java自定义大数(进制可在2-62之间相互转换)

1、 java自定义大数(进制可在262之间相互转化) 闲着没事做，写了一个自定义大数，并实现了两个大数的加减乘除以及比较，以及262进制任意数(包括但不限于正整数与负整数)的相互转化大数类: BigNumber.java/* * 09用09表示,1035用AZ表示,3661用az表示 */SuppressWarnings("serial")public class BigNumber extends Exceptionprivate String MyNumber;/大数private int SystemNumber;/进制数public BigNumber()this(&

2、quot;0",10); public BigNumber(String MyNumber) this(MyNumber,10); public BigNumber(String MyNumber,int SystemNumber) this.MyNumber=MyNumber; this.SystemNumber=SystemNumber; this.Islegal(); public String getMyNumber() return this.MyNumber;public void setMyNumber(String myNumber) this.MyNumber =

3、myNumber;public int getSystemNumber() return this.SystemNumber;public void setSystemNumber(int systemNumber) this.SystemNumber = systemNumber; public void Islegal()/判断该字符串是否合法 if(this.MyNumber=null|this.MyNumber.length()=0)/大数为空或大数字符串长度为0throw (new NumberFormatException("错误!大数为空或大数字符串长度为0 "

4、;+this.MyNumber); if(this.SystemNumber<=1|this.SystemNumber>=63)/进制数不合法throw (new NumberFormatException("错误!进制数不合法 "+this.SystemNumber); if(this.MyNumber.equals("+")|this.MyNumber.equals("-")|this.MyNumber.equals(".") throw (new NumberFormatException(&qu

5、ot;错误!大数不合法 "+this.MyNumber); if(this.MyNumber.equals("+.")|this.MyNumber.equals("-.") throw (new NumberFormatException("错误!大数不合法 "+this.MyNumber); for(int i=0,a,k=-1;i<this.MyNumber.length();i+) a=Chartoint(this.MyNumber.charAt(i); if(i!=0&&(a=-1|a=-2)

6、throw (new NumberFormatException("错误!符号位只能在大数首部 "+this.MyNumber.charAt(i)+"("+i+")"); if(a>=this.SystemNumber|a=-4) throw (new NumberFormatException("错误!该字符不在该进制合法字符中 "+this.MyNumber.charAt(i)+"("+i+")"); if(a=-3) if(k=-1) k=i; else thro

7、w (new NumberFormatException("错误!出现了第二个小数点 "+this.MyNumber.charAt(i)+"("+i+")"); protected static String Add_Positive(String s1,String s2,int n)/自定义两个正数加法运算 String Ins1=getInteger(s1),Dos1=getDecimal(s1),Ins2=getInteger(s2),Dos2=getDecimal(s2);/分别获取整数部分及小数部分 int Inlengt

8、h=Math.max(Ins1.length(), Ins2.length(),Dolength=Math.max(Dos1.length(), Dos2.length(); Ins1=AddToLeft(Ins1,Inlength+1)+AddToRight(Dos1,Dolength); Ins2=AddToLeft(Ins2,Inlength+1)+AddToRight(Dos2,Dolength); String s="" for(int i=Inlength+Dolength,m,y=0;i>=0;i-) m=Chartoint(Ins1.charAt(i)

9、+Chartoint(Ins2.charAt(i)+y; s=Inttochar(m%n)+s; y=m/n; int pointplace=s.length()-Dolength; s=Format(s.substring(0,pointplace)+"."+s.substring(pointplace),true); return s; protected static String Sub_Positive(String s1,String s2,int n)/自定义两个正数减法运算; if(ComparetoString(s1,s2)<0)/如果s1<s

10、2则返回-(s2-s1) return "-"+Sub_Positive(s2,s1,n); String Ins1=getInteger(s1),Dos1=getDecimal(s1),Ins2=getInteger(s2),Dos2=getDecimal(s2);/分别获取整数部分及小数部分 int Inlength=Math.max(Ins1.length(), Ins2.length(),Dolength=Math.max(Dos1.length(), Dos2.length(); String R=getComplement(new BigNumber(AddTo

11、Left(Ins2,Inlength)+"."+AddToRight(Dos2,Dolength),n).MyNumber; R=Add_Positive(s1,R,n); s2="0."+AddToLeft("1",Dolength); R=Add_Positive(R,s2,n); return Format(R.substring(1),true); protected static String Mult_Positive(String s1,String s2,int n)/自定义两个正数乘法运算; String Ins1=

