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// Copyright (c) 2023 GeometryFactory (France), INRIA Saclay - Ile de France (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Number_types/include/CGAL/cpp_float.h $ // $Id: include/CGAL/cpp_float.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Andreas Fabri, Marc Glisse #ifndef CGAL_CPP_FLOAT_H #define CGAL_CPP_FLOAT_H //#define CGAL_DEBUG_CPPF #include #include #include #include namespace CGAL { namespace internal { // Only used with an argument known not to be 0. inline int low_bit (boost::uint64_t x) { #if defined(_MSC_VER) unsigned long ret; _BitScanForward64(&ret, x); return (int)ret; #elif defined(__xlC__) return __cnttz8 (x); #else // Assume long long is 64 bits return __builtin_ctzll (x); #endif } inline int high_bit (boost::uint64_t x) { #if defined(_MSC_VER) unsigned long ret; _BitScanReverse64(&ret, x); return (int)ret; #elif defined(__xlC__) // Macro supposedly not defined on z/OS. return 63 - __cntlz8 (x); #else return 63 - __builtin_clzll (x); #endif } } // namespace internal #if 0 // needs C++20 template void fmt(const T& t) { std::cout << std::format("{:b}", t) << std::endl; } #endif // It would have made sense to make this // boost::multiprecision::number, but we keep that // for later when we contribute to boost::mp class cpp_float { #ifdef CGAL_DEBUG_CPPF boost::multiprecision::cpp_rational rat; #endif typedef boost::multiprecision::number > Mantissa; Mantissa man; int exp; /* The number man (an integer) * 2 ^ exp */ public: cpp_float() : #ifdef CGAL_DEBUG_CPPF rat(), #endif man(), exp() {} cpp_float(short i) : #ifdef CGAL_DEBUG_CPPF rat(i), #endif man(i),exp(0) {} cpp_float(int i) : #ifdef CGAL_DEBUG_CPPF rat(i), #endif man(i),exp(0) {} cpp_float(long i) : #ifdef CGAL_DEBUG_CPPF rat(i), #endif man(i),exp(0) {} #ifdef CGAL_DEBUG_CPPF cpp_float(const Mantissa& man, int exp, const boost::multiprecision::cpp_rational& rat) : rat(rat), man(man),exp(exp) {} #else cpp_float(const Mantissa& man, int exp) : man(man), exp(exp) { CGAL_HISTOGRAM_PROFILER("size (man/exp)", static_cast(man.backend().size())); } #ifndef CGAL_DEBUG_CPPF template cpp_float(const Expression& man, int exp) :man(man), exp(exp) { CGAL_HISTOGRAM_PROFILER("size (expression/exp)", static_cast(this->man.backend().size())); } #endif #endif cpp_float(double d) #ifdef CGAL_DEBUG_CPPF : rat(d) #endif { // std::cout << "\ndouble = " << d << std::endl; using boost::uint64_t; union { #ifdef CGAL_LITTLE_ENDIAN struct { uint64_t man:52; uint64_t exp:11; uint64_t sig:1; } s; #else /* CGAL_BIG_ENDIAN */ //WARNING: untested! struct { uint64_t sig:1; uint64_t exp:11; uint64_t man:52; } s; #endif double d; } u; u.d = d; uint64_t m; uint64_t dexp = u.s.exp; CGAL_assertion_msg(dexp != 2047, "Creating an cpp_float from infinity or NaN."); if (dexp == 0) { if (d == 0) { exp=0; return; } else { // denormal number m = u.s.man; ++dexp; } } else { m = (1LL << 52) | u.s.man; } int idexp = (int)dexp; idexp -= 1023; // std::cout << "m = " << m << std::endl; // std::cout << "idexp = " << idexp << std::endl; int shifted = internal::low_bit(m); m >>= shifted; int nbits = internal::high_bit(m); // std::cout << "nbits = " << nbits << std::endl; exp = idexp - nbits; man = m; if(u.s.sig){ man.backend().negate(); } #ifdef CGAL_DEBUG_CPPF CGAL_assertion(rat.sign() == man.sign()); #endif // std::cout << "m = " << m << " * 2^" << exp << std::endl; // fmt(m); CGAL_HISTOGRAM_PROFILER("size when constructed from double", static_cast(man.backend().size())); } friend std::ostream& operator<<(std::ostream& os, const cpp_float& m) { return os << m.to_double(); #if 0 // dehug output return os << m.man << " * 2 ^ " << m.exp << " ( " << m.to_double() << ") " #ifdef CGAL_DEBUG_CPPF << " " << m.rat #endif ; #endif } friend std::istream& operator>>(std::istream& is, cpp_float& m) { double d; is >> d; m = cpp_float(d); return is; } friend cpp_float operator-(cpp_float