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igInteger

igInteger represents a large integer value that can be arbitrarily large, unbounded by the limits of standard integer types. It is particularly useful in scenarios where extremely large numbers are involved, such as in cryptographic applications or financial calculations where precision is critical.

When working with BigInteger, it's essential to handle arithmetic operations carefully to avoid overflow, as standard integer types cannot accommodate these large values. The class provides methods for addition, subtraction, multiplication, and division, ensuring that operations are performed correctly without loss of data.

BigInteger also supports modular arithmetic, which is crucial in many algorithms, including those in number theory and cryptography. Its ability to handle large exponents and perform operations like exponentiation and modular inversion makes it a versatile tool in these fields.

BigInteger »¹ÌṩÁ˶àÖÖÒªÁìÀ´´¦ÀíÊý×ÖµÄλÔËËãºÍ·ûºÅ²Ù×÷¡£¹ØÓÚÐèÒª¸ß¾«¶ÈÅÌËãµÄÏîÄ¿£¬ BigInteger ÊDz»¿É»òȱµÄ¹¤¾ß¡£

BigInteger

BigInteger ÊÇ Java ÖÐÓÃÓÚ´¦ÀíÈÎÒ⾫¶È´óÕûÊýµÄÀ࣬Äܹ»´¦ÀíÔ¶³¬±ê×¼ÕûÊýÀàÐ͵ÄÊýÖµ¹æÄ££¬ÌرðÊʺϼÓÃÜËã·¨ºÍ½ðÈÚÅÌËãµÈÐèÒª¸ß¾«¶ÈµÄ³¡¾°¡£

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BigInteger ÔÚ¿ÆѧÅÌËãÖÐÒ²ºÜÊÇÓÐÓã¬ÓÈÆäÔÚÉæ¼°´óÖÊÊýÔËËãʱ£¬ÈçRSA¼ÓÃÜÖеÄÄ£ÔËËãºÍÖ¸ÊýÔËËã¡£

BigInteger µÄÁíÒ»¸öÖØÒªÌØÐÔÊÇÏß³ÌÄþ¾²¡£ÓÉÓÚÆä²»¿É±äÐÔ£¬ BigInteger µÄÒªÁ춼ÊÇÏß³ÌÄþ¾²µÄ£¬¶à¸öÏ߳̿ÉÒÔͬʱʹÓÃͬһ¸ö BigInteger ʵÀý¶øÎÞÐèµ£ÐÄÊý¾Ý¾ºÕù¡£

BigInteger µÄ½á¹¹º¯Êý½ÓÊܶàÖÖ²ÎÊýÀàÐÍ£¬Èç int¡¢long¡¢String ÒÔ¼° byte Êý×飬ÌṩÁ˼«´óµÄÁé»îÐÔ¡£Ê¹Óà String ʱעÒâ·ûºÅλµÄ´¦Àí£¬¿ÉÒÔʹÓà BigInteger(String val) ½á¹¹º¯Êý»ò´øÓнøÖƲÎÊýµÄ°æ±¾¡£

ÔÚ½øÐÐËãÊõÔËËãʱ£¬ÓÀÔ¶²»Òª½« BigInteger ת»»ÎªÔ­ÉúÀàÐÍ£¬ÒÔÃâÒòÊýÖµÁè¼Ý¹æÄ£µ¼Ö¹ýʧ»òÊý¾Ýɥʧ¡£¿ÉÒÔÀûÓà add(), subtract(), multiply(), divide(), ºÍ mod() µÈÒªÁì½øÐÐÅÓ´óµÄÊýѧÔËËã¡£

BigInteger ÊÇ Java Öд¦Àí´óÕûÊýÔËËãµÄÊ×Ñ¡¹¤¾ß£¬ÆäÓÅÑŵÄÉè¼ÆºÍ¸»ºñµÄ¹¦Ð§Ê¹ÆäÔÚÖÖÖÖ³¡ºÏÖж¼ÄÜÓÎÈÐÓÐÓà¡£

BigInteger

BigInteger ÊÇ Java ÖÐÓÃÓÚ´¦Àí´óÕûÊýµÄÀ࣬ÌṩÁËÎÞÏÞ¾«¶ÈµÄÕûÊýÔËË㣬ÊǽøÐи߾«¶ÈÊýѧÔËËãºÍ¼ÓÃÜËã·¨µÄÀíÏëÑ¡Ôñ¡£

