Fixed point math
[Math]

Defines
#define	FIX_SHIFT   8
#define	FIX_SCALE   ( 1<<FIX_SHIFT )
#define	FIX_MASK   ( FIX_SCALE-1 )
#define	FIX_SCALEF   ( (float)FIX_SCALE )
#define	FIX_SCALEF_INV   ( 1.0/FIX_SCALEF )
#define	FIX_ONE   FIX_SCALE
#define	FX_RECIPROCAL(a, fp)   ( ((1<<(fp))+(a)-1)/(a) )
	Get the fixed point reciprocal of a, in fp fractional bits.
#define	FX_RECIMUL(x, a, fp)   ( ((x)*((1<<(fp))+(a)-1)/(a))>>(fp) )
	Perform the division x/ a by reciprocal multiplication.
Functions
INLINE FIXED	int2fx (int d)
	Convert an integer to fixed-point.
INLINE FIXED	float2fx (float f)
	Convert a float to fixed-point.
INLINE u32	fx2uint (FIXED fx)
	Convert a FIXED point value to an unsigned integer (orly?).
INLINE u32	fx2ufrac (FIXED fx)
	Get the unsigned fractional part of a fixed point value (orly?).
INLINE int	fx2int (FIXED fx)
	Convert a FIXED point value to an signed integer.
INLINE float	fx2float (FIXED fx)
	Convert a fixed point value to floating point.
INLINE FIXED	fxadd (FIXED fa, FIXED fb)
	Add two fixed point values.
INLINE FIXED	fxsub (FIXED fa, FIXED fb)
	Subtract two fixed point values.
INLINE FIXED	fxmul (FIXED fa, FIXED fb)
	Multiply two fixed point values.
INLINE FIXED	fxdiv (FIXED fa, FIXED fb)
	Divide two fixed point values.
INLINE FIXED	fxmul64 (FIXED fa, FIXED fb)
	Multiply two fixed point values using 64bit math.
INLINE FIXED	fxdiv64 (FIXED fa, FIXED fb)
	Divide two fixed point values using 64bit math.

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Detailed Description

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Define Documentation

#define FIX_SHIFT   8

#define FX_RECIMUL	(	x,
		a,
		fp		)	( ((x)*((1<<(fp))+(a)-1)/(a))>>(fp) )

Perform the division x/ a by reciprocal multiplication.

Division is slow, but you can approximate division by a constant by multiplying with its reciprocal: x/a vs x*(1/a). This routine gives the reciprocal of a as a fixed point number with fp fractional bits.

Parameters:

	a	Value to take the reciprocal of.
	fp	Number of fixed point bits

Note:

The routine does do a division, but the compiler will optimize it to a single constant ... if both a and fp are constants!

Rules for safe reciprocal division, using n = 2^fp and m = (n+a-1)/a (i.e., rounding up)

• Maximum safe numerator x: x < n/(m*a-n)
• Minimum n for known x: n > x*(a-1)

#define FX_RECIPROCAL	(	a,
		fp		)	( ((1<<(fp))+(a)-1)/(a) )

Get the fixed point reciprocal of a, in fp fractional bits.

Parameters:

	a	Value to take the reciprocal of.
	fp	Number of fixed point bits

Note:

The routine does do a division, but the compiler will optimize it to a single constant ... if both a and fp are constants!

See also:

FX_RECIMUL

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