[Boost-users] math round() functions: away from 0

Subject: [Boost-users] math round() functions: away from 0
From: Hicham Mouline (hicham_at_[hidden])
Date: 2010-04-12 15:16:28

Hello,boost/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html says that:  Halfway cases are rounded away from zero, regardless of the current rounding direction.This is compatible with C99 TC3 and therefore the latest C++1x draft.However, when I ran this program:#include <cmath>#include <iostream>#include <boost/math/special_functions/round.hpp>inline double round1(double x){    if (x >= 0.0)        return std::floor(x + 0.5);    else        return std::ceil(x - 0.5);}inline double round2(double x){    return std::floor(x + 0.5);}int main(){  std::cout.setf(std::ios_base::fixed, std::ios_base::floatfield);  std::cout.precision(1);  std::cout<< "d      floor/ceil.5        floor.5      boostmathround"<<std::endl;  for (double d=-10.5; d<11; d+=0.5)    std::cout<< d<<"        "<< round1(d)<<"         "<<round2(d)<<"       "<< boost::math::iround<double>(d)<<std::endl;  return 0;}under g++4.3.x and msvc2008 with trunk, the output for all the negative halves does not seem to be away from 0.The same for boost::math::round<double>(d)This stuff most likely depends on the bit pattern, so I investigated further. I raised the precision of std::cout to 18 decimals.I then rounded this:const double dd = -10.5;which yieldedd                                                    floor/ceil.5                                      floor.5                    boostmathround-10.500000000000000000        -11.000000000000000000         -10.000000000000000000       -10and for (double d=-10.6; d<-10.4; d+=0.01)    std::cout<< d<<"        "<< round1(d)<<"         "<<round2(d)<<"       "<< boost::math::iround(d)<<std::endl;-10.600000000000000000        -11.000000000000000000         -11.000000000000000000       -11-10.590000000000000000        -11.000000000000000000         -11.000000000000000000       -11-10.580000000000000000        -11.000000000000000000         -11.000000000000000000       -11-10.570000000000000000        -11.000000000000000000         -11.000000000000000000       -11-10.560000000000000000        -11.000000000000000000         -11.000000000000000000       -11-10.550000000000001000        -11.000000000000000000         -11.000000000000000000       -11-10.540000000000001000        -11.000000000000000000         -11.000000000000000000       -11-10.530000000000001000        -11.000000000000000000         -11.000000000000000000       -11-10.520000000000001000        -11.000000000000000000         -11.000000000000000000       -11-10.510000000000002000        -11.000000000000000000         -11.000000000000000000       -11-10.500000000000002000        -11.000000000000000000         -11.000000000000000000       -11-10.490000000000002000        -10.000000000000000000         -10.000000000000000000       -10-10.480000000000002000        -10.000000000000000000         -10.000000000000000000       -10-10.470000000000002000        -10.000000000000000000         -10.000000000000000000       -10-10.460000000000003000        -10.000000000000000000         -10.000000000000000000       -10-10.450000000000003000        -10.000000000000000000         -10.000000000000000000       -10-10.440000000000003000        -10.000000000000000000         -10.000000000000000000       -10-10.430000000000003000        -10.000000000000000000         -10.000000000000000000       -10-10.420000000000003000        -10.000000000000000000         -10.000000000000000000       -10-10.410000000000004000        -10.000000000000000000         -10.000000000000000000       -10-10.400000000000004000        -10.000000000000000000         -10.000000000000000000       -10-10.5 has the exact representation in IEEE754 as the 64bit:0000000000000000000000000000000000000000000000001010010000000011with, accross all the bits (not bytes), the least significant first.It is an _exact_ representation as far as I can tell.therefore the round function should round _away_ from 0, to give -11, shouldn't it?round1() however seems to do the right thing....Regards,