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8 #ifndef OPENVDB_MATH_HAS_BEEN_INCLUDED
9 #define OPENVDB_MATH_HAS_BEEN_INCLUDED
13 #include <boost/numeric/conversion/conversion_traits.hpp>
20 #include <type_traits>
27 #if defined(__INTEL_COMPILER)
28 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
29 _Pragma("warning (push)") \
30 _Pragma("warning (disable:1572)")
31 #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
32 _Pragma("warning (pop)")
33 #elif defined(__clang__)
34 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
35 PRAGMA(clang diagnostic push) \
36 PRAGMA(clang diagnostic ignored "-Wfloat-equal")
37 #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
38 PRAGMA(clang diagnostic pop)
47 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
48 #define OPENVDB_NO_FP_EQUALITY_WARNING_END
59 template<
typename T>
inline T
zeroVal() {
return T(0); }
61 template<>
inline std::string zeroVal<std::string>() {
return ""; }
67 inline std::string
operator+(
const std::string& s,
bool) {
return s; }
70 inline std::string
operator+(
const std::string& s,
int) {
return s; }
71 inline std::string
operator+(
const std::string& s,
float) {
return s; }
72 inline std::string
operator+(
const std::string& s,
double) {
return s; }
81 template <
typename T>
inline constexpr T
pi() {
return 3.141592653589793238462643383279502884e+00; }
82 template <>
inline constexpr
float pi() {
return 3.141592653589793238462643383279502884e+00F; }
83 template <>
inline constexpr
double pi() {
return 3.141592653589793238462643383279502884e+00; }
84 template <>
inline constexpr
long double pi() {
return 3.141592653589793238462643383279502884e+00L; }
90 template<
typename T>
inline T
negative(
const T& val)
95 #pragma warning(disable:4146)
103 template<>
inline bool negative(
const bool& val) {
return !val; }
105 template<>
inline std::string
negative(
const std::string& val) {
return val; }
109 template<
typename T>
struct Tolerance {
static T value() {
return zeroVal<T>(); } };
116 template<
typename T>
struct Delta {
static T value() {
return zeroVal<T>(); } };
118 template<>
struct Delta<float> {
static float value() {
return 1e-5f; } };
119 template<>
struct Delta<double> {
static double value() {
return 1e-9; } };
127 template<
typename FloatType =
double,
typename EngineType = std::mt19937>
132 std::uniform_real_distribution<FloatType> mRand;
139 Rand01(
const EngineType& engine): mEngine(engine) {}
143 Rand01(
unsigned int seed): mEngine(static_cast<typename EngineType::result_type>(seed)) {}
148 mEngine.seed(
static_cast<typename EngineType::result_type
>(seed));
152 const EngineType&
engine()
const {
return mEngine; }
163 template<
typename IntType =
int,
typename EngineType = std::mt19937>
167 using Distr = std::uniform_int_distribution<IntType>;
175 RandInt(
const EngineType& engine, IntType imin, IntType imax):
183 RandInt(
unsigned int seed, IntType imin, IntType imax):
184 mEngine(static_cast<typename EngineType::result_type>(seed)),
197 mEngine.seed(
static_cast<typename EngineType::result_type
>(seed));
201 const EngineType&
engine()
const {
return mEngine; }
211 return mRand(mEngine,
typename Distr::param_type(lo, hi));
221 template<
typename Type>
231 template<
typename Type>
233 Clamp01(Type x) {
return x > Type(0) ? x < Type(1) ? x : Type(1) : Type(0); }
237 template<
typename Type>
241 if (x >= Type(0) && x <= Type(1))
return false;
242 x = x < Type(0) ? Type(0) : Type(1);
247 template<
typename Type>
251 return x > 0 ? x < 1 ? (3-2*x)*x*x : Type(1) : Type(0);
256 template<
typename Type>
269 inline int32_t
Abs(int32_t i) {
return abs(i); }
271 inline int64_t
Abs(int64_t i)
274 return (i < int64_t(0) ? -i : i);
279 inline float Abs(
float x) {
return std::fabs(x); }
280 inline double Abs(
double x) {
return std::fabs(x); }
281 inline long double Abs(
long double x) {
return std::fabs(x); }
282 inline uint32_t