12、getInteger(s1),Dos1=getDecimal(s1),Ins2=getInteger(s2),Dos2=getDecimal(s2);/分别获取整数部分及小数部分 Ins1+=Dos1; Ins2+=Dos2; intA=new intIns1.length()+Ins2.length()-1; for(int i=Ins1.length()-1;i>=0;i-) for(int j=Ins2.length()-1;j>=0;j-) Ai+j+=Chartoint(Ins1.charAt(i)*Chartoint(Ins2.charAt(j); String s=&

13、quot;" for(int i=A.length-1;i>=1;i-) s=Inttochar(Ai%n)+s; Ai-1+=Ai/n; s=Inttochar(A0/n)+""+Inttochar(A0%n)+s;/特别要注意+"" int pointlength=Dos1.length()+Dos2.length();/获取小数点后的位数 return Format(s.substring(0,s.length()-pointlength)+"."+s.substring(s.length()-pointleng

14、th),true); protected static String Division_Positive(String s1, String s2,int n,int f)/自定义两个正数相除(f为小数点后的位数,能被除尽，且小数点后的位数少于f,则直接返回结果); String Ins1=getInteger(s1),Dos1=getDecimal(s1),Ins2=getInteger(s2),Dos2=getDecimal(s2); /分别获取整数部分及小数部分 int Dolength=Math.max(Dos1.length(), Dos2.length(); Ins1+=AddTo

15、Right(Dos1,Dolength); Ins2+=AddToRight(Dos2,Dolength); StringB=new Stringn;B0="0" for(int i=1;i<n;i+) Bi=Add_Positive(Bi-1,Ins2,n);/Bi=Mult_Positive(Ins2,Inttochar(i)+"", n); int i=Math.min(Ins1.length(), Ins2.length()-2,j; String Ds0="",Ds1=Ins1.substring(0,i);/初始化整

16、数部分余数部分 while(true) if(i!=Ins1.length() if(i<Ins1.length() Ds1+=Ins1.charAt(i); else Ds1+="0" if(Ds1.equals("00")|i-Ins1.length()-1=f) break; /下面开始求Ds1/Ins2的整数部分及余数,结果分别赋值为Ds0,Ds1;采用二分查找获取整数部分 j=Binary(B,Ds1); Ds0+=Inttochar(j);Ds1=Sub_Positive(Ds1,Bj,n); else Ds0+=".&quo

17、t; i+; return Format(Ds0,true); protected static int Binary(StringA,String key)/二分查找key(数组A已经按从小到大的顺序排好序) int low=0,height=A.length-1,middle,Compare;while(low<=height)middle=(low+height)/2;Compare=ComparetoString(key,Amiddle);if(Compare=0)return middle;else if(Compare>0)low=middle+1;elseheight

18、=middle-1;return height; public BigNumber Add(BigNumber b)/自定义加法运算 if(this.SystemNumber!=b.SystemNumber) throw (new NumberFormatException("错误!这两个大数进制数不一致 ("+this.SystemNumber+","+b.SystemNumber+")"); String s; if(IsPositive(this.MyNumber)&&IsPositive(b.MyNumber)

19、 s=Add_Positive(this.MyNumber,b.MyNumber,this.SystemNumber); else if(IsPositive(this.MyNumber)&&!IsPositive(b.MyNumber) s=Sub_Positive(this.MyNumber,Opposite(b.MyNumber),this.SystemNumber); else if(!IsPositive(this.MyNumber)&&IsPositive(b.MyNumber) s=Sub_Positive(b.MyNumber,Opposite(

20、this.MyNumber),this.SystemNumber); else s=Add_Positive(Opposite(this.MyNumber),Opposite(b.MyNumber),this.SystemNumber); s=(s.equals("0")?"":"-")+s; return new BigNumber(s,this.SystemNumber); public BigNumber Sub(BigNumber b)/自定义减法运算 return this.Add(new BigNumber(Opposit

21、e(b.MyNumber),b.SystemNumber); public BigNumber Mult(BigNumber b)/自定义乘法运算 if(this.SystemNumber!=b.SystemNumber) throw (new NumberFormatException("错误!这两个大数进制数不一致 ("+this.SystemNumber+","+b.SystemNumber+")"); String s; if(IsPositive(this.MyNumber)&&IsPositive(b.My

