#include <math.h>

Definition

Provides constants and static methods for trigonometric, logarithmic, and other common mathematical functions.

Namespace: xtd

Library: xtd.core

Remarks: This class cannot be inherited.

Examples: The following example uses several mathematical and trigonometric functions from the xtd::math class to calculate the inner angles of a trapezoid.
#include <xtd/xtd>

using namespace xtd;

namespace examples {

// The following class represents simple functionality of the trapezoid.

class math_trapezoid_sample : public object {

public:

// The main entry point for the application.

static void main() {

math_trapezoid_sample trpz(20.0, 10.0, 8.0, 6.0);

console::write_line("The trapezoid's bases are 20.0 and 10.0, the trapezoid's legs are 8.0 and 6.0");

double h = trpz.get_height();

console::write_line("trapezoid height is: {0}", h);

double dx_r = trpz.get_left_base_radian_angle();

console::write_line("trapezoid left base angle is: {0} Radians", dx_r);

double dy_r = trpz.get_right_base_radian_angle();

console::write_line("trapezoid right base angle is: {0} Radians", dy_r);

double dx_d = trpz.get_left_base_degree_angle();

console::write_line("trapezoid left base angle is: {0} Degrees", dx_d);

double dy_d = trpz.get_right_base_degree_angle();

console::write_line("trapezoid left base angle is: {0} Degrees", dy_d);

}

math_trapezoid_sample(double long_base, double short_base, double left_leg, double right_leg) {

long_base_ = math::abs(long_base);

short_base_ = math::abs(short_base);

left_leg_ = math::abs(left_leg);

right_leg_ = math::abs(right_leg);

}

double get_height() {

double x = get_right_small_base();

return math::sqrt(math::pow(right_leg_, 2.0) - math::pow(x, 2.0));

}

double get_square() {

return get_height() * long_base_ / 2.0;

}

double get_left_base_radian_angle() {

double sin_x = get_height() / left_leg_;

return math::round(math::asin(sin_x), 2);

}

double get_right_base_radian_angle() {

double x = get_right_small_base();

double cos_x = (math::pow(right_leg_, 2.0) + math::pow(x, 2.0) - math::pow(get_height(), 2.0)) / (2 * x * right_leg_);

return math::round(math::acos(cos_x), 2);

}

double get_left_base_degree_angle() {

double x = math::radians_to_degrees(get_left_base_radian_angle());

return math::round(x, 2);

}

double get_right_base_degree_angle() {

double x = math::radians_to_degrees(get_right_base_radian_angle());

return math::round(x, 2);

}

private:

double long_base_;

double short_base_;

double left_leg_;

double right_leg_;

double get_right_small_base() {

return (math::pow(right_leg_, 2.0) - math::pow(left_leg_, 2.0) + math::pow(long_base_, 2.0) + math::pow(short_base_, 2.0) - 2 * short_base_ * long_base_) / (2 * (long_base_ - short_base_));

}

};

}

startup_(examples::math_trapezoid_sample);

// This code produces the following output:

//

// The trapezoid's bases are 20.0 and 10.0, the trapezoid's legs are 8.0 and 6.0

// trapezoid height is: 4.8

// trapezoid left base angle is: 0.64 Radians

// trapezoid right base angle is: 0.93 Radians

// trapezoid left base angle is: 36.67 Degrees

// trapezoid left base angle is: 53.29 Degrees

xtd::console::write_line
static void write_line()
Writes the current line terminator to the standard output stream using the specified format informati...

xtd::math::sqrt
static double sqrt(double value)
Returns the square root of a specified number.

xtd::math::radians_to_degrees
static double radians_to_degrees(double radians)
Convert radians to degrees.

xtd::math::abs
static decimal_t abs(decimal_t value)
Returns the absolute value of a decimal number.

xtd::math::pow
static double pow(double x, double y)
Returns a specified number raised to the specified power.

xtd::math::round
static decimal_t round(decimal_t value)
Rounds a double-precision floating-point value to the nearest integral value.

xtd::math::acos
static double acos(double value)
Returns the angle whose cosine is the specified number.

xtd::math::asin
static double asin(double value)
Returns the angle whose sine is the specified number.

startup_
#define startup_(main_class)
Defines the entry point to be called when the application loads. Generally this is set either to the ...
Definition: startup.h:49

xtd::console_key::h
@ h
The H key.

xtd::console_key::x
@ x
The X key.

xtd
The xtd namespace contains all fundamental classes to access Hardware, Os, System,...
Definition: system_report.h:17

Static Public Attributes
static constexpr double	e
	Represents the natural logarithmic base, specified by the constant, e. This field is constant. More...

static constexpr double	epsilon
	Represents the smallest positive Double value greater than zero. This field is constant. More...

static constexpr double	infinity
	Represents infinity. This field is constant. More...

static constexpr double	max_value
	Represents the largest possible value of double. This field is constant. More...

static constexpr double	min_value
	Represents the smallest possible value of double. This field is constant. More...

static constexpr double	NaN
	Represents not a number (NaN). This field is constant. More...

static constexpr double	negative_infinity
	Represents negative infinity. This field is constant. More...

static constexpr double	pi
	Represents the ratio of the circumference of a circle to its diameter, specified by the constant, π. This field is constant. More...

static constexpr double	positive_infinity
	Represents positive infinity. This field is constant. More...

static constexpr double	tau
	Represents the number of radians in one turn, specified by the constant, τ. More...