const&x) { #ifdef CGAL_DEBUG_CPPF return cpp_float(-x.man,x.exp, -x.rat); #else return cpp_float(-x.man,x.exp); #endif } cpp_float& operator*=(const cpp_float& other) { #ifdef CGAL_DEBUG_CPPF rat *= other.rat; #endif man *= other.man; exp += other.exp; return *this; } friend cpp_float operator*(const cpp_float& a, const cpp_float&b){ #ifdef CGAL_DEBUG_CPPF return cpp_float(a.man*b.man, a.exp+b.exp, a.rat * b.rat); #else return cpp_float(a.man*b.man, a.exp+b.exp); #endif } // Marc Glisse commented on github: // We can sometimes end up with a mantissa that has quite a few zeros at the end, // but the cases where the mantissa is too long by more than 1 limb should be negligible, // and normalizing so the mantissa is always odd would have a cost. cpp_float operator+=(const cpp_float& other) { #ifdef CGAL_DEBUG_CPPF rat += other.rat; #endif int shift = exp - other.exp; if(shift > 0){ man = (man << shift) + other.man; exp = other.exp; }else if(shift < 0){ man = man + (other.man << -shift); }else{ man += other.man; } return *this; } #ifdef CGAL_DEBUG_CPPF friend cpp_float operator+(const cpp_float& a, const cpp_float&b){ int shift = a.exp - b.exp; if(shift > 0){ return cpp_float((a.man << shift) + b.man, b.exp, a.rat+b.rat); }else if(shift < 0){ return cpp_float(a.man + (b.man << -shift), a.exp, a.rat+b.rat); } return cpp_float(a.man + b.man, a.exp, a.rat+b.rat); } #else friend cpp_float operator+(const cpp_float& a, const cpp_float&b){ int shift = a.exp - b.exp; CGAL_HISTOGRAM_PROFILER("shift+", CGAL::abs(shift)); if(shift > 0){ return cpp_float((a.man << shift) + b.man, b.exp); }else if(shift < 0){ return cpp_float(a.man + (b.man << -shift), a.exp); } return cpp_float(a.man + b.man, a.exp); } #endif cpp_float operator-=(const cpp_float& other) { #ifdef CGAL_DEBUG_CPPF rat -= other.rat; #endif int shift = exp - other.exp; if(shift > 0){ man <<= shift; man -= other.man; exp = other.exp; }else if(shift < 0){ man -= (other.man << -shift); }else{ man -= other.man; } return *this; } #ifdef CGAL_DEBUG_CPPF friend cpp_float operator-(const cpp_float& a, const cpp_float&b){ int shift = a.exp - b.exp; if(shift > 0){ return cpp_float((a.man << shift) - b.man, b.exp, a.rat-b.rat); }else if(shift < 0){ return cpp_float(a.man - (b.man << -shift), a.exp, a.rat-b.rat); } return cpp_float(a.man - b.man, a.exp, a.rat-b.rat); } #else friend cpp_float operator-(const cpp_float& a, const cpp_float&b){ int shift = a.exp - b.exp; CGAL_HISTOGRAM_PROFILER("shift-", CGAL::abs(shift)); if(shift > 0){ return cpp_float((a.man << shift) - b.man, b.exp); }else if(shift < 0){ return cpp_float(a.man - (b.man << -shift), a.exp); } return cpp_float(a.man - b.man, a.exp); } #endif bool is_positive() const { return CGAL::is_positive(man); } bool is_negative() const { return CGAL::is_negative(man); } // Would it make sense to compare the sign of the exponent? // to distinguish the interval between ]-1,1[ from the rest. friend bool operator<(const cpp_float& a, const cpp_float& b) { if(((! a.is_positive()) && b.is_positive()) || (a.is_negative() && b.is_zero()))return true; if(((! b.is_positive()) && a.is_positive()) || (b.is_negative() && a.is_zero()))return false; #ifdef CGAL_DEBUG_CPPF bool qres = a.rat < b.rat; #endif cpp_float d = b-a; #ifdef CGAL_DEBUG_CPPF CGAL_assertion(qres == d.is_positive()); #endif return d.is_positive(); } friend bool operator>(cpp_float const&a, cpp_float const&b){ return b=(cpp_float const&a, cpp_float const&b){ return !(ab); } friend bool operator==(cpp_float const&a, cpp_float const&b){ #ifdef CGAL_DEBUG_CPPF bool qres = a.rat == b.rat; #endif int shift = a.exp - b.exp; CGAL_HISTOGRAM_PROFILER("shift==", CGAL::abs(shift)); if(shift > 0){ Mantissa ac = a.man << shift; #ifdef CGAL_DEBUG_CPPF CGAL_assertion( qres == (ac == b.man)); #endif return ac == b.man; }else if(shift < 0){ Mantissa bc = b.man << -shift; #ifdef CGAL_DEBUG_CPPF CGAL_assertion(qres == (a.man == bc)); #endif return a.man == bc; } #ifdef CGAL_DEBUG_CPPF CGAL_assertion(qres == (a.man == b.man)); #endif return a.man==b.man; } Comparison_result compare(const cpp_float& other) const { if(*this < other) return SMALLER; if(*this > other) return LARGER; return EQUAL; } friend bool operator!