On 12/13/2012 6:30 AM, Simen Kjaeraas wrote:
Walter does not seem to agree (see his post in this discussion).
Note that the following implementation of halffloat does work, allowing explicit
cast to halffloat and implicit conversion from.
(The halffloat literals don't work at the moment because of a limitation in
CTFE, I'm working with Don to resolve that.)
-----------------------------------------------------------
/*
* References:
* http://en.wikipedia.org/wiki/Half-precision_floating-point_format
*/
module halffloat;
struct HF {
/* Provide implicit conversion of HF to float
*/
@property float toFloat() { return shortToFloat(s); }
alias toFloat this;
/* Done as a template in order to prevent implicit conversion
* of argument to float.
*/
this(T : float)(T f)
{
static assert(is(T == float));
s = floatToShort(f);
}
/* These are done as properties to avoid
* circular reference problems.
*/
static @property HF min_normal() { HF hf = void; hf.s = 0x0400; return hf;
/* fp16!0x1p-14; */ }
static @property HF max() { HF hf = void; hf.s = 0x7BFF; return hf;
/* fp16!0x1.FFCp+15; */ }
static @property HF nan() { HF hf = void; hf.s = EXPMASK | 1; return
hf; /* fp16!(float.nan); */ }
static @property HF infinity() { HF hf = void; hf.s = EXPMASK; return hf;
/* fp16!(float.infinity); */ }
static @property HF epsilon() { HF hf = void; hf.s = 0x3C01; return hf;
/* fp16!0x1p-10; */ }
enum dig = 3;
enum mant_dig = 11;
enum max_10_exp = 5;
enum max_exp = 16;
enum min_10_exp = -5;
enum min_exp = -14;
private:
ushort s = EXPMASK | 1; // .init is HF.nan
}
/********************
* User defined literal for Half Float.
*/
template fp16(float v)
{
enum fp16 = HF(v);
}
private:
// Half float values
enum SIGNMASK = 0x8000;
enum EXPMASK = 0x7C00;
enum MANTMASK = 0x03FF;
enum HIDDENBIT = 0x0400;
// float values
enum FSIGNMASK = 0x80000000;
enum FEXPMASK = 0x7F800000;
enum FMANTMASK = 0x007FFFFF;
enum FHIDDENBIT = 0x00800000;
// Rounding mode
enum ROUND { TONEAREST, UPWARD, DOWNWARD, TOZERO };
enum ROUNDMODE = ROUND.TONEAREST;
union U { uint u; float f; }
ushort floatToShort(float f)
{
/* If the target CPU has a conversion instruction, this code could be
* replaced with inline asm or a compiler intrinsic, but leave this
* as the CTFE path so CTFE can work on it.
*/
/* The code currently does not set INEXACT, UNDERFLOW, or OVERFLOW,
* but is marked where those would go.
*/
U uf = void;
uf.f = f;
uint s = uf.u;
ushort u = (s & FSIGNMASK) ? SIGNMASK : 0;
int exp = s & FEXPMASK;
if (exp == FEXPMASK) // if nan or infinity
{
if ((s & FMANTMASK) == 0) // if infinity
{
u |= EXPMASK;
}
else // else nan
{
u |= EXPMASK | 1;
}
return u;
}
uint significand = s & FMANTMASK;
if (exp == 0) // if subnormal or zero
{
if (significand == 0) // if zero
return u;
/* A subnormal float is going to give us a zero result anyway,
* so just set UNDERFLOW and INEXACT and return +-0.
