/* * 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 * WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.  NO ASSURANCES ARE * PROVIDED BY THE COPYRIGHT HOLDERS THAT THE SOFTWARE DOES NOT INFRINGE * THE PATENT OR OTHER INTELLECTUAL PROPERTY RIGHTS OF ANY OTHER ENTITY. * 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 * SYSTEMS, DIRECT LIFE SUPPORT MACHINES, OR WEAPONS SYSTEMS, IN WHICH * 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 * EXPRESS OR IMPLIED WARRANTY OF FITNESS FOR HIGH RISK ACTIVITIES. *  * __END_OF_JASPER_LICENSE__ */ /*! * @file jas_math.h * @brief Math-Related Code */ #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_compiler.h>#include <jasper/jas_types.h> #ifdef __cplusplusextern "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)#if 0#define	JAS_ONES_X(type, n) \  ((JAS_CAST(type, 1) << (n)) - 1)#endif#define	JAS_POW2_X(type, n) \  (JAS_CAST(type, 1) << (n)) /******************************************************************************\*\******************************************************************************/ #if defined(__clang__) || (defined(__GNUC__) && __GNUC__ > 6)/* suppress clang warning "shifting a negative signed value is   undefined" in the assertions below */#pragma GCC diagnostic push#pragma GCC diagnostic ignored "-Wshift-negative-value"#endif JAS_ATTRIBUTE_CONSTJAS_ATTRIBUTE_DISABLE_UBSANinline static int jas_int_asr(int x, unsigned n){	// Ensure that the shift of a negative value appears to behave as a	// signed arithmetic shift.	assert(((-1) >> 1) == -1);	// 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_CONSTJAS_ATTRIBUTE_DISABLE_UBSANinline static int jas_int_asl(int x, unsigned n){	// Ensure that the shift of a negative value appears to behave as a	// signed arithmetic shift.	assert(((-1) << 1) == -2);	// 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_CONSTJAS_ATTRIBUTE_DISABLE_UBSANinline static int_least32_t jas_least32_asr(int_least32_t x, unsigned n){	// Ensure that the shift of a negative value appears to behave as a	// signed arithmetic shift.	assert(((JAS_CAST(int_least32_t, -1)) >> 1) == JAS_CAST(int_least32_t, -1));	// 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_CONSTJAS_ATTRIBUTE_DISABLE_UBSANinline static int_least32_t jas_least32_asl(int_least32_t x, unsigned n){	// Ensure that the shift of a negative value appears to behave as a	// signed arithmetic shift.	assert(((JAS_CAST(int_least32_t, -1)) << 1) == JAS_CAST(int_least32_t, -2));	// 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_CONSTJAS_ATTRIBUTE_DISABLE_UBSANinline static int_fast32_t jas_fast32_asr(int_fast32_t x, unsigned 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));	// 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_CONSTJAS_ATTRIBUTE_DISABLE_UBSANinline static int_fast32_t jas_fast32_asl(int_fast32_t x, unsigned 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));	// The behavior is undefined when x is negative.	// We tacitly assume the behavior is equivalent to a signed	// arithmetic left shift.	return x << n;} #if defined(__clang__) || (defined(__GNUC__) && __GNUC__ > 6)#pragma GCC diagnostic pop#endif /******************************************************************************\* 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){#if jas_has_builtin(__builtin_mul_overflow) || (defined(__GNUC__) && __GNUC__ > 5)	size_t result_buffer;	bool valid = !__builtin_mul_overflow(x, y, &result_buffer);	if (valid && result) {		*result = result_buffer;	}	return valid;#else	/* Check if overflow would occur */	if (x && y > SIZE_MAX / x) {		/* Overflow would occur. */		return false;	}	if (result) {		*result = x * y;	}	return true;#endif} /* 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 jas_has_builtin(__builtin_add_overflow) || (defined(__GNUC__) && __GNUC__ > 5)	size_t result_buffer;	bool valid = !