Sanitize sizes to avoid integer overflow. More...

Classes
struct	Bounded
	Bound the maximum possible value of an integer. More...

class	Cast
	Cast an integer in a function call. More...

struct	Constant
	Integer constant. More...

class	Exact
	Do not cast an integer in a function call. More...

struct	is_Bounded

struct	is_Bounded< Bounded< Integer_, max_ > >

struct	is_Constant

struct	is_Constant< Constant< Integer_, value_ > >

Functions
template<typename Max_ , Max_ new_max_, typename Value_ >
constexpr auto	set_bound (Value_ x)

template<typename MaxType_ , typename Value_ >
constexpr auto	set_bound_by_type (Value_ x)

template<typename Max_ , Max_ new_max_, typename Value_ >
constexpr auto	set_bound_unsafe (Value_ x)

template<typename MaxType_ , typename Value_ >
constexpr auto	set_bound_by_type_unsafe (Value_ x)

template<typename Dest_ , typename Value_ >
constexpr Dest_	cap (Value_ x)

template<typename Dest_ , typename Value_ >
constexpr bool	can_cast (Value_ x)

template<typename Dest_ , typename Value_ >
constexpr Dest_	cast (Value_ x)

template<typename Left_ , typename Right_ >
constexpr bool	is_equal (Left_ left, Right_ right)

template<typename Left_ , typename Right_ >
constexpr bool	is_less_than (Left_ left, Right_ right)

template<typename Left_ , typename Right_ >
constexpr bool	is_less_than_or_equal (Left_ left, Right_ right)

template<typename Left_ , typename Right_ >
constexpr bool	is_greater_than (Left_ left, Right_ right)

template<typename Left_ , typename Right_ >
constexpr bool	is_greater_than_or_equal (Left_ left, Right_ right)

template<typename First_ , typename Second_ >
constexpr auto	min (First_ first, Second_ second)

template<typename First_ , typename Second_ >
constexpr auto	max (First_ first, Second_ second)

template<typename Container_ , typename Value_ >
constexpr auto	as_size_type (Value_ x)

template<class Container_ , typename Value_ , typename ... Args_>
Container_	create (Value_ x, Args_ &&... args)

template<class Container_ , typename Value_ , typename ... Args_>
void	resize (Container_ &container, Value_ x, Args_ &&... args)

template<class Container_ , typename Value_ , typename ... Args_>
void	reserve (Container_ &container, Value_ x, Args_ &&... args)

template<typename Float_ >
int	required_bits_for_float (Float_ x)

template<typename Integer_ , typename Float_ >
Integer_	from_float (Float_ x)

template<typename Float_ , typename Value_ >
Float_	to_float (Value_ x)

template<typename Value_ >
constexpr auto	get_value (const Value_ x)

template<typename Value_ >
constexpr auto	get_max ()

template<typename Size_ , typename FirstIndex_ , typename FirstExtent_ , typename SecondIndex_ , typename... Remaining_>
constexpr Size_	nd_offset (FirstIndex_ x1, FirstExtent_ extent1, SecondIndex_ x2, Remaining_... remaining)

template<typename Dest_ , typename First_ , typename ... Args_>
constexpr std::optional< Dest_ >	product_maybe (First_ first, Args_... more)

template<typename Dest_ , typename First_ , typename ... Args_>
constexpr Dest_	product (First_ first, Args_... more)

template<typename Dest_ , typename First_ , typename ... Args_>
constexpr Dest_	product_unsafe (First_ first, Args_... more)

template<typename Dest_ , typename First_ , typename ... Args_>
constexpr std::optional< Dest_ >	sum_maybe (First_ first, Args_... more)

template<typename Dest_ , typename First_ , typename ... Args_>
constexpr Dest_	sum (First_ first, Args_... more)

template<typename Dest_ , typename Value_ >
Dest_	plus_one (Value_ x)

template<typename Integer_ >
Integer_ &	increment (Integer_ &x)

template<typename Dest_ , typename First_ , typename ... Args_>
constexpr Dest_	sum_unsafe (First_ first, Args_... more)

Detailed Description

Sanitize sizes to avoid integer overflow.

Function Documentation

◆ as_size_type()

template<typename Container_ , typename Value_ >

auto sanisizer::as_size_type ( Value_ x )

constexpr

Cast an integer to the size type of a container. This protects against overflow/wraparound when using this integer in the container's constructor or resize()/reserve() methods.

