fp_math.h

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#ifndef _FP_MATH_H_
#define _FP_MATH_H_
 
#include <stdint.h>
#include <stdbool.h>
 
typedef int16_t q8_8;   
typedef int32_t q24_8;  
typedef int32_t q16_16; 
typedef int32_t q8_24;  
 
typedef uint16_t uq8_8;   
typedef uint32_t uq24_8;  
typedef uint32_t uq16_16; 
typedef uint32_t uq8_24;  
 
#define FRAC_BITS        8                      
#define Q24_8_DECI_MASK  ((1 << FRAC_BITS) - 1) 
#define Q24_8_WHOLE_MASK (~Q24_8_DECI_MASK)     
 
#define Q16_16_FRAC_BITS  16                            
#define Q16_16_DECI_MASK  ((1 << Q16_16_FRAC_BITS) - 1) 
#define Q16_16_WHOLE_MASK (~Q16_16_DECI_MASK)           
 
#define Q8_24_FRAC_BITS  24                           
#define Q8_24_DECI_MASK  ((1 << Q8_24_FRAC_BITS) - 1) 
#define Q8_24_WHOLE_MASK (~Q8_24_DECI_MASK)           
 
typedef struct
{
    q24_8 x; 
    q24_8 y; 
} vec_q24_8;
 
//==============================================================================
// Fixed Point Math Functions
//==============================================================================
 
void fastNormVec(q24_8* xp, q24_8* yp);
 
vec_q24_8 fpvAdd(vec_q24_8 a, vec_q24_8 b);
vec_q24_8 fpvSub(vec_q24_8 a, vec_q24_8 b);
vec_q24_8 fpvMulSc(vec_q24_8 vec, q24_8 scalar);
vec_q24_8 fpvDivSc(vec_q24_8 vec, q24_8 scalar);
 
q24_8 fpvDot(vec_q24_8 a, vec_q24_8 b);
q24_8 fpvSqMag(vec_q24_8 a);
vec_q24_8 fpvNorm(vec_q24_8 vec);
 
float fixToFloat(q24_8 fx);
 
// Switch to use macros or inline functions
#define FP_MATH_DEFINES
 
#ifdef FP_MATH_DEFINES
 
    #define TO_FX(in) ((in) * (1 << FRAC_BITS))
 
    #define FROM_FX(in) ((in) >> FRAC_BITS)
 
    #define ADD_FX(a, b) ((a) + (b))
 
    #define SUB_FX(a, b) ((a) - (b))
 
    #define MUL_FX(a, b) (((a) * (b)) >> FRAC_BITS)
 
    #define DIV_FX(a, b) (((a) << FRAC_BITS) / (b))
 
    #define FLOOR_FX(a) ((a) & (~((1 << FRAC_BITS) - 1)))
 
    #define TO_FX_FRAC(num, denom) DIV_FX(num, denom)
 
#else
 
static inline q24_8 TO_FX(uint32_t in)
{
    return (q24_8)(in * (1 << FRAC_BITS));
}
 
static inline int32_t FROM_FX(q24_8 in)
{
    return in / (1 << FRAC_BITS);
}
 
static inline q24_8 ADD_FX(q24_8 a, q24_8 b)
{
    return a + b;
}
 
static inline q24_8 SUB_FX(q24_8 a, q24_8 b)
{
    return a - b;
}
 
static inline q24_8 MUL_FX(q24_8 a, q24_8 b)
{
    // could be simpler without rounding
    return ((a * b) + (1 << (FRAC_BITS - 1))) / (1 << FRAC_BITS);
}
 
static inline q24_8 DIV_FX(q24_8 a, q24_8 b)
{
    return ((a * (1 << FRAC_BITS)) / b);
}
 
static inline q24_8 FLOOR_FX(q24_8 a)
{
    return a & (~((1 << FRAC_BITS) - 1));
}
 
// #define FMT_FX    "%s%d.%03d"
// #define STR_FX(x) ((x) < 0 ? "-" : ""), ABS(FROM_FX(x)), DEC_PART(x)
 
// static inline int32_t DEC_PART(q24_8 in)
// {
//     return (1000 * (int32_t)(ABS(in) & ((1 << FRAC_BITS) - 1))) / (1 << FRAC_BITS);
// }
#endif
 
#endif