diff --git a/source/numerics.tex b/source/numerics.tex
index 559d5ec913..bee954157b 100644
--- a/source/numerics.tex
+++ b/source/numerics.tex
@@ -173,7 +173,7 @@
 \end{note}
 
 \pnum
-A separate floating-point environment shall be maintained for each thread. Each function
+A separate floating-point environment is maintained for each thread. Each function
 accesses the environment corresponding to its calling thread.
 
 \xrefc{7.6}
@@ -201,15 +201,15 @@
 \pnum
 If \tcode{z} is an lvalue of type \cv{} \tcode{complex<T>} then:
 \begin{itemize}
-\item the expression \tcode{reinterpret_cast<\cv{} T(\&)[2]>(z)} shall be well-formed,
-\item \tcode{reinterpret_cast<\cv{} T(\&)[2]>(z)[0]} shall designate the real part of \tcode{z}, and
-\item \tcode{reinterpret_cast<\cv{} T(\&)[2]>(z)[1]} shall designate the imaginary part of \tcode{z}.
+\item the expression \tcode{reinterpret_cast<\cv{} T(\&)[2]>(z)} is well-formed,
+\item \tcode{reinterpret_cast<\cv{} T(\&)[2]>(z)[0]} designates the real part of \tcode{z}, and
+\item \tcode{reinterpret_cast<\cv{} T(\&)[2]>(z)[1]} designates the imaginary part of \tcode{z}.
 \end{itemize}
 
 Moreover, if \tcode{a} is an expression of type \cv{}~\tcode{complex<T>*} and the expression \tcode{a[i]} is well-defined for an integer expression \tcode{i}, then:
 \begin{itemize}
-\item \tcode{reinterpret_cast<\cv{} T*>(a)[2*i]} shall designate the real part of \tcode{a[i]}, and
-\item \tcode{reinterpret_cast<\cv{} T*>(a)[2*i + 1]} shall designate the imaginary part of \tcode{a[i]}.
+\item \tcode{reinterpret_cast<\cv{} T*>(a)[2*i]} designates the real part of \tcode{a[i]}, and
+\item \tcode{reinterpret_cast<\cv{} T*>(a)[2*i + 1]} designates the imaginary part of \tcode{a[i]}.
 \end{itemize}
 
 \rSec2[complex.syn]{Header \tcode{<complex>} synopsis}
@@ -449,14 +449,10 @@
 \end{itemdecl}
 
 \begin{itemdescr}
-\pnum
-\effects
-Constructs an object of class
-\tcode{complex}.
 
 \pnum
 \ensures
-\tcode{real() == re \&\& imag() == im}.
+\tcode{real() == re \&\& imag() == im} is \tcode{true}.
 \end{itemdescr}
 
 \indexlibrarymember{real}{complex}%
@@ -663,9 +659,6 @@
 \returns
 \tcode{complex<T>(lhs)}.
 
-\pnum
-\remarks
-unary operator.
 \end{itemdescr}
 
 \begin{itemdecl}
@@ -691,8 +684,6 @@
 \tcode{complex<T>(-lhs.real(),-lhs.imag())}.
 
 \pnum
-\remarks
-unary operator.
 \end{itemdescr}
 
 \indexlibrarymember{operator-}{complex}%
@@ -762,8 +753,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-The input values shall be convertible to
+\expects
+The input values are convertible to
 \tcode{T}.
 
 \pnum
@@ -919,8 +910,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-\tcode{rho} shall be non-negative and non-NaN\@. \tcode{theta} shall be finite.
+\expects
+\tcode{rho} is non-negative and non-NaN\@. \tcode{theta} is finite.
 
 \pnum
 \returns
@@ -1342,6 +1333,14 @@
 \end{itemdecl}
 
 \begin{itemdescr}
+\pnum
+\constraints
+\begin{itemize}
+\item \tcode{sizeof(To) == sizeof(From)} is \tcode{true};
+\item \tcode{is_trivially_copyable_v<To>} is \tcode{true}; and
+\item \tcode{is_trivially_copyable_v<From>} is \tcode{true}.
+\end{itemize}
+
 \pnum
 \returns
 An object of type \tcode{To}.
@@ -1354,13 +1353,7 @@
 