=(cpp_float const&a, cpp_float const&b){ return !(a==b); } double to_double() const { if(exp == 0){ return CGAL::to_double(man); } if(exp > 0){ Mantissa as(man); as <<= exp; return CGAL::to_double(as); } Mantissa pow(1); pow <<= -exp; boost::multiprecision::cpp_rational r(man, pow); return CGAL::to_double(r); } std::pair to_interval() const { if(exp == 0){ return CGAL::to_interval(man); } if(exp > 0){ Mantissa as = man << exp; return CGAL::to_interval(as); } Mantissa pow(1); pow <<= -exp; boost::multiprecision::cpp_rational r(man, pow); return CGAL::to_interval(r); } bool is_zero () const { return CGAL::is_zero(man); } bool is_one () const { if(! is_positive()) return false; int msb = static_cast(boost::multiprecision::msb(man)); if (msb != -exp) return false; int lsb = static_cast(boost::multiprecision::lsb(man)); return (msb == lsb); } CGAL::Sign sign () const { return CGAL::sign(man); } std::size_t size() const { return man.backend().size(); } }; template <> struct Algebraic_structure_traits< cpp_float > : public Algebraic_structure_traits_base< cpp_float, Integral_domain_without_division_tag > { typedef Tag_true Is_exact; typedef Tag_false Is_numerical_sensitive; struct Is_zero : public CGAL::cpp98::unary_function< Type, bool > { bool operator()( const Type& x ) const { return x.is_zero(); } }; struct Is_one : public CGAL::cpp98::unary_function< Type, bool > { bool operator()( const Type& x ) const { return x.is_one(); } }; struct Gcd : public CGAL::cpp98::binary_function< Type, Type, Type > { Type operator()( const Type& /* x */, const Type& /* y */ ) const { CGAL_assertion(false); return Type(); // cpp_float_gcd(x, y); } }; struct Square : public CGAL::cpp98::unary_function< Type, Type > { Type operator()( const Type& x ) const { return x*x ; // cpp_float_square(x); } }; struct Integral_division : public CGAL::cpp98::binary_function< Type, Type, Type > { Type operator()( const Type& /* x */, const Type& /* y */ ) const { CGAL_assertion(false); return Type(); // x / y; } }; struct Sqrt : public CGAL::cpp98::unary_function< Type, Type > { Type operator()( const Type& /* x */) const { CGAL_assertion(false); return Type(); // cpp_float_sqrt(x); } }; struct Is_square : public CGAL::cpp98::binary_function< Type, Type&, bool > { bool operator()( const Type& /* x */, Type& /* y */ ) const { // TODO: avoid doing 2 calls. CGAL_assertion(false); return true; } bool operator()( const Type& /* x */) const { CGAL_assertion(false); return true; } }; }; template <> struct Real_embeddable_traits< cpp_float > : public INTERN_RET::Real_embeddable_traits_base< cpp_float , CGAL::Tag_true > { struct Sgn : public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > { ::CGAL::Sign operator()( const Type& x ) const { return x.sign(); } }; struct To_double : public CGAL::cpp98::unary_function< Type, double > { double operator()( const Type& x ) const { return x.to_double(); } }; struct Compare : public CGAL::cpp98::binary_function< Type, Type, Comparison_result > { Comparison_result operator()( const Type& x, const Type& y ) const { return x.compare(y); } }; struct To_interval : public CGAL::cpp98::unary_function< Type, std::pair< double, double > > { std::pair operator()( const Type& x ) const { return x.to_interval(); } }; }; CGAL_DEFINE_COERCION_TRAITS_FOR_SELF(cpp_float) CGAL_DEFINE_COERCION_TRAITS_FROM_TO(short ,cpp_float) CGAL_DEFINE_COERCION_TRAITS_FROM_TO(int ,cpp_float) CGAL_DEFINE_COERCION_TRAITS_FROM_TO(long ,cpp_float) CGAL_DEFINE_COERCION_TRAITS_FROM_TO(float ,cpp_float) CGAL_DEFINE_COERCION_TRAITS_FROM_TO(double ,cpp_float) } // namespace CGAL #endif // CGAL_CPP_FLOAT_H