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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: Real.cpp * Synopsis: The Real class is a superclass for all the number * systems in the Core Library (int, long, float, double, * BigInt, BigRat, BigFloat, etc) * * Written by * Koji Ouchi * Chee Yap * Chen Li * Zilin Du * Sylvain Pion * * 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/Real_impl.h $ * $Id: include/CGAL/CORE/Real_impl.h b26b07a1242 $ * SPDX-License-Identifier: LGPL-3.0-or-later ***************************************************************************/ #ifdef CGAL_HEADER_ONLY #define CGAL_INLINE_FUNCTION inline #else #define CGAL_INLINE_FUNCTION #endif #include #include #include #include #include #ifdef CGAL_HEADER_ONLY #include // for FiveTo #endif namespace CORE { CGAL_INLINE_FUNCTION const Real& Real::getZero() { init_CORE(); CGAL_STATIC_THREAD_LOCAL_VARIABLE(Real, Zero, 0); return Zero; } CGAL_INLINE_FUNCTION BigInt floor(const Real& r, Real &sub) { BigInt f = r.approx(CORE_INFTY, 2).BigIntValue(); sub = r-f; // Adjustment if (sub<0) ++sub, --f; if (sub>=1) --sub, ++f; CGAL_assertion(sub >=0 && sub<1); return f; } // pow(r,n) and power(r, n) are the same function // CGAL_INLINE_FUNCTION Real pow(const Real& r, unsigned long n) { if (n == 0) return Real(1); else if (n == 1) return r; else { Real x = r; while ((n % 2) == 0) { // n is even x *= x; n >>= 1; } Real u = x; while (true) { n >>= 1; if (n == 0) return u; x *= x; if ((n % 2) == 1) // n is odd u *= x; } //return u; // unreachable } }//pow extern BigInt FiveTo(unsigned long exp); // Construct Real from String // Note: // -- Zilin Du: 06/03/2003 // -- Original it is the code for Real's constructor for "const char*". // I change it to a function so that two constructors can share the code. // now it is private and no default value. // // --Default value of the argument "prec" is get_static_defInputDigits() // --If prec is CORE_posInfty, then the input is // read in exactly. Otherwise, we convert to a RealBigFloat // with absolute error at most 10^{-prec} // Constructor Real( char *str, extLong& prec) // is very similar to // BigFloatRep::fromString( char *str, extLong& prec); // Differences: // In BigFloat(str, prec), the value of prec cannot be infinity, and // it defaults to defBigFloatInputDigits; // In Real(str, prec), the value of prec is allowed to be infinity, and // it defaults to defInputDigits. // // Why do we have the two versions? It allows us to use the BigFloat class // directly, without relying on Real class. CGAL_INLINE_FUNCTION void Real::constructFromString(const char *str, const extLong& prec ) // NOTE: prec defaults to get_static_defInputDigits() (see Real.h) { // 8/8/01, Chee and Zilin: add a new rational string format: // this format is indicated by the presence of a slash "/" // Moreover, the value of prec is ignored (basically // assumed to be infinity). if (std::strchr(str, '/') != nullptr) { // this is a rational number rep = new RealBigRat(BigRat(str)); return; } const char *e = std::strchr(str, 'e'); int dot = 0; long e10 = 0; if (e != nullptr) e10 = std::atol(e+1); // e10 is decimal precision of the input string // i.e., input is A/10^{e10}. else { e = str + std::strlen(str); #ifdef CORE_DEBUG CGAL_assertion(*e == '\0'); #endif } const char *p = str; if (*p == '-' || *p == '+') p++; BigInt m(0); for (; p < e; p++) { if (*p == '.') { dot = 1; continue; } m = m * 10 + (*p - '0'); if (dot) e10--; } long t = (e10 < 0) ? -e10 : e10; BigInt one(1); BigInt ten = FiveTo(t) * (one << static_cast(t)); if (*str == '-') m = -m; if (e10 >= 0) { // convert exactly from integer numbers m *= ten; rep = new RealBigInt(m); } else { // e10 < 0, fractional numbers // HERE IS WHERE WE USE THE SYSTEM CONSTANT // get_static_defInputDigits() // Note: get_static_defInputDigits() should be at least log_2(10). // We default get_static_defInputDigits() to 4. //std::cout << "(m,ten)=" << m << "," << ten << std::endl; BigRat r(m, ten); if (prec.isInfty()) { // convert exactly! to a big rational rep = new RealBigRat(r); } else { // convert approximately, to a BigFloat within the // specified precision: // BigFloat bf(r, CORE_posInfty, prec * lgTenM) ; BigFloat bf(r, CORE_posInfty, prec * 4) ; rep = new RealBigFloat(bf); } } }// Real(str, prec) // The operator >>(i,x) calls the constructor Real(char*) CGAL_INLINE_FUNCTION std::istream& operator >>(std::istream& i, Real& x) { int size = 20; std::string str; str.reserve(size); char c; int d = 0, e = 0, s = 0; // int done = 0; // Chen Li: fixed a bug, the original statement is // for (i.get(c); c == ' '; i.get(c)); // use isspace instead of testing c == ' ', since it must also // skip tab, catridge/return, etc. // Change to: // int status; do { i.get(c); } while (!i.eof() && isspace(c)); /* loop if met end-of-file, or char read in is white-space. */ // Chen Li, // original "if (c == EOF) ..." is unsafe since c is of char type and // EOF is of int type with a negative value -1 if (i.eof()) { i.clear(std::ios::eofbit | std::ios::failbit); return i; } // the current content in "c" should be the first non-whitespace char if (c == '-' || c == '+') { str += c; i.get(c); } for (; isdigit(c) || (!d && c=='.') || (!e && c=='e') || (!s && (c=='-' || c=='+')); i.get(c)) { if (!i) break; if (!e && (c == '-' || c == '+')) break; // Chen Li: put one more rule to prohibite input like // xxxx.xxxe+xxx.xxx: if (e && (c == '.')) break; str += c; if (c == '.') d = 1; // Chen Li: fix a bug -- the sign of exponent can not happen before // the character "e" appears! It must follow the "e" actually. // if (e || c == '-' || c == '+') s = 1; if (e) s = 1; if (c == 'e') e = 1; } if (!i && !i.eof()) { return i; } i.putback(c); i.clear(); // old: x = Real(str, i.precision()); // use precision of input stream. x = Real(str.c_str()); // default precision = get_static_defInputDigits() return i; }//operator >> (std::istream&, Real&) } //namespace CORE #include