Integer overflow
Some languages support one or more integer types of the underlying processor.
You are encouraged to solve this task according to the task description, using any language you may know.
This integer types have fixed size; usually 8-bit, 16-bit, 32-bit, or 64-bit.
The integers supported by such a type can be signed or unsigned.
Arithmetic for machine level integers can often be done by single CPU instructions.
This allows high performance and is the main reason to support machine level integers.
- Definition
An integer overflow happens when the result of a computation does not fit into the fixed size integer. The result can be too small or too big to be representable in the fixed size integer.
- Task
When a language has fixed size integer types, create a program that does arithmetic computations for the fixed size integers of the language.
These computations must be done such that the result would overflow.
The program should demonstrate what the following expressions do.
For 32-bit signed integers:
| Expression | Result that does not fit into a 32-bit signed integer |
|---|---|
| -(-2147483647-1) | 2147483648 |
| 2000000000 + 2000000000 | 4000000000 |
| -2147483647 - 2147483647 | -4294967294 |
| 46341 * 46341 | 2147488281 |
| (-2147483647-1) / -1 | 2147483648 |
For 64-bit signed integers:
| Expression | Result that does not fit into a 64-bit signed integer |
|---|---|
| -(-9223372036854775807-1) | 9223372036854775808 |
| 5000000000000000000+5000000000000000000 | 10000000000000000000 |
| -9223372036854775807 - 9223372036854775807 | -18446744073709551614 |
| 3037000500 * 3037000500 | 9223372037000250000 |
| (-9223372036854775807-1) / -1 | 9223372036854775808 |
For 32-bit unsigned integers:
| Expression | Result that does not fit into a 32-bit unsigned integer |
|---|---|
| -4294967295 | -4294967295 |
| 3000000000 + 3000000000 | 6000000000 |
| 2147483647 - 4294967295 | -2147483648 |
| 65537 * 65537 | 4295098369 |
For 64-bit unsigned integers:
| Expression | Result that does not fit into a 64-bit unsigned integer |
|---|---|
| -18446744073709551615 | -18446744073709551615 |
| 10000000000000000000 + 10000000000000000000 | 20000000000000000000 |
| 9223372036854775807 - 18446744073709551615 | -9223372036854775808 |
| 4294967296 * 4294967296 | 18446744073709551616 |
When the integer overflow does trigger an exception show how the exception is caught.
When the integer overflow produces some value print it.
It should be explicitly noted when an integer overflow is not recognized and the program continues with wrong results.
This should be done for signed and unsigned integers of various sizes supported by the language.
When a language has no fixed size integer type or when no integer overflow can occur
for other reasons this should be noted.
It is okay to mention, when a language supports unlimited precision integers, but
this task is NOT the place to demonstrate the capabilities of unlimited precision integers.
360 Assembly
You can choose to manage or not the binary integer overflow with the program mask bits of the PSW (Program Status Word). Bit 20 enables fixed-point overflow. Two non-privileged instructions (IPM,SPM) are available for retrieving and setting the program mask of the current PSW.
If you mask, you can test it in your program:
<lang 360asm> L 2,=F'2147483647' 2**31-1
L 3,=F'1' 1
AR 2,3 add register3 to register2
BO OVERFLOW branch on overflow
....
OVERFLOW EQU *</lang> 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: <lang 360asm> IPM 1 Insert Program Mask
O 1,BITFPO unmask Fixed Overflow
SPM 1 Set Program Mask
...
DS 0F alignment
BITFPO DC BL1'00001000' bit20=1 [start at 16]</lang>
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 does not continue with a wrong result, but instead raises an exception.
<lang Ada>with Ada.Text_IO; use Ada.Text_IO;
procedure Overflow is
generic
type T is Range <>;
Name_Of_T: String;
procedure Print_Bounds; -- first instantiate this with T, Name
-- then call the instantiation
procedure Print_Bounds is
begin
Put_Line(" " & Name_Of_T & " " & T'Image(T'First)
& " .." & T'Image(T'Last));
end Print_Bounds; procedure P_Int is new Print_Bounds(Integer, "Integer "); procedure P_Nat is new Print_Bounds(Natural, "Natural "); procedure P_Pos is new Print_Bounds(Positive, "Positive"); procedure P_Long is new Print_Bounds(Long_Integer, "Long "); type Unsigned_Byte is range 0 .. 255; type Signed_Byte is range -128 .. 127; type Unsigned_Word is range 0 .. 2**32-1; type Thousand is range 0 .. 999; type Signed_Double is range - 2**63 .. 2**63-1; type Crazy is range -11 .. -3; procedure P_UB is new Print_Bounds(Unsigned_Byte, "U 8 "); procedure P_SB is new Print_Bounds(Signed_Byte, "S 8 "); procedure P_UW is new Print_Bounds(Unsigned_Word, "U 32 "); procedure P_Th is new Print_Bounds(Thousand, "Thous"); procedure P_SD is new Print_Bounds(Signed_Double, "S 64 "); procedure P_Cr is new Print_Bounds(Crazy, "Crazy"); A: Crazy := Crazy'First;
begin
Put_Line("Predefined Types:");
P_Int; P_Nat; P_Pos; P_Long;
New_Line;
Put_Line("Types defined by the user:");
P_UB; P_SB; P_UW; P_Th; P_SD; P_Cr;
New_Line;
Put_Line("Forcing a variable of type Crazy to overflow:");
loop -- endless loop
Put(" " & Crazy'Image(A) & "+1");
A := A + 1; -- line 49 -- this will later raise a CONSTRAINT_ERROR
end loop;
end Overflow;</lang>
- Output:
Predefined Types: Integer -2147483648 .. 2147483647 Natural 0 .. 2147483647 Positive 1 .. 2147483647 Long -9223372036854775808 .. 9223372036854775807 Types defined by the user: U 8 0 .. 255 S 8 -128 .. 127 U 32 0 .. 4294967295 Thous 0 .. 999 S 64 -9223372036854775808 .. 9223372036854775807 Crazy -11 ..-3 Forcing a variable of type Crazy to overflow: -11+1 -10+1 -9+1 -8+1 -7+1 -6+1 -5+1 -4+1 -3+1 raised CONSTRAINT_ERROR : overflow.adb:49 range check failed
ALGOL 68
In this instance, one must distinguish between the language and a particular implementation of the language. The Algol 68 Genie manual describes its behaviour thusly:
- As mentioned, the maximum integer which a68g can represent is max int and the maximum real is max real. Addition could give a sum which exceeds those two values, which is called overflow. Algol 68 leaves such case [sic] undefined, meaning that an implementation can choose what to do. a68g will give a runtime error in case of arithmetic overflow.
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). <lang algol68>BEGIN
print (max int); print (1+max int)
END</lang>
- Output:
+2147483647
3 print (1+max int)
1
a68g: runtime error: 1: INT math error (numerical result out of range) (detected in VOID closed-clause starting at "BEGIN" in line 1).
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.
<lang algol68>BEGIN
print (long max int); print (1+ long max int)
END </lang>
- Output:
+99999999999999999999999999999999999
3 print (1+ long max int)
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).
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 not recognize a signed integer overflow and the program continues with wrong results. <lang AutoHotkey>Msgbox, % "Testing signed 64-bit integer overflow with AutoHotkey:`n" -(-9223372036854775807-1) "`n" 5000000000000000000+5000000000000000000 "`n" -9223372036854775807-9223372036854775807 "`n" 3037000500*3037000500 "`n" (-9223372036854775807-1)//-1</lang>
- Output:
Testing signed 64-bit integer overflow with AutoHotkey: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808
This shows AutoHotkey does not handle integer overflow, and produces wrong results.
Axe
Axe supports 16-bit unsigned integers. It also supports 16-bit unsigned integers, but only for comparison. The task has been modified accordingly to accommodate this.
Overflow does not trigger an exception (because Axe does not support exceptions). After an overflow the program continues with wrong results (specifically, the value modulo 65536).
<lang axe>Disp -65535▶Dec,i Disp 40000+40000▶Dec,i Disp 32767-65535▶Dec,i Disp 257*257▶Dec,i</lang>
- Output:
1 14464 32768 513
Befunge
The Befunge-93 specification defines the range for stack cells as being the equivalent of a C signed long int on the same platform. However, in practice it will often depend on the underlying language of the interpreter, with Python-base implementations typically having an unlimited range, and JavaScript implementations using floating point.
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.
<lang befunge>"a9jc>"*:*+*+:0\- "(-",,:.048*"="99")1 -" >:#,_$v v,,,9"="*84 .: ,,"+"*84 .: **:*" }}" ,+55 .-\0-1< >:+. 55+, ::0\- :. 48*"-",, \:. 48*"="9,,, -. 55v v.*: ,,,,,999"="*84 .: ,,"*"*84 .: *+8*7"s9" ,+< >55+, 0\- "(",:.048*"="99"1-/)1 -">:#,_$ 1-01-/.@</lang>
- Output:
-(-2147483647 - 1) = -2147483648 2000000000 + 2000000000 = -294967296 -2147483647 - 2147483647 = 2 46341 * 46341 = -2147479015 (-2147483647 - 1)/-1 = -2147483648
Bracmat
Bracmat does arithmetic with arbitrary precision integer and rational numbers. No fixed size number types are supported.
