Package icyllis.arc3d.core

Class MathUtil

java.lang.Object

icyllis.arc3d.core.MathUtil

Direct Known Subclasses:

MathUtil

public class MathUtil
extends Object

Utility class that provides auxiliary operations.

Field Summary

Fields

Modifier and Type	Field	Description
static final float	DEG_TO_RAD
static final float	EPS
static final float	INV_EPS
static final float	INV_SQRT2
static final float	PATH_TOLERANCE	The tolerance (error) for 2D renderer.
static final float	PI
static final float	PI_O_2
static final float	PI_O_3
static final float	PI_O_4
static final float	PI_O_6
static final float	PI2
static final float	PI3
static final float	PI4
static final float	RAD_TO_DEG
static final float	SQRT2

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	MathUtil()

Method Summary

Modifier and Type	Method	Description
static float	acos(float a)
static int	align2(int a)	Aligns a up to 2 (half-word).
static long	align2(long a)	Aligns a up to 2 (half-word).
static int	align4(int a)	Aligns a up to 4 (word).
static long	align4(long a)	Aligns a up to 4 (word).
static int	align8(int a)	Aligns a up to 8 (double word).
static long	align8(long a)	Aligns a up to 8 (double word).
static int	alignDown(int a, int alignment)
static int	alignTo(int a, int alignment)	Aligns a up to a power of two.
static long	alignTo(long a, long alignment)	Aligns a up to a power of two.
static int	alignUp(int a, int alignment)
static int	alignUpPad(int a, int alignment)
static float	asin(float a)
static float	atan2(float a, float b)
static double	biLerp(double q00, double q10, double q01, double q11, double tx, double ty)	2D bilinear interpolation between four values (a rect).
static float	biLerp(float q00, float q10, float q01, float q11, float tx, float ty)	2D bilinear interpolation between four values (a rect).
static int	ceilLog16(float v)	Returns ceil(log2(sqrt(sqrt(x)))):
static int	ceilLog2(float v)	Returns the log2 of the provided value, were that value to be rounded up to the next power of 2.
static int	ceilLog2(int a)	Returns the log2 of a, were that value to be rounded up to the next power of 2.
static int	ceilLog2(long a)	Returns the log2 of a, were that value to be rounded up to the next power of 2.
static int	ceilLog4(float v)	Returns ceil(log2(sqrt(x))):
static int	ceilPow2(int a)	Returns the smallest power of two greater than or equal to a.
static long	ceilPow2(long a)	Returns the smallest power of two greater than or equal to a.
static double	clamp(double x, double min, double max)	Clamps x between min and max, exactly.
static float	clamp(float x, float min, float max)	Clamps x between min and max, exactly.
static int	clamp(int x, int min, int max)	If x compares less than min, returns min; otherwise if max compares less than x, returns max; otherwise returns x.
static long	clamp(long x, long min, long max)	If x compares less than min, returns min; otherwise if max compares less than x, returns max; otherwise returns x.
static float	cos(float a)
static short	floatToHalf(float f)	Converts the specified single-precision float value into a half-precision float value.
static int	floorLog2(int a)	Returns the log2 of a, were that value to be rounded down to the previous power of 2.
static int	floorLog2(long a)	Returns the log2 of a, were that value to be rounded down to the previous power of 2.
static int	floorPow2(int a)	Returns the largest power of two less than or equal to a.
static long	floorPow2(long a)	Returns the largest power of two less than or equal to a.
static float	frexp(float x, int[] exp)	Decomposes x into a floating-point significand in the range (-1,-0.5], [0.5,1.0), and an integral exponent of two, such that