Template Parameters

Container_	Container class with a `size()` method and a constructor that accepts the size as the first argument.
Value_	Integer type of the input size.

Parameters

x	Non-negative value representing the desired container size.

Returns: x as the container's size's type.

◆ can_cast()

template<typename Dest_ , typename Value_ >

bool sanisizer::can_cast ( Value_ x )

constexpr

Template Parameters

Dest_	Integer type of the destination.
Value_	Integer type, `Bounded` or `Constant`.

Parameters

x	Representation of an integer value.

Returns: Whether x's value would overflow/wraparound when stored in Dest_.

◆ cap()

template<typename Dest_ , typename Value_ >

Dest_ sanisizer::cap ( Value_ x )

constexpr

Cap a non-negative integer at the largest value of a destination type. This is primarily intended for setting appropriate default values of function arguments and class variables.

Template Parameters

Dest_	Integer type of the destination.
Value_	Integer, `Bounded` or `Constant`.

Parameters

x	Non-negative value to be capped.

Returns: x if it can be represented in Dest_, otherwise the maximum value of Dest_.

◆ cast()

template<typename Dest_ , typename Value_ >

Dest_ sanisizer::cast ( Value_ x )

constexpr

Cast a non-negative integer to a destination type, typically the size type of a C-style array or STL container. This avoids accidental overflow/wraparound from an implicit cast when x is used in new or the container's constructor.

Template Parameters

Dest_	Integer type of the destination.
Value_	Integer type, `Bounded` or `Constant`.

Parameters

x	Non-negative value to be casted.

Returns: x as a Dest_. An error is thrown if overflow/wraparound would occur.

◆ create()

template<class Container_ , typename Value_ , typename ... Args_>

Container_ sanisizer::create	(	Value_	x,
		Args_ &&...	args )

Create a new container of a specified size. This protects against overflow/wraparound when casting the integer size to the container's size type, see as_size_type() for details.

Template Parameters

Container_	Container class with a `size()` method and a constructor that accepts the size as the first argument.
Value_	Integer type of the input size.
Args_	Further arguments to pass to the container's constructor.

Parameters

x	Non-negative value representing the desired container size.
args	Additional arguments to pass to the `Container_` constructor after the size.

Returns: An instance of the container, constructed to be of size x.

◆ from_float()

template<typename Integer_ , typename Float_ >

Integer_ sanisizer::from_float ( Float_ x )

Cast a non-negative floating-point number to an integer. This checks that the conversion is possible, otherwise it throws an exception. Such a cast is occasionally necessary when floating-point calculations are used to derive the size of a container, number of loop iterations, etc.

Template Parameters

Integer_	Integer type.
Float_	Floating-point type.

Parameters

x	Floating-point number, usually holding some kind of size.

Returns: The value of x as an integer, after truncation.

Exceptions

std::domain_error	Thrown if `x` is negative or non-finite.
std::overflow_error	Thrown if `x` is too large to be stored in `Integer_`.

◆ get_max()

template<typename Value_ >

auto sanisizer::get_max ( )

constexpr

Template Parameters

Value_ Integer type, Bounded, or Constant.

Returns: The maximum value of all instances of Value_.

◆ get_value()

template<typename Value_ >

auto sanisizer::get_value ( const Value_ x )

constexpr

Template Parameters

Value_ Integer type, Bounded or Constant.

Parameters

x	Integer value or an `Bounded` about an integer.

Returns: x if it is already an integer, otherwise Bounded::value.

◆ increment()

template<typename Integer_ >

Integer_ & sanisizer::increment ( Integer_ & x )

Convenience wrapper for x = plus_one<Dest_>(x), i.e., ++x with an exception if overflow/wraparound is detected.

Template Parameters

Dest_	Integer type of the destination.
Value_	Integer type of the value.

Parameters

x	Non-negative value. On output, this is incremented by 1.

Returns: Reference to x after increment.

◆ is_equal()

template<typename Left_ , typename Right_ >

bool sanisizer::is_equal	(	Left_	left,
		Right_	right )

constexpr

Template Parameters

Left_	Integer type of the value on the left hand side of the comparison. This may also be a `Constant` or `Bounded`.
Right_	Integer type of the value on the right hand side of the comparison. This may also be a `Constant` or `Bounded`.

Parameters

left	Non-negative value on the left hand side of the comparison.
right	Non-negative value on the right hand side of the comparison.

