/*-
 * Copyright (c) 2005 Colin Percival
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted providing that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Redistributions of source code must ensure that the list of
 *    copyright notices is complete, and the lack of a copyright notice
 *    corresponding to a copyrightable contribution or modification may
 *    be taken as an affirmative statement that said contribution or
 *    modification has been placed in the public domain.
 * 4. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *      This product includes software developed by Colin Percival.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */
/*
 * $Id: roots.h,v 1.2 2005/07/11 11:31:39 cperciva Exp $
 */

#ifndef _TRICL_ROOTS_H_
#define _TRICL_ROOTS_H_

/**T
The value {\em TRICL\_ROOTS\_SQRTHALF} is the correctly rounded double 
precision value of $\sqrt{1 / 2}$.  It is approximately $0.435 \cdot 
2^{-53}$ larger than the exact value.
*/
#define TRICL_ROOTS_SQRTHALF	0x1.6A09E667F3BCDp-1

/**T
For inputs $2 \leq n \leq 29$, {\em tricl\_roots\_makelut} computes the 
value $\exp(2 \pi i k / 2^n)$ for all values ${0 \leq k < 2^{n - 2}}$, 
and stores the real part into {\em LUT}[$2 k$] and the imaginary part 
into {\em LUT}[$2 k + 1$].  {\em LUT} must be a pointer to sufficient 
space to store $2^{n - 1}$ doubles.

The complex values stored are within $1.5 \cdot 2^{-53}$ of the exact 
values.
*/
void tricl_roots_makelut(double * LUT, int n);

#endif /* !_TRICL_ROOTS_H_ */