Abs(uint32_t i) {
return i; }
283 inline uint64_t
Abs(uint64_t i) {
return i; }
284 inline bool Abs(
bool b) {
return b; }
286 #if defined(__APPLE__) || defined(MACOSX)
287 inline size_t Abs(
size_t i) {
return i; }
299 template<
typename Type>
304 return x == zeroVal<Type>();
311 template<
typename Type>
316 return !(x > tolerance) && !(x < -tolerance);
320 template<
typename Type>
324 return !(x > tolerance) && !(x < -tolerance);
329 template<
typename Type>
339 isFinite(
const float x) {
return std::isfinite(x); }
342 template<typename Type, typename std::enable_if<std::is_arithmetic<Type>::value,
int>::type = 0>
344 isFinite(
const Type& x) {
return std::isfinite(
static_cast<double>(x)); }
352 template<typename Type, typename std::enable_if<std::is_arithmetic<Type>::value,
int>::type = 0>
354 isInfinite(
const Type& x) {
return std::isinf(
static_cast<double>(x)); }
359 isNan(
const float x) {
return std::isnan(x); }
362 template<typename Type, typename std::enable_if<std::is_arithmetic<Type>::value,
int>::type = 0>
364 isNan(
const Type& x) {
return std::isnan(
static_cast<double>(x)); }
369 template<
typename Type>
374 return !(
Abs(a - b) > tolerance);
379 template<
typename Type>
383 return !(
Abs(a - b) > tolerance);
386 #define OPENVDB_EXACT_IS_APPROX_EQUAL(T) \
387 template<> inline bool isApproxEqual<T>(const T& a, const T& b) { return a == b; } \
388 template<> inline bool isApproxEqual<T>(const T& a, const T& b, const T&) { return a == b; } \
397 template<typename Type>
401 return (b - a < tolerance);
406 template<
typename T0,
typename T1>
416 template<
typename Type>
422 if (!(
Abs(a - b) > absTol))
return true;
429 relError =
Abs((a - b) / b);
431 relError =
Abs((a - b) / a);
433 return (relError <= relTol);
450 union FloatOrInt32 {
float floatValue; int32_t int32Value; };
451 const FloatOrInt32* foi =
reinterpret_cast<const FloatOrInt32*
>(&aFloatValue);
452 return foi->int32Value;
459 union DoubleOrInt64 {
double doubleValue; int64_t int64Value; };
460 const DoubleOrInt64* dol =
reinterpret_cast<const DoubleOrInt64*
>(&aDoubleValue);
461 return dol->int64Value;
470 isUlpsEqual(
const double aLeft,
const double aRight,
const int64_t aUnitsInLastPlace)
475 longLeft = INT64_C(0x8000000000000000) - longLeft;
481 longRight = INT64_C(0x8000000000000000) - longRight;
484 int64_t difference = labs(longLeft - longRight);
485 return (difference <= aUnitsInLastPlace);
489 isUlpsEqual(
const float aLeft,
const float aRight,
const int32_t aUnitsInLastPlace)
494 intLeft = 0x80000000 - intLeft;
500 intRight = 0x80000000 - intRight;
503 int32_t difference = abs(intLeft - intRight);
504 return (difference <= aUnitsInLastPlace);
514 template<
typename Type>
515 inline Type
Pow2(Type x) {
return x*x; }
518 template<
typename Type>
519 inline Type
Pow3(Type x) {
return x*x*x; }
522 template<
typename Type>
526 template<
typename Type>
535 while (n--) ans *= x;
544 assert( b >= 0.0f &&
"Pow(float,float): base is negative" );
551 assert( b >= 0.0 &&
"Pow(double,double): base is negative" );
552 return std::pow(b,e);
560 template<
typename Type>
562 Max(
const Type& a,
const Type& b)
568 template<
typename Type>
570 Max(
const Type& a,
const Type& b,
const Type& c)
576 template<
typename Type>
578 Max(
const Type& a,
const Type& b,
const Type& c,
const Type& d)
584 template<
typename Type>
586 Max(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
const Type& e)
592 template<
typename Type>
594 Max(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
const Type& e,
const Type& f)
600 template<
typename Type>
602 Max(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
603 const Type& e,
const Type& f,
const Type& g)
609 template<
typename Type>
611 Max(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
612 const Type& e,
const Type& f,
const Type& g,
const Type& h)
621 template<
typename Type>
626 template<
typename Type>