Static Public Member Functions
static decimal_t	abs (decimal_t value)
	Returns the absolute value of a decimal number. More...

static double	abs (double value)
	Returns the absolute value of a double-precision floating-point number. More...

static float	abs (float value)
	Returns the absolute value of a single-precision floating-point number. More...

static int16_t	abs (int16_t value)
	Returns the absolute value of a 16-bit signed integer. More...

static int32_t	abs (int32_t value)
	Returns the absolute value of a 32-bit signed integer. More...

static int64_t	abs (int64_t value)
	Returns the absolute value of a 64-bit signed integer. More...

static llong_t	abs (llong_t value)
	Returns the absolute value of a 64-bit signed integer. More...

static sbyte_t	abs (sbyte_t value)
	Returns the absolute value of a 8-bit signed integer. More...

static double	acos (double value)
	Returns the angle whose cosine is the specified number. More...

static double	asin (double value)
	Returns the angle whose sine is the specified number. More...

static double	atan (double value)
	Returns the angle whose tangent is the specified number. More...

static double	atan2 (double y, double x)
	Returns the angle whose tangent is the specified number. More...

static int64_t	big_mul (int32_t a, int32_t b)
	Produces the full product of two 32-bit numbers. More...

static decimal	ceiling (decimal value)
	Returns the smallest integer greater than or equal to the specified double-precision floating-point number. More...

static double	ceiling (double value)
	Returns the smallest integer greater than or equal to the specified double-precision floating-point number. More...

static double	cos (double value)
	Returns the cosine of the specified angle. More...

static double	cosh (double value)
	Returns the hyperbolic cosine of the specified angle. More...

static double	degrees_to_radians (double degrees)
	Convert degrees to radians. More...

static int32_t	div_rem (int32_t dividend, int32_t divisor, int32_t &remainder)
	Calculates the quotient of two 32-bit signed integers and also returns the remainder in an output parameter. More...

static int64_t	div_rem (int64_t dividend, int64_t divisor, int64_t &remainder)
	Calculates the quotient of two 64-bit signed integers and also returns the remainder in an output parameter. More...

static double	exp (double value)
	Returns e raised to the specified power. More...

static decimal_t	floor (decimal_t value)
	Returns the largest integer less than or equal to the specified decimal number. More...

static double	floor (double value)
	Returns the largest integer less than or equal to the specified decimal number. More...

static double	ieee_remainder (double dividend, double divisor)
	Returns the remainder resulting from the division of a specified number by another specified number. More...

static bool	is_infinity (double value)
	Returns a value indicating whether the specified number evaluates to negative or positive infinity. More...

static bool	is_NaN (double value)
	Returns a value indicating whether the specified number evaluates to not a number. More...

static bool	is_negative_infinity (double value)
	Returns a value indicating whether the specified number evaluates to negative infinity. More...

static bool	is_positive_infinity (double value)
	Returns a value indicating whether the specified number evaluates to positive infinity. More...

static double	log (double a, double new_base)
	Returns the logarithm of a specified number in a specified base. More...

static double	log (double value)
	Returns the natural (base e) logarithm of a specified number. More...

static double	log10 (double value)
	Returns the base 10 logarithm of a specified number. More...

static byte_t	max (byte_t a, byte_t b)
	Returns the larger of two 8-bit unsigned integers. More...

static decimal_t	max (decimal_t a, decimal_t b)
	Returns the larger of two double single. More...

static double	max (double a, double b)
	Returns the larger of two double single. More...

static float	max (float a, float b)
	Returns the larger of two single single. More...

static int16_t	max (int16_t a, int16_t b)
	Returns the larger of two 16-bit signed integers. More...

static int32_t	max (int32_t a, int32_t b)
	Returns the larger of two 32-bit signed integers. More...

static int64_t	max (int64_t a, int64_t b)
	Returns the larger of two 64-bit signed integers. More...

static llong_t	max (llong_t a, llong_t b)
	Returns the larger of two 64-bit signed integers. More...

static sbyte_t	max (sbyte_t a, sbyte_t b)
	Returns the larger of two 8-bit signed integers. More...

static uint16_t	max (uint16_t a, uint16_t b)
	Returns the larger of two 16-bit unsigned integers. More...

static uint32_t	max (uint32_t a, uint32_t b)
	Returns the larger of two 32-bit unsigned integers. More...

static uint64_t	max (uint64_t a, uint64_t b)
	Returns the larger of two 64-bit unsigned integers. More...

static ullong_t	max (ullong_t a, ullong_t b)
	Returns the larger of two 64-bit unsigned integers. More...

static byte_t	min (byte_t a, byte_t b)
	Returns the smaller of two 8-bit unsigned integers. More...

static decimal_t	min (decimal_t a, decimal_t b)
	Returns the smaller of two double single. More...

static double	min (double a, double b)
	Returns the smaller of two double single. More...

static float	min (float a, float b)
	Returns the smaller of two single single. More...

static int16_t	min (int16_t a, int16_t b)
	Returns the smaller of two 16-bit signed integers. More...

static int32_t	min (int32_t a, int32_t b)
	Returns the smaller of two 32-bit signed integers. More...

static int64_t	min (int64_t a, int64_t b)
	Returns the smaller of two 64-bit signed integers. More...

static llong_t	min (llong_t a, llong_t b)
	Returns the smaller of two 64-bit signed integers. More...

static sbyte_t	min (sbyte_t a, sbyte_t b)
	Returns the smaller of two 8-bit signed integers. More...

static uint16_t	min (uint16_t a, uint16_t b)
	Returns the smaller of two 16-bit unsigned integers. More...

static uint32_t	min (uint32 a, uint32 b)
	Returns the smaller of two 32-bit unsigned integers. More...

