.<ref>{{Cite web |url=https://doc.rust-lang.org/std/num/struct.Wrapping.html |title=Struct std::num::Wrapping |website=The Rust Standard Library |access-date=2019-11-18}}</ref>

{{works with|Java|8}}

Math.addExact works for both 32-bit unsigned and 64-bit unsigned integers, but Java does not support signed integers.

 

def requireOverflow(f: => Unit) =

println("Test - Expect Undetected overflow:")

requireOverflow(++(1,1)) // Undetected overflow

 

=={{header|Seed7}}==

The type [http://seed7.sourceforge.net/manual/types.htm#integer integer] is a 64-bit signed integer type.

All computations with the type integer are checked for overflow.

 

const proc: writeResult (ref func integer: expression) is func

writeResult(3037000500 * 3037000500);

writeResult((-9223372036854775807-1) div -1);

 

{{out}}

{{trans|Raku}}

Sidef has unlimited precision integers.

{{out}}

<pre>

9223372036854775808

</pre>

 

=={{header|Swift}}==

// However, you can opt-in to overflow behavior with the overflow operators and continue with wrong results

 

println(uInt64)

uInt64 = 4294967296 &* 4294967296

{{out}}

<pre>

=={{header|Standard ML}}==

PolyML

poly: : error: Overflow exception raised while converting ~9223372036854775807 to int

Int.maxInt ;

2147483648 * 2147483648 ;

Exception- Overflow raised

 

=={{header|Tcl}}==

Tcl (since 8.5) uses logical signed integers throughout that are “large enough to hold the number you are using” (being internally anything from a single machine word up to a bignum). The only way to get 32-bit and 64-bit values in arithmetic is to apply a clamping function at appropriate points:

expr {$x<0 ? -((-$x) & 0x7fffffff) : $x & 0x7fffffff}

}

Tcl 8.4 used a mix of 32-bit and 64-bit numbers on 32-bit platforms and 64-bit numbers only on 64-bit platforms. Users are recommended to upgrade to avoid this complexity.

 

=={{header|VBScript}}==

<br>- Yes, because typename(2147483647)="Long" and typename(2147483648)="Double", so we have switched from fixed binary integer to double floating point. But thanks to mantissa precision there is no harm. The integer overflow is when you reach 10^15, because you are now out of the integer set : (1E+15)+1=1E+15 !?.

<br>A good way to test integer overflow is to use the vartype() or typename() builtin functions.

i=(-2147483647-1)/-1

wscript.echo i

i1=1000000000000000-1 '1E+15-1

i2=i1+1 '1E+15

{{out}}

<pre>

{{works with|Visual Basic|VB6 Standard}}

Overflow is well handled, except for a strange bug in the computation of f the constant -(-2147483648).

Dim i As Long '32-bit signed integer

i = -(-2147483647 - 1) '=-2147483648 ?! bug

i = 46341 * 46341 'Run-time error '6' : Overflow

i = (-2147483647 - 1) / -1 'Run-time error '6' : Overflow

'''Error handling - method 1'''

On Error Resume Next

i = 2147483647 + 1

Debug.Print i 'i=0

'''Error handling - method 2'''

On Error GoTo overflow

i = 2147483647 + 1

overflow:

Debug.Print "Error: " & Err.Description '-> Error: Overflow

'''Error handling - method 3'''

i = 2147483647 + 1 'Run-time error '6' : Overflow

Debug.Print i

 

=={{header|Visual Basic .NET}}==

 

'''32-bit signed integer'''

Pre-compilation error:

'Error: Constant expression not representable in type 'Integer'

for:

i = 0 - (-2147483647 - 1)

i = -(-2147483647L - 1)

i = -2147483647 - 2147483647

i = 46341 * 46341

Execution error:

'An unhandled exception of type 'System.OverflowException' occurred

'Additional information: Arithmetic operation resulted in an overflow.

for:

'''32-bit unsigned integer'''<br>

In Visual Basic .Net there is no specific UInteger constants as in C.

Pre-compilation error:

'Error: Constant expression not representable in type 'UInteger'

for:

i = 3000000000 + 3000000000

i = 2147483647 - 4294967295

Execution error:

'An unhandled exception of type 'System.OverflowException' occurred

'Additional information: Arithmetic operation resulted in an overflow.

for:

'''64-bit signed integer'''

Pre-compilation error:

'Error: Constant expression not representable in type 'Long'

for:

i = 5000000000000000000 + 5000000000000000000

i = -9223372036854775807 - 9223372036854775807

i = 3037000500 * 3037000500

Execution error:

'An unhandled exception of type 'System.OverflowException' occurred

'Additional information: Arithmetic operation resulted in an overflow.

for:

 

'''64-bit unsigned integer'''<br>

In Visual Basic .Net there is no specific ULong constants as in C.

And 'Long' constants are not good enough.

Pre-compilation error:

'Error: Overflow

for:

i = 10000000000000000000 + 10000000000000000000

Pre-compilation error:

'Error: Constant expression not representable in type 'Long'

for:

Execution error:

'An unhandled exception of type 'System.OverflowException' occurred

'Additional information: Arithmetic operation resulted in an overflow.

for:

 

'''how the exception is catched'''

Try

i = -2147483647 : i = -(i - 1)

Catch ex As Exception

Debug.Print("Exception raised : " & ex.Message)

{{out}}

<pre>

 

However, within this overall framework, Wren also has an unsigned 32-bit integer sub-system when dealing with bitwise operations. All values are converted internally to such integers before the corresponding C bitwise operation is performed (Wren's VM is written in C) and can therefore overflow without warning. Fortunately, we can easily observe these effects by performing the operations required by the task and then (for example) right shifting them by 0 places.

System.print("Unsigned 32-bit:")

{{out}}

Results agree with those for the corresponding C entry above.

continues with wrong results.

 

[N:= -(-2147483647-1);

IntOut(0, N); CrLf(0);

N:= (-2147483647-1)/-1;

IntOut(0, N); CrLf(0);

 

{{out}}

-2147483648

</pre>

 

=={{header|zkl}}==

zkl uses C's 64 bit integer math and the results are OS dependent. Integers are signed. GMP can be used for big ints.

A zkl program does <b>not</b> recognize an integer overflow and the program <b>continues with wrong results</b>.

println(-(-9223372036854775807-1));

println(5000000000000000000+5000000000000000000);

println(-9223372036854775807 - 9223372036854775807);

println(3037000500 * 3037000500);

{{out}}

Linux/BSD/clang