Jens Maurer <Jens.Maurer@gmx.net>

Target audience: LEWG

2018-11-22

This paper proposes to add simple free functions for basic bit operations on all unsigned integer types.

A previous proposal was in "N3864: A constexpr bitwise operations library for C++" by Matthew Fioravante.

The papers P0237Rx propose to introduce bit_value, bit_reference, and bit_iterator, higher-level concepts for manipulating individual bits and sequences of bits. In order to implement efficient standard algorithms on bit_iterator, it is expected that implementations use the facilities presented in this paper. By directly exposing the low-level facilities to programmers, they can use them for their own purposes, independent of higher-level abstractions in the standard library.

It is expected that the functions provided with this proposal will be,
at some later time, overloaded for `std::datapar`

, the
nascent SIMD data type (see P0214R2: "Data-Parallel Vector Types &
Operations" by Matthias Kretz).

P0553R1 was favorably reviewed by LEWG with removing the nested inline namespace and using the header <bit>, and forwarded to LWG at the Albuquerque, Fall 2017 meeting.

P0553R2 contains small edits in preparation for LWG review.

P0553R3 reflects LWG review (introduce "Constraints" items, harmonize phrasing "0/1 bits in the value of x", add "nodiscard" for rotl/rotr). It was sent back to LEWG to clarify the open issues (see below).

- Tentative YES: Should the rotation count be signed, and should a negative value mean rotation in the opposite direction? (Geoffrey Romer)
- Tentative YES: "count" should return the same type as the rotation count of rotl/rotr:
`std::rotr(val, std::countl_zero(val))`

(Ville Voutilainen) - Tentative YES: Is it intentional that the "unsigned" requirement excludes std::byte or char, even on platforms where char is unsigned?

`<bit>`

header proposed by P0237R4, or in a separate
header. LEWG decided to use `<bit>`

.
The bit rotation operations are not limited to rotation counts less than the bit-width of the integer; it seems most (all?) CPU instruction sets support longer rotations by simply discarding upper bits. Different from bit shifts, this behavior is reasonable because rotating a 32-bit quantity by 33 bits is indistinguishable from rotating it by 1 bit.

The counting operations return "int" quantities, consistent with the rule "use an int unless you need something else". This choice does not reflect, in the type, the fact that counts are always non-negative.

This proposal uses readable English names for the operations, except that "left" (towards/affecting the most significant bits) and "right" (towards/affecting the least significant bits) is abbreviate "l" and "r", respectively. The use of "left" and "right" in the operation names is consistent with the "left" and "right" built-in shift operators.

An earlier draft of this paper had names such as "countl1", but lower-case "ell" and the digit "one" are nearly indistinguishable in some fonts, so now a name like "countl_one" is proposed. This is slightly baroque, so alternatively "countl(T, bool)" could be used, with the understanding that the second parameter is often a compile-time constant, allowing for optimization opportunities.

Per prevailing LWG convention, only those functions are marked
`noexcept`

that have a wide constract, i.e. no restrictions
on the values of the function arguments.

All functions are marked `constexpr`

, assuming that
either compiler intrinsics that work in constant evaluation are
available to the implementation, or the optimizer is good enough to
use the appropriate hardware instructions for operations described
with potentially verbose expressions with built-in operators.

A tangentially related `std::bit_cast`

is proposed
in P0476R1: "Bit-casting object representations" by JF
Bastien.

operation | Intel/AMD | ARM | PowerPC |
---|---|---|---|

rotl | ROL | - | rldicl |

rotr | ROR | ROR, EXTR | - |

popcount | POPCNT | - | popcntb |

countl_zero | BSR, LZCNT | CLZ | cntlzd |

countl_one | - | CLS | - |

countr_zero | BSF, TZCNT | - | - |

countr_one | - | - | - |

`<bit>`

to the table in 17.5.1.2 [headers].
Append a new subsection to clause 20 [utilities] with the following content:

