sin_aprox.h

#pragma once

//
#define uint32 unsigned int
#define sint32   signed int
#define uint16 unsigned short
#define sint16   signed short
#define uint8  unsigned char

// 16 bit sin tables
extern uint16 sin_16_512[];
extern uint16 sin_16_256[];
extern uint16 sin_16_128[];

// 8 bit sin tables
extern uint8  sin_8_512 [];
extern uint8  sin_8_256 [];
extern uint8  sin_8_128 [];

//
#define fpsin( X ) sin_aprox_16bit( X )
#define fpcos( X ) cos_aprox_16bit( X )


// integer sin aproximation
// input  range [-0x80, +0x80] wrapped if exeeds
// output tange [-0x80, +0x80]
inline sint32 sin_aprox_8bit( sint32 x )
{
    // wrap into range
    x = ((x+0x80) & 0xFF) - 0x80;
    // ax = absolute value
    sint32 ax = (x > 0) ? x : -x;
    return ((x << 2) - (((x << 2) * ax ) >> 7));
}

// integer sin aproximation
// input  range [-0x80, +0x80] wrapped if exeeds
// output tange [-0x80, +0x80]
inline sint32 cos_aprox_8bit( sint32 x )
{
    // wrap into range
    x += 0x40;
    x = ((x+0x80) & 0xFF) - 0x80;
    // ax = absolute value
    sint32 ax = (x > 0) ? x : -x;
    return ((x << 2) - (((x << 2) * ax ) >> 7));
}

// integer sin aproximation
// input  range [-0x8000, +0x8000] wrapped if exeeds
// output tange [-0x8000, +0x8000]
inline sint32 sin_aprox_16bit( sint32 x )
{
    // wrap into range
    x = ((x+0x8000) & 0xFFFF) - 0x8000;
    // ax = absolute value
    sint32 ax = (x > 0) ? x : -x;
    sint32 y  = (x - ((x * (ax >> 2) ) >> 13));
    return y << 2;
}

// integer cos aproximation
// input  range [-0x8000, +0x8000] wrapped if exeeds
// output tange [-0x8000, +0x8000]
inline sint32 cos_aprox_16bit( sint32 x )
{
    // wrap into range
    x += 0x4000;
    x  = ((x+0x8000) & 0xFFFF) - 0x8000;
    // ax = absolute value
    sint32 ax = (x > 0) ? x : -x;
    sint32 y  = (x - ((x * (ax >> 2) ) >> 13));
    return y << 2;
}

// fixed point, unsigned, quantised, 16 bit 512 sample sin table lookup
// input  is a 16 bit value unsigned
// output is a 16 bit value unsigned
inline uint16 qi_sin_u_16_512( uint32 index )
{
    // bound and shift index
    index = (index & 0xFFFF) >> 7;
    // index the table
    return sin_16_512[ index ];
}

// fixed point, signed, quantised, 16 bit, 512 sample sin table lookup
inline sint16 qi_sin_s_16_512( uint32 index )
{
    // bound and shift index
    index = (index & 0xFFFF) >> 7;
    // index the table
    return (sint32)(sin_16_512[ index ]) - 0x8000;
}

// fixed point, unsigned quantised, 8 bit 128 sample sin table lookup
// input  is a 16 bit value unsigned
// output is a 16 bit value unsigned
inline uint16 qi_sin_u_08_128( uint32 index )
{
    // bound and shift index
    index = (index & 0xFFFF) >> 9;
    // index table and shift
    return sin_8_128[ index ] << 8;
}

// fixed point, unsigned, linear interpolation, 8 bit 128 sample sin table lookup
// input  is a 16 bit value unsigned
// output is a 16 bit value unsigned
inline uint16 li_sin_u_08_128( uint32 index )
{
    //
    uint8 i1 =  (index>>9)    & 0x7F;
    uint8 i2 = ((index>>9)+1) & 0x7F;
    uint8 f  =  (index>>1)    & 0xFF;
    //
    i1 = sin_8_128[ i1 ];
    i2 = sin_8_128[ i2 ];
    //
    return ( ((uint32)i1) * (0x100-f) + ((uint32)i2 * f) );
}

// fixed point, unsigned, linear interpolation, 8 bit 128 sample cos table lookup
// input  is a 16 bit value unsigned
// output is a 16 bit value unsigned
inline uint16 li_cos_u_08_128( uint32 index )
{
    // adjust into next quadrant
    index += 0x4000;
    //
    uint8 i1 =  (index>>9)    & 0x7F;
    uint8 i2 = ((index>>9)+1) & 0x7F;
    uint8 f  =  (index>>1)    & 0xFF;
    //
    i1 = sin_8_128[ i1 ];
    i2 = sin_8_128[ i2 ];
    //
    return ( ((uint32)i1) * (0x100-f) + ((uint32)i2 * f) );
}


// fixed point, unsigned, linear interpolation, 8 bit 128 sample sin table lookup
// input  is a 16 bit value unsigned
// output is a 16 bit value unsigned
inline sint16 li_sin_s_08_128( uint32 index )
{
    // find indices and fraction
    uint8 i1 =  (index>>9)    & 0x7F;
    uint8 i2 = ((index>>9)+1) & 0x7F;
    uint8 f  =  (index>>1)    & 0xFF;
    // index the array
    i1 = sin_8_128[ i1 ];
    i2 = sin_8_128[ i2 ];
    // linear interpolate value
    sint32 v = ( ((uint32)i1) * (0x100-f) + ((uint32)i2 * f) );
    // adjust into signed region
    return v - 0x8000;
}

// fixed point, unsigned, linear interpolation, 8 bit 128 sample cos table lookup
// input  is a 16 bit value unsigned
// output is a 16 bit value unsigned
inline sint16 li_cos_s_08_128( uint32 index )
{
    // adjust into next quadrant
    index += 0x4000;
    // find indices and fraction
    uint8 i1 =  (index>>9)    & 0x7F;
    uint8 i2 = ((index>>9)+1) & 0x7F;
    uint8 f  =  (index>>1)    & 0xFF;
    // index the array
    i1 = sin_8_128[ i1 ];
    i2 = sin_8_128[ i2 ];
    // linear interpolate value
    sint32 v = ( ((uint32)i1) * (0x100-f) + ((uint32)i2 * f) );
    // adjust into signed region
    return v - 0x8000;
}