123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241 |
- 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(unsigned int i_) :
- i(i_)
- {}
- float f;
- unsigned int 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 = static_cast<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 = static_cast<unsigned int>((s << 31) | 0x7f800000);
- return result.f;
- }
- else
- {
- //
- // Nan -- preserve sign and significand bits
- //
- uif32 result;
- result.i = static_cast<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 = static_cast<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 = static_cast<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 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
|