12 bytes LongReal type

{ For those who want to understand the structure of the double extended format, here is a little program which may be helpful : (I'll appreciate comments to improve it)

-- «Couperin» }

Program Lr2Scr;

{ ---------------------------------------------------------------------- What is Intel IEEE Double-Extended format (12 bytes) ? "Couperin" f.couperin@online.fr ---------------------------------------------------------------------- }

Const LongRealSize = 12;

Type T_LongRealBis = Packed Array [1..LongRealSize] Of Byte; String2 = String(2); String11 = String(11); String16 = String(16); String27 = String(27); Int16 = Integer(16); Word16 = Word(16); Word64 = Word(64);

Var A : LongReal; Abis : T_LongRealBis Absolute A;

Function Byte2Hex(X : Byte): String2; Const Hexa : Array [0..15] Of Char = '0123456789ABCDEF'; Begin Byte2Hex := Hexa[X Shr 4] + Hexa[X And 15] End;

Function ExtractE(X : T_LongRealBis): Word16; Var E : Word16; Begin E := X[10] And 2#01111111; ExtractE := (E Shl 8) + X[9] End;

Function F2Hex(X : T_LongRealBis): String16; Var S : String16 = ''; I : Byte; Begin For I := 8 DownTo 2 Do S := S + Byte2Hex((X[I] Shl 1) + (X[I-1] Shr 7)); S := S + Byte2Hex(X[1] Shl 1); F2Hex := S End;

Function Exponent(X : T_LongRealBis): Int16; Var E : Word16; Begin E := ((X[10] And 2#01111111) Shl 8) + X[9]; If E = 0 Then Exponent := -16382 Else Exponent := E - 16383 End;

Function Int2String(X:Integer):String11; Var S:String11; Begin Str(X,S); Int2String := S End;

Function LR2HexFloat(X : T_LongRealBis): String27; Var S : String27 = '$'; Begin If (Abis[10] And 2#10000000) > 0 {sign} Then S := S + '-' Else S := S + '+'; If (Abis[8] And 2#10000000) > 0 {explicit leading significand bit} Then S := S + '1.' Else S := S + '0.'; LR2HexFloat := S + F2Hex(X) + 'p' + Int2String(Exponent(X)) End;

Procedure DisplayA; Var N : Byte; Begin Writeln(A:28,' = '); Writeln(LR2HexFloat(Abis),' ("Hex Float") = '); For N := LongRealSize DownTo 1 Do Write(Byte2Hex(Abis[N])); Writeln(' (internal representation)'); Write('s (sign) = '); Writeln(Ord((Abis[10] And 2#10000000) > 0)); Write('e (biased exponent) = ',ExtractE(Abis)); Writeln(' (e - 16383 = ',ExtractE(Abis) - 16383,')'); Write('j (explicit leading significand bit) = '); Writeln(Ord((Abis[8] And 2#10000000) > 0)); Write('f (fraction) = 16#',F2Hex(Abis)); Writeln End;

Begin Writeln('Size of the LongReal type (in Bytes) : ',SizeOf(LongReal)); If LongRealSize <> SizeOf(LongReal) Then Writeln('Sorry, this LongReal format (Size : ',SizeOf(LongReal), ') is unknown to this program.') Else Begin {$ifdef __BYTES_BIG_ENDIAN__} {Is this really useful ?} Writeln('Big endian format.'#10#13, 'Sorry, this program is made for the little endian format.') {$else} Writeln('Little endian format'); Repeat Writeln; Writeln('Enter a real number (0 to Quit)'); Readln(A); Writeln; DisplayA; Until A = 0 {$endif} End End.