339 lines
8.2 KiB
Text
339 lines
8.2 KiB
Text
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/// @ref gtc_ulp
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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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#include "../detail/type_int.hpp"
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#include "epsilon.hpp"
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#include <cmath>
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#include <cfloat>
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#include <limits>
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#if(GLM_COMPILER & GLM_COMPILER_VC)
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# pragma warning(push)
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# pragma warning(disable : 4127)
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#endif
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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(abs(y - x) <= epsilon<float>())
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return y; // x=y, return y
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if(ix==0)
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{ // 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(abs(t - x) <= epsilon<float>())
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return t;
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else
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return x; // raise underflow flag
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}
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if(hx>=0)
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{ // 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
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{ // 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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hy = hx&0x7f800000;
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if(hy>=0x7f800000)
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return x+x; // overflow
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if(hy<0x00800000) // underflow
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{
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t = x*x;
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if(abs(t - x) > epsilon<float>())
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{ // 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(abs(y - x) <= epsilon<double>())
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return y; // x=y, return y
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if((ix|lx)==0)
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{ // 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(abs(t - x) <= epsilon<double>())
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return t;
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else
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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)
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return x+x; // overflow
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if(hy<0x00100000)
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{ // underflow
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t = x*x;
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if(abs(t - x) > epsilon<double>())
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{ // 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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# pragma warning(pop)
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#endif
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namespace glm
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{
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template<>
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GLM_FUNC_QUALIFIER float next_float(float const& x)
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{
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# if GLM_HAS_CXX11_STL
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return std::nextafter(x, std::numeric_limits<float>::max());
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# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
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return detail::nextafterf(x, FLT_MAX);
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# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
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return __builtin_nextafterf(x, FLT_MAX);
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# else
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return nextafterf(x, FLT_MAX);
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# endif
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}
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template<>
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GLM_FUNC_QUALIFIER double next_float(double const& x)
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{
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# if GLM_HAS_CXX11_STL
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return std::nextafter(x, std::numeric_limits<double>::max());
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# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
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return detail::nextafter(x, std::numeric_limits<double>::max());
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# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
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return __builtin_nextafter(x, FLT_MAX);
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# else
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return nextafter(x, DBL_MAX);
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# endif
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}
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template<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<L, T, Q> next_float(vec<L, T, Q> const& x)
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{
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vec<L, T, Q> Result;
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for(length_t i = 0, n = Result.length(); i < n; ++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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# if GLM_HAS_CXX11_STL
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return std::nextafter(x, std::numeric_limits<float>::min());
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# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
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return detail::nextafterf(x, FLT_MIN);
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# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
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return __builtin_nextafterf(x, FLT_MIN);
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# else
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return nextafterf(x, FLT_MIN);
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# endif
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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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# if GLM_HAS_CXX11_STL
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return std::nextafter(x, std::numeric_limits<double>::min());
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# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
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return _nextafter(x, DBL_MIN);
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# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
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return __builtin_nextafter(x, DBL_MIN);
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# else
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return nextafter(x, DBL_MIN);
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# endif
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}
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template<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<L, T, Q> prev_float(vec<L, T, Q> const& x)
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{
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vec<L, T, Q> Result;
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for(length_t i = 0, n = Result.length(); i < n; ++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(uint 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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<L, T, Q> next_float(vec<L, T, Q> const& x, vec<L, uint, Q> const& ulps)
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{
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vec<L, T, Q> Result;
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for(length_t i = 0, n = Result.length(); i < n; ++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(uint 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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<L, T, Q> prev_float(vec<L, T, Q> const& x, vec<L, uint, Q> const& ulps)
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{
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vec<L, T, Q> Result;
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for(length_t i = 0, n = Result.length(); i < n; ++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(glm::epsilonNotEqual(temp, y, glm::epsilon<T>()))// && 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(glm::epsilonNotEqual(temp, x, glm::epsilon<T>()))// && 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<length_t L, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<L, uint, Q> float_distance(vec<L, T, Q> const& x, vec<L, T, Q> const& y)
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{
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vec<L, uint, Q> Result;
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for(length_t i = 0, n = Result.length(); i < n; ++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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