static float	halfToFloat(short h)	Converts the specified half-precision float value into a single-precision float value.
static boolean	isAlign2(int a)	Returns true if a is a multiple of 2.
static boolean	isAlign2(long a)	Returns true if a is a multiple of 2.
static boolean	isAlign4(int a)	Returns true if a is a multiple of 4.
static boolean	isAlign4(long a)	Returns true if a is a multiple of 4.
static boolean	isAlign8(int a)	Returns true if a is a multiple of 8.
static boolean	isAlign8(long a)	Returns true if a is a multiple of 8.
static boolean	isApproxEqual(float a, float b)
static boolean	isApproxEqual(float a, float b, float tolerance)
static boolean	isApproxZero(float a)
static boolean	isApproxZero(float a, float tolerance)
static boolean	isFinite(float[] values, int offset, int count)	Returns true if all values are finite.
static boolean	isFinite(float v0, float v1, float v2, float v3)	Returns true if all values are finite.
static boolean	isFinite(float v0, float v1, float v2, float v3, float v4, float v5)	Returns true if all values are finite.
static boolean	isFinite(float v0, float v1, float v2, float v3, float v4, float v5, float v6, float v7, float v8)	Returns true if all values are finite.
static boolean	isPow2(int a)	Returns true if a is a power of 2.
static boolean	isPow2(long a)	Returns true if a is a power of 2.
static float	ldexp(float x, int exp)	Composes a floating-point number from x and the corresponding integral exponent of two in exp, resulting
static double	lerp(double a, double b, double t)	Linear interpolation between two values.
static float	lerp(float a, float b, float t)	Linear interpolation between two values.
static double	max(double a, double b, double c)	Component-wise maximum of a vector.
static double	max(double a, double b, double c, double d)	Component-wise maximum of a vector.
static float	max(float a, float b, float c)	Component-wise maximum of a vector.
static float	max(float a, float b, float c, float d)	Component-wise maximum of a vector.
static float	max3(float[] v)	Component-wise maximum of a vector.
static double	median(double a, double b, double c)	Median of three numbers.
static float	median(float a, float b, float c)	Median of three numbers.
static double	min(double a, double b, double c)	Component-wise minimum of a vector.
static double	min(double a, double b, double c, double d)	Component-wise minimum of a vector.
static float	min(float a, float b, float c)	Component-wise minimum of a vector.
static float	min(float a, float b, float c, float d)	Component-wise minimum of a vector.
static float	min3(float[] v)	Component-wise minimum of a vector.
static double	mix(double a, double b, double t)	Linear interpolation between two values, matches GLSL mix intrinsic function.
static float	mix(float a, float b, float t)	Linear interpolation between two values, matches GLSL mix intrinsic function.
static double	pin(double x, double min, double max)	Clamps x between min and max.
static float	pin(float x, float min, float max)	Clamps x between min and max.
static float	sin(float a)
static float	sqrt(float f)
static float	tan(float a)
static double	triLerp(double c000, double c100, double c010, double c110, double c001, double c101, double c011, double c111, double tx, double ty, double tz)	3D trilinear interpolation between eight values (a cuboid).
static float	triLerp(float c000, float c100, float c010, float c110, float c001, float c101, float c011, float c111, float tx, float ty, float tz)	3D trilinear interpolation between eight values (a cuboid).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

