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@BeRo1985
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MiniSoftFP32 - A simple small software 32-bit single precision floating point implementation
unit MiniSoftFP32; // Copyright (C) 2018, Benjamin "BeRo" Rosseaux (benjamin@rosseaux.de) - License: CC0
// Declaimer / Notice of caution:
// Attention, this code implements only the basic functions, but for example not the correct handling of
// Infinity, NaN, division-by-zero special cases and so on.
// In short, this code is only intended for demystifying the base floating point arithmetics (using 32-bit
// single precision floating point values in this implementation).
{$ifdef fpc}
{$mode delphi}
{$if defined(cpu386) or defined(cpuamd64)}
{$asmmode intel}
{$ifend}
{$endif}
interface
type PPmsfp32Int8=^Pmsfp32Int8;
Pmsfp32Int8=^Tmsfp32Int8;
Tmsfp32Int8={$ifdef fpc}Int8{$else}shortint{$endif};
PPmsfp32UInt8=^Pmsfp32UInt8;
Pmsfp32UInt8=^Tmsfp32UInt8;
Tmsfp32UInt8={$ifdef fpc}UInt8{$else}byte{$endif};
PPmsfp32Int16=^Pmsfp32Int16;
Pmsfp32Int16=^Tmsfp32Int16;
Tmsfp32Int16={$ifdef fpc}Int16{$else}smallint{$endif};
PPmsfp32UInt16=^Pmsfp32UInt16;
Pmsfp32UInt16=^Tmsfp32UInt16;
Tmsfp32UInt16={$ifdef fpc}UInt16{$else}word{$endif};
PPmsfp32Int32=^Pmsfp32Int32;
Pmsfp32Int32=^Tmsfp32Int32;
Tmsfp32Int32={$ifdef fpc}Int32{$else}longint{$endif};
PPmsfp32UInt32=^Pmsfp32UInt32;
Pmsfp32UInt32=^Tmsfp32UInt32;
Tmsfp32UInt32={$ifdef fpc}UInt32{$else}longword{$endif};
PPmsfp32Int64=^Pmsfp32Int64;
Pmsfp32Int64=^Tmsfp32Int64;
Tmsfp32Int64=Int64;
PPmsfp32UInt64=^Pmsfp32UInt64;
Pmsfp32UInt64=^Tmsfp32UInt64;
Tmsfp32UInt64=UInt64;
PPmsfp32Void=^Pmsfp32Void;
Pmsfp32Void=Pointer;
PPmsfp32Float=^Pmsfp32Float;
Pmsfp32Float=^Tmsfp32Float;
Tmsfp32Float=Single;
function MiniSoftFP32Add(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
function MiniSoftFP32Sub(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
function MiniSoftFP32Mul(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
function MiniSoftFP32Div(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
implementation
{$ifndef fpc}
function SARLongint(Value,Shift:Tmsfp32Int32):Tmsfp32Int32;
{$ifdef cpu386}
{$ifdef fpc} assembler; inline;
asm
mov ecx,edx
sar eax,cl
end ['eax','edx','ecx'];
{$else} assembler; register;
asm
mov ecx,edx
sar eax,cl
end;
{$endif}
{$else}
{$ifdef cpuarm} assembler; inline;
asm
mov r0,r0,asr R1
end ['r0','R1'];
{$else}{$ifdef fpc}inline;{$endif}
begin
{$ifdef HasSAR}
result:=SARLongint(Value,Shift);
{$else}
Shift:=Shift and 31;
result:=(Tmsfp32UInt32(Value) shr Shift) or (Tmsfp32UInt32(Tmsfp32Int32(Tmsfp32UInt32(0-Tmsfp32UInt32(Tmsfp32UInt32(Value) shr 31)) and Tmsfp32UInt32(0-Tmsfp32UInt32(ord(Shift<>0))))) shl (32-Shift));
{$endif}
end;
{$endif}
{$endif}
{$endif}
function MiniSoftFP32Add(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
var Left,Right,
SignLeft,SignRight,
AbsoluteLeft,AbsoluteRight,
BaseLeft,BaseRight,
ExponentLeft,ExponentRight,
MantissaLeft,MantissaRight,
Exponent,
Mantissa,
Shift,SignMagnitude,NormalizedMantissa,
Value:Tmsfp32Int32;
begin
Left:=Tmsfp32Int32(pointer(@aLeft)^);
Right:=Tmsfp32Int32(pointer(@aRight)^);
SignLeft:=Left shr 31;
SignRight:=Right shr 31;
ExponentLeft:=(Left shr 23) and $ff;
ExponentRight:=(Right shr 23) and $ff;
MantissaLeft:=((Left and $7fffff) shl 1) or $1000000;
MantissaRight:=((Right and $7fffff) shl 1) or $1000000;
if SignLeft<>0 then begin
AbsoluteLeft:=-MantissaLeft;
end else begin
AbsoluteLeft:=MantissaLeft;
end;
if SignRight<>0 then begin
AbsoluteRight:=-MantissaRight;
end else begin
AbsoluteRight:=MantissaRight;
end;
if ExponentRight>ExponentLeft then begin
Shift:=ExponentRight-ExponentLeft;
if Shift>31 then begin
Shift:=31;
end;
Exponent:=ExponentRight;
BaseLeft:=SARLongint(AbsoluteLeft,Shift);
BaseRight:=AbsoluteRight;
end else begin
