proposal: math: overflow detecting arithmetic

[Verseth]

Currently there is no standard, efficient way of detecting overflow/underflow in integer arithmetic.

Everyone has to devise their own functions and algorithms for checking if an overflow/underflow happened, which is tedious and likely to be inefficient.

I propose a new suite of functions in the math package.
Each one would return the result together with a boolean flag set to false when an overflow/underflow took place.

func AddOverflow[T int | uint | int64 | uint64 | int32 | uint32 | int16 | uint16 | int8 | uint8](i T) (T, bool)

Add two integers and detect overflow.

func SubOverflow[T int | uint | int64 | uint64 | int32 | uint32 | int16 | uint16 | int8 | uint8](i T) (T, bool)

Subtract two integers and detect overflow.

func MulOverflow[T int | uint | int64 | uint64 | int32 | uint32 | int16 | uint16 | int8 | uint8](i T) (T, bool)

Multiply two integers and detect overflow.

func DivOverflow[T int | uint | int64 | uint64 | int32 | uint32 | int16 | uint16 | int8 | uint8](i T) (T, bool)

Divide two integers and detect overflow.

Example usage:

import "math"

var a int8 = 127
var b int8 = 1
c, ok := math.AddOverflow(a, b)
//  c = -128
// ok = false

a = 25
b = 4
c, ok = math.AddOverflow(a, b)
//  c = 29
// ok = true

Another option would be to enhance the arithmetic operators to optionally allow two return values.
This however would constitute a language change.

var a int8 = 127
var b int8 = 1
c, ok := a + b
//  c = -128
// ok = false

[icholy]

Integer division cannot overflow.

[Verseth]

@icholy Consider the following example

var a int8 = -128
var b int8 = -1
fmt.Println(a / b)
// -128

[randall77]

Closing as dup of #24853, and related to #30209 and #32063. Some of these functions are easily simulateable with math/bits operations.

Integer division can overflow, in the very special case of math.MinInt / -1.
And arguably, /0 also. Presumably DivOverflow would return false and not panic if dividing by 0.