static uint64	min (uint64_t a, uint64_t b)
	Returns the smaller of two 64-bit unsigned integers. More...

static ullong_t	min (ullong_t a, ullong_t b)
	Returns the smaller of two 64-bit unsigned integers. More...

static double	pow (double x, double y)
	Returns a specified number raised to the specified power. More...

static double	radians_to_degrees (double radians)
	Convert radians to degrees. More...

static decimal_t	round (decimal_t value)
	Rounds a double-precision floating-point value to the nearest integral value. More...

static decimal_t	round (decimal_t value, int32_t decimals)
	Rounds a decimal value to a specified number of fractional digits. More...

static double	round (double value)
	Rounds a double-precision floating-point value to the nearest integral value. More...

static double	round (double value, int32_t decimals)
	Rounds a decimal value to a specified number of fractional digits. More...

static int32_t	sign (decimal_t value)
	Returns a value indicating the sign of a double-precision floating-point number. More...

static int32_t	sign (double value)
	Returns a value indicating the sign of a double-precision floating-point number. More...

static int32_t	sign (float value)
	Returns a value indicating the sign of a single-precision floating-point number. More...

static int32_t	sign (int16_t value)
	Returns a value indicating the sign of a 16-bit signed integer. More...

static int32_t	sign (int32_t value)
	Returns a value indicating the sign of a 32-bit signed integer. More...

static int32_t	sign (int64_t value)
	Returns a value indicating the sign of a 64-bit signed integer. More...

static int32_t	sign (llong_t value)
	Returns a value indicating the sign of a 64-bit signed integer. More...

static int32_t	sign (sbyte_t value)
	Returns a value indicating the sign of an 8-bit signed integer. More...

static double	sin (double value)
	Returns the sine of the specified angle. More...

static double	sinh (double value)
	Returns the hyperbolic sine of the specified angle. More...

static double	sqrt (double value)
	Returns the square root of a specified number. More...

static double	tan (double value)
	Returns the tangent of the specified angle. More...

static double	tanh (double value)
	Returns the hyperbolic tangent of the specified angle. More...

static decimal_t	truncate (decimal_t value)
	Calculates the integral part of a specified double-precision floating-point number. More...

static double	truncate (double value)
	Calculates the integral part of a specified double-precision floating-point number. More...

Member Function Documentation

◆ abs() [1/8]

static decimal_t xtd::math::abs ( decimal_t value )

static

Returns the absolute value of a decimal number.

Parameters

value A number in the range std::numeric_limit<decimal_t>::lowest() <= value <= std::numeric_limit<decimal_t>::max().

Returns: A decimal number, x, such that 0 <= x <= std::numeric_limit<decimal_t>::max()std::numeric_limit<decimal_t>::max().

◆ abs() [2/8]

static double xtd::math::abs ( double value )

static

Returns the absolute value of a double-precision floating-point number.

Parameters

value A number in the range std::numeric_limit<double>::lowest() <= value <= std::numeric_limit<double>::max().

Returns: A double-precision floating-point number, x, such that 0 <= x <= std::numeric_limit<double>::max().

◆ abs() [3/8]

static float xtd::math::abs ( float value )

static

Returns the absolute value of a single-precision floating-point number.

Parameters

value A number in the range std::numeric_limit<float>::lowest() <= value <= std::numeric_limit<float>::max().

Returns: A single-precision floating-point number, x, such that 0 <= x <= std::numeric_limit<float>::max().

◆ abs() [4/8]

static int16_t xtd::math::abs ( int16_t value )

static

Returns the absolute value of a 16-bit signed integer.

Parameters

value A number in the range std::numeric_limit<int16_t>::lowest() <= value <= std::numeric_limit<int16_t>::max().

Returns: A 16-bit signed integer, x, such that 0 <= x <= std::numeric_limit<int16_t>::max().

Exceptions

xtd::overflow_exception value equals std::numeric_limit<int16_t>::lowest().

◆ abs() [5/8]

static int32_t xtd::math::abs ( int32_t value )

static

Returns the absolute value of a 32-bit signed integer.

Parameters

value A number in the range std::numeric_limit<int32_t>::lowest() <= value <= std::numeric_limit<int32_t>::max().

Returns: A 32-bit signed integer, x, such that 0 <= x <= std::numeric_limit<int32_t>::max().

Exceptions

xtd::overflow_exception value equals std::numeric_limit<int32_t>::lowest().

◆ abs() [6/8]

static int64_t xtd::math::abs ( int64_t value )

static

Returns the absolute value of a 64-bit signed integer.

Parameters

value A number in the range std::numeric_limit<int64_t>::min() <= value <= std::numeric_limit<int64_t>::max().

Returns: A 64-bit signed integer, x, such that 0 <= x <= std::numeric_limit<int64_t>::max().

Exceptions

xtd::overflow_exception value equals std::numeric_limit<int64_t>::lowest().

◆ abs() [7/8]

static llong_t xtd::math::abs ( llong_t value )

static

Returns the absolute value of a 64-bit signed integer.

Parameters

value A number in the range std::numeric_limit<llong_t>::lowest() <= value <= std::numeric_limit<llong_t>::max().

Returns: A 8-bit signed integer, x, such that 0 <= x <= std::numeric_limit<llong_t>::max().

Exceptions

xtd::overflow_exception value equals std::numeric_limit<llong_t>::lowest().

◆ abs() [8/8]

static sbyte_t xtd::math::abs ( sbyte_t value )

static

Returns the absolute value of a 8-bit signed integer.

Parameters

value A number in the range std::numeric_limit<sbyte_t>::lowest() <= value <= std::numeric_limit<sbyte_t>::max().

