maths.h

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#ifndef _MATHS_H_
#define _MATHS_H_


extern const fix32 sintab32[1024];
extern const fix16 sintab16[1024];

extern const fix16 log2tab16[0x10000];
extern const fix16 log10tab16[0x10000];
extern const fix16 sqrttab16[0x10000];


#define min(X, Y)   (((X) < (Y))?(X):(Y))

#define max(X, Y)   (((X) > (Y))?(X):(Y))

#define clamp(X, L, H)   (min(max((X), (L)), (H)))

#if (ENABLE_NEWLIB == 0)

#define abs(X)      (((X) < 0)?-(X):(X))
#endif  // ENABLE_NEWLIB

#ifndef PI

#define PI 3.14159265358979323846
#endif


#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)))

#define intToFix32(value)           ((fix32) ((value) << FIX32_FRAC_BITS))

#define fix32ToInt(value)           ((s32) ((value) >> FIX32_FRAC_BITS))

#define fix32Round(value)           \
    ((fix32Frac(value) > FIX32(0.5))?fix32Int(value + FIX32(1)) + 1:fix32Int(value))

#define fix32ToRoundedInt(value)    \
    ((fix32Frac(value) > FIX32(0.5))?fix32ToInt(value) + 1:fix32ToInt(value))

#define fix32Frac(value)            ((value) & FIX32_FRAC_MASK)

#define fix32Int(value)             ((value) & FIX32_INT_MASK)

#define fix32Add(val1, val2)        ((val1) + (val2))

#define fix32Sub(val1, val2)        ((val1) - (val2))

#define fix32Neg(value)             (0 - (value))

#define fix32Mul(val1, val2)        (((val1) >> (FIX32_FRAC_BITS / 2)) * ((val2) >> (FIX32_FRAC_BITS / 2)))

#define fix32Div(val1, val2)        (((val1) << (FIX32_FRAC_BITS / 2)) / ((val2) >> (FIX32_FRAC_BITS / 2)))

#define fix32Avg(val1, val2)        (((val1) + (val2)) >> 1)

#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)))

#define intToFix16(value)           ((fix16) ((value) << FIX16_FRAC_BITS))

#define fix16ToInt(value)           ((s16) ((value) >> FIX16_FRAC_BITS))

#define fix16Round(value)           \
    ((fix16Frac(value) > FIX16(0.5))?fix16Int(value + FIX16(1)) + 1:fix16Int(value))

#define fix16ToRoundedInt(value)    \
    ((fix16Frac(value) > FIX16(0.5))?fix16ToInt(value) + 1:fix16ToInt(value))

#define fix16Frac(value)            ((value) & FIX16_FRAC_MASK)

#define fix16Int(value)             ((value) & FIX16_INT_MASK)

#define fix16Add(val1, val2)        ((val1) + (val2))

#define fix16Sub(val1, val2)        ((val1) - (val2))

#define fix16Neg(value)             (0 - (value))

#define fix16Mul(val1, val2)        (muls(val1, val2) >> FIX16_FRAC_BITS)

#define fix16Div(val1, val2)        (divs(val1 << FIX16_FRAC_BITS, val2))

#define fix16Avg(val1, val2)        (((val1) + (val2)) >> 1)

#define fix16Log2(v)                log2tab16[v]

#define fix16Log10(v)               log10tab16[v]

#define fix16Sqrt(v)                sqrttab16[v]


#define fix32ToFix16(value)         (((value) << FIX16_FRAC_BITS) >> FIX32_FRAC_BITS)

#define fix16ToFix32(value)         (((value) << FIX32_FRAC_BITS) >> FIX16_FRAC_BITS)

#define sinFix32(value)             sintab32[(value) & 1023]

#define cosFix32(value)             sintab32[((value) + 256) & 1023]

#define sinFix16(value)             sintab16[(value) & 1023]

#define cosFix16(value)             sintab16[((value) + 256) & 1023]


