Provides mathematical functions and utilities, primarily focused on fixed-point arithmetic. More...

#include <submath.h>
#include <fixed.h>
#include <fxmath.h>
#include <b8/type.h>

Classes
class	Vec

struct	Line
	Represents a line segment in 2D space defined by two points. More...

struct	Poly
	Represents a triangle in 2D space using three points. More...

struct	Rect
	A structure for representing rectangles with fixed-point coordinates. More...

struct	Xorshift32

Macros
#define	M_E 2.71828182845904523536028747135266250 /* e */

#define	M_LOG2E 1.44269504088896340735992468100189214 /* log2(e) */

#define	M_LOG10E 0.434294481903251827651128918916605082 /* log10(e) */

#define	M_LN2 0.693147180559945309417232121458176568 /* loge(2) */

#define	M_LN10 2.30258509299404568401799145468436421 /* loge(10) */

#define	M_PI 3.14159265358979323846264338327950288 /* pi */

#define	M_PI_2 1.57079632679489661923132169163975144 /* pi/2 */

#define	M_PI_4 0.785398163397448309615660845819875721 /* pi/4 */

#define	M_1_PI 0.318309886183790671537767526745028724 /* 1/pi */

#define	M_2_PI 0.636619772367581343075535053490057448 /* 2/pi */

#define	M_2_SQRTPI 1.12837916709551257389615890312154517 /* 2/sqrt(pi) */

#define	M_SQRT2 1.41421356237309504880168872420969808 /* sqrt(2) */

#define	M_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */

#define	MAXFLOAT 0x1.fffffep+127f

Typedefs
using	fx8 = fpm::fixed<std::int32_t, std::int64_t, 8>
	Alias for fixed-point type with 8 fractional bits.

using	fx12 = fpm::fixed<std::int32_t, std::int64_t, 12>
	Alias for fixed-point type with 12 fractional bits.

Functions
std::string	tostr (const fx8 &val)

std::string	tostr (const Vec &val)

std::string	tostr (const Rect &val)

const fx8 &	_min (const fx8 &lhs_, const fx8 &rhs_)
	Get the minimum of two fixed-point values.

const fx8 &	_max (const fx8 &lhs_, const fx8 &rhs_)
	Get the maximum of two fixed-point values.

const fx8 &	_lim (const fx8 &x_, const fx8 &lhs_, const fx8 &rhs_)
	Limit a fixed-point value within a specified range.

const fx8	_abs (const fx8 &x_)
	Get the absolute value of a fixed-point number.

template<typename T , typename U , typename V >
T	lim (const T &x_, const U &lhs_, const V &rhs_)
	Limit a value within a specified range.

s16	sin_12 (u32 th)
	Calculate the sine of an angle using a 12-bit angle representation.

s16	cos_12 (u32 th)
	Calculate the cosine of an angle using a 12-bit angle representation.

fx8	rad_cos_12 (fx8 rad, u32 th)
	Calculate the cosine of an angle and scale a fixed-point value by it.

fx8	rad_sin_12 (fx8 rad, u32 th)
	Calculate the sine of an angle and scale a fixed-point value by it.

fx8	genrand_min_max_fx8 (fx8 min_, fx8 max_)
	Generate a random fixed-point number within a specified range.

uint32_t	qmod (uint32_t x, uint32_t N)
	Computes the remainder of x divided by N using an optimized method.

uint32_t	qdiv (uint32_t x, uint32_t N)
	Computes the quotient of x divided by N using an optimized method.

Variables
constexpr fx8	FX8_E = fx8(696, 256)

constexpr fx8	FX8_LOG2E = fx8(369, 256)

constexpr fx8	FX8_LOG10E = fx8(111, 256)

constexpr fx8	FX8_LN2 = fx8(178, 256)

constexpr fx8	FX8_LN10 = fx8(590, 256)

constexpr fx8	FX8_1_PI = fx8(82, 256)

constexpr fx8	FX8_2_PI = fx8(163, 256)

constexpr fx8	FX8_2_SQRTPI = fx8(289, 256)

constexpr fx8	FX8_SQRT2 = fx8(362, 256)

constexpr fx8	FX8_SQRT1_2 = fx8(181, 256)

constexpr fx8	FX8_2PI = fx8(1608, 256)

constexpr fx8	FX8_PI = fx8(804, 256)

constexpr fx8	FX8_PI_2 = fx8(402, 256)

constexpr fx8	FX8_PI_3 = fx8(268, 256)

constexpr fx8	FX8_PI_4 = fx8(201, 256)

constexpr fx8	FX8_PI_5 = fx8(161, 256)

constexpr fx8	FX8_PI_6 = fx8(134, 256)