Returns: Whether left is equal to right.

◆ is_greater_than()

template<typename Left_ , typename Right_ >

bool sanisizer::is_greater_than	(	Left_	left,
		Right_	right )

constexpr

Template Parameters

Left_	Integer type of the value on the left hand side of the comparison. This may also be a `Constant` or `Bounded`.
Right_	Integer type of the value on the right hand side of the comparison. This may also be a `Constant` or `Bounded`.

Parameters

left	Non-negative value on the left hand side of the comparison.
right	Non-negative value on the right hand side of the comparison.

Returns: Whether left is greater than right.

◆ is_greater_than_or_equal()

template<typename Left_ , typename Right_ >

bool sanisizer::is_greater_than_or_equal	(	Left_	left,
		Right_	right )

constexpr

Template Parameters

Left_	Integer type of the value on the left hand side of the comparison. This may also be a `Constant` or `Bounded`.
Right_	Integer type of the value on the right hand side of the comparison. This may also be a `Constant` or `Bounded`.

Parameters

left	Non-negative value on the left hand side of the comparison.
right	Non-negative value on the right hand side of the comparison.

Returns: Whether left is greater than or equal to right.

◆ is_less_than()

template<typename Left_ , typename Right_ >

bool sanisizer::is_less_than	(	Left_	left,
		Right_	right )

constexpr

Template Parameters

Left_	Integer type of the value on the left hand side of the comparison. This may also be a `Constant` or `Bounded`.
Right_	Integer type of the value on the right hand side of the comparison. This may also be a `Constant` or `Bounded`.

Parameters

left	Non-negative value on the left hand side of the comparison.
right	Non-negative value on the right hand side of the comparison.

Returns: Whether left is less than right.

◆ is_less_than_or_equal()

template<typename Left_ , typename Right_ >

bool sanisizer::is_less_than_or_equal	(	Left_	left,
		Right_	right )

constexpr

Template Parameters

Left_	Integer type of the value on the left hand side of the comparison. This may also be a `Constant` or `Bounded`.
Right_	Integer type of the value on the right hand side of the comparison. This may also be a `Constant` or `Bounded`.

Parameters

left	Non-negative value on the left hand side of the comparison.
right	Non-negative value on the right hand side of the comparison.

Returns: Whether left is less than or equal to right.

◆ max()

template<typename First_ , typename Second_ >

auto sanisizer::max	(	First_	first,
		Second_	second )

constexpr

Template Parameters

First_	Integer type of the first value. This may also be a `Bounded` or `Constant`.
Second_	Integer type of the second value. This may also be a `Bounded` or `Constant`.

Parameters

first	First non-negative value.
second	Second non-negative value.

Returns: The larger of first and second, in the larger integer type of First_ and Second_.

◆ min()

template<typename First_ , typename Second_ >

auto sanisizer::min	(	First_	first,
		Second_	second )

constexpr

Template Parameters

First_	Integer type of the first value. This may also be a `Bounded` or `Constant`.
Second_	Integer type of the second value. This may also be a `Bounded` or `Constant`.

Parameters

first	First non-negative value.
second	Second non-negative value.

Returns: The smaller of first and second, in the smaller integer type of First_ and Second_.

◆ nd_offset()

template<typename Size_ , typename FirstIndex_ , typename FirstExtent_ , typename SecondIndex_ , typename... Remaining_>

Size_ sanisizer::nd_offset	(	FirstIndex_	x1,
		FirstExtent_	extent1,
		SecondIndex_	x2,
		Remaining_...	remaining )

constexpr

Compute offsets for accessing elements in a flattened N-dimensional array (for N > 1). The first dimension is assumed to be the fastest-changing, followed by the second dimension, and so on.

Template Parameters

Size_	Integer type to represent the size of the flattened array.
FirstIndex_	Type of the index on the first dimension. This may be an integer type, `Bounded` or `Constant`. It is assumed that this can be safely cast to `Size_`, as overflow/wraparound checks should have been performed during array allocation, e.g., via `product()`.
FirstExtent_	Type of the extent of the first dimension. This may be an integer type, `Bounded` or `Constant`. It is assumed that this can be safely cast to `Size_`, as overflow/wraparound checks should have been performed during array allocation, e.g., via `product()`.
SecondIndex_	Type of the index on the second dimension. This may be an integer type, `Bounded` or `Constant`. It is assumed that this can be safely cast to `Size_`, as overflow/wraparound checks should have been performed during array allocation, e.g., via `product()`.
Remaining_	Additional arguments for further dimensions. Each argument should should be either an integer type, `Bounded` or `Constant`. It is assumed that all types can be safely cast to `Size_`, as overflow/wraparound checks should have been performed during array allocation, e.g., `product()`.

