The 6502 Microprocessor Resource
http://forum.6502.org/
Code: Select all
awk 'BEGIN
{
x=4*atan2(1,1); # pi
m=0; # we'll shift the mantissa in, eventually
e=129; # the exponent offset
while(x>1){ # repeatedly halve if x is large
e++; # account for the exponent
x/=2
}
while(x<1){ # repeatedly double if x is small
e--; # account for the exponent
x*=2
}
x-=1; # remove the leading 1 bit
for(i=0;i<31;i++){ #extract 31 bits of mantissa by repeated doubling
if(x>=1){
m++; # adjust the mantissa
x-=1
};
x*=2;
m*=2 # shift the mantissa to the left
}
# we're finished - x might have a small residue - we didn't try to round
printf "%s,%02x,%04x\n",x,e,m
}'Code: Select all
awk 'BEGIN
{
x=4*atan2(1,1); # pi
m=0; # we'll shift the mantissa in, eventually
e=129; # the exponent offset
while(x>1){ # repeatedly halve if x is large
e++; # account for the exponent
x/=2
}
while(x<1){ # repeatedly double if x is small
e--; # account for the exponent
x*=2
}
x-=1; # remove the leading 1 bit
for(i=0;i<31;i++){ #extract 31 bits of mantissa by repeated doubling
if(x>=1){
m++; # adjust the mantissa
x-=1
};
x*=2;
m*=2 # shift the mantissa to the left
}
# we're finished - x might have a small residue - we didn't try to round
printf "%s,%02x,%04x\n",x,e,m
}'Code: Select all
if(x>1)m++Code: Select all
if(2*x>1)m++Code: Select all
if(x>1)m++Code: Select all
if(2*x>1)m++Code: Select all
program C64_Math_Test;
{$APPTYPE CONSOLE}
uses
SysUtils;
type
TFloatFunc = (
ffNone,
ffRound,
ffTrunc
);
function atan2(y : extended ; x : extended) : extended ; assembler;
asm
fld [y];
fld [x];
fpatan
end;
procedure FloatToC64Float(var x: Extended; var e,m: Integer; FloatFunc: TFloatFunc);
var
i: Integer;
begin
m := 0; // we'll shift the mantissa in, eventually
e := 129; // the exponent offset
while (x > 1) do
begin // repeatedly halve if x is large
e := e + 1; // account for the exponent
x := x / 2;
end;
while (x < 1) do
begin // repeatedly double if x is small
e := e - 1; // account for the exponent
x := x * 2;
end;
x := x - 1; // remove the leading 1 bit
for i := 0 to 30 do
begin //extract 31 bits of mantissa by repeated doubling
if (x >= 1) then
begin
m := m + 1; // adjust the mantissa
x := x - 1;
end;
x := x * 2;
m := m * 2; // shift the mantissa to the left
end;
// we're finished - x might have a small residue - we didn't try to round
case FloatFunc of
ffRound : if (x > 1) then m := m + 1;
ffTrunc : if (2*x > 1) then m := m + 1;
else
end;
end;
var
x: Extended;
e,m: Integer;
begin
x := 4*atan2(1,1); // pi
FloatToC64Float(x,e,m,ffNone);
WriteLn(LowerCase(Format('%f,%02x,%04x',[x,e,m])));
ReadLn;
end.
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0.13,82,490fdaa2
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procedure FloatToC64Float(num: Double);
// converted from original code found here:
// http://www.softwolves.com/arkiv/cbm-hackers/7/7617.html
//
var
i,sign,bit,byte_val,flag,count,ei: Integer;
digit: array[0..4] of Byte;
a: Double;
begin
if Abs(num) < 0.000001 then WriteLn('Oh come on. Zero! 00 00 00 00 00');
WriteLn(Format('Original number = %.10f',[num]));
if (num < 0) then
begin
sign := 128;
num := -num;
end
else
sign := 0;
a := 1;
for i := 0 to 126 - 1 do // a = 2^126
begin
a := a * 2;
end;
byte_val := 0;
flag := 0;
count := 0;
ei := 0;
i := 126;
while (i >= -128) and (byte_val < 4) do
begin
if num >= a then
begin
bit := 1;
if flag = 0 then
ei := i;
flag := 1;
end
else
bit := 0;
if flag = 1 then
begin
digit[byte_val] := digit[byte_val] * 2 + bit;
Inc(count);
if count > 7 then
begin
count := 0;
Inc(byte_val);
end;
num := num - a * bit;
end;
a := a / 2;
Dec(i);
end;
digit[0] := (digit[0] - 128) or sign;
Inc(ei,129);
WriteLn(Format('C64 float = $%.2x $%.2x $%.2x $%.2x $%.2x',
[ei,digit[0],digit[1],digit[2],digit[3]]));
end;Code: Select all
FloatToC64Float(4*ArcTan2(1,1))Code: Select all
type
PC64MemFloat = ^TC64MemFloat;
TC64MemFloat = packed record
Exponent: Byte;
Mantissa: array[0..3] of Byte;
end;
PC64RegFloat = ^TC64RegFloat;
TC64RegFloat = packed record
Exponent: Byte;
Mantissa: array[0..3] of Byte;
Sign: Byte;
end;
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procedure FloatToC64Float(num: Double; out aC64Float: TC64MemFloat);
// converts a floating point number to 5-byte memory FP representation: exponent (1), mantissa (4)
//ftp://n2dvm.com/Commodore/Commie-CDs/Kazez%20FREE-CD/c64-knowledge-base/197.htm