 \pnum
 \remarks
-This function shall not participate in overload resolution unless:
-\begin{itemize}
-\item \tcode{sizeof(To) == sizeof(From)} is \tcode{true};
-\item \tcode{is_trivially_copyable_v<To>} is \tcode{true}; and
-\item \tcode{is_trivially_copyable_v<From>} is \tcode{true}.
-\end{itemize}
-This function shall be \tcode{constexpr} if and only if
+This function is \tcode{constexpr} if and only if
 \tcode{To}, \tcode{From}, and the types of all subobjects
 of \tcode{To} and \tcode{From} are types \tcode{T} such that:
 \begin{itemize}
@@ -1381,15 +1374,15 @@
 \end{itemdecl}
 
 \begin{itemdescr}
+\pnum
+\constraints
+\tcode{T} is an unsigned integer type\iref{basic.fundamental}.
+
 \pnum
 \returns
 \tcode{true} if \tcode{x} is an integral power of two;
 \tcode{false} otherwise.
 
-\pnum
-\remarks
-This function shall not participate in overload resolution
-unless \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
 \end{itemdescr}
 
 \indexlibraryglobal{ceil2}%
@@ -1432,16 +1425,16 @@
 \end{itemdecl}
 
 \begin{itemdescr}
+\pnum
+\constraints
+\tcode{T} is an unsigned integer type\iref{basic.fundamental}.
+
 \pnum
 \returns
 If \tcode{x == 0}, \tcode{0};
 otherwise the maximal value \tcode{y}
 such that \tcode{ispow2(y)} is \tcode{true} and \tcode{y <= x}.
 
-\pnum
-\remarks
-This function shall not participate in overload resolution
-unless \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
 \end{itemdescr}
 
 \indexlibraryglobal{log2p1}%
@@ -1451,16 +1444,16 @@
 \end{itemdecl}
 
 \begin{itemdescr}
+\pnum
+\constraints
+\tcode{T} is an unsigned integer type\iref{basic.fundamental}.
+
 \pnum
 \returns
 If \tcode{x == 0}, \tcode{0};
 otherwise one plus the base-2 logarithm of \tcode{x},
 with any fractional part discarded.
 
-\pnum
-\remarks
-This function shall not participate in overload resolution
-unless \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
 \end{itemdescr}
 
 \rSec2[bit.rotate]{Rotating}
@@ -2132,7 +2125,6 @@
 \indextext{seed sequence!requirements|)}%
 
 
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Uniform Random Number Generator requirements:
 
@@ -2436,7 +2428,7 @@
     provided that there have been no intervening invocations
     of \tcode{x} or of \tcode{v}.
 
-    \requires
+    \expects
     \tcode{is} provides a textual representation
     that was previously written
     using an output stream
@@ -2511,7 +2503,6 @@
  Otherwise returns \tcode{false}.
 \end{itemdescr}
 
-
 \begin{itemdecl}
 A::A(result_type s);
 \end{itemdecl}
@@ -2523,7 +2514,6 @@
  with \tcode{s}.
 \end{itemdescr}
 
-
 \begin{itemdecl}
 template<class Sseq> A::A(Sseq& q);
 \end{itemdecl}
@@ -2825,7 +2815,8 @@
     calls \tcode{is.setstate(ios::failbit)}
     (which may throw \tcode{ios::failure}\iref{iostate.flags}).
 
-    \requires \tcode{is} provides a textual representation
+    \expects
+    \tcode{is} provides a textual representation
     that was previously written
     using an \tcode{os} whose imbued locale
     and whose type's template specialization arguments
@@ -3071,7 +3062,6 @@
 \begin{itemdescr}
 \pnum
 \effects
-Constructs a \tcode{linear_congruential_engine} object.
  If $c \bmod m$ is $0$ and $\tcode{s} \bmod m$ is $0$,
  sets the engine's state to $1$,
  otherwise sets the engine's state to $\tcode{s} \bmod m$.
@@ -3085,7 +3075,6 @@
 \begin{itemdescr}
 \pnum
 \effects
-Constructs a \tcode{linear_congruential_engine} object.
  With
  $k = \left\lceil \frac{\log_2 m}{32} \right\rceil$
  and $a$ an array (or equivalent)
@@ -3245,7 +3234,6 @@
 \begin{itemdescr}
 \pnum
 \effects
-Constructs a \tcode{mersenne_twister_engine} object.
 Sets $X_{-n}$ to $\tcode{value} \bmod 2^w$.
 Then, iteratively for $i = 1 - n, \dotsc, -1$, sets $X_i$ to
 \[%
@@ -3270,7 +3258,6 @@
 \begin{itemdescr}
 \pnum
 \effects
-Constructs a \tcode{mersenne_twister_engine} object.
  With
  $k = \left\lceil w / 32 \right\rceil$
  and $a$ an array (or equivalent)
@@ -3393,7 +3380,6 @@
  $X_{i-r}, \dotsc, X_{i-1}$,
 in that order, followed by $c$.
 
