/// @ref core /// @file glm/detail/type_half.inl namespace glm{ namespace detail { GLM_FUNC_QUALIFIER float overflow() { volatile float f = 1e10; for(int i = 0; i < 10; ++i) f *= f; // this will overflow before the for loop terminates return f; } union uif32 { GLM_FUNC_QUALIFIER uif32() : i(0) {} GLM_FUNC_QUALIFIER uif32(float f_) : f(f_) {} GLM_FUNC_QUALIFIER uif32(uint32 i_) : i(i_) {} float f; uint32 i; }; GLM_FUNC_QUALIFIER float toFloat32(hdata value) { int s = (value >> 15) & 0x00000001; int e = (value >> 10) & 0x0000001f; int m = value & 0x000003ff; if(e == 0) { if(m == 0) { // // Plus or minus zero // detail::uif32 result; result.i = (unsigned int)(s << 31); return result.f; } else { // // Denormalized number -- renormalize it // while(!(m & 0x00000400)) { m <<= 1; e -= 1; } e += 1; m &= ~0x00000400; } } else if(e == 31) { if(m == 0) { // // Positive or negative infinity // uif32 result; result.i = (unsigned int)((s << 31) | 0x7f800000); return result.f; } else { // // Nan -- preserve sign and significand bits // uif32 result; result.i = (unsigned int)((s << 31) | 0x7f800000 | (m << 13)); return result.f; } } // // Normalized number // e = e + (127 - 15); m = m << 13; // // Assemble s, e and m. // uif32 Result; Result.i = (unsigned int)((s << 31) | (e << 23) | m); return Result.f; } GLM_FUNC_QUALIFIER hdata toFloat16(float const & f) { uif32 Entry; Entry.f = f; int i = (int)Entry.i; // // Our floating point number, f, is represented by the bit // pattern in integer i. Disassemble that bit pattern into // the sign, s, the exponent, e, and the significand, m. // Shift s into the position where it will go in in the // resulting half number. // Adjust e, accounting for the different exponent bias // of float and half (127 versus 15). // int s = (i >> 16) & 0x00008000; int e = ((i >> 23) & 0x000000ff) - (127 - 15); int m = i & 0x007fffff; // // Now reassemble s, e and m into a half: // if(e <= 0) { if(e < -10) { // // E is less than -10. The absolute value of f is // less than half_MIN (f may be a small normalized // float, a denormalized float or a zero). // // We convert f to a half zero. // return hdata(s); } // // E is between -10 and 0. F is a normalized float, // whose magnitude is less than __half_NRM_MIN. // // We convert f to a denormalized half. // m = (m | 0x00800000) >> (1 - e); // // Round to nearest, round "0.5" up. // // Rounding may cause the significand to overflow and make // our number normalized. Because of the way a half's bits // are laid out, we don't have to treat this case separately; // the code below will handle it correctly. // if(m & 0x00001000) m += 0x00002000; // // Assemble the half from s, e (zero) and m. // return hdata(s | (m >> 13)); } else if(e == 0xff - (127 - 15)) { if(m == 0) { // // F is an infinity; convert f to a half // infinity with the same sign as f. // return hdata(s | 0x7c00); } else { // // F is a NAN; we produce a half NAN that preserves // the sign bit and the 10 leftmost bits of the // significand of f, with one exception: If the 10 // leftmost bits are all zero, the NAN would turn // into an infinity, so we have to set at least one // bit in the significand. // m >>= 13; return hdata(s | 0x7c00 | m | (m == 0)); } } else { // // E is greater than zero. F is a normalized float. // We try to convert f to a normalized half. // // // Round to nearest, round "0.5" up // if(m & 0x00001000) { m += 0x00002000; if(m & 0x00800000) { m = 0; // overflow in significand, e += 1; // adjust exponent } } // // Handle exponent overflow // if (e > 30) { overflow(); // Cause a hardware floating point overflow; return hdata(s | 0x7c00); // if this returns, the half becomes an } // infinity with the same sign as f. // // Assemble the half from s, e and m. // return hdata(s | (e << 10) | (m >> 13)); } } }//namespace detail }//namespace glm