Cos(pi/2) gives an exact zero. Cos(3*pi/2) gives a value less than €. But cos(7*pi/2) gives a large negative value which is not less than €. Anshu On Thu, 16 Jan, 2020, 11:29 PM John Maddock via Boost, < boost@lists.boost.org> wrote:

On 16/01/2020 15:08, anshu khare via Boost wrote:

...

cos(3*pi(cpp_bin_float_50>()/2)) does not give correct value.

What do you call "correct"? If you're expecting an exact 0 result, then you're going to be disappointed - likewise with double which also does not yield an exact 0 in your test case (at least on msvc).

John.

...

Only cos(pi(cpp_bin_float_50>()/2)) gives correct value. All odd multiples of cos(pi/2) do not give correct value.

The issue with sin() as well.

Anshu

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On running cos(3*pi/2) , cos(5*pi/2) , cos(7*pi/2) , cos(9*pi/2) all give the same answer, which is less than epsilon except cos(7*pi/2) which gives a highly negative value. On Fri, 17 Jan, 2020, 5:41 AM Damian Vicino via Boost, < boost@lists.boost.org> wrote:

That's because pi is not pi but an approximation of it. When you multiply you amplify the error.

On Thu, Jan 16, 2020, 18:48 anshu khare via Boost wrote:

...

Cos(pi/2) gives an exact zero. Cos(3*pi/2) gives a value less than €. But cos(7*pi/2) gives a large negative value which is not less than €.

Anshu

On Thu, 16 Jan, 2020, 11:29 PM John Maddock via Boost, < boost@lists.boost.org> wrote:

...

On 16/01/2020 15:08, anshu khare via Boost wrote:

...

cos(3*pi(cpp_bin_float_50>()/2)) does not give correct value.

What do you call "correct"? If you're expecting an exact 0 result,

then

...

you're going to be disappointed - likewise with double which also does not yield an exact 0 in your test case (at least on msvc).

John.

...

Only cos(pi(cpp_bin_float_50>()/2)) gives correct value. All odd multiples of cos(pi/2) do not give correct value.

The issue with sin() as well.

Anshu

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I ran the following code : #include <iostream> using namespace std; #include using boost::math::constants::pi; using boost::multiprecision::cpp_bin_float_50; int main() { cout << cos(3 * pi/2) << endl; cout << cos(5 * pi/2) << endl; cout << cos(7 * pi/2) << endl; cout << cos(9 * pi/2) << endl; return 0; } Output is as follows: 1.06911e - 50 1.06911e - 50 -1.06911e - 50 1.06911e - 50 Anshu On Fri, 17 Jan, 2020, 3:29 PM John Maddock via Boost, wrote:

On 17/01/2020 01:52, anshu khare via Boost wrote:

...

On running cos(3*pi/2) , cos(5*pi/2) , cos(7*pi/2) , cos(9*pi/2) all give the same answer, which is less than epsilon except cos(7*pi/2) which gives a highly negative value.

Not seeing it, I'm running:

for (unsigned i = 3; i < 20; i += 2) { std::cout << std::setw(20) << i << std::setw(20) << ceil(fabs(cos(i * boost::math::constants::half_piboost::multiprecision::cpp_bin_float_50())

/ std::numeric_limitsboost::multiprecision::cpp_bin_float_50::epsilon())) << std::endl; }

Which gives:

N abs error / epsilon

3 2 5 2 7 2 9 2 11 6 13 10 15 10 17 6 19 6

And if I switch to testing type double I see:

3 1 5 2 7 2 9 3 11 12 13 5 15 13 17 4 19 14

Best, John.

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