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unit CnFloatConvert;
{* |<PRE>
================================================================================
* 软件名称：开发包基础库
* 单元名称：浮点数转换
* 单元作者：王乾元(wqyfavor@163.com)
* 备 注：该单元实现了三个将Extended类型转换为二、八、十六进制字符串的函数
* 开发平台：WinXP + Delphi 2009
* 兼容测试：Delphi 2007
* 本 地 化：该单元中的字符串均符合本地化处理方式
* 单元标识：$Id: CnFloatConvert.pas, 2009/01/12 13:00 wqyfavor
* 修改记录：2009.1.12
* 创建单元
================================================================================
|</PRE>}
interface
uses
SysUtils;
{ 我写程序时比较喜欢用英文写注释(再不练就忘了)，所以下面的注释都是英文的。
算法是读取Extended类型在内存中的二进制内容进行转换。关于Extended类型的说明
可以参考其它资料。Double与Single类型为系统通用支持的浮点类型，与Delphi特有的
Extended在存储形式上稍有不同。三者均将尾数规格化，但Double与Single尾数部分略
掉了默认的1。比如尾数二进制内容为1.001，则在Double与Single中存储为001，略去
小数点前的1，而在Extended里存储为1001。
NaN意为 "not a number"，不是个数，定义参看Math.pas单元中的常量NaN
Infinity为无穷大，定义参看Math.pas单元中的常量Infinity与NegInfinity.
解释一下DecimalExp与AlwaysUseExponent参数。
将十进制浮点数度转换成其他进制时，如果用指数形式（科学计算法）表达（有些情况
也只能用指数形式，比如1E-1000，不用指数时是0.0000000...0001)，转换后指数部分
也应该用相应进制表示。但有时可以仍用十进制表示指数部分，比如二进制串
1.001E101，真值为100100，将指数用十进制表达更清楚一些1.001D5，表示将小数点
右移5位。DecimalExp这个参数就是指定是否用十进制表达指数部分的。注意，用十进制
数表示指数并无规定表达法，程序中使用"D"来表示，"E"为用相应进制表示。另外，由于
十六进制比较特殊，"D"与"E"均为十六进制特殊字符，所以十六进制表达时使用了"^"
字符，输出样例3.BD^D(12)、A.BD^E(ABCE)。如不喜欢这种格式可以自行修改。
AlwaysUseExponent参数指定是否一定用科学读数法表达，比如100.111位数比较少，
程序自动判断不需要使用科学计数法，当AlwaysUseExponent为真时则一定表达为指数
形式1.00111E2。
const
MaxBinDigits = 120;
MaxHexDigits = 30;
MaxOctDigits = 40;
这三个常量指定最长能输出多少位，当结果超过这个数时，则一定使用科学计数法。
FloatDecimalToBinExtended, FloatDecimalToOctExtended，FloatDecimalToHexExtended
均调用了FloatDecimalToBinaryExtended过程，FloatDecimalToBinaryExtended不公开。}
function FloatDecimalToBinExtended(fIn: Extended; DecimalExp,
AlwaysUseExponent: Boolean): AnsiString; // Convert to binary
function FloatDecimalToOctExtended(fIn: Extended; DecimalExp,
AlwaysUseExponent: Boolean): AnsiString; // Convert to octal
function FloatDecimalToHexExtended(fIn: Extended; DecimalExp,
AlwaysUseExponent: Boolean): AnsiString; // Convert to hexdecimal
implementation
type
PConvertFloatSystem = ^TConvertFloatSystem;
TConvertFloatSystem = record
Negative: Boolean;
ExpFlag, ExponentI: Integer;
end;
const
MaxBinDigits = 120;
MaxHexDigits = 30;
MaxOctDigits = 40;
function FloatDecimalToBinaryExtended(fIn: Extended; DecimalExp,
AlwaysUseExponent: Boolean; var ForHexOct: PConvertFloatSystem): AnsiString;
var
Neg: Boolean;
i, Flag, IntExp: Integer;
Exp: AnsiString;
label UseExponent;
begin
{
Extended(32.125) in memory:
0 100000000000100 10000000 10000000 00000000 00000000 00000000 00000000 00000000 00000000
9 8 7 6 5 4 3 2nd Byte 1stByte 0
sign exponent digits
0 111111111111111 1000000000000000000000000000000000000000000000000000000000000000 + Inf
1 111111111111111 1000000000000000000000000000000000000000000000000000000000000000 - Inf
1 111111111111111 1100000000000000000000000000000000000000000000000000000000000000 Nan
0 111111111111111 1100000000000000000000000000000000000000000000000000000000000000 -Nan
}
SetLength(Result, 255);
SetLength(Exp, 2 * SizeOf(Extended) + 1);
Neg := False;
asm
push EBX
push ESI
mov EBX, Result // Address of Result
mov EBX, [EBX]
mov EAX, 0
// Test if fIN equals 0
lea ESI, fIn[7] // get the first byte of digits
