/////////////////////////////////////////////////////////////////////////////////// /// OpenGL Mathematics (glm.g-truc.net) /// /// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net) /// Permission is hereby granted, free of charge, to any person 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, sublicense, 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: /// /// The above copyright notice and this permission notice shall be included in /// all copies or substantial portions of the Software. /// /// THE SOFTWARE IS PROVIDED "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. IN NO EVENT SHALL THE /// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER /// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, /// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN /// THE SOFTWARE. /// /// @ref core /// @file glm/core/func_common.hpp /// @date 2008-03-08 / 2010-01-26 /// @author Christophe Riccio /// /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> /// /// @defgroup core_func_common Common functions /// @ingroup core /// /// These all operate component-wise. The description is per component. /////////////////////////////////////////////////////////////////////////////////// #ifndef GLM_FUNC_COMMON_INCLUDED #define GLM_FUNC_COMMON_INCLUDED #include "setup.hpp" #include "precision.hpp" #include "type_int.hpp" #include "_fixes.hpp" namespace glm { /// @addtogroup core_func_common /// @{ /// Returns x if x >= 0; otherwise, it returns -x. /// /// @tparam genType floating-point or signed integer; scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/abs.xml">GLSL abs man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType abs(genType const & x); /// Returns 1.0 if x > 0, 0.0 if x == 0, or -1.0 if x < 0. /// /// @tparam genType Floating-point or signed integer; scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/sign.xml">GLSL sign man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType sign(genType const & x); /// Returns a value equal to the nearest integer that is less then or equal to x. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/floor.xml">GLSL floor man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType floor(genType const & x); /// Returns a value equal to the nearest integer to x /// whose absolute value is not larger than the absolute value of x. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/trunc.xml">GLSL trunc man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType trunc(genType const & x); /// Returns a value equal to the nearest integer to x. /// The fraction 0.5 will round in a direction chosen by the /// implementation, presumably the direction that is fastest. /// This includes the possibility that round(x) returns the /// same value as roundEven(x) for all values of x. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/round.xml">GLSL round man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType round(genType const & x); /// Returns a value equal to the nearest integer to x. /// A fractional part of 0.5 will round toward the nearest even /// integer. (Both 3.5 and 4.5 for x will return 4.0.) /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/roundEven.xml">GLSL roundEven man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> /// @see <a href="http://developer.amd.com/documentation/articles/pages/New-Round-to-Even-Technique.aspx">New round to even technique</a> template <typename genType> GLM_FUNC_DECL genType roundEven(genType const & x); /// Returns a value equal to the nearest integer /// that is greater than or equal to x. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/ceil.xml">GLSL ceil man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType ceil(genType const & x); /// Return x - floor(x). /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/fract.xml">GLSL fract man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType fract(genType const & x); /// Modulus. Returns x - y * floor(x / y) /// for each component in x using the floating point value y. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/mod.xml">GLSL mod man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType mod( genType const & x, genType const & y); /// Modulus. Returns x - y * floor(x / y) /// for each component in x using the floating point value y. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/mod.xml">GLSL mod man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType mod( genType const & x, typename genType::value_type const & y); /// Returns the fractional part of x and sets i to the integer /// part (as a whole number floating point value). Both the /// return value and the output parameter will have the same /// sign as x. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/modf.xml">GLSL modf man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType modf( genType const & x, genType & i); /// Returns y if y < x; otherwise, it returns x. /// /// @tparam genType Floating-point or integer; scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/min.xml">GLSL min man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a><<<<<<< HEAD template <typename genType> GLM_FUNC_DECL genType min( genType const & x, genType const & y); template <typename genType> GLM_FUNC_DECL genType min( genType const & x, typename genType::value_type const & y); /// Returns y if x < y; otherwise, it returns x. /// /// @tparam genType Floating-point or integer; scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/max.xml">GLSL max man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType max( genType const & x, genType const & y); template <typename genType> GLM_FUNC_DECL genType max( genType const & x, typename genType::value_type const & y); /// Returns min(max(x, minVal), maxVal) for each component in x /// using the floating-point values minVal and maxVal. /// /// @tparam genType Floating-point or integer; scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/clamp.xml">GLSL clamp man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType clamp( genType const & x, genType const & minVal, genType const & maxVal); template <typename genType, precision P> GLM_FUNC_DECL genType clamp( genType const & x, typename genType::value_type const & minVal, typename genType::value_type const & maxVal); /// If genTypeU is a floating scalar or vector: /// Returns x * (1.0 - a) + y * a, i.e., the linear blend of /// x and y using the floating-point value a. /// The value for a is not restricted to the range [0, 1]. /// /// If genTypeU is a boolean scalar or vector: /// Selects which vector each returned component comes /// from. For a component of <a> that is false, the /// corresponding component of x is returned. For a /// component of a that is true, the corresponding /// component of y is returned. Components of x and y that /// are not selected are allowed to be invalid floating point /// values and will have no effect on the results. Thus, this /// provides different functionality than /// genType mix(genType x, genType y, genType(a)) /// where a is a Boolean vector. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/mix.xml">GLSL mix man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> /// /// @param[in] x Value to interpolate. /// @param[in] y Value to interpolate. /// @param[in] a Interpolant. /// /// @tparam genTypeT Floating point scalar or vector. /// @tparam genTypeU Floating point or boolean scalar or vector. It can't be a vector if it is the length of genTypeT. /// /// @code /// #include <glm/glm.hpp> /// ... /// float a; /// bool b; /// glm::dvec3 e; /// glm::dvec3 f; /// glm::vec4 g; /// glm::vec4 h; /// ... /// glm::vec4 r = glm::mix(g, h, a); // Interpolate with a floating-point scalar two vectors. /// glm::vec4 s = glm::mix(g, h, b); // Teturns g or h; /// glm::dvec3 t = glm::mix(e, f, a); // Types of the third parameter is not required to match with the first and the second. /// glm::vec4 u = glm::mix(g, h, r); // Interpolations can be perform per component with a vector for the last parameter. /// @endcode template <typename T, typename U, precision P, template <typename, precision> class vecType> GLM_FUNC_DECL vecType<T, P> mix( vecType<T, P> const & x, vecType<T, P> const & y, vecType<U, P> const & a); template <typename T, typename U, precision P, template <typename, precision> class vecType> GLM_FUNC_DECL vecType<T, P> mix( vecType<T, P> const & x, vecType<T, P> const & y, U const & a); template <typename genTypeT, typename genTypeU> GLM_FUNC_DECL genTypeT mix( genTypeT const & x, genTypeT const & y, genTypeU const & a); /// Returns 0.0 if x < edge, otherwise it returns 1.0 for each component of a genType. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/step.xml">GLSL step man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType step( genType const & edge, genType const & x); /// Returns 0.0 if x < edge, otherwise it returns 1.0. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/step.xml">GLSL step man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <template <typename, precision> class vecType, typename T, precision P> GLM_FUNC_DECL vecType<T, P> step( T const & edge, vecType<T, P> const & x); /// Returns 0.0 if x <= edge0 and 1.0 if x >= edge1 and /// performs smooth Hermite interpolation between 0 and 1 /// when edge0 < x < edge1. This is useful in cases where /// you would want a threshold function with a smooth /// transition. This is equivalent to: /// genType t; /// t = clamp ((x - edge0) / (edge1 - edge0), 0, 1); /// return t * t * (3 - 2 * t); /// Results are undefined if edge0 >= edge1. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/smoothstep.xml">GLSL smoothstep man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType smoothstep( genType const & edge0, genType const & edge1, genType const & x); template <typename genType> GLM_FUNC_DECL genType smoothstep( typename genType::value_type const & edge0, typename genType::value_type const & edge1, genType const & x); /// Returns true if x holds a NaN (not a number) /// representation in the underlying implementation's set of /// floating point representations. Returns false otherwise, /// including for implementations with no NaN /// representations. /// /// /!\ When using compiler fast math, this function may fail. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/isnan.xml">GLSL isnan man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL typename genType::bool_type isnan(genType const & x); /// Returns true if x holds a positive infinity or negative /// infinity representation in the underlying implementation's /// set of floating point representations. Returns false /// otherwise, including for implementations with no infinity /// representations. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/isinf.xml">GLSL isinf man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL typename genType::bool_type isinf(genType const & x); /// Returns a signed integer value representing /// the encoding of a floating-point value. The floating-point /// value's bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/floatBitsToInt.xml">GLSL floatBitsToInt man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> GLM_FUNC_DECL int floatBitsToInt(float const & v); /// Returns a signed integer value representing /// the encoding of a floating-point value. The floatingpoint /// value's bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/floatBitsToInt.xml">GLSL floatBitsToInt man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <template <typename, precision> class vecType, precision P> GLM_FUNC_DECL vecType<int, P> floatBitsToInt(vecType<float, P> const & v); /// Returns a unsigned integer value representing /// the encoding of a floating-point value. The floatingpoint /// value's bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/floatBitsToUint.xml">GLSL floatBitsToUint man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> GLM_FUNC_DECL uint floatBitsToUint(float const & v); /// Returns a unsigned integer value representing /// the encoding of a floating-point value. The floatingpoint /// value's bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/floatBitsToUint.xml">GLSL floatBitsToUint man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <template <typename, precision> class vecType, precision P> GLM_FUNC_DECL vecType<uint, P> floatBitsToUint(vecType<float, P> const & v); /// Returns a floating-point value corresponding to a signed /// integer encoding of a floating-point value. /// If an inf or NaN is passed in, it will not signal, and the /// resulting floating point value is unspecified. Otherwise, /// the bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/intBitsToFloat.xml">GLSL intBitsToFloat man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> GLM_FUNC_DECL float intBitsToFloat(int const & v); /// Returns a floating-point value corresponding to a signed /// integer encoding of a floating-point value. /// If an inf or NaN is passed in, it will not signal, and the /// resulting floating point value is unspecified. Otherwise, /// the bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/intBitsToFloat.xml">GLSL intBitsToFloat man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <template <typename, precision> class vecType, precision P> GLM_FUNC_DECL vecType<float, P> intBitsToFloat(vecType<int, P> const & v); /// Returns a floating-point value corresponding to a /// unsigned integer encoding of a floating-point value. /// If an inf or NaN is passed in, it will not signal, and the /// resulting floating point value is unspecified. Otherwise, /// the bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/uintBitsToFloat.xml">GLSL uintBitsToFloat man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> GLM_FUNC_DECL float uintBitsToFloat(uint const & v); /// Returns a floating-point value corresponding to a /// unsigned integer encoding of a floating-point value. /// If an inf or NaN is passed in, it will not signal, and the /// resulting floating point value is unspecified. Otherwise, /// the bit-level representation is preserved. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/uintBitsToFloat.xml">GLSL uintBitsToFloat man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <template <typename, precision> class vecType, precision P> GLM_FUNC_DECL vecType<float, P> uintBitsToFloat(vecType<uint, P> const & v); /// Computes and returns a * b + c. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/fma.xml">GLSL fma man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType> GLM_FUNC_DECL genType fma(genType const & a, genType const & b, genType const & c); /// Splits x into a floating-point significand in the range /// [0.5, 1.0) and an integral exponent of two, such that: /// x = significand * exp(2, exponent) /// /// The significand is returned by the function and the /// exponent is returned in the parameter exp. For a /// floating-point value of zero, the significant and exponent /// are both zero. For a floating-point value that is an /// infinity or is not a number, the results are undefined. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/frexp.xml">GLSL frexp man page</a> /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType, typename genIType> GLM_FUNC_DECL genType frexp(genType const & x, genIType & exp); /// Builds a floating-point number from x and the /// corresponding integral exponent of two in exp, returning: /// significand * exp(2, exponent) /// /// If this product is too large to be represented in the /// floating-point type, the result is undefined. /// /// @tparam genType Floating-point scalar or vector types. /// /// @see <a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/ldexp.xml">GLSL ldexp man page</a>; /// @see <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.3 Common Functions</a> template <typename genType, typename genIType> GLM_FUNC_DECL genType ldexp(genType const & x, genIType const & exp); /// @} }//namespace glm #include "func_common.inl" #endif//GLM_FUNC_COMMON_INCLUDED