PI

public static final float PI

See Also:

• Constant Field Values

PI2

public static final float PI2

See Also:

• Constant Field Values

PI3

public static final float PI3

See Also:

• Constant Field Values

PI4

public static final float PI4

See Also:

• Constant Field Values

PI_O_2

public static final float PI_O_2

See Also:

• Constant Field Values

PI_O_3

public static final float PI_O_3

See Also:

• Constant Field Values

PI_O_4

public static final float PI_O_4

See Also:

• Constant Field Values

PI_O_6

public static final float PI_O_6

See Also:

• Constant Field Values

EPS

public static final float EPS

See Also:

• Constant Field Values

INV_EPS

public static final float INV_EPS

See Also:

• Constant Field Values

DEG_TO_RAD

public static final float DEG_TO_RAD

See Also:

• Constant Field Values

RAD_TO_DEG

public static final float RAD_TO_DEG

See Also:

• Constant Field Values

SQRT2

public static final float SQRT2

See Also:

• Constant Field Values

INV_SQRT2

public static final float INV_SQRT2

See Also:

• Constant Field Values

PATH_TOLERANCE

public static final float PATH_TOLERANCE

The tolerance (error) for 2D renderer.

See Also:

• Constant Field Values

Constructor Details

MathUtil

protected MathUtil()

Method Details

sin

public static float sin(float a)

cos

public static float cos(float a)

tan

public static float tan(float a)

frexp

public static float frexp(float x,
 int[] exp)

Decomposes x into a floating-point significand in the range (-1,-0.5], [0.5,1.0), and an integral exponent of two, such that

x = significand * 2exponent

If x is +- zero, +- Inf, or NaN, returns the input value as-is, and sets exp to 0.

Parameters:

x - the input value

exp - the resulting exponent

Returns:

the resulting significand

ldexp

public static float ldexp(float x,
 int exp)

Composes a floating-point number from x and the corresponding integral exponent of two in exp, resulting

significand * 2exponent

If x is +- zero, +- Inf, or NaN, returns the input value as-is. If overflow or underflow occurs, returns a rounded value.

Parameters:

x - the input significand

exp - the input exponent

Returns:

the resulting value

isApproxZero

public static boolean isApproxZero(float a)

Returns:

true if a is approximately equal to zero

isApproxZero

public static boolean isApproxZero(float a,
 float tolerance)

Returns:

true if a is approximately equal to zero within a given tolerance

isApproxEqual

public static boolean isApproxEqual(float a,
 float b)

Returns:

true if a is approximately equal to b

isApproxEqual

public static boolean isApproxEqual(float a,
 float b,
 float tolerance)

Returns:

true if a is approximately equal to b within a given tolerance

sqrt

public static float sqrt(float f)

asin

public static float asin(float a)

acos

public static float acos(float a)

atan2

public static float atan2(float a,
 float b)

clamp

public static int clamp(int x,
 int min,
 int max)

If x compares less than min, returns min; otherwise if max compares less than x, returns max; otherwise returns x.

Returns:

x clamped between min and max, inclusively.

clamp

public static long clamp(long x,
 long min,
 long max)

If x compares less than min, returns min; otherwise if max compares less than x, returns max; otherwise returns x.

Returns:

x clamped between min and max, inclusively.

clamp

public static float clamp(float x,
 float min,
 float max)

Clamps x between min and max, exactly. If x is NaN, returns NaN.

Returns:

x clamped between min and max

clamp

public static double clamp(double x,
 double min,
 double max)

Clamps x between min and max, exactly. If x is NaN, returns NaN.

Returns:

x clamped between min and max

pin

public static float pin(float x,
 float min,
 float max)

Clamps x between min and max. If x is NaN, returns min. Note the result is incorrect if min is negative zero.

Returns:

x clamped between min and max

pin

public static double pin(double x,
 double min,
 double max)

Clamps x between min and max. If x is NaN, returns min. Note the result is incorrect if min is negative zero.

Returns:

x clamped between min and max

min

public static float min(float a,
 float b,
 float c)

Component-wise minimum of a vector.

min3

public static float min3(float[] v)

Component-wise minimum of a vector.

min

public static double min(double a,
 double b,
 double c)

Component-wise minimum of a vector.

min

public static float min(float a,
 float b,
 float c,
 float d)

Component-wise minimum of a vector.

min

public static double min(double a,
 double b,
 double c,
 double d)

Component-wise minimum of a vector.

max

public static float max(float a,
 float b,
 float c)

Component-wise maximum of a vector.

max3

public static float max3(float[] v)

Component-wise maximum of a vector.

max

public static double max(double a,
 double b,
 double c)

Component-wise maximum of a vector.

max

public static float max(float a,
 float b,
 float c,
 float d)

Component-wise maximum of a vector.

max

public static double max(double a,
 double b,
 double c,
 double d)

Component-wise maximum of a vector.

median

public static float median(float a,
 float b,
 float c)