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BigInteger »¹ÌṩÁ˶àÖÖ¾²Ì¬ÒªÁ죬Èç valueOf() ÓÃÓÚ´Ó int »ò long Öµ´´Á¢ÊµÀý£¬ZERO, ONE, TEN µÈ³£Á¿£¬¼«´óµØ±ãµ±ÁË¿ª·¢Õß¡£ÔÚ½øÐбȽϲÙ×÷ʱ£¬¿ÉÒÔÖ±½ÓʹÓà compareTo() ÒªÁ죬¶ø²»±Øµ£ÐÄÓëÔ­ÉúÀàÐͱȽÏʱµÄÎÊÌâ¡£

BigInteger Ö§³ÖËØÊý¼ì²âºÍÒòʽÆÊÎö£¬Õâ¹ØÓÚÃÜÂëѧÖеÄÓ¦ÓúÜÊÇÖØÒª¡£Ê¹Óà isProbablePrime() ÒªÁì¿ÉÒÔ¿ìËÙÅжÏÒ»¸ö´óÕûÊýÊÇ·ñΪËØÊý£¬Õâ¹ØÓÚ RSA Ëã·¨ÖеÄÃÜÔ¿Éú³ÉºÜÊÇÓÐÓá£

BigInteger µÄ¼òµ¥ÐԺ͸ßЧÐÔʹÆäÔÚÖÖÖÖ³¡¾°Öж¼ÄÜ·¢»ÓÖØÒª×÷Óá£ÎÞÂÛÊÇ¿ÆѧÑо¿¡¢½ðÈÚÅÌË㣬Õվɵç×ÓÉÌÎñºÍÐÅÏ¢Äþ¾²£¬ BigInteger ¶¼ÊDz»¿É»òȱµÄÒ»²¿·Ö¡£

BigInteger ƾ½èÆäÇ¿´óµÄ¹¦Ð§ºÍÁé»îÐÔ£¬³ÉΪ Java ¿ª·¢Õß´¦Àí´óÕûÊýÔËËãµÄµÃÁ¦ÖúÊÖ¡£

BigInteger

BigInteger ÊÇ Java ±ê×¼¿âÖÐÌṩµÄÒ»¸öÓÃÓÚ´¦Àí´óÕûÊýµÄÀ࣬Äܹ»½â¾ö¹Å°åÕûÊýÀàÐÍÔÚ´¦Àí´óÊý¾ÝʱµÄ¾ÖÏÞÐÔ¡£

ÔÚʹÓà BigInteger ʱ£¬Ó¦¸ÃÖÆÖ¹Ö±½ÓʹÓÃÔ­ÉúÀàÐÍ£¬ÒòΪËüÃÇÎÞ·¨´¦Àí´óÕûÊýÔËË㣬»áµ¼ÖÂÒç³ö»òÆäËû¹ýʧ¡£ BigInteger µÄ²»¿É±äÐÔÒâζ×Åÿ´Î²Ù×÷¶¼»áÉú³ÉÐµĹ¤¾ß£¬Õâ¶ÔÄÚ´æÖÎÀíÌá³öÁËÒ»¶¨µÄÒªÇ󣬵«Í¬Ê±Ò²°ü¹ÜÁËÏß³ÌÄþ¾²¡£

BigInteger »¹Ö§³ÖÐòÁл¯£¬¿ÉÒÔͨ¹ý Serializable ½Ó¿Ú½øÐй¤¾ßµÄ³¤ÆÚ»¯»òÔÚÍøÂçÖд«Êä¡£¹ØÓÚÐèÒªÉú´æ»ò´«Êä´óÊý¾ÝµÄÓ¦Óó¡¾°£¬Õâ¸ö¹¦Ð§ºÜÊÇÓÐÓá£

ÔÚ¼ÓÃÜËã·¨ÖУ¬ BigInteger ¹ã·ºÓ¦ÓÃÓÚÃÜÔ¿Éú³É¡¢¼ÓÃÜÏ¢ÕùÃÜÀú³Ì£¬È·±£Êý¾ÝµÄÄþ¾²ÐÔ¡£ËäÈ» BigInteger ÔÚ´¦Àí´óÊýʱЧÂʽϸߣ¬µ«¹ØÓÚ¼«ÆäÅÓ´óµÄÊý£¬ÈÔÐ迼ÂDz¢ÐÐÅÌËã»òʹÓøü¸ßЧµÄËã·¨ÒÔÌá¸ßÐÔÄÜ¡£

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BigInteger ÊÇ Java ¿ª·¢Õß´¦Àí´óÕûÊýÔËËãµÄÊ×Ñ¡¹¤¾ß£¬Æ主ºñµÄ¹¦Ð§ºÍÎȶ¨ÐÔʹÆäÔÚÖÖÖÖÓ¦ÓÃÖж¼ÄÜ·¢»Ó×÷Óá£

BigInteger # Arbitrary Precision # Java Programming

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