mov AL, [ESI]
test AL, 128 // 10000000B
jz @Zero
mov ECX, 0
lea ESI, fIn[8]
mov AX, [ESI] // Get first two bytes
test AX, 32768 // 32768D = 1000000000000000B
jz @Positive
mov Neg, 1
sub AX, 32768 // Sign bit <- 0
@Positive:
// Test if fIn is NaN or Infinity
cmp AX, 32767
jnz @NotNAN_INF
mov DL, [ESI - 1]
test DL, 64 // 01000000B
jz @INF
mov Flag, 4 // NaN
jmp @Done
@INF:
mov Flag, 3 // INF
jmp @Done
@NotNAN_INF:
sub AX, 16383 // AX = AX - 011111111111111B
jns @ExpPositive
sub AX, 1
not AX
mov Flag, 2 // // Exponent sign negative
jmp @JudgeDecimalExp
@ExpPositive:
mov Flag, 1 // Exponent sign positive
@JudgeDecimalExp:
mov IntExp, EAX
cmp DecimalExp, 1
je @MoveDigits
// Binary string exponent. Convert AX to binary string and store it in Exp
lea EBX, Exp
mov EBX, [EBX]
push ECX
mov [EBX], 'E' // "D" for decimal exponent
mov ECX, 1
cmp Flag, 2
jnz @NoNegativeInExp
mov [EBX + 1], '-' // Add a "-" to exponent string
mov ECX, 2
@NoNegativeInExp:
mov ESI, 0 // flag whehter "1" appears
// Move exponent digits to Exp
mov DX, 32768 // 1000000000000000
@NextExpDigit:
test AX, DX
jz @AppendExp0
mov [EBX + ECX], '1'
mov ESI, 1
jmp @NextExpIncECX
@AppendExp0:
cmp ESI, 0
jz @NextExpNoIncECX // do not append this "0"
mov [EBX + ECX], '0'
@NextExpIncECX:
inc ECX
@NextExpNoIncECX:
shr DX, 1
cmp DX, 0
jne @NextExpDigit
pop ECX
mov EBX, Result
mov EBX, [EBX]
jmp @MoveDigits
@MoveDigits:
// Move digits to Result
mov ESI, 8
@NextByte:
dec ESI
mov EAX, EBX
lea EBX, fIn[ESI]
mov DL, [EBX]
mov EBX, EAX
mov AL, 128 // 10000000
@NextDigit:
test DL, AL
jz @Append0
mov [EBX + ECX], '1'
mov i, ECX
jmp @Next
@Append0:
mov [EBX + ECX], '0'
@Next:
inc ECX
shr AL, 1
cmp AL, 0
jne @NextDigit
cmp ESI, 0 // if the last byte
jne @NextByte
jmp @Done
@Zero:
mov Flag, 0
@Done:
pop ESI
pop EBX
end;
case Flag of
0:
begin
ForHexOct := nil;
Result := '0';
Exit;
end;
1, 2:
begin
// Delete redundant "0" in Result
Delete(Result, i + 2, MaxInt); // i stores the position of the last 1 in Result
if Assigned(ForHexOct) then
begin
// Copy to ForHexOct
with ForHexOct^ do
begin
Negative := Neg;
ExpFlag := Flag;
ExponentI := IntExp;
end;
Exit;
end;
// Add dot and exponent to Result
if (IntExp = 0) then
begin
if (Length(Result) > 1) then
Insert('.', Result, 2);
end
else
begin
{ Decide whether use exponent. For example "1000.101" shouldn't be output
as 1.000101E11 when AlwaysUseExponent is False. }
if AlwaysUseExponent then
begin
UseExponent:
if DecimalExp then
if Flag = 1 then
Exp := 'D' + IntToStr(IntExp)
else
Exp := 'D-' + IntToStr(IntExp);
if Length(Result) >=2 then
Insert('.', Result, 2);
Result := Result + Exp;
end
else
begin
// IntExp may be negative.
if Flag = 1 then
begin
// Calculate all digits required without exponent
if IntExp <= Length(Result) - 2 then
begin
// Do not use exponent
Insert('.', Result, IntExp + 2);
end
else if IntExp = Length(Result) - 1 then
{ 1.001, Exp = 3, output 1001 }
else
begin
if IntExp + 1> MaxBinDigits then
goto UseExponent
else
begin
Inc(IntExp);
i := Length(Result);
// Add zeros at tail
SetLength(Result, IntExp);
for i := i + 1 to IntExp do
Result := '0';
end;
end;
end
else
begin
if IntExp + Length(Result) > MaxBinDigits then
goto UseExponent
else
begin
// Add leading zeros and place "."