## 23.20 Bit operations [bitops]

## 23.20.1 Header <bit> synopsis [bit.syn]

namespace std { // 23.20.2, rotating template<class T> [[nodiscard]] constexpr T rotl(T x,In the following descriptions, let N denoteints) noexcept; template<class T> [[nodiscard]] constexpr T rotr(T x,ints) noexcept; // 23.20.3, counting template<class T> constexpr int countl_zero(T x) noexcept; template<class T> constexpr int countl_one(T x) noexcept; template<class T> constexpr int countr_zero(T x) noexcept; template<class T> constexpr int countr_one(T x) noexcept; template<class T> constexpr int popcount(T x) noexcept; }`std::numeric_limits<T>::digits`

.## 23.20.2 Rotating [bitops.rot]

template<class T> [[nodiscard]] constexpr T rotl(T x,ints) noexcept;Constraints:`T`

is an unsigned integer type (3.9.1 [basic.fundamental]).

Let r be`s % N`

.

Returns:If r is 0, x; if r is positive,`(x << r) | (x >> (N - r))`

; if r is negative,`rotr(x, -r)`

.template<class T> [[nodiscard]] constexpr T rotr(T x,ints) noexcept;Constraints:`T`

is an unsigned integer type (3.9.1 [basic.fundamental]).

Let r be`s % N`

.

Returns:If r is 0, x; if r is positive,`(x >> r) | (x << (N - r))`

; if r is negative,`rotl(x, -r)`

.## 23.20.3 Counting [bitops.count]

template<class T> constexpr int countl_zero(T x) noexcept;Constraints:`T`

is an unsigned integer type (3.9.1 [basic.fundamental]).

Returns:The number of consecutive 0 bits in the value of x, starting from the most significant bit. [ Note: Returns N if`x == 0`

. ]template<class T> constexpr int countl_one(T x) noexcept;Constraints:`T`

is an unsigned integer type (3.9.1 [basic.fundamental]).

Returns:The number of consecutive 1 bits in the value of x, starting from the most significant bit. [ Note: Returns N if`x == std::numeric_limits<T>::max()`

. ]template<class T> constexpr int countr_zero(T x) noexcept;Constraints:`T`

is an unsigned integer type (3.9.1 [basic.fundamental]).

Returns:The number of consecutive 0 bits in the value of x, starting from the least significant bit. [ Note: Returns N if x == 0. ]template<class T> constexpr int countr_one(T x) noexcept;Constraints:`T`

is an unsigned integer type (3.9.1 [basic.fundamental]).

Returns:The number of consecutive 1 bits in the value of x, starting from the least significant bit. [ Note: Returns N if`x == std::numeric_limits<T>::max()`

. ]template<class T> constexpr int popcount(T x) noexcept;Constraints:`T`

is an unsigned integer type (3.9.1 [basic.fundamental]).

Returns:The number of 1 bits in the value of x.

- ISO/IEC JTC1 SC22 WG21 N3864: "A constexpr bitwise operations library for C++" by Matthew Fioravante
- ISO/IEC JTC1 SC22 WG21 P0214R2: "Data-Parallel Vector Types & Operations" by Matthias Kretz
- ISO/IEC JTC1 SC22 WG21 P0237R0: "On the standardization of fundamental bit manipulation utilities" by Vincent Reverdy and Robert J. Brunner
- ISO/IEC JTC1 SC22 WG21 P0237R4: "Wording for fundamental bit manipulation utilities" by Vincent Reverdy and Robert J. Brunner
- ISO/IEC JTC1 SC22 WG21 P0476R1: "Bit-casting object representations" by JF Bastien
- ARM Compiler User Guide [large PDF]
- Intel x86 Instruction Set Reference [large PDF]
- PowerPC Architecture Book, Version 2.02: Book I: PowerPC User Instruction Set Architecture [large PDF inside ZIP]