Parameters

x1	Position on the first dimension.
extent1	Extent of the first dimension.
x2	Position on the second dimension.
remaining	Additional arguments for further dimensions. These should be `(extentP, xQ)` pairs where `extentP` is the extent of the `P`-th dimension and `xQ` is the position on the `Q = P + 1`-th dimension. For example, for a 3-dimensional array, we would expect an `extent2` and `x3` argument.

Returns: Offset into the array for element (x1, x2, ...).

◆ plus_one()

template<typename Dest_ , typename Value_ >

Dest_ sanisizer::plus_one ( Value_ x )

Convenience wrapper for sum<Dest_>(x, 1), i.e., get_value(x) + 1 with an exception if overflow/wraparound is detected.

Template Parameters

Dest_	Integer type of the destination.
Value_	Integer type of the value. This may also be a `Bounded` or `Constant`.

Parameters

x	Non-negative value.

Returns: The value of x plus 1.

◆ product()

template<typename Dest_ , typename First_ , typename ... Args_>

Dest_ sanisizer::product	(	First_	first,
		Args_...	more )

constexpr

Multiply two or more non-negative values, e.g., to compute the size of a flattened N-dimensional array as the product of its dimension extents. If overflow/wraparound in the destination type is detected, an exception is thrown. (See also product_maybe() to return an empty object upon overflow/wraparound.)

For consistency, this function will also check that each input value can be cast to Dest_. This ensures that per-dimension indices/extents can be safely represented as Dest_ in later steps (e.g., nd_offset()). These checks are necessary as the product may fit in Dest_ but not the input values if any one of the inputs is zero.

Template Parameters

Dest_	Integer type of the destination.
First_	Integer type of the first value. This may be also be a `Bounded` or `Constant`.
Args_	Integer types of additional values. Any number of these may also be `Bounded` or `Constant`.

Parameters

first	Non-negative value to multiply.
more	Additional non-negative values to multiply.

Returns: Product of all arguments as a Dest_.

Exceptions

std::overflow_error Thrown if an overflow/wraparound would occur.

◆ product_maybe()

template<typename Dest_ , typename First_ , typename ... Args_>

std::optional< Dest_ > sanisizer::product_maybe	(	First_	first,
		Args_...	more )

constexpr

Multiply two or more non-negative values. If overflow/wraparound in the destination type is detected, an empty object is returned. See also product() to throw an exception upon overflow/wraparound.

For consistency, this function will also check that each input value can be cast to Dest_. See product() for more details.

Template Parameters

Dest_	Integer type of the destination.
First_	Integer type of the first value. This may be also be a `Bounded` or `Constant`.
Args_	Integer types of additional values. Any number of these may also be `Bounded` or `Constant`.

Parameters

first	Non-negative value to multiply.
more	Additional non-negative values to multiply.

Returns: Product of all arguments as a Dest_.

Exceptions

std::overflow_error Thrown if an overflow/wraparound would occur.

◆ product_unsafe()

template<typename Dest_ , typename First_ , typename ... Args_>

Dest_ sanisizer::product_unsafe	(	First_	first,
		Args_...	more )

constexpr

Unsafe alternative to product() that casts its arguments to Dest_ but does not check for overflow/wraparound. This is more efficent than product() if it is already known that the product will not overflow, e.g., when computing std::size_t offsets into a pre-allocated array.

Template Parameters

Dest_	Integer type of the destination.
First_	Type of the first multiplication term. This should be an integer type, `Bounded` or `Constant`.
Args_	Types of additional terms. Each of these should be either an integer type, `Bounded` or `Constant`.

Parameters

first	Non-negative term to multiply.
more	Additional non-negative terms to multiply.

Returns: Product of all arguments as a Dest_.

◆ required_bits_for_float()

template<typename Float_ >

int sanisizer::required_bits_for_float ( Float_ x )

Template Parameters

Float_ Floating-point type.

Parameters

x	A finite non-negative integer. Specifically, a floating-point number for which the following is true: `std::isfinite(x)`, `x >= 0` and `x == std::trunc(x)`.

