Number

abs

template<class num >

using metal::abs = typedef metal::max<num, metal::neg<num> >

#include <metal/number/abs.hpp>

Description

Computes absolute value of a Number.

Usage

For any Number num

using result = metal::abs<num>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<(num{} > 0) ? num{} : -num{}>;

Example

IS_SAME(metal::abs<metal::number<-10>>, metal::number<10>);
IS_SAME(metal::abs<metal::number<0>>, metal::number<0>);

See Also

See also

number, inc, dec, neg, add, sub, mul, div, mod, pow

add

template<class... nums>

using metal::add = typedef fold_left<lambda<detail::add>, nums..., number<0> >

#include <metal/number/add.hpp>

Description

Computes the arithmetic addition of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::add<num_0, ..., num_n-1>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} + ... + num_n-1{}>;

Example

using num = metal::add<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<-9>);

See Also

See also

number, abs, inc, dec, neg, sub, mul, div, mod, pow

and_

template<class... nums>

using metal::and_ = typedef metal::same<metal::false_, metal::not_<nums>...>

#include <metal/number/and.hpp>

Description

Computes the logical conjunction of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::and_<num_0, ..., num_n-1>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} && ... && num_n-1{}>;

Example

IS_SAME(metal::and_<>, metal::true_);
IS_SAME(metal::and_<metal::number<0>>, metal::false_);
IS_SAME(metal::and_<metal::number<42>>, metal::true_);
IS_SAME(metal::and_<metal::number<42>, metal::number<0>>, metal::false_);

See Also

See also

number, not_, or_

as_number

template<class val >

using metal::as_number = typedef typename detail::_as_number<val>::type

#include <metal/number/number.hpp>

Description

Constructs a Number out of any Value that defines a nested integral constant value convertible to metal::int_.

Usage

For any Value val

using result = metal::as_number<val>;

Returns

: Number

Example

struct one { static const auto value = 1L; };
enum two { value = 2U };
 
IS_SAME(metal::as_number<one>, metal::number<1>);
IS_SAME(metal::as_number<two>, metal::number<2>);
IS_SAME(metal::as_number<std::integral_constant<short, 42>>, metal::number<42>);

See Also

See also

number

dec

template<class num >

using metal::dec = typedef metal::sub<num, metal::number<1> >

#include <metal/number/dec.hpp>

Description

Decrements a Number.

Usage

For any Number num

using result = metal::dec<num>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num{} - 1>;

Example

IS_SAME(metal::dec<metal::number<-10>>, metal::number<-11>);
IS_SAME(metal::dec<metal::number<0>>, metal::number<-1>);

See Also

See also

number, abs, inc, neg, add, sub, mul, div, mod, pow

div

template<class... nums>

using metal::div = typedef fold_left<lambda<detail::div>, nums..., number<1> >

#include <metal/number/div.hpp>

Description

Computes the quotient of the arithmetic division of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::div<num_0, ..., num_n-1>;

Precondition

: All Numbers in num_1, ..., num_n-1 are nonzero

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} / ... / num_n-1{}>;

Example

using num = metal::div<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<-1>);
IS_SAME(
    metal::is_invocable<metal::lambda<metal::div>, num, metal::number<0>>,
    metal::false_
);

See Also

See also

number, abs, inc, dec, neg, add, sub, mul, mod, pow

false_

using metal::false_ = typedef metal::number<false>

#include <metal/number/number.hpp>

Description

A Number that represents the boolean constant false.

See Also

See also

number

greater

template<class x , class y >

using metal::greater = typedef metal::less<y, x>

#include <metal/number/greater.hpp>

Description

Checks whether a Number is greater than another.

Usage

For any Numbers x and y

using result = metal::greater<x, y>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<(x{} > y{})>;

Example

IS_SAME(metal::greater<metal::number<-10>, metal::number<10>>, metal::false_);
IS_SAME(metal::greater<metal::number<10>, metal::number<10>>, metal::false_);
IS_SAME(metal::greater<metal::number<10>, metal::number<-10>>, metal::true_);

See Also

See also

number, less, max, min

if_

template<class cond , class... then>

using metal::if_ = typedef detail::call<detail::_if_<cond>::template type, then...>

#include <metal/number/if.hpp>

Description

A conditional expression.

Usage

For any Number num and Values x, y

using result = metal::if<num, x, y>;

Returns

: Value

Semantics:

If num{} != false, then

using result = x;

otherwise

using result = y;

Tip

If num{} != false, y may be omitted.

