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+/*
+ * Copyright (c) 1999-2000 Image Power, Inc. and the University of
+ *   British Columbia.
+ * Copyright (c) 2001-2002 Michael David Adams.
+ * All rights reserved.
+ */
+
+/* __START_OF_JASPER_LICENSE__
+ * 
+ * JasPer Software License
+ * 
+ * IMAGE POWER JPEG-2000 PUBLIC LICENSE
+ * ************************************
+ * 
+ * GRANT:
+ * 
+ * Permission is hereby granted, free of charge, to any person (the "User")
+ * obtaining a copy of this software and associated documentation, to deal
+ * in the JasPer Software without restriction, including without limitation
+ * the right to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the JasPer Software (in source and binary forms),
+ * and to permit persons to whom the JasPer Software is furnished to do so,
+ * provided further that the License Conditions below are met.
+ * 
+ * License Conditions
+ * ******************
+ * 
+ * A.  Redistributions of source code must retain the above copyright notice,
+ * and this list of conditions, and the following disclaimer.
+ * 
+ * B.  Redistributions in binary form must reproduce the above copyright
+ * notice, and this list of conditions, and the following disclaimer in
+ * the documentation and/or other materials provided with the distribution.
+ * 
+ * C.  Neither the name of Image Power, Inc. nor any other contributor
+ * (including, but not limited to, the University of British Columbia and
+ * Michael David Adams) may be used to endorse or promote products derived
+ * from this software without specific prior written permission.
+ * 
+ * D.  User agrees that it shall not commence any action against Image Power,
+ * Inc., the University of British Columbia, Michael David Adams, or any
+ * other contributors (collectively "Licensors") for infringement of any
+ * intellectual property rights ("IPR") held by the User in respect of any
+ * technology that User owns or has a right to license or sublicense and
+ * which is an element required in order to claim compliance with ISO/IEC
+ * 15444-1 (i.e., JPEG-2000 Part 1).  "IPR" means all intellectual property
+ * rights worldwide arising under statutory or common law, and whether
+ * or not perfected, including, without limitation, all (i) patents and
+ * patent applications owned or licensable by User; (ii) rights associated
+ * with works of authorship including copyrights, copyright applications,
+ * copyright registrations, mask work rights, mask work applications,
+ * mask work registrations; (iii) rights relating to the protection of
+ * trade secrets and confidential information; (iv) any right analogous
+ * to those set forth in subsections (i), (ii), or (iii) and any other
+ * proprietary rights relating to intangible property (other than trademark,
+ * trade dress, or service mark rights); and (v) divisions, continuations,
+ * renewals, reissues and extensions of the foregoing (as and to the extent
+ * applicable) now existing, hereafter filed, issued or acquired.
+ * 
+ * E.  If User commences an infringement action against any Licensor(s) then
+ * such Licensor(s) shall have the right to terminate User's license and
+ * all sublicenses that have been granted hereunder by User to other parties.
+ * 
+ * F.  This software is for use only in hardware or software products that
+ * are compliant with ISO/IEC 15444-1 (i.e., JPEG-2000 Part 1).  No license
+ * or right to this Software is granted for products that do not comply
+ * with ISO/IEC 15444-1.  The JPEG-2000 Part 1 standard can be purchased
+ * from the ISO.
+ * 
+ * THIS DISCLAIMER OF WARRANTY CONSTITUTES AN ESSENTIAL PART OF THIS LICENSE.
+ * NO USE OF THE JASPER SOFTWARE IS AUTHORIZED HEREUNDER EXCEPT UNDER
+ * THIS DISCLAIMER.  THE JASPER SOFTWARE IS PROVIDED BY THE LICENSORS AND
+ * CONTRIBUTORS UNDER THIS LICENSE ON AN ``AS-IS'' BASIS, WITHOUT WARRANTY
+ * OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION,
+ * WARRANTIES THAT THE JASPER SOFTWARE IS FREE OF DEFECTS, IS MERCHANTABLE,
+ * IS FIT FOR A PARTICULAR PURPOSE OR IS NON-INFRINGING.  THOSE INTENDING
+ * TO USE THE JASPER SOFTWARE OR MODIFICATIONS THEREOF FOR USE IN HARDWARE
+ * OR SOFTWARE PRODUCTS ARE ADVISED THAT THEIR USE MAY INFRINGE EXISTING
+ * PATENTS, COPYRIGHTS, TRADEMARKS, OR OTHER INTELLECTUAL PROPERTY RIGHTS.
+ * THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE JASPER SOFTWARE
+ * IS WITH THE USER.  SHOULD ANY PART OF THE JASPER SOFTWARE PROVE DEFECTIVE
+ * IN ANY RESPECT, THE USER (AND NOT THE INITIAL DEVELOPERS, THE UNIVERSITY
+ * OF BRITISH COLUMBIA, IMAGE POWER, INC., MICHAEL DAVID ADAMS, OR ANY
+ * OTHER CONTRIBUTOR) SHALL ASSUME THE COST OF ANY NECESSARY SERVICING,
+ * REPAIR OR CORRECTION.  UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY,
+ * WHETHER TORT (INCLUDING NEGLIGENCE), CONTRACT, OR OTHERWISE, SHALL THE
+ * INITIAL DEVELOPER, THE UNIVERSITY OF BRITISH COLUMBIA, IMAGE POWER, INC.,
+ * MICHAEL DAVID ADAMS, ANY OTHER CONTRIBUTOR, OR ANY DISTRIBUTOR OF THE
+ * JASPER SOFTWARE, OR ANY SUPPLIER OF ANY OF SUCH PARTIES, BE LIABLE TO
+ * THE USER OR ANY OTHER PERSON FOR ANY INDIRECT, SPECIAL, INCIDENTAL, OR
+ * CONSEQUENTIAL DAMAGES OF ANY CHARACTER INCLUDING, WITHOUT LIMITATION,
+ * DAMAGES FOR LOSS OF GOODWILL, WORK STOPPAGE, COMPUTER FAILURE OR
+ * MALFUNCTION, OR ANY AND ALL OTHER COMMERCIAL DAMAGES OR LOSSES, EVEN IF
+ * SUCH PARTY HAD BEEN INFORMED, OR OUGHT TO HAVE KNOWN, OF THE POSSIBILITY
+ * OF SUCH DAMAGES.  THE JASPER SOFTWARE AND UNDERLYING TECHNOLOGY ARE NOT
+ * FAULT-TOLERANT AND ARE NOT DESIGNED, MANUFACTURED OR INTENDED FOR USE OR
+ * RESALE AS ON-LINE CONTROL EQUIPMENT IN HAZARDOUS ENVIRONMENTS REQUIRING
+ * FAIL-SAFE PERFORMANCE, SUCH AS IN THE OPERATION OF NUCLEAR FACILITIES,
+ * AIRCRAFT NAVIGATION OR COMMUNICATION SYSTEMS, AIR TRAFFIC CONTROL, DIRECT
+ * LIFE SUPPORT MACHINES, OR WEAPONS SYSTEMS, IN WHICH THE FAILURE OF THE
+ * JASPER SOFTWARE OR UNDERLYING TECHNOLOGY OR PRODUCT COULD LEAD DIRECTLY
+ * TO DEATH, PERSONAL INJURY, OR SEVERE PHYSICAL OR ENVIRONMENTAL DAMAGE
+ * ("HIGH RISK ACTIVITIES").  LICENSOR SPECIFICALLY DISCLAIMS ANY EXPRESS
+ * OR IMPLIED WARRANTY OF FITNESS FOR HIGH RISK ACTIVITIES.  USER WILL NOT
+ * KNOWINGLY USE, DISTRIBUTE OR RESELL THE JASPER SOFTWARE OR UNDERLYING
+ * TECHNOLOGY OR PRODUCTS FOR HIGH RISK ACTIVITIES AND WILL ENSURE THAT ITS
+ * CUSTOMERS AND END-USERS OF ITS PRODUCTS ARE PROVIDED WITH A COPY OF THE
+ * NOTICE SPECIFIED IN THIS SECTION.
+ * 
+ * __END_OF_JASPER_LICENSE__
+ */
+
+/*
+ * Fixed-Point Number Class
+ *
+ * $Id$
+ */
+
+#ifndef JAS_FIX_H
+#define JAS_FIX_H
+
+/******************************************************************************\
+* Includes.