Returns: A 8-bit signed integer, x, such that 0 <= x <= std::numeric_limit<sbyte_t>::max().

Exceptions

xtd::overflow_exception value equals std::numeric_limit<sbyte_tsbyte_t>::lowest().

◆ acos()

static double xtd::math::acos ( double value )

static

Returns the angle whose cosine is the specified number.

Parameters

value A number representing a cosine, where -1 <= value <= 1.

Returns: An angle, A, measured in radians, such that 0 <= A <= PI. -or- math::NaN if value < -1 or d > 1.

◆ asin()

static double xtd::math::asin ( double value )

static

Returns the angle whose sine is the specified number.

Parameters

value A number representing a sine, where -1 <= value <= 1.

Returns: An angle, A, measured in radians, such that -PI/2 <= A <= PI/2. -or- math::NaN if value < -1 or d > 1.

◆ atan()

static double xtd::math::atan ( double value )

static

Returns the angle whose tangent is the specified number.

Parameters

value A number representing a tangent.

Returns: An angle, A, measured in radians, such that -PI/2 <= ? <= PI/2. -or- math::NaN if value equals math::NaN, -PI/2 rounded to double precision (-1.5707963267949) if d equals math::negative_infinity, or PI/2 rounded to double precision (1.5707963267949) if d equals math::positive_infinity

◆ atan2()

static double xtd::math::atan2	(	double	y,
		double	x
	)

static

Returns the angle whose tangent is the specified number.

Parameters

y	The y coordinate of a point.
x	The x coordinate of a point.

Returns

An angle, A, measured in radians, such that -PI <= A <= PI, and tan(?) = y / x, where (x, y) is a point in the Cartesian plane. Observe the following:

For (x, y) in quadrant 1, 0 < A < PI/2.
For (x, y) in quadrant 2, PI/2 < A <= PI.
For (x, y) in quadrant 3, -PI < A < -PI/2.
For (x, y) in quadrant 4, -PI/2 < A < 0.
For points on the boundaries of the quadrants, the return value is the following:
If x is 0 and y is not negative, A = 0.
If x is 0 and y is negative, A = PI.
If x is positive and y is 0, A = PI/2.
If x is negative and y is 0, A = -PI/2.

Remarks: The return value is the angle in the Cartesian plane formed by the x-axis, and a vector starting from the origin, (0,0), and terminating at the point, (x,y).

◆ big_mul()

static int64_t xtd::math::big_mul	(	int32_t	a,
		int32_t	b
	)

static

Produces the full product of two 32-bit numbers.

Parameters

a	The first int32 to multiply.
b	The second int32 to multiply.

Returns: The int64 containing the product of the specified numbers.

◆ ceiling() [1/2]

static decimal xtd::math::ceiling ( decimal value )

static

Returns the smallest integer greater than or equal to the specified double-precision floating-point number.

Parameters

value A double-precision floating-point number.

Returns: The smallest integer greater than or equal to value. If value is equal to xtd::math::NaN, xtd::math::negative_infinity, or xtd::math::positive_infinity, that value is returned.

◆ ceiling() [2/2]

static double xtd::math::ceiling ( double value )

static

Returns the smallest integer greater than or equal to the specified double-precision floating-point number.

Parameters

value A double-precision floating-point number.

Returns: The smallest integer greater than or equal to value. If value is equal to xtd::math::NaN, xtd::math::negative_infinity, or xtd::math::positive_infinity, that value is returned.

◆ cos()

static double xtd::math::cos ( double value )

static

Returns the cosine of the specified angle.

Parameters

value An angle, measured in radians.

Returns: The cosine of value. If value is equal to xtd::math::NaN, xtd::math::negative_infinity, or xtd::math::positive_infinity, this method returns xtd::math::NaN.

◆ cosh()

static double xtd::math::cosh ( double value )

static

Returns the hyperbolic cosine of the specified angle.

Parameters

value An angle, measured in radians.

Returns: The hyperbolic cosine of value. If value is equal to xtd::math::negative_infinity() or xtd::math::positive_:infinity, xtd::math::positive_infinity is returned. If value is equal to xtd::math::NaN, xtd::math::NaN is returned.

◆ degrees_to_radians()

static double xtd::math::degrees_to_radians ( double degrees )

static

Convert degrees to radians.

Parameters

degrees A double-precision floating-point number.

Returns: A converted degrees from radians.

◆ div_rem() [1/2]

static int32_t xtd::math::div_rem	(	int32_t	dividend,
		int32_t	divisor,
		int32_t &	remainder
	)

static

Calculates the quotient of two 32-bit signed integers and also returns the remainder in an output parameter.

Parameters

dividend	The dividend.
divisor	The divisor.
remainder	An angle, measured in radians.

Returns: The remainder.

◆ div_rem() [2/2]

static int64_t xtd::math::div_rem	(	int64_t	dividend,
		int64_t	divisor,
		int64_t &	remainder
	)

static

Calculates the quotient of two 64-bit signed integers and also returns the remainder in an output parameter.

Parameters

dividend	The dividend.
divisor	The divisor.
remainder	An angle, measured in radians.

Returns: The remainder.

◆ exp()

static double xtd::math::exp ( double value )

static

Returns e raised to the specified power.

Parameters

value A number specifying a power.

Returns: The number e raised to the power d. If value equals xtd::math::NaN or xtd::math::positive_infinity, that value is returned. If value equals xtd::math::negative_infinity, 0 is returned.

◆ floor() [1/2]

static decimal_t xtd::math::floor ( decimal_t value )

static

Returns the largest integer less than or equal to the specified decimal number.

