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603 lines
17 KiB
603 lines
17 KiB
7 years ago
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// Copyright (c) 2009-2010 Satoshi Nakamoto
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// Copyright (c) 2009-2012 The Bitcoin developers
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// Distributed under the MIT/X11 software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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#ifndef BITCOIN_BIGNUM_H
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#define BITCOIN_BIGNUM_H
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#ifndef PROTOCOL_VERSION
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#define PROTOCOL_VERSION 70001
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#endif
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#include <map>
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#include <limits>
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#include <algorithm>
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#include <stdexcept>
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#include <vector>
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#include "uint256.h"
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#include <openssl/bn.h>
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#include "serialize.hpp"
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using namespace std;
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/** Errors thrown by the bignum class */
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class bignum_error : public std::runtime_error
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{
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public:
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explicit bignum_error(const std::string& str) : std::runtime_error(str) {}
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};
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/** RAII encapsulated BN_CTX (OpenSSL bignum context) */
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class CAutoBN_CTX
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{
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protected:
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BN_CTX* pctx;
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BN_CTX* operator=(BN_CTX* pnew) { return pctx = pnew; }
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public:
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CAutoBN_CTX()
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{
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pctx = BN_CTX_new();
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if (pctx == NULL)
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throw bignum_error("CAutoBN_CTX : BN_CTX_new() returned NULL");
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}
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~CAutoBN_CTX()
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{
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if (pctx != NULL)
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BN_CTX_free(pctx);
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}
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operator BN_CTX*() { return pctx; }
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BN_CTX& operator*() { return *pctx; }
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BN_CTX** operator&() { return &pctx; }
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bool operator!() { return (pctx == NULL); }
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};
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/** C++ wrapper for BIGNUM (OpenSSL bignum) */
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class CBigNum : public BIGNUM
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{
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public:
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CBigNum()
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{
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BN_init(this);
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}
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CBigNum(const CBigNum& b)
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{
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BN_init(this);
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if (!BN_copy(this, &b))
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{
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BN_clear_free(this);
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throw bignum_error("CBigNum::CBigNum(const CBigNum&) : BN_copy failed");
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}
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}
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CBigNum& operator=(const CBigNum& b)
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{
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if (!BN_copy(this, &b))
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throw bignum_error("CBigNum::operator= : BN_copy failed");
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return (*this);
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}
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~CBigNum()
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{
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BN_clear_free(this);
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}
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//CBigNum(char n) is not portable. Use 'signed char' or 'unsigned char'.
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CBigNum(signed char n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
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CBigNum(short n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
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CBigNum(int n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
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CBigNum(long n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
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CBigNum(int64 n) { BN_init(this); setint64(n); }
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CBigNum(unsigned char n) { BN_init(this); setulong(n); }
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CBigNum(unsigned short n) { BN_init(this); setulong(n); }
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CBigNum(unsigned int n) { BN_init(this); setulong(n); }
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CBigNum(unsigned long n) { BN_init(this); setulong(n); }
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CBigNum(uint64 n) { BN_init(this); setuint64(n); }
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explicit CBigNum(uint256 n) { BN_init(this); setuint256(n); }
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explicit CBigNum(const std::vector<unsigned char>& vch)
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{
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BN_init(this);
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setvch(vch);
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}
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void setulong(unsigned long n)
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{
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if (!BN_set_word(this, n))
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throw bignum_error("CBigNum conversion from unsigned long : BN_set_word failed");
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}
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unsigned long getulong() const
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{
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return (unsigned long) BN_get_word(this);
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}
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unsigned int getuint() const
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{
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return (unsigned int) BN_get_word(this);
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}
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int getint() const
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{
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unsigned long n = (unsigned long) BN_get_word(this);
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if (!BN_is_negative(this))
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return (n > (unsigned long)std::numeric_limits<int>::max() ? std::numeric_limits<int>::max() : n);
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else
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return (n > (unsigned long)std::numeric_limits<int>::max() ? std::numeric_limits<int>::min() : -(int)n);
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}
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void setint64(int64 sn)
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{
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unsigned char pch[sizeof(sn) + 6];
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unsigned char* p = pch + 4;
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bool fNegative;
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uint64 n;
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if (sn < 0LL)
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{
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// Since the minimum signed integer cannot be represented as positive so long as its type is signed,
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// and it's not well-defined what happens if you make it unsigned before negating it,
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// we instead increment the negative integer by 1, convert it, then increment the (now positive) unsigned integer by 1 to compensate
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n = -(sn + 1);
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++n;
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fNegative = true;
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} else {
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n = sn;
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fNegative = false;
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}
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bool fLeadingZeroes = true;
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for (int i = 0; i < 8; i++)