C
C supports integer types of various sizes with and without signedness. Unsigned integer arithmetic is defined to be modulus a power of two. An overflow for signed integer arithmetic is undefined behavior. A C program does not recognize a signed integer overflow and the program continues with wrong results. <lang c>#include <stdio.h>
int main (int argc, char *argv[]) {
printf("Signed 32-bit:\n");
printf("%d\n", -(-2147483647-1));
printf("%d\n", 2000000000 + 2000000000);
printf("%d\n", -2147483647 - 2147483647);
printf("%d\n", 46341 * 46341);
printf("%d\n", (-2147483647-1) / -1);
printf("Signed 64-bit:\n");
printf("%ld\n", -(-9223372036854775807-1));
printf("%ld\n", 5000000000000000000+5000000000000000000);
printf("%ld\n", -9223372036854775807 - 9223372036854775807);
printf("%ld\n", 3037000500 * 3037000500);
printf("%ld\n", (-9223372036854775807-1) / -1);
printf("Unsigned 32-bit:\n");
printf("%u\n", -4294967295U);
printf("%u\n", 3000000000U + 3000000000U);
printf("%u\n", 2147483647U - 4294967295U);
printf("%u\n", 65537U * 65537U);
printf("Unsigned 64-bit:\n");
printf("%lu\n", -18446744073709551615LU);
printf("%lu\n", 10000000000000000000LU + 10000000000000000000LU);
printf("%lu\n", 9223372036854775807LU - 18446744073709551615LU);
printf("%lu\n", 4294967296LU * 4294967296LU);
return 0;
}</lang>
- Output:
Signed 32-bit: -2147483648 -294967296 2 -2147479015 -2147483648 Signed 64-bit: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808 Unsigned 32-bit: 1 1705032704 2147483648 131073 Unsigned 64-bit: 1 1553255926290448384 9223372036854775808 0
C#
C# has 2 modes for doing arithmetic: checked and unchecked.
Constant arithmetic (i.e. compile-time) is checked by default. Since all the examples use constant expressions, all these statements would result in compile-time exceptions. To change this behaviour, the statements can be wrapped inside a block marked with the 'unchecked' keyword.
Runtime arithmetic is unchecked by default. Values that overflow will simply 'wrap around' and the program will continue with wrong results. To make C# recognize overflow and throw an OverflowException, the statements can be wrapped inside a block marked with the 'checked' keyword.
The default behavior can be changed with a compiler flag.
<lang csharp>using System;
public class IntegerOverflow {
public static void Main() {
unchecked {
Console.WriteLine("For 32-bit signed integers:");
Console.WriteLine(-(-2147483647 - 1));
Console.WriteLine(2000000000 + 2000000000);
Console.WriteLine(-2147483647 - 2147483647);
Console.WriteLine(46341 * 46341);
Console.WriteLine((-2147483647 - 1) / -1);
Console.WriteLine();
Console.WriteLine("For 64-bit signed integers:");
Console.WriteLine(-(-9223372036854775807L - 1));
Console.WriteLine(5000000000000000000L + 5000000000000000000L);
Console.WriteLine(-9223372036854775807L - 9223372036854775807L);
Console.WriteLine(3037000500L * 3037000500L);
Console.WriteLine((-9223372036854775807L - 1) / -1);
Console.WriteLine();
Console.WriteLine("For 32-bit unsigned integers:");
//Negating a 32-bit unsigned integer will convert it to a signed 64-bit integer.
Console.WriteLine(-4294967295U);
Console.WriteLine(3000000000U + 3000000000U);
Console.WriteLine(2147483647U - 4294967295U);
Console.WriteLine(65537U * 65537U);
Console.WriteLine();
Console.WriteLine("For 64-bit unsigned integers:");
// The - operator cannot be applied to 64-bit unsigned integers; it will always give a compile-time error.
//Console.WriteLine(-18446744073709551615UL);
Console.WriteLine(10000000000000000000UL + 10000000000000000000UL);
Console.WriteLine(9223372036854775807UL - 18446744073709551615UL);
Console.WriteLine(4294967296UL * 4294967296UL);
Console.WriteLine();
}
int i = 2147483647;
Console.WriteLine(i + 1);
try {
checked { Console.WriteLine(i + 1); }
} catch (OverflowException) {
Console.WriteLine("Overflow!");
}
}
}</lang>
- Output:
For 32-bit signed integers: -2147483648 -294967296 2 -2147479015 -2147483648 For 64-bit signed integers: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808 For 32-bit unsigned integers: -4294967295 1705032704 2147483648 131073 For 64-bit unsigned integers: 1553255926290448384 9223372036854775808 0 -2147483648 Overflow!
C++
Same as C, except that if std::numeric_limits<IntegerType>::is_modulo is true, then the type IntegerType uses modulo arithmetic (the behavior is defined), even if it is a signed type.
A C++ program does not recognize a signed integer overflow and the program continues with wrong results.
<lang cpp>#include <iostream>
- include <cstdint>
- include <limits>
int main (int argc, char *argv[]) {
std::cout << std::boolalpha << std::numeric_limits<std::int32_t>::is_modulo << '\n' << std::numeric_limits<std::uint32_t>::is_modulo << '\n' // always true << std::numeric_limits<std::int64_t>::is_modulo << '\n' << std::numeric_limits<std::uint64_t>::is_modulo << '\n' // always true << "Signed 32-bit:\n" << -(-2147483647-1) << '\n' << 2000000000 + 2000000000 << '\n' << -2147483647 - 2147483647 << '\n' << 46341 * 46341 << '\n' << (-2147483647-1) / -1 << '\n' << "Signed 64-bit:\n" << -(-9223372036854775807-1) << '\n' << 5000000000000000000+5000000000000000000 << '\n' << -9223372036854775807 - 9223372036854775807 << '\n' << 3037000500 * 3037000500 << '\n' << (-9223372036854775807-1) / -1 << '\n' << "Unsigned 32-bit:\n" << -4294967295U << '\n' << 3000000000U + 3000000000U << '\n' << 2147483647U - 4294967295U << '\n' << 65537U * 65537U << '\n' << "Unsigned 64-bit:\n" << -18446744073709551615LU << '\n' << 10000000000000000000LU + 10000000000000000000LU << '\n' << 9223372036854775807LU - 18446744073709551615LU << '\n' << 4294967296LU * 4294967296LU << '\n'; return 0;
}</lang>
- Output:
true true true true Signed 32-bit: -2147483648 -294967296 2 -2147479015 -2147483648 Signed 64-bit: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808 Unsigned 32-bit: 1 1705032704 2147483648 131073 Unsigned 64-bit: 1 1553255926290448384 9223372036854775808 0
Clojure
Clojure supports Java's primitive integers, int (32-bit signed) and long (64-bit signed). However, Clojure automatically promotes the smaller int to a 64-bit long internally, so no 32-bit integer overflow issues can occur. For more information, see the documentation.
By default, Clojure throws Exceptions on overflow conditions: <lang clojure>(* -1 (dec -9223372036854775807)) (+ 5000000000000000000 5000000000000000000) (- -9223372036854775807 9223372036854775807) (* 3037000500 3037000500)</lang>
- Output:
for all of the above statements
ArithmeticException integer overflow clojure.lang.Numbers.throwIntOverflow
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.. <lang clojure>(set! *unchecked-math* true) (* -1 (dec -9223372036854775807)) ;=> -9223372036854775808 (+ 5000000000000000000 5000000000000000000) ;=> -8446744073709551616 (- -9223372036854775807 9223372036854775807) ;=> 2 (* 3037000500 3037000500) ;=> -9223372036709301616
- Note
- The following division will currently silently overflow regardless of *unchecked-math*
- See
- http://dev.clojure.org/jira/browse/CLJ-1253
(/ (dec -9223372036854775807) -1) ;=> -9223372036854775808</lang>
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.
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. <lang cobol>IDENTIFICATION DIVISION. PROGRAM-ID. PROCRUSTES-PROGRAM. DATA DIVISION. WORKING-STORAGE SECTION. 01 WS-EXAMPLE.
05 X PIC 999.
PROCEDURE DIVISION.
MOVE 1002 TO X. DISPLAY X UPON CONSOLE. STOP RUN.</lang>
- Output:
002
Update:
COBOL is by specification designed to be safe for use in financial situations. All standard native types are fixed size.
BINARY-CHAR [SIGNED/UNSIGNED], is 8 bits, alwaysBINARY-SHORT [SIGNED/UNSIGNED], is fixed at 16 bits, alwaysBINARY-LONG [SIGNED/UNSIGNED], is fixed at 32 bits, by specBINARY-DOUBLE [SIGNED/UNSIGNED]is 64 bits, alwaysPICTUREdata is sized according to picture, a9means decimal display storage, holding one digit within the grouping.
All data types are fully specified.
All COBOL basic arithmetic operations support ON SIZE ERROR and NOT ON SIZE ERROR clauses, which trap any attempt to store invalid data, for both native and PICTURE types. Programmers are free to ignore these features, but that willful ignorance is unlikely in production systems. Especially in programs destined for use in banking, government, or other industries where correctness of result is paramount.
A small example:
<lang cobol> identification division.
program-id. overflowing.
data division.
working-storage section.
01 bit8-sized usage binary-char. *> standard
01 bit16-sized usage binary-short. *> standard
01 bit32-sized usage binary-long. *> standard
01 bit64-sized usage binary-double. *> standard
01 bit8-unsigned usage binary-char unsigned. *> standard
01 nebulous-size usage binary-c-long. *> extension
01 picture-size picture s999. *> standard
*> ***************************************************************
procedure division.