__builtin_add_overflow(x, y, &result_buffer);	if (valid && result) {		*result = result_buffer;	}	return valid;#else	if (y > SIZE_MAX - x) {		return false;	}	if (result) {		*result = x + y;	}	return true;#endif} /* 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 jas_has_builtin(__builtin_sub_overflow) || (defined(__GNUC__) && __GNUC__ > 5)	size_t result_buffer;	bool valid = !__builtin_sub_overflow(x, y, &result_buffer);	if (valid && result) {		*result = result_buffer;	}	return valid;#else	if (y > x) {		return false;	}	if (result) {		*result = x - y;	}	return true;#endif} /* 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 jas_has_builtin(__builtin_mul_overflow) || (defined(__GNUC__) && __GNUC__ > 5)	int_fast32_t result_buffer;	bool valid = !__builtin_mul_overflow(x, y, &result_buffer);	if (valid && result) {		*result = result_buffer;	}	return valid;#else	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;#endif} /* 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 jas_has_builtin(__builtin_add_overflow) || (defined(__GNUC__) && __GNUC__ > 5)	int_fast32_t result_buffer;	bool valid = !__builtin_add_overflow(x, y, &result_buffer);	if (valid && result) {		*result = result_buffer;	}	return valid;#else	if ((y > 0 && x > INT_FAST32_MAX - y) ||	  (y < 0 && x < INT_FAST32_MIN - y)) {		return false;	}	if (result) {		*result = x + y;	}	return true;#endif} #if 0/*This function is potentially useful but not currently used.So, it is commented out.*/inline static bool jas_safe_uint_mul(unsigned x, unsigned y, unsigned *result){	/* Check if overflow would occur */	if (x && y > UINT_MAX / x) {		/* Overflow would occur. */		return false;	}	if (result) {		*result = x * y;	}	return true;}#endif /******************************************************************************\* Safe 32-bit unsigned integer arithmetic (i.e., with overflow checking).\******************************************************************************/ #define JAS_SAFEUI32_MAX (0xffffffffU) typedef struct {	bool valid;	uint_least32_t value;} jas_safeui32_t; JAS_ATTRIBUTE_CONSTstatic inline jas_safeui32_t jas_safeui32_from_ulong(unsigned long x){	jas_safeui32_t result;	result.valid = 1;	result.value = JAS_CAST(uint_least32_t, x);	return result;} JAS_ATTRIBUTE_PUREstatic inline bool jas_safeui32_to_intfast32(jas_safeui32_t x,  int_fast32_t* y){	if (x.value <= INT_FAST32_MAX) {		*y = x.value;		return true;	} else {		return false;	}} JAS_ATTRIBUTE_CONSTstatic inline jas_safeui32_t jas_safeui32_add(jas_safeui32_t x,  jas_safeui32_t y){	jas_safeui32_t result;	if (x.valid && y.valid && y.value <= UINT_LEAST32_MAX - x.value) {		result.valid = true;		result.value = x.value + y.value;	} else {		result.valid = false;		result.value = 0;	}	return result;} JAS_ATTRIBUTE_CONSTstatic inlinejas_safeui32_t jas_safeui32_sub(jas_safeui32_t x, jas_safeui32_t y){	jas_safeui32_t result;	if (x.valid && y.valid && y.value <= x.value) {		result.valid = true;		result.value = x.value - y.value;	} else {		result.valid = false;		result.value = 0;	}	return result;} JAS_ATTRIBUTE_CONSTstatic inline jas_safeui32_t jas_safeui32_mul(jas_safeui32_t x,  jas_safeui32_t y){	jas_safeui32_t result;	if (!x.valid || !y.valid || (x.value && y.value > UINT_LEAST32_MAX /	  x.value)) {		result.valid = false;		result.value = 0;	} else {		result.valid = true;		result.value = x.value * y.value;	}	return result;} /******************************************************************************\* Safe 64-bit signed integer arithmetic (i.e., with overflow checking).\******************************************************************************/ typedef struct {	bool valid;	int_least64_t value;} jas_safei64_t; JAS_ATTRIBUTE_CONSTstatic inlinejas_safei64_t jas_safei64_from_intmax(intmax_t x){	jas_safei64_t result;	result.valid = true;	result.value = JAS_CAST(int_least64_t, x);	return result;} JAS_ATTRIBUTE_CONSTstatic inlinejas_safei64_t jas_safei64_add(jas_safei64_t x, jas_safei64_t y)

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