General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at least arbitrary numeric value types)  
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| template<typename T> | 
| constexpr T | zeroVal () | 
|  | Return the value of type T that corresponds to zero. 
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| std::string | zeroVal< std::string > () | 
|  | Return the std::stringvalue that corresponds to zero.
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| constexpr bool | zeroVal< bool > () | 
|  | Return the boolvalue that corresponds to zero.
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| std::string | operator+ (const std::string &s, bool) | 
|  | Needed to support the (zeroVal<ValueType>() + val)idiom whenValueTypeisstd::string.
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| std::string | operator+ (const std::string &s, int) | 
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| std::string | operator+ (const std::string &s, float) | 
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| std::string | operator+ (const std::string &s, double) | 
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| template<typename Type1, typename Type2> | 
| auto | cwiseAdd (const Type1 &v, const Type2 s) | 
|  | Componentwise adder for POD types. 
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| template<typename Type1, typename Type2> | 
| bool | cwiseLessThan (const Type1 &a, const Type2 &b) | 
|  | Componentwise less than for POD types. 
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| template<typename Type1, typename Type2> | 
| bool | cwiseGreaterThan (const Type1 &a, const Type2 &b) | 
|  | Componentwise greater than for POD types. 
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| template<typename T> | 
| constexpr T | pi () | 
|  | Pi constant taken from Boost to match old behaviour. 
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| constexpr float | pi () | 
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| constexpr double | pi () | 
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| constexpr long double | pi () | 
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| T | negative (const T &val) | 
|  | Return the unary negation of the given value. 
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| bool | negative (const bool &val) | 
|  | Return the negation of the given boolean. 
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| std::string | negative (const std::string &val) | 
|  | Return the "negation" of the given string. 
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| Type | Clamp (Type x, Type min, Type max) | 
|  | Return x clamped to [min, max]. 
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| template<typename Type> | 
| Type | Clamp01 (Type x) | 
|  | Return x clamped to [0, 1]. 
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| template<typename Type> | 
| bool | ClampTest01 (Type &x) | 
|  | Return trueif x is outside [0,1].
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| template<typename Type> | 
| Type | SmoothUnitStep (Type x) | 
|  | Return 0 if x < 0, 1 if x > 1 or else (3 − 2 x) x². 
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| template<typename Type> | 
| Type | SmoothUnitStep (Type x, Type min, Type max) | 
|  | Return 0 if x < min, 1 if x > max or else (3 − 2 t) t², where t = (x − min)/(max − min). 
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| int32_t | Abs (int32_t i) | 
|  | Return the absolute value of the given quantity. 
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| int64_t | Abs (int64_t i) | 
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| float | Abs (float x) | 
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| double | Abs (double x) | 
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| long double | Abs (long double x) | 
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| uint32_t | Abs (uint32_t i) | 
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| uint64_t | Abs (uint64_t i) | 
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| bool | Abs (bool b) | 
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| template<typename T> | 
| std::enable_if< std::is_same< T, size_t >::value, T >::type | Abs (T i) | 
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| template<typename Type> | 
| bool | isZero (const Type &x) | 
|  | Return trueif x is exactly equal to zero.
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| template<typename Type> | 
| bool | isApproxZero (const Type &x) | 
|  | Return trueif x is equal to zero to within the default floating-point comparison tolerance.
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| template<typename Type> | 
| bool | isApproxZero (const Type &x, const Type &tolerance) | 
|  | Return trueif x is equal to zero to within the given tolerance.
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| bool | isNegative (const Type &x) | 
|  | Return trueif x is less than zero.
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| bool | isNegative< bool > (const bool &) | 
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| bool | isFinite (const float x) | 
|  | Return trueif x is finite.
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| template<typename Type, typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0> | 
| bool | isFinite (const Type &x) | 
|  | Return trueif x is finite.
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| bool | isInfinite (const float x) | 
|  | Return trueif x is an infinity value (either positive infinity or negative infinity).
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| template<typename Type, typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0> | 
| bool | isInfinite (const Type &x) | 
|  | Return trueif x is an infinity value (either positive infinity or negative infinity).
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| bool | isNan (const float x) | 
|  | Return trueif x is a NaN (Not-A-Number) value.
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| template<typename Type, typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0> | 
| bool | isNan (const Type &x) | 
|  | Return trueif x is a NaN (Not-A-Number) value.
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| template<typename Type> | 
| bool | isApproxEqual (const Type &a, const Type &b, const Type &tolerance) | 
|  | Return trueif a is equal to b to within the given tolerance.
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| template<typename Type> | 
| bool | isApproxEqual (const Type &a, const Type &b) | 
|  | Return trueif a is equal to b to within the default floating-point comparison tolerance.
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| bool | isApproxEqual< bool > (const bool &a, const bool &b) | 
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| bool | isApproxEqual< bool > (const bool &a, const bool &b, const bool &) | 
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| bool | isApproxEqual< std::string > (const std::string &a, const std::string &b) | 
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| bool | isApproxEqual< std::string > (const std::string &a, const std::string &b, const std::string &) | 
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| template<typename Type> | 
| bool | isApproxLarger (const Type &a, const Type &b, const Type &tolerance) | 
|  | Return trueif a is larger than b to within the given tolerance, i.e., if b - a < tolerance.
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| template<typename T0, typename T1> | 
| bool | isExactlyEqual (const T0 &a, const T1 &b) | 
|  | Return trueif a is exactly equal to b.
