General math utility functions. More...

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

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Macros
#define	fxp_shift 8

#define	fxp_base (1 << fxp_shift)

#define	ftofxp(x) (fixed_t((x) * fxp_base))
	IN: float or int - OUT: fixed_t. More...

#define	fxpmult(x, y) (((x)*(y)) >> fxp_shift)
	IN: unsigned and fixed_t - OUT: unsigned. More...

#define	fxpdiv(x, y) (((x) << fxp_shift) / (y))
	IN: unsigned and int - OUT: fixed_t. More...

#define	fxptoi(x) ( ((x)>0) ? ((x) >> fxp_shift) : (-((-(x)) >> fxp_shift)) )
	IN: fixed_t - OUT: int. More...

Typedefs
typedef int32_t	fixed_t

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

template<typename T >
bool	is_odd (T num)

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

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...

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 >
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 >
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 >
unsigned int	count_ones (N n)
	Returns the quantity of `1` bits in `n` — i.e., `n`’s population count. More...

template<typename N >
unsigned int	count_leading_zeros_impl (N n, std::size_t w)

template<typename 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 >
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)

Detailed Description

General math utility functions.

Definition in file math.hpp.

Macro Definition Documentation

◆ ftofxp

#define ftofxp ( x ) (fixed_t((x) * fxp_base))

IN: float or int - OUT: fixed_t.

Definition at line 297 of file math.hpp.

Referenced by font::floating_label::create_surface(), unit_drawer::draw_bar(), gui::textbox::draw_contents(), image::get_brightened(), game_display::new_turn(), image::o_modification::operator()(), unit_frame::redraw(), unit_drawer::redraw_unit(), display::render_image(), scale_surface(), scale_surface_legacy(), image::simplify_type(), and submerge_alpha().

◆ fxp_base

#define fxp_base (1 << fxp_shift)

Definition at line 294 of file math.hpp.

◆ fxp_shift

#define fxp_shift 8

Definition at line 293 of file math.hpp.

◆ fxpdiv

#define fxpdiv	(	x,
		y
	)	(((x) << fxp_shift) / (y))

IN: unsigned and int - OUT: fixed_t.

Definition at line 303 of file math.hpp.

Referenced by unit_drawer::draw_bar(), game_display::new_turn(), scale_surface(), and scale_surface_legacy().

◆ fxpmult

#define fxpmult	(	x,
		y
	)	(((x)*(y)) >> fxp_shift)

IN: unsigned and fixed_t - OUT: unsigned.

Definition at line 300 of file math.hpp.

Referenced by brighten_image(), unit_drawer::draw_bar(), image::o_modification::operator()(), and submerge_alpha().

◆ fxptoi

#define fxptoi ( x ) ( ((x)>0) ? ((x) >> fxp_shift) : (-((-(x)) >> fxp_shift)) )

IN: fixed_t - OUT: int.

Definition at line 306 of file math.hpp.

Referenced by unit_drawer::draw_bar(), scale_surface(), and scale_surface_legacy().

Typedef Documentation

◆ fixed_t

typedef int32_t fixed_t

Definition at line 292 of file math.hpp.

Function Documentation

◆ bit_width() [1/2]

template<typename T >

std::size_t bit_width ( )

inline

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 85 of file math.hpp.

Referenced by BOOST_AUTO_TEST_CASE(), and count_leading_zeros().

◆ bit_width() [2/2]

template<typename T >

std::size_t bit_width ( const T & )

inline

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 100 of file math.hpp.

◆ bounded_add()

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

inline

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 46 of file math.hpp.

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

◆ count_leading_ones()

template<typename N >

unsigned int count_leading_ones ( N n )

inline

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 277 of file math.hpp.

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

◆ count_leading_zeros()

template<typename N >

unsigned int count_leading_zeros ( N n )

inline

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.