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+///////////////////////////////////////////////////////////////////////////////////
+/// OpenGL Mathematics (glm.g-truc.net)
+///
+/// Copyright (c) 2005 - 2013 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 gtc_ulp
+/// @file glm/gtc/ulp.inl
+/// @date 2011-03-07 / 2012-04-07
+/// @author Christophe Riccio
+///////////////////////////////////////////////////////////////////////////////////
+/// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+///
+/// Developed at SunPro, a Sun Microsystems, Inc. business.
+/// Permission to use, copy, modify, and distribute this
+/// software is freely granted, provided that this notice
+/// is preserved.
+///////////////////////////////////////////////////////////////////////////////////
+
+#include <cmath>
+#include <cfloat>
+
+#if(GLM_COMPILER & GLM_COMPILER_VC)
+# pragma warning(push)
+# pragma warning(disable : 4127)
+#endif
+
+typedef union
+{
+ float value;
+ /* FIXME: Assumes 32 bit int. */
+ unsigned int word;
+} ieee_float_shape_type;
+
+typedef union
+{
+ double value;
+ struct
+ {
+ glm::detail::int32 lsw;
+ glm::detail::int32 msw;
+ } parts;
+} ieee_double_shape_type;
+
+#define GLM_EXTRACT_WORDS(ix0,ix1,d) \
+ do { \
+ ieee_double_shape_type ew_u; \
+ ew_u.value = (d); \
+ (ix0) = ew_u.parts.msw; \
+ (ix1) = ew_u.parts.lsw; \
+ } while (0)
+
+#define GLM_GET_FLOAT_WORD(i,d) \
+ do { \
+ ieee_float_shape_type gf_u; \
+ gf_u.value = (d); \
+ (i) = gf_u.word; \
+ } while (0)
+
+#define GLM_SET_FLOAT_WORD(d,i) \
+ do { \
+ ieee_float_shape_type sf_u; \
+ sf_u.word = (i); \
+ (d) = sf_u.value; \
+ } while (0)
+
+#define GLM_INSERT_WORDS(d,ix0,ix1) \
+ do { \
+ ieee_double_shape_type iw_u; \
+ iw_u.parts.msw = (ix0); \
+ iw_u.parts.lsw = (ix1); \
+ (d) = iw_u.value; \
+ } while (0)
+
+namespace glm{
+namespace detail
+{
+ GLM_FUNC_QUALIFIER float nextafterf(float x, float y)
+ {
+ volatile float t;
+ glm::detail::int32 hx, hy, ix, iy;
+
+ GLM_GET_FLOAT_WORD(hx, x);
+ GLM_GET_FLOAT_WORD(hy, y);
+ ix = hx&0x7fffffff; // |x|
+ iy = hy&0x7fffffff; // |y|
+
+ if((ix>0x7f800000) || // x is nan
+ (iy>0x7f800000)) // y is nan
+ return x+y;
+ if(x==y) return y; // x=y, return y
+ if(ix==0) { // x == 0
+ GLM_SET_FLOAT_WORD(x,(hy&0x80000000)|1);// return +-minsubnormal
+ t = x*x;
+ if(t==x) return t; else return x; // raise underflow flag
+ }
+ if(hx>=0) { // x > 0
+ if(hx>hy) { // x > y, x -= ulp
+ hx -= 1;
+ } else { // x < y, x += ulp
+ hx += 1;
+ }
+ } else { // x < 0
+ if(hy>=0||hx>hy){ // x < y, x -= ulp
+ hx -= 1;
+ } else { // x > y, x += ulp
+ hx += 1;
+ }
+ }
+ hy = hx&0x7f800000;
+ if(hy>=0x7f800000) return x+x; // overflow
+ if(hy<0x00800000) { // underflow
+ t = x*x;
+ if(t!=x) { // raise underflow flag
+ GLM_SET_FLOAT_WORD(y,hx);
+ return y;
+ }
+ }
+ GLM_SET_FLOAT_WORD(x,hx);
+ return x;
+ }
+
+ GLM_FUNC_QUALIFIER double nextafter(double x, double y)
+ {
+ volatile double t;
+ glm::detail::int32 hx, hy, ix, iy;
+ glm::detail::uint32 lx, ly;
+
+ GLM_EXTRACT_WORDS(hx, lx, x);
+ GLM_EXTRACT_WORDS(hy, ly, y);
+ ix = hx & 0x7fffffff; // |x|
+ iy = hy & 0x7fffffff; // |y|
+
+ if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || // x is nan
+ ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) // y is nan
+ return x+y;
+ if(x==y) return y; // x=y, return y
+ if((ix|lx)==0) { // x == 0
+ GLM_INSERT_WORDS(x, hy & 0x80000000, 1); // return +-minsubnormal
+ t = x*x;
+ if(t==x) return t; else return x; // raise underflow flag
+ }
+ if(hx>=0) { // x > 0
+ if(hx>hy||((hx==hy)&&(lx>ly))) { // x > y, x -= ulp
+ if(lx==0) hx -= 1;
+ lx -= 1;
+ } else { // x < y, x += ulp
+ lx += 1;
+ if(lx==0) hx += 1;
+ }
+ } else { // x < 0