SetLength(Exp, 1 + IntExp);
Exp[1] := '0';
Exp[2] := '.';
for i := 3 to IntExp + 1 do
Exp := '0'; //}
Result := Exp + Result;
end;
end;
end;
end;
end;
3: // INF
begin
ForHexOct := nil;
Result := 'INF';
end;
4: // NaN
begin
ForHexOct := nil;
Result := 'NaN';
Exit;
end;
end;
if Neg then
Result := '-' + Result;
end;
function FloatDecimalToBinExtended(fIn: Extended; DecimalExp,
AlwaysUseExponent: Boolean): AnsiString;
var
PTmp: PConvertFloatSystem;
begin
PTmp := nil;
Result := FloatDecimalToBinaryExtended(fIn, DecimalExp, AlwaysUseExponent, PTmp);
end;
function FloatDecimalToHexExtended(fIn: Extended; DecimalExp,
AlwaysUseExponent: Boolean): AnsiString;
const
DecToHex: array[0..15] of AnsiChar =
('0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F');
function IntToHex(Int: Integer): AnsiString;
var
k ,t: Integer;
Buf: array[1..5] of AnsiChar;
begin
k := 1;
while (Int <> 0) do
begin
Buf[k] := DecToHex[Int mod 16];
Inc(k);
Int := Int div 16;
end;
Dec(k);
SetLength(Result, k);
t := 1;
while (k > 0) do
begin
Result[t] := Buf[k];
Inc(t);
Dec(k);
end;
end;
const
BinPow: array[0..3] of Integer = (8, 4, 2, 1);
function ToHex(const S: AnsiString; LeftToDot: Boolean): AnsiString;
var
i, l, t, m, k: Integer;
Buf: array[1..20] of AnsiChar;
begin
{ LeftToDot = True, S will be patched with zeroes on its left side.
For example, S = '110', after patching, S = '0110'.
LeftToDot = False, S will be patched with zeroes on its right side.
S = '110', after patching, S = '1100'. }
l := Length(S);
if LeftToDot then
t := (4 - (l mod 4)) mod 4
else
t := 0;
i := 1;
m := 1;
k := 0;
while i <= l do
begin
k := k + BinPow[t] * (Ord(S) - Ord('0'));
Inc(t);
if (t = 4) or (i = l) then
begin
Buf[m] := DecToHex[k];
Inc(m);
k := 0;
t := 0;
end;
Inc(i);
end;
Dec(m);
SetLength(Result, m);
t := 1;
while (m > 0) do
begin
Result[m] := Buf[m];
Dec(m);
end;
end;
var
PConvertData: PConvertFloatSystem;
ConvertData: TConvertFloatSystem;
tmpS: AnsiString;
k, t, i, m: Integer;
label UseExponent;
begin
PConvertData := @ConvertData;
Result := FloatDecimalToBinaryExtended(fIn, True, True, PConvertData);
// See FloatDecimalToBinaryExtended, PConvertData is set to nil when result is definite.