Shift:=ExponentLeft-ExponentRight;
if Shift>31 then begin
Shift:=31;
end;
Exponent:=ExponentLeft;
BaseLeft:=AbsoluteLeft;
BaseRight:=SARLongint(AbsoluteRight,Shift);
end;
Mantissa:=((SignLeft shl 26) or (SignLeft shl 25) or (BaseLeft and $1ffffff))+
((SignRight shl 26) or (SignRight shl 25) or (BaseRight and $1ffffff));
if (Mantissa and (1 shl 26))<>0 then begin
SignMagnitude:=(1-Mantissa) and $7ffffff;
end else begin
SignMagnitude:=(Mantissa+1) and $7ffffff;
end;
inc(Exponent);
NormalizedMantissa:=SignMagnitude shr 1;
if (SignMagnitude and $3fffffc)<>0 then begin
while (NormalizedMantissa and (1 shl 24))=0 do begin
NormalizedMantissa:=NormalizedMantissa shl 1;
dec(Exponent);
end;
end else begin
NormalizedMantissa:=NormalizedMantissa shl 24;
dec(Exponent,24);
end;
if (Left and $7fffffff)=0 then begin
if (Right and $7fffffff)=0 then begin
Value:=0;
end else begin
Value:=Right;
end;
end else if (Right and $7fffffff)=0 then begin
Value:=Left;
end else if ((NormalizedMantissa and $1ffffff)=0) or ((Exponent and $100)<>0) then begin
Value:=0;
end else begin
Value:=((Mantissa and $4000000) shl 5) or (Exponent shl 23) or ((NormalizedMantissa shr 1) and $7fffff);
end;
result:=Tmsfp32Float(pointer(@Value)^);
end;
function MiniSoftFP32Sub(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
var Right:Tmsfp32UInt32;
begin
Right:=Tmsfp32UInt32(pointer(@aRight)^) xor $80000000;
result:=MiniSoftFP32Add(aLeft,Tmsfp32Float(pointer(@Right)^));
end;
function MiniSoftFP32Mul(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
const Bit47:Tmsfp32Int64=Tmsfp32Int64(1) shl 47;
var Left,Right,
Sign,
ExponentLeft,ExponentRight,
MantissaLeft,MantissaRight,
Exponent,Mantissa,
Value:Tmsfp32Int32;
Mantissa64:Tmsfp32Int64;
begin
Left:=Tmsfp32Int32(pointer(@aLeft)^);
Right:=Tmsfp32Int32(pointer(@aRight)^);
Sign:=(Left xor Right) and $80000000;
ExponentLeft:=(Left shr 23) and $ff;
ExponentRight:=(Right shr 23) and $ff;
MantissaLeft:=(Left and $7fffff) or $800000;
MantissaRight:=(Right and $7fffff) or $800000;
Mantissa64:=Tmsfp32Int64(MantissaLeft)*MantissaRight;
Exponent:=(ExponentLeft+ExponentRight)-127;
if (Mantissa64 and Bit47)<>0 then begin
inc(Exponent);
Mantissa:=(Tmsfp32Int32(Mantissa64 shr 23)+1) and $ffffff;
end else begin
Mantissa:=(Tmsfp32Int32(Mantissa64 shr 22)+1) and $ffffff;
end;
if (ExponentLeft=0) or (ExponentRight=0) then begin
Value:=0;
end else if (Exponent and $100)=0 then begin
Value:=Sign or ((Exponent and $ff) shl 23) or (Mantissa shr 1);
end else if (Exponent and $80)=0 then begin
Value:=Sign or ($ff shl 23) or (Mantissa shr 1);
end else begin
Value:=0;
end;
result:=Tmsfp32Float(pointer(@Value)^);
end;
function MiniSoftFP32Div(const aLeft,aRight:Tmsfp32Float):Tmsfp32Float;
const Bit25:Tmsfp32Int64=Tmsfp32Int64(1) shl 25;
var Left,Right,
Sign,
ExponentLeft,ExponentRight,
MantissaLeft,MantissaRight,
Mantissa,Exponent,
Value:Tmsfp32Int32;
begin
Left:=Tmsfp32Int32(pointer(@aLeft)^);
Right:=Tmsfp32Int32(pointer(@aRight)^);
Sign:=(Left xor Right) and $80000000;
ExponentLeft:=(Left shr 23) and $ff;
ExponentRight:=(Right shr 23) and $ff;
MantissaLeft:=(Left and $7fffff) or $800000;
MantissaRight:=(Right and $7fffff) or $800000;
Mantissa:=(MantissaLeft*Bit25) div MantissaRight;
Exponent:=(ExponentLeft-ExponentRight)+126;
if (Mantissa and Bit25)<>0 then begin
inc(Exponent);
Mantissa:=(Mantissa shr 1) and $ffffff;
end else begin
Mantissa:=Mantissa and $ffffff;
end;
if ExponentLeft=0 then begin
Value:=0;
end else if ExponentRight=0 then begin
Value:=Sign or ($ff shl 23);
end else if (Exponent and $100)=0 then begin
Value:=Sign or ((Exponent and $ff) shl 23) or ((Mantissa+1) shr 1);
end else if (Exponent and $80)=0 then begin
Value:=Sign or ($ff shl 23) or (Mantissa shr 1);
end else begin
Value:=0;
end;
result:=Tmsfp32Float(pointer(@Value)^);
end;
end.
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