Merge 2018-11 CWG Motion 10

P1236R1 Alternative Wording for P0907R4 Signed Integers are Two's Complement

Fixes #2402

Author: zygoloid

source/atomics.tex

@@ -1029,8 +1029,13 @@
 \pnum
 \indextext{signed integer representation!two's complement}%
 \remarks For signed integer types,
-arithmetic is defined to use two's complement representation.
-There are no undefined results.
+the result is as if the object value and parameters
+were converted to their corresponding unsigned types,
+the computation performed on those types, and
+the result converted back to the signed type.
+\begin{note}
+There are no undefined results arising from the computation.
+\end{note}
 \end{itemdescr}
 
 \indexlibrarymember{operator+=}{atomic_ref<\placeholder{integral}>}%
@@ -1894,8 +1899,15 @@
 
 \pnum
 \indextext{signed integer representation!two's complement}%
-\remarks For signed integer types, arithmetic is defined to use two's complement representation.
-There are no undefined results.
+\remarks For signed integer types,
+the result is as if the object value and parameters
+were converted to their corresponding unsigned types,
+the computation performed on those types, and
+the result converted back to the signed type.
+\begin{note}
+There are no undefined results arising from the computation.
+\end{note}
+
 \end{itemdescr}
 
 \indexlibrarymember{operator+=}{atomic<T*>}%

source/basic.tex

@@ -4165,51 +4165,7 @@
 \rSec2[basic.fundamental]{Fundamental types}
 
 \pnum
-\indextext{type!integral}%
-\indextext{floating-point type|see{type, floating-point}}%
 \indextext{type!implementation-defined \tcode{sizeof}}%
-\indextext{type!Boolean}%
-\indextext{type!\idxcode{char}}%
-\indextext{type!character}%
-Objects declared as characters (\tcode{char}) shall be large enough to
-store any member of the implementation's basic character set. If a
-character from this set is stored in a character object, the integral
-value of that character object is equal to the value of the single
-character literal form of that character. It is \impldef{signedness of \tcode{char}}
-whether a \tcode{char} object can hold negative values.
-\indextext{\idxcode{char}!implementation-defined sign of}%
-\indextext{type!\idxcode{signed char}}%
-\indextext{type!\idxcode{unsigned char}}%
-Characters can be explicitly declared \tcode{unsigned} or
-\tcode{signed}.
-\indextext{character!\idxcode{signed}}%
-Plain \tcode{char}, \tcode{signed char}, and \tcode{unsigned char} are
-three distinct types, collectively called
-\defnx{narrow character types}{type!narrow character}.
-A \tcode{char}, a \tcode{signed char}, and an
-\tcode{unsigned char} occupy the same amount of storage and have the
-same alignment requirements\iref{basic.align}; that is, they have the
-same object representation. For narrow character types, all bits of the object
-representation participate in the value representation.
-\begin{note}
-A bit-field of narrow character type whose length is larger than
-the number of bits in the object representation of that type has
-padding bits; see~\ref{basic.types}.
-\end{note}
-For unsigned narrow
-character types, each possible bit pattern of the value representation
-represents a distinct number. These requirements do not hold for other types. In
-any particular implementation, a plain \tcode{char} object can take on
-either the same values as a \tcode{signed char} or an \tcode{unsigned
-char}; which one is \impldef{representation of \tcode{char}}.
-For each value \placeholder{i} of type \tcode{unsigned char} in the range
-0 to 255 inclusive, there exists a value \placeholder{j} of type
-\tcode{char} such that the result of an integral
-conversion\iref{conv.integral} from \placeholder{i} to \tcode{char} is
-\placeholder{j}, and the result of an integral conversion from
-\placeholder{j} to \tcode{unsigned char} is \placeholder{i}.
-
-\pnum
 \indextext{type!standard signed integer}%
 There are five \defnx{standard signed integer types}{standard signed integer type} :
 \indextext{type!\idxcode{signed char}}%
@@ -4225,20 +4181,21 @@
 \indextext{type!signed integer}%
 There may also be \impldef{extended signed integer types}
 \defnx{extended signed integer types}{extended signed integer type}.
-The standard and
-extended signed integer types are collectively called
+The standard and extended signed integer types are collectively called
 \defnx{signed integer types}{signed integer type}.
+The range of representable values for a signed integer type is
+$-2^{N-1}$ to $2^{N-1}-1$ (inclusive),
+where \placeholder{N} is called the \defn{range exponent} of the type.
 \indextext{integral type!implementation-defined \tcode{sizeof}}%
 \begin{note}
-Plain \tcode{int}s
-are intended to have
-the natural size suggested by the architecture of the
-execution environment;
+Plain \tcode{int}s are intended to have
+the natural size suggested by the architecture of the execution environment;
 the other signed integer types are provided to meet special needs.
 \end{note}
 