Parameters

value A double-precision floating-point number.

Returns: The largest integer less than or equal to value.

◆ floor() [2/2]

static double xtd::math::floor ( double value )

static

Returns the largest integer less than or equal to the specified decimal number.

Parameters

value A double-precision floating-point number.

Returns: The largest integer less than or equal to value.

◆ ieee_remainder()

static double xtd::math::ieee_remainder	(	double	dividend,
		double	divisor
	)

static

Returns the remainder resulting from the division of a specified number by another specified number.

Parameters

dividend	A dividend.
divisor	A divisor.

Returns

A number equal to x - (y Q), where Q is the quotient of x / y rounded to the nearest integer (if x / y falls halfway between two integers, the even integer is returned).

If x - (y Q) is zero, the value +0 is returned if x is positive, or -0 if x is negative.
If y = 0, xtd::math::NaN is returned.

◆ is_infinity()

static bool xtd::math::is_infinity ( double value )

static

Returns a value indicating whether the specified number evaluates to negative or positive infinity.

Parameters

value A double-precision floating-point number.

Returns: true if value evaluates to xtd::math::positive_infinity or xtd::math::negative_infinity; otherwise, false.

◆ is_NaN()

static bool xtd::math::is_NaN ( double value )

static

Returns a value indicating whether the specified number evaluates to not a number.

Parameters

value A double-precision floating-point number.

Returns: true if value evaluates to not a number; otherwise, false.

◆ is_negative_infinity()

static bool xtd::math::is_negative_infinity ( double value )

static

Returns a value indicating whether the specified number evaluates to negative infinity.

Parameters

value A double-precision floating-point number.

Returns: true if value evaluates to xtd::math::negative_infinity; otherwise, false.

◆ is_positive_infinity()

static bool xtd::math::is_positive_infinity ( double value )

static

Returns a value indicating whether the specified number evaluates to positive infinity.

Parameters

value A double-precision floating-point number.

Returns: true if value evaluates to xtd::math::positive_infinity; otherwise, false.

◆ log() [1/2]

static double xtd::math::log	(	double	a,
		double	new_base
	)

static

Returns the logarithm of a specified number in a specified base.

Parameters

a	The number whose logarithm is to be found.
new_base	The base of the logarithm.

Returns

One of the values in the following table. (+Infinity denotes math::positive_infinity, -Infinity denotes math::negative_infinity, and math::NaN denotes math::NaN.)

a	new_base	Return value
a > 0	(0 < new_base < 1) -or- (new_base > 1)	log new_base (a)
a < 0	(any value)	xtd::math::NaN
(any value)	new_base < 0	xtd::math::NaN
a != 1	new_base = 0	xtd::math::NaN
a != 1	new_base = xtd::math::positive_infinity	xtd::math::NaN
a = xtd::math::NaN	(any value)	xtd::math::NaN
(any value)	new_base = xtd::math::NaN	xtd::math::NaN
(any value)	new_base = 1	xtd::math::NaN
a = 0	0 < new_base < 1	xtd::math::positive_infinity
a = 0	new_base > 1	xtd::math::negative_infinity
a = xtd::math::positive_infinity	0 < new_base < 1	xtd::math::negative_infinity
a = xtd::math::positive_infinity	new_base > 1	xtd::math::positive_infinity
a = 1	new_base = 0	0
a = 1	new_base = xtd::math::positive_infinity	0

◆ log() [2/2]

static double xtd::math::log ( double value )

static

Returns the natural (base e) logarithm of a specified number.

Parameters

value A number whose logarithm is to be found.

Returns

One of the values in the following table.

value parameter	Return value
Positive	The natural logarithm of d; that is, ln value, or log e value
Zero	xtd::math::negative_infinity
Negative	xtd::math::NaN
Equal to xtd::math::NaN	xtd::math::NaN
Equal to xtd::math::positive_infinity	xtd::math::positive_infinity

Remarks: Parameter value is specified as a base 10 number.

◆ log10()

static double xtd::math::log10 ( double value )

static

Returns the base 10 logarithm of a specified number.

Parameters

value A number whose logarithm is to be found.

Returns

One of the values in the following table.

value parameter	Return value
Positive	The natural logarithm of d; that is, ln value, or log e value
Zero	xtd::math::negative_infinity
Negative	xtd::math::NaN
Equal to xtd::math::NaN	xtd::math::NaN
Equal to xtd::math::positive_infinity	xtd::math::positive_infinity

Remarks: Parameter value is specified as a base 10 number.

◆ max() [1/13]

static byte_t xtd::math::max	(	byte_t	a,
		byte_t	b
	)

static

Returns the larger of two 8-bit unsigned integers.

Parameters

a	The first of two 8-bit unsigned integers to compare.
b	The second of two 8-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [2/13]

static decimal_t xtd::math::max	(	decimal_t	a,
		decimal_t	b
	)

static

Returns the larger of two double single.

Parameters

a	The first of two double single to compare.
b	The second of two double single to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [3/13]

static double xtd::math::max	(	double	a,
		double	b
	)

static

Returns the larger of two double single.

Parameters

a	The first of two double single to compare.
b	The second of two double single to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [4/13]

static float xtd::math::max	(	float	a,
		float	b
	)

static

Returns the larger of two single single.

Parameters

a	The first of two single single to compare.
b	The second of two single single to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [5/13]

static int16_t xtd::math::max	(	int16_t	a,
		int16_t	b
	)

static

Returns the larger of two 16-bit signed integers.