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| template<typename Type> | 
| bool | isRelOrApproxEqual (const Type &a, const Type &b, const Type &absTol, const Type &relTol) | 
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| bool | isRelOrApproxEqual (const bool &a, const bool &b, const bool &, const bool &) | 
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| int32_t | floatToInt32 (const float f) | 
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| int64_t | doubleToInt64 (const double d) | 
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| bool | isUlpsEqual (const double aLeft, const double aRight, const int64_t aUnitsInLastPlace) | 
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| bool | isUlpsEqual (const float aLeft, const float aRight, const int32_t aUnitsInLastPlace) | 
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| Type | Pow2 (Type x) | 
|  | Return x2. 
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| Type | Pow3 (Type x) | 
|  | Return x3. 
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| Type | Pow4 (Type x) | 
|  | Return x4. 
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| template<typename Type> | 
| Type | Pow (Type x, int n) | 
|  | Return xn. 
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| float | Pow (float b, float e) | 
|  | Return be. 
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| double | Pow (double b, double e) | 
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| const Type & | Max (const Type &a, const Type &b) | 
|  | Return the maximum of two values. 
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| const Type & | Max (const Type &a, const Type &b, const Type &c) | 
|  | Return the maximum of three values. 
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| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d) | 
|  | Return the maximum of four values. 
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| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e) | 
|  | Return the maximum of five values. 
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| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f) | 
|  | Return the maximum of six values. 
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| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g) | 
|  | Return the maximum of seven values. 
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| 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. 
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| const Type & | Min (const Type &a, const Type &b) | 
|  | Return the minimum of two values. 
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| const Type & | Min (const Type &a, const Type &b, const Type &c) | 
|  | Return the minimum of three values. 
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| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d) | 
|  | Return the minimum of four values. 
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| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e) | 
|  | Return the minimum of five values. 
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| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f) | 
|  | Return the minimum of six values. 
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| template<typename Type> | 
| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g) | 
|  | Return the minimum of seven values. 
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| template<typename Type> | 
| 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. 
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| template<typename Type> | 
| Type | Exp (const Type &x) | 
|  | Return ex. 
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| float | Sin (const float &x) | 
|  | Return sin x. 
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| double | Sin (const double &x) | 
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| float | Cos (const float &x) | 
|  | Return cos x. 
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| double | Cos (const double &x) | 
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| int | Sign (const Type &x) | 
|  | Return the sign of the given value as an integer (either -1, 0 or 1). 
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| bool | SignChange (const Type &a, const Type &b) | 
|  | Return trueif a and b have different signs.
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| bool | ZeroCrossing (const Type &a, const Type &b) | 
|  | Return trueif the interval [a, b] includes zero, i.e., if either a or b is zero or if they have different signs.
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| float | Sqrt (float x) | 
|  | Return the square root of a floating-point value. 
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| double | Sqrt (double x) | 
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| long double | Sqrt (long double x) | 
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| float | Cbrt (float x) | 
|  | Return the cube root of a floating-point value. 
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| double | Cbrt (double x) | 
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| long double | Cbrt (long double x) | 
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| int | Mod (int x, int y) | 
|  | Return the remainder of x / y. 
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| float | Mod (float x, float y) | 
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| double | Mod (double x, double y) | 
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| long double | Mod (long double x, long double y) | 
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| Type | Remainder (Type x, Type y) | 
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| float | RoundUp (float x) | 
|  | Return x rounded up to the nearest integer. 
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| double | RoundUp (double x) | 
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| long double | RoundUp (long double x) | 
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| Type | RoundUp (Type x, Type base) | 
|  | Return x rounded up to the nearest multiple of base. 
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| float | RoundDown (float x) | 
|  | Return x rounded down to the nearest integer. 
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| double | RoundDown (double x) | 
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| long double | RoundDown (long double x) | 
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| Type | RoundDown (Type x, Type base) | 
|  | Return x rounded down to the nearest multiple of base. 
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| float | Round (float x) | 
|  | Return x rounded to the nearest integer. 
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| double | Round (double x) | 
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| long double | Round (long double x) | 
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| Type | EuclideanRemainder (Type x) | 
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| template<typename Type> | 
| Type | IntegerPart (Type x) | 
|  | Return the integer part of x. 
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| Type | FractionalPart (Type x) | 
|  | Return the fractional part of x. 
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| int | Floor (float x) | 
|  | Return the floor of x. 
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| int | Floor (double x) | 
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| int | Floor (long double x) | 
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| int | Ceil (float x) | 
|  | Return the ceiling of x. 
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| int | Ceil (double x) | 
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| int | Ceil (long double x) | 
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| Type | Chop (Type x, Type delta) | 
|  | Return x if it is greater or equal in magnitude than delta. Otherwise, return zero. 
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| Type | Truncate (Type x, unsigned int digits) | 
|  | Return x truncated to the given number of decimal digits. 
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| template<typename T> | 
| auto | PrintCast (const T &val) -> typename std::enable_if<!std::is_same< T, int8_t >::value &&!std::is_same< T, uint8_t >::value, const T & >::type | 
|  | 8-bit integer values print to std::ostreams as characters. Cast them so that they print as integers instead. 
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| int32_t | PrintCast (int8_t val) | 
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| uint32_t | PrintCast (uint8_t val) | 
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| template<typename Type> | 
| Type | Inv (Type x) | 
|  | Return the inverse of x. 
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| template<typename Vec3T> | 
| size_t | MinIndex (const Vec3T &v) | 
|  | Return the index [0,1,2] of the smallest value in a 3D vector. 
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| template<typename Vec3T> | 
| size_t | MaxIndex (const Vec3T &v) | 
|  | Return the index [0,1,2] of the largest value in a 3D vector. 
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