 \pnum
 \indextext{type!\idxcode{unsigned}}%
+\indextext{type!unsigned integer}%
 For each of the standard signed integer types,
 there exists a corresponding (but different)
 \indextext{type!standard unsigned integer}%
@@ -4250,98 +4207,176 @@
 \indextext{type!\idxcode{unsigned long long}}%
 ``\tcode{unsigned char}'', ``\tcode{unsigned short int}'',
 ``\tcode{unsigned int}'', ``\tcode{unsigned long int}'', and
-``\tcode{unsigned long long int}'', each of
-which occupies the same amount of storage and has the same alignment
-requirements\iref{basic.align} as the corresponding signed integer
-type\footnote{See~\ref{dcl.type.simple} regarding the correspondence between types and
-the sequences of \grammarterm{type-specifier}{s} that designate them.};
-that is, each signed integer type has the same object representation as
-its corresponding unsigned integer type.
+``\tcode{unsigned long long int}''.
 \indextext{type!extended unsigned integer}%
-\indextext{type!unsigned integer}%
-Likewise, for each of the extended signed integer types there exists a
-corresponding
-\defn{extended unsigned integer type} with the same amount of storage and alignment
-requirements. The standard and extended unsigned integer types are
-collectively called \defnx{unsigned integer types}{unsigned integer type}. The range of non-negative
-values of a signed integer type is
-a subrange of the corresponding unsigned integer type,
-the representation of the same value in each of the two types is the same, and
-the value representation of each corresponding signed/unsigned type shall be the same.
+Likewise, for each of the extended signed integer types,
+there exists a corresponding \defn{extended unsigned integer type}.
+The standard and extended unsigned integer types
+are collectively called \defnx{unsigned integer types}{unsigned integer type}.
+An unsigned integer type has the same range exponent \placeholder{N}
+as the corresponding signed integer type.
+\indextext{arithmetic!\idxcode{unsigned}}%
+The range of representable values for the unsigned type is
+$0$ to $2^N-1$ (inclusive);
+arithmetic for the unsigned type is performed modulo $2^N$.
+\begin{note}
+Unsigned arithmetic does not overflow.
+Overflow for signed arithmetic yields undefined behavior\iref{expr.pre}.
+\end{note}
+
+\pnum
+\indextext{signed integer representation!two's complement}%
+An unsigned integer type has the same
+object representation,
+value representation, and
+alignment requirements\iref{basic.align}
+as the corresponding signed integer type.
+For each value $x$ of a signed integer type,
+the value of the corresponding unsigned integer type
+congruent to $x$ modulo $2^N$ has the same value
+of corresponding bits in its value representation.\footnote{This
+is also known as two's complement representation.}
+\begin{example}
+The value $-1$ of a signed integer type has the same representation as
+the largest value of the corresponding unsigned type.
+\end{example}
+
+\begin{floattable}{Minimum range exponent}{tab:range.exponent}{ll}
+\topline
+\lhdr{Type} & \rhdr{Minimum range exponent $N$} \\
+\capsep
+\tcode{signed char} & 8 \\
+\tcode{short} & 16 \\
+\tcode{int} & 16 \\
+\tcode{long} & 32 \\
+\tcode{long long} & 64 \\
+\end{floattable}
+
+\pnum
+The range exponent of each signed integer type
+shall not be less than the values specified in \tref{range.exponent}.
+The value representation of a signed or unsigned integer type
+comprises $N$ bits, where N is the respective range exponent.
+Each set of values for any padding bits\iref{basic.types}
+in the object representation are
+alternative representations of the value specified by the value representation.
+\begin{note}
+Padding bits have unspecified value, but do not cause traps.
+See also ISO C 6.2.6.2.
+\end{note}
+\begin{note}
+The signed and unsigned integer types satisfy
+the constraints given in ISO C 5.2.4.2.1.
+\end{note}
+Except as specified above,
+the range exponent of a signed or unsigned integer type is
+\impldef{range exponent of integral type}.
+
+\pnum
+Each value $x$ of an unsigned integer type with range exponent $N$ has
+a unique representation $x = x_0 2^0 + x_1 2^1 + \ldots + x_{N-1} 2^{N-1}$,
+where each coefficient $x_i$ is either 0 or 1;
+this is called the \defn{base-2 representation} of $x$.
+The base-2 representation of a value of signed integer type is
+the base-2 representation of the congruent value
+of the corresponding unsigned integer type.
 \indextext{type!standard integer}%
 \indextext{type!extended integer}%
 The standard signed integer types and standard unsigned integer types
 are collectively called the \defnx{standard integer types}{standard integer type}, and the extended
 signed integer types and extended
 unsigned integer types are collectively called the
 \defnx{extended integer types}{extended integer type}.
-The signed and unsigned integer types shall satisfy
-the constraints given in the C standard, subclause 5.2.4.2.1.
 