+\******************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include <jasper/jas_types.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/******************************************************************************\
+* Constants.
+\******************************************************************************/
+
+/* The representation of the value zero. */
+#define	JAS_FIX_ZERO(fix_t, fracbits) \
+	JAS_CAST(fix_t, 0)
+
+/* The representation of the value one. */
+#define	JAS_FIX_ONE(fix_t, fracbits) \
+	(JAS_CAST(fix_t, 1) << (fracbits))
+
+/* The representation of the value one half. */
+#define	JAS_FIX_HALF(fix_t, fracbits) \
+	(JAS_CAST(fix_t, 1) << ((fracbits) - 1))
+
+/******************************************************************************\
+* Conversion operations.
+\******************************************************************************/
+
+/* Convert an int to a fixed-point number. */
+#define JAS_INTTOFIX(fix_t, fracbits, x) \
+	JAS_CAST(fix_t, (x) << (fracbits))
+
+/* Convert a fixed-point number to an int. */
+#define JAS_FIXTOINT(fix_t, fracbits, x) \
+	JAS_CAST(int, (x) >> (fracbits))
+
+/* Convert a fixed-point number to a double. */
+#define JAS_FIXTODBL(fix_t, fracbits, x) \
+	(JAS_CAST(double, x) / (JAS_CAST(fix_t, 1) << (fracbits)))
+
+/* Convert a double to a fixed-point number. */
+#define JAS_DBLTOFIX(fix_t, fracbits, x) \
+	JAS_CAST(fix_t, ((x) * JAS_CAST(double, JAS_CAST(fix_t, 1) << (fracbits))))
+
+/******************************************************************************\
+* Basic arithmetic operations.
+* All other arithmetic operations are synthesized from these basic operations.
+* There are three macros for each type of arithmetic operation.
+* One macro always performs overflow/underflow checking, one never performs
+* overflow/underflow checking, and one is generic with its behavior
+* depending on compile-time flags.
+* Only the generic macros should be invoked directly by application code.
+\******************************************************************************/
+
+/* Calculate the sum of two fixed-point numbers. */
+#if !defined(DEBUG_OVERFLOW)
+#define JAS_FIX_ADD			JAS_FIX_ADD_FAST
+#else
+#define JAS_FIX_ADD			JAS_FIX_ADD_OFLOW
+#endif
+
+/* Calculate the sum of two fixed-point numbers without overflow checking. */
+#define	JAS_FIX_ADD_FAST(fix_t, fracbits, x, y)	((x) + (y))
+
+/* Calculate the sum of two fixed-point numbers with overflow checking. */
+#define	JAS_FIX_ADD_OFLOW(fix_t, fracbits, x, y) \
+	((x) >= 0) ? \
+	  (((y) >= 0) ? ((x) + (y) >= 0 || JAS_FIX_OFLOW(), (x) + (y)) : \
+	  ((x) + (y))) : \
+	  (((y) >= 0) ? ((x) + (y)) : ((x) + (y) < 0 || JAS_FIX_OFLOW(), \
+	  (x) + (y)))
+
+/* Calculate the product of two fixed-point numbers. */
+#if !defined(DEBUG_OVERFLOW)
+#define JAS_FIX_MUL			JAS_FIX_MUL_FAST
+#else
+#define JAS_FIX_MUL			JAS_FIX_MUL_OFLOW
+#endif
+
+/* Calculate the product of two fixed-point numbers without overflow
+  checking. */
+#define	JAS_FIX_MUL_FAST(fix_t, fracbits, bigfix_t, x, y) \
+	JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y)) >> \
+	  (fracbits))
+
+/* Calculate the product of two fixed-point numbers with overflow
+  checking. */
+#define JAS_FIX_MUL_OFLOW(fix_t, fracbits, bigfix_t, x, y) \