if PConvertData = nil then
Exit;
with ConvertData do
begin
{ 3.BD^D(12)
A.BD^E(ABCE)
AB.FFFF }
k := Length(Result) - 1;
if AlwaysUseExponent then
begin
UseExponent:
{ Algorithm:
X.XXXXXXXX^Y Shift Count Exp
1.00000001^0 = 1.00000001 = 1.01^0 (16)
1.00000001^1 = 10.0000001 = 2.02^0 (16)
1.00000001^2 = 100.000001 = 4.04^0 (16)
1.00000001^3 = 1000.00001 = 8.08^0 (16)
1.00000001^4 = 1.00000001^100 = 1.01^1 (16)
1.00000001^5 = 10.0000001^100 = 2.02^1 (16)
Shift Count = Y mod 4
Exp = Y div 4
X.XXXXXXXXX^Y Y < 0 Exp
1.00000001^-1 = 0.100000001 = 1000.00001^-100 = 8.08^-1
1.00000001^-2 = 0.0100000001 = 100.000001^-100 = 4.04^-1
1.00000001^-3 = 0.00100000001 = 10.0000001^-100 = 2.02^-1
1.00000001^-4 = 0.000100000001 = 1.00000001^-100 = 1.01^-1
1.00000001^-5 = 0.0000100000001 = 1000.00001^-100 = 8.08^-2
Shift Count = 4 - (Abs(Y) mod 4)
Exp = -(Abs(Y) div 4 + 1) }
if ExpFlag = 1 then
begin
t := ExponentI div 4; // Exp
i := ExponentI mod 4; // Shift Count
end
else
begin
t := -((ExponentI - 1) div 4 + 1); // Exp
i := (4 - (ExponentI mod 4)) mod 4; // Shift Count
end;
// Get hex digits
if k < i then
begin
// Add extra zeroes
SetLength(Result, i + 1);
for m := k + 2 to i + 1 do
Result[m] := '0';
Result := ToHex(Result, True);
end
else if k = i then
Result := ToHex(Result, True)
else
begin
tmpS := Copy(Result, 1, i + 1);
Delete(Result, 1, i + 1);
Result := ToHex(tmpS, True) + '.' + ToHex(Result, False);
end;
if t <> 0 then
begin
// Format exponent
if DecimalExp then
Result := Result + '^D(' + IntToStr(t) + ')'
else
begin
if ExpFlag = 1 then
Result := Result + '^E(' + IntToHex(t) + ')'
else // t < 0
Result := Result + '^E(-' + IntToHex(-t) + ')';
end;
end;
end
else
begin
{ Always remember that Result equals "XXXXXXXX" not "X.XXXXXXX".
Judge whether to use exponent:
There are K "X" after '.', K = Length(Result) - 1, no "." in Result originally.
X.XXXXXXX^Y (Binary string, ExponentI = Abs(Y))
case Y >= 0 (Condition: ExpFlag = 2)
Y <= K:
Y+1 binary digits on left side of '.', K-Y digits on right side，
totally requires ((Y+1 - 1) div 4 + 1) + ((K-Y - 1) div 4 + 1) hex digits
Y > K:
Y+1 binary digits on left side, totally ((Y+1 - 1) div 4 + 1) hex digits
case Y<0 (Condition: ExpFlag = 1) 0.XXXX or 0.000XXXX
One digit '0' on left side and K+1+Abs(Y)-1 digits on right side,
totally 1 + ((K+1+Abs(Y)-1-1) div 4 + 1) hex digits.
Compare hdc = hex digit count with MaxHexDigits. If hdc > MaxHexDigits,
goto UseExponent. }
if ExponentI = 0 then
begin
if (Length(Result) > 1) then
Result := '1.' + ToHex(Copy(Result, 2, MaxInt), False);
end
else
begin
if ExpFlag = 1 then
begin
if ExponentI < k then
begin
// No possible that "ExponentI div 4 + (k - ExponentI - 1) div 4 + 2" > MaxHexDigits
tmpS := Copy(Result, 1, ExponentI + 1);
Delete(Result, 1, ExponentI + 1);
Result := ToHex(tmpS, True) + '.' + ToHex(Result, False);
end
else if ExponentI = k then
// 1.01^2 = 101, no ".", no extra "0".
Result := ToHex(Result, True)
else
begin
t := ExponentI div 4 + 1;
if t > MaxHexDigits then
goto UseExponent
else
begin
// Append "0" after Result
Inc(ExponentI);
// Add '0' to Result
SetLength(Result, ExponentI);
for t := k + 2{original Length(Result) + 1} to ExponentI do
Result[t] := '0';
Result := ToHex(Result, True);
end;
end;
end
else
begin
// ExpFlag = 2, X.XXXXXXX^Y, Y < 0
t := 2 + (k + ExponentI - 1) div 4; {1 + ((K+1+Abs(Y)-1-1) div 4 + 1)}
if t > MaxHexDigits then
goto UseExponent
else
begin
// Add leading zeroes before Result
SetLength(tmpS, ExponentI - 1); // tmpS stores extra zeroes
for t := 1 to ExponentI - 1 do
tmpS[t] := '0';
Result := '0.' + ToHex(tmpS + Result, False);
end;
end;
end;
end;
if Negative then
Result := '-' + Result;
end;
end;
function FloatDecimalToOctExtended(fIn: Extended; DecimalExp,
AlwaysUseExponent: Boolean): AnsiString;
const
DecToOct: array[0..7] of AnsiChar =
('0', '1', '2', '3', '4', '5', '6', '7');
function IntToOct(Int: Integer): AnsiString;
var
k ,t: Integer;
Buf: array[1..10] of AnsiChar;
begin
k := 1;
while (Int <> 0) do
begin
Buf[k] := DecToOct[Int mod 8];
Inc(k);
Int := Int div 8;
end;
Dec(k);
SetLength(Result, k);
t := 1;
while (k > 0) do
begin
Result[t] := Buf[k];
Inc(t);
Dec(k);
end;
end;
const
BinPow: array[0..2] of Integer = (4, 2, 1);
function ToOct(const S: AnsiString; LeftToDot: Boolean): AnsiString;
var
i, l, t, m, k: Integer;
Buf: array[1..30] of AnsiChar;
begin
{ LeftToDot = True, S will be patched with zeroes on its left side.
