315 lines
9.8 KiB
Plaintext
315 lines
9.8 KiB
Plaintext
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///////////////////////////////////////////////////////////////////////////////////
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/// OpenGL Mathematics (glm.g-truc.net)
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///
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/// Copyright (c) 2005 - 2012 G-Truc Creation (www.g-truc.net)
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/// Permission is hereby granted, free of charge, to any person obtaining a copy
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/// of this software and associated documentation files (the "Software"), to deal
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/// in the Software without restriction, including without limitation the rights
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/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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/// copies of the Software, and to permit persons to whom the Software is
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/// furnished to do so, subject to the following conditions:
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///
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/// The above copyright notice and this permission notice shall be included in
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/// all copies or substantial portions of the Software.
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///
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/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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/// THE SOFTWARE.
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///
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/// @ref gtc_ulp
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/// @file glm/gtc/ulp.inl
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/// @date 2011-03-07 / 2012-04-07
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/// @author Christophe Riccio
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///////////////////////////////////////////////////////////////////////////////////
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/// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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///
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/// Developed at SunPro, a Sun Microsystems, Inc. business.
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/// Permission to use, copy, modify, and distribute this
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/// software is freely granted, provided that this notice
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/// is preserved.
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///////////////////////////////////////////////////////////////////////////////////
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#include <cmath>
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#include <cfloat>
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#pragma warning(push)
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#pragma warning(disable : 4127)
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typedef union
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{
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float value;
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/* FIXME: Assumes 32 bit int. */
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unsigned int word;
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} ieee_float_shape_type;
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typedef union
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{
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double value;
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struct
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{
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glm::detail::int32 lsw;
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glm::detail::int32 msw;
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} parts;
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} ieee_double_shape_type;
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#define GLM_EXTRACT_WORDS(ix0,ix1,d) \
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do { \
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ieee_double_shape_type ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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} while (0)
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#define GLM_GET_FLOAT_WORD(i,d) \
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do { \
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ieee_float_shape_type gf_u; \
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gf_u.value = (d); \
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(i) = gf_u.word; \
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} while (0)
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#define GLM_SET_FLOAT_WORD(d,i) \
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do { \
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ieee_float_shape_type sf_u; \
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sf_u.word = (i); \
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(d) = sf_u.value; \
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} while (0)
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#define GLM_INSERT_WORDS(d,ix0,ix1) \
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do { \
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ieee_double_shape_type iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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} while (0)
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namespace glm{
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namespace detail
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{
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GLM_FUNC_QUALIFIER float nextafterf(float x, float y)
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{
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volatile float t;
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glm::detail::int32 hx, hy, ix, iy;
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GLM_GET_FLOAT_WORD(hx, x);
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GLM_GET_FLOAT_WORD(hy, y);
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ix = hx&0x7fffffff; // |x|
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iy = hy&0x7fffffff; // |y|
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if((ix>0x7f800000) || // x is nan
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(iy>0x7f800000)) // y is nan
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return x+y;
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if(x==y) return y; // x=y, return y
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if(ix==0) { // x == 0
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GLM_SET_FLOAT_WORD(x,(hy&0x80000000)|1);// return +-minsubnormal
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t = x*x;
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if(t==x) return t; else return x; // raise underflow flag
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}
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if(hx>=0) { // x > 0
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if(hx>hy) { // x > y, x -= ulp
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hx -= 1;
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} else { // x < y, x += ulp
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hx += 1;
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}
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} else { // x < 0
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if(hy>=0||hx>hy){ // x < y, x -= ulp
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hx -= 1;
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} else { // x > y, x += ulp
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hx += 1;
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}
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}
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hy = hx&0x7f800000;
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if(hy>=0x7f800000) return x+x; // overflow
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if(hy<0x00800000) { // underflow
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t = x*x;
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if(t!=x) { // raise underflow flag
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GLM_SET_FLOAT_WORD(y,hx);
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return y;
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}
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}
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GLM_SET_FLOAT_WORD(x,hx);
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return x;
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}
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GLM_FUNC_QUALIFIER double nextafter(double x, double y)
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{
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volatile double t;
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glm::detail::int32 hx, hy, ix, iy;
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glm::detail::uint32 lx, ly;
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GLM_EXTRACT_WORDS(hx, lx, x);
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GLM_EXTRACT_WORDS(hy, ly, y);
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ix = hx & 0x7fffffff; // |x|
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iy = hy & 0x7fffffff; // |y|
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if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || // x is nan
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((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) // y is nan
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return x+y;
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if(x==y) return y; // x=y, return y
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if((ix|lx)==0) { // x == 0
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GLM_INSERT_WORDS(x, hy & 0x80000000, 1); // return +-minsubnormal
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t = x*x;
