16 位浮点运行 Pascal/delphi
具有16位精度的浮点数主要用于计算机图形学。它们也被称为半精度浮点数(有一半的精度为32位浮点数)。这里有一个符号位，5位指数，还有10位为mantissa。由于有限的精度(在普通的cpus/fpus中没有支持)，半浮点数实际上并不是用于计算计算的。在2000年代初，有一半的漂浮物出现在图像和纹理的样本中。float提供的动态范围比常规的8位或16位的整数示例要高。另一方面，常用的单和双精度浮点数的每个像素的内存成本要高得多。一半的浮动有更合理的内存要求，并且它们的精度对于许多在成像方面的应用来说是足够的。多年来，ATI和NVidia GPUs一直支持16bit的浮动格式。我不确定其他的ihv，但是至少Direct3D 10有能力的gpu都应该支持它。如果您对如何在一半和单个精度浮点数之间转换(对象Pascal代码)感兴趣，请继续阅读。最后，半/单转换代码，这里是转换成半浮点数的代码，并返回到单个精度浮点数。它基于OpenEXR库中的C++代码(半类)。首先，一些类型和常量注意到，地中海式的类型只是Word的别名。
type
THalfFloat = type Word;
const
HalfMin: Single = 5.96046448e-08; // Smallest positive half
HalfMinNorm: Single = 6.10351562e-05; // Smallest positive normalized half
HalfMax: Single = 65504.0; // Largest positive half
// Smallest positive e for which half (1.0 + e) != half (1.0)
HalfEpsilon: Single = 0.00097656;
HalfNaN: THalfFloat = 65535;
HalfPosInf: THalfFloat = 31744;
HalfNegInf: THalfFloat = 64512;
function FloatToHalf(Float: Single): THalfFloat;
var
Src: LongWord;
Sign, Exp, Mantissa: LongInt;
begin
Src := PLongWord(@Float)^;
// Extract sign, exponent, and mantissa from Single number
Sign := Src shr 31;
Exp := LongInt((Src and $7F800000) shr 23) - 127 + 15;
Mantissa := Src and $007FFFFF;
if (Exp > 0) and (Exp < 30) then
begin
// Simple case - round the significand and combine it with the sign and exponent
Result := (Sign shl 15) or (Exp shl 10) or ((Mantissa + $00001000) shr 13);
end
else if Src = 0 then
begin
// Input float is zero - return zero
Result := 0;
end
else
begin
// Difficult case - lengthy conversion
if Exp <= 0 then
begin
if Exp < -10 then
begin
// Input float's value is less than HalfMin, return zero
Result := 0;
end
else
begin
// Float is a normalized Single whose magnitude is less than HalfNormMin.
// We convert it to denormalized half.
Mantissa := (Mantissa or $00800000) shr (1 - Exp);
// Round to nearest
if (Mantissa and $00001000) > 0 then
Mantissa := Mantissa + $00002000;
// Assemble Sign and Mantissa (Exp is zero to get denormalized number)
Result := (Sign shl 15) or (Mantissa shr 13);
end;
end
else if Exp = 255 - 127 + 15 then
begin
if Mantissa = 0 then
begin
// Input float is infinity, create infinity half with original sign
Result := (Sign shl 15) or $7C00;
end
else
begin
// Input float is NaN, create half NaN with original sign and mantissa
Result := (Sign shl 15) or $7C00 or (Mantissa shr 13);
end;
end
else
begin
// Exp is > 0 so input float is normalized Single
// Round to nearest
if (Mantissa and $00001000) > 0 then
begin
Mantissa := Mantissa + $00002000;
if (Mantissa and $00800000) > 0 then
begin
Mantissa := 0;
Exp := Exp + 1;
end;
end;
if Exp > 30 then
begin
// Exponent overflow - return infinity half
Result := (Sign shl 15) or $7C00;
end
else
// Assemble normalized half
Result := (Sign shl 15) or (Exp shl 10) or (Mantissa shr 13);
end;
end;
end;
function HalfToFloat(Half: THalfFloat): Single;
var
Dst, Sign, Mantissa: LongWord;
Exp: LongInt;
begin
// Extract sign, exponent, and mantissa from half number
Sign := Half shr 15;
Exp := (Half and $7C00) shr 10;
Mantissa := Half and 1023;
if (Exp > 0) and (Exp < 31) then
begin
// Common normalized number
Exp := Exp + (127 - 15);
Mantissa := Mantissa shl 13;
Dst := (Sign shl 31) or (LongWord(Exp) shl 23) or Mantissa;
// Result := Power(-1, Sign) * Power(2, Exp - 15) * (1 + Mantissa / 1024);
end
else if (Exp = 0) and (Mantissa = 0) then
begin
// Zero - preserve sign
Dst := Sign shl 31;
end
else if (Exp = 0) and (Mantissa <> 0) then
begin
// Denormalized number - renormalize it
while (Mantissa and $00000400) = 0 do
begin
Mantissa := Mantissa shl 1;
Dec(Exp);
end;
Inc(Exp);
Mantissa := Mantissa and not $00000400;
// Now assemble normalized number
Exp := Exp + (127 - 15);
Mantissa := Mantissa shl 13;
Dst := (Sign shl 31) or (LongWord(Exp) shl 23) or Mantissa;
// Result := Power(-1, Sign) * Power(2, -14) * (Mantissa / 1024);
end
else if (Exp = 31) and (Mantissa = 0) then
begin
// +/- infinity
Dst := (Sign shl 31) or $7F800000;
end
else //if (Exp = 31) and (Mantisa <> 0) then
begin
// Not a number - preserve sign and mantissa
Dst := (Sign shl 31) or $7F800000 or (Mantissa shl 13);
end;
// Reinterpret LongWord as Single
Result := PSingle(@Dst)^;
end;
program Half_test;
{$APPTYPE CONSOLE}
{$Include HalfFloat.pas}
var
X, Z : single;
Y : THalfFloat;
begin { TODO -oUser -cConsole Main : Insert code here }
decimalseparator := ‘.’;
x := 1439.156;
y := FloatToHalf(X);
z := HalfToFloat(y);
writeln(x:10:3);
writeln(z:10:3);
readln;
end.
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