///////////////////////////////////////////////////////////////////////////////////
/// 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 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 "../detail/type_int.hpp"
#include <cmath>
#include <cfloat>
#include <limits>
#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
namespace glm
{
template <>
GLM_FUNC_QUALIFIER float next_float(float const & x)
{
# if((GLM_LANG & GLM_LANG_CXX11_FLAG))
return std::nextafter(x, std::numeric_limits<float>::max());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafterf(x, FLT_MAX);
# else
return nextafterf(x, FLT_MAX);
# endif
}
template <>
GLM_FUNC_QUALIFIER double next_float(double const & x)
{
# if((GLM_LANG & GLM_LANG_CXX11_FLAG))
return std::nextafter(x, std::numeric_limits<double>::max());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafter(x, std::numeric_limits<double>::max());
# else
return nextafter(x, DBL_MAX);
# endif
}
template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P> next_float(vecType<T, P> const & x)
{
vecType<T, P> Result;
for(length_t i = 0; i < Result.length(); ++i)
Result[i] = next_float(x[i]);
return Result;
}
GLM_FUNC_QUALIFIER float prev_float(float const & x)
{
# if((GLM_LANG & GLM_LANG_CXX11_FLAG))
return std::nextafter(x, std::numeric_limits<float>::min());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafterf(x, FLT_MIN);
# else
return nextafterf(x, FLT_MIN);
# endif
}
GLM_FUNC_QUALIFIER double prev_float(double const & x)
{
# if((GLM_LANG & GLM_LANG_CXX11_FLAG))
return std::nextafter(x, std::numeric_limits<double>::min());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return _nextafter(x, DBL_MIN);
# else
return nextafter(x, DBL_MIN);
# endif
}
template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P> prev_float(vecType<T, P> const & x)
{
vecType<T, P> Result;
for(length_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(uint i = 0; i < ulps; ++i)
temp = next_float(temp);
return temp;
}
template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P> next_float(vecType<T, P> const & x, vecType<uint, P> const & ulps)
{
vecType<T, P> Result;
for(length_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(uint i = 0; i < ulps; ++i)
temp = prev_float(temp);
return temp;
}
template<typename T, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<T, P> prev_float(vecType<T, P> const & x, vecType<uint, P> const & ulps)
{
vecType<T, P> Result;
for(length_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, precision P, template<typename, precision> class vecType>
GLM_FUNC_QUALIFIER vecType<uint, P> float_distance(vecType<T, P> const & x, vecType<T, P> const & y)
{
vecType<uint, P> Result;
for(length_t i = 0; i < Result.length(); ++i)
Result[i] = float_distance(x[i], y[i]);
return Result;
}
}//namespace glm