Mathematical methods. More...

Classes
struct	Vect2D_u16
	2D Vector structure - u16 type. More...
struct	Vect2D_s16
	2D Vector structure - s16 type. More...
struct	Vect2D_u32
	2D Vector structure - u32 type. More...
struct	Vect2D_s32
	2D Vector structure - s32 type. More...
struct	Vect2D_f16
	2D Vector structure - f16 (fix16) type. More...
struct	Vect2D_f32
	2D Vector structure - f32 (fix32) type. More...
struct	Mat2D_f16
	2x2 Matrice structure - f16 (fix16) type. Internally uses 2 2D vectors. More...
struct	Mat2D_f32
	2x2 Matrice structure - f32 (fix32) type. Internally uses 2 2D vectors. More...
struct	Vect3D_u16
	3D Vector structure - u16 type. More...
struct	Vect3D_s16
	3D Vector structure - s16 type. More...
struct	Vect3D_u32
	3D Vector structure - u32 type. More...
struct	Vect3D_s32
	3D Vector structure - s32 type. More...
struct	Vect3D_f16
	3D Vector structure - f16 (fix16) type. More...
struct	Vect3D_f32
	3D Vector structure - f32 (fix32) type. More...
struct	Mat3D_f16
	3x3 Matrice structure - f16 (fix16) type. Internally uses 3 3D vectors. More...
struct	Mat3D_f32
	3x3 Matrice structure - f32 (fix32) type. Internally uses 3 3D vectors. More...
struct	Vect4D_f16
	4D Vector structure - f16 (fix16) type. More...
struct	Vect4D_f32
	4D Vector structure - f32 (fix32) type. More...
struct	Mat4D_f16
	4x4 Matrice structure - f16 (fix16) type. Internally uses 4 4D vectors. More...
struct	Mat4D_f32
	4x4 Matrice structure - f32 (fix32) type. Internally uses 4 4D vectors. More...
Defines
#define	min(X, Y) (((X) < (Y))?(X):(Y))
	Returns the lowest value between X an Y.
#define	max(X, Y) (((X) > (Y))?(X):(Y))
	Returns the highest value between X an Y.
#define	clamp(X, L, H) (min(max((X), (L)), (H)))
	Returns L if X is less than L, H if X is greater than H or X if in between L and H.
#define	abs(X) (((X) < 0)?-(X):(X))
	Returns the absolute value of X.
#define	PI 3.14159265358979323846
	PI number (3,1415..)
#define	FIX32_INT_BITS 22
#define	FIX32_FRAC_BITS (32 - FIX32_INT_BITS)
#define	FIX32_INT_MASK (((1 << FIX32_INT_BITS) - 1) << FIX32_FRAC_BITS)
#define	FIX32_FRAC_MASK ((1 << FIX32_FRAC_BITS) - 1)
#define	FIX32(value) ((fix32) ((value) * (1 << FIX32_FRAC_BITS)))
	Convert specified value to fix32.
#define	intToFix32(value) ((fix32) ((value) << FIX32_FRAC_BITS))
	Convert integer to fix32.
#define	fix32ToInt(value) ((s32) ((value) >> FIX32_FRAC_BITS))
	Convert fix32 to integer.
#define	fix32Round(value) ((fix32Frac(value) > FIX32(0.5))?fix32Int(value + FIX32(1)) + 1:fix32Int(value))
	Round the specified value to nearest integer (fix32).
#define	fix32ToRoundedInt(value) ((fix32Frac(value) > FIX32(0.5))?fix32ToInt(value) + 1:fix32ToInt(value))
	Round and convert the specified fix32 value to integer.
#define	fix32Frac(value) ((value) & FIX32_FRAC_MASK)
	Return fractional part of the specified value (fix32).
#define	fix32Int(value) ((value) & FIX32_INT_MASK)
	Return integer part of the specified value (fix32).
#define	fix32Add(val1, val2) ((val1) + (val2))
	Compute and return the result of the addition of val1 and val2 (fix32).
#define	fix32Sub(val1, val2) ((val1) - (val2))
	Compute and return the result of the substraction of val2 from val1 (fix32).
#define	fix32Neg(value) (0 - (value))
	Return negate of specified value (fix32).
#define	fix32Mul(val1, val2) (((val1) >> (FIX32_FRAC_BITS / 2)) * ((val2) >> (FIX32_FRAC_BITS / 2)))