631 template<
typename Type>
633 Min(
const Type& a,
const Type& b,
const Type& c,
const Type& d)
639 template<
typename Type>
641 Min(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
const Type& e)
647 template<
typename Type>
649 Min(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
const Type& e,
const Type& f)
655 template<
typename Type>
657 Min(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
658 const Type& e,
const Type& f,
const Type& g)
664 template<
typename Type>
666 Min(
const Type& a,
const Type& b,
const Type& c,
const Type& d,
667 const Type& e,
const Type& f,
const Type& g,
const Type& h)
676 template<
typename Type>
677 inline Type
Exp(
const Type& x) {
return std::exp(x); }
682 inline float Sin(
const float& x) {
return std::sin(x); }
685 inline double Sin(
const double& x) {
return std::sin(x); }
691 inline float Cos(
const float& x) {
return std::cos(x); }
694 inline double Cos(
const double& x) {
return std::cos(x); }
702 template <
typename Type>
703 inline int Sign(
const Type &x) {
return (zeroVal<Type>() < x) - (x < zeroVal<Type>()); }
708 template <
typename Type>
712 return ( (a<zeroVal<Type>()) ^ (b<zeroVal<Type>()) );
718 template <
typename Type>
722 return a * b <= zeroVal<Type>();
727 inline float Sqrt(
float x) {
return std::sqrt(x); }
729 inline double Sqrt(
double x) {
return std::sqrt(x); }
730 inline long double Sqrt(
long double x) {
return std::sqrt(x); }
735 inline float Cbrt(
float x) {
return std::cbrt(x); }
737 inline double Cbrt(
double x) {
return std::cbrt(x); }
738 inline long double Cbrt(
long double x) {
return std::cbrt(x); }
743 inline int Mod(
int x,
int y) {
return (x % y); }
745 inline float Mod(
float x,
float y) {
return std::fmod(x, y); }
746 inline double Mod(
double x,
double y) {
return std::fmod(x, y); }
747 inline long double Mod(
long double x,
long double y) {
return std::fmod(x, y); }
748 template<
typename Type>
inline Type
Remainder(Type x, Type y) {
return Mod(x, y); }
753 inline float RoundUp(
float x) {
return std::ceil(x); }
755 inline double RoundUp(
double x) {
return std::ceil(x); }
756 inline long double RoundUp(
long double x) {
return std::ceil(x); }
758 template<
typename Type>
764 return remainder ? x-remainder+base : x;
769 inline float RoundDown(
float x) {
return std::floor(x); }
771 inline double RoundDown(
double x) {
return std::floor(x); }
772 inline long double RoundDown(
long double x) {
return std::floor(x); }
774 template<
typename Type>
780 return remainder ? x-remainder : x;
794 template<
typename Type>
800 template<
typename Type>
808 template<
typename Type>
822 inline int Ceil(
float x) {
return int(
RoundUp(x)); }
830 template<
typename Type>
831 inline Type
Chop(Type x, Type delta) {
return (
Abs(x) < delta ? zeroVal<Type>() : x); }
835 template<
typename Type>
839 Type tenth =
Pow(10,digits);
850 inline auto PrintCast(
const T& val) ->
typename std::enable_if<!std::is_same<T, int8_t>::value
851 && !std::is_same<T, uint8_t>::value,
const T&>::type {
return val; }
852 inline int32_t
PrintCast(int8_t val) {
return int32_t(val); }
853 inline uint32_t
PrintCast(uint8_t val) {
return uint32_t(val); }
860 template<
typename Type>
888 template <
typename S,
typename T>
890 using type =
typename boost::numeric::conversion_traits<S, T>::supertype;
901 template<
typename Vec3T>
905 static const size_t hashTable[8] = { 2, 1, 9, 1, 2, 9, 0, 0 };
906 const size_t hashKey =
907 ((v[0] < v[1]) << 2) + ((v[0] < v[2]) << 1) + (v[1] < v[2]);
908 return hashTable[hashKey];
919 template<
typename Vec3T>
923 static const size_t hashTable[8] = { 2, 1, 9, 1, 2, 9, 0, 0 };
924 const size_t hashKey =
925 ((v[0] > v[1]) << 2) + ((v[0] > v[2]) << 1) + (v[1] > v[2]);
926 return hashTable[hashKey];
933 #endif // OPENVDB_MATH_MATH_HAS_BEEN_INCLUDED
@ YXZ_ROTATION
Definition: Math.h:879
Type IntegerPart(Type x)
Return the integer part of x.
