Slides for P3724R1 — Integer division

Document number:: P3895R0
Date:: 2025-03-11
Audience:: SG6
Project:: ISO/IEC 14882 Programming Languages — C++, ISO/IEC JTC1/SC22/WG21
Reply-to:: Jan Schultke <janschultke@gmail.com>
Source:: github.com/Eisenwave/cpp-proposals/blob/master/src/intdiv-slides.cow

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Integer division
P3724R1

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 1

Introduction

C++ supports integer division with rounding towards zero
many other rounding modes are useful:

int

bucket_size

1000

elements

100

;

int

buckets_req

elements

bucket_size

;

WRONG, zero

int

buckets_req

div_to_inf

(

elements

bucket_size

)

;

OK, one

hardware division always rounds towards zero
- only mode where r = x - y * q doesn't overflow
software division in other langs. sometimes supports other modes

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 2

Why does this need to be in the standard?

users need it all the time, and try to implement it
they fail miserably: almost all attempts on StackOverflow/blogs wrong

[StackOverflowCeil] answer (67 upvotes) fails at rounding to $+ \infty$ :

(

)

;

Mistake: incrementing negative quotients: x=-1, y=2, q=1

pulling in third-party library for one division function is silly

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 3

Computing remainders is hard

The following function has unintended UB:

auto

div_rem_ceil

(

_BitInt

(

)

_BitInt

(

)

{

_BitInt

(

)

div_ceil

(

)

;

round to

+ \infty

_BitInt

(

)

;

overflow

return

div_result

_BitInt

(

)

{

}

;

}

div_rem_ceil(7, 2) overflows: q == 4, y * q == 8

Conclusion

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 4

Which rounding modes to support

`div_to_zero`_📘_(trunc)	`div_ties_to_zero`
`div_away_zero`	`div_ties_away_zero`_📘_(round)
`div_to_inf`_📘_(ceil)	`div_ties_to_inf`
`div_to_neg_inf`_📘_(floor)	`div_ties_to_neg_inf`
`div_to_even`_⚖️	`div_ties_to_even`_⚖️📘
`div_to_odd`_⚖️	`div_ties_to_odd`_⚖️

marked functions are must-have, others fill the gaps
⚖️ — unbiased | 📘 — ISO/IEC 60559
each div_mode function has div_rem_mode counterpart (24 total)

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 5

Library interface

template

class

struct

div_result

{

quotient

remainder

;

friend

constexpr

auto

operator

<=>

(

...

)

default

;

}

;

template

class

constexpr

div_result

div_rem_

mode

(

)

;

template

class

constexpr

div_to_

mode

(

)

;

template

class

constexpr

mod

(

)

;

no noexcept because narrow contract (Preconditions:)
no rounding_mode constant template- or run-time parameter
mod is div_rem_to_neg_inf(x, y).remainder
- as in $- 2 mod 5 = 3$ , and as in mod in Haskell, Ada, CSS, etc.

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 6

Other design considerations

no SIMD overloads, but could be added in the future
- branchless implementation possible
no functions that compute only remainder (except mod)
- these are not usually needed
- undesirable remainder sign for most rounding modes
all functions are in <numeric>
feature-test macro: __cpp_lib_integer_division

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 7

Implementation experience

Appendix A has simplified implementation for educational purposes
eisenwave/integer-division [GitHub] repo has full implementation
all functions can be made branchless and are suitable for SIMD port

Implementation is always in terms of / and %.

div_result

int

div_rem_to_neg_inf

(

int

)

{

bool

quotient_negative

(

)

;

int

adjust

int

(

)

quotient_negative

)

;

return

{

adjust

}

;

}

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 8

Questions

Agreement with overall design?
SIMD overloads in another proposal?
Forward to LEWG?

Jan Schultke | Slides for P3724R1 — Integer division | Kona 2025 | Slide 9

References

[P3724R1] Jan Schultke. Integer division 2025-09-29 https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2025/p3724r1.html

[GitHub] Jan Schultke. integer-division GitHub repository https://github.com/Eisenwave/integer-division

[StackOverflowCeil] Fast ceiling of an integer division in C / C++ https://stackoverflow.com/q/2745074/5740428

Slides for P3724R1 — Integer division

Integer division P3724R1

Introduction

Why does this need to be in the standard?

Computing remainders is hard

Which rounding modes to support

Library interface

Other design considerations

Implementation experience

Questions

References

Integer division
P3724R1