+	((JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> (fracbits)) == \
+	  JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> \
+	  (fracbits))) ? \
+	  JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) * JAS_CAST(bigfix_t, y) >> \
+	  (fracbits))) : JAS_FIX_OFLOW())
+
+/* Calculate the product of a fixed-point number and an int. */
+#if !defined(DEBUG_OVERFLOW)
+#define	JAS_FIX_MULBYINT	JAS_FIX_MULBYINT_FAST
+#else
+#define	JAS_FIX_MULBYINT	JAS_FIX_MULBYINT_OFLOW
+#endif
+
+/* Calculate the product of a fixed-point number and an int without overflow
+  checking. */
+#define	JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y) \
+	JAS_CAST(fix_t, ((x) * (y)))
+
+/* Calculate the product of a fixed-point number and an int with overflow
+  checking. */
+#define	JAS_FIX_MULBYINT_OFLOW(fix_t, fracbits, x, y) \
+	JAS_FIX_MULBYINT_FAST(fix_t, fracbits, x, y)
+
+/* Calculate the quotient of two fixed-point numbers. */
+#if !defined(DEBUG_OVERFLOW)
+#define JAS_FIX_DIV			JAS_FIX_DIV_FAST
+#else
+#define JAS_FIX_DIV			JAS_FIX_DIV_UFLOW
+#endif
+
+/* Calculate the quotient of two fixed-point numbers without underflow
+  checking. */
+#define	JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y) \
+	JAS_CAST(fix_t, (JAS_CAST(bigfix_t, x) << (fracbits)) / (y))
+
+/* Calculate the quotient of two fixed-point numbers with underflow
+  checking. */
+#define JAS_FIX_DIV_UFLOW(fix_t, fracbits, bigfix_t, x, y) \
+	JAS_FIX_DIV_FAST(fix_t, fracbits, bigfix_t, x, y)
+
+/* Negate a fixed-point number. */
+#if !defined(DEBUG_OVERFLOW)
+#define	JAS_FIX_NEG			JAS_FIX_NEG_FAST
+#else
+#define	JAS_FIX_NEG			JAS_FIX_NEG_OFLOW
+#endif
+
+/* Negate a fixed-point number without overflow checking. */
+#define	JAS_FIX_NEG_FAST(fix_t, fracbits, x) \
+	(-(x))
+
+/* Negate a fixed-point number with overflow checking. */
+/* Yes, overflow is actually possible for two's complement representations,
+  although highly unlikely to occur. */
+#define	JAS_FIX_NEG_OFLOW(fix_t, fracbits, x) \
+	(((x) < 0) ? (-(x) > 0 || JAS_FIX_OFLOW(), -(x)) : (-(x)))
+
+/* Perform an arithmetic shift left of a fixed-point number. */
+#if !defined(DEBUG_OVERFLOW)
+#define	JAS_FIX_ASL			JAS_FIX_ASL_FAST
+#else
+#define	JAS_FIX_ASL			JAS_FIX_ASL_OFLOW
+#endif
+
+/* Perform an arithmetic shift left of a fixed-point number without overflow
+  checking. */
+#define	JAS_FIX_ASL_FAST(fix_t, fracbits, x, n) \
+	((x) << (n))
+
+/* Perform an arithmetic shift left of a fixed-point number with overflow
+  checking. */
+#define	JAS_FIX_ASL_OFLOW(fix_t, fracbits, x, n) \
+	((((x) << (n)) >> (n)) == (x) || JAS_FIX_OFLOW(), (x) << (n))
+
+/* Perform an arithmetic shift right of a fixed-point number. */
+#if !defined(DEBUG_OVERFLOW)
+#define	JAS_FIX_ASR			JAS_FIX_ASR_FAST
+#else
+#define	JAS_FIX_ASR			JAS_FIX_ASR_UFLOW
+#endif
+
+/* Perform an arithmetic shift right of a fixed-point number without underflow
+  checking. */
+#define	JAS_FIX_ASR_FAST(fix_t, fracbits, x, n) \
+	((x) >> (n))
+
+/* Perform an arithmetic shift right of a fixed-point number with underflow
+  checking. */
+#define	JAS_FIX_ASR_UFLOW(fix_t, fracbits, x, n) \
+	JAS_FIX_ASR_FAST(fix_t, fracbits, x, n)
+
+/******************************************************************************\
+* Other basic arithmetic operations.
