jas_math.h

/*
 * 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 License Version 2.0
 * 
 * Copyright (c) 2001-2006 Michael David Adams
 * Copyright (c) 1999-2000 Image Power, Inc.
 * Copyright (c) 1999-2000 The University of British Columbia
 * 
 * All rights reserved.
 * 
 * Permission is hereby granted, free of charge, to any person (the
 * "User") obtaining a copy of this software and associated documentation
 * files (the "Software"), to deal in the Software without restriction,
 * including without limitation the rights to use, copy, modify, merge,
 * publish, distribute, and/or sell copies of the Software, and to permit
 * persons to whom the Software is furnished to do so, subject to the
 * following conditions:
 * 
 * 1.  The above copyright notices and this permission notice (which
 * includes the disclaimer below) shall be included in all copies or
 * substantial portions of the Software.
 * 
 * 2.  The name of a copyright holder shall not be used to endorse or
 * promote products derived from the Software without specific prior
 * written permission.
 * 
 * THIS DISCLAIMER OF WARRANTY CONSTITUTES AN ESSENTIAL PART OF THIS
 * LICENSE.  NO USE OF THE SOFTWARE IS AUTHORIZED HEREUNDER EXCEPT UNDER
 * THIS DISCLAIMER.  THE SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS
 * "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 OF THIRD PARTY RIGHTS.  IN NO
 * EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, OR ANY SPECIAL
 * INDIRECT OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING
 * FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
 * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION
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 * EACH COPYRIGHT HOLDER DISCLAIMS ANY LIABILITY TO THE USER FOR CLAIMS
 * BROUGHT BY ANY OTHER ENTITY BASED ON INFRINGEMENT OF INTELLECTUAL
 * PROPERTY RIGHTS OR OTHERWISE.  AS A CONDITION TO EXERCISING THE RIGHTS
 * GRANTED HEREUNDER, EACH USER HEREBY ASSUMES SOLE RESPONSIBILITY TO SECURE
 * ANY OTHER INTELLECTUAL PROPERTY RIGHTS NEEDED, IF ANY.  THE SOFTWARE
 * IS NOT FAULT-TOLERANT AND IS NOT INTENDED FOR USE IN MISSION-CRITICAL
 * SYSTEMS, SUCH AS THOSE USED IN THE OPERATION OF NUCLEAR FACILITIES,
 * AIRCRAFT NAVIGATION OR COMMUNICATION SYSTEMS, AIR TRAFFIC CONTROL
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 * THE FAILURE OF THE SOFTWARE OR SYSTEM COULD LEAD DIRECTLY TO DEATH,
 * PERSONAL INJURY, OR SEVERE PHYSICAL OR ENVIRONMENTAL DAMAGE ("HIGH
 * RISK ACTIVITIES").  THE COPYRIGHT HOLDERS SPECIFICALLY DISCLAIM ANY
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 * 
 * __END_OF_JASPER_LICENSE__
 */
 
/*
 * Math-Related Code
 *
 * $Id$
 */
 
#ifndef JAS_MATH_H
#define JAS_MATH_H
 
/******************************************************************************\
* Includes
\******************************************************************************/
 
/* The configuration header file should be included first. */
#include <jasper/jas_config.h>
 
#include <jasper/jas_types.h>
 
#include <assert.h>
#include <stdio.h>
#include <string.h>
#include <stdint.h>
 
#ifdef __cplusplus
extern "C" {
#endif
 
/******************************************************************************\
* Macros
\******************************************************************************/
 
#define JAS_KIBI        JAS_CAST(size_t, 1024)
#define JAS_MEBI        (JAS_KIBI * JAS_KIBI)
 
/* Compute the absolute value. */
#define JAS_ABS(x) \
        (((x) >= 0) ? (x) : (-(x)))
 
/* Compute the minimum of two values. */
#define JAS_MIN(x, y) \
        (((x) < (y)) ? (x) : (y))
 
/* Compute the maximum of two values. */
#define JAS_MAX(x, y) \
        (((x) > (y)) ? (x) : (y))
 
/* Compute the remainder from division (where division is defined such
  that the remainder is always nonnegative). */
#define JAS_MOD(x, y) \
        (((x) < 0) ? (((-x) % (y)) ? ((y) - ((-(x)) % (y))) : (0)) : ((x) % (y)))
 
/* Compute the integer with the specified number of least significant bits
  set to one. */
#define JAS_ONES(n) \
  ((1 << (n)) - 1)
 
/******************************************************************************\
*
\******************************************************************************/
 
JAS_ATTRIBUTE_DISABLE_USAN
inline static int jas_int_asr(int x, int n)
{
        // Ensure that the shift of a negative value appears to behave as a
        // signed arithmetic shift.
        assert(((-1) >> 1) == -1);
        assert(n >= 0);
        // The behavior is undefined when x is negative. */
        // We tacitly assume the behavior is equivalent to a signed
        // arithmetic right shift.
        return x >> n;
}
 
