# Fixed point math [Math]

## Defines

#define FIX_SHIFT   8
#define FIX_SCALE   ( 1<<FIX_SHIFT )
#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)
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.

## 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 = 2fp 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!