-
 \indexlibraryctor{subtract_with_carry_engine}%
 \begin{itemdecl}
 explicit subtract_with_carry_engine(result_type value);
@@ -3402,7 +3388,6 @@
 \begin{itemdescr}
 \pnum
 \effects
-Constructs a \tcode{subtract_with_carry_engine} object.
  Sets the values of
  $X_{-r}, \dotsc, X_{-1}$,
  in that order, as specified below.
@@ -3429,8 +3414,6 @@
  of \tcode{e}.
 \end{itemdescr}
 
-
-
 \indexlibraryctor{subtract_with_carry_engine}%
 \begin{itemdecl}
 template<class Sseq> explicit subtract_with_carry_engine(Sseq& q);
@@ -3439,7 +3422,6 @@
 \begin{itemdescr}
 \pnum
 \effects
-Constructs a \tcode{subtract_with_carry_engine} object.
  With
  $k = \left\lceil w / 32 \right\rceil$
  and $a$ an array (or equivalent)
@@ -3747,8 +3729,7 @@
 The textual representation%
 \indextext{\idxcode{independent_bits_engine}!textual representation}%
 \indextext{textual representation!\idxcode{independent_bits_engine}}
-consists of
- the textual representation of \tcode{e}.
+consists of the textual representation of \tcode{e}.
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -3894,7 +3875,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{minstd_rand0}
- shall produce the value $1043618065$.
+ produces the value $1043618065$.
 \end{itemdescr}
 
 \indexlibraryglobal{minstd_rand}%
@@ -3910,7 +3891,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{minstd_rand}
- shall produce the value $399268537$.
+ produces the value $399268537$.
 \end{itemdescr}
 
 \indexlibraryglobal{mt19937}%
@@ -3927,7 +3908,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{mt19937}
- shall produce the value $4123659995$.
+ produces the value $4123659995$.
 \end{itemdescr}
 
 \indexlibraryglobal{mt19937_64}%
@@ -3945,7 +3926,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{mt19937_64}
- shall produce the value $9981545732273789042$.
+ produces the value $9981545732273789042$.
 \end{itemdescr}
 
 \indexlibraryglobal{ranlux24_base}%
@@ -3961,7 +3942,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{ran\-lux24_base}
- shall produce the value
+ produces the value
  $7937952$.
 \end{itemdescr}
 
@@ -3978,7 +3959,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{ran\-lux48_base}
- shall produce the value
+ produces the value
  $61839128582725$.
 \end{itemdescr}
 
@@ -3994,7 +3975,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{ranlux24}
- shall produce the value
+ produces the value
  $9901578$.
 \end{itemdescr}
 
@@ -4010,7 +3991,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{ranlux48}
- shall produce the value
+ produces the value
  $249142670248501$.
 \end{itemdescr}
 
@@ -4026,7 +4007,7 @@
  The $10000^\text{th}$ consecutive invocation
  of a default-constructed object
  of type \tcode{knuth_b}
- shall produce the value $1112339016$.
+ produces the value $1112339016$.
 \end{itemdescr}%
 
 \indexlibraryglobal{default_random_engine}%
@@ -4120,16 +4101,13 @@
 
 \begin{itemdescr}
 \pnum
-\effects
-Constructs a \tcode{random_device}
- nondeterministic uniform random bit generator object.
+\remarks
  The semantics of the \tcode{token} parameter
  and the token value used by the default constructor are
  \impldef{semantics of \tcode{token} parameter and default token value used by \tcode{random_device} constructors}.%
 \footnote{The parameter is intended
    to allow an implementation to differentiate
-   between different sources of randomness.
- }
+   between different sources of randomness.}
 
 \pnum
 \throws
@@ -4230,7 +4208,7 @@
 private:
   vector<result_type> v;        // \expos
 };
-\end{codeblock}%
+\end{codeblock}
 
 
 \indexlibraryctor{seed_seq}%
@@ -4240,9 +4218,8 @@
 
 \begin{itemdescr}
 \pnum
-\effects
-Constructs a \tcode{seed_seq} object
- as if by default-constructing its member \tcode{v}.
+\ensures
+\tcode{v.empty()} is \tcode{true}.
 