Returns: Number of bits required to store x exactly in a (two's complement) integer type.

The return value can be compared to std::numeric_limits<Integer_>::digits to determine if Integer_ is large enough to store x.

◆ reserve()

template<class Container_ , typename Value_ , typename ... Args_>

void sanisizer::reserve	(	Container_ &	container,
		Value_	x,
		Args_ &&...	args )

Reserve a container to the desired size. This protects against overflow/wraparound when casting the integer size to the container's size type, see as_size_type() for details.

In most cases involving std::vector, this protection is not necessary as the size type is unsigned and x would harmlessly wrap around to some smaller non-negative value. The reserved size would be smaller than x but would silently reallocate as necessary upon push_back() or insert() operations beyond that size. However, this function becomes useful when the user wants to ensure that no reallocations occur, either for performance reasons or to maintain iterator/pointer validity.

Template Parameters

Container_	Container class with a `size()` method and a `reserve()` method that accepts the size as the first argument.
Value_	Integer type of the input size.
Args_	Further arguments to pass to the container's `reserve()` method.

Parameters

container	An existing instance of the container. On return, its allocation is set to `x`.
x	Non-negative value representing the desired container size.
args	Additional arguments to pass to `reserve()` after the size.

◆ resize()

template<class Container_ , typename Value_ , typename ... Args_>

void sanisizer::resize	(	Container_ &	container,
		Value_	x,
		Args_ &&...	args )

Resize a container to the desired size. This protects against overflow/wraparound when casting the integer size to the container's size type, see as_size_type() for details.

Template Parameters

Container_	Container class with a `size()` method and a `resize()` method that accepts the size as the first argument.
Value_	Integer type of the input size.
Args_	Further arguments to pass to the container's `resize()` method.

Parameters

container	An existing instance of the container. This is resized to size `x`.
x	Non-negative value representing the desired container size.
args	Additional arguments to pass to `resize()` after the size.

◆ set_bound()

template<typename Max_ , Max_ new_max_, typename Value_ >

auto sanisizer::set_bound ( Value_ x )

constexpr

Template Parameters

Max_	Integer type of the new compile-time maximum.
new_max_	The new compile-time maximum.
Value_	Integer type, `Bounded` or `Constant`.

Parameters

x	Representation of an integer value.

Returns: x if its maximum value is less than or equal to new_max_. Otherwise, an Bounded that declares this constraint.

Exceptions

std::domain_error Thrown if the value of x is greater than new_max_.

If x is known to be less than or equal to max_, users can call set_bound_unsafe() to avoid the check.

◆ set_bound_by_type()

template<typename MaxType_ , typename Value_ >

auto sanisizer::set_bound_by_type ( Value_ x )

constexpr

Variant of set_bound() that uses the maximum value of an integer type.

Template Parameters

MaxType_	Integer type of the new compile-time maximum.
Value_	Integer type, `Bounded` or `Constant`.

Parameters

x	Representation of an integer value.

Returns: x if its maximum value is less than or equal to that of MaxType_. Otherwise, an Bounded that declares this constraint.

If x is known to be less than or equal to max_, users can call set_bound_by_type_unsafe() to avoid the check.

◆ set_bound_by_type_unsafe()

template<typename MaxType_ , typename Value_ >

auto sanisizer::set_bound_by_type_unsafe ( Value_ x )

constexpr

Variant of set_bound_unsafe() that uses the maximum value of an integer type.

Template Parameters

MaxType_	Integer type of the new compile-time maximum.
Value_	Integer type, `Bounded` or `Constant`.

Parameters

x	Representation of an integer value. This should be less than or equal to the maximum value of `MaxType_`.

Returns: x if its maximum value is less than or equal to that of MaxType_. Otherwise, an Bounded that declares this constraint.

◆ set_bound_unsafe()

template<typename Max_ , Max_ new_max_, typename Value_ >

auto sanisizer::set_bound_unsafe ( Value_ x )

constexpr

Variant of set_bound() that assumes x <= new_max_ and does not throw exceptions.

Template Parameters

Max_	Integer type of the new compile-time maximum.
new_max_	The new compile-time maximum.
Value_	Integer type, `Bounded` or `Constant`.

Parameters

x	Representation of an integer value. This should be no greater than `new_max_`.

Returns: x if its maximum value is less than or equal to new_max_. Otherwise, an Bounded that declares this constraint.