*> 32 bit signed integer
subtract 2147483647 from zero giving bit32-sized
display bit32-sized
subtract 1 from bit32-sized giving bit32-sized
ON SIZE ERROR display "32bit signed SIZE ERROR"
end-subtract
*> value was unchanged due to size error trap and trigger
display bit32-sized
display space
*> 8 bit unsigned, size tested, invalid results discarded
add -257 to zero giving bit8-unsigned
ON SIZE ERROR display "bit8-unsigned SIZE ERROR"
end-add
display bit8-unsigned
*> programmers can ignore the safety features
compute bit8-unsigned = -257
display "you asked for it: " bit8-unsigned
display space
*> fixed size
move 999 to picture-size
add 1 to picture-size
ON SIZE ERROR display "picture-sized SIZE ERROR"
end-add
display picture-size
*> programmers doing the following, inadvertently,
*> do not stay employed at banks for long
move 999 to picture-size
add 1 to picture-size
*> intermediate goes to 1000, left end truncated on storage
display "you asked for it: " picture-size
add 1 to picture-size
display "really? you want to keep doing this?: " picture-size
display space
*> C values are undefined by spec, only minimums givens
display "How many bytes in a C long? "
length of nebulous-size
", varies by platform"
display "Regardless, ON SIZE ERROR will catch any invalid result"
*> on a 64bit machine, C long of 8 bytes
add 1 to h'ffffffffffffffff' giving nebulous-size
ON SIZE ERROR display "binary-c-long SIZE ERROR"
end-add
display nebulous-size
*> value will still be in initial state, GnuCOBOL initializes to 0
*> value now goes to 1, no size error, that ship has sailed
add 1 to nebulous-size
ON SIZE ERROR display "binary-c-long size error"
end-add
display "error state is not persistent: ", nebulous-size
goback.
end program overflowing.</lang>
- Output:
prompt$ cobc -xj overflowing.cob -2147483647 32bit signed SIZE ERROR -2147483647 bit8-unsigned SIZE ERROR 000 you asked for it: 001 picture-sized SIZE ERROR +999 you asked for it: +000 really? you want to keep doing this?: +001 How many bytes in a C long? 8, varies by platform Regardless, ON SIZE ERROR will catch any invalid result binary-c-long SIZE ERROR +00000000000000000000 error state is not persistent: +00000000000000000001
Computer/zero Assembly
Arithmetic is performed modulo 256; overflow is not detected. This fragment: <lang czasm> LDA ff
ADD one
...
ff: 255 one: 1</lang> 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".
D
In D both signed and unsigned integer arithmetic is defined to be modulus a power of two. Such overflow is not detected at run-time and the program continues with wrong results.
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.
<lang d>void main() @safe {
import std.stdio;
writeln("Signed 32-bit:");
writeln(-(-2_147_483_647 - 1));
writeln(2_000_000_000 + 2_000_000_000);
writeln(-2147483647 - 2147483647);
writeln(46_341 * 46_341);
writeln((-2_147_483_647 - 1) / -1);
writeln("\nSigned 64-bit:");
writeln(-(-9_223_372_036_854_775_807 - 1));
writeln(5_000_000_000_000_000_000 + 5_000_000_000_000_000_000);
writeln(-9_223_372_036_854_775_807 - 9_223_372_036_854_775_807);
writeln(3_037_000_500 * 3_037_000_500);
writeln((-9_223_372_036_854_775_807 - 1) / -1);
writeln("\nUnsigned 32-bit:");
writeln(-4_294_967_295U);
writeln(3_000_000_000U + 3_000_000_000U);
writeln(2_147_483_647U - 4_294_967_295U);
writeln(65_537U * 65_537U);
writeln("\nUnsigned 64-bit:");
writeln(-18_446_744_073_709_551_615UL);
writeln(10_000_000_000_000_000_000UL + 10_000_000_000_000_000_000UL);
writeln(9_223_372_036_854_775_807UL - 18_446_744_073_709_551_615UL);
writeln(4_294_967_296UL * 4_294_967_296UL);
import core.checkedint;
bool overflow = false;
// Checked signed multiplication.
// Eventually such functions will be recognized by D compilers
// and they will be implemented with efficient intrinsics.
immutable r = muls(46_341, 46_341, overflow);
writeln("\n", r, " ", overflow);
}</lang>
- Output:
Signed 32-bit: -2147483648 -294967296 2 -2147479015 -2147483648 Signed 64-bit: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808 Unsigned 32-bit: 1 1705032704 2147483648 131073 Unsigned 64-bit: 1 1553255926290448384 9223372036854775808 0 -2147479015 true
Factor
fixnum integers are automatically promoted to bignum integers when they no longer fit in a machine cell, and no overflow occurs. Note, however, that bignums are not demoted back to fixnums automatically.
Fortran
The Fortran standard does not specify the behaviour of program during integer overflow, so it depends on compiler implementation. Intel Fortran compiler does not have integer overflow detection. GNU gfortran runs some limited checks during compilations. The standard's model of integers is symmetric around zero, and using intrinsic function huge(my_integer) one can only discover the maximal number for kind of integer my_integer but cannot go beyond that.
FreeBASIC
For the 64-bit integer type a FreeBASIC program does not recognize a signed integer overflow and the program continues with wrong results. <lang c>#include <stdio.h>
<lang freebasic>' FB 1.05.0 Win64
' The suffixes L, LL, UL and ULL are added to the numbers to make it ' clear to the compiler that they are to be treated as: ' signed 4 byte, signed 8 byte, unsigned 4 byte and unsigned 8 byte ' integers, respectively.
' Integer types in FB are freely convertible to each other. ' In general if the result of a computation would otherwise overflow ' it is converted to a higher integer type.
' Consequently, although the calculations are the same as the C example, ' the results for the 32-bit integers are arithmetically correct (and different ' therefore from the C results) because they are converted to 8 byte integers.
' However, as 8 byte integers are the largest integral type, no higher conversions are ' possible and so the results 'wrap round'. The 64-bit results are therefore the ' same as the C examples except the one where the compiler warns that there is an overflow ' which, frankly, I don't understand.
Print "Signed 32-bit:" Print -(-2147483647L-1L) Print 2000000000L + 2000000000L Print -2147483647L - 2147483647L Print 46341L * 46341L Print (-2147483647L-1L) \ -1L Print Print "Signed 64-bit:" Print -(-9223372036854775807LL-1LL) Print 5000000000000000000LL + 5000000000000000000LL Print -9223372036854775807LL - 9223372036854775807LL Print 3037000500LL * 3037000500LL Print (-9223372036854775807LL - 1LL) \ -1LL ' compiler warning : Overflow in constant conversion Print Print "Unsigned 32-bit:" Print -4294967295UL Print 3000000000UL + 3000000000UL Print 2147483647UL - 4294967295UL Print 65537UL * 65537UL Print Print "Unsigned 64-bit:" Print -18446744073709551615ULL ' compiler warning : Implicit conversion Print 10000000000000000000ULL + 10000000000000000000ULL Print 9223372036854775807ULL - 18446744073709551615ULL Print 4294967296ULL * 4294967296ULL Print Print "Press any key to quit" Sleep</lang>
- Output:
Signed 32-bit: 2147483648 4000000000 -4294967294 2147488281 2147483648 Signed 64-bit: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 0 Unsigned 32-bit: -4294967295 6000000000 -2147483648 4295098369 Unsigned 64-bit: 1 1553255926290448384 9223372036854775808 0
Frink
Frink's numerical type is designed to "do the right thing" with all mathematics. It will not overflow, and integers can be of any size.
Frink's numerical type automatically promotes and demotes between arbitrary-size integers, arbitrary-size rational numbers, arbitrary-precision floating-point numbers, complex numbers, and arbitrary-sized intervals of real values.
Go
Run this in the Go playground. A Go program does not recognize an integer overflow and the program continues with wrong results. <lang go>package main
import "fmt"
func main() { // Go's builtin integer types are: // int, int8, int16, int32, int64 // uint, uint8, uint16, uint32, uint64 // byte, rune, uintptr // // int is either 32 or 64 bit, depending on the system // uintptr is large enough to hold the bit pattern of any pointer // byte is 8 bits like int8 // rune is 32 bits like int32 // // Overflow and underflow is silent. The math package defines a number // of constants that can be helpfull, e.g.: // math.MaxInt64 = 1<<63 - 1 // math.MinInt64 = -1 << 63 // math.MaxUint64 = 1<<64 - 1 // // The math/big package implements multi-precision // arithmetic (big numbers). // // In all cases assignment from one type to another requires // an explicit cast, even if the types are otherwise identical // (e.g. rune and int32 or int and either int32 or int64). // Casts silently truncate if required. // // Invalid: // var i int = int32(0) // var r rune = int32(0) // var b byte = int8(0) // // Valid: var i64 int64 = 42 var i32 int32 = int32(i64) var i16 int16 = int16(i64) var i8 int8 = int8(i16) var i int = int(i8) var r rune = rune(i) var b byte = byte(r) var u64 uint64 = uint64(b) var u32 uint32
//const c int = -(-2147483647 - 1) // Compiler error on 32 bit systems, ok on 64 bit const c = -(-2147483647 - 1) // Allowed even on 32 bit systems, c is untyped i64 = c //i32 = c // Compiler error //i32 = -(-2147483647 - 1) // Compiler error i32 = -2147483647 i32 = -(-i32 - 1) fmt.Println("32 bit signed integers") fmt.Printf(" -(-2147483647 - 1) = %d, got %d\n", i64, i32)
i64 = 2000000000 + 2000000000 //i32 = 2000000000 + 2000000000 // Compiler error i32 = 2000000000 i32 = i32 + i32 fmt.Printf(" 2000000000 + 2000000000 = %d, got %d\n", i64, i32) i64 = -2147483647 - 2147483647 i32 = 2147483647 i32 = -i32 - i32 fmt.Printf(" -2147483647 - 2147483647 = %d, got %d\n", i64, i32) i64 = 46341 * 46341 i32 = 46341 i32 = i32 * i32 fmt.Printf(" 46341 * 46341 = %d, got %d\n", i64, i32) i64 = (-2147483647 - 1) / -1 i32 = -2147483647 i32 = (i32 - 1) / -1 fmt.Printf(" (-2147483647-1) / -1 = %d, got %d\n", i64, i32)
fmt.Println("\n64 bit signed integers") i64 = -9223372036854775807 fmt.Printf(" -(%d - 1): %d\n", i64, -(i64 - 1)) i64 = 5000000000000000000 fmt.Printf(" %d + %d: %d\n", i64, i64, i64+i64) i64 = 9223372036854775807 fmt.Printf(" -%d - %d: %d\n", i64, i64, -i64-i64) i64 = 3037000500 fmt.Printf(" %d * %d: %d\n", i64, i64, i64*i64) i64 = -9223372036854775807 fmt.Printf(" (%d - 1) / -1: %d\n", i64, (i64-1)/-1)
fmt.Println("\n32 bit unsigned integers:") //u32 = -4294967295 // Compiler error u32 = 4294967295 fmt.Printf(" -%d: %d\n", u32, -u32) u32 = 3000000000 fmt.Printf(" %d + %d: %d\n", u32, u32, u32+u32) a := uint32(2147483647) u32 = 4294967295 fmt.Printf(" %d - %d: %d\n", a, u32, a-u32) u32 = 65537 fmt.Printf(" %d * %d: %d\n", u32, u32, u32*u32)
fmt.Println("\n64 bit unsigned integers:") u64 = 18446744073709551615 fmt.Printf(" -%d: %d\n", u64, -u64) u64 = 10000000000000000000 fmt.Printf(" %d + %d: %d\n", u64, u64, u64+u64) aa := uint64(9223372036854775807) u64 = 18446744073709551615 fmt.Printf(" %d - %d: %d\n", aa, u64, aa-u64) u64 = 4294967296 fmt.Printf(" %d * %d: %d\n", u64, u64, u64*u64) }</lang>
- Output:
32 bit signed integers -(-2147483647 - 1) = 2147483648, got -2147483646 2000000000 + 2000000000 = 4000000000, got -294967296 -2147483647 - 2147483647 = -4294967294, got 2 46341 * 46341 = 2147488281, got -2147479015 (-2147483647-1) / -1 = 2147483648, got -2147483648 64 bit signed integers -(-9223372036854775807 - 1): -9223372036854775808 5000000000000000000 + 5000000000000000000: -8446744073709551616 -9223372036854775807 - 9223372036854775807: 2 3037000500 * 3037000500: -9223372036709301616 (-9223372036854775807 - 1) / -1: -9223372036854775808 32 bit unsigned integers: -4294967295: 1 3000000000 + 3000000000: 1705032704 2147483647 - 4294967295: 2147483648 65537 * 65537: 131073 64 bit unsigned integers: -18446744073709551615: 1 10000000000000000000 + 10000000000000000000: 1553255926290448384 9223372036854775807 - 18446744073709551615: 9223372036854775808 4294967296 * 4294967296: 0
Groovy
+ assertions + BigInteger + Groovy differences
Type int is a signed 32-bit integer. Type long is a signed 64-bit integer. Type BigInteger (also in Java) is a signed unbounded integer.