 \pnum
 \throws
@@ -4258,7 +4235,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires \tcode{T} shall be an integer type.
+\mandates
+\tcode{T} is an integer type.
 
 \pnum
 \effects
@@ -4274,17 +4252,19 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-  \tcode{InputIterator} shall meet the
-  \oldconcept{InputIterator} requirements\iref{input.iterators}.
-  Moreover,
+\mandates
   \tcode{iterator_traits<InputIterator>::value_type}
-  shall denote an integer type.
+  is an integer type.
+
+\pnum
+\expects
+  \tcode{InputIterator} meets the
+  \oldconcept{InputIterator} requirements\iref{input.iterators}.
 
 \pnum
 \effects
-Constructs a \tcode{seed_seq} object
- by the following algorithm:
+Initializes \tcode{v}
+by the following algorithm:
 \begin{codeblock}
 for (InputIterator s = begin; s != end; ++s)
  v.push_back((*s)@$\bmod 2^{32}$@);
@@ -4299,14 +4279,15 @@
 
 \begin{itemdescr}
 \pnum
-\requires \tcode{RandomAccessIterator}
-  shall meet the
+\mandates
+  \tcode{iterator_traits<RandomAccessIterator>::\brk{}value_type}
+  is an unsigned integer type capable of accommodating 32-bit quantities.
+
+\pnum
+\expects
+  \tcode{RandomAccessIterator} meets the
   \oldconcept{RandomAccessIterator} requirements\iref{random.access.iterators}
   and the requirements of a mutable iterator.
-  Moreover,
-  \tcode{iterator_traits<RandomAccessIterator>::\brk{}value_type}
-  shall denote an unsigned integer type
-  capable of accommodating 32-bit quantities.
 
 \pnum
 \effects
@@ -4413,13 +4394,13 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-  \tcode{OutputIterator} shall meet the
+\mandates
+  Values of type \tcode{result_type} are writable\iref{iterator.requirements.general} to \tcode{dest}.
+
+\pnum
+\expects
+  \tcode{OutputIterator} meets the
   \oldconcept{OutputIterator} requirements\iref{output.iterators}.
-  Moreover,
-  the expression
-  \tcode{*dest = rt}
-  shall be valid for a value \tcode{rt} of type \tcode{result_type}.
 
 \pnum
 \effects
@@ -4624,12 +4605,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- $\tcode{a} \leq \tcode{b}$.
+\expects
+$\tcode{a} \leq \tcode{b}$.
 
 \pnum
-\effects
-Constructs a \tcode{uniform_int_distribution} object;
+\remarks
  \tcode{a} and \tcode{b}
  correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -4718,14 +4698,13 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- $\tcode{a} \leq \tcode{b}$
- and
- $\tcode{b} - \tcode{a} \leq \tcode{numeric_limits<RealType>::max()}$.
+\expects
+$\tcode{a} \leq \tcode{b}$
+and
+$\tcode{b} - \tcode{a} \leq \tcode{numeric_limits<RealType>::max()}$.
 
 \pnum
-\effects
-Constructs a \tcode{uniform_real_distribution} object;
+\remarks
  \tcode{a} and \tcode{b}
  correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -4825,12 +4804,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- $0 \leq \tcode{p} \leq 1$.
+\expects
+$0 \leq \tcode{p} \leq 1$.
 
 \pnum
-\effects
-Constructs a \tcode{bernoulli_distribution} object;
+\remarks
  \tcode{p}
  corresponds to the parameter of the distribution.
 \end{itemdescr}
@@ -4903,12 +4881,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- $0 \leq \tcode{p} \leq 1$ and $0 \leq \tcode{t} $.
+\expects
+$0 \leq \tcode{p} \leq 1$ and $0 \leq \tcode{t} $.
 
 \pnum
-\effects
-Constructs a \tcode{binomial_distribution} object;
+\remarks
  \tcode{t} and \tcode{p}
  correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -4991,12 +4968,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- $0 < \tcode{p} < 1$.
+\expects
+$0 < \tcode{p} < 1$.
 
 \pnum
-\effects
-Constructs a \tcode{geometric_distribution} object;
+\remarks
  \tcode{p}
  corresponds to the parameter of the distribution.
 \end{itemdescr}
@@ -5073,13 +5049,12 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- $0 < \tcode{p} \leq 1$
- and $0 < \tcode{k} $.
+\expects
+$0 < \tcode{p} \leq 1$
+and $0 < \tcode{k} $.
 
