General math utility functions. More...

#include <cmath>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <limits>
#include <vector>
#include <algorithm>
#include <cassert>

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Functions
template<typename T >
constexpr bool	is_even (T num)

template<typename T >
constexpr bool	is_odd (T num)

constexpr int	div100rounded (int num)
	Guarantees portable results for division by 100; round half up, to the nearest integer. More...

constexpr int	bounded_add (int base, int increment, int max_sum, int min_sum=0)
	Returns base + increment, but will not increase base above max_sum, nor decrease it below min_sum. More...

template<typename T >
constexpr T	modulo (T num, int mod, T min=0)

constexpr int	round_damage (int base_damage, int bonus, int divisor)
	round (base_damage * bonus / divisor) to the closest integer, but up or down towards base_damage More...

template<typename Cmp >
bool	in_ranges (const Cmp c, const std::vector< std::pair< Cmp, Cmp >> &ranges)

template<typename T >
constexpr std::size_t	bit_width ()
	Returns the size, in bits, of an instance of type `T`, providing a convenient and self-documenting name for the underlying expression: More...

template<typename T >
constexpr std::size_t	bit_width (const T &)
	Returns the size, in bits, of `x`, providing a convenient and self-documenting name for the underlying expression: More...

template<typename N >
constexpr std::enable_if_t< std::is_integral_v< N >, unsigned int >	count_leading_zeros (N n)
	Returns the quantity of leading `0` bits in `n` — i.e., the quantity of bits in `n`, minus the 1-based bit index of the most significant `1` bit in `n`, or minus 0 if `n` is 0. More...

template<typename N >
constexpr unsigned int	count_leading_ones (N n)
	Returns the quantity of leading `1` bits in `n` — i.e., the quantity of bits in `n`, minus the 1-based bit index of the most significant `0` bit in `n`, or minus 0 if `n` contains no `0` bits. More...

int	rounded_division (int a, int b)

constexpr unsigned	fixed_point_multiply (int32_t n1, int32_t n2)

constexpr int32_t	fixed_point_divide (int n1, int n2)

constexpr int	fixed_point_to_int (int32_t n)
	If positive, just bit shift. More...

Detailed Description

General math utility functions.

Definition in file math.hpp.

Function Documentation

◆ bit_width() [1/2]

template<typename T >

constexpr std::size_t bit_width ( )

constexpr

Returns the size, in bits, of an instance of type T, providing a convenient and self-documenting name for the underlying expression:

sizeof(T) * std::numeric_limits<unsigned char>::digits

Template Parameters

T	The return value is the size, in bits, of an instance of this type.

Returns: the size, in bits, of an instance of type T.

Definition at line 106 of file math.hpp.

◆ bit_width() [2/2]

template<typename T >

constexpr std::size_t bit_width ( const T & )

constexpr

Returns the size, in bits, of x, providing a convenient and self-documenting name for the underlying expression:

sizeof(x) * std::numeric_limits<unsigned char>::digits

Template Parameters

T	The return value is the size, in bits, of the type of this object.

Returns: the size, in bits, of an instance of type T.

Definition at line 121 of file math.hpp.

◆ bounded_add()

constexpr int bounded_add	(	int	base,
		int	increment,
		int	max_sum,
		int	min_sum = `0`
	)

constexpr

Returns base + increment, but will not increase base above max_sum, nor decrease it below min_sum.

(If base is already below the applicable limit, base will be returned.)

Definition at line 48 of file math.hpp.

Referenced by tod_manager::get_illuminated_time_of_day(), and terrain_type::light_bonus().

◆ count_leading_ones()

template<typename N >

constexpr unsigned int count_leading_ones ( N n )

constexpr

Returns the quantity of leading 1 bits in n — i.e., the quantity of bits in n, minus the 1-based bit index of the most significant 0 bit in n, or minus 0 if n contains no 0 bits.

Template Parameters

N	The type of `n`. This should be a fundamental integer type that (a) is not wider than `unsigned long long int`, and (b) is no greater than `INT_MAX` bits in width; if `N` does not satisfy these constraints, the return value is undefined.

Parameters

n	An integer upon which to operate.

Returns: the quantity of leading 1 bits in n, if N satisfies the above constraints.

See also: count_leading_zeros()

Definition at line 179 of file math.hpp.

References n.

Referenced by ucs4_convert_impl::utf8_impl::byte_size_from_utf8_first(), and utf8::byte_size_from_utf8_first().

◆ count_leading_zeros()

template<typename N >

constexpr std::enable_if_t<std::is_integral_v<N>, unsigned int> count_leading_zeros ( N n )

constexpr

Returns the quantity of leading 0 bits in n — i.e., the quantity of bits in n, minus the 1-based bit index of the most significant 1 bit in n, or minus 0 if n is 0.

