ref: f7e5af47f117be34669dc1e532d525dcbbff73f0
dir: /jasper/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
* 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 __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)
#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_CONST
JAS_ATTRIBUTE_DISABLE_UBSAN
inline 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_CONST
JAS_ATTRIBUTE_DISABLE_UBSAN
inline 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_CONST
JAS_ATTRIBUTE_DISABLE_UBSAN
inline 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_CONST
JAS_ATTRIBUTE_DISABLE_UBSAN
inline 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_CONST
JAS_ATTRIBUTE_DISABLE_UBSAN
inline 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_CONST
JAS_ATTRIBUTE_DISABLE_UBSAN
inline 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_CONST
static 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_PURE
static 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_CONST
static 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_CONST
static inline
jas_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_CONST
static 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_CONST
static inline
jas_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_CONST
static inline
jas_safei64_t jas_safei64_add(jas_safei64_t x, jas_safei64_t y)
{
jas_safei64_t result;
if (((y.value > 0) && (x.value > (INT_LEAST64_MAX - y.value))) ||
((y.value < 0) && (x.value < (INT_LEAST64_MIN - y.value)))) {
result.value = false;
result.value = 0;
} else {
result.valid = true;
result.value = x.value + y.value;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_safei64_t jas_safei64_sub(jas_safei64_t x, jas_safei64_t y)
{
jas_safei64_t result;
if ((y.value > 0 && x.value < INT_LEAST64_MIN + y.value) ||
(y.value < 0 && x.value > INT_LEAST64_MAX + y.value)) {
result.valid = false;
result.value = 0;
} else {
result.valid = true;
result.value = x.value - y.value;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_safei64_t jas_safei64_mul(jas_safei64_t x, jas_safei64_t y)
{
jas_safei64_t result;
if (x.value > 0) { /* x.value is positive */
if (y.value > 0) { /* x.value and y.value are positive */
if (x.value > (INT_LEAST64_MAX / y.value)) {
goto error;
}
} else { /* x.value positive, y.value nonpositive */
if (y.value < (INT_LEAST64_MIN / x.value)) {
goto error;
}
} /* x.value positive, y.value nonpositive */
} else { /* x.value is nonpositive */
if (y.value > 0) { /* x.value is nonpositive, y.value is positive */
if (x.value < (INT_LEAST64_MIN / y.value)) {
goto error;
}
} else { /* x.value and y.value are nonpositive */
if ( (x.value != 0) && (y.value < (INT_LEAST64_MAX / x.value))) {
goto error;
}
} /* End if x.value and y.value are nonpositive */
} /* End if x.value is nonpositive */
result.valid = true;
result.value = x.value * y.value;
return result;
error:
result.valid = false;
result.value = 0;
return result;
}
#if 0
JAS_ATTRIBUTE_CONST
static inline
jas_safei64_t jas_safei64_div(jas_safei64_t x, jas_safei64_t y)
{
// TODO/FIXME: Not yet implemented.
jas_safei64_t result;
result.valid = false;
result.value = 0;
return result;
}
#endif
JAS_ATTRIBUTE_CONST
static inline
jas_i32_t jas_safei64_to_i32(jas_safei64_t x, jas_i32_t invalid_value)
{
jas_i32_t result;
if (x.valid && x.value >= JAS_I32_MIN && x.value <= JAS_I32_MAX) {
result = JAS_CAST(jas_i32_t, x.value);
} else {
result = invalid_value;
}
return result;
}
/******************************************************************************\
* Safe 64-bit unsigned integer arithmetic (i.e., with overflow checking).
\******************************************************************************/
typedef struct {
bool valid;
uint_least64_t value;
} jas_safeui64_t;
JAS_ATTRIBUTE_CONST
static inline
jas_safeui64_t jas_safeui64_from_intmax(intmax_t x)
{
jas_safeui64_t result;
if (x >= 0) {
result.valid = true;
result.value = JAS_CAST(uint_least64_t, x);
} else {
result.valid = false;
result.value = 0;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_safeui64_t jas_safeui64_add(jas_safeui64_t x, jas_safeui64_t y)
{
jas_safeui64_t result;
if (x.valid && y.valid && y.value <= UINT_LEAST64_MAX - x.value) {
result.valid = true;
result.value = x.value + y.value;
} else {
result.valid = false;
result.value = 0;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_safeui64_t jas_safeui64_sub(jas_safeui64_t x, jas_safeui64_t y)
{
jas_safeui64_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_CONST
static inline
jas_safeui64_t jas_safeui64_mul(jas_safeui64_t x, jas_safeui64_t y)
{
jas_safeui64_t result;
if (!x.valid || !y.valid || (x.value && y.value > UINT_LEAST64_MAX /
x.value)) {
result.valid = false;
result.value = 0;
} else {
result.valid = true;
result.value = x.value * y.value;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_safeui64_t jas_safeui64_div(jas_safeui64_t x, jas_safeui64_t y)
{
jas_safeui64_t result;
if (x.valid && y.valid && y.value) {
result.valid = true;
result.value = x.value / y.value;
} else {
result.valid = false;
result.value = 0;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_safeui64_t jas_safeui64_pow2_intmax(intmax_t x)
{
jas_safeui64_t result;
if (x >= 0 && x < 64) {
result.valid = true;
result.value = JAS_CAST(uint_least64_t, 1) << x;
} else {
result.valid = false;
result.value = 0;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
int jas_safeui64_to_int(jas_safeui64_t x, int invalid_value)
{
int result;
if (x.valid && x.value <= INT_MAX) {
result = JAS_CAST(int, x.value);
} else {
result = invalid_value;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_ui32_t jas_safeui64_to_ui32(jas_safeui64_t x, jas_ui32_t invalid_value)
{
jas_ui32_t result;
if (x.valid && x.value <= JAS_UI32_MAX) {
result = JAS_CAST(jas_ui32_t, x.value);
} else {
result = invalid_value;
}
return result;
}
JAS_ATTRIBUTE_CONST
static inline
jas_i32_t jas_safeui64_to_i32(jas_safeui64_t x, jas_i32_t invalid_value)
{
jas_i32_t result;
if (x.valid && x.value <= JAS_I32_MAX) {
result = JAS_CAST(jas_i32_t, x.value);
} else {
result = invalid_value;
}
return result;
}
/******************************************************************************\
\******************************************************************************/
#ifdef __cplusplus
}
#endif
#endif