Parameters

a	The first of two 16-bit signed integers to compare.
b	The second of two 16-bit signed integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [6/13]

static int32_t xtd::math::max	(	int32_t	a,
		int32_t	b
	)

static

Returns the larger of two 32-bit signed integers.

Parameters

a	The first of two 32-bit signed integers to compare.
b	The second of two 32-bit signed integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [7/13]

static int64_t xtd::math::max	(	int64_t	a,
		int64_t	b
	)

static

Returns the larger of two 64-bit signed integers.

Parameters

a	The first of two 64-bit signed integers to compare.
b	The second of two 64-bit signed integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [8/13]

static llong_t xtd::math::max	(	llong_t	a,
		llong_t	b
	)

static

Returns the larger of two 64-bit signed integers.

Parameters

a	The first of two 64-bit signed integers to compare.
b	The second of two 64-bit signed integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [9/13]

static sbyte_t xtd::math::max	(	sbyte_t	a,
		sbyte_t	b
	)

static

Returns the larger of two 8-bit signed integers.

Parameters

a	The first of two 8-bit signed integers to compare.
b	The second of two 8-bit signed integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [10/13]

static uint16_t xtd::math::max	(	uint16_t	a,
		uint16_t	b
	)

static

Returns the larger of two 16-bit unsigned integers.

Parameters

a	The first of two 16-bit unsigned integers to compare.
b	The second of two 16-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [11/13]

static uint32_t xtd::math::max	(	uint32_t	a,
		uint32_t	b
	)

static

Returns the larger of two 32-bit unsigned integers.

Parameters

a	The first of two 32-bit unsigned integers to compare.
b	The second of two 32-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [12/13]

static uint64_t xtd::math::max	(	uint64_t	a,
		uint64_t	b
	)

static

Returns the larger of two 64-bit unsigned integers.

Parameters

a	The first of two 64-bit unsigned integers to compare.
b	The second of two 64-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ max() [13/13]

static ullong_t xtd::math::max	(	ullong_t	a,
		ullong_t	b
	)

static

Returns the larger of two 64-bit unsigned integers.

Parameters

a	The first of two 64-bit unsigned integers to compare.
b	The second of two 64-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is larger.

◆ min() [1/13]

static byte_t xtd::math::min	(	byte_t	a,
		byte_t	b
	)

static

Returns the smaller of two 8-bit unsigned integers.

Parameters

a	The first of two 8-bit unsigned integers to compare.
b	The second of two 8-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [2/13]

static decimal_t xtd::math::min	(	decimal_t	a,
		decimal_t	b
	)

static

Returns the smaller of two double single.

Parameters

a	The first of two double single to compare.
b	The second of two double single to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [3/13]

static double xtd::math::min	(	double	a,
		double	b
	)

static

Returns the smaller of two double single.

Parameters

a	The first of two double single to compare.
b	The second of two double single to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [4/13]

static float xtd::math::min	(	float	a,
		float	b
	)

static

Returns the smaller of two single single.

Parameters

a	The first of two single single to compare.
b	The second of two single single to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [5/13]

static int16_t xtd::math::min	(	int16_t	a,
		int16_t	b
	)

static

Returns the smaller of two 16-bit signed integers.

Parameters

a	The first of two 16-bit signed integers to compare.
b	The second of two 16-bit signed integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [6/13]

static int32_t xtd::math::min	(	int32_t	a,
		int32_t	b
	)

static

Returns the smaller of two 32-bit signed integers.

Parameters

a	The first of two 32-bit signed integers to compare.
b	The second of two 32-bit signed integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [7/13]

static int64_t xtd::math::min	(	int64_t	a,
		int64_t	b
	)

static

Returns the smaller of two 64-bit signed integers.

Parameters

a	The first of two 64-bit signed integers to compare.
b	The second of two 64-bit signed integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [8/13]

static llong_t xtd::math::min	(	llong_t	a,
		llong_t	b
	)

static

Returns the smaller of two 64-bit signed integers.

Parameters

a	The first of two 64-bit signed integers to compare.
b	The second of two 64-bit signed integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [9/13]

static sbyte_t xtd::math::min	(	sbyte_t	a,
		sbyte_t	b
	)

static

Returns the smaller of two 8-bit signed integers.

Parameters

a	The first of two 8-bit signed integers to compare.
b	The second of two 8-bit signed integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [10/13]

static uint16_t xtd::math::min	(	uint16_t	a,
		uint16_t	b
	)

static

Returns the smaller of two 16-bit unsigned integers.

Parameters

a	The first of two 16-bit unsigned integers to compare.
b	The second of two 16-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [11/13]

static uint32_t xtd::math::min	(	uint32	a,
		uint32	b
	)

static

Returns the smaller of two 32-bit unsigned integers.

Parameters

a	The first of two 32-bit unsigned integers to compare.
b	The second of two 32-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [12/13]

static uint64 xtd::math::min	(	uint64_t	a,
		uint64_t	b
	)

static

Returns the smaller of two 64-bit unsigned integers.

Parameters

a	The first of two 64-bit unsigned integers to compare.
b	The second of two 64-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ min() [13/13]

static ullong_t xtd::math::min	(	ullong_t	a,
		ullong_t	b
	)

static

Returns the smaller of two 64-bit unsigned integers.

Parameters

a	The first of two 64-bit unsigned integers to compare.
b	The second of two 64-bit unsigned integers to compare.

Returns: Parameter a or b, whichever is smaller.

◆ pow()

static double xtd::math::pow	(	double	x,
		double	y
	)

static

Returns a specified number raised to the specified power.

Parameters

x	A double-precision floating-point number to be raised to a power.
y	A double-precision floating-point number that specifies a power.

