/usr/include/CGAL/MP_Float_impl.h is in libcgal-dev 4.7-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Sylvain Pion
#ifndef CGAL_MP_FLOAT_IMPL_H
#define CGAL_MP_FLOAT_IMPL_H
#include <CGAL/basic.h>
#include <CGAL/Quotient.h>
#include <functional>
#include <cmath>
#include <CGAL/MP_Float.h>
namespace CGAL {
namespace INTERN_MP_FLOAT {
const unsigned log_limb = 8 * sizeof(MP_Float::limb);
const MP_Float::limb2 base = 1 << log_limb;
const MP_Float::V::size_type limbs_per_double = 2 + 53/log_limb;
const double trunc_max = double(base)*(base/2-1)/double(base-1);
const double trunc_min = double(-base)*(base/2)/double(base-1);
} // namespace INTERN_MP_FLOAT
// We face portability issues with the ISO C99 functions "nearbyint",
// so I re-implement it for my need.
template < typename T >
inline
int my_nearbyint(const T& d)
{
int z = int(d);
T frac = d - z;
CGAL_assertion(CGAL::abs(frac) < T(1.0));
if (frac > 0.5)
++z;
else if (frac < -0.5)
--z;
else if (frac == 0.5 && (z&1) != 0) // NB: We also need the round-to-even rule.
++z;
else if (frac == -0.5 && (z&1) != 0)
--z;
CGAL_assertion(CGAL::abs(T(z) - d) < T(0.5) ||
(CGAL::abs(T(z) - d) == T(0.5) && ((z&1) == 0)));
return z;
}
template < typename T >
inline
void MP_Float::construct_from_builtin_fp_type(T d)
{
if (d == 0)
return;
// Protection against rounding mode != nearest, and extended precision.
Set_ieee_double_precision P;
CGAL_assertion(is_finite(d));
// This is subtle, because ints are not symetric against 0.
// First, scale d, and adjust exp accordingly.
while (d < INTERN_MP_FLOAT::trunc_min || d > INTERN_MP_FLOAT::trunc_max) {
++exp;
d /= INTERN_MP_FLOAT::base;
}
while (d >= INTERN_MP_FLOAT::trunc_min/ INTERN_MP_FLOAT::base && d <= INTERN_MP_FLOAT::trunc_max/ INTERN_MP_FLOAT::base) {
--exp;
d *= INTERN_MP_FLOAT::base;
}
// Then, compute the limbs.
// Put them in v (in reverse order temporarily).
T orig = d, sum = 0;
while (true) {
int r = my_nearbyint(d);
if (d-r >= T( INTERN_MP_FLOAT::base/2-1)/( INTERN_MP_FLOAT::base-1))
++r;
v.push_back(r);
// We used to do simply "d -= v.back();", but when the most significant
// limb is 1 and the second is -32768, then it can happen that
// |d - v.back()| > |d|, hence a bit of precision can be lost.
// Hence the need for sum/orig.
sum += v.back();
d = orig-sum;
if (d == 0)
break;
sum *= INTERN_MP_FLOAT::base;
orig *= INTERN_MP_FLOAT::base;
d *= INTERN_MP_FLOAT::base;
--exp;
}
// Reverse v.
std::reverse(v.begin(), v.end());
CGAL_assertion(v.back() != 0);
}
inline
MP_Float::MP_Float(float d):exp(0)
{
construct_from_builtin_fp_type(d);
CGAL_expensive_assertion(CGAL::to_double(*this) == d);
}
inline
MP_Float::MP_Float(double d):exp(0)
{
construct_from_builtin_fp_type(d);
CGAL_expensive_assertion(CGAL::to_double(*this) == d);
}
inline
MP_Float::MP_Float(long double d):exp(0)
{
construct_from_builtin_fp_type(d);
// CGAL_expensive_assertion(CGAL::to_double(*this) == d);
}
inline
Comparison_result
INTERN_MP_FLOAT::compare (const MP_Float & a, const MP_Float & b)
{
typedef MP_Float::exponent_type exponent_type;
if (a.is_zero())
return (Comparison_result) - b.sign();
if (b.is_zero())
return (Comparison_result) a.sign();
for (exponent_type i = (std::max)(a.max_exp(), b.max_exp()) - 1;
i >= (std::min)(a.min_exp(), b.min_exp()); i--)
{
if (a.of_exp(i) > b.of_exp(i))
return LARGER;
if (a.of_exp(i) < b.of_exp(i))
return SMALLER;
}
return EQUAL;
}
// Common code for operator+ and operator-.