 \pnum
-\effects
-Constructs a \tcode{negative_binomial_distribution} object;
+\remarks
  \tcode{k} and \tcode{p}
  correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -5181,11 +5156,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{mean}$.
+\expects
+$0 < \tcode{mean}$.
 
 \pnum
-\effects
-Constructs a \tcode{poisson_distribution} object;
+\remarks
 \tcode{mean} corresponds to the parameter of the distribution.
 \end{itemdescr}
 
@@ -5256,11 +5231,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{lambda}$.
+\expects
+$0 < \tcode{lambda}$.
 
 \pnum
-\effects
-Constructs an \tcode{exponential_distribution} object;
+\remarks
 \tcode{lambda} corresponds to the parameter of the distribution.
 \end{itemdescr}
 
@@ -5334,11 +5309,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{alpha}$ and $0 < \tcode{beta}$.
+\expects
+$0 < \tcode{alpha}$ and $0 < \tcode{beta}$.
 
 \pnum
-\effects
-Constructs a \tcode{gamma_distribution} object;
+\remarks
 \tcode{alpha} and \tcode{beta}
 correspond to the parameters of the distribution.
 \end{itemdescr}
@@ -5426,11 +5401,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{a}$ and $0 < \tcode{b}$.
+\expects
+$0 < \tcode{a}$ and $0 < \tcode{b}$.
 
 \pnum
-\effects
-Constructs a \tcode{weibull_distribution} object;
+\remarks
 \tcode{a} and \tcode{b}
 correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -5525,11 +5500,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{b}$.
+\expects
+$0 < \tcode{b}$.
 
 \pnum
-\effects
-Constructs an \tcode{extreme_value_distribution} object;
+\remarks
 \tcode{a} and \tcode{b}
 correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -5645,11 +5620,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{stddev}$.
+\expects
+$0 < \tcode{stddev}$.
 
 \pnum
-\effects
-Constructs a \tcode{normal_distribution} object;
+\remarks
 \tcode{mean} and \tcode{stddev}
 correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -5737,11 +5712,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{s}$.
+\expects
+$0 < \tcode{s}$.
 
 \pnum
-\effects
-Constructs a \tcode{lognormal_distribution} object;
+\remarks
 \tcode{m} and \tcode{s}
 correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -5826,11 +5801,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{n}$.
+\expects
+$0 < \tcode{n}$.
 
 \pnum
-\effects
-Constructs a \tcode{chi_squared_distribution} object;
+\remarks
 \tcode{n} corresponds to the parameter of the distribution.
 \end{itemdescr}
 
@@ -5903,11 +5878,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{b}$.
+\expects
+$0 < \tcode{b}$.
 
 \pnum
-\effects
-Constructs a \tcode{cauchy_distribution} object;
+\remarks
 \tcode{a} and \tcode{b}
 correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -5997,11 +5972,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{m}$ and $0 < \tcode{n}$.
+\expects
+$0 < \tcode{m}$ and $0 < \tcode{n}$.
 
 \pnum
-\effects
-Constructs a \tcode{fisher_f_distribution} object;
+\remarks
 \tcode{m} and \tcode{n}
 correspond to the respective parameters of the distribution.
 \end{itemdescr}
@@ -6089,11 +6064,11 @@
 
 \begin{itemdescr}
 \pnum
-\requires $0 < \tcode{n}$.
+\expects
+$0 < \tcode{n}$.
 
 \pnum
-\effects
-Constructs a \tcode{student_t_distribution} object;
+\remarks
 \tcode{n} corresponds to the parameter of the distribution.
 \end{itemdescr}
 
@@ -6211,17 +6186,19 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-  \tcode{InputIterator} shall meet the
+\mandates
+\tcode{is_convertible_v<iterator_traits<InputIterator>::value_type,
+double>} is \tcode{true}.
+
+\pnum
+\expects
+  \tcode{InputIterator} meets the
   \oldconcept{InputIterator} requirements\iref{input.iterators}.
-  Moreover,
-  \tcode{iterator_traits<InputIterator>::value_type}
-  shall denote a type that is convertible to \tcode{double}.
  If \tcode{firstW == lastW},
  let $n = 1$ and $w_0 = 1$.
  Otherwise,
  $\bigl[\tcode{firstW}, \tcode{lastW}\bigr)$
- shall form a sequence $w$ of length $n > 0$.
+ forms a sequence $w$ of length $n > 0$.
 