	Compute and return the result of the multiplication of val1 and val2 (fix32). WARNING: result can easily overflow so its recommended to stick with fix16 type for mul and div operations.
#define	fix32Div(val1, val2) (((val1) << (FIX32_FRAC_BITS / 2)) / ((val2) >> (FIX32_FRAC_BITS / 2)))
	Compute and return the result of the division of val1 by val2 (fix32). WARNING: result can easily overflow so its recommended to stick with fix16 type for mul and div operations.
#define	fix32Avg(val1, val2) (((val1) + (val2)) >> 1)
	Compute and return the result of the average of val1 by val2 (fix32).
#define	FIX16_INT_BITS 10
#define	FIX16_FRAC_BITS (16 - FIX16_INT_BITS)
#define	FIX16_INT_MASK (((1 << FIX16_INT_BITS) - 1) << FIX16_FRAC_BITS)
#define	FIX16_FRAC_MASK ((1 << FIX16_FRAC_BITS) - 1)
#define	FIX16(value) ((fix16) ((value) * (1 << FIX16_FRAC_BITS)))
	Convert specified value to fix16.
#define	intToFix16(value) ((fix16) ((value) << FIX16_FRAC_BITS))
	Convert integer to fix16.
#define	fix16ToInt(value) ((s16) ((value) >> FIX16_FRAC_BITS))
	Convert fix16 to integer.
#define	fix16Round(value) ((fix16Frac(value) > FIX16(0.5))?fix16Int(value + FIX16(1)) + 1:fix16Int(value))
	Round the specified value to nearest integer (fix16).
#define	fix16ToRoundedInt(value) ((fix16Frac(value) > FIX16(0.5))?fix16ToInt(value) + 1:fix16ToInt(value))
	Round and convert the specified fix16 value to integer.
#define	fix16Frac(value) ((value) & FIX16_FRAC_MASK)
	Return fractional part of the specified value (fix16).
#define	fix16Int(value) ((value) & FIX16_INT_MASK)
	Return integer part of the specified value (fix16).
#define	fix16Add(val1, val2) ((val1) + (val2))
	Compute and return the result of the addition of val1 and val2 (fix16).
#define	fix16Sub(val1, val2) ((val1) - (val2))
	Compute and return the result of the substraction of val2 from val1 (fix16).
#define	fix16Neg(value) (0 - (value))
	Return negate of specified value (fix16).
#define	fix16Mul(val1, val2) (muls(val1, val2) >> FIX16_FRAC_BITS)
	Compute and return the result of the multiplication of val1 and val2 (fix16).
#define	fix16Div(val1, val2) (divs(val1 << FIX16_FRAC_BITS, val2))
	Compute and return the result of the division of val1 by val2 (fix16).
#define	fix16Avg(val1, val2) (((val1) + (val2)) >> 1)
	Compute and return the result of the average of val1 by val2 (fix16).
#define	fix16Log2(v) log2tab16[v]
	Compute and return the result of the Log2 of specified value (fix16).
#define	fix16Log10(v) log10tab16[v]
	Compute and return the result of the Log10 of specified value (fix16).
#define	fix16Sqrt(v) sqrttab16[v]
	Compute and return the result of the root square of specified value (fix16).
#define	fix32ToFix16(value) (((value) << FIX16_FRAC_BITS) >> FIX32_FRAC_BITS)
	Convert specified fix32 value to fix16.
#define	fix16ToFix32(value) (((value) << FIX32_FRAC_BITS) >> FIX16_FRAC_BITS)
	Convert specified fix16 value to fix32.
#define	sinFix32(value) sintab32[(value) & 1023]
	Compute sinus of specified value and return it as fix32. The input value is an integer defined as [0..1024] range corresponding to radian [0..2PI] range.
#define	cosFix32(value) sintab32[((value) + 256) & 1023]
	Compute cosinus of specified value and return it as fix32. The input value is an integer defined as [0..1024] range corresponding to radian [0..2PI] range.