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{
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unsigned char c = (n >> 56) & 0xff;
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n <<= 8;
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if (fLeadingZeroes)
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{
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if (c == 0)
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continue;
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if (c & 0x80)
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*p++ = (fNegative ? 0x80 : 0);
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else if (fNegative)
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c |= 0x80;
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fLeadingZeroes = false;
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}
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*p++ = c;
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}
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unsigned int nSize = (unsigned int) (p - (pch + 4));
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pch[0] = (nSize >> 24) & 0xff;
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pch[1] = (nSize >> 16) & 0xff;
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pch[2] = (nSize >> 8) & 0xff;
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pch[3] = (nSize) & 0xff;
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BN_mpi2bn(pch, (int) (p - pch), this);
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}
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void setuint64(uint64 n)
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{
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unsigned char pch[sizeof(n) + 6];
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unsigned char* p = pch + 4;
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bool fLeadingZeroes = true;
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for (int i = 0; i < 8; i++)
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{
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unsigned char c = (n >> 56) & 0xff;
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n <<= 8;
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if (fLeadingZeroes)
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{
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if (c == 0)
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continue;
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if (c & 0x80)
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*p++ = 0;
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fLeadingZeroes = false;
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}
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*p++ = c;
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}
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unsigned int nSize = (unsigned int) (p - (pch + 4));
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pch[0] = (nSize >> 24) & 0xff;
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pch[1] = (nSize >> 16) & 0xff;
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pch[2] = (nSize >> 8) & 0xff;
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pch[3] = (nSize) & 0xff;
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BN_mpi2bn(pch, (int) (p - pch), this);
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}
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void setuint256(uint256 n)
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{
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unsigned char pch[sizeof(n) + 6];
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unsigned char* p = pch + 4;
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bool fLeadingZeroes = true;
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unsigned char* pbegin = (unsigned char*)&n;
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unsigned char* psrc = pbegin + sizeof(n);
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while (psrc != pbegin)
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{
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unsigned char c = *(--psrc);
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if (fLeadingZeroes)
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{
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if (c == 0)
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continue;
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if (c & 0x80)
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*p++ = 0;
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fLeadingZeroes = false;
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}
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*p++ = c;
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}
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unsigned int nSize = (unsigned int) (p - (pch + 4));
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pch[0] = (nSize >> 24) & 0xff;
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pch[1] = (nSize >> 16) & 0xff;
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pch[2] = (nSize >> 8) & 0xff;
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pch[3] = (nSize >> 0) & 0xff;
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BN_mpi2bn(pch, (int) (p - pch), this);
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}
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uint256 getuint256() const
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{
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unsigned int nSize = BN_bn2mpi(this, NULL);
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if (nSize < 4)
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return 0;
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std::vector<unsigned char> vch(nSize);
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BN_bn2mpi(this, &vch[0]);
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if (vch.size() > 4)
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vch[4] &= 0x7f;
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uint256 n = 0;
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for (unsigned int i = 0, j = (unsigned int) vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
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((unsigned char*)&n)[i] = vch[j];
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return n;
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}
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void setvch(const std::vector<unsigned char>& vch)
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{
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std::vector<unsigned char> vch2(vch.size() + 4);
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unsigned int nSize = (unsigned int) vch.size();
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// BIGNUM's byte stream format expects 4 bytes of
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// big endian size data info at the front
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vch2[0] = (nSize >> 24) & 0xff;
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vch2[1] = (nSize >> 16) & 0xff;
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vch2[2] = (nSize >> 8) & 0xff;
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vch2[3] = (nSize >> 0) & 0xff;
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// swap data to big endian
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reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
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BN_mpi2bn(&vch2[0], (int) vch2.size(), this);
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}
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std::vector<unsigned char> getvch() const
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{
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unsigned int nSize = BN_bn2mpi(this, NULL);
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if (nSize <= 4)
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return std::vector<unsigned char>();
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std::vector<unsigned char> vch(nSize);
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BN_bn2mpi(this, &vch[0]);
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vch.erase(vch.begin(), vch.begin() + 4);
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reverse(vch.begin(), vch.end());
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return vch;
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}
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// The "compact" format is a representation of a whole
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// number N using an unsigned 32bit number similar to a
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// floating point format.
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// The most significant 8 bits are the unsigned exponent of base 256.
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// This exponent can be thought of as "number of bytes of N".
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// The lower 23 bits are the mantissa.
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// Bit number 24 (0x800000) represents the sign of N.
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// N = (-1^sign) * mantissa * 256^(exponent-3)
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//
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// Satoshi's original implementation used BN_bn2mpi() and BN_mpi2bn().
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// MPI uses the most significant bit of the first byte as sign.
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// Thus 0x1234560000 is compact (0x05123456)
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// and 0xc0de000000 is compact (0x0600c0de)
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// (0x05c0de00) would be -0x40de000000
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//
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// Bitcoin only uses this "compact" format for encoding difficulty
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// targets, which are unsigned 256bit quantities. Thus, all the
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// complexities of the sign bit and using base 256 are probably an
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// implementation accident.