For example, S = '110', after patching, S = '0110'.
LeftToDot = False, S will be patched with zeroes on its right side.
S = '110', after patching, S = '1100'. }
l := Length(S);
if LeftToDot then
t := (3 - (l mod 3)) mod 3
else
t := 0;
i := 1;
m := 1;
k := 0;
while i <= l do
begin
k := k + BinPow[t] * (Ord(S) - Ord('0'));
Inc(t);
if (t = 3) or (i = l) then
begin
Buf[m] := DecToOct[k];
Inc(m);
k := 0;
t := 0;
end;
Inc(i);
end;
Dec(m);
SetLength(Result, m);
t := 1;
while (m > 0) do
begin
Result[m] := Buf[m];
Dec(m);
end;
end;
var
PConvertData: PConvertFloatSystem;
ConvertData: TConvertFloatSystem;
tmpS: AnsiString;
k, t, i, m: Integer;
label UseExponent;
begin
PConvertData := @ConvertData;
Result := FloatDecimalToBinaryExtended(fIn, True, True, PConvertData);
// See FloatDecimalToBinaryExtended, PConvertData is set to nil when result is definite.
if PConvertData = nil then
Exit;
with ConvertData do
begin
{ 3.333D12 // 12 is decimal
2.22E33 // 33 is octal}
k := Length(Result) - 1;
if AlwaysUseExponent then
begin
UseExponent:
if ExpFlag = 1 then
begin
t := ExponentI div 3; // Exp
i := ExponentI mod 3; // Shift Count
end
else
begin
t := -((ExponentI - 1) div 3 + 1); // Exp
i := (3 - (ExponentI mod 3)) mod 3; // Shift Count
end;
// Get hex digits
if k < i then
begin
// Add extra zeroes
SetLength(Result, i + 1);
for m := k + 2 to i + 1 do
Result[m] := '0';
Result := ToOct(Result, True);
end
else if k = i then
Result := ToOct(Result, True)
else
begin
tmpS := Copy(Result, 1, i + 1);
Delete(Result, 1, i + 1);
Result := ToOct(tmpS, True) + '.' + ToOct(Result, False);
end;
if t <> 0 then
begin
// Format exponent
if DecimalExp then
Result := Result + 'D' + IntToStr(t)
else
begin
if ExpFlag = 1 then
Result := Result + 'E' + IntToOct(t)
else // t < 0
Result := Result + 'E-' + IntToOct(-t);
end;
end;
end
else
begin
if ExponentI = 0 then
begin
if (Length(Result) > 1) then
Result := '1.' + ToOct(Copy(Result, 2, MaxInt), False);
end
else
begin
if ExpFlag = 1 then
begin
if ExponentI < k then
begin
tmpS := Copy(Result, 1, ExponentI + 1);
Delete(Result, 1, ExponentI + 1);
Result := ToOct(tmpS, True) + '.' + ToOct(Result, False);
end
else if ExponentI = k then
// 1.01^2 = 101, no ".", no extra "0".
Result := ToOct(Result, True)
else
begin
t := ExponentI div 3 + 1;
if t > MaxHexDigits then
goto UseExponent
else
begin
// Append "0" after Result
Inc(ExponentI);
// Add '0' to Result
SetLength(Result, ExponentI);
for t := k + 2{original Length(Result) + 1} to ExponentI do
Result[t] := '0';
Result := ToOct(Result, True);
end;
end;
end
else
begin
// ExpFlag = 2, X.XXXXXXX^Y, Y < 0
t := 2 + (k + ExponentI - 1) div 3;
if t > MaxHexDigits then
goto UseExponent
else
begin
// Add leading zeroes before Result
SetLength(tmpS, ExponentI - 1); // tmpS stores extra zeroes
for t := 1 to ExponentI - 1 do
tmpS[t] := '0';
Result := '0.' + ToOct(tmpS + Result, False);
end;
end;
end;
end;
if Negative then
Result := '-' + Result;
end;
end;
end.
Attachment:
[单元和例子]
FloatConvert.rar (2009-1-13 14:13, 9.59 K) / Download count 464