template <class BinOp>
inline
MP_Float
Add_Sub(const MP_Float &a, const MP_Float &b, const BinOp &op)
{
typedef MP_Float::exponent_type exponent_type;
CGAL_assertion(!b.is_zero());
exponent_type min_exp, max_exp;
if (a.is_zero()) {
min_exp = b.min_exp();
max_exp = b.max_exp();
}
else {
min_exp = (std::min)(a.min_exp(), b.min_exp());
max_exp = (std::max)(a.max_exp(), b.max_exp());
}
MP_Float r;
r.exp = min_exp;
r.v.resize(static_cast<int>(max_exp - min_exp + 1)); // One more for carry.
r.v[0] = 0;
for(int i = 0; i < max_exp - min_exp; i++)
{
MP_Float::limb2 tmp = r.v[i] + op(a.of_exp(i+min_exp),
b.of_exp(i+min_exp));
MP_Float::split(tmp, r.v[i+1], r.v[i]);
}
r.canonicalize();
return r;
}
inline
MP_Float
operator+(const MP_Float &a, const MP_Float &b)
{
if (a.is_zero())
return b;
if (b.is_zero())
return a;
return Add_Sub(a, b, std::plus<MP_Float::limb2>());
}
inline
MP_Float
operator-(const MP_Float &a, const MP_Float &b)
{
if (b.is_zero())
return a;
return Add_Sub(a, b, std::minus<MP_Float::limb2>());
}
inline
MP_Float
operator*(const MP_Float &a, const MP_Float &b)
{
if (a.is_zero() || b.is_zero())
return MP_Float();
// Disabled until square() is fixed.
// if (&a == &b)
// return square(a);
MP_Float r;
r.exp = a.exp + b.exp;
CGAL_assertion_msg(CGAL::abs(r.exp) < (1<<30)*1.0*(1<<23),
"Exponent overflow in MP_Float multiplication");
r.v.assign(a.v.size() + b.v.size(), 0);
for(unsigned i = 0; i < a.v.size(); ++i)
{
unsigned j;
MP_Float::limb carry = 0;
for(j = 0; j < b.v.size(); ++j)
{
MP_Float::limb2 tmp = carry + (MP_Float::limb2) r.v[i+j]
+ std::multiplies<MP_Float::limb2>()(a.v[i], b.v[j]);
MP_Float::split(tmp, carry, r.v[i+j]);
}
r.v[i+j] = carry;
}
r.canonicalize();
return r;
}
// Squaring simplifies things and is faster, so we specialize it.
inline
MP_Float
INTERN_MP_FLOAT::square(const MP_Float &a)
{
// There is a bug here (see test-case in test/NT/MP_Float.C).
// For now, I disable this small optimization.
// See also the comment code in operator*().
return a*a;
#if 0
typedef MP_Float::limb limb;
typedef MP_Float::limb2 limb2;
if (a.is_zero())
return MP_Float();
MP_Float r;
r.exp = 2*a.exp;
r.v.assign(2*a.v.size(), 0);
for(unsigned i=0; i<a.v.size(); i++)
{
unsigned j;
limb2 carry = 0;
limb carry2 = 0;
for(j=0; j<i; j++)
{
// There is a risk of overflow here :(
// It can only happen when a.v[i] == a.v[j] == -2^15 (log_limb...)
limb2 tmp0 = std::multiplies<limb2>()(a.v[i], a.v[j]);
limb2 tmp1 = carry + (limb2) r.v[i+j] + tmp0;
limb2 tmp = tmp0 + tmp1;
limb tmpcarry;
MP_Float::split(tmp, tmpcarry, r.v[i+j]);
carry = tmpcarry + (limb2) carry2;
// Is there a more efficient way to handle this carry ?
if (tmp > 0 && tmp0 < 0 && tmp1 < 0)
{
// If my calculations are correct, this case should never happen.