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//
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// This implementation directly uses shifts instead of going
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// through an intermediate MPI representation.
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CBigNum& SetCompact(unsigned int nCompact)
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{
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unsigned int nSize = nCompact >> 24;
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bool fNegative =(nCompact & 0x00800000) != 0;
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unsigned int nWord = nCompact & 0x007fffff;
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if (nSize <= 3)
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{
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nWord >>= 8*(3-nSize);
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BN_set_word(this, nWord);
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}
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else
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{
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BN_set_word(this, nWord);
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BN_lshift(this, this, 8*(nSize-3));
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}
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BN_set_negative(this, fNegative);
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return *this;
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}
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unsigned int GetCompact() const
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{
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unsigned int nSize = BN_num_bytes(this);
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unsigned int nCompact = 0;
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if (nSize <= 3)
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nCompact = (unsigned int) BN_get_word(this) << 8*(3-nSize);
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else
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{
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CBigNum bn;
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BN_rshift(&bn, this, 8*(nSize-3));
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nCompact = (unsigned int) BN_get_word(&bn);
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}
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// The 0x00800000 bit denotes the sign.
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// Thus, if it is already set, divide the mantissa by 256 and increase the exponent.
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if (nCompact & 0x00800000)
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{
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nCompact >>= 8;
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nSize++;
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}
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nCompact |= nSize << 24;
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nCompact |= (BN_is_negative(this) ? 0x00800000 : 0);
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return nCompact;
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}
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void SetHex(const std::string& str)
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{
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// skip 0x
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const char* psz = str.c_str();
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while (isspace(*psz))
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psz++;
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bool fNegative = false;
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if (*psz == '-')
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{
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fNegative = true;
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psz++;
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}
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if (psz[0] == '0' && tolower(psz[1]) == 'x')
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psz += 2;
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while (isspace(*psz))
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psz++;
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// hex string to bignum
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static const signed char phexdigit[256] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8,9,0,0,0,0,0,0, 0,0xa,0xb,0xc,0xd,0xe,0xf,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0xa,0xb,0xc,0xd,0xe,0xf,0,0,0,0,0,0,0,0,0 };
|
||
|
|
*this = 0;
|
||
|
|
while (isxdigit(*psz))
|
||
|
|
{
|
||
|
|
*this <<= 4;
|
||
|
|
int n = phexdigit[(unsigned char)*psz++];
|
||
|
|
*this += n;
|
||
|
|
}
|
||
|
|
if (fNegative)
|
||
|
|
*this = 0 - *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
std::string ToString(int nBase=10) const
|
||
|
|
{
|
||
|
|
CAutoBN_CTX pctx;
|
||
|
|
CBigNum bnBase = nBase;
|
||
|
|
CBigNum bn0 = 0;
|
||
|
|
std::string str;
|
||
|
|
CBigNum bn = *this;
|
||
|
|
BN_set_negative(&bn, false);
|
||
|
|
CBigNum dv;
|
||
|
|
CBigNum rem;
|
||
|
|
if (BN_cmp(&bn, &bn0) == 0)
|
||
|
|
return "0";
|
||
|
|
while (BN_cmp(&bn, &bn0) > 0)
|
||
|
|
{
|
||
|
|
if (!BN_div(&dv, &rem, &bn, &bnBase, pctx))
|
||
|
|
throw bignum_error("CBigNum::ToString() : BN_div failed");