Other integral types (also in Java): byte (8-bit signed), short (16-bit signed), char (16-bit signed)
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.
<lang groovy>println "\nSigned 32-bit (failed):" assert -(-2147483647-1) != 2147483648g println(-(-2147483647-1)) assert 2000000000 + 2000000000 != 4000000000g println(2000000000 + 2000000000) assert -2147483647 - 2147483647 != -4294967294g println(-2147483647 - 2147483647) assert 46341 * 46341 != 2147488281g println(46341 * 46341) //Groovy converts divisor and dividend of "/" to floating point. Use "intdiv" to remain integral //assert (-2147483647-1) / -1 != 2147483648g assert (-2147483647-1).intdiv(-1) != 2147483648g println((-2147483647-1).intdiv(-1))
println "\nSigned 64-bit (passed):" assert -(-2147483647L-1) == 2147483648g println(-(-2147483647L-1)) assert 2000000000L + 2000000000L == 4000000000g println(2000000000L + 2000000000L) assert -2147483647L - 2147483647L == -4294967294g println(-2147483647L - 2147483647L) assert 46341L * 46341L == 2147488281g println(46341L * 46341L) assert (-2147483647L-1).intdiv(-1) == 2147483648g println((-2147483647L-1).intdiv(-1))
println "\nSigned 64-bit (failed):" assert -(-9223372036854775807L-1) != 9223372036854775808g println(-(-9223372036854775807L-1)) assert 5000000000000000000L+5000000000000000000L != 10000000000000000000g println(5000000000000000000L+5000000000000000000L) assert -9223372036854775807L - 9223372036854775807L != -18446744073709551614g println(-9223372036854775807L - 9223372036854775807L) assert 3037000500L * 3037000500L != 9223372037000250000g println(3037000500L * 3037000500L) //Groovy converts divisor and dividend of "/" to floating point. Use "intdiv" to remain integral //assert (-9223372036854775807L-1) / -1 != 9223372036854775808g assert (-9223372036854775807L-1).intdiv(-1) != 9223372036854775808g println((-9223372036854775807L-1).intdiv(-1))
println "\nSigned unbounded (passed):" assert -(-2147483647g-1g) == 2147483648g println(-(-2147483647g-1g)) assert 2000000000g + 2000000000g == 4000000000g println(2000000000g + 2000000000g) assert -2147483647g - 2147483647g == -4294967294g println(-2147483647g - 2147483647g) assert 46341g * 46341g == 2147488281g println(46341g * 46341g) assert (-2147483647g-1g).intdiv(-1) == 2147483648g println((-2147483647g-1g).intdiv(-1)) assert -(-9223372036854775807g-1) == 9223372036854775808g println(-(-9223372036854775807g-1)) assert 5000000000000000000g+5000000000000000000g == 10000000000000000000g println(5000000000000000000g+5000000000000000000g) assert -9223372036854775807g - 9223372036854775807g == -18446744073709551614g println(-9223372036854775807g - 9223372036854775807g) assert 3037000500g * 3037000500g == 9223372037000250000g println(3037000500g * 3037000500g) assert (-9223372036854775807g-1g).intdiv(-1) == 9223372036854775808g println((-9223372036854775807g-1g).intdiv(-1))</lang>
Output:
Signed 32-bit (failed): -2147483648 -294967296 2 -2147479015 -2147483648 Signed 64-bit (passed): 2147483648 4000000000 -4294967294 2147488281 2147483648 Signed 64-bit (failed): -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808 Signed unbounded (passed): 2147483648 4000000000 -4294967294 2147488281 2147483648 9223372036854775808 10000000000000000000 -18446744073709551614 9223372037000250000 9223372036854775808
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). <lang Haskell>import Data.Int import Data.Word import Control.Exception
f x = do
catch (print x) (\e -> print (e :: ArithException))
main = do
f ((- (-2147483647 - 1)) :: Int32) f ((2000000000 + 2000000000) :: Int32) f (((-2147483647) - 2147483647) :: Int32) f ((46341 * 46341) :: Int32) f ((((-2147483647) - 1) `div` (-1)) :: Int32) f ((- ((-9223372036854775807) - 1)) :: Int64) f ((5000000000000000000 + 5000000000000000000) :: Int64) f (((-9223372036854775807) - 9223372036854775807) :: Int64) f ((3037000500 * 3037000500) :: Int64) f ((((-9223372036854775807) - 1) `div` (-1)) :: Int64) f ((-4294967295) :: Word32) f ((3000000000 + 3000000000) :: Word32) f ((2147483647 - 4294967295) :: Word32) f ((65537 * 65537) :: Word32) f ((-18446744073709551615) :: Word64) f ((10000000000000000000 + 10000000000000000000) :: Word64) f ((9223372036854775807 - 18446744073709551615) :: Word64) f ((4294967296 * 4294967296) :: Word64)</lang>
- Output:
-2147483648 -294967296 2 -2147479015 arithmetic overflow -9223372036854775808 -8446744073709551616 2 -9223372036709301616 arithmetic overflow 1 1705032704 2147483648 131073 1 1553255926290448384 9223372036854775808 0
J
J has both 32 bit implementations and 64 bit implementations. Integers are signed and overflow is handled by yielding a floating point result (ieee 754's 64 bit format in both implementations).
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:
<lang J> -(_2147483647-1) 2.14748e9
2000000000 + 2000000000
4e9
_2147483647 - 2147483647
_4.29497e9
46341 * 46341
2.14749e9
(_2147483647-1) % -1
2.14748e9
-(_9223372036854775807-1)
9.22337e18
5000000000000000000+5000000000000000000
1e19
_9223372036854775807 - 9223372036854775807
_1.84467e19
3037000500 * 3037000500
9.22337e18
(_9223372036854775807-1) % -1
9.22337e18
_4294967295
_4.29497e9
3000000000 + 3000000000
6e9
2147483647 - 4294967295
_2.14748e9
65537 * 65537
4.2951e9
_18446744073709551615
_1.84467e19
10000000000000000000 + 10000000000000000000
2e19
9223372036854775807 - 18446744073709551615
_9.22337e18
4294967296 * 4294967296
1.84467e19</lang>
And, here's what it looks like in a 64 bit version of J:
<lang J> -(_2147483647-1) 2147483648
2000000000 + 2000000000
4000000000
_2147483647 - 2147483647
_4294967294
46341 * 46341
2147488281
(_2147483647-1) % -1
2.14748e9
-(_9223372036854775807-1)
9.22337e18
5000000000000000000+5000000000000000000
1e19
_9223372036854775807 - 9223372036854775807
_1.84467e19
3037000500 * 3037000500
9.22337e18
(_9223372036854775807-1) % -1
9.22337e18
_4294967295
_4294967295
3000000000 + 3000000000
6000000000
2147483647 - 4294967295
_2147483648
65537 * 65537
4295098369
_18446744073709551615
_1.84467e19
10000000000000000000 + 10000000000000000000
2e19
9223372036854775807 - 18446744073709551615
_9.22337e18
4294967296 * 4294967296
1.84467e19</lang>
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:
<lang J> -(_2147483647-1) 2147483648
2000000000 + 2000000000
4000000000
_2147483647 - 2147483647
_4294967294
46341 * 46341
2147488281
(_2147483647-1) % -1
2147483648
-(_9223372036854775807-1)
9223372036854775800
5000000000000000000+5000000000000000000
10000000000000000000
_9223372036854775807 - 9223372036854775807
_18446744073709552000
3037000500 * 3037000500
9223372037000249300
(_9223372036854775807-1) % -1
9223372036854775800
_4294967295
_4294967295
3000000000 + 3000000000
6000000000
2147483647 - 4294967295
_2147483648
65537 * 65537
4295098369
_18446744073709551615
_18446744073709552000
10000000000000000000 + 10000000000000000000
20000000000000000000
9223372036854775807 - 18446744073709551615
_9223372036854775800
4294967296 * 4294967296
18446744073709552000</lang>
64 bit J:
<lang J> -(_2147483647-1) 2147483648
2000000000 + 2000000000
4000000000
_2147483647 - 2147483647
_4294967294
46341 * 46341
2147488281
(_2147483647-1) % -1
2147483648
-(_9223372036854775807-1)
9223372036854775800
5000000000000000000+5000000000000000000
10000000000000000000
_9223372036854775807 - 9223372036854775807
_18446744073709552000
3037000500 * 3037000500
9223372037000249300
(_9223372036854775807-1) % -1
9223372036854775800
_4294967295
_4294967295
3000000000 + 3000000000
6000000000
2147483647 - 4294967295
_2147483648
65537 * 65537
4295098369
_18446744073709551615
_18446744073709552000
10000000000000000000 + 10000000000000000000
20000000000000000000
9223372036854775807 - 18446744073709551615
_9223372036854775800
4294967296 * 4294967296
18446744073709552000</lang>
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.