+ if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){// x < y, x -= ulp
+ if(lx==0) hx -= 1;
+ lx -= 1;
+ } else { // x > y, x += ulp
+ lx += 1;
+ if(lx==0) hx += 1;
+ }
+ }
+ hy = hx&0x7ff00000;
+ if(hy>=0x7ff00000) return x+x; // overflow
+ if(hy<0x00100000) { // underflow
+ t = x*x;
+ if(t!=x) { // raise underflow flag
+ GLM_INSERT_WORDS(y,hx,lx);
+ return y;
+ }
+ }
+ GLM_INSERT_WORDS(x,hx,lx);
+ return x;
+ }
+}//namespace detail
+}//namespace glm
+
+#if(GLM_COMPILER & GLM_COMPILER_VC)
+# pragma warning(pop)
+#endif
+
+#if((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
+# define GLM_NEXT_AFTER_FLT(x, toward) glm::detail::nextafterf((x), (toward))
+# define GLM_NEXT_AFTER_DBL(x, toward) _nextafter((x), (toward))
+#else
+# define GLM_NEXT_AFTER_FLT(x, toward) nextafterf((x), (toward))
+# define GLM_NEXT_AFTER_DBL(x, toward) nextafter((x), (toward))
+#endif
+
+namespace glm
+{
+ GLM_FUNC_QUALIFIER float next_float(float const & x)
+ {
+ return GLM_NEXT_AFTER_FLT(x, std::numeric_limits<float>::max());
+ }
+
+ GLM_FUNC_QUALIFIER double next_float(double const & x)
+ {
+ return GLM_NEXT_AFTER_DBL(x, std::numeric_limits<double>::max());
+ }
+
+ template<typename T, template<typename> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T> next_float(vecType<T> const & x)
+ {
+ vecType<T> Result;
+ for(std::size_t i = 0; i < Result.length(); ++i)
+ Result[i] = next_float(x[i]);
+ return Result;
+ }
+
+ GLM_FUNC_QUALIFIER float prev_float(float const & x)
+ {
+ return GLM_NEXT_AFTER_FLT(x, std::numeric_limits<float>::min());
+ }
+
+ GLM_FUNC_QUALIFIER double prev_float(double const & x)
+ {
+ return GLM_NEXT_AFTER_DBL(x, std::numeric_limits<double>::min());
+ }
+
+ template<typename T, template<typename> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T> prev_float(vecType<T> const & x)
+ {
+ vecType<T> Result;
+ for(std::size_t i = 0; i < Result.length(); ++i)
+ Result[i] = prev_float(x[i]);
+ return Result;
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER T next_float(T const & x, uint const & ulps)
+ {
+ T temp = x;
+ for(std::size_t i = 0; i < ulps; ++i)
+ temp = next_float(temp);
+ return temp;
+ }
+
+ template<typename T, template<typename> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T> next_float(vecType<T> const & x, vecType<uint> const & ulps)
+ {
+ vecType<T> Result;
+ for(std::size_t i = 0; i < Result.length(); ++i)
+ Result[i] = next_float(x[i], ulps[i]);
+ return Result;
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER T prev_float(T const & x, uint const & ulps)
+ {
+ T temp = x;
+ for(std::size_t i = 0; i < ulps; ++i)
+ temp = prev_float(temp);
+ return temp;
+ }
+
+ template<typename T, template<typename> class vecType>
+ GLM_FUNC_QUALIFIER vecType<T> prev_float(vecType<T> const & x, vecType<uint> const & ulps)
+ {
+ vecType<T> Result;
+ for(std::size_t i = 0; i < Result.length(); ++i)
+ Result[i] = prev_float(x[i], ulps[i]);
+ return Result;
+ }
+
+ template <typename T>
+ GLM_FUNC_QUALIFIER uint float_distance(T const & x, T const & y)
+ {
+ uint ulp = 0;
+
+ if(x < y)
+ {
+ T temp = x;
+ while(temp != y && ulp < std::numeric_limits<std::size_t>::max())
+ {
+ ++ulp;
+ temp = next_float(temp);
+ }
+ }
+ else if(y < x)
+ {
+ T temp = y;
+ while(temp != x && ulp < std::numeric_limits<std::size_t>::max())
+ {
+ ++ulp;
+ temp = next_float(temp);
+ }
+ }
+ else // ==
+ {
+
+ }
+
+ return ulp;
+ }
+
+ template<typename T, template<typename> class vecType>
+ GLM_FUNC_QUALIFIER vecType<uint> float_distance(vecType<T> const & x, vecType<T> const & y)
+ {
+ vecType<uint> Result;
+ for(std::size_t i = 0; i < Result.length(); ++i)
+ Result[i] = float_distance(x[i], y[i]);
+ return Result;
+ }
+}//namespace glm
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