sine lookup table

sine_lut.c

/**
 * lut.c: quadrature-optimized sine lookup table
 * written in 2014 by william light <wrl@illest.net>
 *
 * This is free and unencumbered software released into the public domain.
 *
 * Anyone is free to copy, modify, publish, use, compile, sell, or
 * distribute this software, either in source code form or as a compiled
 * binary, for any purpose, commercial or non-commercial, and by any
 * means.
 *
 * In jurisdictions that recognize copyright laws, the author or authors
 * of this software dedicate any and all copyright interest in the
 * software to the public domain. We make this dedication for the benefit
 * of the public at large and to the detriment of our heirs and
 * successors. We intend this dedication to be an overt act of
 * relinquishment in perpetuity of all present and future rights to this
 * software under copyright law.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 * IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
 * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
 * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 * OTHER DEALINGS IN THE SOFTWARE.
 *
 * For more information, please refer to <http://unlicense.org/>
 */

#include <stdint.h>
#include <math.h>

/* tweak TABLE_BITS if you need a smaller table */
#define TABLE_BITS 8
#define TABLE_SIZE (1 << TABLE_BITS)

float lut[TABLE_SIZE + 1];

void
lut_init(void)
{
	int i;

	for (i = 0; i < TABLE_SIZE + 1; i++)
		lut[i] = sin(M_PI_2 * (i / (float) TABLE_SIZE));
}

float
lut_sinf(uint32_t phase)
{
	uint32_t quad_phase;
	int table_loc;
	float x, y[2];

	/* strict aliasing blah blah blah (otherwise gcc will complain if we
	 * do this by type-punning) */
	union {
		float f;
		uint32_t i;
	} out;

	/* if we're in the second or fourth quadrant, run the phase backwards */
	quad_phase = (phase & 0x40000000) ? ~phase : phase;

	/* integer part for table index */
	table_loc = (quad_phase & 0x3FFFFFFF) >> (30 - TABLE_BITS);
	y[0] = lut[table_loc];
	y[1] = lut[table_loc + 1];

	/* fractional part for linear interpolation */
	x = (quad_phase & ((1 << (30 - TABLE_BITS)) - 1)) / (float) (1 << (30 - TABLE_BITS));
	out.f = y[0] + ((y[1] - y[0]) * x);

	/* invert the second half of the wave by manually
	 * setting the float's sign bit */
	out.i |= phase & 0x80000000;
	return out.f;
}

where do you get the actual lookup table from?

it's one quarter of a sine wave – so, sin(x) where x is from 0 to pi/2.