Java
The type int is a signed 32-bit integer and the type long is a 64-bit integer. A Java program does not recognize an integer overflow and the program continues with wrong results. <lang java>public class integerOverflow {
public static void main(String[] args) {
System.out.println("Signed 32-bit:");
System.out.println(-(-2147483647-1));
System.out.println(2000000000 + 2000000000);
System.out.println(-2147483647 - 2147483647);
System.out.println(46341 * 46341);
System.out.println((-2147483647-1) / -1);
System.out.println("Signed 64-bit:");
System.out.println(-(-9223372036854775807L-1));
System.out.println(5000000000000000000L+5000000000000000000L);
System.out.println(-9223372036854775807L - 9223372036854775807L);
System.out.println(3037000500L * 3037000500L);
System.out.println((-9223372036854775807L-1) / -1);
}
}</lang>
- Output:
Signed 32-bit: -2147483648 -294967296 2 -2147479015 -2147483648 Signed 64-bit: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808
Julia
Plain Integer Types and Their Limits <lang julia>using Printf S = subtypes(Signed) U = subtypes(Unsigned)
println("Integer limits:") for (s, u) in zip(S, U)
@printf("%8s: [%s, %s]\n", s, typemin(s), typemax(s))
@printf("%8s: [%s, %s]\n", u, typemin(u), typemax(u))
end</lang>
- Output:
Integer limits:
Int128: [-170141183460469231731687303715884105728, 170141183460469231731687303715884105727]
UInt128: [0, 340282366920938463463374607431768211455]
Int16: [-32768, 32767]
UInt16: [0, 65535]
Int32: [-2147483648, 2147483647]
UInt32: [0, 4294967295]
Int64: [-9223372036854775808, 9223372036854775807]
UInt64: [0, 18446744073709551615]
Int8: [-128, 127]
UInt8: [0, 255]
Add to 1 Signed typemax
Julia does not throw an explicit error on integer overflow.
<lang julia>println("Add one to typemax:") for t in S
over = typemax(t) + one(t)
@printf("%8s → %-25s (%s)\n", t, over, typeof(over))
end</lang>
- Output:
Add one to typemax:
Int128 → -170141183460469231731687303715884105728 (Int128)
Int16 → -32768 (Int16)
Int32 → -2147483648 (Int32)
Int64 → -9223372036854775808 (Int64)
Int8 → -128 (Int8)
Kotlin
A Kotlin program does not recognize a signed integer overflow and the program continues with wrong results.
<lang scala>// version 1.0.5-2
/* Kotlin (like Java) does not have unsigned integer types but we can simulate
what would happen if we did have an unsigned 32 bit integer type using this extension function */
fun Long.toUInt(): Long = this and 0xffffffffL
@Suppress("INTEGER_OVERFLOW") fun main(args: Array<String>) {
// The following 'signed' computations all produce compiler warnings that they will lead to an overflow
// which have been ignored
println("*** Signed 32 bit integers ***\n")
println(-(-2147483647 - 1))
println(2000000000 + 2000000000)
println(-2147483647 - 2147483647)
println(46341 * 46341)
println((-2147483647 - 1) / -1)
println("\n*** Signed 64 bit integers ***\n")
println(-(-9223372036854775807 - 1))
println(5000000000000000000 + 5000000000000000000)
println(-9223372036854775807 - 9223372036854775807)
println(3037000500 * 3037000500)
println((-9223372036854775807 - 1) / -1)
// Simulated unsigned computations, no overflow warnings as we're using the Long type
println("\n*** Unsigned 32 bit integers ***\n")
println((-4294967295L).toUInt())
println((3000000000L.toUInt() + 3000000000L.toUInt()).toUInt())
println((2147483647L - 4294967295L.toUInt()).toUInt())
println((65537L * 65537L).toUInt())
}</lang>
- Output:
*** Signed 32 bit integers *** -2147483648 -294967296 2 -2147479015 -2147483648 *** Signed 64 bit integers *** -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808 *** Unsigned 32 bit integers *** 1 1705032704 2147483648 131073
Lingo
Lingo uses 32-bit signed integers. A Lingo program does not recognize a signed integer overflow and the program continues with wrong results. <lang c>#include <stdio.h>
<lang lingo>put -(-2147483647-1) -- -2147483648
put 2000000000 + 2000000000 -- -294967296
put -2147483647 - 2147483647 -- 2
put 46341 * 46341 -- -2147479015
put (-2147483647-1) / -1 --> crashes Director (jeez!)</lang>
M2000 Interpreter
<lang M2000 Interpreter> Long A Try ok {
A=12121221212121
} If not ok then Print Error$ 'Overflow Long Def Integer B Try ok {
B=1212121212
} If not ok then Print Error$ ' Overflow Integer Def Currency C Try ok {
C=121212121232934392898274327927948
} If not ok then Print Error$ ' return Overflow Long, but is overflow Currency Def Decimal D Try ok {
D=121212121232934392898274327927948
} If not ok then Print Error$ ' return Overflow Long, but is overflow Decimal
\\ No overflow for unsigned numbers in structs Structure Struct {
\\ union a1, a2| b
{
a1 as integer
a2 as integer
}
b as long
} \\ structures are type for Memory Block, or other sttructure \\ we use Clear to erase internal Memory Block Buffer Clear DataMem as Struct*20 \\ from a1 we get only the low word Return DataMem, 0!a2:=0xBBBB, 0!a1:=0xFFFFAAAA Print Hex$(Eval(DataMem, 0!b))="BBBBAAAA" Print Eval(DataMem, 0!b)=Eval(DataMem, 0!a2)*0x10000+Eval(DataMem, 0!a1) </lang>
Mathematica
Mathematica uses arbitrary number types. There is a $MaxNumber which is approximately 1.60521676193366172702774105306375828321e1355718576299609, but extensive research has shown it to allow numbers up to <lang Mathematica>$MaxNumber +
10^-15.954589770191003298111788092733772206160314 $MaxNumber</lang>I haven't bothered testing it to any more precision. If you try to use any number above that, it returns an Overflow[].
Nim
Note that some of the UInt64 tests not tested in the code because they raise compile-time errors (alerting the programmer to range errors). The exception text has been included for completeness. In the INT64 case the Nim program does not recognize a signed integer overflow and the program continues with wrong results.