Returns: The number x raised to the power y.

Remarks

The following table indicates the return value when various values or ranges of values are specified for the x and y parameters. For more information, see Double::math::positive_infinity, Double::math::negative_infinity, and Double::NaN.

Parameters	Return value
x or y = math::NaN.	math::NaN
x = Any value except math::NaN; y = 0.	1
x = math::negative_infinity; y < 0.	0
x = math::negative_infinity; y is positive odd integer.	math::negative_infinity
x = math::negative_infinity; y is positive but not an odd integer.	math::positive_infinity
x < 0 but not math::negative_infinity; y is not an integer, math::negative_infinity, or math::positive_infinity.	math::NaN
x = -1; y = math::negative_infinity or math::positive_infinity.	math::NaN
-1 < x < 1; y = math::negative_infinity.	math::positive_infinity
-1 < x < 1; y = math::positive_infinity.	0
x < -1 or x > 1; y = math::negative_infinity.	0
x < -1 or x > 1; y = math::positive_infinity.	math::positive_infinity
x = 0; y < 0.	math::positive_infinity
x = 0; y > 0.	0
x = 1; y is any value except math::NaN.	1
x = math::positive_infinity; y < 0	0
x = math::positive_infinity; y > 0.	math::positive_infinity

◆ radians_to_degrees()

static double xtd::math::radians_to_degrees ( double radians )

static

Convert radians to degrees.

Parameters

radians A double-precision floating-point number.

Returns: A converted radians from degrees.

◆ round() [1/4]

static decimal_t xtd::math::round ( decimal_t value )

static

Rounds a double-precision floating-point value to the nearest integral value.

Parameters

value A double-precision floating-point number to be rounded.

Returns: The integer nearest value. If the fractional component of a is halfway between two integers, one of which is even and the other odd, then the even number is returned. Note that this method returns a double instead of an integral type.

◆ round() [2/4]

static decimal_t xtd::math::round	(	decimal_t	value,
		int32_t	decimals
	)

static

Rounds a decimal value to a specified number of fractional digits.

Parameters

value	A double-precision floating-point number to be rounded.
decimals	The number of decimal places in the return value.

Returns: The number nearest to d that contains a number of fractional digits equal to decimals.

◆ round() [3/4]

static double xtd::math::round ( double value )

static

Rounds a double-precision floating-point value to the nearest integral value.

Parameters

value A double-precision floating-point number to be rounded.

Returns: The integer nearest value. If the fractional component of a is halfway between two integers, one of which is even and the other odd, then the even number is returned. Note that this method returns a double instead of an integral type.

◆ round() [4/4]

static double xtd::math::round	(	double	value,
		int32_t	decimals
	)

static

Rounds a decimal value to a specified number of fractional digits.

Parameters

value	A double-precision floating-point number to be rounded.
decimals	The number of decimal places in the return value.

Returns: The number nearest to d that contains a number of fractional digits equal to decimals.

◆ sign() [1/8]

static int32_t xtd::math::sign ( decimal_t value )

static

Returns a value indicating the sign of a double-precision floating-point number.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

Exceptions

xtd::arithmetic_exception value is equal to NaN.

◆ sign() [2/8]

static int32_t xtd::math::sign ( double value )

static

Returns a value indicating the sign of a double-precision floating-point number.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

Exceptions

xtd::arithmetic_exception value is equal to NaN.

◆ sign() [3/8]

static int32_t xtd::math::sign ( float value )

static

Returns a value indicating the sign of a single-precision floating-point number.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

Exceptions

xtd::arithmetic_exception value is equal to NaN.

◆ sign() [4/8]

static int32_t xtd::math::sign ( int16_t value )

static

Returns a value indicating the sign of a 16-bit signed integer.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

◆ sign() [5/8]

static int32_t xtd::math::sign ( int32_t value )

static

Returns a value indicating the sign of a 32-bit signed integer.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

◆ sign() [6/8]

static int32_t xtd::math::sign ( int64_t value )

static

Returns a value indicating the sign of a 64-bit signed integer.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

◆ sign() [7/8]

static int32_t xtd::math::sign ( llong_t value )

static

Returns a value indicating the sign of a 64-bit signed integer.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

◆ sign() [8/8]

static int32_t xtd::math::sign ( sbyte_t value )

static

Returns a value indicating the sign of an 8-bit signed integer.

Parameters

value A signed number.

Returns

int32 A number that indicates the sign of value, as shown in the following table.

Return value	Meaning
-1	value is less than zero.
0	value is equal to zero.
1	value is greater than zero.

◆ sin()

static double xtd::math::sin ( double value )

static

Returns the sine of the specified angle.

Parameters

value An angle, measured in radians.

Returns: double The sine of value. If value is equal to math::NaN, math::negative_infinity, or math::positiveI_infinity, this method returns math::NaN.

◆ sinh()

static double xtd::math::sinh ( double value )

static

Returns the hyperbolic sine of the specified angle.

Parameters

value An angle, measured in radians.

Returns: double The sine of a. If a is equal to math::NaN, math::negative_infinity, or math::positive_infinity, this method returns math::NaN.

◆ sqrt()

static double xtd::math::sqrt ( double value )

static

Returns the square root of a specified number.

Parameters

value The number whose square root is to be found.

Returns

One of the values in the following table.

value parameter	Return value
Zero or positive	The positive square root of d.
Negative	math::NaN
Equals math::NaN	math::NaN
Equals math::positive_infinity	math::positive_infinity

◆ tan()

static double xtd::math::tan ( double value )

static

Returns the tangent of the specified angle.