Template Parameters

N The type of n. This should be a fundamental integer type that (a) is not wider than unsigned long long int (the GCC count-leading-zeros built-in functions are defined for unsigned int, unsigned long int, and unsigned long long int), and (b) is no greater than INT_MAX bits in width (the GCC built-in functions return instances of type int); if N does not satisfy these constraints, the return value is undefined.

Parameters

n	An integer upon which to operate.

Returns: the quantity of leading 0 bits in n, if N satisfies the above constraints.

See also: count_leading_ones()

Definition at line 146 of file math.hpp.

References i, and n.

◆ div100rounded()

constexpr int div100rounded ( int num )

constexpr

Guarantees portable results for division by 100; round half up, to the nearest integer.

Definition at line 39 of file math.hpp.

Referenced by utils::apply_modifier().

◆ fixed_point_divide()

constexpr int32_t fixed_point_divide	(	int	n1,
		int	n2
	)

constexpr

Parameters

n1	The numerator, which gets bit shifted left.
n2	The divisor.

Returns: n1 bit shifted left then divided by n1.

Definition at line 207 of file math.hpp.

Referenced by scale_surface(), and scale_surface_legacy().

◆ fixed_point_multiply()

constexpr unsigned fixed_point_multiply	(	int32_t	n1,
		int32_t	n2
	)

constexpr

Parameters

n1	The first number to multiply.
n2	The second number to multiply.

Returns: The unsigned result of n1 * n2, then bitshifting the result to the right.

Definition at line 197 of file math.hpp.

Referenced by brighten_image().

◆ fixed_point_to_int()

constexpr int fixed_point_to_int ( int32_t n )

constexpr

If positive, just bit shift.

Else, make positive, bit shift, then make negative again.

Parameters

n	The number to bit shift right.

Returns: The result of the bit shift.

Definition at line 219 of file math.hpp.

References n.

Referenced by scale_surface(), and scale_surface_legacy().

◆ in_ranges()

template<typename Cmp >

bool in_ranges	(	const Cmp	c,
		const std::vector< std::pair< Cmp, Cmp >> &	ranges
	)

Definition at line 87 of file math.hpp.

References c.

Referenced by check_side_number(), game_events::builtin_conditions::have_unit(), terrain_filter::match_internal(), and matches_simple_filter().

◆ is_even()

template<typename T >

constexpr bool is_even ( T num )

constexpr

Definition at line 33 of file math.hpp.

Referenced by actions::shroud_clearer::clear_loc(), default_map_generator_job::default_generate_map(), is_odd(), and is_vertically_higher_than().

◆ is_odd()

template<typename T >

constexpr bool is_odd ( T num )

constexpr

Definition at line 36 of file math.hpp.

References is_even().

Referenced by actions::shroud_clearer::clear_loc(), display::draw_minimap_units(), default_map_generator::generate_map(), display::get_location(), intf_terrain_mask(), version_info::is_dev_version(), is_vertically_higher_than(), image::prep_minimap_for_rendering(), rotate_180_surface(), editor::map_fragment::rotate_60_ccw(), and editor::map_fragment::rotate_60_cw().

◆ modulo()

template<typename T >

constexpr T modulo	(	T	num,
		int	mod,
		T	min = `0`
	)

constexpr

Returns: : the number n in [min, min+mod ) so that (n - num) is a multiple of mod.

Definition at line 62 of file math.hpp.

References n.

Referenced by tod_manager::calculate_time_index_at_turn(), playsingle_controller::find_viewing_side(), tod_manager::fix_time_index(), wesnothd::game::get_next_nonempty(), and playsingle_controller::skip_empty_sides().

◆ round_damage()

constexpr int round_damage	(	int	base_damage,
		int	bonus,
		int	divisor
	)

constexpr

round (base_damage * bonus / divisor) to the closest integer, but up or down towards base_damage

Definition at line 80 of file math.hpp.

Referenced by attack_info(), and battle_context_unit_stats::battle_context_unit_stats().

◆ rounded_division()

int rounded_division	(	int	a,
		int	b
	)

inline

Definition at line 186 of file math.hpp.

References b.

Referenced by gui2::slider_base::set_slider_position(), gui2::slider::set_value(), and gui2::slider_base::update_slider_position().

Functions

Detailed Description

Function Documentation

◆ bit_width() [1/2]

◆ bit_width() [2/2]

◆ bounded_add()

◆ count_leading_ones()

◆ count_leading_zeros()

◆ div100rounded()

◆ fixed_point_divide()

◆ fixed_point_multiply()

◆ fixed_point_to_int()

◆ in_ranges()

◆ is_even()

◆ is_odd()

◆ modulo()

◆ round_damage()

◆ rounded_division()