Median of three numbers.

median

public static double median(double a,
 double b,
 double c)

Median of three numbers.

lerp

public static float lerp(float a,
 float b,
 float t)

Linear interpolation between two values.

lerp

public static double lerp(double a,
 double b,
 double t)

Linear interpolation between two values.

mix

public static float mix(float a,
 float b,
 float t)

Linear interpolation between two values, matches GLSL mix intrinsic function. Slower than lerp(float, float, float) but without intermediate overflow or underflow.

mix

public static double mix(double a,
 double b,
 double t)

Linear interpolation between two values, matches GLSL mix intrinsic function. Slower than lerp(double, double, double) but without intermediate overflow or underflow.

biLerp

public static float biLerp(float q00,
 float q10,
 float q01,
 float q11,
 float tx,
 float ty)

2D bilinear interpolation between four values (a rect).

biLerp

public static double biLerp(double q00,
 double q10,
 double q01,
 double q11,
 double tx,
 double ty)

2D bilinear interpolation between four values (a rect).

triLerp

public static float triLerp(float c000,
 float c100,
 float c010,
 float c110,
 float c001,
 float c101,
 float c011,
 float c111,
 float tx,
 float ty,
 float tz)

3D trilinear interpolation between eight values (a cuboid).

triLerp

public static double triLerp(double c000,
 double c100,
 double c010,
 double c110,
 double c001,
 double c101,
 double c011,
 double c111,
 double tx,
 double ty,
 double tz)

3D trilinear interpolation between eight values (a cuboid).

isFinite

public static boolean isFinite(float v0,
 float v1,
 float v2,
 float v3)

Returns true if all values are finite.

Returns:

true if no member is infinite or NaN

isFinite

public static boolean isFinite(float v0,
 float v1,
 float v2,
 float v3,
 float v4,
 float v5)

Returns true if all values are finite.

Returns:

true if no member is infinite or NaN

isFinite

public static boolean isFinite(float v0,
 float v1,
 float v2,
 float v3,
 float v4,
 float v5,
 float v6,
 float v7,
 float v8)

Returns true if all values are finite.

Returns:

true if no member is infinite or NaN

isFinite

public static boolean isFinite(float[] values,
 int offset,
 int count)

Returns true if all values are finite.

Returns:

true if no member is infinite or NaN

align2

public static int align2(int a)

Aligns a up to 2 (half-word).

align4

public static int align4(int a)

Aligns a up to 4 (word).

align8

public static int align8(int a)

Aligns a up to 8 (double word).

align2

public static long align2(long a)

Aligns a up to 2 (half-word).

align4

public static long align4(long a)

Aligns a up to 4 (word).

align8

public static long align8(long a)

Aligns a up to 8 (double word).

isAlign2

public static boolean isAlign2(int a)

Returns true if a is a multiple of 2. Asserts a >= 0.

isAlign4

public static boolean isAlign4(int a)

Returns true if a is a multiple of 4. Asserts a >= 0.

isAlign8

public static boolean isAlign8(int a)

Returns true if a is a multiple of 8. Asserts a >= 0.

isAlign2

public static boolean isAlign2(long a)

Returns true if a is a multiple of 2. Asserts a >= 0.

isAlign4

public static boolean isAlign4(long a)

Returns true if a is a multiple of 4. Asserts a >= 0.

isAlign8

public static boolean isAlign8(long a)

Returns true if a is a multiple of 8. Asserts a >= 0.

alignTo

public static int alignTo(int a,
 int alignment)

Aligns a up to a power of two.

alignTo

public static long alignTo(long a,
 long alignment)

Aligns a up to a power of two.

alignUp

public static int alignUp(int a,
 int alignment)

alignUpPad

public static int alignUpPad(int a,
 int alignment)

alignDown

public static int alignDown(int a,
 int alignment)

isPow2

public static boolean isPow2(int a)

Returns true if a is a power of 2. Asserts a > 0.

isPow2

public static boolean isPow2(long a)