var
ExpCount: Integer;
SignBit: Integer;
Index: Integer;
begin
Write(Format('%.10f = ',[num]));
// save sign bit
SignBit := 0;
if num < 0 then
begin
SignBit := 128;
num := -num;
end;
if Abs(num) < 0.000001 then
begin
aC64Float.Exponent := 0;
aC64Float.Mantissa[0] := 0;
aC64Float.Mantissa[1] := 0;
aC64Float.Mantissa[2] := 0;
aC64Float.Mantissa[3] := 0;
C64FloatToStr(aC64Float);
Exit;
end;
// calculate exponent byte
ExpCount := 0;
if num < 1 then
while num < 1 do
begin
Dec(ExpCount);
num := num * 2;
end
else
if num >= 2 then
while num >= 2 do
begin
Inc(ExpCount);
num := num / 2;
end;
aC64Float.Exponent := 129 + ExpCount;
num := num / 2; // 'un-normalize' it for forther processing (immediate mantissa)
// calculate mantissa digits
for Index := 0 to 3 do
begin
num := num * 256;
aC64Float.Mantissa[Index] := Trunc(num);
num := Frac(num);
end;
// round last mantissa digit when required
if num > 0.5 then Inc(aC64Float.Mantissa[3]);
// include sign bit in first mantissa digit
aC64Float.Mantissa[0] := (aC64Float.Mantissa[0] and $7F) or SignBit;
C64FloatToStr(aC64Float);
end;Code: Select all
procedure FloatToC64Float(num: Double; out aC64Float: TC64RegFloat);
// converts a floating point number to 6-byte register FP representation: exponent (1), mantissa (4), separate sign (1)
//ftp://n2dvm.com/Commodore/Commie-CDs/Kazez%20FREE-CD/c64-knowledge-base/197.htm
var
ExpCount: Integer;
SignBit: Integer;
Index: Integer;
begin
Write(Format('%.10f = ',[num]));
// save sign bit
SignBit := 0;
if num < 0 then
begin
SignBit := 128;
num := -num;
end;
if Abs(num) < 0.000001 then
begin
aC64Float.Exponent := 0;
aC64Float.Mantissa[0] := 0;
aC64Float.Mantissa[1] := 0;
aC64Float.Mantissa[2] := 0;
aC64Float.Mantissa[3] := 0;
aC64Float.Sign := 0;
C64FloatToStr(aC64Float);
Exit;
end;
// calculate exponent byte
ExpCount := 0;
if num < 1 then
while num < 1 do
begin
Dec(ExpCount);
num := num * 2;
end
else
if num >= 2 then
while num >= 2 do
begin
Inc(ExpCount);
num := num / 2;
end;
aC64Float.Exponent := 129 + ExpCount;
num := num / 2; // 'un-normalize' it for forther processing (immediate mantissa)
// calculate mantissa digits
for Index := 0 to 3 do
begin
num := num * 256;
aC64Float.Mantissa[Index] := Trunc(num);
num := Frac(num);
end;
// round last mantissa digit when required
if num > 0.5 then Inc(aC64Float.Mantissa[3]);
// include sign bit in sign part
aC64Float.Mantissa[4] := SignBit;
C64FloatToStr(aC64Float);
end;Code: Select all
function C64FloatToStr(var aC64Float: TC64MemFloat): String;
begin
//output C64 mem floating point as hex (Exponent, Mantissa)
Result := Format('$%.2x $%.2x $%.2x $%.2x $%.2x (mem FP)',
[aC64Float.Exponent,
aC64Float.Mantissa[0],
aC64Float.Mantissa[1],
aC64Float.Mantissa[2],
aC64Float.Mantissa[3]]);
end;Code: Select all
function C64FloatToStr(var aC64Float: TC64RegFloat): String;
begin
//output C64 reg floating point as hex (Exponent, Mantissa, Sign)
Result := Format('$%.2x $%.2x $%.2x $%.2x $%.2x $%.2x (reg FP)',
[aC64Float.Exponent,
aC64Float.Mantissa[0],
aC64Float.Mantissa[1],
aC64Float.Mantissa[2],
aC64Float.Mantissa[3],
aC64Float.Sign]);
end;Code: Select all
Single: 4 byte 32seee eeee 24emmm mmmm 16mmmm mmmm 08mmmm mmmm
Double: 8 byte 64seee eeee 56eeee mmmm 48mmmm mmmm 40mmmm mmmm 32mmmm mmmm 24mmmm mmmm 16mmmm mmmm 08mmmm mmmm
C64Flp: 5 byte 16mmmm mmmm 24mmmm mmmm 32mmmm mmmm 48smmm mmmm 08 eeee eeee
s: sign bit
m: mantissa
e: exponent
Caveat: byte order C64 is reversed compared to IEEE!
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function Str2C64Flp(floatstr : string) : string;ยด{result will contain 5-byte C64-float}
var sr : record {those records for juggling the bytes}
case integer of
1 : (s : single);
2 : (b : array[0..3] of byte);
3 : (l : longint);
4 : (w1: word; w2: word);
end;
dr : record
case integer of
1 : (d : double);
2 : (b : array[0..7] of byte);
3 : (c : comp);
4 : (l1,l2 : longint);
end;
w : word;
vorzeichen : byte; {sign}
exponent : byte;
mantisse : longint;
begin
dr.d := fval(floatstr,w); {one might want to catch some conversion errors here}
sr.s := dr.d;
vorzeichen := sr.b[3] shr 7;
sr.l := sr.l shl 1;
exponent := sr.b[3]+2;
mantisse := (((dr.l2 shl 12) or (dr.l1 shr 20)) shr 1) + (vorzeichen *$80000000);
sr.l := mantisse;
Str2C64Flp := chr(exponent)+chr(sr.b[3])+chr(sr.b[2])+chr(sr.b[1])+chr(sr.b[0]);
end;
)