#define	sinFix16(value) sintab16[(value) & 1023]
	Compute sinus of specified value and return it as fix16. The input value is an integer defined as [0..1024] range corresponding to radian [0..2PI] range.
#define	cosFix16(value) sintab16[((value) + 256) & 1023]
	Compute cosinus of specified value and return it as fix16. The input value is an integer defined as [0..1024] range corresponding to radian [0..2PI] range.
Typedefs
typedef Vect2D_u16	V2u16
	alias for Vect2D_u16
typedef Vect2D_s16	V2s16
	alias for Vect2D_s16
typedef Vect2D_u32	V2u32
	alias for Vect2D_u32
typedef Vect2D_s32	V2s32
	alias for Vect2D_s32
typedef Vect2D_f16	V2f16
	alias for Vect2D_f16
typedef Vect2D_f32	V2f32
	alias for Vect2D_f32
typedef Vect3D_u16	V3u16
	alias for Vect3D_u16
typedef Vect3D_s16	V3s16
	alias for Vect3D_s16
typedef Vect3D_u32	V3u32
	alias for Vect3D_u32
typedef Vect3D_s32	V3s32
	alias for Vect3D_s32
typedef Vect3D_f16	V3f16
	alias for Vect3D_f16
typedef Vect3D_f32	V3f32
	alias for Vect3D_f32
typedef Vect4D_f16	V4f16
	alias for Vect4D_f16
typedef Vect4D_f32	V4f32
	alias for Vect4D_f32
typedef Mat2D_f16	M2f16
	alias for Mat2D_f16
typedef Mat2D_f32	M2f32
	alias for Mat2D_f32
typedef Mat3D_f16	M3f16
	alias for Mat3D_f16
typedef Mat3D_f32	M3f32
	alias for Mat3D_f32
typedef Mat4D_f16	M4f16
	alias for Mat4D_f16
typedef Mat4D_f32	M4f32
	alias for Mat4D_f32
Functions
u32	mulu (u16 op1, u16 op2)
	16x16=32 unsigned multiplication. Force GCC to use proper 68000 mulu instruction.
s32	muls (s16 op1, s16 op2)
	16x16=32 signed multiplication. Force GCC to use proper 68000 muls instruction.
u16	divu (u32 op1, u16 op2)
	Direct divu instruction (unsigned 32/16=16:16) access using inline assembly to process op1/op2 operation.
s16	divs (s32 op1, s16 op2)
	Direct divs instruction (signed 32/16=16:16) access using inline assembly to process op1/op2 operation.
u16	modu (u32 op1, u16 op2)
	Direct divu instruction (unsigned 32/16=16:16) access using inline assembly.
s16	mods (s32 op1, s16 op2)
	Direct divs instruction (signed 32/16=16:16) access using inline assembly.
u32	divmodu (u32 op1, u16 op2)
	Direct divu instruction (unsigned 32/16=16:16) access using inline assembly to process op1/op2 operation and op1op2 at same time.
s32	divmods (s32 op1, s16 op2)
	Direct divs instruction (signed 32/16=16:16) access using inline assembly to process op1/op2 operation and op1op2 at same time.
u32	intToBCD (u32 value)
	Binary to Decimal conversion.
u32	distance_approx (s32 dx, s32 dy)
u32	getApproximatedDistance (s32 dx, s32 dy)
	Return euclidean distance approximation for specified vector. The returned distance is not 100% perfect but calculation is fast.
s32	getApproximatedLog2 (s32 value)
	Return 16.16 fixed point approximation of log2 of the specified 16.16 fixed point value. Ex: getLog2(1 << 16) = 0 getLog2(12345 << 16) = ~9.5 (real value = ~13.6)
u16	getLog2Int (u32 value)
	Return integer log2 of specified 32 bits unsigned value. Ex: getLog2Int(1024) = 10 getLog2Int(12345) = 13
u32	getNextPow2 (u32 value)
	Return next pow2 value which is greater than specified 32 bits unsigned value. Ex: getNextPow2(700) = 1024 getNextPow2(18) = 32
Variables
const fix32	sintab32 [1024]
const fix16	sintab16 [1024]
const fix16	log2tab16 [0x10000]
const fix16	log10tab16 [0x10000]
const fix16	sqrttab16 [0x10000]

