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/**************************************************************************** * Core Library Version 1.7, August 2004 * Copyright (c) 1995-2004 Exact Computation Project * All rights reserved. * * This file is part of CGAL (www.cgal.org); * * File: BigFloatRep.h * Synopsis: * Internal Representation BigFloat. * * Written by * Chee Yap * Chen Li * Zilin Du * * WWW URL: https://cs.nyu.edu/exact/ * Email: exact@cs.nyu.edu * * $URL: https://github.com/CGAL/cgal/blob/v6.1/CGAL_Core/include/CGAL/CORE/BigFloatRep.h $ * $Id: include/CGAL/CORE/BigFloatRep.h b26b07a1242 $ * SPDX-License-Identifier: LGPL-3.0-or-later ***************************************************************************/ #ifndef _CORE_BIGFLOATREP_H_ #define _CORE_BIGFLOATREP_H_ #include #include #include #include namespace CORE { // forward reference class BigFloat; // class BigFloatRep (internal representation for BigFloat) class CGAL_CORE_EXPORT BigFloatRep : public RCRepImpl { public: static long chunkCeil(long bits); //inline static long chunkFloor(long bits); //inline static long bits(long chunks); //inline static BigInt chunkShift(const BigInt& x, long s); //inline static double lg10(BigInt x); //inline static long floorlg10(BigInt x); //inline /// exp2(e) returns 2^e : called by BigFloat::exp2(e) /** e can be negative */ static BigFloatRep* exp2(int e); struct DecimalOutput; friend class BigFloat; BigInt m; unsigned long err; long exp; public: // constructors BigFloatRep(int=0); //inline BigFloatRep(unsigned int); //inline BigFloatRep(short); //inline BigFloatRep(float); //inline BigFloatRep(long); //inline BigFloatRep(double); //inline BigFloatRep(const BigInt& I, unsigned long u, long l); //inline BigFloatRep(const BigInt& I, long l); //inline BigFloatRep(const BigInt& I); //inline BigFloatRep(const char *); //inline BigRat BigRatize() const; //inline // the destructor ~BigFloatRep(); //inline CORE_NEW(BigFloatRep) // allocate the memory pool, unless CORE_DELETE(BigFloatRep) // memory pool feature is disabled. // approximation void trunc(const BigInt&, const extLong&, const extLong&); void truncM(const BigFloatRep&, const extLong&, const extLong&); void approx(const BigFloatRep&, const extLong&, const extLong&); void div(const BigInt&, const BigInt&, const extLong&, const extLong&); void approx(const BigRat&, const extLong&, const extLong&); //inline // error-normalization void eliminateTrailingZeroes(); //inline void normal(); void bigNormal(BigInt&); // arithmetic public: void add(const BigFloatRep&, const BigFloatRep&); void sub(const BigFloatRep&, const BigFloatRep&); void mul(const BigFloatRep&, const BigFloatRep&); void div(const BigFloatRep&, const BigFloatRep&, const extLong&); void div2(const BigFloatRep&); ///< exact division by 2 /// Converts a pair of BigFloatReps into one with error bounds void centerize(const BigFloatRep&, const BigFloatRep&); private: // squareroot // arguments: r = value whose square root we want // a = absolute precision of the desired result // init = initial approx. to the square root (for Newton) void sqrt(const BigInt& r, const extLong& a); /// sqrt(r,a,rr) -- compute sqrt(r) to absolute precision a, /// starting from initial approximation of rr. void sqrt(const BigInt& r, const extLong& a, const BigFloat& init); void sqrt(const BigFloatRep& r, const extLong& a); /// sqrt(r,a,rr) -- compute sqrt(r) to absolute precision a, /// starting from initial approximation of rr. void sqrt(const BigFloatRep& r, const extLong& a, const BigFloat& init); // comparison int compareMExp(const BigFloatRep&) const; // builtin