constexpr fx8	FX8_PI_7 = fx8(115, 256)

constexpr fx8	FX8_PI_8 = fx8(100, 256)

constexpr fx8	FX8_PI_9 = fx8(89, 256)

constexpr fx8	FX8_PI_10 = fx8(80, 256)

constexpr fx8	FX8_PI_11 = fx8(73, 256)

constexpr fx8	FX8_PI_12 = fx8(67, 256)

constexpr fx8	FX8_PI_13 = fx8(62, 256)

constexpr fx8	FX8_PI_14 = fx8(57, 256)

constexpr fx8	FX8_PI_15 = fx8(54, 256)

constexpr fx8	FX8_PI_16 = fx8(50, 256)

constexpr fx12	FX12_E = fx12(11135, 4096)

constexpr fx12	FX12_LOG2E = fx12(5912, 4096)

constexpr fx12	FX12_LOG10E = fx12(1785, 4096)

constexpr fx12	FX12_LN2 = fx12(2831, 4096)

constexpr fx12	FX12_LN10 = fx12(9438, 4096)

constexpr fx12	FX12_1_PI = fx12(1317, 4096)

constexpr fx12	FX12_2_PI = fx12(2634, 4096)

constexpr fx12	FX12_2_SQRTPI = fx12(4613, 4096)

constexpr fx12	FX12_SQRT2 = fx12(5793, 4096)

constexpr fx12	FX12_SQRT1_2 = fx12(2896, 4096)

constexpr fx12	FX12_PI = fx12(12868, 4096)

constexpr fx12	FX12_PI_2 = fx12(6434, 4096)

constexpr fx12	FX12_PI_3 = fx12(4290, 4096)

constexpr fx12	FX12_PI_4 = fx12(3217, 4096)

constexpr fx12	FX12_PI_5 = fx12(2574, 4096)

constexpr fx12	FX12_PI_6 = fx12(2145, 4096)

constexpr fx12	FX12_PI_7 = fx12(1838, 4096)

constexpr fx12	FX12_PI_8 = fx12(1609, 4096)

constexpr fx12	FX12_PI_9 = fx12(1432, 4096)

constexpr fx12	FX12_PI_10 = fx12(1287, 4096)

constexpr fx12	FX12_PI_11 = fx12(1171, 4096)

constexpr fx12	FX12_PI_12 = fx12(1072, 4096)

constexpr fx12	FX12_PI_13 = fx12(989, 4096)

constexpr fx12	FX12_PI_14 = fx12(919, 4096)

constexpr fx12	FX12_PI_15 = fx12(858, 4096)

constexpr fx12	FX12_PI_16 = fx12(804, 4096)

Detailed Description

Provides mathematical functions and utilities, primarily focused on fixed-point arithmetic.

This module offers a set of mathematical functions and utilities, including trigonometric calculations, fixed-point number operations, and random number generation using the Mersenne Twister algorithm. It is particularly useful in resource-constrained environments, such as embedded systems or game development.

The module includes:

Trigonometric functions using a 12-bit angle representation
Random number generation within a specified range for fixed-point numbers
Mathematical constants like M_PI, M_E, etc.
Utility functions for fixed-point arithmetic
A structure for representing rectangles with fixed-point coordinates

Note: This module relies on fixed-point number representations using the fx8 and fx12 types.

Example usage:

#include <submath.h>
#include <iostream>
 
int main() {
    // Generate a random fixed-point number within a specified range
    fx8 min_value(1.0);
    fx8 max_value(10.0);
    fx8 random_value = genrand_min_max_fx8(min_value, max_value);
    std::cout << "Random value: " << random_value << std::endl;
 
    // Calculate sine and cosine for a given angle
    u32 angle = 1024;  // 90 degrees
    fx8 radius(5.0);
    fx8 sin_result = rad_sin_12(radius, angle);
    fx8 cos_result = rad_cos_12(radius, angle);
    std::cout << "sin(90 degrees): " << sin_result << std::endl;
    std::cout << "cos(90 degrees): " << cos_result << std::endl;
 
    return 0;
}

Typedef Documentation

◆ fx12

using fx12 = fpm::fixed<std::int32_t, std::int64_t, 12>

Alias for fixed-point type with 12 fractional bits.

This type represents a fixed-point number with 12 bits for the fractional part, using a 32-bit integer for storage and a 64-bit integer for intermediate calculations.

◆ fx8

using fx8 = fpm::fixed<std::int32_t, std::int64_t, 8>

Alias for fixed-point type with 8 fractional bits.

This type represents a fixed-point number with 8 bits for the fractional part, using a 32-bit integer for storage and a 64-bit integer for intermediate calculations.

