Re: [Boost-users] [Math] Accuracy test failures on QNX 6.4.0

Subject: Re: [Boost-users] [Math] Accuracy test failures on QNX 6.4.0
From: Niklas Angare (li51ckf02_at_[hidden])
Date: 2008-11-19 14:52:21

> Thanks, but I admit to being stuck... somewhere around line 320 of 
> boost/math/tools/roots.hpp there's a NaN being generated for type 
> real_concept, but not for type long double (and real_concept is just a 
> very thin wrapper around long double).  Can you set a breakpoint at that 
> location and see what the problem is?

It's on line 299, f(result), which in the end results in a call to 
std::pow(0.5, 16.182502746582031), the result of which is a NaN... The 
numbers may not be exact since they're just from the debugger's 
presentation. I've attached the call stack.

After some experimentation I arrived at this test:
#include <cmath>
#include <iostream>
#include <iomanip>
#include <limits>

int main()
{
typedef std::numeric_limits<long double> ldlimits;
unsigned int raw1[3]; // garbage
unsigned int raw2[3]; // garbage
long double a = 0.5L;
long double b1 = 16.182502746582031;
long double b2 = 16.182502746582031L;
long double b3 = 1.0L; // garbage
long double b4 = 2.0L; // garbage
long double r1 = std::pow(a, b1);
long double r2 = std::pow(a, b2);
long double r3 = std::pow(a, b3); // garbage
#ifdef VERSION2
long double r4 = std::pow(a, b4); // garbage
#endif
std::cout << std::setprecision(30);
std::cout << ldlimits::radix << "^" << ldlimits::digits
          << " (" << sizeof(long double) << ")" << std::endl;
std::cout << "1) " << b1 << " " << r1 << std::endl;
std::cout << "2) " << b2 << " " << r2 << std::endl;
}

Results with VERSION2 undefined:
2^64 (12)
1) 16.18250274658203125 nan
2) 16.18250274658203099988 1.3445633476723758172e-05

Results with VERSION2 defined:
2^64 (12)
1) 16.18250274658203125 1.3445633476723755844e-05
2) 16.18250274658203099988 1.3445633476723758172e-05

I discovered 1) when I forgot to put the L on the literal. Then I discovered 
that the result is sometimes correct depending on other nearby code. 
Seriously weird. Any ideas what could be causing this?