Example

IS_SAME(metal::if_<metal::true_, int>, int);
IS_SAME(metal::if_<metal::true_, int, void>, int);
IS_SAME(metal::if_<metal::false_, int, void>, void);

See Also

See also

number

inc

template<class num >

using metal::inc = typedef metal::add<num, metal::number<1> >

#include <metal/number/inc.hpp>

Description

Increments a Number.

Usage

For any Number num

using result = metal::inc<num>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num::{} + 1>;

Example

IS_SAME(metal::inc<metal::number<-10>>, metal::number<-9>);
IS_SAME(metal::inc<metal::number<0>>, metal::number<1>);

See Also

See also

number, abs, dec, neg, add, sub, mul, div, mod, pow

int_

using metal::int_ = typedef detail::int_

#include <metal/number/number.hpp>

Description

The underlying integral representation of Numbers.

See Also

See also

number

is_number

template<class val >

using metal::is_number = typedef typename detail::_is_number<val>::type

#include <metal/number/number.hpp>

Description

Checks whether some Value is a Number.

Usage

For any Value val

using result = metal::is_number<val>;

Returns

: Number

Semantics:

If val is a Number, then

using result = metal::true_;

otherwise

using result = metal::false_;

Example

struct one { static const auto value = 1L; };
enum two { value = 2U };
 
IS_SAME(metal::is_number<void>, metal::false_);
IS_SAME(metal::is_number<one>, metal::false_);
IS_SAME(metal::is_number<two>, metal::false_);
IS_SAME(metal::is_number<std::integral_constant<short, 42>>, metal::false_);
IS_SAME(metal::is_number<metal::number<-10>>, metal::true_);
IS_SAME(metal::is_number<metal::false_>, metal::true_);

See Also

See also

number, is_value, is_lambda, is_pair, is_list, is_map

less

template<class x , class y >

using metal::less = typedef typename detail::_less<x, y>::type

#include <metal/number/less.hpp>

Description

Checks whether a Number is less than another.

Usage

For any Numbers x and y

using result = metal::less<x, y>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<(x{} < y{})>;

Example

IS_SAME(metal::less<metal::number<-10>, metal::number<10>>, metal::true_);
IS_SAME(metal::less<metal::number<10>, metal::number<10>>, metal::false_);
IS_SAME(metal::less<metal::number<10>, metal::number<-10>>, metal::false_);

See Also

See also

number, greater, max, min

max

template<class... nums>

using metal::max = typedef fold_left<lambda<detail::max>, if_<is_number<nums>, nums>...>

#include <metal/number/max.hpp>

Description

Computes the maximum of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::max<num_0, ..., num_n-1>;

Returns

: Number

Semantics:

If M the maximum between all Numbers in num_0, ..., num_n-1, then

using result = M;

Example

using num = metal::max<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<5>);

See Also

See also

number, greater, less, min

min

template<class... nums>

using metal::min = typedef fold_left<lambda<detail::min>, if_<is_number<nums>, nums>...>

#include <metal/number/min.hpp>

Description

Computes the minimum of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::min<num_0, ..., num_n-1>;

Returns

: Number

Semantics:

If m the minimum between all Numbers in num_0, ..., num_n-1, then

using result = m;

Example

using num = metal::min<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<-17>);

See Also

See also

number, greater, less, max

mod

template<class... nums>

using metal::mod = typedef fold_left<lambda<detail::mod>, if_<is_number<nums>, nums>...>

#include <metal/number/mod.hpp>

Description

Computes the remainder of the arithmetic division of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::mod<num_0, ..., num_n-1>;

Precondition

: All Numbers in num_1, ..., num_n-1 are nonzero

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} % ... % num_n-1{}>;

Example

using num = metal::mod<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<-2>);
IS_SAME(
    metal::is_invocable<metal::lambda<metal::mod>, num, metal::number<0>>,
    metal::false_
);

See Also

See also

number, abs, inc, dec, neg, add, sub, mul, div, pow

mul

template<class... nums>

using metal::mul = typedef fold_left<lambda<detail::mul>, nums..., number<1> >

#include <metal/number/mul.hpp>

Description

Computes the arithmetic multiplication of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::mul<num_0, ..., num_n-1>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} * ... * num_n-1{}>;

Example

using num = metal::mul<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<-255>);

See Also

See also

number, abs, inc, dec, neg, add, sub, div, mod, pow

neg

template<class num >

using metal::neg = typedef metal::sub<metal::number<0>, num>

#include <metal/number/neg.hpp>

Description

Computes the additive inverse of a Number.