22、Number) s=Mult_Positive(this.MyNumber,b.MyNumber,this.SystemNumber); else if(IsPositive(this.MyNumber)&&!IsPositive(b.MyNumber) s=Mult_Positive(this.MyNumber,Opposite(b.MyNumber),this.SystemNumber); s=(s.equals("0")?"":"-")+s; else if(!IsPositive(this.MyNumber)&

23、amp;&IsPositive(b.MyNumber) s=Mult_Positive(Opposite(this.MyNumber),b.MyNumber,this.SystemNumber); s=(s.equals("0")?"":"-")+s; else s=Mult_Positive(Opposite(this.MyNumber),Opposite(b.MyNumber),this.SystemNumber); return new BigNumber(s,this.SystemNumber); public Big

24、Number Division(BigNumber b,int f)/自定义除法运算(f为小数点后的位数,能被除尽,且小数点后的位数少于f,则直接返回精确结果); if(b.toString().equals("-0")|b.toString().equals("0") throw (new NumberFormatException("错误!除数不能为零:"+b); if(this.SystemNumber!=b.SystemNumber) throw (new NumberFormatException("错误!这两个大

25、数进制数不一致! ("+this.SystemNumber+","+b.SystemNumber+")"); if(f<0) throw (new NumberFormatException("错误!小数点后的位数应为非负值!("+f+")"); String s; if(IsPositive(this.MyNumber)&&IsPositive(b.MyNumber) s=Division_Positive(this.MyNumber,b.MyNumber,this.SystemN

26、umber,f); else if(IsPositive(this.MyNumber)&&!IsPositive(b.MyNumber) s=Division_Positive(this.MyNumber,Opposite(b.MyNumber),this.SystemNumber,f); s=(s.equals("0")?"":"-")+s; else if(!IsPositive(this.MyNumber)&&IsPositive(b.MyNumber) s=Division_Positive(O

27、pposite(this.MyNumber),b.MyNumber,this.SystemNumber,f); s=(s.equals("0")?"":"-")+s; else s=Division_Positive(Opposite(this.MyNumber),Opposite(b.MyNumber),this.SystemNumber,f); return new BigNumber(s,this.SystemNumber); public BigNumber Division(BigNumber b)/自定义除法运算,默认为保

28、留50位小数(若能被除尽,且小数点后的位数少于50,则直接返回精确结果); return Division(b,50); protected static int ComparetoString(String s1,String s2)/判断两个正数的大小s1>s2返回1,s1=s2返回0,s1<s2返回-1 String Ins1=getInteger(s1),Dos1=getDecimal(s1),Ins2=getInteger(s2),Dos2=getDecimal(s2); int Dolength=Math.max(Dos1.length(), Dos2.length()

29、; Ins1+=AddToRight(Dos1,Dolength); Ins2+=AddToRight(Dos2,Dolength); if(Ins1.length()>Ins2.length() return 1; else if(Ins1.length()<Ins2.length() return -1; for(int i=0;i<Ins1.length();i+) if(Ins1.charAt(i)>Ins2.charAt(i) return 1; else if(Ins1.charAt(i)<Ins2.charAt(i) return -1; retur

30、n 0; public int Compareto(BigNumber b) if(this.SystemNumber!=b.SystemNumber) throw (new NumberFormatException("错误!这两个大数进制数不一致 ,暂时无法比较("+this.SystemNumber+","+b.SystemNumber+")"); String s1=Format(this.MyNumber,false),s2=Format(b.MyNumber,false); if(IsPositive(s1)&&a

31、mp;IsPositive(s2) return ComparetoString(s1,s2);/int a=s1.CompareTo(s2); return a!=0?(a>0?1:-1):0; else if(IsPositive(s1)&&!IsPositive(s2) return 1; else if(!IsPositive(s1)&&IsPositive(s2) return -1; else return -ComparetoString(s1.substring(1),s2.substring(1); protected static St

32、ring Conver1(long n,int R)/将十进制数n转换为R进制数 if(R=10) return n+"" String s="" while(true) s=Inttochar(int)(n%R)+s; n/=R; if(n=0) return s; /* * 将R1进制正整数s转化为R2进制数 * (由于Conversion频繁调用该函数,为提高效率,引入两个辅助数组Hex1,Hex2): * Hex1i是十进制数i转换为R2进制数后的数,0<=i<=R1;Hex2i=Hex1R1i,0<=i<=s.lengt