 \pnum
 \effects
@@ -6249,17 +6226,15 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- Each instance of type \tcode{UnaryOperation}
- shall be a function object\iref{function.objects}
- whose return type shall be convertible to \tcode{double}.
- Moreover,
- \tcode{double} shall be convertible
- to the type of \tcode{UnaryOperation}'s sole parameter.
+\mandates
+\tcode{is_invocable_r_v<double, UnaryOperation\&, double>} is \tcode{true}.
+
+\pnum
+\expects
  If $\tcode{nw} = 0$, let $n = 1$, otherwise let $n = \tcode{nw}$.
  The relation
    $0 < \delta = (\tcode{xmax} - \tcode{xmin}) / n$
- shall hold.
+ holds.
 
 \pnum
 \effects
@@ -6274,7 +6249,7 @@
 
 \pnum
 \complexity
- The number of invocations of \tcode{fw} shall not exceed $n$.
+The number of invocations of \tcode{fw} does not exceed $n$.
 \end{itemdescr}
 
 \indexlibrarymember{probabilities}{discrete_distribution}%
@@ -6395,15 +6370,19 @@
 
 \begin{itemdescr}
 \pnum
-\requires
+\mandates
+Both of
+\begin{itemize}
+\item{\tcode{is_convertible_v<iterator_traits<InputIteratorB>::value_type, double>}}
+\item{\tcode{is_convertible_v<iterator_traits<InputIteratorW>::value_type, double>}}
+\end{itemize}
+are \tcode{true}.
+
+\pnum
+\expects
   \tcode{InputIteratorB} and \tcode{InputIteratorW}
-  shall each meet the
+   each meet the
   \oldconcept{InputIterator} requirements\iref{input.iterators}.
-  Moreover,
-  the \grammarterm{id-expression}s
-  \tcode{iterator_traits<InputIteratorB>::value_type} and
-  \tcode{iterator_traits<Input\-IteratorW>::value_type}
-  shall each denote a type that is convertible to \tcode{double}.
  If \tcode{firstB == lastB}
  or \tcode{++firstB == lastB},
  let $n = 1$,
@@ -6412,10 +6391,10 @@
  and $b_1 = 1$.
  Otherwise,
  $\bigl[\tcode{firstB}, \tcode{lastB}\bigr)$
- shall form a sequence $b$ of length $n+1$,
+ forms a sequence $b$ of length $n+1$,
  the length of the sequence $w$ starting from \tcode{firstW}
- shall be at least $n$,
- and any $w_k$ for  $k \geq n$ shall be ignored by the distribution.
+ is at least $n$,
+ and any $w_k$ for  $k \geq n$ are ignored by the distribution.
 
 \pnum
 \effects
@@ -6432,13 +6411,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- Each instance of type \tcode{UnaryOperation}
- shall be a function object\iref{function.objects}
- whose return type shall be convertible to \tcode{double}.
- Moreover,
- \tcode{double} shall be convertible
- to the type of \tcode{UnaryOperation}'s sole parameter.
+\mandates
+\tcode{is_invocable_r_v<double, UnaryOperation\&, double>} is \tcode{true}.
 
 \pnum
 \effects
@@ -6459,7 +6433,7 @@
 
 \pnum
 \complexity
- The number of invocations of \tcode{fw} shall not exceed $n$.
+The number of invocations of \tcode{fw} does not exceed $n$.
 \end{itemdescr}
 
 
@@ -6471,16 +6445,14 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- Each instance of type \tcode{UnaryOperation}
- shall be a function object\iref{function.objects}
- whose return type shall be convertible to \tcode{double}.
- Moreover,
- \tcode{double} shall be convertible
- to the type of \tcode{UnaryOperation}'s sole parameter.
+\mandates
+\tcode{is_invocable_r_v<double, UnaryOperation\&, double>} is \tcode{true}.
+
+\pnum
+\expects
  If $\tcode{nw} = 0$, let $n = 1$, otherwise let $n = \tcode{nw}$.
  The relation $0 < \delta = (\tcode{xmax} - \tcode{xmin}) / n$
- shall hold.
+ holds.
 