JAS_ATTRIBUTE_DISABLE_USAN
inline static int jas_int_asl(int x, int n)
{
        // Ensure that the shift of a negative value appears to behave as a
        // signed arithmetic shift.
        assert(((-1) << 1) == -2);
        assert(n >= 0);
        // The behavior is undefined when x is negative. */
        // We tacitly assume the behavior is equivalent to a signed
        // arithmetic left shift.
        return x << n;
}
 
JAS_ATTRIBUTE_DISABLE_USAN
inline static int jas_fast32_asr(int_fast32_t x, int n)
{
        // Ensure that the shift of a negative value appears to behave as a
        // signed arithmetic shift.
        assert(((JAS_CAST(int_fast32_t, -1)) >> 1) == JAS_CAST(int_fast32_t, -1));
        assert(n >= 0);
        // The behavior is undefined when x is negative. */
        // We tacitly assume the behavior is equivalent to a signed
        // arithmetic right shift.
        return x >> n;
}
 
JAS_ATTRIBUTE_DISABLE_USAN
inline static int jas_fast32_asl(int_fast32_t x, int n)
{
        // Ensure that the shift of a negative value appears to behave as a
        // signed arithmetic shift.
        assert(((JAS_CAST(int_fast32_t, -1)) << 1) == JAS_CAST(int_fast32_t, -2));
        assert(n >= 0);
        // The behavior is undefined when x is negative. */
        // We tacitly assume the behavior is equivalent to a signed
        // arithmetic left shift.
        return x << n;
}
 
/******************************************************************************\
* Safe integer arithmetic (i.e., with overflow checking).
\******************************************************************************/
 
/* Compute the product of two size_t integers with overflow checking. */
inline static bool jas_safe_size_mul(size_t x, size_t y, size_t *result)
{
        /* Check if overflow would occur */
        if (x && y > SIZE_MAX / x) {
                /* Overflow would occur. */
                return false;
        }
        if (result) {
                *result = x * y;
        }
        return true;
}
 
/* Compute the product of three size_t integers with overflow checking. */
inline static bool jas_safe_size_mul3(size_t a, size_t b, size_t c,
  size_t *result)
{
        size_t tmp;
        if (!jas_safe_size_mul(a, b, &tmp) ||
          !jas_safe_size_mul(tmp, c, &tmp)) {
                return false;
        }
        if (result) {
                *result = tmp;
        }
        return true;
}
 
/* Compute the sum of two size_t integers with overflow checking. */
inline static bool jas_safe_size_add(size_t x, size_t y, size_t *result)
{
        if (y > SIZE_MAX - x) {
                return false;
        }
        if (result) {
                *result = x + y;
        }
        return true;
}
 
/* Compute the difference of two size_t integers with overflow checking. */
inline static bool jas_safe_size_sub(size_t x, size_t y, size_t *result)
{
        if (y > x) {
                return false;
        }
        if (result) {
                *result = x - y;
        }
        return true;
}
 
/* Compute the product of two int_fast32_t integers with overflow checking. */
inline static bool jas_safe_intfast32_mul(int_fast32_t x, int_fast32_t y,
  int_fast32_t *result)
{
        if (x > 0) {
                /* x is positive */
                if (y > 0) {
                        /* x and y are positive */
                        if (x > INT_FAST32_MAX / y) {
                                return false;
                        }
                } else {
                        /* x positive, y nonpositive */
                        if (y < INT_FAST32_MIN / x) {
                                return false;
                        }
                }
        } else {
                /* x is nonpositive */
                if (y > 0) {
                        /* x is nonpositive, y is positive */
                        if (x < INT_FAST32_MIN / y) {
                                return false;
                        }
                } else { /* x and y are nonpositive */
                        if (x != 0 && y < INT_FAST32_MAX / x) {
                                return false;
                        }
                }
        }
 
        if (result) {
                *result = x * y;
        }
        return true;
}
 
/* Compute the product of three int_fast32_t integers with overflow checking. */
inline static bool jas_safe_intfast32_mul3(int_fast32_t a, int_fast32_t b,
  int_fast32_t c, int_fast32_t *result)
{
        int_fast32_t tmp;
        if (!jas_safe_intfast32_mul(a, b, &tmp) ||
          !jas_safe_intfast32_mul(tmp, c, &tmp)) {
                return false;
        }
        if (result) {
                *result = tmp;
        }
        return true;
}
 
/* Compute the sum of two int_fast32_t integers with overflow checking. */
inline static bool jas_safe_intfast32_add(int_fast32_t x, int_fast32_t y,
  int_fast32_t *result)
{
        if ((y > 0 && x > INT_FAST32_MAX - y) ||
          (y < 0 && x < INT_FAST32_MIN - y)) {
                return false;
        }
        if (result) {
                *result = x + y;
        }
        return true;
}
 
#ifdef __cplusplus
}
#endif
 
#endif