Returns true if a is a power of 2. Asserts a > 0.

ceilLog2

public static int ceilLog2(int a)

Returns the log2 of a, were that value to be rounded up to the next power of 2. Asserts a > 0. NextLog2.

ceilLog2

public static int ceilLog2(long a)

Returns the log2 of a, were that value to be rounded up to the next power of 2. Asserts a > 0. NextLog2.

ceilPow2

public static int ceilPow2(int a)

Returns the smallest power of two greater than or equal to a. Asserts a > 0 && a <= 2^30. NextPow2.

ceilPow2

public static long ceilPow2(long a)

Returns the smallest power of two greater than or equal to a. Asserts a > 0 && a <= 2^62. NextPow2.

floorLog2

public static int floorLog2(int a)

Returns the log2 of a, were that value to be rounded down to the previous power of 2. Asserts a > 0. PrevLog2.

floorLog2

public static int floorLog2(long a)

Returns the log2 of a, were that value to be rounded down to the previous power of 2. Asserts a > 0. PrevLog2.

floorPow2

public static int floorPow2(int a)

Returns the largest power of two less than or equal to a. Asserts a > 0. PrevPow2.

floorPow2

public static long floorPow2(long a)

Returns the largest power of two less than or equal to a. Asserts a > 0. PrevPow2.

ceilLog2

public static int ceilLog2(float v)

Returns the log2 of the provided value, were that value to be rounded up to the next power of 2. Returns 0 if value invalid input: '<'= 0:
Never returns a negative number, even if value is NaN.

     ceilLog2((-inf..1]) -> 0
     ceilLog2((1..2])    -> 1
     ceilLog2((2..4])    -> 2
     ceilLog2((4..8])    -> 3
     ceilLog2(+inf)      -> 128
     ceilLog2(NaN)       -> 0
 

NextLog2.

ceilLog4

public static int ceilLog4(float v)

Returns ceil(log2(sqrt(x))):

     log2(sqrt(x)) == log2(x^(1/2)) == log2(x)/2 == log2(x)/log2(4) == log4(x)
 

ceilLog16

public static int ceilLog16(float v)

Returns ceil(log2(sqrt(sqrt(x)))):

     log2(sqrt(sqrt(x))) == log2(x^(1/4)) == log2(x)/4 == log2(x)/log2(16) == log16(x)
 

halfToFloat

public static float halfToFloat(short h)

Converts the specified half-precision float value into a single-precision float value. The following special cases are handled:

• If the input is FP16.NaN, the returned value is Float.NaN
• If the input is FP16.POSITIVE_INFINITY or FP16.NEGATIVE_INFINITY, the returned value is respectively Float.POSITIVE_INFINITY or Float.NEGATIVE_INFINITY
• If the input is 0 (positive or negative), the returned value is +/-0.0f
• Otherwise, the returned value is a normalized single-precision float value

Parameters:

h - The half-precision float value to convert to single-precision

Returns:

A normalized single-precision float value

floatToHalf

public static short floatToHalf(float f)

Converts the specified single-precision float value into a half-precision float value. The following special cases are handled:

• If the input is NaN (see Float.isNaN(float)), the returned value is FP16.NaN
• If the input is Float.POSITIVE_INFINITY or Float.NEGATIVE_INFINITY, the returned value is respectively FP16.POSITIVE_INFINITY or FP16.NEGATIVE_INFINITY
• If the input is 0 (positive or negative), the returned value is FP16.POSITIVE_ZERO or FP16.NEGATIVE_ZERO
• If the input is a less than FP16.MIN_VALUE, the returned value is flushed to FP16.POSITIVE_ZERO or FP16.NEGATIVE_ZERO
• If the input is a less than FP16.MIN_NORMAL, the returned value is a denorm half-precision float
• Otherwise, the returned value is rounded to the nearest representable half-precision float value

Parameters:

f - The single-precision float value to convert to half-precision

Returns:

A half-precision float value