Detailed Description

Mathematical methods.

Author:: Stephane Dallongeville

Date:: 08/2011

This unit provides basic maths methods.
You can find a tutorial about how use maths with SGDK here.

Define Documentation

#define FIX16 ( value ) ((fix16) ((value) * (1 << FIX16_FRAC_BITS)))

Convert specified value to fix16.

EX:
f16 v = FIX16(-27.12);

#define FIX32 ( value ) ((fix32) ((value) * (1 << FIX32_FRAC_BITS)))

Convert specified value to fix32.

EX:
f32 v = FIX32(34.567);

Function Documentation

u32 distance_approx	(	s32	dx,
		s32	dy
	)

Deprecated:: Use getApproximatedDistance(..) instead.

s32 divmods	(	s32	op1,
		s16	op2
	)

Direct divs instruction (signed 32/16=16:16) access using inline assembly to process op1/op2 operation and op1op2 at same time.

Parameters:

op1	first operand - dividende (32 bit)
op2	second operand - divisor (16 bit)

Returns:: 16 bit (signed) result of the division in low 16 bit (0-15) and 16 bit (signed) result of the modulo operation in high 16 bit (16-31)

u32 divmodu	(	u32	op1,
		u16	op2
	)

Direct divu instruction (unsigned 32/16=16:16) access using inline assembly to process op1/op2 operation and op1op2 at same time.

Parameters:

op1	first operand - dividende (32 bit)
op2	second operand - divisor (16 bit)

Returns:: 16 bit (unsigned) result of the division in low 16 bit (0-15) and 16 bit (unsigned) result of the modulo operation in high 16 bit (16-31)

s16 divs	(	s32	op1,
		s16	op2
	)

Direct divs instruction (signed 32/16=16:16) access using inline assembly to process op1/op2 operation.

Parameters:

op1	first operand (32 bit)
op2	second operand (16 bit)

Returns:: 16 bit (signed) result of the division

u16 divu	(	u32	op1,
		u16	op2
	)

Direct divu instruction (unsigned 32/16=16:16) access using inline assembly to process op1/op2 operation.

Parameters:

op1	first operand - dividende (32 bit)
op2	second operand - divisor (16 bit)

Returns:: 16 bit (unsigned) result of the division

u32 getApproximatedDistance	(	s32	dx,
		s32	dy
	)

Return euclidean distance approximation for specified vector.
The returned distance is not 100% perfect but calculation is fast.

Parameters:

dx	delta X.
dy	delta Y.

s32 getApproximatedLog2 ( s32 value )

Return 16.16 fixed point *approximation* of log2 of the specified 16.16 fixed point value. Ex:
getLog2(1 << 16) = 0
getLog2(12345 << 16) = ~9.5 (real value = ~13.6)

Parameters:

value 16.16 fixed point value to return log2 of

u16 getLog2Int ( u32 value )

Return integer log2 of specified 32 bits unsigned value. Ex:
getLog2Int(1024) = 10
getLog2Int(12345) = 13

Parameters:

value value to return log2 of

u32 getNextPow2 ( u32 value )

Return next pow2 value which is greater than specified 32 bits unsigned value. Ex:
getNextPow2(700) = 1024
getNextPow2(18) = 32

Parameters:

value value to return next pow2

u32 intToBCD ( u32 value )

Binary to Decimal conversion.

Parameters:

value Value to convert.

s16 mods	(	s32	op1,
		s16	op2
	)

Direct divs instruction (signed 32/16=16:16) access using inline assembly.

Parameters:

op1	first operand (32 bit)
op2	second operand (16 bit)

Returns:: 16 bit (signed) modulo result of the division

u16 modu	(	u32	op1,
		u16	op2
	)

Direct divu instruction (unsigned 32/16=16:16) access using inline assembly.

Parameters:

op1	first operand (32 bit)
op2	second operand (16 bit)

Returns:: 16 bit (unsigned) modulo result of the division

s32 muls	(	s16	op1,
		s16	op2
	)

16x16=32 signed multiplication. Force GCC to use proper 68000 muls instruction.

Parameters:

op1	first operand
op2	second operand

Returns:: 32 bit (signed) result of multiply

u32 mulu	(	u16	op1,
		u16	op2
	)

16x16=32 unsigned multiplication. Force GCC to use proper 68000 mulu instruction.

Parameters:

op1	first operand
op2	second operand

Returns:: 32 bit (unsigned) result of multiply

Classes

Defines

Typedefs

Functions

Variables

Detailed Description

Define Documentation

Function Documentation