 \pnum
-\indextext{arithmetic!\idxcode{unsigned}}%
-Unsigned integers shall obey the laws of arithmetic modulo $2^n$ where $n$ is
-the number of bits in the value representation of that particular size of
-integer.\footnote{This implies that
-unsigned arithmetic does not overflow because a result
-that cannot be represented by the resulting unsigned integer type is
-reduced modulo the number that is one greater than the largest value
-that can be represented by the resulting unsigned integer type.}
+A fundamental type specified to have
+a signed or unsigned integer type as its \defn{underlying type} has
+the same object representation,
+value representation,
+alignment requirements\iref{basic.align}, and
+range of representable values as the underlying type.
+Further, each value has the same representation in both types.
+
+\pnum
+\indextext{type!\idxcode{char}}%
+\indextext{type!character}%
+\indextext{type!narrow character}%
+\indextext{\idxcode{char}!implementation-defined sign of}%
+\indextext{type!\idxcode{signed char}}%
+\indextext{character!\idxcode{signed}}%
+\indextext{type!\idxcode{unsigned char}}%
+Type \tcode{char} is a distinct type
+that has an \impldef{underlying type of \tcode{char}} choice of
+``\tcode{signed char}'' or ``\tcode{unsigned char}'' as its underlying type.
+The values of type \tcode{char} can represent distinct codes
+for all members of the implementation's basic character set.
+The three types \tcode{char}, \tcode{signed char}, and \tcode{unsigned char}
+are collectively called \defnx{narrow character types}{narrow character type}.
+For narrow character types,
+each possible bit pattern of the object representation represents
+a distinct value.
+\begin{note}
+This requirement does not hold for other types.
+\end{note}
+\begin{note}
+A bit-field of narrow character type whose width is larger than
+the range exponent of that type has padding bits; see \ref{basic.types}.
+\end{note}
 