 \pnum
 \effects
@@ -6492,7 +6464,7 @@
 
 \pnum
 \complexity
- The number of invocations of \tcode{fw} shall not exceed $n$.
+The number of invocations of \tcode{fw} does not exceed $n$.
 \end{itemdescr}
 
 \indexlibrarymember{intervals}{piecewise_constant_distribution}%
@@ -6624,15 +6596,14 @@
 
 \begin{itemdescr}
 \pnum
-\requires
+\mandates
+\tcode{is_invocable_r_v<double, UnaryOperation\&, double>} is \tcode{true}.
+
+\pnum
+\expects
   \tcode{InputIteratorB} and \tcode{InputIteratorW}
-  shall each meet the
+   each meet the
   \oldconcept{InputIterator} requirements\iref{input.iterators}.
-  Moreover,
-  the \grammarterm{id-expression}s
-  \tcode{iterator_traits<InputIteratorB>::value_type} and
-  \tcode{iterator_traits<Input\-IteratorW>::value_type}
-  shall each denote a type that is convertible to \tcode{double}.
  If \tcode{firstB == lastB}
  or \tcode{++firstB == lastB},
  let $n = 1$,
@@ -6641,10 +6612,10 @@
  and $b_1 = 1$.
  Otherwise,
  $\bigl[\tcode{firstB}, \tcode{lastB}\bigr)$
- shall form a sequence $b$ of length $n+1$,
+ forms a sequence $b$ of length $n+1$,
  the length of the sequence $w$ starting from \tcode{firstW}
- shall be at least $n+1$,
- and any $w_k$ for $k \geq n + 1$ shall be ignored by the distribution.
+ is at least $n+1$,
+ and any $w_k$ for $k \geq n + 1$ are ignored by the distribution.
 
 \pnum
 \effects
@@ -6661,13 +6632,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- Each instance of type \tcode{UnaryOperation}
- shall be a function object\iref{function.objects}
- whose return type shall be convertible to \tcode{double}.
- Moreover,
- \tcode{double} shall be convertible
- to the type of \tcode{UnaryOperation}'s sole parameter.
+\mandates
+\tcode{is_invocable_r_v<double, UnaryOperation\&, double>} is \tcode{true}.
 
 \pnum
 \effects
@@ -6688,7 +6654,7 @@
 
 \pnum
 \complexity
- The number of invocations of \tcode{fw} shall not exceed $n+1$.
+The number of invocations of \tcode{fw} does not exceed $n+1$.
 \end{itemdescr}
 
 
@@ -6700,16 +6666,14 @@
 
 \begin{itemdescr}
 \pnum
-\requires
- Each instance of type \tcode{UnaryOperation}
- shall be a function object\iref{function.objects}
- whose return type shall be convertible to \tcode{double}.
- Moreover,
- \tcode{double} shall be convertible
- to the type of \tcode{UnaryOperation}'s sole parameter.
+\mandates
+\tcode{is_invocable_r_v<double, UnaryOperation\&, double>} is \tcode{true}.
+
+\pnum
+\expects
  If $\tcode{nw} = 0$, let $n = 1$, otherwise let $n = \tcode{nw}$.
  The relation $0 < \delta = (\tcode{xmax} - \tcode{xmin}) / n$
- shall hold.
+ holds.
 
 \pnum
 \effects
@@ -6721,7 +6685,7 @@
 
 \pnum
 \complexity
- The number of invocations of \tcode{fw} shall not exceed $n+1$.
+The number of invocations of \tcode{fw} does not exceed $n+1$.
 \end{itemdescr}
 
 \indexlibrarymember{intervals}{piecewise_linear_distribution}%
@@ -7203,10 +7167,10 @@
 \end{itemdecl}
 
 \begin{itemdescr}
+
 \pnum
-\requires
-\tcode{p} points to an array\iref{dcl.array} of at least
-\tcode{n} elements.
+\expects
+\range{p}{p + n} is a valid range.
 
 \effects
 Constructs a \tcode{valarray} that has length \tcode{n}.
@@ -7375,7 +7339,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires The length of the array to which the argument refers equals \tcode{size()}.
+\expects
+The length of the array to which the argument refers equals \tcode{size()}.
 The value of an element in the left-hand side of a \tcode{valarray} assignment
 operator does not depend on the value of another element in that left-hand side.
 
@@ -7395,8 +7360,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-\tcode{n < size()}.
+\expects
+\tcode{n < size()} is \tcode{true}.
 