Definition: Math.h:802
IntType operator()()
Return a randomly-generated integer in the current range.
Definition: Math.h:204
bool ClampTest01(Type &x)
Return true if x is outside [0,1].
Definition: Math.h:239
const Type & Min(const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h)
Return the minimum of eight values.
Definition: Math.h:666
bool SignChange(const Type &a, const Type &b)
Return true if a and b have different signs.
Definition: Math.h:710
@ XZY_ROTATION
Definition: Math.h:878
double Pow(double b, double e)
Definition: Math.h:549
@ Z_AXIS
Definition: Math.h:872
@ XYZ_ROTATION
Definition: Math.h:877
long double Cbrt(long double x)
Definition: Math.h:738
@ YZX_ROTATION
Definition: Math.h:880
bool isInfinite(const Type &x)
Return true if x is an infinity value (either positive infinity or negative infinity).
Definition: Math.h:354
void setRange(IntType imin, IntType imax)
Change the range over which integers are distributed to [imin, imax].
Definition: Math.h:189
Type Pow3(Type x)
Return x3.
Definition: Math.h:519
int Floor(long double x)
Definition: Math.h:817
Type RoundDown(Type x, Type base)
Return x rounded down to the nearest multiple of base.
Definition: Math.h:777
FloatType operator()()
Return a uniformly distributed random number in the range [0, 1).
Definition: Math.h:155
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:201
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:146
int Sign(const Type &x)
Return the sign of the given value as an integer (either -1, 0 or 1).
Definition: Math.h:703
Type Clamp01(Type x)
Return x clamped to [0, 1].
Definition: Math.h:233
T zeroVal()
Return the value of type T that corresponds to zero.
Definition: Math.h:59
Simple random integer generator.
Definition: Math.h:165
Type RoundUp(Type x, Type base)
Return x rounded up to the nearest multiple of base.
Definition: Math.h:761
int64_t doubleToInt64(const double aDoubleValue)
Definition: Math.h:457
static double value()
Definition: Math.h:119
bool ZeroCrossing(const Type &a, const Type &b)
Return true if the interval [a, b] includes zero, i.e., if either a or b is zero or if they have diff...
Definition: Math.h:720
@ ZXY_ROTATION
Definition: Math.h:881
int32_t floatToInt32(const float aFloatValue)
Definition: Math.h:448
@ X_AXIS
Definition: Math.h:870
Simple generator of random numbers over the range [0, 1)
Definition: Math.h:129
Library and file format version numbers.
size_t MinIndex(const Vec3T &v)
Return the index [0,1,2] of the smallest value in a 3D vector.
Definition: Math.h:903
IntType operator()(IntType imin, IntType imax)
Return a randomly-generated integer in the new range [imin, imax], without changing the current range...
Definition: Math.h:208
Tolerance for floating-point comparison.
Definition: Math.h:110
bool isNegative< bool >(const bool &)
Definition: Math.h:334
double Sin(const double &x)
Definition: Math.h:685
Type Chop(Type x, Type delta)
Return x if it is greater or equal in magnitude than delta. Otherwise, return zero.
Definition: Math.h:831
Rand01(unsigned int seed)
Initialize the generator.