*/
return u;
}
else // else normal
{
// normalize exponent and remove bias
exp = (exp >> 23) - 127;
significand |= FHIDDENBIT;
}
exp += 15; // bias the exponent
bool guard = false; // guard bit
bool sticky = false; // sticky bit
uint shift = 13; // lop off rightmost 13 bits
if (exp <= 0) // if subnormal
{ shift += -exp + 1; // more bits to lop off
exp = 0;
}
if (shift > 23)
{
// Set UNDERFLOW, INEXACT, return +-0
return u;
}
// Lop off rightmost 13 bits, but save guard and sticky bits
guard = (significand & (1 << (shift - 1))) != 0;
sticky = (significand & ((1 << (shift - 1)) - 1)) != 0;
significand >>= shift;
if (guard || sticky)
{
// Lost some bits, so set INEXACT and round the result
switch (ROUNDMODE)
{
case ROUND.TONEAREST:
if (guard && (sticky || (significand & 1)))
++significand;
break;
case ROUND.UPWARD:
if (!(s & FSIGNMASK))
++significand;
break;
case ROUND.DOWNWARD:
if (s & FSIGNMASK)
++significand;
break;
case ROUND.TOZERO:
break;
default:
assert(0);
}
if (exp == 0) // if subnormal
{
if (significand & HIDDENBIT) // and not a subnormal no more
++exp;
}
else if (significand & (HIDDENBIT << 1))
{
significand >>= 1;
++exp;
}
}
if (exp > 30)
{ // Set OVERFLOW and INEXACT, return +-infinity
return u | EXPMASK;
}
/* Add exponent and significand into result.
*/
u |= exp << 10; // exponent
u |= (significand & ~HIDDENBIT); // significand
return u;
}
float shortToFloat(ushort s)
{
/* If the target CPU has a conversion instruction, this code could be
* replaced with inline asm or a compiler intrinsic, but leave this
* as the CTFE path so CTFE can work on it.
*/
/* This one is fairly easy because there are no possible errors
* and no necessary rounding.
*/
int exp = s & EXPMASK;
if (exp == EXPMASK) // if nan or infinity
{
float f;
if ((s & MANTMASK) == 0) // if infinity
{
f = float.infinity;
}
else // else nan
{
f = float.nan;
}
return (s & SIGNMASK) ? -f : f;
}
uint significand = s & MANTMASK;
if (exp == 0) // if subnormal or zero
{
if (significand == 0) // if zero
return (s & SIGNMASK) ? -0.0f : 0.0f;
// Normalize by shifting until the hidden bit is 1
while (!(significand & HIDDENBIT))
{
significand <<= 1;
--exp;
}
significand &= ~HIDDENBIT; // hidden bit is, well, hidden
exp -= 14;
}
else // else normal
{
// normalize exponent and remove bias
exp = (exp >> 10) - 15;
}
/* Assemble sign, exponent, and significand into float.
* Don't have to deal with overflow, inexact, or subnormal
* because the range of floats is big enough.
*/
assert(-126 <= exp && exp <= 127); // just to be sure
//printf("exp = %d, significand = x%x\n", exp, significand);
uint u = (s & SIGNMASK) << 16; // sign bit
u |= (exp + 127) << 23; // bias the exponent and shift into
position
u |= significand << (23 - 10);
U uf = void;
uf.u = u;
return uf.f;
}
import std.stdio;
void main() {
// HF h = fp16!27.2f;
// HF j = cast(HF)( fp16!3.5f + fp16!5 );
HF f = HF(0.0f);
f.s = 0x3C00;
writeln("1 ", cast(float)f);
f.s = 0x3C01;
writeln("1.0009765625 ", cast(float)f);
assert(f == HF.epsilon);
f.s = 0xC000;
writeln("-2 ", cast(float)f);
f.s = 0x7BFF;
writeln("65504 ", cast(float)f);
assert(f == HF.max);
f.s = 0x0400;
writeln("6.10352e-5 ", cast(float)f);
assert(f == HF.min_normal);
f.s = 0x03FF;
writeln("6.09756e-5 ", cast(float)f);
f.s = 1;
writeln("5.96046e-8 ", cast(float)f);
f.s = 0;
writeln("0 ", cast(float)f);
assert(f == 0.0f);
f.s = 0x8000;
writeln("-0 ", cast(float)f);
assert(f == -0.0f);
f.s = 0x7C00;
writeln("infinity ", cast(float)f);
assert(f == HF.infinity);
f.s = 0xFC00;
writeln("-infinity ", cast(float)f);
assert(f == -HF.infinity);
f.s = 0x3555;
writeln("0.33325 ", cast(float)f);
}