Function Documentation

◆ _abs()

const fx8 _abs ( const fx8 & x_ )

inline

Get the absolute value of a fixed-point number.

Parameters

x_	The value.

Returns: The absolute value.

◆ _lim()

const fx8 & _lim	(	const fx8 &	x_,
		const fx8 &	lhs_,
		const fx8 &	rhs_ )

inline

Limit a fixed-point value within a specified range.

Parameters

x_	The value to limit.
lhs_	The lower bound.
rhs_	The upper bound.

Returns: The limited value.

◆ _max()

const fx8 & _max	(	const fx8 &	lhs_,
		const fx8 &	rhs_ )

inline

Get the maximum of two fixed-point values.

Parameters

lhs_	The first value.
rhs_	The second value.

Returns: The maximum value.

◆ _min()

const fx8 & _min	(	const fx8 &	lhs_,
		const fx8 &	rhs_ )

inline

Get the minimum of two fixed-point values.

Parameters

lhs_	The first value.
rhs_	The second value.

Returns: The minimum value.

◆ cos_12()

s16 cos_12 ( u32 th )

extern

Calculate the cosine of an angle using a 12-bit angle representation.

Parameters

th	The angle in 12-bit representation.

Returns: The cosine of the angle.

◆ genrand_min_max_fx8()

fx8 genrand_min_max_fx8	(	fx8	min_,
		fx8	max_ )

extern

Generate a random fixed-point number within a specified range.

Parameters

min_	The minimum value.
max_	The maximum value.

Returns: The random fixed-point number within the range.

◆ lim()

template<typename T , typename U , typename V >

T lim	(	const T &	x_,
		const U &	lhs_,
		const V &	rhs_ )

inline

Limit a value within a specified range.

Template Parameters

T	The type of the value.
U	The type of the lower bound.
V	The type of the upper bound.

Parameters

x_	The value to limit.
lhs_	The lower bound.
rhs_	The upper bound.

Returns: The limited value.

◆ qdiv()

uint32_t qdiv	(	uint32_t	x,
		uint32_t	N )

extern

Computes the quotient of x divided by N using an optimized method.

This function calculates the quotient (integer division result) of x / N efficiently using different strategies based on the value of the divisor N:

If N is zero, the function returns zero to avoid division by zero errors.
If N is a power of two, the quotient is computed directly using x / N.
If N is less than 128, a precomputed reciprocal table (inv_tbl) is employed to approximate the division through fixed-point multiplication.
If N is 128 or greater, the function falls back to the standard division operator.

Parameters

x	The dividend.
N	The divisor (should be greater than zero).

Returns: The quotient of x divided by N.

Note: This function is designed to optimize division by avoiding slow division instructions whenever possible, leveraging bitwise and multiplication-based methods.

◆ qmod()

uint32_t qmod	(	uint32_t	x,
		uint32_t	N )

extern

Computes the remainder of x divided by N using an optimized method.

This function calculates x % N efficiently using different methods based on the divisor N:

If N is zero, the function returns zero to prevent division by zero errors.
If N is a power of two, the remainder is computed using x & (N - 1), which is significantly faster than division.
If N < 128, a precomputed reciprocal table (inv_tbl) is used to approximate the division, leveraging fixed-point multiplication.
If N >= 128, the function directly falls back to the standard % operator.

Parameters

x	The dividend.
N	The divisor (must be greater than zero).

Returns: The remainder of x divided by N (x % N).

Note: This function optimizes the modulo operation by avoiding slow division instructions whenever possible, making use of bitwise and multiplication-based methods.

◆ rad_cos_12()

fx8 rad_cos_12	(	fx8	rad,
		u32	th )

extern

Calculate the cosine of an angle and scale a fixed-point value by it.

Parameters

rad	The fixed-point value to scale.
th	The angle in 12-bit representation.

Returns: The scaled fixed-point value.

◆ rad_sin_12()

fx8 rad_sin_12	(	fx8	rad,
		u32	th )

extern

Calculate the sine of an angle and scale a fixed-point value by it.

Parameters

rad	The fixed-point value to scale.
th	The angle in 12-bit representation.

Returns: The scaled fixed-point value.

◆ sin_12()

s16 sin_12 ( u32 th )

extern

Calculate the sine of an angle using a 12-bit angle representation.

Parameters

th	The angle in 12-bit representation.

Returns: The sine of the angle.

Classes

Macros

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ fx12

◆ fx8

Function Documentation

◆ _abs()

◆ _lim()

◆ _max()

◆ _min()

◆ cos_12()

◆ genrand_min_max_fx8()

◆ lim()

◆ qdiv()

◆ qmod()

◆ rad_cos_12()

◆ rad_sin_12()

◆ sin_12()