<lang Nim>import macros, strutils
macro toIntVal(s: static[string]): untyped =
result = parseExpr(s)
proc `/`(x,y:int64): float = return (x.float / y.float)
const
strInt32 = ["-(-2147483647-1)",
"2_000_000_000 + 2_000_000_000",
"-2147483647 - 2147483647",
"46341 * 46341",
"(-2147483647-1) / -1"]
shouldBInt32 = ["2147483648",
"4000000000",
"-4294967294",
"2147488281",
"2147483648"]
strInt64 = ["-(-9_223372_036854_775807-1) ",
"5_000000_000000_000000+5_000000_000000_000000",
"-9_223372_036854_775807 - 9_223372_036854_775807",
"3037_000500 * 3037_000500",
"(-9_223372_036854_775807-1) / -1"]
shouldBInt64 = ["9223372036854775808",
"10000000000000000000",
"-18446744073709551614",
"9223372037000250000",
"9223372036854775808"]
strUInt32 = ["-4294967295",
"3000_000000 +% 3000_000000",
"2147483647 -% 4294967295",
"65537 *% 65537"]
shouldBUInt32 = ["-4294967295",
"6000000000",
"-2147483648",
"4295098369"]
strUInt64 = ["-18446744073709551615",
"10_000000_000000_000000 +% 10_000000_000000_000000",
"9_223372_036854_775807 -% 18_446744_073709_551615",
"4294967296 * 4294967296",
"4294967296 *% 4294967296",] # testing * and *%
shouldBUInt64 = ["-18446744073709551615",
"20000000000000000000",
"-9223372036854775808",
"18446744073709551616",
"18446744073709551616"]
- use compile time macro to convert string expr to numeric value
var
resInt32: seq[string] = @[$toIntVal(strInt32[0]),
$toIntVal(strInt32[1]),
$toIntVal(strInt32[2]),
$toIntVal(strInt32[3]),
$toIntVal(strInt32[4])]
resInt64: seq[string] = @[$toIntVal(strInt64[0]),
$toIntVal(strInt64[1]),
$toIntVal(strInt64[2]),
$toIntVal(strInt64[3]),
$toIntVal(strInt64[4])]
resUInt32: seq[string] = @[$toIntVal(strUInt32[0]),
$toIntVal(strUInt32[1]),
$toIntVal(strUInt32[2]),
$toIntVal(strUInt32[3])]
resUInt64: seq[string] = @["18446744073709551615 out of valid range",
"10_000000_000000_000000 out of valid range",
"18_446744_073709_551615 out of valid range",
$toIntVal(strUInt64[3]),
$toIntVal(strUInt64[4])]
proc main() =
# output format:
#
# stringExpr -> calculatedValueAsAString (expectedValueAsAString)
echo "-- INT32 --"
for i in 0..<resInt32.len:
echo align(strInt32[i], 35), " -> ", align($resInt32[i], 15), " (", $shouldBInt32[i],")"
echo "-- INT64 --"
for i in 0..<resInt64.len:
echo align(strInt64[i], 55), " -> ", align($resInt64[i], 25), " (", $shouldBInt64[i],")"
echo "-- UINT32 --"
for i in 0..<resUInt32.len:
echo align(strUInt32[i], 35), " -> ", align($resUInt32[i], 20), " (", $shouldBUInt32[i],")"
echo "-- UINT64 --"
for i in 0..<resUInt64.len:
echo align(strUInt64[i], 55), " -> ", align($resUInt64[i], 42), " (", $shouldBUInt64[i],")"
main() </lang>
- Output:
-- INT32 --
-(-2147483647-1) -> 2147483648 (2147483648)
2_000_000_000 + 2_000_000_000 -> 4000000000 (4000000000)
-2147483647 - 2147483647 -> -4294967294 (-4294967294)
46341 * 46341 -> 2147488281 (2147488281)
(-2147483647-1) / -1 -> 2147483648.0 (2147483648)
-- INT64 --
-(-9_223372_036854_775807-1) -> -9223372036854775808 (9223372036854775808)
5_000000_000000_000000+5_000000_000000_000000 -> 9223372036854775807 (10000000000000000000)
-9_223372_036854_775807 - 9_223372_036854_775807 -> -9223372036854775808 (-18446744073709551614)
3037_000500 * 3037_000500 -> 9223372036854775807 (9223372037000250000)
(-9_223372_036854_775807-1) / -1 -> 9.223372036854776e+018 (9223372036854775808)
-- UINT32 --
-4294967295 -> -4294967295 (-4294967295)
3000_000000 +% 3000_000000 -> 6000000000 (6000000000)
2147483647 -% 4294967295 -> -2147483648 (-2147483648)
65537 *% 65537 -> 4295098369 (4295098369)
-- UINT64 --
-18446744073709551615 -> 18446744073709551615 out of valid range (-18446744073709551615)
10_000000_000000_000000 +% 10_000000_000000_000000 -> 10_000000_000000_000000 out of valid range (20000000000000000000)
9_223372_036854_775807 -% 18_446744_073709_551615 -> 18_446744_073709_551615 out of valid range (-9223372036854775808)
4294967296 * 4294967296 -> 9223372036854775807 (18446744073709551616)
4294967296 *% 4294967296 -> 0 (18446744073709551616)
Oforth
Oforth handles arbitrary precision integers. There is no integer overflow nor undefined behavior (unless no more memory) :
- Output:
5000000000000000000 5000000000000000000 + println 10000000000000000000 ok
PARI/GP
Although it appears at a glance that GP offers only t_INT (unlimited precision) integers, in fact machine-sized integers can be used inside a Vecsmall:
<lang parigp>Vecsmall([1])
Vecsmall([2^64])</lang>
- Output:
%1 = Vecsmall([1]) *** at top-level: Vecsmall([2^64]) *** ^---------------- *** Vecsmall: overflow in t_INT-->long assignment. *** Break loop: type 'break' to go back to GP prompt
Of course PARI can use the same techniques as C.
Perl
Using Perl 5.18 on 64-bit Linux with use integer: The Perl 5 program below does not recognize a signed integer overflow and the program continues with wrong results. <lang c>#include <stdio.h>
<lang perl> use strict; use warnings; use integer; use feature 'say';
say("Testing 64-bit signed overflow:"); say(-(-9223372036854775807-1)); say(5000000000000000000+5000000000000000000); say(-9223372036854775807 - 9223372036854775807); say(3037000500 * 3037000500); say((-9223372036854775807-1) / -1); </lang>
- Output:
Testing 64-bit signed overflow: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808
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 64-bit it is -4,611,686,018,427,387,904 to +4,611,686,018,427,387,903 (-#4000000000000000 to #3FFFFFFFFFFFFFFF). 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: <lang Phix>integer i = 1000000000 + 1000000000</lang>
- Output:
C:\Program Files (x86)\Phix\test.exw:1 type check failure, i is 2000000000.0
The overflow is automatically caught and the program does not continue 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.
PicoLisp
PicoLisp supports only integers of unlimited size. An overflow does not occur, except when a number grows larger than the available memory.
Pike
Pike transparently promotes int to bignum when needed, so integer overflows do not occur.
PowerShell
Without explicit casting, as in this example, numbers which are too big are automatically promoted to [decimal] (128 bit, high precision floating point which is save for financial calculations), so no exception is raised.
https://docs.microsoft.com/en-us/dotnet/api/system.decimal?view=netframework-4.8#remarks
<lang powershell> try { # All of these raise an exception, which is caught below. # The try block is aborted after the first exception, # so the subsequent lines are never executed.
[int32] (-(-2147483647-1)) [int32] (2000000000 + 2000000000) [int32] (-2147483647 - 2147483647) [int32] (46341 * 46341) [int32] ((-2147483647-1) / -1)
[int64] (-(-9223372036854775807-1)) [int64] (5000000000000000000+5000000000000000000) [int64] (-9223372036854775807 - 9223372036854775807) [int64] (3037000500 * 3037000500) [int64] ((-9223372036854775807-1) / -1)
[uint32] (-4294967295) [uint32] (3000000000 + 3000000000) [uint32] (2147483647 - 4294967295) [uint32] (65537 * 65537)
[uint64] (-18446744073709551615) [uint64] (10000000000000000000 + 10000000000000000000) [uint64] (9223372036854775807 - 18446744073709551615) [uint64] (4294967296 * 4294967296) } catch { $Error.Exception } </lang>
PureBasic
CPU=x64, OS=Windows7 <lang purebasic>#MAX_BYTE =127
- MAX_ASCII=255 ;=MAX_CHAR Ascii-Mode
CompilerIf #PB_Compiler_Unicode=1
- MAX_CHAR =65535 ;Unicode-Mode
CompilerElse
- MAX_CHAR =255
CompilerEndIf
- MAX_WORD =32767
- MAX_UNIC =65535
- MAX_LONG =2147483647
CompilerIf #PB_Compiler_Processor=#PB_Processor_x86
- MAX_INT =2147483647 ;32-bit CPU
CompilerElseIf #PB_Compiler_Processor=#PB_Processor_x64
- MAX_INT =9223372036854775807 ;64-bit CPU
CompilerEndIf
- MAX_QUAD =9223372036854775807
Macro say(Type,maxv,minv,sz)
PrintN(Type+#TAB$+RSet(Str(minv),30,Chr(32))+#TAB$+RSet(Str(maxv),30,Chr(32))+#TAB$+RSet(Str(sz),6,Chr(32))+" Byte")
EndMacro
OpenConsole() PrintN("TYPE"+#TAB$+RSet("MIN",30,Chr(32))+#TAB$+RSet("MAX",30,Chr(32))+#TAB$+RSet("SIZE",6,Chr(32)))
Define.b b1=#MAX_BYTE, b2=b1+1 say("Byte",b1,b2,SizeOf(b1))
Define.a a1=#MAX_ASCII, a2=a1+1 say("Ascii",a1,a2,SizeOf(a1))
Define.c c1=#MAX_CHAR, c2=c1+1 say("Char",c1,c2,SizeOf(c1))
Define.w w1=#MAX_WORD, w2=w1+1 say("Word",w1,w2,SizeOf(w1))
Define.u u1=#MAX_UNIC, u2=u1+1 say("Unicode",u1,u2,SizeOf(u1))
Define.l l1=#MAX_LONG, l2=l1+1 say("Long ",l1,l2,SizeOf(l1))
Define.i i1=#MAX_INT, i2=i1+1 say("Int",i1,i2,SizeOf(i1))
Define.q q1=#MAX_QUAD, q2=q1+1 say("Quad",q1,q2,SizeOf(q1))
Input()</lang>
- Output:
TYPE MIN MAX SIZE Byte -128 127 1 Byte Ascii 0 255 1 Byte Char 0 65535 2 Byte Word -32768 32767 2 Byte Unicode 0 65535 2 Byte Long -2147483648 2147483647 4 Byte Int -9223372036854775808 9223372036854775807 8 Byte Quad -9223372036854775808 9223372036854775807 8 Byte
Python
Python 2.X
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.