◆ sum()

template<typename Dest_ , typename First_ , typename ... Args_>

Dest_ sanisizer::sum	(	First_	first,
		Args_...	more )

constexpr

Add two or more non-negative values, e.g., to compute the size of an array that is a concatenation of smaller arrays. If overflow/wraparound in the destination type is detected, an exception is thrown. (See also sum_maybe() to return an empty object upon overflow/wraparound.)

Template Parameters

Dest_	Integer type of the destination.
First_	Integer type of the first value. This may also be a `Bounded` or `Constant`.
Args_	Integer types of additional values. Any number of these may also be `Bounded` or `Constant`.

Parameters

first	First non-negative value to add.
more	Additional non-negative values to add.

Returns: Sum of all arguments as a Dest_.

Exceptions

std::overflow_error Thrown if an overflow/wraparound occurs at any summation step.

◆ sum_maybe()

template<typename Dest_ , typename First_ , typename ... Args_>

std::optional< Dest_ > sanisizer::sum_maybe	(	First_	first,
		Args_...	more )

constexpr

Add two or more non-negative values. If overflow/wraparound in the destination type is detected, an empty object is returned. (See also sum() to throw an exception upon overflow/wraparound.)

Template Parameters

Dest_	Integer type of the destination.
First_	Integer type of the first value. This may also be a `Bounded` or `Constant`.
Args_	Integer types of additional values. Any number of these may also be `Bounded` or `Constant`.

Parameters

first	First non-negative value to add.
more	Additional non-negative values to add.

Returns: Sum of all arguments as a Dest_, wrapped in a std::optional. An empty object is returned if overflow/wraparound is detected in the destination type at any step of the summation.

◆ sum_unsafe()

template<typename Dest_ , typename First_ , typename ... Args_>

Dest_ sanisizer::sum_unsafe	(	First_	first,
		Args_...	more )

constexpr

Unsafe alternative to sum() that casts its arguments to Dest_ before summation but does not check for overflow/wraparound. This is more efficent than sum() if it is already known that the sum will not overflow, e.g., when computing std::size_t offsets into a pre-allocated array.

Template Parameters

Dest_	Integer type of the destination.
First_	Type of the first summation term. This should be an integer type, `Bounded` or `Constant`.
Args_	Types of additional terms. Each of these should be either an integer type, `Bounded` or `Constant`.

Parameters

first	Non-negative term to sum.
more	Additional non-negative terms to add.

Returns: Sum of all arguments as a Dest_.

◆ to_float()

template<typename Float_ , typename Value_ >

Float_ sanisizer::to_float ( Value_ x )

Cast a non-negative integer into a (IEE-754 compliant) floating-point number. This checks that (i) there is no loss of precision and (ii) all integers smaller than the input can also be represented by the specified floating-point type.

This is motivated by the fact that some environments do not have a dedicated integer type (e.g., Javascript). In such cases, array lengths need to be stored as floating-point values. Our checks ensure that both the array length and all valid array indices can be exactly represented in the floating-point type.

Note that the purpose of this function is to preserve precision rather than to avoid undefined behavior. For IEEE-754 floats, very large integers already have a well-defined cast to positive infinity.

Template Parameters

Float_	Floating-point type. This should be one of the IEEE-754 binary formats.
Value_	Integer type, `Bounded` or `Constant`.

Parameters

x	Non-negative integer, usually holding some kind of size.

Returns: The value of x as a floating-point number.

Exceptions

std::overflow_error Thrown if Float_ cannot exactly represent all non-negative integers less than or equal to x.

Classes

Functions

Detailed Description

Function Documentation

◆ as_size_type()

◆ can_cast()

◆ cap()

◆ cast()

◆ create()

◆ from_float()

◆ get_max()

◆ get_value()

◆ increment()

◆ is_equal()

◆ is_greater_than()

◆ is_greater_than_or_equal()

◆ is_less_than()

◆ is_less_than_or_equal()

◆ max()

◆ min()

◆ nd_offset()

◆ plus_one()

◆ product()

◆ product_maybe()

◆ product_unsafe()

◆ required_bits_for_float()

◆ reserve()

◆ resize()

◆ set_bound()

◆ set_bound_by_type()

◆ set_bound_by_type_unsafe()

◆ set_bound_unsafe()

◆ sum()

◆ sum_maybe()

◆ sum_unsafe()

◆ to_float()