33、h() * Hex2i是十进制数R1转换为R2进制数后的i次方 */ protected static String Conver(String s,int R1,int R2,StringHex1,StringHex2)String Ins="0"/初始化新进制对应的大数for(int i=0;i<s.length();i+) Ins=Add_Positive(Ins,Mult_Positive(Hex1Chartoint(s.charAt(s.length()-1-i),Hex2i,R2),R2); return Ins; protected static Str

34、ing Conversion(String MyNumber,int R1,int R2,int N,int f)/将R1进制大数MyNumber转换为R2进制的大数(f为小数点后的位数,能被除尽,且小数点后的位数少于f,则直接返回结果),N为将MyNumber分组后每组字符串的长度; if(R2=R1) int a=getDecimal(MyNumber).length()-f; if(a>0) return MyNumber.substring(0,MyNumber.length()-a); return MyNumber; if(MyNumber.charAt(0)='+&

35、#39;|MyNumber.charAt(0)='-') char c=MyNumber.charAt(0); return c+Conversion(MyNumber.substring(1),R1,R2,N,f); StringHex1=new StringR1+1;for(int i=0;i<=R1;i+)/将0R1的所有数字转换为R2进制Hex1i=Conver1(i,R2);StringHex2=new StringN+1;Hex20="1"for(int i=1;i<=N;i+)/求十进制数R1转换为R2进制数后的i次方Hex2i=M

36、ult_Positive(Hex2i-1,Hex1R1,R2); String Ins1=getInteger(MyNumber),Dos1=getDecimal(MyNumber);/获取整数部分及小数部分/* * 经过计算当转化后的R2进制数只需保留f位小数时,原R1进制数MyNumber只需保留a位 * 当MyNumber小数位很多，而f较小时在一定程度上能提高效率 */int a=(int)Math.ceil(f*Math.log(R2)/Math.log(R1)+1;if(a<=Dos1.length()Dos1=Dos1.substring(0,a);Ins1=AddToLe

37、ft(Ins1,Ins1.length()+(N-Ins1.length()%N)%N);/扩充Ins1Dos1=AddToRight(Dos1,Dos1.length()+(N-Dos1.length()%N)%N);/扩充Dos1String Ins="0",Dos="0",x="1"/new BigNumber(Conver1(R1,R2),R2).Power(N).MyNumber;初始化新进制对应的大数的整数部分及小数部分 ,设置初值及权 int Count=Math.max(Ins1.length()/N,Dos1.len

38、gth()/N);/循环次数 for(int i=0,i1=Ins1.length()/N,i2=Dos1.length()/N;i<Count;i+) if(i<i1)Ins=Add_Positive(Ins,Mult_Positive(Conver(Ins1.substring(Ins1.length()-(i+1)*N,Ins1.length()-i*N),R1,R2,Hex1,Hex2),x,R2),R2);if(i<i2) Dos=Add_Positive(Dos,Mult_Positive(Conver(Dos1.substring(Dos1.length()-(

39、i+1)*N,Dos1.length()-i*N),R1,R2,Hex1,Hex2),x,R2),R2);if(i=i2-1) Dos=Division_Positive(Dos,Mult_Positive(x,Hex2N,R2),R2,f); x=Mult_Positive(x,Hex2N,R2);return Ins+Dos.substring(1);/或Add_Positive(Ins,Dos,R2); public BigNumber HexConversion(int R,int N,int f) if(R<=1|R>=63)/进制数不合法throw (new Numbe

40、rFormatException("错误!进制数不合法 "+this.SystemNumber); if(N<=0) throw (new NumberFormatException("错误!每小组的字符串长度不能小于1!("+N+")"); if(f<0) throw (new NumberFormatException("错误!小数点后的位数应为非负值!("+f+")"); return new BigNumber(Conversion(this.MyNumber,this.Sy

41、stemNumber,R,N,f),R); public BigNumber HexConversion(int R,int f) int N=(int)Math.pow(Math.max(getInteger(this.MyNumber).length(),getDecimal(this.MyNumber).length(),0.6)+1; return HexConversion(R,N,f); public BigNumber HexConversion(int R) return HexConversion(R,50); public BigNumber Power(int n,int