// 2D STUFF

typedef struct
{
    u16 x;
    u16 y;
} Vect2D_u16;

typedef struct
{
    s16 x;
    s16 y;
} Vect2D_s16;

typedef struct
{
    u32 x;
    u32 y;
} Vect2D_u32;

typedef struct
{
    s32 x;
    s32 y;
} Vect2D_s32;

typedef struct
{
    fix16 x;
    fix16 y;
} Vect2D_f16;

typedef struct
{
    fix32 x;
    fix32 y;
} Vect2D_f32;

typedef struct
{
    Vect2D_f16 a;
    Vect2D_f16 b;
} Mat2D_f16;

typedef struct
{
    Vect2D_f32 a;
    Vect2D_f32 b;
} Mat2D_f32;


// 3D STUFF

typedef struct
{
    u16 x;
    u16 y;
    u16 z;
} Vect3D_u16;

typedef struct
{
    s16 x;
    s16 y;
    s16 z;
} Vect3D_s16;

typedef struct
{
    u32 x;
    u32 y;
    u32 z;
} Vect3D_u32;

typedef struct
{
    s32 x;
    s32 y;
    s32 z;
} Vect3D_s32;

typedef struct
{
    fix16 x;
    fix16 y;
    fix16 z;
} Vect3D_f16;

typedef struct
{
    fix32 x;
    fix32 y;
    fix32 z;
} Vect3D_f32;

typedef struct
{
    Vect3D_f16 a;
    Vect3D_f16 b;
    Vect3D_f16 c;
} Mat3D_f16;

typedef struct
{
    Vect3D_f32 a;
    Vect3D_f32 b;
    Vect3D_f32 c;
} Mat3D_f32;


// 4D STUFF

typedef struct
{
    fix16 x;
    fix16 y;
    fix16 z;
    fix16 w;
} Vect4D_f16;

typedef struct
{
    fix32 x;
    fix32 y;
    fix32 z;
    fix32 w;
} Vect4D_f32;

typedef struct
{
    Vect4D_f16 a;
    Vect4D_f16 b;
    Vect4D_f16 c;
    Vect4D_f16 d;
} Mat4D_f16;

typedef struct
{
    Vect4D_f32 a;
    Vect4D_f32 b;
    Vect4D_f32 c;
    Vect4D_f32 d;
} Mat4D_f32;


// short alias

typedef Vect2D_u16 V2u16;
typedef Vect2D_s16 V2s16;
typedef Vect2D_u32 V2u32;
typedef Vect2D_s32 V2s32;
typedef Vect2D_f16 V2f16;
typedef Vect2D_f32 V2f32;

typedef Vect3D_u16 V3u16;
typedef Vect3D_s16 V3s16;
typedef Vect3D_u32 V3u32;
typedef Vect3D_s32 V3s32;
typedef Vect3D_f16 V3f16;
typedef Vect3D_f32 V3f32;

typedef Vect4D_f16 V4f16;
typedef Vect4D_f32 V4f32;

typedef Mat2D_f16 M2f16;
typedef Mat2D_f32 M2f32;
typedef Mat3D_f16 M3f16;
typedef Mat3D_f32 M3f32;
typedef Mat4D_f16 M4f16;
typedef Mat4D_f32 M4f32;


u32 mulu(u16 op1, u16 op2);
s32 muls(s16 op1, s16 op2);
u16 divu(u32 op1, u16 op2);
s16 divs(s32 op1, s16 op2);
u16 modu(u32 op1, u16 op2);
s16 mods(s32 op1, s16 op2);

u32 divmodu(u32 op1, u16 op2);
s32 divmods(s32 op1, s16 op2);

u32 intToBCD(u32 value);

u32 distance_approx(s32 dx, s32 dy);
u32 getApproximatedDistance(s32 dx, s32 dy);
s32 getApproximatedLog2(s32 value);
u16 getLog2Int(u32 value);

u32 getNextPow2(u32 value);


#endif // _MATHS_H_