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if(t==x) return t; else return x; // raise underflow flag
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}
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if(hx>=0) { // x > 0
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if(hx>hy||((hx==hy)&&(lx>ly))) { // x > y, x -= ulp
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if(lx==0) hx -= 1;
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lx -= 1;
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} else { // x < y, x += ulp
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lx += 1;
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if(lx==0) hx += 1;
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}
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} else { // x < 0
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if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){// x < y, x -= ulp
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if(lx==0) hx -= 1;
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lx -= 1;
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} else { // x > y, x += ulp
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lx += 1;
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if(lx==0) hx += 1;
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}
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}
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hy = hx&0x7ff00000;
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if(hy>=0x7ff00000) return x+x; // overflow
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if(hy<0x00100000) { // underflow
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t = x*x;
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if(t!=x) { // raise underflow flag
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GLM_INSERT_WORDS(y,hx,lx);
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return y;
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}
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}
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GLM_INSERT_WORDS(x,hx,lx);
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return x;
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}
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}//namespace detail
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}//namespace glm
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#pragma warning(pop)
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#if((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
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# define GLM_NEXT_AFTER_FLT(x, toward) glm::detail::nextafterf((x), (toward))
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# define GLM_NEXT_AFTER_DBL(x, toward) _nextafter((x), (toward))
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#else
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# define GLM_NEXT_AFTER_FLT(x, toward) nextafterf((x), (toward))
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# define GLM_NEXT_AFTER_DBL(x, toward) nextafter((x), (toward))
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#endif
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namespace glm
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{
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GLM_FUNC_QUALIFIER float next_float(float const & x)
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{
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return GLM_NEXT_AFTER_FLT(x, std::numeric_limits<float>::max());
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}
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GLM_FUNC_QUALIFIER double next_float(double const & x)
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{
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return GLM_NEXT_AFTER_DBL(x, std::numeric_limits<double>::max());
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}
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template<typename T, template<typename> class vecType>
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GLM_FUNC_QUALIFIER vecType<T> next_float(vecType<T> const & x)
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{
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vecType<T> Result;
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for(std::size_t i = 0; i < Result.length(); ++i)
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Result[i] = next_float(x[i]);
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return Result;
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}
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GLM_FUNC_QUALIFIER float prev_float(float const & x)
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{
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return GLM_NEXT_AFTER_FLT(x, std::numeric_limits<float>::min());
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}
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GLM_FUNC_QUALIFIER double prev_float(double const & x)
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{
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return GLM_NEXT_AFTER_DBL(x, std::numeric_limits<double>::min());
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}
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template<typename T, template<typename> class vecType>
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GLM_FUNC_QUALIFIER vecType<T> prev_float(vecType<T> const & x)
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{
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vecType<T> Result;
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for(std::size_t i = 0; i < Result.length(); ++i)
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Result[i] = prev_float(x[i]);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER T next_float(T const & x, uint const & ulps)
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{
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T temp = x;
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for(std::size_t i = 0; i < ulps; ++i)
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temp = next_float(temp);
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return temp;
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}
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template<typename T, template<typename> class vecType>
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GLM_FUNC_QUALIFIER vecType<T> next_float(vecType<T> const & x, vecType<uint> const & ulps)
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{
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vecType<T> Result;
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for(std::size_t i = 0; i < Result.length(); ++i)
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Result[i] = next_float(x[i], ulps[i]);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER T prev_float(T const & x, uint const & ulps)
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{
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T temp = x;
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for(std::size_t i = 0; i < ulps; ++i)
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temp = prev_float(temp);
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return temp;
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}
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template<typename T, template<typename> class vecType>
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GLM_FUNC_QUALIFIER vecType<T> prev_float(vecType<T> const & x, vecType<uint> const & ulps)
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{
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vecType<T> Result;
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for(std::size_t i = 0; i < Result.length(); ++i)
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Result[i] = prev_float(x[i], ulps[i]);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER uint float_distance(T const & x, T const & y)
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{
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uint ulp = 0;
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if(x < y)
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{
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T temp = x;
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while(temp != y && ulp < std::numeric_limits<std::size_t>::max())
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{
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++ulp;
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temp = next_float(temp);
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}
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}
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else if(y < x)
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{
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T temp = y;
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while(temp != x && ulp < std::numeric_limits<std::size_t>::max())
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{
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++ulp;
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temp = next_float(temp);
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}
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}
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else // ==
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{
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}
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return ulp;
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}
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template<typename T, template<typename> class vecType>
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GLM_FUNC_QUALIFIER vecType<uint> float_distance(vecType<T> const & x, vecType<T> const & y)
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{
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vecType<uint> Result;
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for(std::size_t i = 0; i < Result.length(); ++i)
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Result[i] = float_distance(x[i], y[i]);
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return Result;
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}
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}//namespace glm
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