Parameters

value An angle, measured in radians.

Returns: The tangent of value. If value is equal to math::NaN, math::negative_infinity, or math::positive_infinity, this method returns math::NaN.

◆ tanh()

static double xtd::math::tanh ( double value )

static

Returns the hyperbolic tangent of the specified angle.

Parameters

value An angle, measured in radians.

Returns: The hyperbolic tangent of value. If value is equal to math::negative_infinity, this method returns -1. If value is equal to math::positive_infinity, this method returns 1. If value is equal to math::NaN, this method returns math::NaN.

◆ truncate() [1/2]

static decimal_t xtd::math::truncate ( decimal_t value )

static

Calculates the integral part of a specified double-precision floating-point number.

Parameters

value A number to truncate.

Returns

The integral part of d; that is, the number that remains after any fractional digits have been discarded, or one of the values listed in the following table.

value	Return value
NaN	NaN
NegativeInfinity	NegativeInfinity
PositiveInfinity	PositiveInfinity

◆ truncate() [2/2]

static double xtd::math::truncate ( double value )

static

Calculates the integral part of a specified double-precision floating-point number.

Parameters

value A number to truncate.

Returns

The integral part of d; that is, the number that remains after any fractional digits have been discarded, or one of the values listed in the following table.

value	Return value
math::NaN	math::NaN
math::negative_infinity	math::negative_infinity
math::positive_infinity	math::positive_infinity

Member Data Documentation

◆ e

constexpr double xtd::math::e

staticconstexpr

Represents the natural logarithmic base, specified by the constant, e. This field is constant.

Remarks: The value of this field is 2.7182818284590452354.

◆ epsilon

constexpr double xtd::math::epsilon

staticconstexpr

Represents the smallest positive Double value greater than zero. This field is constant.

Remarks: The value of this field is 4.94066e-324.

◆ infinity

constexpr double xtd::math::infinity

staticconstexpr

Represents infinity. This field is constant.

Remarks: The value of this field is std::numeric_limits<double>::infinity().

◆ max_value

constexpr double xtd::math::max_value

staticconstexpr

Represents the largest possible value of double. This field is constant.

Remarks: The value of this field is 1.7976931348623157E+308.

◆ min_value

constexpr double xtd::math::min_value

staticconstexpr

Represents the smallest possible value of double. This field is constant.

Remarks: The value of this field is -1.7976931348623157E+308.

◆ NaN

constexpr double xtd::math::NaN

staticconstexpr

Represents not a number (NaN). This field is constant.

Remarks: The value of this field is std::numeric_limits<double>::quiet_NaN().

◆ negative_infinity

constexpr double xtd::math::negative_infinity

staticconstexpr

Represents negative infinity. This field is constant.

Remarks: The value of this field is -std::numeric_limits<double>::infinity().

◆ pi

constexpr double xtd::math::pi

staticconstexpr

Represents the ratio of the circumference of a circle to its diameter, specified by the constant, π. This field is constant.

Remarks: The value of this field is 3.14159265358979323846.

◆ positive_infinity

constexpr double xtd::math::positive_infinity

staticconstexpr

Represents positive infinity. This field is constant.

Remarks: The value of this field is std::numeric_limits<double>::infinity().

◆ tau

constexpr double xtd::math::tau

staticconstexpr

Represents the number of radians in one turn, specified by the constant, τ.

Remarks: The value of this field is 2.7182818284590451.

The documentation for this class was generated from the following file:

xtd.core/include/xtd/math.h

Definition

Static Public Attributes

Static Public Member Functions

Member Function Documentation

◆ abs() [1/8]

◆ abs() [2/8]

◆ abs() [3/8]

◆ abs() [4/8]

◆ abs() [5/8]

◆ abs() [6/8]

◆ abs() [7/8]

◆ abs() [8/8]

◆ acos()

◆ asin()

◆ atan()

◆ atan2()

◆ big_mul()

◆ ceiling() [1/2]

◆ ceiling() [2/2]

◆ cos()

◆ cosh()

◆ degrees_to_radians()

◆ div_rem() [1/2]

◆ div_rem() [2/2]

◆ exp()

◆ floor() [1/2]

◆ floor() [2/2]

◆ ieee_remainder()

◆ is_infinity()

◆ is_NaN()

◆ is_negative_infinity()

◆ is_positive_infinity()

◆ log() [1/2]

◆ log() [2/2]

◆ log10()

◆ max() [1/13]

◆ max() [2/13]

◆ max() [3/13]

◆ max() [4/13]

◆ max() [5/13]

◆ max() [6/13]

◆ max() [7/13]

◆ max() [8/13]

◆ max() [9/13]

◆ max() [10/13]

◆ max() [11/13]

◆ max() [12/13]

◆ max() [13/13]

◆ min() [1/13]

◆ min() [2/13]

◆ min() [3/13]

◆ min() [4/13]

◆ min() [5/13]

◆ min() [6/13]

◆ min() [7/13]

◆ min() [8/13]

◆ min() [9/13]

◆ min() [10/13]

◆ min() [11/13]

◆ min() [12/13]

◆ min() [13/13]

◆ pow()

◆ radians_to_degrees()

◆ round() [1/4]

◆ round() [2/4]

◆ round() [3/4]

◆ round() [4/4]

◆ sign() [1/8]

◆ sign() [2/8]

◆ sign() [3/8]

◆ sign() [4/8]

◆ sign() [5/8]

◆ sign() [6/8]

◆ sign() [7/8]

◆ sign() [8/8]

◆ sin()

◆ sinh()

◆ sqrt()

◆ tan()

◆ tanh()