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393 lines
10 KiB
393 lines
10 KiB
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net) |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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// Created : 2011-03-07 |
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// Updated : 2011-04-26 |
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// Licence : This source is under MIT License |
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// File : glm/gtx/ulp.inl |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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#include <cmath> |
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#include <cfloat> |
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/* |
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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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*/ |
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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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#if(GLM_COMPILER & GLM_COMPILER_VC) |
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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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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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/* |
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inline std::size_t ulp |
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( |
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detail::thalf const & a, |
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detail::thalf const & b |
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) |
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{ |
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std::size_t Count = 0; |
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float TempA(a); |
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float TempB(b); |
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//while((TempA = _nextafterf(TempA, TempB)) != TempB) |
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++Count; |
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return Count; |
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} |
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inline std::size_t ulp |
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( |
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float const & a, |
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float const & b |
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) |
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{ |
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std::size_t Count = 0; |
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float Temp = a; |
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//while((Temp = _nextafterf(Temp, b)) != b) |
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{ |
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std::cout << Temp << " " << b << std::endl; |
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++Count; |
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} |
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return Count; |
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} |
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inline std::size_t ulp |
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( |
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double const & a, |
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double const & b |
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) |
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{ |
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std::size_t Count = 0; |
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double Temp = a; |
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//while((Temp = _nextafter(Temp, b)) != b) |
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{ |
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std::cout << Temp << " " << b << std::endl; |
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++Count; |
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} |
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return Count; |
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} |
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template <typename T> |
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inline std::size_t ulp |
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( |
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detail::tvec2<T> const & a, |
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detail::tvec2<T> const & b |
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) |
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{ |
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std::size_t ulps[] = |
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{ |
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ulp(a[0], b[0]), |
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ulp(a[1], b[1]) |
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}; |
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return glm::max(ulps[0], ulps[1]); |
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} |
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template <typename T> |
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inline std::size_t ulp |
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( |
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detail::tvec3<T> const & a, |
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detail::tvec3<T> const & b |
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) |
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{ |
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std::size_t ulps[] = |
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{ |
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ulp(a[0], b[0]), |
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ulp(a[1], b[1]), |
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ulp(a[2], b[2]) |
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}; |
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return glm::max(glm::max(ulps[0], ulps[1]), ulps[2]); |
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} |
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template <typename T> |
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inline std::size_t ulp |
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( |
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detail::tvec4<T> const & a, |
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detail::tvec4<T> const & b |
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) |
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{ |
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std::size_t ulps[] = |
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{ |
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ulp(a[0], b[0]), |
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ulp(a[1], b[1]), |
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ulp(a[2], b[2]), |
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ulp(a[3], b[3]) |
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}; |
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return glm::max(glm::max(ulps[0], ulps[1]), glm::max(ulps[2], ulps[3])); |
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} |
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*/ |
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}//namespace glm
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