42、 f)/求an,n为十进制整数(f为小数点后的位数,能被除尽,且小数点后的位数少于f,则直接返回结果); if(n<0) return new BigNumber("1",this.SystemNumber).Division(this.Power(-n,f),f); String s=Conver1(n,2);BigNumber r=new BigNumber("1",this.SystemNumber),k=this; for(int i=0;i<s.length();i+) if(s.charAt(s.length()-1-i)=

43、9;1') r=r.Mult(k); k=k.Mult(k); return r; public BigNumber Power(int n)/求ab,b为十进制整数 return Power(n,50); protected static BigNumber getComplement(BigNumber b)/获得 b的每位取反后的大数 String s="" char c=b.MyNumber.charAt(0); if(c='+'|c='-'|c='.') s+=c; else s+=Inttochar(b.S

44、ystemNumber-1-Chartoint(c); for(int i=1;i<b.MyNumber.length();i+) c=b.MyNumber.charAt(i); if(c='.') s+=c; else s+=Inttochar(b.SystemNumber-1-Chartoint(c); return new BigNumber(s,b.SystemNumber); protected static String AddToLeft(String s,int length)/若s的长度大于或等于length,则直接返回s,否则字符串s左边补零,直到s长

45、度达到length if(s.length()>=length) return s; while(s.length()<length) s="0000000000"+s; return s.substring(s.length()-length,s.length(); protected static String AddToRight(String s,int length)/若s的长度大于或等于length,则直接返回s,否则字符串s右边补零,直到s长度达到length if(s.length()>=length) return s; while(s.

46、length()<length) s=s+"0000000000" return s.substring(0,length); protected static String Format(String MyNumber,boolean DealZero)/对于合法的大数,格式化大数为a.b(或-a.b)的形式,若b=0且DealZero为真则返回a(或-a)的形式 new BigNumber(MyNumber,62);/若该大数不合法则抛出异常String s; if(MyNumber.charAt(0)='+'|MyNumber.charAt(0)

47、='-') s=MyNumber.substring(1); else s=MyNumber; if(getPointPlace(s)=0) s="0"+s; else if(getPointPlace(s)=s.length()-1) s=s+"0" else if(getPointPlace(s)=s.length() s=s+".0" int Ins=0,Dos=s.length(),pointplace=getPointPlace(s); for(int i=0;i<pointplace-1;i+) if

48、(s.charAt(i)='0') Ins+; else break; for(int i=s.length()-1;i>pointplace+1;i-) if(s.charAt(i)='0') Dos-; else break; s=(MyNumber.charAt(0)='-'?"-":"")+s.substring(Ins,Dos);if(DealZero&&s.substring(s.length()-2).equals(".0")return s.subs

49、tring(0,s.length()-2);elsereturn s; protected static boolean IsPositive(String MyNumber)/判断该大数是否为正数(负数返回false,0和正数返回true) if(MyNumber.charAt(0)='-') return false; return true; protected static int getPointPlace(String MyNumber)/返回该大数小数点位置 for(int i=0;i<MyNumber.length();i+) if(MyNumber.ch

50、arAt(i)='.') return i; return MyNumber.length(); protected static String Abs(String MyNumber)/返回该大数的绝对值 MyNumber=Format(MyNumber,true); return MyNumber.substring(MyNumber.charAt(0)='-'?1:0); protected static String Opposite(String MyNumber)/返回该大数的相反数 return MyNumber.charAt(0)='-&

51、#39;?Abs(MyNumber):"-"+Abs(MyNumber); protected static String getInteger(String MyNumber)/返回该大数的整数部分 MyNumber=Format(MyNumber,false); return MyNumber.substring(0,getPointPlace(MyNumber); protected static String getDecimal(String MyNumber)/返回该大数的小数部分 MyNumber=Format(MyNumber,false); String

52、s=getPointPlace(MyNumber)=MyNumber.length()?"0":MyNumber.substring(getPointPlace(MyNumber)+1); return (MyNumber.charAt(0)='-'?"-":"")+s; protected static int Chartoint(char c)/字符化为数字if(c>='0'&&c<='9')return c-'0'else if(c>

53、;='A'&&c<='Z')return c-'A'+10;else if(c>='a'&&c<='z')return c-'a'+36;else if(c='+')/正号return -1;else if(c='-')/负号return -2;else if(c='.')/小数点return -3;else/其他return -4; protected static char Inttochar(int n)/数字化为字符if(n>=0&&