+\******************************************************************************/
+
+/* Calculate the difference between two fixed-point numbers. */
+#define JAS_FIX_SUB(fix_t, fracbits, x, y) \
+	JAS_FIX_ADD(fix_t, fracbits, x, JAS_FIX_NEG(fix_t, fracbits, y))
+
+/* Add one fixed-point number to another. */
+#define JAS_FIX_PLUSEQ(fix_t, fracbits, x, y) \
+	((x) = JAS_FIX_ADD(fix_t, fracbits, x, y))
+
+/* Subtract one fixed-point number from another. */
+#define JAS_FIX_MINUSEQ(fix_t, fracbits, x, y) \
+	((x) = JAS_FIX_SUB(fix_t, fracbits, x, y))
+
+/* Multiply one fixed-point number by another. */
+#define	JAS_FIX_MULEQ(fix_t, fracbits, bigfix_t, x, y) \
+	((x) = JAS_FIX_MUL(fix_t, fracbits, bigfix_t, x, y))
+
+/******************************************************************************\
+* Miscellaneous operations.
+\******************************************************************************/
+
+/* Calculate the absolute value of a fixed-point number. */
+#define	JAS_FIX_ABS(fix_t, fracbits, x) \
+	(((x) >= 0) ? (x) : (JAS_FIX_NEG(fix_t, fracbits, x)))
+
+/* Is a fixed-point number an integer? */
+#define	JAS_FIX_ISINT(fix_t, fracbits, x) \
+	(JAS_FIX_FLOOR(fix_t, fracbits, x) == (x))
+
+/* Get the sign of a fixed-point number. */
+#define JAS_FIX_SGN(fix_t, fracbits, x) \
+	((x) >= 0 ? 1 : (-1))
+
+/******************************************************************************\
+* Relational operations.
+\******************************************************************************/
+
+/* Compare two fixed-point numbers. */
+#define JAS_FIX_CMP(fix_t, fracbits, x, y) \
+	((x) > (y) ? 1 : (((x) == (y)) ? 0 : (-1)))
+
+/* Less than. */
+#define	JAS_FIX_LT(fix_t, fracbits, x, y) \
+	((x) < (y))
+
+/* Less than or equal. */
+#define	JAS_FIX_LTE(fix_t, fracbits, x, y) \
+	((x) <= (y))
+
+/* Greater than. */
+#define	JAS_FIX_GT(fix_t, fracbits, x, y) \
+	((x) > (y))
+
+/* Greater than or equal. */
+#define	JAS_FIX_GTE(fix_t, fracbits, x, y) \
+	((x) >= (y))
+
+/******************************************************************************\
+* Rounding functions.
+\******************************************************************************/
+
+/* Round a fixed-point number to the nearest integer. */
+#define	JAS_FIX_ROUND(fix_t, fracbits, x) \
+	(((x) < 0) ? JAS_FIX_FLOOR(fix_t, fracbits, JAS_FIX_ADD(fix_t, fracbits, \
+	  (x), JAS_FIX_HALF(fix_t, fracbits))) : \
+	  JAS_FIX_NEG(fix_t, fracbits, JAS_FIX_FLOOR(fix_t, fracbits, \
+	  JAS_FIX_ADD(fix_t, fracbits, (-(x)), JAS_FIX_HALF(fix_t, fracbits)))))
+
+/* Round a fixed-point number to the nearest integer in the direction of
+  negative infinity (i.e., the floor function). */
+#define	JAS_FIX_FLOOR(fix_t, fracbits, x) \
+	((x) & (~((JAS_CAST(fix_t, 1) << (fracbits)) - 1)))
+
+/* Round a fixed-point number to the nearest integer in the direction
+  of zero. */
+#define JAS_FIX_TRUNC(fix_t, fracbits, x) \
+	(((x) >= 0) ? JAS_FIX_FLOOR(fix_t, fracbits, x) : \
+	  JAS_FIX_CEIL(fix_t, fracbits, x))
+
+/******************************************************************************\
+* The below macros are for internal library use only.  Do not invoke them
+* directly in application code.
+\******************************************************************************/
+
+/* Handle overflow. */
+#define	JAS_FIX_OFLOW() \
+	fprintf(stderr, "overflow error: file %s, line %d\n", __FILE__, __LINE__)
+
+/* Handle underflow. */
+#define	JAS_FIX_UFLOW() \
+	fprintf(stderr, "underflow error: file %s, line %d\n", __FILE__, __LINE__)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif