///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2012 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_CORE_func_common
#define GLM_CORE_func_common GLM_VERSION

#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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
template<typename genType>
genType min(
  genType const & x,
  genType const & y);

template<typename genType>
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>
genType max(
  genType const & x,
  genType const & y);

template<typename genType>
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>
genType clamp(
  genType const & x,
  genType const & minVal,
  genType const & maxVal);

template<typename genType>
genType clamp(
  genType const & x,
  typename genType::value_type const & minVal,
  typename genType::value_type const & maxVal);

//! @return 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].
//!
//! @return 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 genTypeT, typename genTypeU>
genTypeT mix(genTypeT const & x, genTypeT const & y, genTypeU const & a);

//! 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<typename genType>
genType step(
  genType const & edge,
  genType const & x);

template<typename genType>
genType step(
  typename genType::value_type const & edge,
  genType 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>
genType smoothstep(
  genType const & edge0,
  genType const & edge1,
  genType const & x);

template<typename genType>
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.
///
/// @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>
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>
typename genType::bool_type isinf(genType const & x);

/// Returns a signed integer value representing
/// the encoding of a floating-point value. The floatingpoint
/// value's bit-level representation is preserved.
///
/// @tparam genType Single-precision floating-point scalar or vector types.
/// @tparam genIType Signed integer scalar or vector types.
///
/// @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<typename genType, typename genIType>
genIType floatBitsToInt(genType const & value);

/// Returns a unsigned integer value representing
/// the encoding of a floating-point value. The floatingpoint
/// value's bit-level representation is preserved.
///
/// @tparam genType Single-precision floating-point scalar or vector types.
/// @tparam genUType Unsigned integer scalar or vector types.
///
/// @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<typename genType, typename genUType>
genUType floatBitsToUint(genType const & value);

/// 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.
///
/// @tparam genType Single-precision floating-point scalar or vector types.
/// @tparam genIType Signed integer scalar or vector types.
///
/// @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>
///
/// @todo Clarify this declaration, we don't need to actually specify the return type
template<typename genType, typename genIType>
genType intBitsToFloat(genIType const & value);

/// 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.
///
/// @tparam genType Single-precision floating-point scalar or vector types.
/// @tparam genUType Unsigned integer scalar or vector types.
///
/// @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>
///
/// @todo Clarify this declaration, we don't need to actually specify the return type
template<typename genType, typename genUType>
genType uintBitsToFloat(genUType const & value);

/// 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>
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>
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>
genType ldexp(genType const & x, genIType const & exp);

/// @}
} //namespace glm

#include "func_common.inl"

#endif //GLM_CORE_func_common