CGAL_error();
}
else if (tmp < 0 && tmp0 > 0 && tmp1 > 0)
carry2 = 1;
else
carry2 = 0;
}
// last round for j=i :
limb2 tmp0 = carry + (limb2) r.v[i+i]
+ std::multiplies<limb2>()(a.v[i], a.v[i]);
MP_Float::split(tmp0, r.v[i+i+1], r.v[i+i]);
r.v[i+i+1] += carry2;
}
r.canonicalize();
return r;
#endif
}
// Division by Newton (code by Valentina Marotta & Chee Yap) :
/*
Integer reciprocal(const Integer A, Integer k) {
Integer t, m, ld;
Integer e, X, X1, X2, A1;
if (k == 1)
return 2;
A1 = A >> k/2; // k/2 most significant bits
X1 = reciprocal(A1, k/2);
// To avoid the adjustment :
Integer E = (1 << (2*k - 1)) - A*X1;
if (E > A)
X1 = X1 + 1;
e = 1 << 3*k/2; // 2^(3k/2)
X2 = X1*e - X1*X1*A;
X = X2 >> k-1;
return X;
}
*/
inline
MP_Float
approximate_division(const MP_Float &a, const MP_Float &b)
{
CGAL_assertion_msg(! b.is_zero(), " Division by zero");
return MP_Float(CGAL::to_double(a)/CGAL::to_double(b));
}
inline
MP_Float
approximate_sqrt(const MP_Float &d)
{
return MP_Float(CGAL_NTS sqrt(CGAL::to_double(d)));
}
// Returns (first * 2^second), an approximation of b.
inline
std::pair<double, int>
to_double_exp(const MP_Float &b)
{
typedef MP_Float::exponent_type exponent_type;
if (b.is_zero())
return std::make_pair(0.0, 0);
exponent_type exp = b.max_exp();
int steps = static_cast<int>((std::min)( INTERN_MP_FLOAT::limbs_per_double, b.v.size()));
double d_exp_1 = std::ldexp(1.0, - static_cast<int>( INTERN_MP_FLOAT::log_limb));
double d_exp = 1.0;
double d = 0;
for (exponent_type i = exp - 1; i > exp - 1 - steps; i--) {
d_exp *= d_exp_1;
d += d_exp * b.of_exp(i);
}
CGAL_assertion_msg(CGAL::abs(exp* INTERN_MP_FLOAT::log_limb) < (1<<30)*2.0,
"Exponent overflow in MP_Float to_double");
return std::make_pair(d, static_cast<int>(exp * INTERN_MP_FLOAT::log_limb));
}
// Returns (first * 2^second), an interval surrounding b.
inline
std::pair<std::pair<double, double>, int>
to_interval_exp(const MP_Float &b)
{
typedef MP_Float::exponent_type exponent_type;
if (b.is_zero())
return std::make_pair(std::pair<double, double>(0, 0), 0);
exponent_type exp = b.max_exp();
int steps = static_cast<int>((std::min)( INTERN_MP_FLOAT::limbs_per_double, b.v.size()));
double d_exp_1 = std::ldexp(1.0, - (int) INTERN_MP_FLOAT::log_limb);
double d_exp = 1.0;
Interval_nt_advanced::Protector P;
Interval_nt_advanced d = 0;
exponent_type i;
for (i = exp - 1; i > exp - 1 - steps; i--) {
d_exp *= d_exp_1;
if (d_exp == 0) // Take care of underflow.
