/// 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_float.hpp" #include "../ext/scalar_constants.hpp" #include #include #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 { int lsw; int 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; int 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(abs(y - x) <= epsilon()) 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(abs(t - x) <= epsilon()) 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(abs(t - x) > epsilon()) { // 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; int hx, hy, ix, iy; unsigned int 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(abs(y - x) <= epsilon()) 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(abs(t - x) <= epsilon()) 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(abs(t - x) > epsilon()) { // 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 nextFloat(float x) { # if GLM_HAS_CXX11_STL return std::nextafter(x, std::numeric_limits::max()); # elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS))) return detail::nextafterf(x, FLT_MAX); # elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID) return __builtin_nextafterf(x, FLT_MAX); # else return nextafterf(x, FLT_MAX); # endif } template<> GLM_FUNC_QUALIFIER double nextFloat(double x) { # if GLM_HAS_CXX11_STL return std::nextafter(x, std::numeric_limits::max()); # elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS))) return detail::nextafter(x, std::numeric_limits::max()); # elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID) return __builtin_nextafter(x, DBL_MAX); # else return nextafter(x, DBL_MAX); # endif } template GLM_FUNC_QUALIFIER T nextFloat(T x, int ULPs) { GLM_STATIC_ASSERT(std::numeric_limits::is_iec559, "'next_float' only accept floating-point input"); assert(ULPs >= 0); T temp = x; for(int i = 0; i < ULPs; ++i) temp = nextFloat(temp); return temp; } GLM_FUNC_QUALIFIER float prevFloat(float x) { # if GLM_HAS_CXX11_STL return std::nextafter(x, std::numeric_limits::min()); # elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS))) return detail::nextafterf(x, FLT_MIN); # elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID) return __builtin_nextafterf(x, FLT_MIN); # else return nextafterf(x, FLT_MIN); # endif } GLM_FUNC_QUALIFIER double prevFloat(double x) { # if GLM_HAS_CXX11_STL return std::nextafter(x, std::numeric_limits::min()); # elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS))) return _nextafter(x, DBL_MIN); # elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID) return __builtin_nextafter(x, DBL_MIN); # else return nextafter(x, DBL_MIN); # endif } template GLM_FUNC_QUALIFIER T prevFloat(T x, int ULPs) { GLM_STATIC_ASSERT(std::numeric_limits::is_iec559, "'prev_float' only accept floating-point input"); assert(ULPs >= 0); T temp = x; for(int i = 0; i < ULPs; ++i) temp = prevFloat(temp); return temp; } GLM_FUNC_QUALIFIER int floatDistance(float x, float y) { detail::float_t const a(x); detail::float_t const b(y); return abs(a.i - b.i); } GLM_FUNC_QUALIFIER int64 floatDistance(double x, double y) { detail::float_t const a(x); detail::float_t const b(y); return abs(a.i - b.i); } }//namespace glm