 \pnum
 \returns
@@ -7631,10 +7596,9 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-Each of these operators may only be instantiated for a type \tcode{T}
-to which the indicated operator can be applied and for which the indicated
-operator returns a value which is of type \tcode{T} (\tcode{bool} for
+\mandates
+The indicated operator can be applied to operands of type \tcode{T}
+and returns a value of type \tcode{T} (\tcode{bool} for
 \tcode{operator!}) or which may be unambiguously implicitly converted to type
 \tcode{T} (\tcode{bool} for \tcode{operator!}).
 
@@ -7672,10 +7636,13 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-\tcode{size() == v.size()}.
-Each of these operators may only be instantiated for a type \tcode{T}
-if the indicated operator can be applied to two operands of type \tcode{T}.
+\mandates
+The indicated operator can be applied to two operands of type \tcode{T}.
+
+\pnum
+\expects
+\tcode{size() == v.size()} is \tcode{true}.
+
 The value of an element in the left-hand side of a valarray compound
 assignment operator does not depend on the value of another element in that left
 hand side.
@@ -7721,9 +7688,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-Each of these operators may only be instantiated for a type \tcode{T}
-if the indicated operator can be applied to two operands of type \tcode{T}.
+\mandates
+The indicated operator can be applied to two operands of type \tcode{T}.
 
 \pnum
 \effects
@@ -7781,11 +7747,12 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-\tcode{size() > 0}.
-This function may only be instantiated for a type \tcode{T} to which
-\tcode{operator+=}
-can be applied.
+\mandates
+\tcode{operator+=} can be applied to operands of type \tcode{T}.
+
+\pnum
+\expects
+\tcode{size() > 0} is \tcode{true}.
 
 \pnum
 \returns
@@ -7804,8 +7771,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-\tcode{size() > 0}
+\expects
+\tcode{size() > 0} is \tcode{true}.
 
 \pnum
 \returns
@@ -7823,8 +7790,8 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-\tcode{size() > 0}.
+\expects
+\tcode{size() > 0} is \tcode{true}.
 
 \pnum
 \returns
@@ -7935,11 +7902,13 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-Each of these operators may only be instantiated for a type \tcode{T}
-to which the indicated operator can be applied and for which the indicated
-operator returns a value which is of type \tcode{T} or which
-can be unambiguously implicitly converted to type \tcode{T}.
+\mandates
+The indicated operator can be applied to operands of type \tcode{T} and returns
+a value of type \tcode{T} or which can be unambiguously
+implicitly converted to \tcode{T}.
+
+\pnum
+\expects
 The argument arrays have the same length.
 
 \pnum
@@ -8006,11 +7975,10 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-Each of these operators may only be instantiated for a type \tcode{T}
-to which the indicated operator can be applied and for which
-the indicated operator returns a value which is of type \tcode{T}
-or which can be unambiguously implicitly converted to type \tcode{T}.
+\mandates
+The indicated operator can be applied to operands of type \tcode{T} and returns
+a value of type \tcode{T} or which can be unambiguously
+implicitly converted to \tcode{T}.
 
 \pnum
 \returns
@@ -8044,11 +8012,13 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-Each of these operators may only be instantiated for a type \tcode{T}
-to which the indicated operator can be applied and for which
-the indicated operator returns a value which is of type \tcode{bool}
-or which can be unambiguously implicitly converted to type \tcode{bool}.
+\mandates
+The indicated operator can be applied to operands of type \tcode{T} and returns
+a value of type \tcode{bool} or which can be unambiguously
+implicitly converted to \tcode{bool}.
+
+\pnum
+\expects
 The two array arguments have the same length.
 \indextext{undefined}
 
@@ -8106,11 +8076,10 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-Each of these operators may only be instantiated for a type \tcode{T}
-to which the indicated operator can be applied and for which
-the indicated operator returns a value which is of type \tcode{bool}
-or which can be unambiguously implicitly converted to type \tcode{bool}.
+\mandates
+The indicated operator can be applied to operands of type \tcode{T} and returns
+a value of type \tcode{bool} or which can be unambiguously
+implicitly converted to \tcode{bool}.
 
 \pnum
 \returns
@@ -8164,11 +8133,12 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-Each of these functions may only be instantiated for a type \tcode{T}
-to which a unique function with the indicated name can be applied (unqualified).
-This function shall return a value which is of type \tcode{T}
+\mandates
+A unique function with the indicated name can be applied (unqualified)
+to an operand of type \tcode{T}.
+This function returns a value of type \tcode{T}
 or which can be unambiguously implicitly converted to type \tcode{T}.
+
 \end{itemdescr}
 
 \rSec3[valarray.special]{Specialized algorithms}