Definition: Math.h:143
Type Pow4(Type x)
Return x4.
Definition: Math.h:523
Type SmoothUnitStep(Type x, Type min, Type max)
Return 0 if x < min, 1 if x > max or else (3 â 2 t) t², where t = (x â min)/(max â min).
Definition: Math.h:258
@ Y_AXIS
Definition: Math.h:871
Type Pow2(Type x)
Return x2.
Definition: Math.h:515
RandInt(unsigned int seed, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:183
std::string negative(const std::string &val)
Return the "negation" of the given string.
Definition: Math.h:105
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:408
bool isApproxZero(const Type &x, const Type &tolerance)
Return true if x is equal to zero to within the given tolerance.
Definition: Math.h:322
Type Remainder(Type x, Type y)
Definition: Math.h:748
RotationOrder
Definition: Math.h:876
bool isApproxEqual(const Type &a, const Type &b, const Type &tolerance)
Return true if a is equal to b to within the given tolerance.
Definition: Math.h:381
@ ZXZ_ROTATION
Definition: Math.h:884
bool Abs(bool b)
Definition: Math.h:284
const Type & Max(const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h)
Return the maximum of eight values.
Definition: Math.h:611
#define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
Definition: Math.h:47
long double Mod(long double x, long double y)
Definition: Math.h:747
std::string operator+(const std::string &s, double)
Definition: Math.h:72
Rand01(const EngineType &engine)
Initialize the generator.
Definition: Math.h:139
long double Sqrt(long double x)
Definition: Math.h:730
bool isUlpsEqual(const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)
Definition: Math.h:489
static double value()
Definition: Math.h:112
int Ceil(long double x)
Definition: Math.h:825
long double Round(long double x)
Definition: Math.h:788
bool isApproxLarger(const Type &a, const Type &b, const Type &tolerance)
Return true if a is larger than b to within the given tolerance, i.e., if b - a < tolerance.
Definition: Math.h:399
constexpr float pi()
Definition: Math.h:82
Type Exp(const Type &x)
Return ex.
Definition: Math.h:677
bool isFinite(const Type &x)
Return true if x is finite.
Definition: Math.h:344
#define OPENVDB_EXACT_IS_APPROX_EQUAL(T)
Definition: Math.h:386
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:146
Type Inv(Type x)
Return the inverse of x.
Definition: Math.h:862
Type EuclideanRemainder(Type x)
Definition: Math.h:796
size_t MaxIndex(const Vec3T &v)
Return the index [0,1,2] of the largest value in a 3D vector.
Definition: Math.h:921
bool isNegative(const Type &x)
Return true if x is less than zero.
Definition: Math.h:331
Delta for small floating-point offsets.
Definition: Math.h:117
uint32_t PrintCast(uint8_t val)
Definition: Math.h:853
Type Clamp(Type x, Type min, Type max)
Return x clamped to [min, max].
Definition: Math.h:223
static float value()
Definition: Math.h:111
double ValueType
Definition: Math.h:135
RandInt(const EngineType &engine, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:175
@ XZX_ROTATION
Definition: Math.h:883
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:152
Type Truncate(Type x, unsigned int digits)
Return x truncated to the given number of decimal digits.
Definition: Math.h:837
@ ZYX_ROTATION
Definition: Math.h:882
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:94
double Cos(const double &x)
Definition: Math.h:694
bool isZero(const Type &x)
Return true if x is exactly equal to zero.
Definition: Math.h:301
bool isNan(const Type &x)
Return true if x is a NaN (Not-A-Number) value.
Definition: Math.h:364
Definition: Exceptions.h:13
bool isRelOrApproxEqual(const bool &a, const bool &b, const bool &, const bool &)
Definition: Math.h:438
bool zeroVal< bool >()
Return the bool value that corresponds to zero.
Definition: Math.h:63
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:195
static float value()
Definition: Math.h:118
Type FractionalPart(Type x)
Return the fractional part of x.
Definition: Math.h:810
Axis
Definition: Math.h:869
#define OPENVDB_NO_FP_EQUALITY_WARNING_END
Definition: Math.h:48