functions extLong lMSB() const; //inline extLong uMSB() const; //inline extLong MSB() const; //inline extLong flrLgErr() const; //inline extLong clLgErr() const; //inline bool isZeroIn() const; //inline int signM() const; //inline // cast functions double toDouble() const; long toLong() const; BigInt toBigInt() const; // conversion // toString() Joaquin Grech 31/5/2003 std::string toString(long prec=get_static_defBigFloatOutputDigits(), bool sci=false) const; std::string round(std::string inRep, long& L10, unsigned int width) const; DecimalOutput toDecimal(unsigned int width=get_static_defBigFloatOutputDigits(), bool Scientific=false) const; void fromString(const char *p, extLong prec = getBigFloatInputDigits()); void dump() const; //inline long adjustE(long E, BigInt M, long e) const; public: // stream operators std::ostream& operator <<(std::ostream&) const; //inline std::istream& operator >>(std::istream&); };//class BigFloatRep //////////////////////////////////////////////////////////// // Implementations //////////////////////////////////////////////////////////// struct BigFloatRep::DecimalOutput { std::string rep; // decimal output string int sign; // 0, +1 or -1 bool isScientific; // false=positional notation int noSignificant; // number of significant digits // -1 means this information is not explicitly // given, and must be determined from rep, etc. bool isExact; // int errorCode; // 0 = no error // 1 = sign of number is unknown (e.g., mantissa // is smaller than error) DecimalOutput() : rep(""), sign(1), isScientific(false), noSignificant(0), isExact(false), errorCode(0) {} };//DecimalOutput // constants used by BigFloatRep // NOTES: CHUNK_BIT is the number of bits in each Chunk // Since LONG_BIT = 32 or 64, then CHUNK_BIT = 14 or 30. // We have: 0 <= err < 4 * 2^{CHUNK_BIT} const long CHUNK_BIT = (long)(LONG_BIT / 2 - 2); // chunks const long HALF_CHUNK_BIT = (CHUNK_BIT + 1) / 2; const long DBL_MAX_CHUNK = (DBL_MAX_EXP - 1) / CHUNK_BIT + 1; const double lgTenM = 3.321928094887362; inline long BigFloatRep::chunkCeil(long bits) { if (bits > 0) return (bits - 1) / CHUNK_BIT + 1; else return - (- bits) / CHUNK_BIT; }//chunkCeil inline long BigFloatRep::chunkFloor(long bits) { if (bits >= 0) return bits / CHUNK_BIT; else return - (- bits - 1) / CHUNK_BIT - 1; }//chunkFloor // bits(c) returns the number of bits in c chunks: inline long BigFloatRep::bits(long chunks) { return CHUNK_BIT * chunks; } inline BigInt BigFloatRep::chunkShift(const BigInt& x, long s) { if (!s || sign(x) == 0) return x; else if (s > 0) // shift left if (sign(x) > 0) return x << static_cast(bits(s)); else // x < 0 return - ((-x) << static_cast(bits(s))); else // shift right if (sign(x) > 0) return x >> static_cast(bits(-s)); else // x < 0 return - ((-x) >> static_cast(bits(-s))); }//chunkShift inline BigFloatRep* BigFloatRep::exp2(int e) { long ee; // this is going to be the exponent if (e >= 0) ee = e/CHUNK_BIT; else ee = - ((-e + CHUNK_BIT -1)/CHUNK_BIT); int rem = e - (ee * CHUNK_BIT); // Assert: 0 <= rem < CHUNK_BIT return new BigFloatRep((1<m; exp = bfr->exp; } */ inline BigFloatRep::BigFloatRep(const BigInt& I, unsigned long er, long ex) : m(I), err(er), exp(ex) {} inline BigFloatRep::BigFloatRep(const BigInt& I) : m(I), err(0), exp(0) {} //Constructs the BigFloat representing I*2^{ex}. //If ex >=0 then it is clear how to do it. //Otherwise, let |ex| = CHUNK_BIT * q + r. Then //I*2^{ex} = I*2^{CHUNK_BIT -r} 2^{-CHUNK_BIT * (q+1)} inline BigFloatRep::BigFloatRep(const BigInt& I, long ex) { err=0; exp = chunkFloor(ex); if(ex >= 0) m = I<<(ex - bits(exp)); else{//ex < 0 exp = chunkFloor(abs(ex)); m = I << (CHUNK_BIT - (-ex - bits(exp))); exp = -1*(1 + exp); } } inline BigFloatRep::BigFloatRep(const char *str) : m(0), err(0), exp(0) { fromString(str); } inline BigRat BigFloatRep::BigRatize() const { if (exp >= 0) return BigRat(chunkShift(m, exp), 1); else return BigRat(m, chunkShift(1, - exp)); } // the destructor inline BigFloatRep::~BigFloatRep() {} inline void BigFloatRep::approx(const BigRat& R, const extLong& r, const extLong& a) { div(numerator(R), denominator(R), r, a); } // eliminate trailing zeroes inline void BigFloatRep::eliminateTrailingZeroes() { // eliminate trailing 0's -- IP 10/9/98 /*if (err == 0 && m != 0) { while ((m & ((1 << CHUNK_BIT) - 1)) == 0) { m >>= CHUNK_BIT; exp++; } }*/ // new code, much faster, Zilin Du (Nov, 2003) if (err == 0 && sign(m) != 0) { int r = getBinExpo(m) / CHUNK_BIT; m >>= (r * CHUNK_BIT); exp += r; } } // builtin functions inline extLong BigFloatRep::lMSB() const { if (!isZeroIn()) return extLong(floorLg(BigInt(abs(m) - err))) + bits(exp); else return extLong(CORE_negInfty); } /// uMSB() returns an upper bound on log_2(abs(*this)). /** Returns -1 if (*this)=0. * Not well-defined if zero is in the interval. */ inline extLong BigFloatRep::uMSB() const { return extLong(floorLg(BigInt(abs(m) + err))) + bits(exp); } inline extLong BigFloatRep::MSB() const { // Note : MSB is undefined if it's not exact. if (sign(m)) // sign(m) is non-zero return extLong(floorLg(m)) + bits(exp); else return extLong(CORE_negInfty); } inline extLong BigFloatRep::flrLgErr() const { if (err) return extLong(flrLg(err)) + bits(exp); else return extLong(CORE_negInfty); } inline extLong BigFloatRep::clLgErr() const { if (err) return extLong(clLg(err)) + bits(exp); else return extLong(CORE_negInfty); } // isZero() = true iff zero is inside the interval of BigFloat: inline bool BigFloatRep::isZeroIn() const { if (err == 0){ return (m == 0); //Nov 6, 2002: bug fix! } long lm = bitLength(m); if (lm > CHUNK_BIT+2) { return false; // since err < 4 * 2^{CHUNK_BIT} } else { return (abs(m) <= BigInt(err)); } } inline int BigFloatRep::signM() const { return sign(m); } inline double BigFloatRep::lg10(BigInt x) { if (x == 0) return 0; BigInt t(abs(x)); long l = -1; double d = 0; while (t > 0) { l++; d /= 10; d += ulongValue(t%10); t /= 10; } return std::log10(d) + l; } // this is a simpler form of lg10() inline long BigFloatRep::floorlg10(BigInt x) { if (x == 0) return 0; BigInt t(abs(x)); long l = -1; while (t > 0) { l++; t /= 10; } return l; } inline std::ostream& BigFloatRep::operator<<(std::ostream& o) const { bool sci = (o.flags() & std::ios::scientific) > 0; BigFloatRep::DecimalOutput r = toDecimal(o.precision(), sci); if (r.sign == -1) o << "-"; o << r.rep; return o; } /* Returns a std::string with precision and format specified Works as cout << with the exception that if the output contains any error it returns a nullptr Joaquin Grech 31/5/03 */ inline std::string BigFloatRep::toString(long prec, bool sci) const { BigFloatRep::DecimalOutput r = toDecimal(prec, sci); if (r.errorCode == 0) { if (r.sign < 0) return std::string("-")+r.rep; else return r.rep; } return std::string(); } inline void BigFloatRep::dump() const { std::cout << "---- BFRep: " << this << " ----" << std::endl; std::cout << " BF value: "; this->operator<<(std::cout); std::cout << std::endl; std::cout << " m = " << m << std::endl; std::cout << " err = " << err << std::endl; std::cout << " exp = " << exp << std::endl; std::cout << " -- End of BFRep " << this << " -- " << std::endl; } } //namespace CORE #endif // _CORE_BIGFLOATREP_H_