Usage

For any Number num

using result = metal::neg<num>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<-num{}>;

Example

IS_SAME(metal::neg<metal::number<-10>>, metal::number<10>);
IS_SAME(metal::neg<metal::number<0>>, metal::number<0>);

See Also

See also

number, abs, inc, dec, add, sub, mul, div, mod, pow

not_

template<class num >

using metal::not_ = typedef metal::if_<num, metal::false_, metal::true_>

#include <metal/number/not.hpp>

Description

Computes the logical inverse of a Number.

Usage

For any Number num

using result = metal::not_<num>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<!num{}>;

Example

IS_SAME(metal::not_<metal::number<0>>, metal::true_);
IS_SAME(metal::not_<metal::number<-10>>, metal::false_);
IS_SAME(metal::not_<metal::number<'a'>>, metal::false_);
IS_SAME(metal::not_<metal::true_>, metal::false_);

See Also

See also

number, and_, or_

number

template<int_ v>

using metal::number = typedef std::integral_constant<metal::int_, v>

#include <metal/number/number.hpp>

Description

Constructs a Number out of an integral value.

Usage

For any integral constant N

using result = metal::number<N>;

Returns

: Number

See Also

See also

int_, true_, false_, is_number

numbers

template<int_... vs>

using metal::numbers = typedef metal::list<metal::number<vs>...>

#include <metal/number/numbers.hpp>

Description

Constructs a List of Numbers out of a sequence of integral values.

Example

IS_SAME(metal::numbers<>, metal::list<>);
 
IS_SAME(
    metal::numbers<'a', 'b'>,
    metal::list<metal::number<'a'>, metal::number<'b'>>
);
 
IS_SAME(
    metal::numbers<-7, 5, 1>,
    metal::list<metal::number<-7>, metal::number<5>, metal::number<1>>
);

See Also

See also

int_, number, list

or_

template<class... nums>

using metal::or_ = typedef metal::not_<metal::same<metal::true_, metal::not_<nums>...> >

#include <metal/number/or.hpp>

Description

Computes the logical disjunction of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::or_<num_0, ..., num_n-1>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} || ... || num_n-1{}>;

Example

IS_SAME(metal::or_<>, metal::false_);
IS_SAME(metal::or_<metal::number<0>>, metal::false_);
IS_SAME(metal::or_<metal::number<42>>, metal::true_);
IS_SAME(metal::or_<metal::number<42>, metal::number<0>>, metal::true_);

See Also

See also

number, not_, and_

pow

template<class... nums>

using metal::pow = typedef fold_left<lambda<detail::pow>, nums..., number<1> >

#include <metal/number/pow.hpp>

Description

Computes the arithmetic exponentiation of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::pow<num_0, ..., num_n-1>;

Precondition

: metal::pow<num_0, ..., num_m-1> != metal::number<0> for all negative num_m

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} ** ... ** num_n-1{}>;

Where x**y stands for x raised to the power of y

Warning

x**y is always null for y < 0 and |x| > 1 due to inherent limitations of integer arithmetic.

Example

using num = metal::pow<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<-2862423051509815793>);
IS_SAME(
    metal::is_invocable<metal::lambda<metal::pow>, metal::number<0>, num>,
    metal::false_
);

See Also

See also

number, abs, inc, dec, neg, add, sub, mul, div, mod

sub

template<class... nums>

using metal::sub = typedef fold_left<lambda<detail::sub>, nums..., number<0> >

#include <metal/number/sub.hpp>

Description

Computes the arithmetic subtraction of Numbers.

Usage

For any Numbers num_0, ..., num_n-1

using result = metal::sub<num_0, ..., num_n-1>;

Returns

: Number

Semantics:

Equivalent to

using result = metal::number<num_0{} - ... - num_n-1{}>;

Example

using num = metal::sub<metal::number<-17>, metal::number<5>, metal::number<3>>;
 
IS_SAME(num, metal::number<-25>);

See Also

See also

number, abs, inc, dec, neg, add, mul, div, mod, pow

true_

using metal::true_ = typedef metal::number<true>

#include <metal/number/number.hpp>

Description

A Number that represents the boolean constant true.

See Also

See also

number, int_