d_exp = CGAL_IA_MIN_DOUBLE;
d += d_exp * b.of_exp(i);
}
if (i >= b.min_exp() && d.is_point()) {
if (b.of_exp(i) > 0)
d += Interval_nt_advanced(0, d_exp);
else if (b.of_exp(i) < 0)
d += Interval_nt_advanced(-d_exp, 0);
else
d += Interval_nt_advanced(-d_exp, d_exp);
}
#ifdef CGAL_EXPENSIVE_ASSERTION // force it always in early debugging
if (d.is_point())
CGAL_assertion(MP_Float(d.inf()) == b);
else
CGAL_assertion(MP_Float(d.inf()) <= b & MP_Float(d.sup()) >= b);
#endif
CGAL_assertion_msg(CGAL::abs(exp* INTERN_MP_FLOAT::log_limb) < (1<<30)*2.0,
"Exponent overflow in MP_Float to_interval");
return std::make_pair(d.pair(), static_cast<int>(exp * INTERN_MP_FLOAT::log_limb));
}
// to_double() returns, not the closest double, but a one bit error is allowed.
// We guarantee : to_double(MP_Float(double d)) == d.
inline
double
INTERN_MP_FLOAT::to_double(const MP_Float &b)
{
std::pair<double, int> ap = to_double_exp(b);
return ap.first * std::ldexp(1.0, ap.second);
}
inline
double
INTERN_MP_FLOAT::to_double(const Quotient<MP_Float> &q)
{
std::pair<double, int> n = to_double_exp(q.numerator());
std::pair<double, int> d = to_double_exp(q.denominator());
double scale = std::ldexp(1.0, n.second - d.second);
return (n.first / d.first) * scale;
}
// FIXME : This function deserves proper testing...
inline
std::pair<double,double>
INTERN_MP_FLOAT::to_interval(const MP_Float &b)
{
std::pair<std::pair<double, double>, int> ap = to_interval_exp(b);
return ldexp(Interval_nt<>(ap.first), ap.second).pair();
}
// FIXME : This function deserves proper testing...
inline
std::pair<double,double>
INTERN_MP_FLOAT::to_interval(const Quotient<MP_Float> &q)
{
std::pair<std::pair<double, double>, int> n = to_interval_exp(q.numerator());
std::pair<std::pair<double, double>, int> d = to_interval_exp(q.denominator());
CGAL_assertion_msg(CGAL::abs(1.0*n.second - d.second) < (1<<30)*2.0,
"Exponent overflow in Quotient<MP_Float> to_interval");
return ldexp(Interval_nt<>(n.first) / Interval_nt<>(d.first),
n.second - d.second).pair();
}
inline
std::ostream &
operator<< (std::ostream & os, const MP_Float &b)
{
os << CGAL::to_double(b);
return os;
}
inline
std::ostream &
print (std::ostream & os, const MP_Float &b)
{
typedef MP_Float::exponent_type exponent_type;
// Binary format would be nice and not hard to have too (useful ?).
if (b.is_zero())
return os << 0 << " [ double approx == " << 0.0 << " ]";
MP_Float::const_iterator i;
exponent_type exp = b.min_exp() * INTERN_MP_FLOAT::log_limb;
double approx = 0; // only for giving an idea.
for (i = b.v.begin(); i != b.v.end(); i++)
{
os << ((*i > 0) ? " +" : " ") << *i;
if (exp != 0)
os << " * 2^" << exp;
approx += std::ldexp(static_cast<double>(*i),
static_cast<int>(exp));
exp += INTERN_MP_FLOAT::log_limb;
}
os << " [ double approx == " << approx << " ]";
return os;
}
inline
std::istream &
operator>> (std::istream & is, MP_Float &b)
{
double d;
is >> d;
if (is)
b = MP_Float(d);
return is;
}
} //namespace CGAL
#endif // CGAL_MP_FLOAT_IMPL_H
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