<lang python>Python 2.7.5 (default, May 15 2013, 22:43:36) [MSC v.1500 32 bit (Intel)] on win32 Type "copyright", "credits" or "license()" for more information. >>> for calc in -(-2147483647-1)
2000000000 + 2000000000
-2147483647 - 2147483647
46341 * 46341
(-2147483647-1) / -1.split('\n'):
ans = eval(calc) print('Expression: %r evaluates to %s of type %s' % (calc.strip(), ans, type(ans)))
Expression: '-(-2147483647-1)' evaluates to 2147483648 of type <type 'long'>
Expression: '2000000000 + 2000000000' evaluates to 4000000000 of type <type 'long'>
Expression: '-2147483647 - 2147483647' evaluates to -4294967294 of type <type 'long'>
Expression: '46341 * 46341' evaluates to 2147488281 of type <type 'long'>
Expression: '(-2147483647-1) / -1' evaluates to 2147483648 of type <type 'long'>
>>> </lang>
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. <lang python>Python 3.4.1 (v3.4.1:c0e311e010fc, May 18 2014, 10:38:22) [MSC v.1600 32 bit (Intel)] on win32 Type "copyright", "credits" or "license()" for more information. >>> for calc in -(-2147483647-1)
2000000000 + 2000000000
-2147483647 - 2147483647
46341 * 46341
(-2147483647-1) / -1.split('\n'):
ans = eval(calc) print('Expression: %r evaluates to %s of type %s' % (calc.strip(), ans, type(ans)))
Expression: '-(-2147483647-1)' evaluates to 2147483648 of type <class 'int'>
Expression: '2000000000 + 2000000000' evaluates to 4000000000 of type <class 'int'>
Expression: '-2147483647 - 2147483647' evaluates to -4294967294 of type <class 'int'>
Expression: '46341 * 46341' evaluates to 2147488281 of type <class 'int'>
Expression: '(-2147483647-1) / -1' evaluates to 2147483648.0 of type <class 'float'>
>>> </lang>
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 // to get integer division.
Racket
The 32-bit version of Racket stores internally the fixnum n as the signed integer 2n+1, to distinguish it from the pointers to objects that are stored as even integers. This is invisible from inside Racket because in the usual operations when the result is not a fixnum, it's promoted to a bignum.
The effect of this representation is that the fixnums have only 31 bits available, and one of them is used for the sign. So all the examples have to be reduced to the half in order to fit into 31-bit signed values.
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.)
<lang Racket>#lang racket (require racket/unsafe/ops)
(fixnum? -1073741824) ;==> #t (fixnum? (- -1073741824)) ;==> #f
(- -1073741824) ;==> 1073741824 (unsafe-fx- 0 -1073741824) ;==> -1073741824
(+ 1000000000 1000000000) ;==> 2000000000 (unsafe-fx+ 1000000000 1000000000) ;==> -147483648
(- -1073741823 1073741823) ;==> -2147483646 (unsafe-fx- -1073741823 1073741823) ;==> 2
(* 46341 46341) ;==> 2147488281 (unsafe-fx* 46341 46341) ;==> 4633
(/ -1073741824 -1) ;==> 1073741824 (unsafe-fxquotient -1073741824 -1) ;==> -1073741824</lang>
The 64-bit version is similar. The fixnum are effectively 63-bits signed integers.
Raku
(formerly Perl 6)
The Raku program below does not recognize a signed integer overflow and the program continues with wrong results.
<lang perl6>my int64 ($a, $b, $c) = 9223372036854775807, 5000000000000000000, 3037000500; .say for -(-$a - 1), $b + $b, -$a - $a, $c * $c, (-$a - 1)/-1;</lang>
- Output:
-9223372036854775808 -8446744073709551616 2 -9223372036709301616 9223372036854775808
REXX
The REXX language normally uses a fixed amount (but re-definable) amount of decimal digits, the default is 9.
When the value exceeds 9 decimal digits (or whatever was specified via the numeric digits NNN REXX
statement), REXX will quietly automatically change to exponential format and
round the given number, if necessary.
For newer versions of REXX, the signal on lostDigits statement can be used to accomplish the same results
(for detecting a loss of significance [digits]).
<lang rexx>/*REXX program displays values when integers have an overflow or underflow. */
numeric digits 9 /*the REXX default is 9 decimal digits.*/
call showResult( 999999997 + 1 )
call showResult( 999999998 + 1 )
call showResult( 999999999 + 1 )
call showResult( -999999998 - 2 )
call showResult( 40000 * 25000 )
call showResult( -50000 * 20000 )
call showResult( 50000 *-30000 )
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
showResult: procedure; parse arg x,,_; x=x/1 /*normalize X. */
if pos(., x)\==0 then if x>0 then _=' [overflow]' /*did it overflow? */
else _=' [underflow]' /*did it underflow? */
say right(x, 20) _ /*show the result. */
return x /*return the value. */</lang>
output using the default input(s):
Output note: (as it happens, all of the results below are numerically correct)
999999998
999999999
1.00000000E+9 [overflow]
-1.00000000E+9 [underflow]
1.00000000E+9 [overflow]
-1.00000000E+9 [underflow]
-1.50000000E+9 [underflow]
Ruby
Ruby has unlimited precision integers.
The Integer class is the basis for two concrete classes that hold whole numbers, Bignum and Fixnum. Bignum objects hold integers outside the range of Fixnum. 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. <lang ruby>2.1.1 :001 > a = 2**62 -1
=> 4611686018427387903
2.1.1 :002 > a.class
=> Fixnum
2.1.1 :003 > (b = a + 1).class
=> Bignum
2.1.1 :004 > (b-1).class
=> Fixnum
</lang> Since Ruby 2.4 these different classes have disappeared: all numbers in above code are of class Integer.
Rust
To balance the need to catch bugs with the need to remain performant, Rust declares both unsigned and signed integer overflow to be invalid for the basic mathematical operators, but also guarantees that they will have predictable behaviour, resulting in either a panic! (safe program termination) or two's complement wrapping behaviour, depending on whether debug assertions are enabled.[1][2]
If an integer overflow can be determined at compile-time, an error is raised, though this can be converted to a warning or allowed. e.g.
error: attempt to divide with overflow --> src/main.rs:3:23 | 3 | let i32_5 : i32 = (-2_147_483_647 - 1) / -1; | ^^^^^^^^^^^^^^^^^^^^^^^^^ | = note: `#[deny(const_err)]` on by default
If overflow occurs during program execution and overflow checks are enabled (the default for debug builds and an option for release builds), a panic! is raised.
$ ./integer_overflow thread '<main>' panicked at 'attempted to negate with overflow', integer_overflow.rs:2 note: Run with `RUST_BACKTRACE=1` for a backtrace.
The following code will always panic when run in any mode
<lang Rust>
// The following will panic! let i32_1 : i32 = -(-2_147_483_647 - 1); let i32_2 : i32 = 2_000_000_000 + 2_000_000_000; let i32_3 : i32 = -2_147_483_647 - 2_147_483_647; let i32_4 : i32 = 46341 * 46341; let i32_5 : i32 = (-2_147_483_647 - 1) / -1;
// These will panic! also let i64_1 : i64 = -(-9_223_372_036_854_775_807 - 1); let i64_2 : i64 = 5_000_000_000_000_000_000 + 5_000_000_000_000_000_000; let i64_3 : i64 = -9_223_372_036_854_775_807 - 9_223_372_036_854_775_807; 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;
</lang>
In order to declare overflow/underflow behaviour as intended (and, thus, valid in both debug and release modes), Rust provides two mechanisms:
First, the integer types offer methods which provide non-panicking versions of the basic mathematical operators, such as addition, subtraction, multiplication, division, negation, bit-shifting, and so on.
There are three types of functions:
checked_...: Return the result orNoneon overflow/underflowsaturating_...: Return the result or the maximum/minimum possible value for the specified type as appropriate.wrapping_...: Return the result of the calculation, according to two's complement wrapping behaviour.
<lang Rust>
// The following will never panic!
