fast_trig/fast_trig.c

// --------------------------------------------------------------
#define	SINE_TABLE_START_INDEX		2		
#define	COSINE_TABLE_START_INDEX	2		
#define	EXP_TABLE_START_INDEX		0

// --------------------------------------------------------------
#include <math.h>
#include "synth_defs.h"

// Taylor series coefficent for cos(pi*x)
// In this table x is premultiplied with pi!
static const synth_float_t _sg_cos_pmpi_lut[] = 
{
    1.92957430940392e-003,
   -25.8068913900141e-003,
    235.330630358893e-003,
   -1.33526276885459e+000,
    4.05871212641677e+000,
   -4.93480220054468e+000,
    1.00000000000000e+000

};

// Taylor series coefficent for sin(x)
static const synth_float_t _sg_sin_lut[] = 
{
	 1.605904383682161e-010,
	-2.505210838544172e-008,
	 2.755731922398589e-006,
	-1.984126984126984e-004,
	 8.333333333333333e-003,
	-1.666666666666667e-001,
	 1.000000000000000e+000
};

// Taylor series coefficent for sin(x)
static const synth_float_t _sg_cos_lut[] = 
{
	 2.087675698786810e-009,
	-2.755731922398589e-007,
	 2.480158730158730e-005,
	-1.388888888888889e-003,
	 4.166666666666666e-002,
	-5.000000000000000e-001,
	 1.000000000000000e+000
};

// Taylor series coefficent for sin(x)
static const synth_float_t _sg_exp_lut[] = 
{
	1.984126984126984e-004,
	1.388888888888889e-003,
	8.333333333333333e-003,
	4.166666666666666e-002,
	1.666666666666667e-001,
	5.000000000000000e-001,
	1.000000000000000e+000,
	1.000000000000000e+000
};

// --------------------------------------------------------------
// Exported functions
// --------------------------------------------------------------
// Cos (pi*x)
synth_float_t FastTrig_cos_premult_pi(synth_float_t x)
{
	int i, yneg;
	synth_float_t y, xx;

	yneg = 0;

	if (x < 0)
		x = -x;

    if (x > (synth_float_t)0.5)
	{
        if (x > (synth_float_t)1.5)
		{
            x = (synth_float_t)2. - x;
		}
        else
		{
            x = (synth_float_t)1. - x;
            yneg = 1;
		}
	}
	xx = x*x;
	y = _sg_cos_pmpi_lut[0];
	
	for (i=1; i < sizeof(_sg_cos_pmpi_lut)/sizeof(synth_float_t); i++)
		y = y * xx + _sg_cos_pmpi_lut[i];
	
	if (yneg)
		y = -y;

	return y;
}

// sin (x)
// Best in range -0.5*pi .. +0.5*pi
synth_float_t FastTrig_sin(synth_float_t x)
{
	int i = SINE_TABLE_START_INDEX;
	synth_float_t xx, y;

	xx = x*x;
	y = _sg_sin_lut[i++];
	
	for (i=i; i < sizeof(_sg_sin_lut)/sizeof(synth_float_t); i++)
		y = y * xx + _sg_sin_lut[i];

	return y * x;
}

// cos (x)
// Best in range -0.5*pi .. +0.5*pi
synth_float_t FastTrig_cos(synth_float_t x)
{
	int i = COSINE_TABLE_START_INDEX;
	synth_float_t xx, y;

	xx = x*x;
	y = _sg_cos_lut[i++];
	
	for (i=i; i < sizeof(_sg_cos_lut)/sizeof(synth_float_t); i++)
		y = y * xx + _sg_cos_lut[i];

	return y;
}

// exp (x)
synth_float_t FastTrig_exp(synth_float_t x)
{
	int i = EXP_TABLE_START_INDEX;
	synth_float_t y;

	y = _sg_exp_lut[i++];
	
	for (i=i; i < sizeof(_sg_exp_lut)/sizeof(synth_float_t); i++)
		y = y * x + _sg_exp_lut[i];

	return y;
}

// exp (x) - 1
synth_float_t FastTrig_exp_minus_1(synth_float_t x)
{
	int i = EXP_TABLE_START_INDEX;
	synth_float_t y;

	y = _sg_exp_lut[i++];
	
	for (i=i; i < sizeof(_sg_exp_lut)/sizeof(synth_float_t)-1; i++)
		y = y * x + _sg_exp_lut[i];

	return y*x;
}