 \pnum
+\indextext{\idxcode{wchar_t}|see{type, \tcode{wchar_t}}}%
+\indextext{type!\idxcode{wchar_t}}%
+\indextext{underlying type|see{type, underlying}}%
+\indextext{type!underlying!\idxcode{wchar_t}}%
+Type \tcode{wchar_t} is a distinct type that has
+an \impldef{underlying type of \tcode{wchar_t}}
+signed or unsigned integer type as its underlying type.
+The values of type \tcode{wchar_t} can represent
+distinct codes for all members of the largest extended character set
+specified among the supported locales\iref{locale}.
 \indextext{\idxcode{char16_t}|see{type, \tcode{char16_t}}}%
 \indextext{\idxcode{char32_t}|see{type, \tcode{char32_t}}}%
-\indextext{\idxcode{wchar_t}|see{type, \tcode{wchar_t}}}%
 \indextext{type!\idxcode{char16_t}}%
 \indextext{type!\idxcode{char32_t}}%
-\indextext{type!\idxcode{wchar_t}}%
-\indextext{underlying type|see{type, underlying}}%
 \indextext{type!underlying!\idxcode{char16_t}}%
 \indextext{type!underlying!\idxcode{char32_t}}%
-Type \tcode{wchar_t} is a distinct type whose values can represent
-distinct codes for all members of the largest extended character set
-specified among the supported locales\iref{locale}. Type
-\tcode{wchar_t} shall have the same size, signedness, and alignment
-requirements\iref{basic.align} as one of the other integral types,
-called its \defnx{underlying type}{type!underlying!\idxcode{wchar_t}}. Types \tcode{char16_t} and
-\tcode{char32_t} denote distinct types with the same size, signedness,
-and alignment as \tcode{uint_least16_t} and \tcode{uint_least32_t},
-respectively, in \tcode{<cstdint>}, called the underlying types.
+Types \tcode{char16_t} and \tcode{char32_t} denote distinct types
+whose underlying types are \tcode{uint_least16_t} and \tcode{uint_least32_t},
+respectively, in \tcode{<cstdint>}.
 
 \pnum
 \indextext{Boolean type}%
-Values of type \tcode{bool} are either \tcode{true} or
-\tcode{false}.\footnote{Using a \tcode{bool} value in ways described by this document
-as ``undefined'', such as by examining the value of an
-uninitialized automatic object, might cause it to behave as if it is
-neither \tcode{true} nor \tcode{false}.}
-\begin{note} There are no \tcode{signed}, \tcode{unsigned}, \tcode{short},
-or \tcode{long bool} types or values. \end{note} Values of type
-\tcode{bool} participate in integral promotions\iref{conv.prom}.
+\indextext{type!Boolean}%
+Type \tcode{bool} is a distinct type that has
+the same object representation,
+value representation, and
+alignment requirements as
+an \impldef{underlying type of \tcode{bool}} unsigned integer type.
+The values of type \tcode{bool} are
+\tcode{true} and \tcode{false}.\footnote{Using a \tcode{bool} value
+in ways described by this document as ``undefined'',
+such as by examining the value of an uninitialized automatic object,
+might cause it to behave as if it is neither \tcode{true} nor \tcode{false}.}
+\begin{note}
+There are no \tcode{signed}, \tcode{unsigned},
+\tcode{short}, or \tcode{long bool} types or values.
+\end{note}
 
 \pnum
+\indextext{type!integral}%
 Types \tcode{bool}, \tcode{char}, \tcode{char16_t}, \tcode{char32_t},
 \tcode{wchar_t}, and the signed and unsigned integer types are
 collectively called
-\defnx{integral}{integral type} types.\footnote{Therefore, enumerations\iref{dcl.enum} are not integral; however,
-enumerations can be promoted to integral types as specified
-in~\ref{conv.prom}.}
-A synonym for integral type is
-\indextext{signed integer representation!ones' complement}%
-\indextext{signed integer representation!two's complement}%
-\indextext{signed integer representation!signed magnitude}%
-\defn{integer type}. The representations of integral types shall
-define values by use of a pure binary numeration system.\footnote{A positional
-representation for integers that uses the binary digits 0
-and 1, in which the values represented by successive bits are additive,
-begin with 1, and are multiplied by successive integral power of 2,
-except perhaps for the bit with the highest position. (Adapted from the
-\doccite{American National Dictionary for Information Processing Systems}.)}
-\begin{example} This document permits two's complement,
-ones' complement and signed magnitude representations for integral types.
-\end{example}
+\defnx{integral types}{integral type}.
+A synonym for integral type is \defn{integer type}.
+\begin{note}
+Enumerations\iref{dcl.enum} are not integral;
+however, unscoped enumerations can be promoted to integral types
+as specified in \ref{conv.prom}.
+\end{note}
 
 \pnum
+\indextext{floating-point type|see{type, floating-point}}%
 There are three \defnx{floating-point types}{type!floating-point}:
 \indextext{type!\idxcode{float}}%
 \tcode{float},