println!("{:?}", 65_537u32.checked_mul(65_537)); // None
println!("{:?}", 65_537u32.saturating_mul(65_537)); // 4294967295
println!("{:?}", 65_537u32.wrapping_mul(65_537)); // 131073
// These will never panic! either
println!("{:?}", 65_537i32.checked_mul(65_537)); // None
println!("{:?}", 65_537i32.saturating_mul(65_537)); // 2147483647
println!("{:?}", 65_537i32.wrapping_mul(-65_537)); // -131073
</lang>
Second, a generic Wrapping<T> one-element tuple type is provided which implements the same basic operations as the wrapping_... methods, but allows you to use normal operators and then use the .0 field accessor to retrieve the value once you are finished.[3]
Scala
Math.addExact works for both 32-bit unsigned and 64-bit unsigned integers, but Java does not support signed integers. <lang Scala>import Math.{addExact => ++, multiplyExact => **, negateExact => ~~, subtractExact => --}
def requireOverflow(f: => Unit) =
try {f; println("Undetected overflow")} catch{case e: Exception => /* caught */}
println("Testing overflow detection for 32-bit unsigned integers") requireOverflow(~~(--(~~(2147483647), 1))) // -(-2147483647-1) requireOverflow(++(2000000000, 2000000000)) // 2000000000 + 2000000000 requireOverflow(--(~~(2147483647), 2147483647)) // -2147483647 + 2147483647 requireOverflow(**(46341, 46341)) // 46341 * 46341 requireOverflow(**(--(~~(2147483647),1), -1)) // same as (-2147483647-1) / -1
println("Test - Expect Undetected overflow:") requireOverflow(++(1,1)) // Undetected overflow </lang>
Seed7
Seed7 supports unlimited precision integers with the type bigInteger. The type integer is a 64-bit signed integer type. All computations with the type integer are checked for overflow. <lang seed7>$ include "seed7_05.s7i";
const proc: writeResult (ref func integer: expression) is func
begin
block
writeln(expression);
exception
catch OVERFLOW_ERROR: writeln("OVERFLOW_ERROR");
end block;
end func;
const proc: main is func
begin writeResult(-(-9223372036854775807-1)); writeResult(5000000000000000000+5000000000000000000); writeResult(-9223372036854775807 - 9223372036854775807); writeResult(3037000500 * 3037000500); writeResult((-9223372036854775807-1) div -1); end func;</lang>
- Output:
OVERFLOW_ERROR OVERFLOW_ERROR OVERFLOW_ERROR OVERFLOW_ERROR OVERFLOW_ERROR
Sidef
Sidef has unlimited precision integers. <lang ruby>var (a, b, c) = (9223372036854775807, 5000000000000000000, 3037000500); [-(-a - 1), b + b, -a - a, c * c, (-a - 1)/-1].each { say _ };</lang>
- Output:
9223372036854775808 10000000000000000000 -18446744073709551614 9223372037000250000 9223372036854775808
Swift
<lang Swift>// By default, all overflows in Swift result in a runtime exception, which is always fatal // However, you can opt-in to overflow behavior with the overflow operators and continue with wrong results
var int32:Int32 var int64:Int64 var uInt32:UInt32 var uInt64:UInt64
println("signed 32-bit int:") int32 = -1 &* (-2147483647 - 1) println(int32) int32 = 2000000000 &+ 2000000000 println(int32) int32 = -2147483647 &- 2147483647 println(int32) int32 = 46341 &* 46341 println(int32) int32 = (-2147483647-1) &/ -1 println(int32) println()
println("signed 64-bit int:") int64 = -1 &* (-9223372036854775807 - 1) println(int64) int64 = 5000000000000000000&+5000000000000000000 println(int64) int64 = -9223372036854775807 &- 9223372036854775807 println(int64) int64 = 3037000500 &* 3037000500 println(int64) int64 = (-9223372036854775807-1) &/ -1 println(int64) println()
println("unsigned 32-bit int:") println("-4294967295 is caught as a compile time error") uInt32 = 3000000000 &+ 3000000000 println(uInt32) uInt32 = 2147483647 &- 4294967295 println(uInt32) uInt32 = 65537 &* 65537 println(uInt32) println()
println("unsigned 64-bit int:") println("-18446744073709551615 is caught as a compile time error") uInt64 = 10000000000000000000 &+ 10000000000000000000 println(uInt64) uInt64 = 9223372036854775807 &- 18446744073709551615 println(uInt64) uInt64 = 4294967296 &* 4294967296 println(uInt64)</lang>
- Output:
signed 32-bit int: -2147483648 -294967296 2 -2147479015 0 signed 64-bit int: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 0 unsigned 32-bit int: -4294967295 is caught as a compile time error 1705032704 2147483648 131073 unsigned 64-bit int: -18446744073709551615 is caught as a compile time error 1553255926290448384 9223372036854775808 0
Standard ML
PolyML <lang Standard ML>~(~9223372036854775807-1) ; poly: : error: Overflow exception raised while converting ~9223372036854775807 to int Int.maxInt ; val it = SOME 4611686018427387903: int option ~(~4611686018427387903 - 1); Exception- Overflow raised
(~4611686018427387903 - 1) div ~1;
Exception- Overflow raised 2147483648 * 2147483648 ; Exception- Overflow raised </lang>
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: <lang tcl>proc tcl::mathfunc::clamp32 {x} {
expr {$x<0 ? -((-$x) & 0x7fffffff) : $x & 0x7fffffff}
} puts [expr { clamp32(2000000000 + 2000000000) }]; # ==> 1852516352</lang> 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.
VBScript
In VBScript, if we declare a variable, there is no type. "As Integer" or "As Long" cannot be specified. Integer is a flexible type, internally it can be Integer (Fixed 16-bits), Long (Fixed 32-bits) or Double (Floating point).
So, in VBScript is there an integer overflow? Answer: No and Yes.
- No, because 2147483647+1 is equal to 2147483648.
- 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 !?.
A good way to test integer overflow is to use the vartype() or typename() builtin functions.
<lang vb>'Binary Integer overflow - vbs
i=(-2147483647-1)/-1
wscript.echo i
i0=32767 '=32767 Integer (Fixed) type=2
i1=2147483647 '=2147483647 Long (Fixed) type=3
i2=-(-2147483647-1) '=2147483648 Double (Float) type=5
wscript.echo Cstr(i0) & " : " & typename(i0) & " , " & vartype(i0) & vbcrlf _
& Cstr(i1) & " : " & typename(i1) & " , " & vartype(i1) & vbcrlf _
& Cstr(i2) & " : " & typename(i2) & " , " & vartype(i2)
ii=2147483648-2147483647 if vartype(ii)<>3 or vartype(ii)<>2 then wscript.echo "Integer overflow type=" & typename(ii) i1=1000000000000000-1 '1E+15-1 i2=i1+1 '1E+15 wscript.echo Cstr(i1) & " , " & Cstr(i2)</lang>
- Output:
2147483648 32767 : Integer , 2 2147483647 : Long , 3 2147483648 : Double , 5 Integer overflow type=Double 999999999999999 , 1E+15
Visual Basic
Overflow is well handled, except for a strange bug in the computation of f the constant -(-2147483648). <lang vb> 'Binary Integer overflow - vb6 - 28/02/2017
Dim i As Long '32-bit signed integer i = -(-2147483647 - 1) '=-2147483648 ?! bug i = -Int(-2147483647 - 1) '=-2147483648 ?! bug i = 0 - (-2147483647 - 1) 'Run-time error '6' : Overflow i = -2147483647: i = -(i - 1) 'Run-time error '6' : Overflow i = -(-2147483647 - 2) 'Run-time error '6' : Overflow i = 2147483647 + 1 'Run-time error '6' : Overflow i = 2000000000 + 2000000000 'Run-time error '6' : Overflow i = -2147483647 - 2147483647 'Run-time error '6' : Overflow i = 46341 * 46341 'Run-time error '6' : Overflow i = (-2147483647 - 1) / -1 'Run-time error '6' : Overflow
</lang> Error handling - method 1 <lang vb> i=0
On Error Resume Next i = 2147483647 + 1 Debug.Print i 'i=0
</lang> Error handling - method 2 <lang vb> i=0
On Error GoTo overflow i = 2147483647 + 1 ...
overflow:
Debug.Print "Error: " & Err.Description '-> Error: Overflow
</lang> Error handling - method 3 <lang vb> On Error GoTo 0
i = 2147483647 + 1 'Run-time error '6' : Overflow Debug.Print i
</lang>
Visual Basic .NET
All the examples for the task are in error before any compilation or execution! The visual studio editor spots the overflow errors with the message:
Constant expression not representable in type 'Integer/Long/UInteger'
To have an execution time overflow we must have something else than constant expressions.
32-bit signed integer <lang vbnet> Dim i As Integer '32-bit signed integer</lang>
Pre-compilation error: 'Error: Constant expression not representable in type 'Integer' for:
<lang vbnet> i = -(-2147483647 - 1)
i = 0 - (-2147483647 - 1)
i = -(-2147483647L - 1)
i = -(-2147483647 - 2)
i = 2147483647 + 1
i = 2000000000 + 2000000000
i = -2147483647 - 2147483647
i = 46341 * 46341
i = (-2147483647 - 1) / -1 </lang>
Execution error:
'An unhandled exception of type 'System.OverflowException' occurred
'Additional information: Arithmetic operation resulted in an overflow.
for:
<lang vbnet> i = -Int(-2147483647 - 1)
i = -2147483647: i = -(i - 1) </lang>
32-bit unsigned integer
In Visual Basic .Net there is no specific UInteger constants as in C.
<lang vbnet> Dim i As UInteger '32-bit unsigned integer</lang>
Pre-compilation error: 'Error: Constant expression not representable in type 'UInteger' for:
<lang vbnet> i = -4294967295
i = 3000000000 + 3000000000
i = 2147483647 - 4294967295
i = 65537 * 65537 </lang>
Execution error:
'An unhandled exception of type 'System.OverflowException' occurred
'Additional information: Arithmetic operation resulted in an overflow.
for:
<lang vbnet> i = 3000000000 : i = i + i </lang> 64-bit signed integer <lang vbnet> Dim i As Long '64-bit signed integer</lang>
Pre-compilation error: 'Error: Constant expression not representable in type 'Long' for:
<lang vbnet> i = -(-9223372036854775807 - 1)
i = 5000000000000000000 + 5000000000000000000
i = -9223372036854775807 - 9223372036854775807
i = 3037000500 * 3037000500
i = (-9223372036854775807 - 1) / -1</lang>
Execution error:
'An unhandled exception of type 'System.OverflowException' occurred
'Additional information: Arithmetic operation resulted in an overflow.
for:
<lang vbnet> i = -9223372036854775807 : i = -(i - 1)</lang>
64-bit unsigned integer
In Visual Basic .Net there is no specific ULong constants as in C.
And 'Long' constants are not good enough.
<lang vbnet> Dim i As ULong '64-bit unsigned integer</lang>
Pre-compilation error: 'Error: Overflow for:
<lang vbnet> i = -18446744073709551615
i = 10000000000000000000 + 10000000000000000000
i = 9223372036854775807 - 18446744073709551615</lang>
Pre-compilation error:
'Error: Constant expression not representable in type 'Long'
for:
<lang vbnet> i = 4294967296 * 4294967296</lang>
Execution error: 'An unhandled exception of type 'System.OverflowException' occurred 'Additional information: Arithmetic operation resulted in an overflow. for:
<lang vbnet> i = 4294967296 : i = i * i</lang>
how the exception is catched <lang vbnet> Dim i As Integer '32-bit signed integer
Try
i = -2147483647 : i = -(i - 1)
Debug.Print(i)
Catch ex As Exception
Debug.Print("Exception raised : " & ex.Message)
End Try</lang>
- Output:
Arithmetic operation resulted in an overflow.
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 not recognize an integer overflow and the program continues with wrong results. <lang zkl>print("Signed 64-bit:\n"); println(-(-9223372036854775807-1)); println(5000000000000000000+5000000000000000000); println(-9223372036854775807 - 9223372036854775807); println(3037000500 * 3037000500); println((-9223372036854775807-1) / -1);</lang>
- Output:
Linux/BSD/clang
Signed 64-bit: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 uncatchable floating point exception thrown by OS
Windows XP
Signed 64-bit: -9223372036854775808 -8446744073709551616 2 -9223372036709301616 -9223372036854775808