|
||
|
|
bn = dv;
|
||
|
|
unsigned int c = rem.getulong();
|
||
|
|
str += "0123456789abcdef"[c];
|
||
|
|
}
|
||
|
|
if (BN_is_negative(this))
|
||
|
|
str += "-";
|
||
|
|
reverse(str.begin(), str.end());
|
||
|
|
return str;
|
||
|
|
}
|
||
|
|
|
||
|
|
std::string GetHex() const
|
||
|
|
{
|
||
|
|
return ToString(16);
|
||
|
|
}
|
||
|
|
|
||
|
|
unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
|
||
|
|
{
|
||
|
|
return ::GetSerializeSize(getvch(), nType, nVersion);
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename Stream>
|
||
|
|
void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
|
||
|
|
{
|
||
|
|
::Serialize(s, getvch(), nType, nVersion);
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename Stream>
|
||
|
|
void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
|
||
|
|
{
|
||
|
|
std::vector<unsigned char> vch;
|
||
|
|
::Unserialize(s, vch, nType, nVersion);
|
||
|
|
setvch(vch);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
bool operator!() const
|
||
|
|
{
|
||
|
|
return BN_is_zero(this);
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator+=(const CBigNum& b)
|
||
|
|
{
|
||
|
|
if (!BN_add(this, this, &b))
|
||
|
|
throw bignum_error("CBigNum::operator+= : BN_add failed");
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator-=(const CBigNum& b)
|
||
|
|
{
|
||
|
|
*this = *this - b;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator*=(const CBigNum& b)
|
||
|
|
{
|
||
|
|
CAutoBN_CTX pctx;
|
||
|
|
if (!BN_mul(this, this, &b, pctx))
|
||
|
|
throw bignum_error("CBigNum::operator*= : BN_mul failed");
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator/=(const CBigNum& b)
|
||
|
|
{
|
||
|
|
*this = *this / b;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator%=(const CBigNum& b)
|
||
|
|
{
|
||
|
|
*this = *this % b;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator<<=(unsigned int shift)
|
||
|
|
{
|
||
|
|
if (!BN_lshift(this, this, shift))
|
||
|
|
throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator>>=(unsigned int shift)
|
||
|
|
{
|
||
|
|
// Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
|
||
|
|
// if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
|
||
|
|
CBigNum a = 1;
|
||
|
|
a <<= shift;
|
||
|
|
if (BN_cmp(&a, this) > 0)
|
||
|
|
{
|
||
|
|
*this = 0;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (!BN_rshift(this, this, shift))
|
||
|
|
throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
CBigNum& operator++()
|
||
|
|
{
|
||
|
|
// prefix operator
|
||
|
|
if (!BN_add(this, this, BN_value_one()))
|
||
|
|
throw bignum_error("CBigNum::operator++ : BN_add failed");
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
const CBigNum operator++(int)
|
||
|
|
{
|
||
|
|
// postfix operator
|
||
|
|
const CBigNum ret = *this;
|
||
|
|
++(*this);
|
||
|
|
return ret;
|
||
|
|
}
|
||
|
|
|
||
|
|
CBigNum& operator--()
|
||
|
|
{
|
||
|
|
// prefix operator
|
||
|
|
CBigNum r;
|
||
|
|
if (!BN_sub(&r, this, BN_value_one()))
|
||
|
|
throw bignum_error("CBigNum::operator-- : BN_sub failed");
|
||
|
|
*this = r;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
const CBigNum operator--(int)
|
||
|
|
{
|
||
|
|
// postfix operator
|
||
|
|
const CBigNum ret = *this;
|
||
|
|
--(*this);
|
||
|
|
return ret;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
|
||
|
|
friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b);
|
||
|
|
friend inline const CBigNum operator%(const CBigNum& a, const CBigNum& b);
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
|
||
|
|
{
|
||
|
|
CBigNum r;
|
||
|
|
if (!BN_add(&r, &a, &b))
|
||
|
|
throw bignum_error("CBigNum::operator+ : BN_add failed");
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
|
||
|
|
{
|
||
|
|
CBigNum r;
|
||
|
|
if (!BN_sub(&r, &a, &b))
|
||
|
|
throw bignum_error("CBigNum::operator- : BN_sub failed");
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const CBigNum operator-(const CBigNum& a)
|
||
|
|
{
|
||
|
|
CBigNum r(a);
|
||
|
|
BN_set_negative(&r, !BN_is_negative(&r));
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
|
||
|
|
{
|
||
|
|
CAutoBN_CTX pctx;
|
||
|
|
CBigNum r;
|
||
|
|
if (!BN_mul(&r, &a, &b, pctx))
|
||
|
|
throw bignum_error("CBigNum::operator* : BN_mul failed");
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
|
||
|
|
{
|
||
|
|
CAutoBN_CTX pctx;
|
||
|
|
CBigNum r;
|
||
|
|
if (!BN_div(&r, NULL, &a, &b, pctx))
|
||
|
|
throw bignum_error("CBigNum::operator/ : BN_div failed");
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
|
||
|
|
{
|
||
|
|
CAutoBN_CTX pctx;
|
||
|
|
CBigNum r;
|
||
|
|
if (!BN_mod(&r, &a, &b, pctx))
|
||
|
|
throw bignum_error("CBigNum::operator% : BN_div failed");
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
|
||
|
|
{
|
||
|
|
CBigNum r;
|
||
|
|
if (!BN_lshift(&r, &a, shift))
|
||
|
|
throw bignum_error("CBigNum:operator<< : BN_lshift failed");
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
|
||
|
|
{
|
||
|
|
CBigNum r = a;
|
||
|
|
r >>= shift;
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) == 0); }
|
||
|
|
inline bool operator!=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) != 0); }
|
||
|
|
inline bool operator<=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) <= 0); }
|
||
|
|
inline bool operator>=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) >= 0); }
|
||
|
|
inline bool operator<(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) < 0); }
|
||
|
|
inline bool operator>(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) > 0); }
|
||
|
|
|
||
|
|
#endif
|